Expand and combine like terms.
(8 – n^7)(8 +n^7)

21 is composite because its factors are 1, 3, 7 and 21. If a number has 3 or more factors, then it's composite.

46: 1, 23, 46.

57: 1, 3, 19, 57.

Hope this helps!

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[tex]GraceRosalia[/tex]

The numbers 21, 46, and 57 are composite numbers.

Given,

21, 46 and 57

We need to identify which are prime or composite numbers.

Prime number - The numbers whose factor is only 1 and itself.

Example: 2, 5, 7

2 x 1 = 2

5 x 1 = 5

7 x 1 = 7

Composite number - The numbers which have factors other than itself and 1.

Example: 4, 6, 8

4 = 2 x 2

6 = 2 x 3

8 = 2 x 4

Find the factors

21 - 7 x 3

46 - 2 x 23

57 - 3 x 19

We see that each number has factors other than 1 and itself.

So,

21, 46, and 57 are composite numbers.

Thus 21, 46, and 57 are composite numbers.

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Answer:

see explanation

Step-by-step explanation:

Using sum to product identities

cos x - cos y = - 2sin([tex]\frac{x+y}{2}[/tex] )sin([tex]\frac{x-y}{2}[/tex] ) = 2sin([tex]\frac{x+y}{2}[/tex] )sin([tex]\frac{y-x}{2}[/tex] )

cos x + cos y = 2cos([tex]\frac{x+y}{2}[/tex] )cos([tex]\frac{x-y}{2}[/tex] )

Note that

sin10° = sin(90 - 10)° = cos80°

Thus

[tex]\frac{2sin(\frac{10+80}{2})sin(\frac{80-10}{2}) }{2cos(\frac{10+80}{2})cos(\frac{80-10}{2}) }[/tex] ← cancel 2 from numerator/ denominator

= [tex]\frac{sin45}{cos45}[/tex] × [tex]\frac{sin35}{cos35}[/tex]

= tan45° × tan35° { tan45° = 1 ]

= 1 × tan35°

= tan35° ← as required

Answer:    see proof below

Step-by-step explanation:

* Use the following Co-function Identity: sin A = cos(90 - A)

* Use the following Sum to Product Identities:

 cos x - cos y = 2 sin [(x + y)/2] · sin [(x - y)/2]

 cos x + cos y = 2 cos [(x + y)/2] · cos [(x - y)/2]

* Use the Unit Circle to evaluate cos 45 = sin 45 = √2/2

Proof LHS → RHS

[tex]\text{LHS:}\qquad \qquad \qquad \qquad \quad \dfrac{\cos 10-\sin 10}{\cos 10+\sin 10}\\\\\\\text{Co-function Identity:}\qquad \dfrac{\cos 10 -\cos (90-10)}{\cos 10+\cos (90-10)}\\\\\\\text{Product to Sum Identity:}\quad \dfrac{2\sin (\frac{10+80}{2})\sin (\frac{80-10}{2})}{2\cos (\frac{10+80}{2})\cos (\frac{80-10}{2})}\\\\\\\text{Simplify:}\qquad \qquad \qquad \qquad \dfrac{2\sin (45)\sin (35)}{2 \cos (45)\cos (35)}[/tex]

[tex].\qquad \qquad \qquad \qquad \qquad = \dfrac{2(\frac{\sqrt2}{2}) \sin (35)}{2(\frac{\sqrt2}{2}) \cos(35)}\\\\\\.\qquad \qquad \qquad \qquad \qquad = \tan (35)[/tex]

LHS = RHS:   tan 35 = tan 35   [tex]\checkmark[/tex]

Answer:

f(x) = (1/2)(x-2)^2(x+1)(x+2)

Step-by-step explanation:

You can determine this by looking at the zeroes of the graph. For any zero that goes through the x-axis, the power of that zero is odd. For any zero that that "bounces" from the x-axis, the power of that zero is even.

Starting from left to right, we can see that the first zero, -2, goes through the x-axis. That means (x+2) is raised to an odd power. The second zero, -1, also goes through, so (x+1) is raised to an odd power. The last zero, 2, bounces off the x-axis, so (x-2) is raised to an even power. The only functions that satisfy this criteria are function 1 and 2.

