List all the factors of 12.

Equivalent equations (acceptable moves)

(1)  

4(x+3)=32

       x+3 = 8

(2)

[tex]\frac{(9x+4)}{2} =5\\\\9x+4=10[/tex]

(3)

x- 7+ 3x=25

4x-7=25

Not equivalent (unacceptable moves)

(1)

2(x+5) = 10

2x+5 =  5( 20 is wrong)

(2)

2x+4=22

2x= 22-4= 18 (26 is wrong)

(3)

[tex]\frac{(6x-1)}{3} =27\\\\6x-1=81[/tex] (9 is wrong)

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Answer:

[tex]\frac{h^6}{h^8}[/tex]

Step-by-step explanation:

1. For now, let's leave the [tex]g^{-6}[/tex] to the side and just worry about the [tex]\frac{h^8}{h^2}[/tex].

2. When you apply the exponent rule you should have learned in class, we know that when you divide two bases with exponents, the exponents subtract. So, you can subtract 8 - 2, and then the greater digit's place in the fraction stays. So, since [tex]h^8\\[/tex] is the greater number (and it's in the numerator), you put the [tex]h^6[/tex] in the numerator as well.

The equation that passes through the given point 2x-3y=0.

Let the point which they pass be the origin (0,0).

From the given equation we get [tex]y= 2/3x + 19[/tex]

On comparing this with the general equation that is [tex]y= mx+c[/tex]

We get [tex]m= 2/3[/tex]

Thus as we know the equation of line is [tex]y-y1 = x-x1[/tex]

Substituting the values in this equation we get;

[tex]y-0= 2/3(x-0)[/tex]

On cross multiplying we get

[tex]3y=2x[/tex] or [tex]2x-3y=0[/tex]

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the rate from the plane to the radar station increasing 3 minutes later is 19.81 km/min

A plane flying with a constant speed of 14 km/min passes over a ground radar station at an altitude of 4 km and climbs at an angle of 45 degrees. At what rate is the distance from the plane to the radar station increasing one minutes later?

speed (Δs₁)= change in distance(Δd₁) /(Δt₁)change in time

mathematically,

(Δd₁) /(Δt₁) = Δs₁

= 14 km/min = (Δd₁) /(Δt₁)

and will are to find the speed after passes the radar

=Δs₂  km/min = (Δd₂) /(Δt₂)

to find distance d₁ and d₂ with respect to angle 45 degree at 4km

sin 45 = opp/hyp = 4/d₁

d₁ = 4/sin45 = 5.66km

tan 45 == opp/adj = 4/d₂

d₂ =4/tan45 =  4km

for one minute increment,

=1 x d₁ x Δs₁ = 1 x d₂ Δs₂

= 1x5.66x14 = 1x 4 xΔs₂

= 79.24 = 4Δs₂

speed =Δs₂ = 19.81km/min

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Answer: 14 mile/s2

Step-by-step explanation:

Answer:

|-17| = 17, so -3 + |-17| = -3 + 17 = 14

The ways in which the linear systems are similar to quadratic systems includes:

The linear system means the model based on the use of a linear operator and, they exhibit features and properties that are much simpler than the nonlinear case. The quadratic system of equations consists of only quadratic equations.

The linear & quadratic systems are solved by graphing and substitution. In the linear systems, we get the lines and in quadratic systems, we get curves. In conclusion, the point of intersection of two lines or curves are the solutions of the respectively system.

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Answer:

y = 32

Step-by-step explanation:

With this problem, we will use the direct variation form, y = kx.

k = proportionality constant.

Substitute the known inputs of x = 8 and y = 16 into the direct variation form:

y = kx turns into 16 = k(8)

Get k by itself by dividing 8 on both sides:
16/8 = k

2 = k

Now that we know the k value is 2, we input everything we know into the direct variation form if x were equal to 16

k = 2

x = 16

y = kx:

y = 2(16), making y equal to 32

Answer:

lol doofus

Step-by-step explanation:

Answer:

168 straberries was rotten

Step-by-step explanation:

The percent of young men that are shorter than the mean height of young women is 2.5%.

A data set with a normal distribution has the majority of its values clustered in the middle of the range and the remaining values tapering off symmetrically toward either end.

