How do you write a proof for this

The mathematical reasoning for the first step is; Distributive Property

We want to multiply the linear expressions; -2n and ³/₄n.

The first step will be to express them with the multiplication sign to get and factorize;

-2n × ³/₄n

Now, since n is common to both terms, we will factorize it out to get;

n(-2 × ³/₄)

Now, that operation above is termed as a distributive property because we know that the algebra distributive property is;

a(b + c) = ab + ac

Or a(b × c) = ab × ac

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Answer:

communitave property i think

Step-by-step explanation:

Answer:400%

Step-by-step explanation: by the commutativity of multiplication we find (2x)^2=4(x^2)=4(y)

Answer:

dependent: your distance from home

independent: number of miles you walk

Step-by-step explanation:

lmk if you want an explanation

Answer: This looks like it is a reflection of the y-axis and then an enlarging dilation.

Answer:

5.1 yd

Step-by-step explanation:

tan(25°) = x/11

x = 11tan(25°)=5.1 yd

The Voltage of the given Circuit is gotten as; V = 36 - 2j Volts

We are given;

Current; I = 3 + 4j amps

Resistance; R = 4 - 6j ohms

From ohms law, we know that;

V = IR

Thus;

V = (3 + 4j) * (4 - 6j)

V = 12 + 16j - 18j - 24j²

Now, in vector notation; j² = -1. Thus;

V = 12 - 2j + 24

V = 36 - 2j Volts

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The average rate of change of the function in the given interval -3 ≤ x ≤-1 is 10.

The average Rate of Change of the function f(x) can be calculated as;

[tex]f(x) = \dfrac{f(b) - f(a)}{b-a}[/tex]

Interval -3 ≤ x ≤-1

a = -3, b = -1

f(a) = f(-3) = -20

f(b) = f(-1) = 0

Step 2: Find Average

[tex]f(x) = \dfrac{f(b) - f(a)}{b-a}\\\\\\f(x) = \dfrac{f(-1) - f(-3)}{-1-(-3)}\\\\\\f(x) = \dfrac{0 - (-20)}{2}\\\\f(x) = 10[/tex]

Therefore, the average rate of change of the function in the given interval -3 ≤ x ≤-1 is 10.

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Answer:

A(2, 8)

B(4, 4)

C(-4, 2)

Step-by-step explanation:

Multiply all the coordinates by 2

The value of x when y = 2 is -19/7

A direct variation from x to y is represented as:

x = ky

Where k represents the variation constant.

x = -19 when y = 14.

So, we have:

-19 = 14k

Make k the subject

k = -19/14

Substitute k = -19/14 in x = ky

x = -19y/14

When y = 2, we have:

x = -19 * 2/14

Evaluate

x = -19/7

Hence, the value of x when y = 2 is -19/7

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Answer:

BC ≈ 19.4 cm

Step-by-step explanation:

using the cosine ratio in the right triangle

cos71° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AB}{BC}[/tex] = [tex]\frac{6.3}{BC}[/tex] ( multiply both sides by BC )

BC × cos71° = 6.3 ( divide both sides by cos71° )

BC = [tex]\frac{6.3}{cos71}[/tex] ≈ 19.4 cm ( to 3 sig. figs )

Answer:

19.4°

Step-by-step explanation:

I put the image of how I did it if you don't understand let me know

Answer:

See below

Step-by-step explanation:

3 and 5     have a LCM of 15    which is  3 * 5

A function assigns the values. The inverse of the function in terms of the area will be b=(a/7)-5.

A function assigns the value of each element of one set to the other specific element of another set.

The complete question is,

The function a(b) relates the area of a trapezoid with a given height of 14 and one base length of 5 with the length of its other base. It takes as input the other base value, and returns as output the area of the trapezoid. a(b)=14 x b+5/2. Write a function in terms of area to find the length of the other side.

The given is the function of the area of the trapezoid, a(b)=14 x b+5/2.

The area of a trapezoid is given as,

Area = Height × [(Sum of parallel sides)/2]

The given function can be written in terms of area as,

[tex]a = 14\times \dfrac{(b+5)}{2}\\\\\dfrac{2(a)}{14} = b+5\\\\\dfrac{2(a)}{14} -5= b\\\\\dfrac{(a)}{7} -5= b[/tex]

Hence, the inverse of the function in terms of the area will be b=(a/7)-5.

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There are two triangles in the figure(triangular prism) option third is correct.

