Which measurement is the best estimate for the capacity of a bottle of nail polish?A : 10 mL

B : 10 L

C : 10 kL

Answers

Answer 1

Answer: The best estimate for the capacity of a bottle of nail polish is A: 10 mL

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The range of the function f(k) = k2 + 2k + 1 is {25, 64}. What is the function’s domain?{5, 8}
{-5, -8}
{3, 8}
{4, 7}
{4, 8}

Answers

Answer:

Hence, the domain of the function is:

{4,7}

Step-by-step explanation:

We are given the range of the function:

$f(k)=k^2+2k+1$ as {25,16}

The function f(k) could also be written as:

$f(k)=k^2+2k+1=k^2+k+k+1\n\nf(k)=k(k+1)+1(k+1)\n\nf(k)=(k+1)(k+1)\n\nf(k)=(k+1)^2$

The range is the value of the function at some k.

if f(k)=25 then we have to find the value of k.

$f(k)=25=5^2=(k+1)^2$

on taking square root on both side we have:

$k+1=5\n\nk=5-1\n\nk=4$

if f(k)=64 then we have to find the value of k.

$f(k)=64=8^2=(k+1)^2$

on taking square root on both side we have:

$k+1=8\n\nk=8-1\n\nk=7$

Hence, the domain of the function is:

{4,7}

The domain of a function contains the x-values of the function while the range of the function contains the y-values of the function. In this case, we substitute 25 and 64 to y. Then,
25 = k2 + 2 k + 1 (k-4) * (k+6) = 0
64 = k2 + 2 k + 1 (k-7) * (k+9) = 0
hence the domain is {-9,-6, 4,7}

A farmer uses a lever to move a large rock. The force required to move the rock varies inversely with the distance from the pivot to the point the force is applied. A force of 50 pounds applied to the lever 36 inches from the pivot point of the lever will move the rock. Which function models the relationship between f, the amount of force applied to the lever and d the distance of the applied force from the pivot point?

Answers

Answer:f=1800/d Inverse proportion function. Provided f is in pounds & d is in inches.

Step-by-step explanation: the relationship between f & d is inverse proportion.

A constant k has to be derived from the relationship.

If f is inversely proportional to d then f=k(1/d)

K= f X d

= 50 X 36

=> constant K=1800.

Find the constant of variation k for the direct variation. A . K = -2

B . K = 2

C . K = -0.5

D . K= -1.5

Answers

Answer:

K = -2

Step-by-step explanation:

If y varies directly as x, k (constant) can be found by dividing the y-coordinate by the x-coordinate.

$k = (2)/(-1) = -2$

Answer:

Step by step explanation

give two examples of items that weigh less than 1 ounce and two examples of items that weigh more than 1 ton

Answers

under an ounce- paper, feather
more than a ton- Elephant, car

9x+10=11x-10
Please show work

Answers

Answer:

$x=10$

Step-by-step explanation:

1) Subtract 10 from both sides of the equation

$9x+10=11x-10\n9x+10-10=11x-10-10$

2) Simplify

a. Subtract the numbers

b. Subtract the numbers again

$9x=11x-20$

3) Subtract 11x from both sides of the equation

$9x=11x-20\n9x-11=11x-20-11x$

4) Simplify

a. Combine like terms

b. Combine like terms again

$-2x=-20$

5) Divide both sides of the equation by the same term

$-2x=20\n(-2x)/(-2) =(-20)/(-2)$

6) Simplify

a. Cancel terms that are in both the numerator and denominator

$(-2x)/(-2) =(-20)/(-2) \nx=(-20)/(2)$

b. Divide the numbers

$x=(-20)/(-2x) \nx=10$

Simplifying
9x + 10 = 11x + -10

Reorder the terms:
10 + 9x = 11x + -10

Reorder the terms:
10 + 9x = -10 + 11x

Solving
10 + 9x = -10 + 11x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-11x' to each side of the equation.
10 + 9x + -11x = -10 + 11x + -11x

Combine like terms: 9x + -11x = -2x
10 + -2x = -10 + 11x + -11x

Combine like terms: 11x + -11x = 0
10 + -2x = -10 + 0
10 + -2x = -10

Add '-10' to each side of the equation.
10 + -10 + -2x = -10 + -10

Combine like terms: 10 + -10 = 0
0 + -2x = -10 + -10
-2x = -10 + -10

Combine like terms: -10 + -10 = -20
-2x = -20

Divide each side by '-2'.
x = 10

Simplifying
x = 10

Please help I’ll give 40 extra points!!! During a football game, a team lost 12 yards on the first play and then gained 5 yards on each of the next 3
plays. Which method finds the total yards at the end of the first four plays?

O add-12 to 3x5

O add 12 to 3x5

O add-12, 5, and 3

O add 12, 5, and 3