A continuous probability distribution for a real-valued random variable is known as a "normal distribution" in statistics.

Based on the information, the percentage will be calculated thus:

Z = (69.3 - 64) / 2.7 = 1.9630

So P(Z>1.96)= 1-P(Z<1.96)

(check standard normal table)

= 1-0.975

= 0.025

= 2.5%

The percentage is 2.5%.

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The most appropriate choice for complementary angle will be given by:

∠A = 27°

What are complementary angles?

Two angles are said to be complementary if the sum of the two angles is 90°

Here,

∠A = (2x + 5)°

∠B = (4x + 19)°

∠A and ∠B are complementary

(2x + 5) + (4x  + 19) = 90

6x + 24 = 90

6x = 90 - 24

6x = 66

x = [tex]\frac{66}{6}[/tex]

x = 11

∠A = 2 x 11 + 5

     = 22 + 5

     = 27°

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Complete Question

∠ A and ∠B complementary angles. If m∠A =  (2x + 5)°  and m∠B  = (4x + 19)°, then find the measure of ∠A.

The quantity of space inside a form is measured by its volume.
The volume as a function of side length(x) is: V(x) = 4x³ - 40x² + 100x

What is volume functions?
A three-dimensional space's volume can be calculated. It is frequently quantified numerically by different imperial units or SI-derived units. Volume and length have a mutually reliant relationship.

Given, length of the cardboard = 10 units
Width of the cardboard = 10 units
When side length(x) is removed from the cardboard, the dimension of the box becomes:
Length of the new cardboard = (10 - 2x) units
Width of the new cardboard = (10 - 2x) units
Height of the new cardboard = x units
Therefore, volume of the new cardboard box, V(x)
= Length*Width*Height
= x*(10 - 2x)*(10 - 2x) cubic units
= 100x² - 20x² - 20x² + 4x³
= 4x³ - 40x² + 100x

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Answer:

369,962

Step-by-step explanation:

If the rounding digit is 0, 1, 2, 3, or 4, drop all the digits to the right of it

If the rounding digit is 5, 6, 7, 8, or 9, add one to the rounding digit and drop all digits to the right of it

For this question, notice that:

This are 3 different ways to name

Answer: Area= [tex]\frac{bh_{b} }{2}[/tex]

Example:

Let the base be 3 and the height([tex]h_{b\\}[/tex]) 4

So,

Area= [tex]\frac{3*4}{2\\}[/tex]-->[tex]\frac{12}{2}[/tex]=6

Angle A is located in the third quadrant and solved to be a value of  255.522 degrees.

A quadrant refers to fourth division. In a circle, a quadrant represents a quarter of a circle.

In angle calculations, there are 4 quadrants. The first quadrant is between angles 0 to 90 degrees. The second quadrant is between angles 90 to 180 degrees. The third quadrant is between angles 180 to 270 degrees. The fourth quadrant is between 270 to 360 degrees.

The each quadrant is at 90 degrees interval. and the in angle calculations, the rotation is in anticlockwise direction

cos A = 1/4

where 270°

270 degrees represent the third quadrant. Hence angle A is in the third quadrant

solving for angle A

let cos a = 1/4

a = arc cos ( 1/4 )

a = 75.522 degrees ( in first quadrant )

A = a + 180 degrees

A = 75.522 degrees + 180 degrees

A = 255.522 degrees

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Answer:

8,377.58 [tex]mi^{3}[/tex]

Step-by-step explanation:

To solve for the volume of a right circular cone like the one in the picture, you use [tex]\pi[/tex][tex]r^{2}[/tex][tex]\frac{h}{3}[/tex].

Plug in the radius and height to get [tex]\pi[/tex][tex]20^{2}[/tex][tex]\frac{20}{3}[/tex].

Then solve (and round to the nearest hundredth) and you should get 8,377.58.

The exponent that is understood on the base x in the given expression is; 1

The exponent of a number tells us how many times to use the number in a multiplication. Exponents are also called Powers or Indices. For example in the exponent form ab^(x), we can say that;

The base is a and its' exponent is 1.

Applying the above to our question gives us;

If the exponent form is xy^3, then we can say that;

The base is x.

We can see that there is no exponent attached to x and as such we will use 1 as 1 will still give us the value of x.