When a triangle is, stretch it out to produce a stack of triangles, one on top of the other. A triangular prism is a name given to this novel 3D object.

The complete question is:

How many triangles are needed to draw the net of this object?

For the figure please refer to the attached picture.

As we can see in the figure we have given a triangular prism:

The triangular prism has two triangles.

A triangle for the base of the prism and a triangle for the top of the prism.

The lateral faces of the prism are rectangular.

Thus, there are two triangles in the figure(triangular prism) option third is correct.

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Step-by-step explanation:

find the Lcm of 15 and 10 which is 30

multiply the 2fractions by the LCM

8/15*30=16

3/10*30=9

add the products and put them all over the Lcm

(16+9)/30

=25/30 which is equivalent to 5/6 when you divide both the numerator and the denominator by 5

Answer:

The range is all real numbers.

Step-by-step explanation:

The function shown is a line (and not a horizontal line).

The range is all the y's on the graph or all the y's that can be generated by the equation of the function.

f(x) = 3x + 9

You could put ANY, literally any, number in place of the f(x) and be able to calculate an x for it. Looking at the graph of this line, you could go up and down the y-axis to infinity in either direction, and the graph of the line would be there.

The range is All Real Numbers.

Answer:

m= –4

So, you only need to of the points to find the slope, why not choosing the first two:

[tex]m = \frac{y2 - y1}{x2 - x1} = = = > \\ m = \frac{12 - 8}{ - 3 - ( - 2)} = = = > \\ m = \frac{4}{ - 1} = - 4[/tex]

so basically, this is the slope your looking for

Answer:

4500 sec

Step-by-step explanation:

1hr 15min= 75 min

75 x 60=4500

Answer:

DE

Step-by-step explanation:

........................

Answer:

I think the answer is 4

Step-by-step explanation:

The Volume and Surface Area of Prism is 294 in² and 114.33 in³.

A large structure built especially in ancient Egypt that usually has a square base and four triangular sides meeting at a point and that contains tombs.

Surface rea of rectangular prism,

= 2( lb +bh +lh)

= 2 ( 7*7 + 7*7+ 7*7)

= 2 ( 49+49+49)

= 2*3*49

= 294 in²

Now, Volume,

= bhl/3

= 7*7*7/3

= 114.33 in³

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Answer:

$3,272

Step-by-step explanation:

Continuous Compounding Formula

[tex]\large \text{$ \sf A=Pe^{rt} $}[/tex]

where:

Given:

Substitute the given values into the formula and solve for A:

[tex]\sf \implies A=2600e^{(0.023 \times 10)}[/tex]

[tex]\sf \implies A=2600e^{0.23}[/tex]

[tex]\implies \sf A=3272.360026...[/tex]

Therefore, the value of the account after 10 years is $3,272 to the nearest dollar.

Answer:

29.5

Step-by-step explanation:

Use PEDMAS

P - Paraenthesis

E -Exponents

D - Divsion

M - Multiplication

A and S - Addition and subtraction respectively.

First multiply 4.2 and 7 as they are inside the parenthesis

Then find 2² which 4

(4.2 *7) - 10.4 *2² + 2.9*3 - 6 = 29.4 - 10.4 ÷2² + 2.9*3 - 6   {Parenthesis}

                                              = 29.4 - 10.4÷4 + 2.9*3 - 6   {Exponents}

                                               = 29.4 - 2.6 + 2.9*3 - 6    {Division}

                                              = 29.4 - 2.6 + 8.7 - 6   {Multiplication}

                                              = 29.5

The Unpaid balance is $94.32, Finance charge is $1.179 and new balance is $148.079.

Unpaid balance:

Unpaid balance=Previous balance-Payments/credits

Unpaid balance=$179.32-$85.00

Unpaid balance= $94.32

Finance charge:

Finance charge =Finance charge×Monthly rate

Finance charge=$94.32×1.25%

Finance charge=$1.179

New balance:

New balance =Previous balance-(New purchases-Payments/credits)+Finance charges

New balance=$179.32-($117.42-$85.00)+$1.179

New balance=$179.32-$32.42+$1.179

New balance=$148.079

Therefore the Unpaid balance is $94.32, Finance charge is $1.179 and new balance is $148.079.

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Answer:

94.32

1.18

212.92

in order

Step-by-step explanation:

Answer:

the area is 25/4 π

Step-by-step explanation:

diameter is 5 m

area will be 25/4π

Answer:

  17.9 m²

Step-by-step explanation:

The area of the deck is the difference between the area of the square and the area of the circular hot tub.

