I have no idea how to do this. My teacher just threw it on us, please help. <3

Answer:

x = 7

Step-by-step explanation:

x + 7 = 14

Subtract 7 from both sides

x = 14 - 7 = 7

Answer: the answer is 7

Step-by-step explanation:

Answer:

[tex]x^{2} =1, then\ x=1[/tex] is NOT true.

Step-by-step explanation:

1.

[tex]If\ x=1, then\ x^{2} =1[/tex] ......True

( 1 )² = 1

2.

If [tex]x^{2} =1, then\ x=1[/tex] ........ NOT True

∴ x =± 1     .........this is correct

3.

[tex]If\ x=-1, then\ x^{2} =1[/tex] ......True

( -1 )² = 1

4.

x2 = 1 if and only if x = 1 or x = -1. .........True

( 1 )²  = 1

( -1 )² = 1

Answer:

The answer is 41/4.

Step-by-step explanation:

Given:

-41/4 to get the additive inverse.

Now, the additive inverse of any number is a number that, when added to the number the result is zero.

Here, 41/4 is the additive inverse.

Because when it is added to -41/4 the result is 0.

Therefore, the answer is 41/4.

Answer:

2^6

Step-by-step explanation:

2 is being multiplied 6 times meaning it would be 2 to the 6th power.

Answer:

4^5x-5

Step-by-step explanation:

4^5x-7/4^-2

=4^5x-5

The expression 4⁵ × 4⁻⁷ divided by 4⁻² simplifies to 1 by using the properties of exponents. First, add the exponents in the numerator, then subtract the exponents for division, resulting in 4⁰, which equals 1.

We need to simplify the expression:

4⁵ times 4⁻₇ ext{ divided by } 4⁻²

To simplify, let's first combine the powers of 4 in the numerator:

= 4⁵ times 4⁻⁷

= 4⁽⁵⁺⁽⁻⁷⁾⁾

= 4⁻²

= 4⁻² ext{ divided by } 4⁻²

= 4⁽⁻²⁻⁽⁻²⁾⁾

= 4⁽⁻²⁺²⁾

= 4⁰

4⁰ = 1

Therefore, the given expression simplifies to 1.

Answer:

for #4 x=-7

Step-by-step explanation:

a negative times a negative is a positive and 8 times 7 = 56

Answer:

5/63

Step-by-step explanation:

8/9(5/7)(1/8)=

8/9(5/7)=

40/63(1/8)=

5/63

by the way 8/9 x 5/7 x 1/8

is also the same as (8/9)(5/7)(1/8)

To find the product of 8/9, 5/7, and 1/8, multiply the numerators and denominators to get 40/504 and simplify it to 5/63.

To solve the multiplication of fractions, we need to multiply the numerators together and the denominators together. For the expression 8/9 times 5/7 times 1/8, we multiply the numerators 8, 5, and 1 to get 40, and the denominators 9, 7, and 8 to get 504. Simplifying the fraction 40/504 involves finding the greatest common divisor, which is 8 for both numerator and denominator, and dividing them by this number.

Doing so, we get 40 ÷ 8 = 5 and 504 ÷ 8 = 63. Hence, the solution simplified is 5/63.

Answer:

a = 108° and b = 144°

Step-by-step explanation:

The opposite angles of a rhombus are the same and the sum of all the angles of the rhombus is 360°.

So, from the given diagram of the rhombus we can write  

2b + 2× 36 = 360

⇒ 2b = 360 - 72 = 288

⇒ b = 144° (Answer)

Again, the each angles of a pentagon is given to be a.

Hence, we can write 3a + 36 = 360

⇒ 3a = 324

⇒ a = 108° (Answer)

Answer:

[tex]\large\boxed{y-3=-(x+4)}\\or\\\boxed{y+4=-(x-3)}[/tex]

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

(x₁, y₁) - point on a line

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have two points (-4, 3) and (3, -4).

