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3 years ago

If B is the midpoint of AC, AB = 8x + 5, and BC = 5x2 - 16, then find x and AC

Mathematics

1 answer:

Murljashka [212]3 years ago

5 0

Answer:

Step-by-step explanation:

AB = 8x + 5

BC = 5x² - 16

5x² - 16 = 8x + 5

5x² - 8x - 21 = 0

Quadratic formula

x = [8 ± √(8² – 4·5(-21))] / [2·5]

= [8 ± √484] / 10

= [8 ± 22] /10

= -1.4, 3

-1.4 is an extraneous solution.

x = 3

AB = 8x+5 = 29

AC = 58

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Solve the system of equations. x+y=4 y=x^2 - 8x + 16 a) {(-3,7).(-4, 8)} b) [(4,0)} c) {(3,1),(4,0) d) {(3,7). (4.0)} e) none

Marysya12 [62]

Answer: The required solution of the given system is

(x, y) = (3, 1) and (4, 0).

Step-by-step explanation: We are given to solve the following system of equations :

$x+y=4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\y=x^2-8x+16~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

From equation (i), we have

$x+y=4\\\\\Rightarrow y=4-x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)$

Substituting the value of y from equation (iii) in equation (ii), we get

$y=x^2-8x+16\\\\\Rightarrow 4-x=x^2-8x+16\\\\\Rightarrow x^2-8x+16-4+x=0\\\\\Rightarrow x^2-7x+12=0\\\\\Rightarrow x^2-4x-3x+12=0\\\\\Rightarrow x(x-4)-3(x-4)=0\\\\\Rightarrow (x-3)(x-4)=0\\\\\Rightarrow x-3=0,~~~~~~~x-4=0\\\\\Rightarrow x=3,~4.$

When, x = 3, then from (iii), we get

$y=4-3=1.$

And, when x = 4, then from (iii), we get

$y=4-4=0.$

Thus, the required solution of the given system is

(x, y) = (3, 1) and (4, 0).

8 0

3 years ago

Which functions could represent a reflection over the y axis of the given function

fredd [130]

Answer:

g(x) = 1/2*(4)^(–x) and

g(x) =1/2*(1/4)^(x)

Please, see attached picture.

Step-by-step explanation:

Your full question is attached in the picture below

To easily solve this problem, we can graph each equation and see, which one represents a reflection of the function over the y axis.

See, second image.

The answers are

g(x) = 1/2*(4)^(–x) and

g(x) =1/2*(1/4)^(x)

4 0

2 years ago

What is the probability that a group of five friends all have different birthdays? Show all of your work for full credit.

patriot [66]

Answer: 0.98630136986

Step-by-step explanation:

There are 365 possible birthdays. The key to assigning the probability is to think in terms of complements: “Two (or more) people share a birthday” is the complement of “All people in the group have different birthdays.” Each probability is 1 minus the other. What is the probability that any two people have different birthdays? The first person could have any birthday (p = 365÷365 = 1), and the second person could then have any of the other 364 birthdays (p = 364÷365). Multiply those two and you have about 0.9973 as the probability that any two people have different birthdays, or 1−0.9973 = 0.0027 as the probability that they have the same birthday. If you have a group of five, it would mean your equation would have to be (p=360÷365)

8 0

2 years ago

a square measuring 9 inches by 9 inches is cut from the corners of a square measuring 15 inches by 15 inches what is the area of

ss7ja [257]

Answer:

144 in²

Step-by-step explanation:

Find the area of the larger square, then subtract the area of the square we cut out.

The larger square has side length of 15, so it has an area of 15² = 225 in²

The smaller square has side length of 9, so it has an area of 9² = 81 in²

The area left over is

225 - 81 = 144 in²

3 0

3 years ago

Simplify this expansion 3G -9 + 11G -21

VladimirAG [237]

Answer:

14G-30

Step-by-step explanation:

3G -9 + 11G -21

14G-30

4 0

3 years ago