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Nata [24]
2 years ago
14

Dakota Drained his 2,268 ft3 pool to clean it. The pool is a rectangle with an area that can be expressed as 2x4 + 10x2 and a de

pth that can be expressed as x2. If a gallon of water has a volume of 1 60 x2, write a function which represents the gallons of water it takes to fill the pool.
Mathematics
1 answer:
Tamiku [17]2 years ago
7 0
If you sole the equation 2x4+10x2=28+160x2=376
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Laurie has $46,000 invested in stocks. The amount invested in stocks is $8,000 less than three times the amount invested in bond
svet-max [94.6K]

Amount invested in stocks = 46,000

Let "x" be the amount invested in bonds

The amount invested in stock is also = 3x - 8,000

We equate the two amounts above (Since both are related to stock investments), we get,

3x-8000 = 46000

3x = 54000

x =54000/3

x =18000

Amount that Laurie has invested in bonds = $18,000



7 0
2 years ago
Sea level is considered to be 0 feet. A probe released at sea level dropped at a constant rate for 3.25 minutes, reaching an ele
mash [69]
Thank you for posting your question here at brainly. The probe's elevation relative to sea level after the first minute, the probe dropped 11 feet per minute, therefore, it dropped 11 feet in the first minute. I hope the answer helps you. 
8 0
2 years ago
A football player kicks a football downfield. The height of the football increases until it reaches a maximum height of 15 yards
tino4ka555 [31]

Answer:

kick 1 has travelled 15 + 15 = 30 yards before hitting the ground

so kick 2 travels 25 + 25 = 50 yards before hitting the ground

first kick reached 8 yards and 2nd kick reached 20 yards  

Step-by-step explanation:

1st kick travelled 15 yards to reach maximum height of 8 yards

so, it has travelled 15 + 15 = 30 yards before hitting the ground

2nd kick is given by the equation

y (x) = -0.032x(x - 50)

y = 1.6 x - 0.032x^2

we know that maximum height occurs is given as

x = -\frac{b}{2a}

y = - \frac{1.6}{2( - 0.032)} = 25

and maximum height is

y = 1.6(25) - 0.032 (25)^2

y = 20

so kick 2 travels 25 + 25 = 50 yards before hitting the ground

first kick reached 8 yards and 2nd kick reached 20 yards  

6 0
2 years ago
The image shows a geometric representation of the function f(x) = x^2 + 2x + 3 written in standard form. What is this function w
AlekseyPX

Answer:

f(x) = (x + 1)² + 2 in vertex form ⇒ 3rd answer

Step-by-step explanation:

* Lets revise how to find the vertex form the standard form

- Standard form ⇒ x² + bx + c, where a , b , c are constant

- Vertex form ⇒(x - h)² + k, where h , k are constant and  (h , k) is the

  vertex point (minimum or maximum)  of the function

- At first we must find h and k

- By equating the two forms we can find the value of h and k

* Lets solve the problem

∵ f(x) = x² + 2x + 3 ⇒ standard form

∵ f(x) = (x - h)² + k ⇒ vertex form

- Put them equal each other

∴ x² + 2x + 3 = (x - h)² + k ⇒ open the bracket power 2

∴ x² + 2x + 3 = x² - 2hx + h² + k

- Now compare the like terms in both sides

∵ 2x = -2hx ⇒ cancel x from both sides

∴ 2 = -2h ⇒ divide both sides by -2

∴ -1 = h

∴ The value of h is -1

∵ 3 = h² + k

- Substitute the value of h

∴ 3 = (-1)² + k

∴ 3 = 1 + k ⇒ subtract 1 from both sides

∴ 2 = k

∴ The value of k = 2

- Lets substitute the value of h and k in the vertex form

∴ f(x) = (x - -1)² + 2

∴ f(x) = (x + 1)² + 2

* f(x) = (x + 1)² + 2 in vertex form

5 0
2 years ago
Bobby's investment of $225,000 loses value at a rate of 3% per year. Use an exponential function to find the value of the invest
AleksAgata [21]

We have been given that Bobby's investment of $225,000 loses value at a rate of 3% per year. We are asked to find the value of the investment after 10 years.

We will us exponential decay function to solve our given problem.

We know that an exponential function is in form y=a\cdot (1-r)^x, where,

y = Final amount,

a = Initial amount,

r = Decay rate in decimal form,

x = Time.

Let us convert 3% into decimal.

3\%=\frac{3}{100}=0.03

Upon substituting a=\$225,000, r=0.03 and x=10, we will get:

y=\$225,000(1-0.03)^{10}

y=\$225,000(0.97)^{10}

y=\$225,000(0.7374241268949283)

y=\$165,920.4285513588675

Upon rounding to nearest dollar, we will get;

y\approx \$165,920

Therefore, the value of the investment after 10 years would be \$165,920.

5 0
2 years ago
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