The rectangle have length = 4, breath = 16, perimeter = 40, and area = 64.
How to evaluate for the length, breadth, perimeter, and area of the rectangleThe perimeter of a rectangle is the sum of length of its four sides or the sum of its length and breadth, multiplied by two. While the area is the length multiplied by the breadth.
Perimeter = 2(L + B)
Area = L × B
From the question;
2(L + B) = 2LB
32L = 2L(L²)...(1) {since B = L²}
from equation (1), L = 4 by solving for L
so;
B = 4² = 16
perimeter of the rectangle = 2(4 + 16) = 40
area of the rectangle = 4 × 16 = 64
Therefore, the rectangle have length = 4, breath = 16, perimeter = 40, and area = 64.
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Which is the distance between the point with the coordinates (1, 2) and the line with the equation 2x-3y = -2?
a. √13
c. 3√13
13
13
9-
b. 2√13
13
d. 6√13
13
Please select the best answer from the choices provided
A
B
C
D
0
Answer:
To find the distance between a point and a line in a plane, we can use the formula:
distance = |Ax + By + C| / √(A^2 + B^2)
where A, B, and C are the coefficients of the general form of the line equation (Ax + By + C = 0), and (x,y) are the coordinates of the point.
First, we need to rewrite the given line equation in the standard form (y = mx + b):
2x - 3y = -2
-3y = -2x - 2
y = (2/3)x + 2/3
Now we can identify the slope (m) and y-intercept (b) of the line:
m = 2/3
b = 2/3
Next, we can find the equation of the perpendicular line that passes through the point (1,2), since the distance between the point and the line will be the length of the segment connecting the point to the intersection of these two lines. The slope of a line perpendicular to a line with slope m is -1/m, so the equation of the perpendicular line passing through (1,2) is:
y - 2 = (-3/2)(x - 1)
y = (-3/2)x + (7/2)
Now we need to find the intersection of the two lines by solving the system of equations:
y = (2/3)x + 2/3
y = (-3/2)x + (7/2)
(-3/2)x + (7/2) = (2/3)x + 2/3
(-13/6)x = -5/6
x = 5/13
y = (2/3)(5/13) + 2/3
y = 11/13
So the intersection point of the two lines is (5/13, 11/13). Now we can use the distance formula to find the distance between this point and the given point (1,2):
distance = √[(5/13 - 1)^2 + (11/13 - 2)^2]
distance = √[(36/169) + (25/169)]
distance = √(61/169)
distance = √61/13
The closest answer choice is (A) √13, but the simplified expression is actually √61/13. Therefore, none of the answer choices provided are completely accurate.
Step-by-step explanation:
Turner helped his grandfather build a raised garden bed for Tanner’s grandmother. The bed is shaped like a rectangular prism that is 4 1/2 feet wide and a half of a foot tall. Turner and his grandfather use 18 bags of topsoil, each containing three force of a cubic foot, to feel the bed completely. How long is the garden?
The length of the garden containing the soil is L = 24 feet
Given data ,
Volume = Length x Width x Height
Width = 4 1/2 feet
Height = 1/2 foot
Total volume of topsoil used = 18 bags x 3 cubic feet/bag = 54 cubic feet
So , the length of the garden is
54 = Length x 4 1/2 x 1/2
On simplifying , we get
54 = Length x 9/2 x 1/2
Now, let's simplify the right-hand side by multiplying the numerator and denominator by 2
54 / (9/2 x 1/2) = The length of the garden
The length of the garden = 54 /9 x 4
The length of the garden = 6 x 4
The length of the garden = 24 feet
Hence , the length of the garden bed is 24 feet
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graph of the function h(x)=(x^2-3x-4)/x-4
Plotting the graph of the function h(x) = [tex](x^2 - 3x - 4) / (x - 4)[/tex], we get y- intercept = 1, vertical asymptotes at x=4 and horizontal asymptotes at y=1.
What does graph of any function represents?The connection between a function's input values (usually written as x) and output values (often indicated as y) is represented by the function's graph. It gives insights on the function's characteristics, including its domain, range, intercepts, asymptotes, and general form, as well as a visual representation of how the function acts.
