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4 years ago

What is x^2-12x+23=7 in vertex form?

Mathematics

1 answer:

Dmitrij [34]4 years ago

3 0

Answer:

y = (x - 6)^2 - 20

Step-by-step explanation:

Let's start by completing the square for x^2 - 12x. Half of the coefficient of x is (1/2)(-12), or -6. Square this and add it to x^2 - 12x, and then subtract it:

x^2 - 12x + 36 - 36 + 23 = 7

Rewriting the first three terms,

(x - 6)^2 -13 = 7, or

y = (x - 6)^2 - 20

The vertex is located at (h,k), which here is (6, -20).

You might be interested in

The number of cubic units in the volume of a sphere is equal to the number of square units in the surface area of the sphere. Wh

viktelen [127]

Answer:

Radius of sphere is 3 units.

Step-by-step explanation:

Volume of sphere is given by $4/3 \pi r^3$

surface area of sphere is given by $4 \pi r^2$

where r is the radius of the sphere.

Given that

The number of cubic units in the volume of a sphere is equal to the number of square units in the surface area of the sphere.

we equate formula of Volume of sphere and surface area of sphere

assuming r as the radius.

thus,

$4/3 \pi r^3 = 4 \pi r^2\\\\4/3 \pi r^3/ 4 \pi r^2 = 1\\=>r/3 = 1\\=> r = 3$

Thus, radius of sphere is 3 units.

5 0

3 years ago

Marissa is drawing coins from a bag that contains 5 pennies (yellow), 4 nickels (green), 5 dimes

Anna007 [38]

Answer:

$\frac{4}{16}=\frac{1}{4}=0.25=25\%$

Step-by-step explanation:

Total number of coins in the bag = 5 + 4 + 5 + 2 = 16 coins

Number of nickels in the bag = 4

We have to find the probability that Marissa draws a nickels from the bag.

Probability is defined as the ratio of Number of "Favorable Outcomes" to "Total number of possible outcomes"

In this case total number of possible outcomes is the total number of coins which is 16.

Favorable/Desires outcome is drawing a Nickle from the bag which are 4 in number. So, number of favorable outcomes is 4

Therefore, the probability that she will draw a nickel = $\frac{4}{16}=\frac{1}{4}=0.25=25\%$

7 0

3 years ago

Maggie's brother is 8 years younger than twice her age. The sum of their ages is 25.

g100num [7]

Answer:

the sum is 25 not 24?

Step-by-step explanation:

6 0

3 years ago

Please help first person to answer correctly with no links get 50 points and marked as brainliest no links please

icang [17]

Answer:

C, first I'm not sure if it's correct, but hear me out.

Step-by-step explanation:

If we already know that B=34 we need to find out the rest.

B=50 (Estimated)

D=45 (Estimated)

34+50+45

34+50=84+45=129, 129 estimated=130, and since their is no answer choice but C it should be C, I could be very wrong though.

7 0

3 years ago

Which of the following represents a valid first step to solving this system of equations using the substitution method?

Phoenix [80]

Answer:

2(2y - 1) - y = 7

Step-by-step explanation:

I guess the 2 equations are

2x - y = 7

x = 2y - 1

substitution message that you use one equation to express one variable by the other, and then you use that in the other equation to get one equation for one variable. then you solve for that, and use that result in the first equation to since for the second variable.

the equations are already defined that way, that the second equation directly defines x as an excision of y.

so, this needs to be used then in the first equation.

and that makes

2(2y - 1) - y = 7

the correct first step.

7 0

2 years ago