Answers
Question 2.1.1
Answer: 5 unitsReason:
Use the distance formula to find the distance from the origin (0,0) to the terminal point (-3, 4)
[tex](x_1,y_1) = (0,0) \text{ and } (x_2, y_2) = (-3,4)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(0-(-3))^2 + (0-4)^2}\\\\d = \sqrt{(0+3)^2 + (0-4)^2}\\\\d = \sqrt{(3)^2 + (-4)^2}\\\\d = \sqrt{9 + 16}\\\\d = \sqrt{25}\\\\d = 5\\\\[/tex]
The pythagorean theorem is a similarly related alternative path you can take.
This triangle is a 3-4-5 right triangle.
====================================================
Question 2.1.2
Answer: 1/5Reason:
r = distance from origin to terminal point
r = 5, calculated back in the previous problem above.
sin(alpha) = y/r = 4/5
cos(alpha) = x/r = -3/5
sin(alpha)+cos(alpha) = (4/5)+(-3/5) = 1/5
====================================================
Question 2.1.3
Answer: 1Reason:
Recall that tangent is the ratio of sine over cosine
tan = sin/cos
Therefore,
[tex]\tan(\alpha) *\frac{\cos(\alpha)}{\sin(\alpha)}\\\\\frac{\sin(\alpha)}{\cos(\alpha)}*\frac{\cos(\alpha)}{\sin(\alpha)}\\\\\frac{\sin(\alpha)*\cos(\alpha)}{\cos(\alpha)*\sin(\alpha)}\\\\1[/tex]
This assumes that neither sin(alpha) nor cos(alpha) are zero. Otherwise, we have a division by zero error.
Related Questions
Consider the graph of f(x) = (x + 5)2 – 3. Rewrite the equation by making one change in the equation of f(x) so that the graph has no x-intercepts.
Answers
Using the discriminant of a quadratic equation, if the graph is translated shifted up 4 units, the graph will have no x-intercepts.
What is the discriminant of a quadratic equation and how does it influence the solutions?A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The discriminant is:
[tex]\Delta = b^2 - 4ac[/tex]
The solutions are as follows:
If [tex]\mathbf{\Delta > 0}[/tex], and it has 2 x-intercepts.If [tex]\mathbf{\Delta = 0}[/tex], it has 1 x-intercept.If [tex]\mathbf{\Delta < 0}[/tex], it has no x-intercepts.In this problem, the function is given by:
f(x) = (x + 5)² - 3.
In standard form:
f(x) = x² + 10x + 22.
We want to find coefficient k for which the function has [tex]\Delta < 0[/tex], then:
f(x) = x² + 10x + 22 + k.
The coefficients are a = 1, b = 10, c = 22 + k, hence:
[tex]\Delta < 0[/tex]
10² - 4(22 + k) < 0
100 - 88 - 4k < 0
4k > 12
k > 3.
Hence, with k = 4, the function is shifted up 4 units, and the graph will have no x-intercepts.
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PLS HELP ME ASAP!!!!
Answers
B. x^9
just simplify
what is the median of the data set represented by the box plot shown below? 38,45,50,60,75
Answers
Answer:
50
Step-by-step explanation:
Beth gets a sum of 5 when she rolls two fair number cubes. What is the probability that one of the fair number cubes is a 1?
Answers
Using it's concept, it is found that there is a 0.5 = 50% probability that one of the fair number cubes is a 1.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
The outcomes of the pair of cubes that result in a sum of 5 are as follows:
(1,4), (2,3), (3,2), (4,1).
Of those 4 outcomes, 2 involve a number 1, hence the probability is given by:
p = 2/4 = 0.5.
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Q: Wilma estimates that she’ll drive about 18,000 miles during the year. The car she wants to purchase gets an average of 24 miles per gallon, and the average cost per gallon of gas in her neighborhood is $2.72. Locate the error in her calculations, and select the correction.
A: Wilma made a mistake in step 2. Instead of dividing by 12, she should have divided by 24. She should budget $170 per month for fuel expenses.
Answers
The mistake is made in the second step. The correct steps are given below.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Wilma estimates that she’ll drive about 18,000 miles during the year.
The car she wants to purchase gets an average of 24 miles per gallon, and the average cost per gallon of gas in her neighbourhood is $2.72.
Locate the error in her calculations, and select the correction.