Substitute:

[tex]m=\dfrac{-4-3}{3-(-4)}=\dfrac{-7}{7}=-1[/tex]

Put the value of a slope and the coordiantes of the point (-4, 3) or (3, -4) to the equation of a line:

for (-4, 3)

[tex]y-3=-1(x-(-4))\\\\y-3=-(x+4)[/tex]

for (3, -4)

[tex]y-(-4)=-1(x-3)\\\\y+4=-(x-3)[/tex]

Answer:

9

Step-by-step explanation:

It saying 3 times to the power of 2

or

3 squared

so basically it's saying

3^3=9

Answer:

see explanation

Step-by-step explanation:

Where the graph crosses the x- axis the y- coordinate is zero.

Let y = 0 in the equation and solve for x

- 4(0) = 15 - 5x, that is

15 - 5x = 0 ( subtract 15 from both sides )

- 5x = - 15 ( divide both sides by - 5 )

x = 3 ← x- intercept ⇒ (3, 0 )

Where the graph crosses the y- axis the x- coordinate is zero.

Let x = 0 in the equation and solve for y

- 4y = 15 - 5(0), that is

- 4y = 15 ( divide both sides by - 4 )

y = - [tex]\frac{15}{4}[/tex] ← y- intercept ⇒ (0, - [tex]\frac{15}{4}[/tex])

Answer:

1.5

Step-by-step explanation:

12 divided by 8 = 1.5

1.5 x 8 = 12

Answer:

2

Step-by-step explanation:

Because the # ends in a even number, it can be divisible by 2

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]8z\leq 16[/tex]

Solve for z

Divide by 8 both sides

[tex]z\leq 16/8[/tex]

[tex]z\leq 2[/tex]

The solution for z is the interval ----> (-∞,2]

All real numbers less than or equal to 2

In a number line the solution  is the shaded area at left of z=2 (closed circle)

using a graphing tool

see the attached figure

Answer:

p=ak^t

p1=491272*k^0

p2=782341*k^10

782341/491272 = k^10

k=1.047629

growth rate is 4.7629%

2012: predicted population is 491272*1.047629^12=858,642 people

1245863=491272*1.047629^t

1.047629^k=2.5363599

ln both sides is k ln 1.0476=ln 2.5363

t=20.000 years.

Rule of 72 would say 72/4.76 or 15.12 years for doubling

14.90 years

2017 predicted is 491272*1.0476^17 or 1083552, or more than actual, so the rate of growth is slowing down.

The required exponential growth rate, k is 4.7629%

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

The exponential function will be as

p=a[tex]k^t[/tex]

p₁=491272*k⁰

p₂=782341*k¹⁰

782341/491272 = k¹⁰

k = 1.047629

So, the growth rate is 4.7629%

2012: the predicted population is 491272 × 1.047629¹² =858,642 people

1245863=491272 × [tex]1.047629^t[/tex]

[tex]1.047629^k[/tex] = 2.5363599

ln both sides is k ln 1.0476 = ln 2.5363

t = 20.000 years.

Rule of 72 would say 72/4.76 or 15.12 years for doubling

14.90 years

2017 predicted is 491272 × 1.0476¹⁷ or 1083552, or greater than the real rate of increase, hence the rate of growth is decreasing.

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Answer:

x² - 8x + 12 = 0

(x - 6)(x - 2) = 0

x = 2, 6

f(4) = -4

Plot (0, 12), (2, 0), (4, -4), (6, 0), and (8, 12) on the graph. Then draw a smooth curve that goes through these points.

Answer:

[tex]SA=502.4\ ft^2[/tex]

Step-by-step explanation:

we know that

The surface area of a cone is equal to

[tex]SA=\pi r^{2}+\pi rl[/tex]

we have

[tex]r=8\ ft\\l=12\ ft\\\pi=3.14[/tex]

substitute the given values

[tex]SA=(3.14)(8^{2})+(3.14)(8)(12)[/tex]

[tex]SA=200.96+301.44=502.4\ ft^2[/tex]

Answer:

never

Step-by-step explanation:

In a right triangle, every angle has an opposite side and an adjacent side. And there's always a hypotenuse.