However, we are not done yet. We need to figure out which multiplier value (1/2, 1/4) is correct. To do this, we plug in 0 for x, since we know that the y-intercept is 4. When we plug in 0, we see that f(0) = 4 for the first function. Therefore, the first function is the answer.

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Answer:

20

Step-by-step explanation:

(2√5)²=

4*5=20

Answer:

Gaming Functions

Step-by-step explanation:

I think your teacher is implying for you to explain the function and the "works" behind the game. Maybe talk about the game's programming or the way it's overall structured?

Answer: 16 is the correct answer.

Step-by-step explanation: -n if n=-16 --16 two negatives equal positive and makes it +16.

Answer:

Step-by-step explanation:

Y=1/2x - 5/2

Answer:

1. 24 different 4-digit numbers can be formed.

Step-by-step explanation:

2. The probability that the number 3 will be the first or third digit is 1:1, which is equal to 1/2 and 50%

3. The probability is 3:1, 3/4, or 75%

4.  What is the probability that the first digit will be the number 3 and the second digit will be the number 7? Answer: 1/12

Answer:

65000(1.02)^n.

Step-by-step explanation:

Salary = 65000(1.02)^n   where n is the number of years he has worked for the company.

So after one year he earns $6500* 1.02 and after 2 years $65000 * 1.02^2.

The exponential function represents Mark's salary is [tex]65000(1.02)^n.[/tex]

The mathematical expression f(x)=exp or e^x denotes the exponential function.

The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, though it can be extended to complex numbers or adapted to other mathematical objects like matrices or Lie algebras.

Given that Mark just landed a great job as an engineer where he will make $65,000 a year. The company he will work for guarantees a 2% pay increase each year so its employees' salaries keep up with inflation. At the end of the first year, Mark will have made $65,000.

The exponential function for the salary will be written as:-

[tex]Salary = 65000(1.02)^n[/tex]  

where n is the number of years he has worked for the company.

So after one year, he earns $6500 x 1.02, and after 2 years $65000 x 1.02².

Therefore, the exponential function represents Mark's salary is [tex]65000(1.02)^n.[/tex]

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Answer:

£0.83

Step-by-step explanation:

This is a simple subtraction problem.

You have 10 pence. You buy something with 9.17 pence.

10 - 9.17

0.83

Label your answer in pence.

£0.83

Good luck mate :)

Answer:

90 inches³

Step-by-step explanation:

Given that:

A small rectangular prism sitting on top of a larger rectangular prism. The top prism measures 5 inches by 1 inch by 2 inches.

The bottom prism measures 5 inches by 4 inches by 1 plus 3 inches

Volume of rectangular prism = (width * length * height)

Volume of smaller prism: ( 5 * 1 * 2) inches = 10inch³

Volume of larger prism : (5 * 4 * (1 +3)) inches

(5 * 4 * (1 +3)) inches = (5 * 4 * 4) inches = 80 inches³

Total volume of the new packaging:

Volume of smaller + volume of larger prism

10 inches³ + 80 inches³ = 90 inches³

Answer:

$151.20

Step-by-step explanation:

(22.40x0.75)+(22.40x5)+22.40=151.20

Answer:

Step-by-step explanation:

let us total the amount in her portfolio

Company A was worth $2690

Company B was worth $2980.

Total = $5670

when The stock in Company A decreases by 20%  she will have

$2690 *0.8=  $2152

Company A will worth $2152

when The stock in Company B decreases by 10%  she will have

$2980 *0.9=  $2682

Company A will worth  $2682

In all after the decline in are portfolio is $2152+$2682= $4834

the difference for the original amount in her investment is = $5670-$4834

= $836

The total percentage decrease in the investor's stock account

= (836/5670)*100= 0.147*100= 14.7 %

Answer:

14.7%

Step-by-step explanation:

It’s 14.7%

Pls make me brainliest

Answer:

18 yards i think

Step-by-step explanation:

Answer:

Step-by-step explanation:

25

answer is 15

[tex]f(x)=5x+40\\f(-5)=5(-5)+40\\f(-5)=-25+40\\f(-5)=15[/tex]

If f(x) = 5x + 40, then the value of f(x) when x = -5 is: 15.

option D is correct.

