Ask question

Ask question

All categories

2 years ago

7

the sum of ava’s and grace’s ages is 35. Ava is one year less than three time Grace’s age. How old is Ava, x and Grace, y expres

s your answer as an ordered pair

1 answer:

pantera1 [17]2 years ago

6 0

Answer:

Ava is 26 and Grace age is 9

Step-by-step explanation:

x=ava's age

y=grace's age

3y-1=x

x+y=35

Substitute 3y-1 to x+y=35 for the value of x to find grace age

3y-1+y=35

4y-1=35

+1 +1

4y=36

y=9 now substitute 9, the y value in 3y-1=x to find ava's age

3(9)-1=x

x=26

to verify; 26+9=35

true 35=35

You might be interested in

State a true conclusion.

tia_tia [17]

Conclusion: you have accepted the hypothesis

<em>this is because if you accept the hypothesis, then you also accept the conclusion so in order to accept the conclusion you must first accept the hypothesis</em>

4 0

2 years ago

Tara’s jewelry box contains two gold bracelets and two silver bracelets. Tara randomly choose two bracelets. What is the probabi

yan [13]

Answer: well its 25% i think because if you take them each one all chances are 25% bacause bur it would be 50%/50% because to are the same but the chances of pulling the not that sames ones would also be a 50/50

I REALLY DONT KNOW IF IM RIGHT SO IM SORRY IF NOT IM DUMB

7 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,

$f(x)=9000x+286,000$ , where, f(x) represents the value of the house 2, in dollars, after x years.

Therefore, the function $f(x)=9000x+286,000$ represents the value of house 2 after x years.

Part C:

Since values in exponential function increases faster than linear function, so the value of house 1 will be greater than value of house 2.

Let us find the value of house 1 and house 2 by substituting x=25 in our both functions.

$f(25)=286,000(1.03)^{25}$

$f(25)=286,000*2.0937779296542148$

$f(25)=598820.48788$

We can see that value of house 1 after 25 years will be approx $598,820.48.

$f(25)=9000*25+286,000$

$f(25)=225,000+286,000$

$f(25)=511,000$

We can see that value of house 2 after 25 years will be approx $511,000.

Since $511,000 is less than $598820.48, therefore, value of house 1 is greater than value of house 2.

6 0

3 years ago

Read 2 more answers

If the measure of two angles in a triangle are 60 and 100 degrees, what is the measure of the third angle? a. 20 degrees) b. 50

bonufazy [111]

Answer:

A. 20 degrees

Step-by-step explanation:

<u>All triangles have 180 degrees in total !</u>

using that info,

100+60= 160

180-160 = 20

4 0

2 years ago

153 is 0.9% of what number? Tell which equivalent ratios you used to find the solution.

chubhunter [2.5K]

153 = 0.009n

You did not provide a list of options to select from.

To find n, the ratio leading to the answer is 153/(0.009).

8 0

3 years ago