Which of the following values "completes the square," or creates a perfect square trinomial, for x2 − 8x + ___?8
16
–8
–16

Answers

Answer 1

Answer: $Perfect\ square:\ (x\pm y)^2=x^2\pm2xy+y^2\ntherefore\nx^2-OK\n-8x=-2\cdot x\cdot 4\n4^2=16\n\nconclusion\n\nx^2-8x+\boxed{?}=x^2-2\cdot x\cdot4+\boxed{4^2}=x^2-8x+16\n\nYour\ answer:\boxed{\boxed{16}}$

Answer 2

Answer:

Answer: 16

Step-by-step explanation: A more simple approach is realizing that the blocks show 8 x tiles and 1 x^2 tile. The 8 x tiles are on either side of the x^2 tile which is 4 x tiles on each side. So as we can see we can multiply each side together. 4x4 = 16. So that is how you get 16 without having to work it out.

Related Questions

Tomas learned that the product of the polynomials (a + b)(a2 – ab + b2) was a special pattern that would result in a sum of cubes, a3 + b3. His teacher put four products on the board and asked the class to identify which product would result in a sum of cubes if a = 2x and b = 1.Which product should Tomas choose? A) (2x + 1)(2x2 + 2x – 1) B) (2x + 1)(4x3 + 2x – 1) C) (2x + 1)(4x2 – 2x + 1) D) (2x + 1)(2x2 – 2x + 1)
What is the ratio 35 to 56 written as a fraction in lowest terms?
The Johnsons own a home whose market value is $93,000. Their municipality taxes at 80% and the rate is 65 mills or $65 per thousand. What will the Johnsons pay in taxes?
Solve the following system of linear equations by substitution: 8x-y=-13 6x-3y=15
Log3x - log3(x − 8) = 2?????

Find a number between 364 and 384 that is both a multiple of 7 and a multiple of 3

Answers

So the least common multiple of 7 and 3 is 21

So the multiple between 364 and 384 should be a multiple of 21.
21 × 18 = 378
And the number that is between 364 and 384 and is a multiple of 7 and 3 is 378

On a road map, the distance between 2 cities is 2.5 inches. The map scale is 1 inch: 30 miles. What is the actual distance between the cities?

Answers

Answer:

75 miles.

Step-by-step explanation:

By proportion the actual distance is 2.5 * 30

= 75 miles

Two lines have given equations. At what point do they intersect? 2x-y=1 3x=y-6

Answers

2x-y=1 and 3x=y-6,
y=2x-1 and y=3x+6,
y=2x-1 and 2x-1=3x+6,
y=2x-1 and 3x-2x=-1-6,
x=-7 and y=-14-1
x=-7 and y=-15

check:
for x=-7 and y=-15:
2x-y=1 is -14-(-15)=1 is 1=1 ok
3x=y-6 is -21=-15-6 is -21=-21 ok

answer:
lines intersect at (-7;-15)

The hypotenuse AB of a right triangle ABC is 5 ft, and one leg, AC, is decreasing at the rate of 2 ft/sec. The rate, in square feet per second, at which the area is changing when AC = 3 is?

Answers

Answer: $-(7)/(4) \quad \text{ft}^(2)/\sec$

Step-by-step explanation:

Since ABC is a right triangle, at any moment it holds that

$5^2=(AC)^2+(BC)^2$

Moreover, the area A of the triangle is given by

$A= (1)/(2)(AC)(BC)$

and we know that the rate of change of the length (AC) is

constant decreasing 2, which may be written using the Leibniz

notation as

$(d(AC))/(dt)=-2$ .

Using the chain rule and the product rule for derivation, the two

first equations tell us

that

$0 = 2 (d(AC))/(dt)(AC) + 2 (d(BC))/(dt)(BC)$

and

$(dA)/(dt) = (1)/(2) \left( (d(AC))/(dt) \cdot (BC) + (d(BC))/(dt) \cdot (AC)\right)$

Moreover, using the first of the last two equations we get

$(AC)(d(AC))/(dt) = -(BC)(d(BC))/(dt) \Rightarrow\n\n\n(AC)(-2) = -(BC) (d(BC))/(dt) \quad \Rightarrow \quad (d(BC))/(dt)=2 ((AC))/((BC))$

Now, when (AC)=3, we have that

$25=(AC)^2 + (BC)^2 \quad \Rightarrow 25 = 9 + (BC)^2\n \n\Rightarrow \quad 16=(BC)^2 \quad \Rightarrow (BC)=4$

and

$(d(BC))/(dt) = 2 ((AC))/((BC))=2 (3)/(4)=(3)/(2)$ .

Hence, at this moment the rate of change of the area of the triangle is

$(dA)/(dt) = (1)/(2) \left( (d(AC))/(dt) \cdot (BC) + (d(BC))/(dt) \cdot(AC) \right)=(1)/(2)\left( -2 \cdot 4 + (3)/(2)\cdot 3\right ) = -(7)/(4)$

okay
we have the rate of change of AC = d(AC)/dt = -2
the rate of change od BC = d(BC)/dt
area = (1/2) *AC) (BC)
taking differential on both sides we ge
d(A)/dt = 1/2){ (BC) d(AC)/dt + (AC) d(BC)/dt)}....(1)
again
when AC= 3
applying pythagorous thm
we get
(5)^2 =(3)^2 +(BC)^2
hence we get BC = 4
now we need to find d(BC)/dt
we have
(5)^2 = (AC)^2 +(BC)^2
taking differenial
0=2(AC) d(AC/dt) +2BC d(BC)/dt
that is
d(BC)/dt = -(3) *(-2)/4 ..(at AC =3)
hence
d(BC)/dt = 3/2
substituting these values in equation (1)
d(A)/dt = (1/2) {4 * -2 + 3 *3/2}

which gives
d(A)/dt = -7/4

The rate, in square feet per second, at which the area is changing when AC = 3 is -7/4 ft/sec.

I hope my answer has come to your help. Thank you for posting your question here in Brainly.

In 2004, it was reported that "the relationship between body mass, M, and standard metabolic rate, B, among living organisms remains controversial. However, in many cases B is approximately proportional to the three-quarters power of M. a.he average mass of an African forest elephant is 4.6 metric tons, and that of a typical mouse is 25 grams. Use part (a) to determine how many times greater the metabolic rate of an elephant is than that of a mouse. Recall that 1 metric ton = 1,000,000 grams.

Answers

The answer is 8884.37 times

In many cases, B is approximately proportional to the three-quarters power of M:
$B= M^(3/4)$

Elephant:
M1 = 4.6 mt = 4.6 * 1,000,000 g = 4,600,000 g
$B1= 4600000^(3/4)=99327.24$

Mouse
M2 = 25 g
$B2= 25^(3/4)=11.18$

determine how many times greater the metabolic rate of an elephant is than that of a mouse:
B1/B2 = 99327.24 / 11.18 = 8884.37 times

A six-sided number cube is rolled 12 times. An even number is rolled 7 times. what is the experimental probability that even number is rolled?