Step - 1
18000 miles/year
18000 miles / 12 months = 1500 miles/month
Step 2
1500 miles/month
1500 miles/month / 24 miles per gallon = 62.5 gallons/month
62.5 gallons/month
Step 3
(62.5 gallons/month) x ($2.72/gallons) = $170 cost/month
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Reflectional Symmetry
Instructions: If the following figures have
reflectional symmetry, determine the
number of lines of symmetry.
Lines of Symmetry:
Answers
The figure has a rotational symmetry and the number of lines of symmetry is 3
How to determine the rotational symmetry?The given figure is an equilateral triangle.
An equilateral triangle has 3 equal sides and 3 equal angles.
This means that it has a rotational symmetry and the number of lines of symmetry is 3.
The angle of rotational symmetry is calculated as:
Angle = 180/3
Evaluate
Angle = 60
Hence, the angle of rotational symmetry is 60
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Arun took a taxi from his house to the airport. The taxi company charged a pick-up fee of $4 plus $4.25 per mile. The total fare was $110.25, not including the tip. How many miles was the taxi ride?
Answers
Here we must write and solve a linear equation to find the number of miles that Arun traveled in the taxi. We will find that Eva traveled 11 miles.
So we know that the taxi charges a fee of $4.10 and then a plus of $0.50 per mile.
So if you travel for m miles, the cost equation is:
C(m) = $4.10 + $0.50*m
Now, we know that for Eva the total fare (total cost) was $9.60, then we need to solve:
$9.60 = C(m) = $4.10 + $0.50*m
$9.60 = $4.10 + $0.50*m
$9.60 - $4.10 = $0.50*m
$5.50 = $0.50*m
$5.50/$0.50 = m = 11
This means that Arun traveled 11 miles in the taxi.
The Eva traveled 25 miles in the taxi.
It is required to find how many miles was the taxi ride.
What is arithmetic?Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.
Given:
The taxi company charged a pick-up fee of $4 plus $4.25 per mile.
The total fare was $110.25.
The cost equation is:
C(m) = $4 + $4.25*m
Now, we know that for Eva the total fare (total cost) was $110.25, then we need to solve:
$110.25 = C(m) = $4 + $4.25*m
$110.25-$4=$4.25*m
$106.25=$4.25*m
m =25
Therefore, the Eva traveled 25 miles in the taxi.
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( PLEASE HELP URGENT ) A triangular prism has a height of 10 cm and the triangle has a base of 4 cm and a height of 6 cm. Find the volume of the triangular prism.
Answers
The volume of the triangular base prism is 120 centimetre cube.
How to find the volume of a triangular prism?volume of a triangular prism = BH
where
B = base areaH = height of the prismTherefore,
base area = 1 / 2 bh
base area = 1 / 2 × 4 × 6 = 24 / 2 = 12 cm
Hence,
volume of a triangular prism = 12 × 10
volume of a triangular prism = 120cm²
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Two balls are drawn without replacement from a box containing 2black and 3 red balls. What is the probability of drawing a black ball on the second draw? Draw a tree diagram
Answers
The probability that the second ball drawn is black is 4/10 = 2/5
How to find the probability?
There are two cases. The case where the first ball is red is the first one.
The probability of drawing a red ball is equal to the quotient between the number of red balls and the total number of balls.
p = 3/5
Then, the probability of drawing a black ball in the second attempt is computed in the same way, but because we already drew a ball, now the total number of balls is 4, so we have:
q = 2/4 = 1/2.
So the joint probability is:
P = (3/5)*(1/2) = 3/10.
Then we have the case where both balls are black, the probabilities now are:
p = 2/5
q = 1/4
So the joint probability is:
P = (2/5)*(1/4) = 1/10
The total probability is the sum of the two above:
probability = 3/10 + 1/10 = 4/10.
The probability that the second ball drawn is black is 4/10 = 2/5
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What is the ratio of 338 and 508
Answers
RATIO OF 338 : 508
=> 169 : 254
( NEED HELP ASAP! do not comment links to the answer, Would greatly be appreciative )
For number 1 I already answered it but can you tell me if I got it correct? or not ? and if I did
Not get it right, can u correct me? Thank you :)
Answers
Based on the number of children and tricycle wheels, the ratio of children to tricycle wheels is 10 : 18
Solving ratio problemsNumber of children = 10Number of tricycles = 6Number of wheels per tricycle = 3Total wheels of tricycle = Number of tricycles × Number of wheels per tricycle
= 6 × 3
= 18 wheels
Ratio of children to tricycle wheels = 10 : 18
= 5 : 9
Therefore, the ratio of children to tricycle wheels is 10 : 18
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Find the area of the following Triangle.