__

The area of the square is given by the formula ...

  A = s² . . . . where s is the side length

For a side length of 5 m, the area is ...

  A = (5 m)² = 25 m²

The area of a circle is found from the formula ...

  A = (π/4)d² . . . . where d is the diameter

For a diameter of 3 m, the area is ...

  A = (π/4)(3 m)² = 9/4π m² ≈ 7.069 m²

The area of the deck is the difference between the square area and the circle area:

  deck area = 25 m² -7.069 m² ≈ 17.9 m²

The area of the deck surrounding the hot tub is about 17.9 m².

[tex] {a}^{3} . \\ \\ {a}^{5}. \\ \\ {a}^{9} . \\ \\ {a}^{m + n}. \\ \\ {x}^{1} = x.\\ \\ {x}^{3}. \\ \\ {x}^{3}. \\ \\ {x}^{m - n} . \\ \\ {y}^{6} . \\ \\ {y}^{12} . \\ \\ {y}^{18} . \\ \\ {y}^{ab}. \\ \\ 1. \\ \\ 1. \\ \\ {px}^{1} = px.[/tex]

[tex]343 .\\ \\ 16 .\\ \\ 3125 .\\ \\ \frac{ - 8}{27} .[/tex]

Answer: 11

Step-by-step explanation:

By the trapezoid midsegment theorem, x = (9+13)/2 = 11

Answer:

3rd option

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, - 2) and (x₂, y₂ ) = (4, - 1) ← 2 points on the line

m = [tex]\frac{-1-(-2)}{4-0}[/tex] = [tex]\frac{-1+2}{4}[/tex] = [tex]\frac{1}{4}[/tex]

the line crosses the y- axis at (0, - 2 ) ⇒ c = - 2

y = [tex]\frac{1}{4}[/tex] x - 2 ← equation of line

__________________________________________________________

[tex]\text{\textbf{Hello!} In this question, we are trying to figure out the \underline{equation} of the line}\\\text{with the given information.}[/tex]
__________________________________________________________

[tex]\textbf{Explanation:}\\\quad{}\\\text{In the question, we were given our \emph{slope} (gradient) and a \emph{point}. This will help}\\\text{us solve our problem.}\quad{}\\\\\text{Slope: 2 }\\\\\text{Point: (1, 4)}\\\quad{}\\\text{In order to find the equation, we will be using the \underline{point-slope formula:}}\\\quad{}\\y - y1 = m(x - x1)\\\quad{}\\\text{With this equation, we would plug in our given values to its}\\\text{correct variable and solve.}[/tex]
__________________________________________________________

[tex]\textbf{Solve:}\\\\\text{Use the point-slope formula to solve.}\\\\y - y1 = m(x - x1)\quad{}\\\\\text{Plug in 2 to m, 1 to x1, 4 to y1 and then solve.}\\\\y - 4 = 2(x - 1)\\\\\text{Use the \underline{distributive property} to distribute the 2.}\\\\y - 4 = 2x - 2\\\\\text{Add 4 to both sides to cancel the 4 on the left and move the remainder}\\\text{to the right side of the equal sign.}\\\\y = 2x + 2\\\\\text{Since we can't simplify any further, our answer is: \fbox{y = 2x + 2}}[/tex]
__________________________________________________________

[tex]\textbf{Answer:}\\\\\text{Therefore, the equation of the line (our final answer) would be \fbox{y = 2x + 2}}[/tex]
__________________________________________________________

Answer:

AB = 102

Step-by-step explanation:

the median CT bisects the side AB at T , then

BT = AT , that is

7x + 9 = 5x + 21 ( subtract 5x from both sides )

2x + 9 = 21 ( subtract 9 from both sides )

2x = 12 ( divide both sides by 2 )

x = 6

then

AB = 5x + 21 + 7x + 9 = 12x + 30 = 12(6) + 30 = 72 + 30 = 102

The measure of AB is 102.

How to estimate the measure of AB?

The median CT bisects the side AB at T, then

BT = AT

7x + 9 = 5x + 21

subtracting 5x from both sides of the equation, we get

2x + 9 = 21

subtract 9 from both sides, and we get

2x = 12

Divide both sides by 2, we get

x = 6

then, AB = 5x + 21 + 7x + 9

AB = 12x + 30

Substituting the value of x,

12x + 30 = 12(6) + 30

= 72 + 30

AB = 102

Therefore, the measure of AB is 102.

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