Steps to plot the graph of the give function h(x) =[tex](x^2 - 3x - 4) / (x - 4)[/tex]:
Put the numerator [tex](x^2 - 3x - 4)[/tex] equal to zero and solve for x to discover the x-intercepts, if any, to determine the x-intercepts.Finding the y-intercept To get the y-intercept, set x = 0 in the function and solve for y, which gives y- intercept=1.To locate any vertical asymptotes, set the denominator (x - 4) equal to zero and solve for x, which gives x=4.Find horizontal asymptotes: To find the horizontal asymptote, compare the degrees of the numerator and denominator (s). There is no horizontal asymptote if the degree of the numerator is higher than the degree of the denominator. The horizontal asymptote lies at y = ratio of the leading coefficients if the degree of the numerator and denominator are equal. The horizontal asymptote is at y = 0 if the degree of the numerator is smaller than the degree of the denominator, for given problem it is at y=1.Draw the graph of the function h(x), highlighting the x-intercepts, y-intercept, vertical asymptotes, and horizontal asymptotes using the knowledge gained from the aforementioned phases (s). Take attention to how the function behaves as x gets closer to positive or negative infinity.Name the graph, including the x- and y-axes, x- and y-intercepts, vertical and horizontal asymptotes, and any other interesting points.Learn more about Graphs here:
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A certain type of cable has a mean breaking point of 150 pounds with a standard deviation of 8 pounds. What weight should we specify so that we expect 95% of the cables not to break supporting that weight?
Answer:
171.76 Pounds
Step-By-Step Explanation:
So the explanation to how I got the answer is in the link below.
Suppose that the following scatter plot displays the data between the amount of time truck drivers are driving on the road and the average number of stops that they make along the way, from a sample of
30 truck drivers.
What is the correlation between the amount of time truck drivers are driving and the average number of stops that they make?
Answer:
Step-by-step explanation:
There is no correlation between the two.
The graph provided is a scatter plot and the dots are to spread out to have any time of coloration
which of the following number sequences could be produced by the expression
2x+x^2
The given expression is
[tex]2x+x^2[/tex]
So we can write the general rule for the sequence as
[tex]T_x=2x+x^2[/tex]
Recall that the domain of a sequence is the set of natural numbers.
Let us plug in some first few natural numbers to generate the sequence.
When [tex]x=1[/tex], we obtain,
[tex]T_1=2(1)+(1)^2[/tex]
[tex]\rightarrow T_1=2+1[/tex]
[tex]\rightarrow T_1=3[/tex]
When [tex]x=2[/tex], we obtain,
[tex]T_2=2(2)+(2)^2[/tex]
[tex]\rightarrow T_2=4+4[/tex]
[tex]\rightarrow T_2=8[/tex]
When [tex]x=3[/tex], we obtain,
[tex]T_3=2(3)+(3)^2[/tex]
[tex]T_3=6+9[/tex]
[tex]T_3=15[/tex]
When [tex]x=4[/tex], we obtain,
[tex]T_4=2(4)+(4)^2[/tex]
[tex]T_4=8+16[/tex]
[tex]T_4=24[/tex]
Therefore the number sequence produced by the given expression is,
[tex]\boxed{\bold{3, 8, 15, 24.}}[/tex]
Tres amigos van de compras, Juan gasta el doble que Alicia y Ana gasta el triple de Alicia. Si entre los tres han gastado L.
720.00, ¿Cuánto ha gastado cada uno?
the three friends spent L.120.00, L.240.00, and L.360.00, respectively.
How to solve the problem?
Let's denote the amount that Alicia spends as "x". According to the problem statement, we know that Juan spends twice as much as Alicia, which means he spends 2x. Similarly, we know that Ana spends three times as much as Alicia, which means she spends 3x.
We also know that the three friends together have spent L.720.00. So, we can set up an equation to represent this:
x + 2x + 3x = 720
Simplifying this equation, we get:
6x = 720
Dividing both sides by 6, we get:
x = 120
So, Alicia spent L.120.00, Juan spent twice as much as Alicia, which is L.240.00, and Ana spent three times as much as Alicia, which is L.360.00.
Therefore, the three friends spent L.120.00, L.240.00, and L.360.00, respectively.
