The points (-15, r) and (-3, 16) lie on a line with slope 5/4. Find the missing coordinate r.

f(x) is a linear function, so both the domain and the range are the set of real numbers.

Answer:

Step-by-step explanation:

Let the total distance be x.

We have:

Set this as equation and solve for x:

Total distance from the park to the station is approximately 311 m.

Let that be d

The control variable that can be used in the research experiment is to ensure that the two set of plants will receive the same amount of water and light.

According to the information, the researcher wants to seek whether singing to plants causes them to grow taller.

The explanatory variable is singing. Therefore, the researcher can control some of the variables to determine the explanatory variable on the growth of the plant.

Hence, the control variable that can be used in the research experiment is to ensure that the two set of plants will receive the same amount of water and light.

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Answer:

oh.

Step-by-step explanation:

The length of each leg and the hypotenuse of this triangle will be:

AD = 2 units.

AE = 2 units.

DE = 2.8 units

From the information given and the attached diagram, the value or AD and AE are 2 units respectively.

The value of DE will be calculated as the square root of 2² + 2². This will be:

= 2² + 2² = 8

= ✓8 = 2.8

Therefore, the correct options are 2, 2, and 2.8 units.

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The following expressions (1+cosβ)(1−cosβ)sinβ is equivalent to sin³β

In a Right angled triangle , trigonometric ratios can be used to determine the value of angles and sides of the triangle.

The trigonometric expression given in the question is

(1+cosβ)(1−cosβ)sinβ

(a+b)(a-b) = a² - b²

( 1 - cos²β)sinβ

By the trigonometric Identity

1-cos²β = sin² β

 sin² β x sin β

sin³β

Therefore Option B is the correct answer.

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The complex number  -7i into trigonometric form is 7 (cos (90) + sin (90) i) and  3 + 3i in trigonometric form is 4.2426 (cos (45) + sin (45) i)

It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.

We have a complex number shown in the picture:

-7i(3 + 3i)

= -7i

In trigonometric form:

z = 7 (cos (90) + sin (90) i)

= 3 + 3i

z = 4.2426 (cos (45) + sin (45) i)

[tex]\rm 7\:\left(cos\:\left(90\right)\:+\:sin\:\left(90\right)\:i\right)4.2426\:\left(cos\:\left(45\right)\:+\:sin\:\left(45\right)\:i\right)[/tex]

[tex]\rm =7\left(\cos \left(\dfrac{\pi }{2}\right)+\sin \left(\dfrac{\pi }{2}\right)i\right)\cdot \:4.2426\left(\cos \left(\dfrac{\pi }{4}\right)+\sin \left(\dfrac{\pi }{4}\right)i\right)[/tex]

[tex]\rm 7\cdot \dfrac{21213}{5000}e^{i\dfrac{\pi }{2}}e^{i\dfrac{\pi }{4}}[/tex]

[tex]\rm =\dfrac{148491\left(-1\right)^{\dfrac{3}{4}}}{5000}[/tex]

=21-21i

After converting into the exponential form:

[tex]\rm =\dfrac{148491\left(-1\right)^{\dfrac{3}{4}}}{5000}[/tex]

From part (b) and part (c) both results are the same.

Thus, the complex number  -7i into trigonometric form is 7 (cos (90) + sin (90) i) and  3 + 3i in trigonometric form is 4.2426 (cos (45) + sin (45) i)

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Answer:

h ≈ 37 ft

Step-by-step explanation:

let x be the height of the tree from the viewers eye level

using the tangent ratio, then

tan24° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{x}{72}[/tex] ( multiply both sides by 72 )

72 × tan24° = x

then

height of tree = x + 5 = 72tan24° + 5 ≈ 37 ft ( to the nearest foot )

Answer:

37ft

Step-by-step explanation:

It can be considered as a right angle triangle. The height of the tree is equal to the product of tan(24°) and the distance between the man and tree+5 Therefore

In conclusion

The height of the tree is 37ft

Answer: [tex]\sqrt{7}[/tex]

Step-by-step explanation:

Using the Pythagorean theorem,

[tex]3^2 + b^2 = 4^2\\\\9+b^2 = 16\\\\b^2 = 7\\\\b=\boxed{\sqrt{7}}[/tex]

Answer:

good questing it is something

Step-by-step explanation:

1-1-2- --3--1234-3

3-4

Q-

-4

-24

-4

-

q 43-

43-

3 4-3

4-

4-4

- answer is 2def not cap i need 5 poinnts i gues

Answer: [tex]y=x-9[/tex]

Step-by-step explanation:

To find the inverse of a function you must first swap the places of x and y

[tex]x=y+9[/tex]

Now solve for y

Step 1: Flip the equation.

