Answers
Problem 4
Draw any right triangle you want. Afterward, draw a perpendicular segment that goes from the 90 degree angle to the hypotenuse. Call this new segment the altitude. It might help to have the hypotenuse laying flat or horizontal.
The length of this altitude can be found using the geometric mean formula. Search out "geometric mean for triangles" (or similar) and you should get a diagram that visually summarizes what is going on. I've provided a screenshot of an example using GeoGebra. See below.
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Problem 5
The two special types of right triangles are: the 45-45-90 triangle and the 30-60-90 triangle.
If x is the leg length of the first triangle type mentioned, then [tex]x\sqrt{2}[/tex] is the hypotenuse. We can confirm this using the pythagorean theorem. Recall that the legs of any 45-45-90 triangle are the same, meaning we have an isosceles triangle.
For the second type of triangle, the short leg x leads to the hypotenuse 2x and long leg [tex]x\sqrt{3}[/tex]
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Problem 6
If you know say the opposite and adjacent sides of a right triangle, then you can use the tangent ratio because tan = opposite/adjacent.
Sine is used for opposite/hypotenuse, while cosine is used for adjacent/hypotenuse. Those are the main 3 trig functions. Technically there are 3 more, but they are just reciprocals of the previous three.
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Problem 7
Use inverse trig functions to find the missing angles if you know the sides. The inverse trig functions have an exponent of -1.
For instance, let's say the triangle has an opposite side of 10 and hypotenuse of 15
The reference angle would be...
[tex]\sin(\text{angle}) = \frac{\text{opposite}}{\text{hypotenuse}}\\\\\sin(x) = \frac{10}{15}\\\\x = \sin^{-1}\left(\frac{10}{15}\right)\\\\x \approx 41.81^{\circ}\\\\[/tex]
==========================================================
Problem 8
Imagine looking completely horizontal at the horizon. The angle in which you are currently looking is 0 degrees. If you look upward, say 10 degrees, then the angle of elevation is 10 degrees. Looking down means we have an angle of depression. These two types of angles help us determine various distances and lengths.
Use the alternate interior angle theorem to help show that angles of depression are congruent to angles of elevation. It will depend on context which type of angle is more useful.
Related Questions
Submit the answers to the checkpoint questions in the text box with the Lesson Review.
Part A Checkpoint
Directions: Complete each of the following questions.
(PICTURE FOR THE FIRST QUESTION)
1. Indicate the kind of energy represented in each example below:
a. Burning fuel in a car
b. Exploding an atomic bomb
c. Current moving in a wire
d. Tires sliding on pavement when brakes are applied
e. Football player running for a touchdown
2. All forms of energy except nuclear fission come from the _________.
3. Energy is ______________.
Answers
its that one dudee!!!!!
Please i really need help!
Answers
Answer:
21.25=4.25
Ms. Diaz buys 5 pounds of strawberrys
Step-by-step explanation:
Please help me 35 points and Brainliest if your right
Answers
Answer:
y = - 2 | x - 2 | + 4
Step-by-step explanation:
the general equation of an absolute value function is
y = a|x - h| + k
where (h, k ) are the coordinates of the vertex and a is the stretch factor
here (h, k ) = (2, 4 ) , then
y = - 2|x - 2| + 4
Answer:
See below ~
Step-by-step explanation:
Formula for absolute value function :
y = a |x - h| + k
==============================================================
Given :
⇒ a = -2
⇒ Vertex = (h, k) = (2, 4) [based on graph]
=============================================================
Solving by substitution :
⇒ y = -2|x - 2| + 4
Please only 5 and 6 that all i need help with is area
Answers
Answer:
5) 22.95
6) 21.93
Step-by-step explanation:
Area of Triangle = BxH/2
= CxH/2
can anyone help? Need expert advice
Answers
Answer:
C (3,6)
Step-by-step explanation:
So the zeroes are the points that the loop goes through on the x-axis
so three and six
find the length and width of a rectangle whose
Length is 5cm longer than it’s width
Whose area is 50cm
Answers
Step-by-step explanation:
width= x (let)
length= x+5
Area=50 cm
Now ,
area = l ×b
50 = (X×X+5)
50 = (2X + 5)
50÷ 2= X+5
25 -5 = X
X=20
LENGTH = X+5
20+5
=25
Natalie wants to use a sheet of fiberboard 30 inches long to create a skateboard ramp with a 28 angle of elevation from the ground
Answers
Answer:
You should raise one side 14 inches
Step-by-step explanation:
I used a right angle triangle calculater at this sight
https://www.calculator.net/right-triangle-calculator.html
through: (-3, 4), slope
1
4
Answers
Answer:
y = (-1/4)x + (13/4)
Step-by-step explanation:
The general structure of an equation in slope-intercept form is:
y = mx + b
In this form, "m" represents the slope and "b" represents the y-intercept.
