A car dealership is offering $1,500 cash back on the

Drag each tile to the correct location on the table. Each tile can be used more than once, but not all tiles will be used. Lewis

son4ous [18]

The fill up for the 3rd step is y - 250 = 340x.

The fill up of the 5th step is $x = \frac{y-250}{340}$

The fill up of the 6th step is $\frac{8750-250}{340} = 25 = x, \frac{8750-250}{340}= 34 = x$

The justification for the 2nd step is subtraction PE.
The justification for the 4th step is division PE.

<h3>What is the simplification about?</h3>

Note that:

y-250 = 250 + 340 x - 250

y = 250 + 340x.

Make x the subject of the formula:

y - 250 = 340x.

then y-250/340 = x

Then $x = \frac{y-250}{340}$

The justification for the second step is subtraction property of equality because it undergoes subtraction and the collection of like terms and then subtracting them from one another as shown below:

y-250 = 250 + 340 x - 250

y= 250 + 340x - 250 + 250

Note that (-250 + 250) = 0

y = 250 + 340x.

Lastly, The fill up of the 6th step is substitution of the amount of money saved and then simplifying it.

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8 0

2 years ago

7 ^ 8 times 7 ^ 3 times 7 ^ 4 / 7 ^ 9 times 7 ^ 5

Alex777 [14]

Answer:

7^8 =5764801 * 7^3 =343 * 7^4 =2401 ÷ 7^9 = 40353607 * 7^5 =16807

5764801 *343 *2401 ÷ 40353607 *16807

=4747561509943 ÷ 678223072849 = 7

4 0

3 years ago

From place value relationships the 4s in 344 is?

BabaBlast [244]

From place value relationships the 4s in 344 is 86
__4s___ __344__
4 4
<em /><em><u /></em><em><u /></em><u></u>S = 86

ANS : S = 86

7 0

3 years ago

Nick decided to take 2/5 of the money in his bank account and donate it to a local charity. If nick donated $70 to a local chari

S_A_V [24]

Answer:

<u> The total amount = $175</u>

Step-by-step explanation:

Let the total amount in his bank account = x

Nick decided to take 2/5 of the money in his bank account and donate it to a local charity

So, he donates with $\frac{2}{5} x$

If nick donated $70 to a local charity

so, $\frac{2}{5} x = 70$

solve for x

∴ x = 5*70/2 = 350/2 = $175

<u>So, The total amount = $175</u>

3 0

3 years ago

The exponential function f(x) = 3(5)x grows by a factor of 25 between x = 1 and x = 3. What factor does it grow by between x = 5

notsponge [240]

<h2> Question # 1</h2>

Answer:

25 is the factor which grows by between x = 5 and x = 7.

Step-by-step explanation:

Considering the exponential function

$f\left(x\right)\:=\:3\left(5\right)^x$

The growth factor between $x=1$ and $x=3$ is given by:

$\left[3\left(5\right)^3\right]\div \left[3\left(5\right)^1\right]$

$\mathrm{Calculate\:within\:parentheses}\:\left[3\left(5\right)^3\right]\::\quad 375$

$\mathrm{Calculate\:within\:parentheses}\:\left[3\left(5\right)^1\right]\::\quad 15$

So,

= $375\div \:15$

= $25$

Similarly, growth factor between $x=5$ and $x=7$ is given by:

$\left[3\left(5\right)^7\right]\div \left[3\left(5\right)^5\right]$

= $\frac{3\cdot \:5^7}{3\cdot \:5^5}$

$\mathrm{Divide\:the\:numbers:}\:\frac{3}{3}=1$

= $\frac{5^7}{5^5}$

$\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}$

$\frac{5^7}{5^5}=5^{7-5}$

= $5^{7-5}$

= $5^2$

= $25$

Therefore, 25 is the factor which grows by between x = 5 and x = 7.

<h2> Question # 2</h2>

Answer:

The population be in 24 years will be 27000.

Also, the population growth modeled by an exponential function as $y=A\cdot \left(b\right)^t$ is an exponential function.

The graph for $y=A\cdot \left(b\right)^t$ is also shown in attached figure.

Step-by-step explanation:

If a city that currently has a population of 1000 triples in size every 8 years.
what will the population be in 24 years?
Is the population growth modeled by a linear function or an exponential function?

As the city that currently has a population of 1000 triples in size every 8 years.

So, for this case

$y=A\cdot \left(b\right)^t$

where

$A$ = Initial population amount

$b$ = growth rate

$t$ = time

Substituting the values in the function

$y=A\cdot \left(b\right)^t$

$y=1000\cdot \:\:3^{\frac{1}{8}t}$

So, the population be in 24 years

$y=1000\cdot \:\:3^{\frac{1}{8}24}$

As

$3^{\frac{1}{8}\cdot \:24}=3^3$

So

$\:y=3^3\cdot 1000$

$y=1000\cdot \:\:27$

$y=27000$

Therefore, the population be in 24 years will be 27000.

Also, the population growth modeled by an exponential function as $y=A\cdot \left(b\right)^t$ is an exponential function.

<h2 /><h2> Question # 3</h2>

Answer:

the graph of the function will translate horizontally 3/5 units right.

Step-by-step explanation:

We have to find the effect on the graph of the function $f(x)=2x$ when it is replaced by f(x- 3/5).

We already have an idea that rule for horizontal translation:

Given a function $f(x)$ , and a constant c > 0, the function $g(x) = f(x - a)$ represents a horizontal shift c units to the right from f(x). The function $h(x) = f(x + a)$ represents a horizontal shift c units to the left.

As 3/5 > 0, so the graph of the function will translate horizontally 3/5 units right.

Therefore, the graph of the function will translate horizontally 3/5 units right.

Keywords: exponential function, translation function, growth factor

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6 0

3 years ago