The sine of an angle is the ratio of the length of the opposite side divided by the length of the hypotenuse.

The tangent ratio of an angle is the opposite side over adjacent side, it is not the sine ratio of a triangle.

For example, ABC is a right angled triangle having length of the sides are a,b,c.

So

[tex]sine\ C=\frac{a}{c}[/tex]

The sine ratio of an angle sometimes is the opposite side over the adjacent side.

The question pertains to the definition of the sine ratio in trigonometry. The sine ratio of an angle is not defined as the opposite side over the adjacent side; rather, it is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse of a right-angled triangle.

Therefore, the correct statement is the sine ratio of an angle sometimes is the opposite side over the adjacent side, specifically in the case of a 45°-45°-90° triangle where the sides are equal, but this is not generally true for all angles in trigonometry.

The equation of the parallel line in slope-intercept form is;

y = [tex]\frac{5}{2}[/tex] x - [tex]\frac{25}{2}[/tex]

Step-by-step explanation:

Let us revise some facts about parallel lines

The equations of two parallel lines have:

The slope-intercept form of the equation of a line is y = m x + b, where m is the slope of the line and b is the y-intercept

The given line has equation 5x - 2y = 10

Put it in the form of y = m x + b to find its slope

∵ 5x - 2y = 10

- Subtract 5x from both sides

∴ -2y = 10 - 5x

- Divide to sides by -2

∴ y = -5 + [tex]\frac{5}{2}[/tex] x

∴ y =  [tex]\frac{5}{2}[/tex] x - 5

- The value of m is the coefficient of x

∴ m = [tex]\frac{5}{2}[/tex]

∴ The slope of the given line is [tex]\frac{5}{2}[/tex]

∵ Parallel lines have same slopes

∴ The slope of the parallel line is m = [tex]\frac{5}{2}[/tex]

- Substitute the value of m in the form of the equation

∴ The equation of the parallel line is y = [tex]\frac{5}{2}[/tex] x + b

To find b substitute x and y in the equation by the coordinates of any point lies on the line

∵ The parallel line passes through point (3 , -5)

- Substitute x and y by the coordinates of the point (3 , -5)

∵ x = 3 and y = -5

∴ -5 = [tex]\frac{5}{2}[/tex] (3) + b

∴ -5 = [tex]\frac{15}{2}[/tex] + b

- Subtract [tex]\frac{15}{2}[/tex] from both sides

∴ b = [tex]\frac{-25}{2}[/tex]

∴ The equation of the parallel line is y = [tex]\frac{5}{2}[/tex] x + [tex]\frac{-25}{2}[/tex]

∴ The equation of the parallel line is y = [tex]\frac{5}{2}[/tex] x - [tex]\frac{25}{2}[/tex]

The equation of the parallel line in slope-intercept form is;

y = [tex]\frac{5}{2}[/tex] x - [tex]\frac{25}{2}[/tex]

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Answer:

False.

Step-by-step explanation:

Because we have to isolate y and subtracting 2 will not put y alone on one side.

We have to subtract 2x in order to solve for y.

Answer:

False

Step-by-step explanation:

To solve this equation 2x + y = 5, you need another pair equation with the same variables, or one of the variables (x or y) need to be known to solve this equation.

Or you need to subtract 2x from both side to make y subject of formula.

Answer:

45

Step-by-step explanation:

(6 + 3i)(6 − 3i) =6 (6 − 3i)+ 3i(6 − 3i)

= 36 -18i +18i-9[tex]i^{2}[/tex]

if [tex]i^{2} =-1[/tex]

36 -18i +18i-9[tex]i^{2}[/tex] = 36-9(-1)

=36+9

=45

=36-9i^2

=6^2 - (3i)^2

Answer:

[tex]\displaystyle 45[/tex]

Step-by-step explanation:

[tex]\displaystyle (6 + 3i)(6 - 3i) = 36 - 9i^2 = 36 - 9[-1] = 36 + 9 = 45[/tex]

Extended Information on the Complex Number System

[tex]\displaystyle \sqrt{-1} = i \\ -1 = i^2 \\ -i = i^3 \\ 1 = 4\:[Any\:multiple\:of\:four][/tex]

I am joyous to assist you anytime.