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You want to know the number of students in your school that have a January birthday. You survey the students in your math class. Three students have a January birthday, and 32 do not. So, you conclude that about 8.6% of the students in your school have a January birthday. Determine whether the conclusion is valid. Explain. (Sorry it’s so long)
It is not appropriate to generalize the findings of the survey to the entire school population.
What is survey?
The conclusion that about 8.6% of the students in the school have a January birthday is not necessarily valid based on the information provided.
The sample size of the survey is too small (only 3 students with January birthdays) and limited to one math class, so it may not be representative of the whole school population. Additionally, the sample is not randomly selected, which introduces the possibility of selection bias.
Therefore, it is not appropriate to generalize the findings of the survey to the entire school population. A more reliable way to determine the percentage of students with a January birthday would be to collect data from a larger, randomly selected sample of students across the entire school population.
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What is the domain of the function in the graph?
graph on the h-g axis, between the points (6, 80) and (11, 40)
A. 6≤g≤11
B. 40≤g≤80
C. 40≤h≤80
D. 6≤h≤11
Answer:
D
Step-by-step explanation:
The domain of a function refers to the set of all possible input values (independent variable) for which the function is defined. In this case, the graph has points (6,80) and (11,40), which means that the function is defined for the values of g (the independent variable) between 6 and 11. Therefore, the domain of the function is:
D. 6≤g≤11
The domain of the function in the given graph is 6≤h≤11, as it includes all possible values of h between and including 6 and 11 on the horizontal (h) axis. So the correct option is D.
The domain of a function refers to the set of all possible input values for the function. In the given graph, which is plotted on the h-g axis and includes points (6, 80) and (11, 40), we are interested in determining the valid range for the independent variable, h.
The lowest h-value on the graph is 6, corresponding to the point (6, 80), and the highest h-value is 11, corresponding to the point (11, 40). These are the boundaries that define the domain of the function. Any value of h that falls within this range is a valid input for the function, and any value outside this range is not represented on the graph.
Therefore, the domain of the function is 6≤h≤11, as it includes all values of h between and including 6 and 11. This range encompasses all possible inputs for this function as depicted in the graph.
In summary, the domain represents the valid input values, and in this case, it is limited to the interval from 6 to 11 on the h-axis.
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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
The table is completed as below
Interested in NOT Interested in Total
Athletics Athletics
Interested in
Academic Clubs 26 58 84
Not Interested in
Academic Clubs 118 38 156
Total 144 96 240
How to fill the tableTo fill in the table, we start with the total number of students, which is 240.
We know that 35% of students are interested in athletics, so we can find the number of students interested in athletics as:
0.35 x 240 = 84
Similarly, we know that 3/5 of students are interested in academic clubs, so we can find the number of students interested in academic clubs as:
(3/5) x 240 = 144
We also know that 26 students are interested in both athletics and academic clubs, so we can fill in that cell as 26.
To fill in the remaining cells, we can use the fact that the row and column totals must add up correctly. For example, in the "Interested in athletics" row, we know that there are a total of 84 students interested in athletics. We also know that 26 of these students are interested in both athletics and academic clubs. Therefore, the number of students interested in athletics but not academic clubs is:
84 - 26 = 58
We can use similar reasoning to fill in the remaining cells. For example, in the "Not interested in athletics" column, we know that there are a total of 214 students who are not interested in athletics. We also know that 144 students are interested in academic clubs. Therefore, the number of students who are not interested in athletics but are interested in academic clubs is:
144 - 26 = 118
Let x represent "not interested in academics club" and "not interested in athletic". Using the total in the horizontal (bottom row) we have:
144 + 58 + x = 240
x = 240 - 202
x = 38
Hence 58 + 38 = 96 and 118 + 38 = 156
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A nursing student can be assigned in how many different ways?
The total number of different ways that the student can be assigned during a 4-day work week is 81 different ways.
What is student?A student is a person who is enrolled in an educational institution, such as a college, university, or trade school. Students are typically required to attend classes and complete assignments to gain knowledge and develop skills related to their field of study. Depending on their level of education, students may also be required to participate in research or internships in order to gain practical experience.
There are 3 possible floors that the student can be assigned to, so for each day of the 4-day week, there are 3 possible assignments.
Therefore, the total number of different ways that the student can be assigned during a 4-day work week is 3 x 3 x 3 x 3
= 81 different ways.
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12. The measures of alternate exterior angles are
Answer:
The same, Congruent
Step-by-step explanation:
The measures of alternate exterior angles are equal when two parallel lines are intersected by a transversal line. That is, if we have two parallel lines l and m intersected by a transversal line t, then the alternate exterior angles are congruent, which means that they have the same measure. More formally, if angle 1 and angle 2 are alternate exterior angles, then:
angle 1 = angle 2
The reason for this is that when the parallel lines are intersected by the transversal line, they form a Z-shape pattern, and the alternate exterior angles are located on opposite sides of the transversal line, but outside of the two parallel lines. The angles are congruent because they are formed by a pair of corresponding angles and a pair of vertical angles.
Have a Great Day!-
y=9/5X+6. find the equation of the line that is parallel to this line and passes through the point (-5,-2)
Answer:
9/5x+7
Step-by-step explanation:
You can keep the slope the same, because it is parallel, but the y-intercept must change to plus seven in order to go through (-5, -2)
find the limiting value or horizontal asymptote of y= 2x/4x-5
The limiting value or horizontal asymptote of the function y = 2x/4x-5 is y = 0.5
Finding the limiting value or horizontal asymptoteFrom the question, we have the following parameters that can be used in our computation:
y = 2x/4x-5
The limiting value or horizontal asymptote can be calculated by graph
So, we start by plotting the graph of y = 2x/4x-5
See attachment for the graph
From the graph, we can see that
The function does not have a defined value at y = 0.5
This means that the limiting value or horizontal asymptote is y = 0.5
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Yolanda rented a truck for one day. There was a base fee of $10.75, and there was an additional charge of 6 cents for each mile driven. The total cost, C (in dollars), for driving x miles is given by the following.
Answer:
The total cost, C (in dollars), for driving x miles is given by:
C = 0.06x + 10.75
where x is the number of miles driven.
To find the total cost for driving a certain number of miles, simply substitute that value for x in the equation and solve for C.
Find the following angles
The value of angle t is 126⁰.
The value of angle x is 70⁰.
The value of angle 5 is 85⁰.
What is the value of a, t, x and 5?
The value of each of the missing angles is calculated as follows;
angle b = 27⁰ (vertical opposite angles are equal)
The value of angle t is calculated as follows;
b + t + 27 = 180 ( sum of angles on a straight line)
27 + t + 27 = 180
54 + t = 180
t = 180 - 54
t = 126⁰
The value of angle x is calculated as follows;
x + 30 + 80 = 180 (sum of angle in a triangle and vertical opposite angles)
x + 110 = 180
x = 180 - 110
x = 70⁰
The value of angle 5 is calculated as follows;
65 + 70 + (180 - 40) + ∠5 = 360 (sum of angles in a quadrilateral)
65 + 70 + 140 + ∠5 = 360
275 + ∠5 = 360
∠5 = 360 - 275
∠5 = 85⁰
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Find the standard form of the equation for the circle with the following properties.
Endpoints of a diameter are (−6,−1) and (−8,−11)
Standard form of the equation for the circle with the following properties is (x + 7)² + (y + 6)²= 104.
What is diameter?A line segment through the center of a circle with its ends on the circle's circumference. Its value is twice of the radius.
Define equation?An equation is a mathematical statement that asserts the equality between two expressions, typically containing one or more variables. It consists of two sides separated by an equals sign (=), indicating that the expressions on both sides have the same value. Equations are used to describe relationships, solve problems, and make predictions in various branches of mathematics, science, engineering, and other fields. They can be linear or nonlinear, and may involve arithmetic, algebraic, trigonometric, exponential, or other mathematical operations. Solving an equation involves finding the values of the variables that make the equation true.
To find the standard form of the equation for a circle, we can start by finding the center and radius of the circle using the given endpoints of a diameter.
The center of the circle is the midpoint of the diameter, which can be found by averaging the coordinates of the two endpoints. Let's denote the coordinates of the endpoints of the diameter as (x1, y1) and (x2, y2) respectively.