Here, we have,

given that,

f(x) = 5x + 40

now, we have to find the value of f(x) when x = -5.

To find the value of f(x) when x = -5,

we substitute -5 into the function f(x) = 5x + 40:

we get,

f(-5) = 5(-5) + 40

= -25 + 40

= 15

Therefore, f(x) when x = -5 is 15.

Hence, If f(x) = 5x + 40, then the value of f(x) when x = -5 is: 15.

option D is correct.

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Answer:

infinite solutions

y = x - 1/4

Step-by-step explanation:

4x - 4y = 1

4y = 4x - 1

y = x - 1/4

substitute

4x - 4(x - 1/4) = 1

4x - 4x + 1 = 1

0 = 0

infinite solutions

Answer:

t = 10.

Step-by-step explanation:

We can combine like terms, getting 11t - 5 = 105.

Add both sides by 5, getting 11t = 105 + 5 = 110.

We can then divide both sides by 11, getting t = 10.

Answer:

see explanation

Step-by-step explanation:

Given

2x + 3y = 4 ( subtract 2x from both sides )

3y = - 2x + 4 ( divide all terms by 3 )

y = - [tex]\frac{2}{3}[/tex] x + [tex]\frac{4}{3}[/tex]

To determine if the point (2, 1) lies on the line, substitute x = 2 into the right side of the equation and if the value obtained equals the y- coordinate of the point then it lies on the line.

y = - [tex]\frac{4}{3}[/tex] + [tex]\frac{4}{3}[/tex] = 0 ≠ 1

Ths (2, 1) does not lie on the line

Step-by-step explanation:

Remember: the formula for solving for volumes:

l • w • h

An easy way to do this is to convert all the numbers to decimals.

3 1/2 = 3.5

5 1/4 = 5.25

4 = 4

Now, we can multiply.

3.5 • 5.25 • 4 = 73.5

Convert 0.5 to a fraction: 1/2

Our final answer: D: [tex]73 \frac{1}{2}[/tex]

Answer:

About 11.62 by 11.62

A square had equal sides so you find the square root of 135 and that is rounded to 11.62.

So the perimeter would be about 46. But 46.48 exactly.

Answer:

P≈46.48

A= Area

135

Step-by-step explanation:

It is true as A consist {7,8,9,10,11,12} and B consists of{9,11,13} and C consist of {7,8,10,12} and D has{7,12} there are the set of numbers from 7 to 13 only so the answer is true that U={7,8,9,10,11,12,13}.

0t

Step-by-step explanation:

4t-3-(3t+1)=5t-4

4t-3-3t-1=5t-4

t-3-1=5t-4

t-4=5t-4

t=5t

0=6t

0=t

(Im not 100% sure about this but i think this is the answer)

Hi there! :)

Answer:

6x² -xy - y²

---- --- --- --- --- --- --- --- --- --- --- ---

(3x + y) ( 2x - y)

FOIL: (First, Outer, Inner, Last)

3x(2x) + 3x(-y) + y(2x) + y(-y)

Simplify:

6x² -3xy + 2xy - y²

6x² -xy - y²

Answer:

the answer is A

Step-by-step explanation:

just did it

Answer:

a

Step-by-step explanation:

Answer:

Option (3)

Step-by-step explanation:

To construct a line parallel to the line through point Q we will follow the following steps,

1). We join two points P (on the line) and point Q above the line PT with the help of a straightedge.

2). Now we will copy the angle QPT at point P with the help of a compass (Arcs as shown in the figure)

3). Finally we will join points Q and S to construct a line QS parallel to the line PT.

Therefore, Option (3) will be the answer.

===============================================

Work Shown:

1 pint = 2 cups

8 pints = 16 cups (multiply both sides by 8)

We have an 8 pint bottle costing $16.80, so we can say

8 pints = 16.80 dollars

1 pint = 2.10 dollars (divide both sides by 8)

Answer:

$2.10

Step-by-step explanation:

2 cups in 1 pint

16 cups= 8 pints

16 cups = 16.80

16.80 divided by 8 = 2.1

Ans option 3? it can be converted to a fraction!

Answer:

it depends on the number of decimals

Step-by-step explanation: