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Tanya [424]
3 years ago
5

Find the exact solution to the equation. 5^(6-2x) = 25

Mathematics
1 answer:
STatiana [176]3 years ago
3 0

Answer:

x = 2

Step-by-step explanation:

Note that 25 = 5² , then

5^{(6-2x)} = 5²

Since the bases on both sides are 5 then equate the exponents

6 - 2x = 2 ( subtract 6 from both sides )

- 2x = - 4 ( divide both sides by - 2 )

x = 2

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Graph the line y=−3x+b if it is known that the graph goes through point: B(5,2)
Nuetrik [128]

Try this solution:

1. In order to built the line required in the condition it need to determine its equation.

Using the coordinates of point B (5;2), if to substitute them into the given equation: 2=-3*5+b, ⇒ b=17. It means, that the equation of the line required in the condition is y= -3x+17.

2. The graph is in the attachment; point (0;17) is the intersection point of Y-axis and the line.

5 0
3 years ago
The average income, I, in dollars, of a lawyer with an age of x years is modeled with the following function: I = -425x^2 + 45,5
lord [1]

We are given

The average income, I, in dollars is

I=-425x^2+45500x-650000

(a)

now, we are given

average income is $275000

so, I=275000

now, we can set them equal

and then we can solve for x

275000=-425x^2+45500x-650000

-425x^2+45500x-925000=0

we will have to use quadratic formula

x=\frac{-45500+\sqrt{45500^2-4\left(-425\right)\left(-925000\right)}}{2\left(-425\right)}:\quad \frac{-\sqrt{45500^2-1572500000}+45500}{850}

x=\frac{-45500-\sqrt{45500^2-4\left(-425\right)\left(-925000\right)}}{2\left(-425\right)}:\quad \frac{\sqrt{45500^2-1572500000}+45500}{850}

we get

x=27.28199

x=79.776

we need to find youngest age

It means that we need to choose smallest value

so,

x=27............Answer

(b)

we are given

x=40

so, we can plug it and find I

I=-425(40)^2+45500(40)-650000

I=490000..............Answer

6 0
3 years ago
Plz guys step by step with answer​
kotegsom [21]

Answer:

C

Step-by-step explanation:

You can rearrange the equation to make it: 4y=3x-2

The slope right now is 3,but that's not the answer

So you divide the whole equation by 4 (it will give you: y=3/4 x- 0.5

So from that you can see that the slope is 3/4, C

6 0
3 years ago
Please help ill give brainliest and follow my insta lol> widowmaker2007
Karo-lina-s [1.5K]
Do u follo back tho lol
7 0
3 years ago
Select the correct answer. Function f is an exponential function that has an initial value of 64 and decreases by 50% as x incre
lozanna [386]

9514 1404 393

Answer:

  D. Both functions are decreasing at the same average rate on that interval

Step-by-step explanation:

The dashed lines on the attached graph of the two functions (f in red, g in purple) represent the average rate of change of each function on the interval. The lines are parallel, because the average rate of change is the same for each of the functions on that interval.

__

Function f decreases by 60 units from f(0) = 64 to f(4) = 4 on the interval x = [0, 4]. Function g decreases by 60 units from g(0) = 75 to g(4) = 15 on the same interval. The average rate of change is the amount of decrease divided by the interval width. Those values are the same for both functions.

3 0
3 years ago
Read 2 more answers
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