In this case, the coordinates of the endpoints are (x1, y1) = (-6, -1) and (x2, y2) = (-8, -11). Using the midpoint formula, we can find the center of the circle:
Center = ((x1 + x2)/2, (y1 + y2)/2)
Plugging in the values, we get:
Center = ((-6 + (-8))/2, (-1 + (-11))/2)
Center = ((-14)/2, (-12)/2)
Center = (-7, -6)
So, the center of the circle is (-7, -6).
The radius of the circle is half the length of the diameter, which can be found using the distance formula between the two endpoints of the diameter. Let's denote the distance between the endpoints as d.
The distance formula is given by:
d = sqrt((x2 - x1)² + (y2 - y1)²)
Plugging in the values, we get:
d = sqrt((-8 - (-6))² + (-11 - (-1))²)
d = sqrt((-2)² + (-10)²)
d = sqrt(4 + 100)
d = sqrt(104)
So, the radius of the circle is sqrt(104).
Now that we have the center and radius of the circle, we can write the standard form of the equation of the circle as:
(x - h)² + (y - k)²= r²
where (h, k) is the center of the circle and r is the radius of the circle.
Plugging in the values, we get:
(x - (-7))² + (y - (-6))² = (sqrt(104))²
(x + 7)² + (y + 6)²= 104
So, the standard form of the equation for the circle with endpoints of a diameter at (-6, -1) and (-8, -11) is (x + 7)² + (y + 6)² = 104
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A bag contains 3 gold marbles, 8 silver marbles, and 23 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win $3. If it is silver, you win $2. If it is black, you lose $1.
To calculate the expected value of playing this game, we need to multiply the probability of winning each amount by the corresponding payout and then sum them up.
Let's start by calculating the probability of selecting each type of marble:
Probability of selecting a gold marble: 3/34
Probability of selecting a silver marble: 8/34
Probability of selecting a black marble: 23/34
Now, let's calculate the expected value of playing the game:
E(x) = (3/34) * $3 + (8/34) * $2 + (23/34) * (-$1)
E(x) = $0.26
So the expected value of playing this game is $0.26. This means that over many plays of the game, we would expect to win an average of $0.26 per play. However, it's important to remember that this is just an average, and in any individual play of the game, you could win more or less than this amount.
Use the formula for n^p r to evaluate the following expression
Answer:
Use Formula nPr, to solve the following question
6P4 = 360
Writing With Tens and Ones
rite each number described.
1) Write a number with eight tens and one one
2) Write a number with five tens and five ones
3)
Write a number with eight tens and nine ones
) Write a number with five tens and eight ones
O Write a number with one ten and seven ones
O Write a number with five tens and two ones
Write a number with six tens and two ones
Write a number with three tens and zero ones
Write a number with four tens and five ones
A number with eight tens and one one is = 81.
A number with five tens and five ones is = 55.
A number with eight tens and nine ones is 89.
A number with five tens and eight ones = 58.
A number with one ten and seven ones is 17.
A number with five tens and two ones is 52.
A number with six tens and two ones is 62.
A number with three tens and zero ones is 30.
A number with four tens and five ones is 45.
What is the Number about?The phrase "eight tens and one one" denotes a numerical value featuring the digit 8 in the tens position and 1 in the ones position. This is equal to the sum of 80 and 1, resulting in a total value of 81.
Therefore "a numerical figure composed of 5 tens and 5 units" indicates a number where 5 is in the tens position while 5 is in the ones position, resulting in a total of 50 + 5, which equals 55.
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Let’s say that you are the Business Analytics Head at a national bank. From the historical data, you have determined that there is a 0.33 probability that a customer would default on a particular loan. What is the probability that out of the next two customers who apply for the same loan, both would not default on the loan?
Answer:
Step-by-step explanation:
26/7
When Caroline runs the 400 meter dash, her finishing times are normally distributed with a mean of 68 seconds and a standard deviation of 1.5 seconds. Using the empirical rule, determine the interval of times that represents the middle 99.7% of her finishing times in the 400 meter race.
