Juan is three times as old as Gabe and Gabe is six years older than Catherine. If the sum of their ages is 149, how old is each person? Define a variable, write an equation, solve the equation, and answer in a complete sentence. (Remember to clearly show your work on your work page.)

Answer:

The steps below show how I transformed the equation in the question into standard form, where the slope and y-intercept is clearest. The slope is -1/2 and the y-intercept is 32.

[tex]4x + 8y = 512 \\ x + 2y = 64 \\ 2y = - x + 64 \\ y = - \frac{1}{2} x + 32[/tex]

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Explanation:

Recall that quadratic form is ax^2+bx+c.

So we need an x^2 term followed by an x term, then a constant at the end.

It may not look it, but the given equation is nearly in quadratic form.

Rewrite 9^(2x) as (9^x)^2

We get this equivalent equation (9^x)^2 - 2*(9^x) - 3 = 0

From here, let's make w = 9^x. Replace every copy of '9^x' with 'w' and we end up with this new simpler equation: w^2 - 2w - 3 = 0

From here we can use the quadratic formula or factor. I'll factor.

w^2 - 2w - 3 = 0

(w - 3)(w + 1) = 0

w-3 = 0 or w+1 = 0

w = 3 or w = -1

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Now we use these values of w to find x

If w = 3, then,

w = 9^x

3 = 9^x

log(3) = log(9^x)

log(3) = x*log(9)

x = log(3)/log(9)

x = log(3)/log(3^2)

x = log(3)/(2*log(3))

x = 1/2

At the last step, we have the log(3) terms cancel.

Repeat for w = -1

w = 9^x

-1 = 9^x

log(-1) = log(9^x)

We run into a problem. The log of any negative number is not a real number output. In other words, 9^x is never negative. Raising any positive number to a real number output leads the result to be positive. Take a look at the graph of y = 9^x to confirm this.

In short, w = -1 is extraneous so it doesn't lead to any x value solution.

So only w = 3 is useful.

Ultimately, the only solution is x = 1/2.

Step-by-step explanation:

FV=$1000×(1+0.1)5

try solving with this it might help you and if it did please make me brainliest plzzzzxx

Answer:

11:45 PM

Step-by-step explanation:

please mark brainliest :D

Answer:

$73.77

I'm not sure if I understood the question correctly

explain it in the comments

Step-by-step explanation:

If what I think the question is asking is correct, theres a 70% sale on the full price which is $245.89

70% of 245.89 is 172.123, so now you subtract the sale(172.123) from the original price(245.89)

245.89 - 172.123 = 73.767

If the question was asking a different thing explain it in the comments and I'll answer it for you

Answer:

64$

Step-by-step explanation:

Answer:

(4,2)

Step-by-step explanation:

..................................

Answer:

6cm

Step-by-step explanation:

hope this helped

Answer:

60

Step-by-step explanation:

Answer:A square and a rhombus both have sides equal in length. But square has all its angles equal to 90 degrees, but a rhombus only has its opposite angles equal.

Step-by-step explanation:

Answer:

A square has all its angles equal to 90 degrees a rhombus has no 90 degree angles

Answer:

1 out of 9

Step-by-step explanation:

Answer:

option c

Step-by-step explanation:

The zeros of 3x+1

3x=-1

x=-⅓

plug in -⅓ into the trinomial. if it gives an answer of 0 then it's a factor

3(-⅓)²+16(-⅓)+5

=0

Answer:

16%

Step-by-step explanation:

Add all of the dots together, you get 4/25 (the household of 3/total) and multiply top and bottom by same number. the bottom should equal 100. 25*4=100, 4×4=16. 16/100=16%

Answer: 16 quarts of blue paint

Step-by-step explanation:

i divided 3 by 24 to see how many quarts there was then took the answer which is 8 and multiplied it by 2.... i dont know if its right but i tried

Answer:

1

Step-by-step explanation:

[tex] \huge {625}^{ \frac{3}{8} } \times {5}^{ \frac{1}{2} } \div 25 \\ \\ = \huge {( {5}^{4})}^{ \frac{3}{8} } \times {5}^{ \frac{1}{2} } \div {5}^{2} \\ \\ = \huge{5}^{ \cancel4 \times \frac{3}{ \cancel8 \: \: \red{ \bold 2}} } \times {5}^{ \frac{1}{2} } \div {5}^{2} \\ \\ \huge= {5}^{ \frac{3}{2} } \times {5}^{ \frac{1}{2} } \div {5}^{2} \\ \\ \huge= {5}^{ \frac{3}{2} + \frac{1}{2}} \div {5}^{2} \\ \\ \huge= {5}^{ \frac{4}{2} } \div {5}^{2} \\ \\ \huge= {5}^{ 2 } \div {5}^{2} \\ \\ \huge= {5}^{ 2 - 2 } \\ \\ \huge= {5}^{ 0 } \\ \\ \huge= 1[/tex]

Answer:

(8-5) + (16-1)=18

Answer:

it could be C or a

Step-by-step explanation:

more likey c be sorry if it's wrong

Answer:

I think 42

Step-by-step explanation:

Answer:

Line graph

Step-by-step explanation:

Answer:

v = 13

Step-by-step explanation:

Truly hope I helped fast enough:).

Answer:

hlo thanks for free points ❤️❤️

Answer:

x=1

Step-by-step explanation:

is the answer

Answer:

x = 1

Step-by-step explanation:

Answer:

b:-15

Step-by-step explanation:

There are 9 num in the set sowe add all the num and the we divide the answer we got

Answer:

The answer is:

b) - 15

Hope it helps:D

Answer:$293.83

Step-by-step explanation:

Answer:

293.83$

Step-by-step explanation:

total withdrawals = 6*15.72=94.32$

the rest amount before depostit is 153-94.32=58.68$

the rest amount After depostit is 58.68+235.15=293.83$

Answer:

Domain: {2,4,5,9}

Range: {-2,0,2,4}

Function: No

Step-by-step explanation:

Domain = x

Range = y

Domain: {2,4,5,9}

Range: {-2,0,2,4}

Function: No

Answer:

domain = { 2, 4, 5, 9 }

range = { -2, 0, 2, 4 }

function = one-to-many

Answer:

4

Step-by-step explanation:

Although you didn't give me any answers to go with your problem, I am assuming that since 15-7 is 8, and 3 + 1 = 4, the answer should be 4. Now regarding if it is times, it would be x2. Because for times 2 would be 8. Overall the answer should be 4.