The gutierrez family and the kim family both have pools. the gutierrez family is filling their
pool, which is modeled by the equation y = x+1. the kim family is draining their pool,
which is modeled by the equation y = -1.25x + 5. in both equations, x represents the time in
hours and y represents the depth of the water in the pool in feet. these two situations can be
described by the following system of equations:
y
22+1
= -1.25x + 5
a) what is the rate of change for the kim family's pool, and what does it represent in the
context of the problem?
b) looking at the equation for the gutierrez family's pool, what does the 1 represent in the
context of the problem?

keeping in mind that twin sides stemming from a common vertex make twin angles at the "base", Check the picture below.

Answer:

second term: 10

third term: 50

Step-by-step explanation:

The equation for any geometric sequence is [tex]a_{n} = a_{1} *r^{n-1}[/tex] where n is the term number you want to find, [tex]a_{1}[/tex] is the first term in the sequence, and [tex]r[/tex] is the common ratio. The equation for this sequence specifically uses 5 as its common ratio, so the equation is [tex]a_{n} =2*5^{n-1}[/tex]

[tex]a_{1} = 2*5^{1-1}=2*5^{0} =2*1=2[/tex]

[tex]a_{2} = 2*5^{2-1}=2*5^{1} =2*5=10[/tex]

[tex]a_{3} = 2*5^{3-1}=2*5^{2} =2*25=50[/tex]

[tex]a_{4} = 2*5^{4-1}=2*5^{3} =2*125=250[/tex]

Answer:

x = 3

Step-by-step explanation:

if you need an explanation let me know

Answer:

x = 3

Step-by-step explanation:

Given:

[tex] \implies \rm 3 {}^{x} + {3}^{x} = 54[/tex]

To Find:

Solution:

We could re-write 3^x+3^x as:

[tex] \implies \: 2(3 {}^{x} ) = 54[/tex]

Divide both sides by 2

[tex] \implies \cfrac{2(3 {}^{x}) }{2} = \cfrac{54}{2} [/tex]

[tex] \implies \: 3 {}^{x} = 27[/tex]

Take logarithm on both sides

[tex] \implies \: \log(3 {}^{x} ) = \log(27)[/tex]

[tex] \implies \: x \times \log(3) = \rm \: log \: (27)[/tex]

[tex] \implies \: x = \cfrac{ \log(27)}{ \log \:(3)} [/tex]

[tex] \implies \boxed{x = 3}[/tex]

Hence, x = 3 .

Answer:

b. mode = 88, median = 77

Step-by-step explanation:

First, arrange all the numbers least to greatest.

53, 71, 75, 79, 88, 88

The mode is the number that occurs the most.

mode = 88

The median is the middle number. Since there is an even number of numbers, look at the two middle numbers 75 and 79. Add them together and divide by two (finding the average or mean of the numbers).

75 + 79 = 154

154/2 = 77

median = 77

Answer:

See below

Step-by-step explanation:

Think about what happens when you rotate around a circle [tex]-\frac{3\pi}{4}[/tex] radians. This means that you are going clockwise [tex]-\frac{3\pi}{4}[/tex] radians.

Likewise, if you went [tex]\frac{5\pi}{4}[/tex] radians counterclockwise, you'd end up in the same place, so the cosine values must be the same.

The circumference of the circular playing field.

[tex]\huge\boxed{Formula:C= 2\pi{r}}[/tex]

We'll have to multiply 2, π and radius.

Substitute the values according to the formula.

[tex]C= 2× \pi ×7.5[/tex]

[tex]C= 47.12389 [/tex]

[tex]\large\boxed{C= 47.12 \: m}[/tex]

Therefore, the circumference of the circular playing field is 47.12 feets.

Answer:

-4z

Step-by-step explanation:

Hi student! Let me help you out.

_____________________

Note that, -3z and -z are like terms. This means we can combine them right off the bat, which gives us [tex]\mathrm{-4z}[/tex].

[tex]\mathrm{-3z-z=-4z}[/tex]. -4z is our final answer.

Hope that this helped you! have a good day ahead.

Best Wishes!