The empirical rule to determine the interval middle 99.7% of Caroline's finishing times in the 400 meter race is 63.5 seconds to 72.5 seconds
Given data ,
The empirical rule, also known as the 68-95-99.7 rule, states that for a normal distribution:
Approximately 68% of the data falls within one standard deviation of the mean.
Approximately 95% of the data falls within two standard deviations of the mean.
Approximately 99.7% of the data falls within three standard deviations of the mean.
Since the middle 99.7% of data falls within three standard deviations of the mean, we can calculate the upper and lower limits of this interval as follows:
Lower limit = Mean - (3 x Standard Deviation)
Upper limit = Mean + (3 x Standard Deviation)
Plugging in the values for mean and standard deviation:
Lower limit = 68 - (3 x 1.5) = 68 - 4.5 = 63.5 seconds
Upper limit = 68 + (3 x 1.5) = 68 + 4.5 = 72.5 seconds
Hence , the interval of times that represents the middle 99.7% of Caroline's finishing times in the 400 meter race is 63.5 seconds to 72.5 seconds
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Using a table, find the range of the function for the given domain:
f(x)=2x+7 with domain: x = {2, 3, 5, 9}
A. y = {9, 10, 12, 16}
B. y = {11, 13, 17, 25}
C. y = {4, 6, 10, 18}
D. y = {-11, -13, -17, -25}
The range of the function is y = {11, 13, 17, 25}.
What is range of function?In mathematics, the range of a function refers to the set of all possible output values that the function can produce when given a set of input values. It is also known as the image of the function. The range of a function can be found by evaluating the function for all possible input values, or by analyzing the properties of the function.
According to given information:To find the range of the function, we need to substitute each value of the domain into the function and record the corresponding output values.
For x = 2, f(2) = 2(2) + 7 = 11.
For x = 3, f(3) = 2(3) + 7 = 13.
For x = 5, f(5) = 2(5) + 7 = 17.
For x = 9, f(9) = 2(9) + 7 = 25.
Therefore, the range of the function is y = {11, 13, 17, 25}.
The answer is A. y = {9, 10, 12, 16} is not the correct range for this function with the given domain.
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Tom and Philip were given the graph of a linear function and asked to find the slope. Tom says that the slope is 12 while Philip says that the slope is 2.
Which reason correctly justifies Tom's answer?
Without seeing the graph of the linear function, it is impossible to determine if Tom's answer of 12 is correct or incorrect. However, it is important to understand the concept of slope and how it is calculated for a linear function.
The slope of a linear function represents the rate at which the y-coordinate changes for each unit increase in the x-coordinate. In other words, it measures the steepness of the line. Mathematically, the slope of a line is defined as the ratio of the change in the y-coordinate to the change in the x-coordinate between any two points on the line.
To calculate the slope of a line given its graph, one can choose any two points on the line and find the difference in their y-coordinates and x-coordinates. The slope is then the ratio of the change in y-coordinates to the change in x-coordinates. This can be expressed as:
slope = (change in y-coordinate) / (change in x-coordinate)
Now, if Tom has correctly identified two points on the line and calculated the difference in their y-coordinates and x-coordinates, and if he has obtained a ratio of 12 for the change in y-coordinate to the change in x-coordinate, then his answer of 12 for the slope would be correct.
However, it is also possible that Tom made an error in his calculation, or that he misread the graph, and obtained an incorrect answer. Therefore, it would be necessary to verify his calculations by checking the points he used and the formula he applied.
In conclusion, without further information about the graph of the linear function and the points chosen by Tom to calculate the slope, it is impossible to determine if his answer of 12 is correct or incorrect.
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Find the value of x, y, and z in the parallelogram below.
(-3Z-4)°
85°
(-4y+5)
(8x-1)
The values of x, y and z of the given parallelogram are: x = 12, y = -20 and z = -32
What is the value of the angle in the parallelogram?A quadrilateral has two pairs of sides are parallel to each and the four angles at the vertices are not equal to the right angle, and then the quadrilateral is called a parallelogram. Also, the opposite sides are equal in length.