[tex]y+9=x[/tex]

Step 2: Subtract 9 from both sides.

[tex]y+9-9=x-9\\y=x-9[/tex]

Answer:

Y=72

Step-by-step explanation:

First we set up the equation which is (20-2) times 4=Y

Then we solve, 20 minus 2 is risk since it is in the parentheses. 20 minus 2 is 18.

After that 18 times 4 is 72

Y=72

Answer:

18

Step-by-step explanation:

20*3=60 so do 6*3 to get your answer

Answer: x = 23, y = 40

Step-by-step explanation:

By the same-side interior angles theorem, y+30 and 110 are supplementary.

We know that the 3x + 1 angle and y + 30 are also congruent, so:

Answer:

x² - 10x + 9 = (x-9)(x-1)

the factored expression would be (x-9)(x-1)

The beginning, middle and end part of the song is 40, 120 and 240 seconds respectively

let

x + 1/6x + 1/2x = 400

(6x+x+3x) / 6 = 400

10/6x = 400

x = 400 ÷ 10/6

x = 400 × 6/ 10

= 2400 / 10

= 240 seconds

Therefore,

End part = x

= 240 seconds

Beginning = 1/6x

= 1/6 × 240

= 40 seconds

Middle = 1/2x

= 1/2 × 240

= 120 seconds

Complete question:

The beginning is one sixth as long as the end. The middle is one half as long as the end. Find the length of each part

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The value of the variable x and y will be 15 and 5√3. Then the correct option is D.

The complete question is attached below.

The connection between the lengths and angles of a triangular shape is the subject of trigonometry.

The right triangle is shown.

Then the value of x will be

x = 10√3 × sin 60°

x = 15

Then the value of y will be

y = 10√3 × cos 60°

y = 5√3

Then the correct option is D.

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The total volume of the pool is 1040 cubic ft. The correct answer is option B.

The complete question is given below:-

The community centre has an L-shaped swimming pool that is 10 feet deep. What is the volume of the pool

1200

1040

640

880

Volume is defined as the space covered by any solid body in the three-dimensional plane.

We know that the total volume of the pool is the sum of the volume of two rectangular prisms.

One is a rectangular prism with dimensions 20ft.×10ft.×4ft.

and the other rectangular prism has dimensions: 6ft.×4ft.×10ft.

Hence, the volume of a first rectangular prism is:

20×10×4=800 cubic ft.                      

The volume of a second rectangular prism is:

6×4×10=240 cubic ft.                    

Hence, the total volume of the pool is:

800+240=1040 cubic ft.                

Therefore the total volume of the pool is 1040 cubic ft. The correct answer is option B.

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Answer:

V = (s^3)/6  (Answer B )

Step-by-step explanation:

If the length of a side of the base is s, then the height of the pyramid is half that, or s/2.

The volume of a pyramid with a square base and base side length S and height H is V = (1/3)(S^2)(H).

In this case, the formula is V = (1/3)(s^2)(s/2), or V = (s^3)/6  (Answer B)

Answer:

2-4i/5

Step-by-step explanation:

[tex]\frac{2i}{i-2} *\frac{i+2}{i+2}\\=\frac{2i(i+2)}{i^2-4}\\= \frac{2i(i+2)}{-1-4}\\ =\frac{2i(i+2)}{-5} \\ = \frac{-2 + 4i}{-5}\\ =( 2 - 4i )/ 5[/tex]

Answer:

[tex]\frac{2i}{i-2}=\frac{2-4i}{5}[/tex]

Step-by-step explanation:

a)  Z-score for Patrisse test grade is 0.7288

b) z-score for Makayla test grade is -0.7441

c) Patrisse did better.

A Z-score is a numerical measurement that describes a value's relationship to the mean of a group of values.

Z-score for Patrisse test grade.

X= 81.4, [tex]\mu[/tex] = 72.8, [tex]\sigma[/tex] = 11.8

Z= x-  [tex]\mu[/tex] /  [tex]\sigma[/tex]

Z= 81.4 - 72.8/ 11.8

Z= 0.7288

Now, z-score for Makayla test grade.