Remember that in a point (-3,4) you have an "x" and "y" value. As such, you have been given values for the "x", "y", and "m" variables. Therefore, you can plug these values into the general structure to find the value of "b".
y = mx + b <---- General structure
y = (-1/4)x + b <---- Plug (-1/4) in "m"
4 = (-1/4)(-3) + b <---- Plug in values from point
4 = (13/4) + b <---- Multiply (-1/4) and -3
(13/4) = b <---- Subtract (13/4) from both sides
Now that you know the value of "m" and "b", you can determine the formula.
y = (-1/4)x + (13/4)
the sum of two consecutive integers is 65. what are the two integers? show steps please.
Answers
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to find the two integers, given that they are consecutive, and their sum is 65.
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
Consecutive integers are right next to each other, like 12 and 13. or 65 and 66.Let the first integer be x, and let the second integer be x+1.
Their sum is 65. Let's set up our equation:
[tex]\longmapsto\sf{x+x+1=65}[/tex]
Combine like terms:
[tex]\longmapsto\sf{2x+1=65}[/tex]
Subtract 1 from both sides of the equal sign:
[tex]\longmapsto\sf{2x=64}[/tex]
Divide both sides by 2:
[tex]\longmapsto\sf{x=32}[/tex]
To find the second integer, subtract the first integer from the sum of the two integers:
[tex]\longmapsto\pmb{65-32}[/tex]
[tex]\longmapsto\pmb{33}[/tex]
The integers are: 33 and 32.
Hope it helps you out! :D
Ask in comments if any queries arise.
#StudyWithBrainly
~Just a smiley person helping fellow students :)
The formula for converting C to F is C =
5(F-32)
9
where F is the temperature in °F and C is the temperature in °C.
Find F when C= 28°.
Answers
Answer:
f=82.4
Step-by-step explanation:
f=9c/5+32
f=9x28/5+32
f=252/5+32
f=50.4+32
f=82.4
A 6-inch personal pizza has 570 calories. Determine the number of calories in the 14-inch pizza. Round your answer to the nearest calorie.
Answers
Answer:
3103 calories
Step-by-step explanation:
We presume the number of calories is proportional to the area of the pizza. The ratio of areas is the square of the ratio of the linear dimensions, so the number calories in the larger pizza is ...
(14/6)² × 570 calories = 3103 1/3 calories
There are about 3103 calories in the 14-inch pizza.
Khamisi and Harut wrote down two different functions that have the same rate of change. Khamisi's function is represented by the table shown below. x y -1 -5 1 -1 3 3 Write an equation, in slope intercept form, that could be Harut's function.
Answers
The equation of line is x+2y+3=0.
What is a equation of the line?The standard form of equation of a line is ax + by + c = 0. Here a, b, are the coefficients, x, y are the variables, and c is the constant term. It is an equation of degree one, with variables x and y.
Given:
x:-1 -5 1
y:-1 3 3
So,
m= 3-1/-5-(-1)
m= 2/-4
m=-1/2
Now, equation of line
(y-(-1))= m (x-(-1))
y+1= -1/2(x+1)
2y+2=-x-1
x+2y+3=0
Hence, the equation of line is x+2y+3=0.
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!!!!! determine the function being differentiated, and the number at which its derivative is being evaluated. Where possible, evaluate the limits using differentiation.
Answers
Recall that the derivative of a function f(x) at a point x = c is given by
[tex]\displaystyle f'(c) = \lim_{x\to c} \frac{f(x) - f(c)}{x - c}[/tex]
By substituting h = x - c, we have the equivalent expression
[tex]\displaystyle f'(c) = \lim_{h\to0} \frac{f(c+h) - f(c)}h[/tex]
since if x approaches c, then h = x - c approaches c - c = 0.
The two given limits strongly resemble what we have here, so it's just a matter of identifying the f(x) and c.
For the first limit,
[tex]\displaystyle \lim_{h\to0} \frac{\sin\left(\frac\pi3 + h\right) - \frac{\sqrt3}2}h[/tex]
recall that sin(π/3) = √3/2. Then c = π/3 and f(x) = sin(x), and the limit is equal to the derivative of sin(x) at x = π/3. We have
[tex](\sin(x))' = \cos(x)[/tex]
and cos(π/3) = 1/2.
