Find the equation of the linear function represented by the table below in slope intercept form

87 less than the quotient of an unknown number and 43 is -75

Dafna11 [192]

Hm...maybe searching it up on google can help you...

3 0

3 years ago

Triangles Q R S and X Y Z are shown. Angles Q S R and X Z Y are right angles. Angles Q R S and X Y Z are congruent. The length o

kumpel [21]

Answer:

Three-fourths

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

∠QSR≅∠XZY ---> given problem

∠QRS≅∠XYZ ---> given problem

so

△QRS ~ △XYZ ----> by AA Similarity theorem

Remember that, if two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

That means

$\frac{QS}{XZ}=\frac{QR}{XY}=\frac{RS}{YZ}$

∠Q≅∠X

∠R≅∠Y

∠S≅∠Z

In the right triangle XYZ

Find the tangent of angle X

$tan(X)=\frac{YZ}{XZ}$ ---> opposite side angle X divided by adjacent side angle X

substitute the given values

$tan(X)=\frac{9}{12}$

Simplify

$tan(X)=\frac{3}{4}$

Remember that

∠Q≅∠X

so

$tan(Q)=tan(X)$

therefore

$tan(Q)=\frac{3}{4}$ ---->Three-fourths

7 0

2 years ago

Read 2 more answers

What conclusion can you draw about angles of elevation for parasailing boats traveling at the same speed?

melamori03 [73]

Question:

A boat is travelling at 30 mph has a 400 ft. tow line results in the height of the rider in the parasail above the water level of 300 ft.

a) Draw a labelled diagram of the situation

b) Determine the angle of elevation of the parasail rider

c) Parasailing boats traveling at the same speed will have the same angle of elevation

Answer:

a) Please find the attached drawing of the parasail boat created with MS Visio

b) The angle of elevation of the parasail rider from the boat is approximately 48.6°

Step-by-step explanation:

a) Please find the labelled diagram of the parasailing boat created with MS Visio

b) sing trigonometric ratios, we have;

$sin(\theta) = \dfrac{Opposite \ leg \ length}{Hypotenuse \ length}$

The opposite leg = The height of the parasail rider above water = 300 ft.

The hypotenuse = the length of the tow line = 400 ft.

θ = The angle of elevation of the parasail rider

$\therefore sin(\theta) = \dfrac{300 \, ft.}{400 \, ft.} = 0.75$

θ = Arctan(0.75) ≈ 48.6°

The angle of elevation above the horizontal of the parasail rider from the boat, θ ≈ 48.6°

c) From the construction of the drawing and the derivation of the angle of elevation given only the length of the tow line and the height given to the parasail rider by the speed of the both,

Parasailing boats traveling at the same speed, having the same length of tow line, will have the same angle of elevation, provided other factors that have an effect on the angle of elevation are the same

6 0

3 years ago

Part A: Marguerite rented a truck at $125 for 2 days. If she rents the same truck for 5 days, she has to pay a total rent of $27

SOVA2 [1]

Part A: To get an equation into standard form to represent the total amount rented (y) that Marguerite has to pay for renting the truck for x amount of days, we use the formula for the equation of a straight line.

Remember that the equation of a straight line passing through points is ( x_{1} , y_{1} ) and the points ( x_{2} , y_{2} ) is given by
y - y_{1} / x - x_{1} = y - y_{2} / x - x_{2}

Knowing that Marguerite rented a truck at $125 for 2 days, we know if she rents the exact same truck for 5 days, she has to pay a total of $275 for the rent.

This means that the line modeling this situation crosses points at (2, 125) and (5, 275).

The equation modeling the total rent (y) that Marguerite has to pay for renting the truck for x days is given by

y - 125 / x - 2 = 275 - 125 / 5 - 2 = 150 / 3 = 50

But if you are writing the equation in standard form it would be 

50x - y = -25

Part B:
When writing the function using function notation it means you are making y the subject of the formula and then replacing the y with f(x).

If you remember that from part A, we have that the equation for the total rent which is y that Marguerite has to pay for renting the truck for x amount of days is given by
y = 50x + 25.

Writing the equation using the function notation would give us this
f(x) = 50x + 25

Part C:
To graph the function, we name the x-axis the number of days and name the y-axis total rent. The x-axis is numbered using the intervals of 1 while the y-axis is numbered using the intervals of 50.
The points of (2,125) and of (5,275) are marked on the coordinate axis and a straight line is drawn to pass through these two points.

6 0

3 years ago

Is (4,9) a solution to this system of inequalities? y < x + 3 and y > 2x + 1

Setler79 [48]

No

Put (4,9) in equation 1

Mark brainliest please

7 0

3 years ago