Answer:

Step-by-step explanation:

96:24

96 divide by 24 = 4

so it would be 4 cars to 1 truck

so 4:1

Answer:

4:1                                                                                                               Explanation: because of how when you divide the two its 4 and there's one truck left

Answer: 10(x+2)

Step-by-step explanation:

Answer:

(x+2) + 10

Step-by-step explanation:

(x+2) is his current age, then you add the 10 years to get your answer.

Answer:

Your answer is B: F(x)=(x-1)(x-1)(x-1)(x+1)

Answer:

6000

Step-by-step explanation:

Each mp3 sells at $120 per mp3 player multiply that by 100 its $12000

It cost them $45 per mp3 to be made multiply that by 100 its $4500 then add the $1500 for the week and its $6000

$12000-$6000=$6000

They make a profit of $6000 in a week

The company would make a profit of $6,000 from selling 100 MP3 players in one week after subtracting the total costs of $6,000 from a total revenue of $12,000.

The company's profit when selling 100 MP3 players in one week can be calculated by subtracting the total costs from the total revenue. First, we calculate the total revenue by multiplying the selling price of $120 per MP3 player by the number of players sold, which is 100. This results in a total revenue of $12,000 (120 x 100).

Next, we calculate the total costs, which include a fixed overhead of $1,500 per week and a variable cost of $45 per MP3 player. For 100 players, the variable cost sums up to $4,500 (45 x 100). Therefore, the total costs amount to $6,000 ($1,500 + $4,500).

To find the profit, we subtract the total costs from the total revenue:

Total Revenue = 100 x $120 = $12,000

Total Costs = $1,500 (fixed) + 100 x $45 (variable) = $6,000

Profit = Total Revenue - Total Costs = $12,000 - $6,000 = $6,000

Therefore, the company would make a profit of $6,000 if it sold 100 MP3 players in one week.

Answer:

Yes the mean is greater than the median

Step-by-step explanation:

To find the mean of numbers, you add all of them and divide them by how many there are in total.

75+80+81+96+100= 432

There are five numbers so divide the total by 5.

432÷5= 86.4

That is your mean.

The median is the one in the middle. There are five numbers, so the one in the middle is 81.

The mean is 86.4 and the median is 81.

Answer:

the mean is greater

Step-by-step explanation:

well mean is average so lets do that first

to find the mean, you add all of the percentages up and divide it by the amount of percentage

75 + 80 + 81 + 96 + 100 = 155 + 177 + 100 = 432

and now you divide 432 by 5 to get 86.4

so the mean is 86.4

and the median is the middle:

75 80 81 96 100

           ↑

81 is the median since its in the middle

86.4 > 81

so the mean is greater than the median

Answer: 2

Step-by-step explanation:

Answer:

I am not sure but i think 2

Answer:

B

Step-by-step explanation:

Each box of cookies is $3 since 4 x 3 =12, 6 x 3 = 18, and 9 x 3 = 27. So we want to multiply the number of boxes, b, by 3 to get the cost, c. The correct equation is c = 3b.

An equation that models this situation is c = 3b. The correct option is B.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given the data is,

b     c

4     12

6     16

9     27

c = kb

12 = k x 4

k = 12 / 4 = 3

c = 3b

Therefore, the equation that models this situation is c = 3b. The correct option is B.

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Answer:

-216

Step-by-step explanation:

Negative times positive is negative.

27 * 8 = 216

Answer is negative, so

-27 * 8 = -216

Answer:

-216

Step-by-step explanation:

Write the problem as a mathematical expression. ( − 27 ) ⋅ ( 8 )

multiply -27 by 8