The key properties of angles of a parallelogram are:
- If one angle of a parallelogram is a right angle, then all the angles are right angles
- Opposite angles of a parallelogram are equal (or congruent)
- Consecutive angles are supplementary angles to each other (that means they add up to 180 degrees)
Consecutive angles are supplementary and as such:
85 + 8x - 1 = 180
8x = 181 - 85
8x = 96
x = 96/8
x = 12
Opposite angles are equal and as such:
85 = -4y + 5
-4y = 80
y = -20
Similarly:
85 - 3z - 4 = 180
3z = -96
z = -96/3
z = -32
Read more about Parallelogram Angle at: https://brainly.com/question/24056495
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AWARDING 90 POINTS!!!
Question
A survey was conducted to see how the teachers at Blue Pacific School District volunteer. Forty-four teachers volunteer at an animal shelter.
How many teachers volunteer at a senior center?
Enter your answer in the box.
Answer:
Step-by-step explanation:
Please answer, this as quick as possible, it’s very important for me, I’ll give brainliest if it’s correct, and try not to use chatgpt or you’ll get reported
Answer:
Your calculator should be in radian mode.
a)
[tex]f(x) = 56 \sin( \frac{2t\pi}{12} + \frac{\pi}{2} ) + 4[/tex]
b)
[tex]f(x) = 56 \cos( \frac{2t\pi}{12} - \frac{\pi}{2} ) + 4[/tex]
c)
The height of the wheel's central axle is 32 meters.
f(x) = 56sin((2(x + 4)π/12) - (π/2)) + 4
a canoe is seen floating down a creek. the canoe is first spotted 65 ft away. 7 seconds later the canoe is 40. ft away, making a 50° angle between the two settings how far did the canoe travel
The canoe traveled approximately a distance of 21.9ft.
let the distance the canoe travels be "d".
Initial position = 65 ft
After 7s,
The Final position is 40ft away
From the given information the canoe moves =(65-40)=25ft closer
Let x=25ft
Using the tangent function
we know that, tan(50degree)=x/d
therefore, d=25/tan(50 degree)
d=21.9ft
Read more about distance-related problems:
In a town of 42800 people.48% are male.the rest are female. how many more female are there than males
Answer:
First, we need to find out how many people are male and female in the town:
Step-by-step explanation:
Male population = 48% of 42800 = 20544
Female population = 100% - 48% = 52% of 42800 = 22256
To find out how many more females there are than males, we need to subtract the male population from the female population:
Female population - Male population = 22256 - 20544 = 1712
Therefore, there are 1712 more females than males in the town.
Juan wants to see the Grand Cayon, so he is taking a vacation in Arizona. He drove south from his house for 280 miles. Then, He drove east 64 miles.
a. Draw a diagram illustrating Juans Trip
b. How many total miles did Juan travel?
c. If a road was built directly from Juans home to the grand canyon, how long would it be? Round to the nearest mile.
d. Approximately how much shorter would Juans trip be if he was able to take the direct route?
Juan traveled approximately 288.24 miles.
The direct road would be approximately 288 miles long.
Juan's trip would be approximately 0.24 miles shorter if he was able to take the direct route.
We have,
a.
Here is a diagram illustrating Juan's trip:
Grand Canyon
|
|
|
Juan's | x
house --------->
y
b.
To find the total distance Juan traveled, we can use the Pythagorean theorem:
distance² = x² + y²
Juan drove 280 miles south (y direction) and 64 miles east (x direction), so we have:
distance² = 280² + 64²
distance² = 78,976 + 4,096
distance² = 83,072
Taking the square root of both sides, we get:
distance ≈ 288.24 miles
c.
To find the length of the direct road, we can use the Pythagorean theorem again:
distance² = x² + y²
The direct road forms a right triangle with legs of 280 miles and 64 miles, so we have:
distance² = 280² + 64²
distance² = 78,976 + 4,096
distance² = 83,072
Taking the square root of both sides, we get:
distance ≈ 288.24 miles
d.
To find how much shorter Juan's trip would be if he took the direct route, we can subtract the distance he traveled from the direct road distance:
288 - 288.24 ≈ -0.24
Thus,
Juan traveled approximately 288.24 miles.
The direct road would be approximately 288 miles long.
Juan's trip would be approximately 0.24 miles shorter if he was able to take the direct route.
Learn more about the Pythagorean theorem here:
https://brainly.com/question/14930619
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