For the second limit,
[tex]\displaystyle \lim_{a\to0} \frac{e^{2a} - 1}a[/tex]
we observe that e²ˣ = 1 if x = 0. So this limit is the derivative of e²ˣ at x = 0. We have
[tex]\left(e^{2x}\right)' = e^{2x} (2x)' = 2e^{2x}[/tex]
and 2e⁰ = 2.
State the various transformations applied to the base function f(x)=|x| to obtain a graph of the function g(x) = |x| − 2.
Horizontal shift of 1 unit to the right and a vertical shift upward of 2 units.
Horizontal shift of 1 unit to the right and a vertical shift downward of 2 units.
Horizontal shift of 1 unit to the left and a vertical shift downward of 2 units.
Horizontal shift of 1 unit to the left and a vertical shift upward of 2 units.
Answers
Horizontal shift of 1 unit to the left and a vertical shift downward of 2 units.
Transformation of functionTransformation technique is a way of changing the position of an object on an xy-plane.
Given the parent function of a modulus function f(x) = |x|, the graph of the function g(x) = |x| - 2 shows a vertical translation of the parent function down by 2 units.
The resulting graph of the translated function is as shown below
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Simplify −45(30x−40)+(42x+4) . Write your answer in factored form.
Answers
solution
-4(327x-451)
A spherical balloon is inflated with gas at the rate of 500 cubic centimeters per minute. How fast is the radius of the balloon increasing at the instant the radius is 70 centimeters
Answers
Using implicit differentiation, it is found that the radius is increasing at a rate of 0.0081 cm per minute.
What is the volume of a sphere?The volume of a sphere of radius r is given by:
[tex]V = \frac{4\pi r^3}{3}[/tex]
Applying implicit differentiation, the rate of change is given by:
[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]
In this problem, we have that:
[tex]\frac{dV}{dt} = 500, r = 70[/tex]
Hence the rate of change of the radius is given as follows:
[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]
[tex]19600\pi\frac{dr}{dt} = 500[/tex]
[tex]\frac{dr}{dt} = \frac{500}{19600\pi}[/tex]
[tex]\frac{dr}{dt} = 0.0081[/tex]
The radius is increasing at a rate of 0.0081 cm per minute.
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1. Using the above
scatterplot, does there
seem to be a positive
correlation, a negative
or no
correlation,
correlation between
the number of
customers and sales?
Answers
Answer:
yes there is a correlation
Step-by-step explanation:
here's how I found this by looking up all key words.
Give the prime factorization of 28.
Answers
The area of a rectangle is 44 square units. Its length measures 4 units. Find the length of its diagonal. Round to the nearest tenth of a unit.
Answers
Answer:
√(137)
Step-by-step explanation:
First, you will need to find the other side length.....then you can use the Pythagorean Theorem to find the diagonal:
L x W = 44
4 x W = 44
W =11
Now the Pythag, Theorem:
diagonal^2 = 4^2 + 11^2
d^2 = 16+121
d^2 = 137
d = √(137)
Answer:
about 11.7 units (Pls mark me as brainy)
Step-by-step explanation:
Find the width:
length⋅width= area
4w=44 Plug in known values.
4w/4=44/4 Divide both sides by 4
w=11
Find the diagonal:
(4)^2+(11)^2= c^2 Use the Pythagorean Theorem.
16+121= c^2 Simplify.
137=c^2 Simplify.
±√137= √c^2 Square root both sides.
11.704699...= c Simplify. Ignore the negative root, as the length must be positive.
11.7≈ c Round to the nearest tenth.
The length of the diagonal is 11.7 units.
What should be done so that the expression will have a value of 10?
12 - 2 + 2 2 ÷ 8
Answers
use (PEMDAS)
P parentheses ()
E exponents
M multiplication • , () , x
D division
A addition +
S subtraction -
Explanation:
There are no parentheses.
There are exponents.
The multiplication is the exponents.
There is division.
There is addition and subtraction.
-how to solve-
First, do 2 to the second power and get 4.
Next, do 12-2+4 divided by 8.
Next do multiplication: there’s no more.
Next do division: you can’t do 4 divided by 8 so instead, do 12-2 = 10 plus 8.
Hope this helps!
here is the histogram of a data distribution. All class widths are 1.
what is the median of the distribution?