Answers
Answer:
6.25cm²
Step-by-step explanation:
Hello!
The formula for the area of a triangle is [tex]A = \frac12 b*h[/tex]
A = areab = baseh = heightSolve[tex]A = \frac12 b*h[/tex][tex]A = \frac12(5)*2.5[/tex][tex]A = 2.5 * 2.5[/tex][tex]A = 6.25[/tex]The area of the triangle is 6.25 cm²
When there is no traffic, it takes Rina 4 hours to get from Boston to New York. Once, Rina started her trip to New York at a speed of 60 mph, but after 2 1/3 hours of driving she stopped for 40 minutes. She had to drive at a speed of 45 mph for the rest of her trip. How long was her trip?
Answers
The whole trip was 0.185 Km or 185 m long.
What is speed ?Speed is the time rate at which an object is moving along a path.
Given:
For 7/3 hours speed is = 60 mph = 0.06 kmph
For 40 minutes or 2/3 hours = 0 mph
for 1 hours = 45 mph or 0.045 kmph
The total distance she travels
= 7/3*0.06+ 2/3*0+ 1*0.045
=0.185 Km or 185 m
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Pls help meee!!!!!!!!!
Answers
Answer: x = 103
Step-by-step explanation:
this is a 90 degree angle indicated by the box in the corner of the angle.
90 degree angles total 90 degrees.
X - 15 + 2 = 90
move the numbers to the other side of the equal sign to isolate the X
by doing the opposite
x = 90 + 15 -2
x = 103
check your work, X - 15 + 2 = 90
103 - 15 + 2 = 90
answer is correct
Write the standard form of the equation of the circle with the given characteristics.
Center: (0, 0); Radius: 2
Answers
To determine the equation of a circle, use the standard form of a circle (x - h)² + (y - k)² = r² where,
(h, k) is the center; andr is the radiusSubstitute the values of the center and radius to the standard form.
Given:
(0, 0) - center
2 - radius
(x - h)² + (y - k)² = 2²(x - 0)² + (y - 0)² = 4x² + y² = 4Answer:
The equation of the circle is x² + y² = 4.Wxndy~~
Use the net to determine the total surface area.
134.4 in
92.8 in
103.2 in
72 in
Answers
What is the radius of the circle with center at (-6, -4) that goes through the point (1, -7) rounded to the nearest tenth?
Answers
Answer:
dhususbdgdg
Step-by-step explanation:
hdhakuxtsjwkbevdvsiw in e
The following exercises present you with fairly straightforward ratio and proportion situations.
On one map, -inch represents 18 miles. If two cities are inches apart on the map, what is the actual distance (in miles)
between them?
Answers
Answer:
36+ Miles
Step-by-step explanation:
One in being 18 miles, and two cities that are inches apart. So 2 or more inches. Would make it anywhere from 36 or more miles.
HI HELP PLEASE
The height of female students in Cromartie High is normally distributed. If 95% of females are
between 57.6 and 70.4 inches tall centered about the mean, find the average height and standard
deviation for female students at Cromartie High.
Answers
Using the Empirical Rule, it is found that the mean is of 64 inches and the standard deviation is of 3.2 inches.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.The normal distribution is symmetric, hence the mean is given by:
M = (57.6 + 70.4)/2 = 64.
57.6 is two standard deviations below the mean, hence the standard deviation is found as follows:
57.6 = 64 - 2s.
2s = 6.4
s = 3.2.
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n⃗ =〈−2,−1〉 and D=[−4 4 2 3].
What is D⋅n⃗ ?
Enter your answer as a vector by filling in the boxes.
Answers
The dot product of the two matrices D and n is determine as (4, - 7).
Dot product of the vector
The dot product of the two matrices is calculated as follows;
n = (-2, -1), and D = [-4 2]
[4 3]
D.n = (-2, -1). [-4 2] = (-2 x -4) + (-1 x 4) = 4
[4 3] = (-2 x 2) + (-1 x 3) = -7
D.n = (4, - 7)
Thus, the dot product of the two matrices D and n is determine as (4, - 7).