[tex]\star\bigstar\underline{\underline{\overline{\overline{\textsf{Reach far. AIm high. Dream big.}}}}}\bigstar\star[/tex]

◈◈-Greetings!-◆◆

___________________

Answer:

-4z

Step-by-step explanation:

-3z-z

On combining like terms,

= -4z

Answer:

how many hours a week the employees are working?

Step-by-step explanation:

I could be wrong but that's my fault if it's wrong sorry

Answer:

hope you can understand

The initial amount of the water is 15 gallons

These are functions that has a leading degree of 1. Given the equation that represents the amount of water remaining after x minutes;

y - 12 = -3(x- 1)

y -12 = -3x + 3

y = -3x +3 + 12

y = -3x + 15

In order to determine the initial amount of water, we will substitute x =0 into the function

y = -3(0) + 15

y = 15

Hence the initial amount of the water is 15 gallons

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Answer:

15

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

v=2

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

x^32

Step-by-step explanation:

A fraction bar is a division symbol. When you are dividing, you can subtract the exponents.

x^56 / x^24

= x ^ (56-24)

= x^32

Answer:

x^32

Step-by-step explanation:

a^m/a^n = a^(m-n)

so, x^56/x^24 = x^(56-24) = x^32

Answer:

times and divide

they are both diffrent equations

Answer:

B. 4^8

Step-by-step explanation:

The indices of the base 4 can be added while multiplying i.e. 3+5=8 but the base remains the same.

Answer:

B

Step-by-step explanation:

Because in powers we just add so it will be 4^3+5

=4^8

Answer:

1.1x= 132

Step-by-step explanation:

Answer:

I think the answer would be 28

Answer:

Factor and set each factor equal to zero. Y=x2+5x−8

Step-by-step explanation:

The answer to each question in the image is given below:

An equivalent equation can be defined as an equation that has the same meaning and also has the same answer with another equation or with an equation it is said to be equivalent with.

The above equation are equivalent to each other meaning they can be used to derive each other.

In conclusion, the list above is the right pairs of equivalent equations.

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Answer:

2 miles

Step-by-step explanation:

Peter takes 7 minutes and 30 seconds per mile.

7 times 2 is 14 minutes.

30 seconds times 2 is 1 minute.

If you add these 2 values together you get 15 minutes.

So we need to times the miles by 2 to get 2 miles.

I hope this helps, have a lovely day.

Answer:

period pi and amplitude 5

Answer:

bacteria and fungi

Step-by-step explanation:

Single organism makes an exact copy of itself

Bacteria, some plants and fungi, few animals (sponges)

Offspring are identical to parent

Using a geometric sequence, it is found that the approximate value of the car at the end of the 10th year will be given by:

A. $6,974.

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

In this problem, the first term and the common ratio are given, respectively, by:

[tex]a_1 = 18000, q = \frac{16200}{18000} = 0.9[/tex]

Hence the equation is:

[tex]a_n = 18000(0.9)^{n-1}[/tex]

At the end of the 10th year, the value will be of:

[tex]a_{10} = 18000(0.9)^{10-1} = 6974[/tex]

Hence option A is correct.

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Answer:

1.65 N

Step-by-step explanation:

Step 1: convert cm^2 to m^2

1 cm^2 = 0.0001 m^2

750 cm^2 = 0.075 m^2

Step 2: multiply pressure by area

F = P*A = 22 N/m^2 * 0.075 m^2 = 1.65 N

Answer:

0.05

explanation

value means total value

so it's 5*0.01

=0.05

Answer:

[tex] \frac{x}{12} = - 4[/tex]

[tex] \frac{x}{12} = \frac { - 4}{1} [/tex]

[tex]x \times 1 = 12 \times - 4[/tex]

[tex]x = - 48[/tex]

value of x is -48

Answer:

x=-48.

Step-by-step explanation:

To find x we should multiply both sides, by 12:

[tex]\sf \cfrac{x}{12}\times12=\-4\times12[/tex]

                                       ↪

The 12s cancel on the left:

[tex]x=-4\times12[/tex]

After multiplying we obtain [tex]\sf x=-48[/tex]. Which is our answer.

Hope that this helped you! Have a good day ahead.

Best Wishes!

[tex]\star\bigstar\underline{\underline{\overline{\overline{\text{Reach far. Aim high. Dream big.}}}}}\bigstar\star[/tex]

◆◆-Greetings!-◈◈

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