Answers
The median of the data is 5 if the all class widths are 1, option (C) is correct.
What is the median?A median is a middle number in a series of numbers that have been arranged to lift, and it might be more informative of the set of data than the average. When there are extremes in the sequences that might affect the average of the numbers, the median is sometimes employed instead of the mean.
In the histogram, 15 data values are given:
1, 2, 2, 3, 3, 3, 4, 5, 6, 6, 7, 7, 7, 8, 9
The mid-value is 5 which is on the 8th place
Thus, the median of the data is 5 if the all class widths are 1, option (C) is correct.
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A biologist started with a population of 1,000 bacteria that doubled in size every day.
Which equation and graph show the number of days, d, as a function of the population
p, in thousands?
Answers
Answer: C. [tex]p = 2^{d}[/tex]
Step-by-step explanation:
The population rises exponentially, so the graph will have to go up. It also means the population is doubled directly in relation to days
Help me calculate
I think it's 35, is that right?
Answers
The value of the [tex]\rm 6x^5y^3[/tex] is 35 if the value of [tex]\rm 2x^2y = 5[/tex] and [tex]\rm 3x^3y^2 = 7[/tex]
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
We have:
[tex]\rm 2x^2y = 5\\\\\rm 3x^3y^2 = 7[/tex]
We have to find the value of [tex]\rm 6x^5y^3[/tex]
[tex]=\rm 6x^5y^3\\\\= \rm 6(x^2y)(x^3)(y^2)[/tex]
=6(5/2)(7/3)
= (5)(7)
= 35
Thus, the value of the [tex]\rm 6x^5y^3[/tex] is 35 if the value of [tex]\rm 2x^2y = 5[/tex] and [tex]\rm 3x^3y^2 = 7[/tex]
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Find the volume of cone pictured below. Use 3.14
for T. Round your answer to the nearest
hundredth.
8 yd
8 yd
Answers
The top four teams in a local tournament move onto the playoffs. if 7 teams enter the tournament how many different
combination of teams can make it to the playoffs?
Answers
Using the combination formula, it is found that 35 different combination of teams can make it to the playoffs.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, 4 students are taken from a set of 7, hence the number of combinations is given by:
[tex]C_{7,4} = \frac{7!}{4!3!} = 35[/tex]
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HUGE POINTS
PLEASE ANSWER
BE INFORMATIVE AS POSSIBLE
Question:
A parallelogram fencing area is to be constructed for a general swimming pool area. The total perimeter of the parallelogram fence is 220m. If one of the lengths is 50m, determine the dimension of the other length and draw it out.
If you want more information let me know
Answers
Answer:
The other length is 60m.
Step-by-step explanation:
If you look at the shape of a parallelogram, you will see that a parallelogram has two parallel sides. So, if the total perimeter is 220m, then 50m and 50m together would be 100m, so 220- 100= 120m left to fill in both sides left. so, 120÷2= 60m. 60m is the other length.
help me plss ty in advance:))
Answers
Answer:
AACBC7Step-by-step explanation:
Q1
A graph which uses horizontal or vertical bars with no gaps to represent data is called bar graph.
Q2
Data plotted against the frequency in a histogram is class interval.
Q3
The data plotted against the frequency in an ogive is cumulative frequency.
Q4
A score of 50 under the column > c.f. with the boundaries 23.5 - 28.5 means 50 students got a score greater than 23.5.
Q5
Mean = 2(2) + 3 + 4 + 7(3) + 10 + 11 + 2(12) / 11
Mean = 4 + 7 + 21 + 21 + 24 / 11
Mean = 77/11
The mean is 7
Q6
The median is the middle term.
The median of the distribution is 7
11.3 9 9 9 7.8 surface area of triangular prism
Answers
Answer:
Total area = 187.65 cm^2
Step-by-step explanation:
AREA of a triangle = 1/2 base * height
THREE sides 3 * 1/2 *9 * 11.3 = 152.55 cm^2
Bottom 1/2 * 9 * 7.8 = 35.1 cm^2
total = 187.65 cm^2
Convert 650 ml into litres
Answers
Answer:
.65 litres
Step-by-step explanation:
Look at the corners of the shape below. Which of the following points is located at one of the corners?
Answers
Answer: Coordinate (1,6)
Step-by-step explanation: Because it is located on one of the corners already if you count the spaces! I hope this helped!! :D
Answer:
the person above me is right its (1,6) its the only one thats located on a corner
Step-by-step explanation: