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3 years ago

Factor the given expression x squared + 16x +64

2 answers:

5 0

X^2+16x+64 is a perfect square so by simply finding the square root of 64 we can factor it

The square root of 64 is 8 and as you can see 2*8 is 16 so the middle also works out

(x+8)^2 is the answer

eduard3 years ago

3 0

Answer:

(x + 8)^2.

Step-by-step explanation:

x^2 + 16x + 64

8 + 8 = 16 and 8^2 = 64 so the factors are

(x + 8)(x + 8) or (x + 8)^2

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Solve x2 = 12x – 15 by completing the square. Which is the solution set of the equation? Solve x2 = 12x – 15 by completing the s

Svetlanka [38]

Answer: $6+\sqrt{21}\ \text{and}\ 6-\sqrt{21}$

Step-by-step explanation:

Given

Quadratic equation is

$x^2-12x+15=0$

Solving by completing the square method

$\Rightarrow x^2-2\cdot 6\cdot x+15=0\\\text{add and subtract 36}\\\Rightarrow x^2-2\cdot 6\cdot x+15+36-36=0\\\Rightarrow x^2-2\cdot 6\cdot x+36+(-36+15)=0\\\text{using}\ (a-b)^2=a^2+b^2-2ab\\\Rightarrow (x-6)^2-21=0\\\Rightarrow (x-6)^2=21\\\Rightarrow x-6=\pm \sqrt{21}\\\Rightarrow x=6\pm \sqrt{21}$

The solution set of the equation is $6+\sqrt{21}\ \text{and}\ 6-\sqrt{21}$

6 0

3 years ago

Read 2 more answers

Which graph represents the function? f(x) = ∛x+2

Gnoma [55]

Answer:

graph shown in image below

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

A frightened child is restrained by her mother as the child slides down a frictionless playground slide. If the force on the chi

MissTica

Answer:

Step-by-step explanation:

Given

Restrained Force $F=116 N$

Increase in Kinetic Energy $\Delta K.E.=30 J$

Distance moved d=1.9 m

Work done by all the forces is equal to change in Kinetic Energy of Object i.e. by gravity force, Normal force and Applied Force

$\Delta K.E.=W_g+W_f+W_N$

$30=W_g-F\cdot d$

$30=W_g-116\cdot 1.9$

$W_g=250.4 J$

(b)In absence of applied force thus

work done by gravity will be equal to change in kinetic Energy

change in Kinetic Energy $=210 J$

6 0

3 years ago

You ask a neighbor to water a sickly plant while you are on vacation. Without water the plant will die with probability 0.75. Wi

Dafna1 [17]

Answer:

0.2915

Step-by-step explanation:

Let W represent water and D represent Dying probability

W = water

D = die

->If with water, it will die with probability 0.4

P(W & D) = 0.82 x 0.4 = 0.328

->Without water the plant will die with probability 0.75

P(W ' & D) = 0.18 x 0.75 = 0.135

Taking sum of the above values with water and without water.

P(D) = P(W & D) + P(W ' & D) = 0.4643

P(W ' | D) = P(W ' & D) / P(D)

= 0.135 /0.463

= 0.2915 ≈ 29.15%

Thus, the probability the neighbor forgot to water is 0.2915

4 0

3 years ago

A special box designed to hold an antique artifact is shaped like a triangular prism. The surface area of the box is 421.2 squar

Oksanka [162]

The area of the base is:
A = root ((s-a) * (s-b) * (s-c) * (s))
Where,
a, b, c: sides of the triangle
s = (a + b + c) / 2
We have then:
s = (9 + 9 + 9) / 2
s = 13.5
A = root ((13.5-9) * (13.5-9) * (13.5-9) * (13.5))
A = 35.07
Then, the surface area of the prism is:
S.A = 2 * A + 9h + 9h + 9h
Where,
h: height of the prism:
Substituting values:
421.2 = 2 * (35.07) + 9h + 9h + 9h
Clearing h:
27h = (421.2 - 2 * (35.07))
h = (421.2 - 2 * (35.07)) / (27)
h = 13
Answer:
the height of the box is:
h = 13 inches

8 0

3 years ago