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2 years ago

2. Solve 9 = 1 + 8x – 8. A. x = 2 B. x = 10

Mathematics

2 answers:

My name is Ann [436]2 years ago

8 0

A. X=2
Combine like terms 9=-7+8x
Add 7 to both sides 16=8x
Divide 8 from both sides x=2

Gnesinka [82]2 years ago

6 0

9 = -7 + 8x
add 7
16 = 8x
x = 2

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Which number satisfies the inequality 9h + 15 > 55?

zalisa [80]

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9h + 15 > 55

Subtract 15 from each side: 9h > 40

Divide each side by 9 : <em> h > 40/9</em>

Any number greater than (4 and 4/9) satisfies the inequality.

5 0

3 years ago

Read 2 more answers

HELP!! 50 POINTS!!!

aalyn [17]

Step-by-step explanation:

We have been given a table, which represents the projected value of two different houses for three years.

Part A:

$\text{Increase in value of house 1 after one year}=294,580-286,000$

$\text{Increase in value of house 1 after one year}=8580$

$\text{Increase in value of house 1 after two years}=303,417.40-294,580$

$\text{Increase in value of house 1 after two years}=8837.4$

We can see from our given table that the value of house 1 is not increasing at a constant rate, while a linear function has a constant rate of change, therefore, an exponential function can be used to describe the value of the house 1 after a fixed number of years.

$\text{Increase in value of house 2 after one year}=295,000-286,000$

$\text{Increase in value of house 2 after one year}=9,000$

$\text{Increase in value of house 2 after two years}=304,000-295,000$

$\text{Increase in value of house 2 after two years}=9,000$

We can see from our given table that the value of house 2 is increasing at a constant rat that is $9,000 per year. Since a linear function has a constant rate of change, therefore, a linear function can be used to describe the value of the house 2 after a fixed number of years.

Part B:

Let x be the number of years after Dominique bought the house 1.

Since value of house 1 is increasing exponentially, so let us find increase percent of value of house 1.

$\text{Increase }\%=\frac{\text{Final value-Initial value}}{\text{Initial value}}\times 100$

$\text{Increase }\%=\frac{294,580-286,000}{286,000}\times 100$

$\text{Increase }\%=\frac{8580}{286,000}\times 100$

$\text{Increase }\%=0.03\times 100$

$\text{Increase }\%=3$

$\text{Increase }\%=\frac{303,417.40-294,580}{294,580}\times 100$

$\text{Increase }\%=\frac{8837.4}{294,580}\times 100$

$\text{Increase }\%=0.03\times 100$

$\text{Increase }\%=3$

Therefore, the growth rate of house 1's value is 3%.

Since we know that an exponential function is in form: $y=a*b^x$ , where,

a = Initial value,

b = For growth b is in form (1+r), where, r is rate in decimal form.

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

Upon substituting our values in exponential function form we will get,

$f(x)=286,000(1+0.03)^x$ , where, f(x) represents the value of the house 1, in dollars, after x years.

Therefore, the function $f(x)=286,000(1.03)^x$ represents the value of house 1 after x years.

Let x be the number of years after Dominique bought the house 2.

We can see that when Dominique bought house 2 it has a value of $286,000. This means that at x equals 0 value of house will be $286,000 and it will be our y-intercept.

Since value of house 2 is increasing 9000 per year, therefore, slope of our line be 9000.

Upon substituting these values in slope-intercept form of equation $(y=mx+b)$ we will get,