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3 years ago

5

Mrs. Mack teaches three art classes, and there are 30 students in each dass. She has a supply

1 answer:

laila [671]3 years ago

6 0

Answer: 3/5

Step-by-step explanation:

1. Multiply 30 by 3 (90)

2. 90 becomes the numerator and 150 becomes the denominator

3. Divide the numerator (90) and the denominator (150) by the greatest common factor (30), to simplify the fraction

4. You should come to the answer 3/5

Hope this helps.

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Paige invested 1200 at an interest rate of 5.75% compounded quarterly. Determine the value of her investments in 7 years.

iragen [17]

Use the formula A=p(1+r)^n
where
A= value of investment
r= rate
n= time period
p= amount invested
in this question
r= 5.75% but compounded quarterly means divide this by 4
r= 23/1600
n=7*4
n=28
p= $1200
A=1200(1+23/1600)^28

A= $1789.54

Therefore the value of her investment in 7 years is $1789.54

4 0

3 years ago

Find the exact value of csc theta if tan theta = sqrt3 and the terminal side of theta is in Quadrant III.

WARRIOR [948]

Answer:

3rd option

Step-by-step explanation:

Using the identities

cot x = $\frac{1}{tanx}$

csc² x = 1 + cot² x

Given

tanθ = $\sqrt{3}$ , then cotθ = $\frac{1}{\sqrt{3} }$

csc²θ = 1 + ( $\frac{1}{\sqrt{3} }$ )² = 1 + $\frac{1}{3}$ = $\frac{4}{3}$

cscθ = ± $\sqrt{\frac{4}{3} }$ = ± $\frac{2}{\sqrt{3} }$

Since θ is in 3rd quadrant, then cscθ < 0

cscθ = - $\frac{2}{\sqrt{3} }$ × $\frac{\sqrt{3} }{\sqrt{3} }$ = - $\frac{2\sqrt{3} }{3}$

8 0

3 years ago

Solve the system of equations using substitution. y = 2x – 10 y = 4x – 8

Dmitry_Shevchenko [17]

If this paper dosent help u solve it on Your own i can walk u through it

3 0

3 years ago

Read 2 more answers

A ladder is leaning against a wall. The top of the ladder is 9 feet (ft) above the ground. If the bottom of the ladder is moved

Komok [63]

Step 1

<u>First situation</u>

when a ladder is leaning against a wall

Let

x-------> the distance of the bottom of the ladder from the wall

L-------> the length of the ladder

<u>Find the length of the ladder</u>

Applying the Pythagorean Theorem

$L^{2} =x^{2}+ 9^{2}$ ------> equation $1$

Step 2

<u>Second situation</u>

when the ladder will be lying flat on the ground

<u>Find the length of the ladder</u>

In this situation the length of the ladder is equal to

$L=x+3$

square both sides

$L^{2}=(x+3)^{2}$ ------> equation $2$

Step 3

equate equation $1$ and equation $2$

$x^{2}+ 9^{2}=(x+3)^{2}\\x^{2}+81=x^{2} +6x+9\\ 6x=81-9\\6x=72\\x=12\ ft$

therefore

<u>the answer is</u>

the length of the ladder is $12\ ft$

see the attached figure to better understand the problem

5 0

3 years ago

Graph the following lines and write the equation in slope-intercept form. With y intercept of −3 and an x intercept of −4.5.

makvit [3.9K]

Answer:

$y=-\frac{2}{3}x-3$

Step-by-step explanation:

To write the equation of a line we need 2 points. We know:

If the y-intercept of the line is -3 then the point is (0,-3).

If the x-intercept of the line is -4.5 then the point is (-4.5,0).

Using these two point, we will find the slope and then substitute it into the point slope form $y-y_1=m(x-x_1)$ with a point.

Slope: $m=\frac{0--3}{-4.5-0}=\frac{0+3}{-4.5}=\frac{3}{-4.5}=-0.6667$

This decimal is -2/3. We will now substitute -2/3 and (0,-3) into the point slope form.

$y--3=-\frac{2}{3}(x-0)\\y+3=-\frac{2}{3}(x)\\y+3=-\frac{2}{3}x\\y=-\frac{2}{3}x-3$

6 0

3 years ago