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2 years ago

What is the value of x that makes the given equation true?

Mathematics

2 answers:

kvasek [131]2 years ago

5 0

Answer:

x = -4

Step-by-step explanation:

Expand the brackets:

2(x−8)=x+5x

2x - 16 = x + 5x

Simplify:

2x - 16 = 6x

Subtract 2x from both sides of the equation:

2x - 16 - 2x = 6x - 2x

-16 = 4x

Divide both sides by 4:

-16 ÷ 4 = 4x ÷ 4

-4 = x

Hope this helps!

vlabodo [156]2 years ago

4 0

Answer: x=-4

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What conclusions can be made about the amount of money in each account if f represents Molly's account and g represents her brot

Nat2105 [25]

Answer:

(b) is true

Step-by-step explanation:

Given

Molly

$a = 500$ --- starting balance

$m = 10$ --- monthly rate

Her brother

$a = 100$ ---- starting balance

$r = 10\%$ --- annual rate

Required

Determine which option is true

First, we calculate her brother's function.

The function is an exponential function calculated as:

$y = ab^x$

Where $b = 1 + r$

So, we have:

$y = ab^x$

$y = 100 *(1 + 10\%) ^x$

$y = 100 *(1 + 0.10) ^x$

$y = 100 *(1.10) ^x$

Hence:

$g(x) = 100 *(1.10) ^x$

Next, we calculate Molly's function (a linear function)

The monthly function is:

$y = mx + a$

So, we have:

$y = 10x + 500$

Annually, the function will be:

$y = 10x*12 + 500$

$y = 120x + 500$

So, we have:

$f(x) = 120x + 500$

At this point, we have:

$f(x) = 120x + 500$ ---- Molly

$g(x) = 100 *(1.10) ^x$ ---- Her brother

<u>Next, we test each option</u>

(a): Molly's account will have a faster rate of change over [32,40]

We calculated Molly's function to be:

$y = 120x + 500$

The slope of a linear function with the form: $y = mx + b$ is m

By comparison:

$m = 120$

Since Molly's account is a linear function, the rate of change over any interval will always be the same; i.e.

$m = 120$

For his brother:

Rate of change is calculated using:

$m = \frac{g(b) - g(a)}{b - a}$

$m = \frac{g(40) - g(32)}{40 - 32}$

$m = \frac{g(40) - g(32)}{8}$

Calculate g(40) and g(32)

$g(x) = 100 *(1.10) ^x$

$g(40) = 100 * 1.10^{40} =4526$

$g(32) = 100 * 1.10^{32} = 2111$

So, we have:

$m = \frac{4526 - 2111}{8}$

$m = \frac{2415}{8}$

$m = 302$

By comparison: $302 > 120$

Hence, her brother's account has a faster rate over [32,40]

(a) is false

(b): Molly's account will have a slower rate of change over [24,30]

$m = 120$ --- Molly's rate of change

For his brother:

$m = \frac{g(b) - g(a)}{b - a}$

$m = \frac{g(30) - g(24)}{30 - 24}$

$m = \frac{g(30) - g(24)}{6}$

Calculate g(30) and g(24)

$g(x) = 100 *(1.10) ^x$

$g(40) = 100 * 1.10^{30} =1745$

$g(32) = 100 * 1.10^{24} = 985$

So, we have:

$m = \frac{g(30) - g(24)}{6}$

$m = \frac{1745 - 985}{6}$

$m = \frac{760}{6}$

$m = 127$

By comparison: $127 > 120$

Hence, Molly's account has a slower rate over [24,30]

(b) is false

(c): Molly's account will have a slower rate of change over [0,4]

$m = 120$ --- Molly's rate of change

For his brother:

$m = \frac{g(b) - g(a)}{b - a}$

$m = \frac{g(4) - g(0)}{4 - 0}$

$m = \frac{g(4) - g(0)}{4}$

Calculate g(4) and g(0)

$g(x) = 100 *(1.10) ^x$

$g(4) = 100 * 1.10^4 =146$

$g(0) = 100 * 1.10^{0} = 100$

So, we have:

$m = \frac{g(4) - g(0)}{4}$

$m = \frac{146 - 100}{4}$

$m = \frac{46}{4}$

$m = 11.5$

By comparison: $120>11.5$

Hence, Molly's account has a faster rate over [0,4]

(c) is false

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The Answer of the question is "B" or 1,600

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3 years ago

Do you know What is h(t)=-10t+6

DochEvi [55]

-10t+6=0

-10t=-6

Divide both side by -10

t=3/5

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3 years ago

Which function would be produced by a horizontal stretch of the of y=

sladkih [1.3K]

Answer: the answer to you question is c

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3 years ago

There are 205 coins in a jar all of which are either nickles or quarters . The vaule of the coin in the jar is $31.85. if both o

Gnesinka [82]

Answer: There are 97 nickels and 108 quarters.

Step-by-step explanation:

Let x = Number of nickels, y = Number of quarters.

As per given,

x+y = 205 ...(i)

0.05x+0.25y = 31.85 ... (ii) [1 nickel = $0.05, 1 quarter = $ 0.25]

Multiply (ii) by 20, we get

x+5y=637 ...(iii)

Eliminate (i) from (iii)

4y = 432

⇒ y = 108 [Divide both sides by 4]

Put value of y in (i), we get

$108+x=205\Rightarrow\ x= 97$

Hence, there are 97 nickels and 108 quarters.

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3 years ago