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Answer:

Not 100% sure what it's asking but if it's asking what number she used to estimate the 240, she used 100 because it's one-off 99. The actual number would be 237.6

Step-by-step explanation:

The bonus based upon the given formula is $2606.15 approximately

Given,

Annual salary = $48,000

Yearly sales = $76,000

Bonus is given according to the formula:

2 weeks salary + 1 percentage commission

Here,

Annual salary is given as $48,000

We have to find the weekly salary:

There is 52 weeks in a year.

So, salary for one week = Annual salary / number of weeks =  48000/52 = $923.077

Now, salary for two weeks = 923.077 × 2 = $1846.154

Rate of annual commission is 1%

The commission amount:

1% of yearly sales = 1% of 76000 = (1/100) × 76000 = $760

So,

The bonus amount = 2 weeks salary + 1 percentage commission

The bonus amount = 1846.154 + 760

The bonus amount = 2606.154

Therefore, the bonus given based upon the given formula is $2606.154

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Given,

Decrement of 17 inches takes  1 year.

So, Decrement of 1  inches takes [tex]\frac{1}{17}[/tex] year.

therefore, decrement of 255 inches will take [tex]\frac{255}{17}[/tex] years, which is, 15 years.

So, the answer is 15 years.

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Answer:

Step-by-step explanation:

Answer:

-31

Step-by-step explanation:

[tex]-38-16-(-23) \\ \\ =-38-16+23 \\ \\ =-54+23 \\ \\ =-31[/tex]

The solution of each of the given exponents are;

1) 10x⁸y⁴/(-6x⁴y⁵) = -5x⁴/3y

2) (-4x³ * x² y⁴)/(-2x³y⁴) = 2x²

3) (3n⁴)² = 9n⁸

4) (5x⁶y⁰)² = 25x¹²

The Laws of Exponents are;

Thus;

1) 10x⁸y⁴/(-6x⁴y⁵) = -(10/6)x⁸⁻⁴y⁴⁻⁵

= -5x⁴/3y

2) (-4x³ * x² y⁴)/(-2x³y⁴)

= (-4/-2)(x⁵⁻³)(y⁴⁻⁴)

= 2x²

3) (3n⁴)² = 3² * n⁴*²

= 9n⁸

4) (5x⁶y⁰)²

= 5²x⁶*²y⁰*²

= 25x¹²

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Answer:

4/ 25x¹²

Step-by-step explanation:

Because y^0 will cancel any thing!

So we have left 5x^6 times 5x^6

Same base so add square root of ^6 = 5x^12

well, let's keep in mind that whenever the x-coordinate is the same, we have a vertical line, so, Check the picture below.

Using the slope concept, the distance from point AA to point BB ≅ 360 feet.

The slope is given by the vertical change divided by the horizontal change.

It's also the tangent of the angle of depression.

We can get, the vertical change is of 144 feet.

At point A, the angle is of 9º, while the horizontal position is of [tex]x_{A}[/tex] ,

Then, we can write,

tan 9º =  [tex]\frac{144}{x_{A} }[/tex]

[tex]x_{A}[/tex] = 144/tan 9º

Hence, tan 9º = 0.15

[tex]x_{A} =[/tex] 144/0.15

[tex]x_{A}[/tex] = 960

At point A, the angle is of 14º, while the horizontal position is of [tex]x_{B}[/tex] ,

Then, we can write,

[tex]x_{B}[/tex] = 144/tan 14º

Hence, tan 14º = 0.24

[tex]x_{B}[/tex] = 144/0.24

[tex]x_{B}[/tex] = 600

So, the distance in feet is of:

d = [tex]x_{A} -x_{B}[/tex]

d = 960 - 600

d = 360

d ≅ 360

Therefore,

A boat is heading towards a lighthouse, then the distance from point AA to point BB ≅ 360 feet.

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The probability that a randomly chosen applicant has over 5 years of experience is 0.2768.

It should be noted that probability simply has to do with the likelihood that an event will happen.

From the information, out of 457 applicants for a job, 271 have over 5 years of experience and 75 have over 5 years of experience.

Therefore, the probability that a randomly chosen applicant has over 5 years of experience will be:

= Number of graduate over 5 years / Number of people over 5 years experience

= 75 / 271

= 0.2768

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