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Subtract 5x - 4 from the sum of -3x - 4 + y and 4x - y
Answers
Answer:
-4x
Step-by-step explanation:
((-3x-4+y) + (4x-y)) - (5x-4)
= (-3x-4+y+4x-y) - 5x+4
= (x-4) -5x+4
=x-4-5x+4
=-4x
Select from the drop-down menus to correctly complete the sentence. The probability of a chance event is a number between 0 and 1 that expresses the __?___ that an event __?___ occur.
Answers
The probability of a chance event is a number between 0 and 1 that expresses the likelihood that an event would occur.
How to complete the blanks?As a general rule in probability, we have:
Minimum probability = 0Maximum probability = 1The above represents the range of a valid probability (both inclusive).
This also represents the likelihood that an event would occur
Hence, the words that complete the blank are likelihood and would.
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If a population consisted of 75,000 people surveying 75,000 people from the population could result in a parameter but not a point estimate. True or false?
Answers
A soda factory makes 9 flavors of soda. Each case of soda has 5 cans of each flavor. They produce enough soda to fill 7 cases per hour, 14 hours a day. How many cans of soda does the factory produce in 6 days?
Answers
26,460 cans of soda
Step-by-step explanation:
First times 9 and 5 together then times 7 with it then times 14 then times 6 and you should end up with 26,460
Describe a sequence of transformations that take isosceles trapezoid T to its image T. You may use the transformations reflection, rotation, and translation.
EARN FREE EASY POINTS BY GIVING ME THE RIGHT ANSWER!!
Answers
The types of rotation are:
Reflection: it is where the graph is inverted and each point is the same distance from the point of reflectionRotation: it is the act of rotating something around the axisTranslation: it is where every point shift by the same unitIn this case:
⇒ it is reflection since the graph is inverted and each point is the same distance from the line of reflection
Answer: reflection
Hope that helps!
7x^2+3y^2+12x+2y-6=0 Help me find the value of a,b,c and the discriminant number
Answers
Answer:
b o a h d
Step-by-step explanation:
1*5 3%9 46% &45 that is the answer
Gabrielle needs to rent a car while on vacation. The rental company charges $19.95, plus 15 cents for each mile driven. If Gabrielle only has $40 to spend on the car rental, what is the maximum number of miles she can drive?
Round your answer down to the nearest mile.
Answers
Answer:
133 miles
Step-by-step explanation:
The limited budget gives rise to an inequality that can be solved for the maximum number of miles.
__
setupThe rental cost for m miles will be the sum of the fixed charges and the product of the mileage charge and the number of miles.
cost = 19.95 +0.15m
We want this to be no greater than 40, so we have the inequality ...
40 ≥ 19.95 +0.15m
solutionThis two-step inequality can be solved in the usual way:
20.05 ≥ 0.15m . . . . . step 1, subtract 19.95 from both sides
133.667 ≥ m . . . . . . . step 2, divide by the coefficient of the variable
The maximum whole number of miles Gabrielle can drive is 133.
Calculate the percent change if a city that used to produce 2050 kilowatt hours has reduced their consumption to 1125 kilowatt hours
Answers
The percent change if a city that used to produce 2050 kilowatt hours has reduced their consumption to 1125 kilowatt hours is 45.122% decrease.
What is percentage change?Percent increase and percent decrease are measures of percent change, which is the extent to which a variable gains or loses intensity, magnitude, extent, or value.
we know,
% change = (final- initial) / initial * 100
=(1125-2050)/1125 *100
=45.122%
Hence, percentage change be 45.122% decrease.
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which function below has the smallest slope?
f(x)
f(x) = 2x - 3
Answers
Answer:
f(x)
Step-by-step explanation:
f(x) is a little represented number after solving for x but
f(x)=2x-3 is more bigger
I have 1/3 of a pie. You have 1/3 of a pie. Add the pieces of pie together. How much pie do we have?
Answers
Answer:
2/3
Step-by-step explanation:
To add fractions add the numbers on top to each other and leave the bottom numbers alone if they are the same number.
[tex]\frac{1}{3}+\frac{1}{3}=\frac{1+1}{3}=\frac{2}{3}[/tex]