Which of the following are right triangle congruence theorems

Which equation is y=6x^2+12-10 rewritten in vertex form

Andre45 [30]

The formula in order to obtain the vertex form of a quadratic equation is given as

y=a(x-h)^2+k where (h,k) is the vertex of the quadratic equation which is parabolic in shape and it is opening upward.

As given in the problem, y=6x^2+12x-10

Using the formula, we can transformed the quadratic equation y=6x^2+12x-10 into its vertex form:

y=6x^2+12x-10

y= (6x^2+12x)-10 (grouping)

y=6(x^2+2x)-10 (factoring Common terms per group)

y=6(x^2+2x+1)-10-6 (Completing the squares)

y=6(x+1)^2-16 (Factor and Simplify)

Hence, the vertex form of y=6x^2+12x-10 is y=6(x+1)^2-16

7 0

4 years ago

Find the volume of a cylinder that has a diameter of 12 in. and a height of 15 in

daser333 [38]

Answer:

<h3> $\sf{ \boxed{ \bold{1697.14}}}$ </h3>

Step-by-step explanation:

Given,

diameter ( d ) = 12 in

height ( h ) = 15 in

finding the radius of a cylinder

Radius is just half of diameter.

Radius ( r ) = 12 / 2 = 6 in

finding the volume of a cylinder having radius of 6 in and height of 15 in

Volume of a cylinder =  $\sf{\pi \: {r}^{2} h}$ 

⇒ $\sf{ \frac{22}{7} \times {6}^{2} \times 15}$

⇒ $\sf{ \frac{22}{7} \times 36 \times 15}$

⇒ $\sf{1697.14} \: in$ 

Hope I helped!

Best regards!!

6 0

4 years ago

Read 2 more answers

The parabolas defined by the equations y=-x^2-x+1 and y=2x^2-1 intersect at points (a, b) and (c, d), where c>=a. What is c-a

Fittoniya [83]

Answer:

c - a = $\frac{5}{3}$

Step-by-step explanation:

Since the parabolas intersect we can equate them, that is

2x² - 1 = - x² - x + 1 ← subtract terms on right side from terms on left side

3x² + x - 2 = 0

Consider the factors of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 3 × - 2 = - 6 and sum = + 1

The factors are + 3 and - 2

Use these factors to split the x- term

3x² + 3x - 2x - 2 = 0 ( factor the first/second and third/fourth terms )

3x(x + 1) - 2(x + 1) = 0 ← factor out (x + 1) from each term

(x + 1)(3x - 2) = 0

Equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

3x - 2 = 0 ⇒ 3x = 2 ⇒ x = $\frac{2}{3}$

Since c > a, then

a = - 1 and c = $\frac{2}{3}$

Thus

c - a = $\frac{2}{3}$ - (- 1) = $\frac{2}{3}$ + 1 = $\frac{2}{3}$ + $\frac{3}{3}$ = $\frac{5}{3}$

3 0

3 years ago

Subtract.

jeka94

(x+1)-(-2x-5)
=x+1+2x+5
=3x+6
=3(x+2)

7 0

3 years ago

Read 2 more answers

The pool at a resort needs a fence added around its lounge area for safety. The pool measures 20 feet by 40 feet and the lounge

Sergeeva-Olga [200]

Answer:

The amount of fence needed to surround the mentioned space is:

200 feet.

Step-by-step explanation:

To identify the amount of fence, you must take all the measurements given in the exercise:

Pool width = 20 ft
Pool length = 40 ft
Aditional area in each side = 10 ft

As each side has 10 additional feet, that is the lounge area, you must add 20 feet to each side of the pool, this is because, in the case of the width, you must add 10 feet to the right side and 10 feet to the left side, in the case of the length, you must add to each side 10 feet to the upper part and 10 feet to the lower part, in this form, the measurements of the fence must be:

Width of fenced area = 40 ft
Length of fenced area = 60 ft

As you know, the length has two sides and the length has two sides too, by this reason, we must multiply each value by 2 to obtain the amount of fence to all four sides of the lounge area:

Amount of fence = 2(40 ft) + 2(60 ft)
Amount of fence = 80 ft + 120 ft
Amount of fence = 200 ft

As you can see, the amount of fence needed to go around the lounge area is 200 feet.

3 0

3 years ago