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Zielflug [23.3K]

2 years ago

10

To join a local square dancing routine has to pay $100 sign up fee plus $25 per month write an equation for the cost (y)based on

the number of months (x)

1 answer:

Lemur [1.5K]2 years ago

8 0

Answer:

y = 25x + 100

Step-by-step explanation:

The cost (y) is the sum of the sign-up fee (100), and the monthly cost (25) multiplied by the number of months (x).

y = 100 +25x

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A teenager who is 5 feet tall throws an object into the air. The quadratic function LaTeX: f\left(x\right)=-16x^2+64x+5f ( x ) =

tia_tia [17]

Answer:

At approximately x = 0.08 and x = 3.92.

Step-by-step explanation:

The height of the ball is modeled by the function:

$f(x)=-16x^2+64x+5$

Where f(x) is the height after x seconds.

We want to determine the time(s) when the ball is 10 feet in the air.

Therefore, we will set the function equal to 10 and solve for x:

$10=-16x^2+64x+5$

Subtracting 10 from both sides:

$-16x^2+64x-5=0$

For simplicity, divide both sides by -1:

$16x^2-64x+5=0$

We will use the quadratic formula. In this case a = 16, b = -64, and c = 5. Therefore:

$\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Substitute:

$\displaystyle x=\frac{-(-64)\pm\sqrt{(-64)^2-4(16)(5)}}{2(16)}$

Evaluate:

$\displaystyle x=\frac{64\pm\sqrt{3776}}{32}$

Simplify the square root:

$\sqrt{3776}=\sqrt{64\cdot 59}=8\sqrt{59}$

Therefore:

$\displaystyle x=\frac{64\pm8\sqrt{59}}{32}$

Simplify:

$\displaystyle x=\frac{8\pm\sqrt{59}}{4}$

Approximate:

$\displaystyle x=\frac{8+\sqrt{59}}{4}\approx 3.92\text{ and } x=\frac{8-\sqrt{59}}{4}\approx0.08$

Therefore, the ball will reach a height of 10 feet at approximately x = 0.08 and x = 3.92.

7 0

2 years ago

the area of a trapezoid is 21 inches, one of its bases is 8 inches and its height is 3 inches. What is the length of the last ba

jarptica [38.1K]

Answer:

6 inches

Step-by-step explanation:

A=b1+b2/2*h

Fill in the equation with what we know

21=8+x/2*3

Isolate x

Quick steps: 21/3=7*2=14-8=6

x=6

3 0

2 years ago

GEOMETRY<br><br> *image is attached above*

Keith_Richards [23]

Answer:

(-9.5, -4)

Step-by-step explanation:

Given the ratio a:b (a to b) of two segments formed by a point of partition, and the endpoints of the original segment, we can calculate the point of partition using this formula:

$( \frac{a }{a + b} (x_{2} - x_{1}) + x_{1}, \frac{a}{a + b} (y_{2} - y_{1})+y_{1})$ .

Given two endpoints of the original segment

→ (-10, -8) [(x₁, y₁)] and (-8, 8) [(x₂, y₂)]

Along with the ratio of the two partitioned segments

→ 1 to 3 = 1:3 [a:b]

Formed by the point that partitions the original segment to create the two partitioned ones

→ (x?, y?)

We can apply this formula and understand how it was derived to figure out where the point of partition is.

Here is the substitution:

x₁ = -10

y₁ = -8

x₂ = -8

y₂ = 8

a = 1

b = 3

$( \frac{a }{a + b} (x_{2} - x_{1}) + x_{1}, \frac{a}{a + b} (y_{2} - y_{1})+y_{1})$ . →

$( \frac{(1) }{(1) + (3)} ((-8) - (-10)) + (-10), \frac{(1)}{(1) + (3)} ((8) - (-8))+ (-8))$ →

$( \frac{1}{4} ((-8) - (-10)) + (-10), \frac{1}{4}((8) - (-8)) + (-8))$ →

$( \frac{1}{4} (2) + (-10), \frac{1}{4}(16) + (-8))$ →

$( (\frac{1}{2}) + (-10), (4) + (-8))$ →

$( (-\frac{19}{2}), (-4))$ →

$( -\frac{19}{2}, -4)$ →

* $( -9.5, -4)$ *

Now the reason why this

6 0

3 years ago

1. Find the value for a/b=2 But make each side have the same value.

Vladimir [108]

Step-by-step explanation:

a/b=662

a%chess issues

8=a/b equals exponent

8 0

3 years ago

Estimate the amount of water that fits inside a kitchen sink?

nadezda [96]

About 9 gallons (average)

5 0

3 years ago