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2 years ago

What is the missing constant term in the perfect square that starts with x^2-16x? Pretty stumped on this one. Thanks in advance!

2 answers:

8 0

You'll have to find a number, in which, when factored, the factors would add up to -16

x^2 - 16x + 64 (for example)
x -8
x -8

(x - 8) (x - 8). If you use FOIL, you will get the trinomial again.

64 can be your answer

hope this helps

vlabodo [156]2 years ago

6 0

Perfect squares are the result of an integer being multiplied by itself.

The trinomial is given by the following formula:

$ax^2 + bx + c$

We are missing c from this trinomial, so we must solve for c.

An equation that we can use to solve for c in this equation is the following formula:

$c = (\frac{b}{2})^2$

Plug b into the equation:

$b = -16$
$\frac{-16}{2} = -8$
$-8^2 = 64$

$c = 64$

The missing constant term is 64.

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Janisa researched fast-growing industries and occupations, while Rylan researched industries and occupations that have the highe

topjm [15]

Answer:

Janisa found that home health care is the fastest-growing occupation and services for the elderly is the fastest growing industry, while Rylan found that elementary and secondary school teaching are the occupations with the highest employment and retail sales is the industry with the highest employment.

Explanation:

We make this conclusion because when we look at all the other options none matches the definition of occupations and industries. However, if Janisa found that home health care is the fastest-growing occupation, and then services for the elderly are the fastest growing industry, it matches what we know an industry and occupation mean.

While, if Rylan found that elementary and secondary school teaching are the occupations with the highest employment, it matches an example of occupation also, and if he discovers that retail sales is the industry with the highest employment it also falls under industry types.

However, the other options mismatched industry examples for occupations.

9 0

2 years ago

PROBLEM SOLVING You are participating in an orienteering competition. The diagram shows the position of a river that cuts throug

Wewaii [24]

Answer:

The shortest distance is 2.2 miles

Step-by-step explanation:

we know that

The shortest distance you must travel to reach the river is the perpendicular distance to the river

step 1

Find the slope of the line perpendicular to the river

we have

$y=3x+2$

The slope of the river is m=3

Remember that if two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is -1)

therefore

The slope of the line perpendicular to the river is

$m=-1/3$

step 2

Find the equation of the line into point slope form

$y-y1=m(x-x1)$

we have

$m=-1/3$

$point(2,1)$

substitute

$y-1=-(1/3)(x-2)$

step 3

Find the intersection point of the river and the line perpendicular to the river

we have

$y=3x+2$ ------> equation A

$y-1=-(1/3)(x-2)$ -----> equation B

Solve the system by graphing

The intersection point is (-0.1,1,7)

see the attached figure

step 3

Find the distance between the points (2,1) and (-0,1,1.7)

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

substitute

$d=\sqrt{(1.7-1)^{2}+(-0.1-2)^{2}}$

$d=\sqrt{(0.7)^{2}+(-2.1)^{2}}$

$d=2.2\ miles$

6 0

2 years ago

The equation 4x2 – 24x + 4y2 + 72y = 76 is equivalent to

DerKrebs [107]

Answer:

Option 4 is correct.

The equation $4x^2 -24x + 4y^2 + 72y = 76$ is equivalent to $4(x-3)^2 + 4(y+9)^2 =436$

Step-by-step explanation:'

Given equation: $4x^2 -24x + 4y^2 + 72y = 76$

First group the terms with x and those with y;

$(4x^2-24x)+(4y^2+72y) = 76$

Next, we complete the squares.

We can do this by adding a third term such that the x terms and the y terms are perfect squares.

For this we must either add the same value on the other side of the equation or subtract the same value on the same side so that the equality is maintained.

⇒ $4(x^2-6x) +4(y+18y) = 76$