X= 60.6, [tex]\mu[/tex] = 67, [tex]\sigma[/tex] = 8.6

Z= x-  [tex]\mu[/tex] /  [tex]\sigma[/tex]

Z= 60.6 - 67/ 8.6

Z= -0.7441

Hence, Patrisse did better as she had better z- score.

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Answer: He must have atleast 98 points on the next exam in order to get an average of 92 points.

Step-by-step explanation: To calculate average, you need to add all the numbers given, and divide the sum by how many numbers there are. 87 + 89 + 94 + 98 (equals 368), and divide 368 by 4. You will get the average of 92 as its result.

Answer:

hi

Step-by-step explanation:

no

8) 5 + 4 + 2 = 11

Since there are 5 guavas, the correct answer is B. 5/11

9) 3 + 4 = 7

Since there are 4 blue papers, the correct answer is A. 4/7

10) Count all of the numbers and add them. There are 4 twos, 2 fives, and 1 three:

4 + 2 + 1 = 7

Since there are 4 twos, the correct answer is C. 4/7

The values that are part of the solution are x = -5 and x = -4.5

Number lines are lines that are used to represent the solution to inequalities.

From the given number line with he solution x > -4, this shows that all the solutions must be values that are greater than -4.

The values that are part of the solution are x = -5 and x = -4.5

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The question is asking you to understand that a population which is raised by a common ratio over a certain time period follows an exponential pattern. See:

After 1 hour, the population is 3*10

After 2 hours, the population is 3*3*10

After 3 hours, the population is 3*3*3*10

.....

This can be generalised as a function of t, the time in hours:

f(t) = (3^t) * 10

Since the function determines the population at a given time, it is more prudent to replace f(t) with P, the population after time t:

P = (3^t) * 10

Since 20 minutes is equal to (1/3) hours, t can be substituted for (1/3) in order to calculate the population size after 20 minutes:

P = (3^(1/3)) * 10 = 14.4224957031 ≈ 14

Therefore the population after 20 minutes is 14.

Answer:

y = 2x + 8

Explanation:

Equation: y = 2x - 4

Comparing it with slope intercept form "y = mx + b" where 'm' is slope and 'b' is y-intercept. This function has slope: 2 and y intercept of -4

Parallel lines has same slope.

Passes through (-2, 4)

[tex]\sf y - y_1 = m(x - x_1)[/tex]

[tex]\sf y - 4 = 2(x - (-2))[/tex]

[tex]\sf y - 4 = 2(x + 2)[/tex]

[tex]\sf y = 2x + 4 + 4[/tex]

[tex]\sf y = 2x + 8[/tex]

Answer: y = 2x + 8

Step-by-step explanation:

This is a fairly simple problem. I hope this helps!

So, to find a line parallel, it's simple, and it only requires that for the other line to have the same slope and a different y-intercept (or same "m" and different "b" in the equation y = mx + b).

To find a line parallel to a point is slightly harder, but don't worry, I'll teach you how.

To do this, we have to recognize the point. The point given is (-2, 4) where -2 is the x-value and 4 is the y-value. Remember, points always go by (x, y).

So, we set y to 4, and we set x to -2.

When testing out lines that are parallel to a point, you must always be careful that you end up with the same value. Such as 4 = 4 or 8 = 8, etcetera.

We get:

4 = 2 × (-2) + 8

Simplifying, we get:

4 = -4 + 8

Adding -4 to 8, we get 4:

4 = 4

Thus, y = 2x + 8 is parallel to the point (-2, 4)

[tex]f { }^{ - } (x) = \frac{2(x + 4)}{2 |x + 4| {}^{} } = \frac{x + 4}{ |x + 4| } [/tex]

[tex] |x + 4| \: is \: always \: positive[/tex]

[tex]solve \: x + 4 > 0[/tex]

[tex]x > - 4[/tex]

[tex]f(x) \: is \: incresing \: from \\[/tex]

Answer:

*79.40*

Step-by-step explanation:

using sine rule..

a/sinA = b/sinB

42/sin19= x/sin142

x= sin142*42/sin19

= 79.42356..

to the nearest tenth = 79.40.

Answer:

Step-by-step explanation:

a/sinA = b/sinB

(42/sin19) = (x/sin142)

x = (sin142 *42 / sin19)

Round to the nearest tenth -> 79.4