An accountant receives a yearly salary of $72,000. Find his monthly salary.​

Answer:

22

Step-by-step explanation:

AB + BC = AC

4x -6 + 4 = 2x + 10  Combine like terms

4x -2 = 2x + 10  Subtract 2s from both sides of the equation

2x -2 = 10  Add 2 to both sides

2x = 12  Divide both sides by 2

x = 6

Plug in 6 for x in AC

2x + 10

2(6) + 10

12 + 10

22

Answer:

1.5 hour

Step-by-step explanation:

since 1 hour =70km . Then x hour =105 ÷70=1.5 hour

Answer: 6400kg=6.4*10⁶ g

Step-by-step explanation:

6400 kg=

6.4*10³ kg=

6.4*10³*10³ g=

6.4*10³⁺³ g=

6,4*10⁶ g

Answer - 6.4 × 10^6

Step by step Explaination-

6400 kg=

6.4*10³ kg=

6.4*10³*10³ g=

6.4*10³⁺³ g=

6,4*10⁶ g

Firstly, we'll discuss the units of digits -

1. We'll convert 6400 kilograms into grams. Multiply the value in kilograms by the factor '1000'.

2.  Standard form may be a means of writing variety thus it's easier to browse. it's typically used for terribly large or small numbers.

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c.(4x+8y)=60

it is equivalent

Answer:

A and C

Step-by-step explanation:

Substitute 4x + 8y = 12

A:

12+3=15

15=15 ✓

B:

12=10 ×

C:

5(12)=60

60=60 ✓

D:

Multiply 4 to x+2y=6 to make it 4x+8y=12

x+2y=6

4x+8y=24

12=24 ×

Answer:

1) 54+2x=5x−6−18x Distributive Property

2) 60=−15x Division Property of Equality

3) −4=x Division Property of Equality

Explanation:

1.) This answer is Distributive Property because the parenthesis in the original equation were removed through the process of distributing.

3(–2 – 6x) was distributed by multiplying 3 • –2 and 3 • –6x to get –6 – 18x

2.) This answer is Division Property of Equality because for all real numbers x, y, and z, if x = y and z ≠ 0, then x/z = y/z. This is true in this equation because of 60/–15 = −15x/–15.

3.) Division is used to get the value of x, which is –4.

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The amount of money that Ahmed gave to his brother is AED 140.

It is given in the question that Ahmed has AED 180. He gives his brother 0.7  with bar notation of the amount he has.

We have to find the amount given by Ahmed to his brother.

Here, we have to convert a non-terminating but recurring rational number into fraction form.

Let 0.7 bar = x

Multiplying the equation by 10, we get

7.7 bar  = 10x

10x - x = 7.7 bar - 0.7 bar

9x = 7

x = 7/9

Hence, Ahmed gave 7/9 of the amount he had to his brother.

Hence, we can write,

Amount given to Ahmed's brother by Ahmed = (7/9)*180 = AED 140.

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The measure of m∠ABD in the figure shown is 19°.

Given:

∠BCD = 71°

In the figure, ΔABC is an isosceles triangle where AB = BC.

According to the Isosceles Triangle Theorem, an isosceles triangle has equal angles on either side of its equal sides.

So, ∠BAD = ∠BCD = 71°

The sum of angles in a triangle sums to 180°.

∠ABC + ∠BAD + ∠BCD = 180°

∠ABC + 71° + 71° = 180°

∠ABC + 142° = 180°

∠ABC = 180° - 142° = 38°

DB is the angle bisector of ∠ABC.

Now, ∠ABD = ∠CBD = 38°/2 = 19°

The measure of ∠ABD is 19°.

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By using the properties of the 30-60-90 right triangles, the lengths of the long leg and the hypotenuse are √3 · L and 2 · L, respectively.

Right triangles are triangles where one of its internal angles is a right angle, that is, has a measure of 90°. 30-60-90 triangles are right triangles whose internal angles have measures of 30°, 60° and 90°, respectively.

This kind of right triangles have the following features:

If we know that the short leg has a length of L, then the lengths of the long leg and the hypotenuse are √3 · L and 2 · L, respectively.

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Answer: $13,713.75

Step-by-step explanation: 10% of $13,250 = $1,325 (the raise given)

$13,250 - $1,325 = $11,925 (original salary)

15% of $11,925 = $1,788.75

$11,925 + $1,788.75 = $13,713.75

Answer:

what is the symbol between the 2 fractions?

Answer:

x = 9

Step-by-step explanation:

To solve for x, you must isolate the variable.

First, start by adding 2 to BOTH sides to eliminate the 2.

3=1/3x. then divide each side by 1/3

3÷1/3 = x

3/1 × 3/1 = x

9 = x

The least number of visits he needs to make in order to earn a free movie ticket is approximately 15 visits.

Points received for signing up = 85 rewards points

Points received for each visit to the movie theater = 10.5 points

Points needed for a free movie ticket = 240 points

Number of visits = x

85 + 10.5x ≤ 240

10.5x ≤ 240 - 85

10.5x ≤ 155

x ≤ 155 / 10.5

x ≤ 14.761

Approximately,

x ≤ 15 visits

Therefore, Jordan needs at least 15 visits to earn a free movie ticket.

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Step-by-step explanation:

divide volume by product of length and width

54cm³= 3cm x 2cm

54/6= 9cm

L = lbs lost by Leila

N = lbs lost by Nina

since we know that Leila lost "L" lbs and Nina lost 43lbs more than that, so Nina lost then "L + 43", and we also know their total weight was 95lbs hmmmm so

[tex]\stackrel{Leila's}{L}~~ + ~~\stackrel{Nina's}{(L+43)}~~ = ~~\stackrel{total}{95}\implies 2L+43=95\implies 2L=52 \\\\\\ L=\cfrac{52}{2}\implies L=26\hspace{15em}\underset{Nina~lost}{\stackrel{26~~ + ~~43}{\text{\LARGE 69}~lbs}}[/tex]

Answer:

b

Step-by-step explanation:

because he borrowed $2 everyday and now he owes 10 so b

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The constant of the proportionality is 5.

Constant of proportionality:

The word constant of proportionality refers the ratio that relates two given values in what is known as a proportional relationship.

Given,

Greg has to find the area of a rectangle. The area can be determined by the equation A=5I, where A is area and I is the length of rectangle.

Here we need to find the constant of proportionality.

Through the given question we know that the area of the rectangle is

A = 5l

Here A represents the area of the rectangle

and the letter "l" denotes the length of the rectangle.

While we compare these with the standard form,

y = mx

Here m represents the constant of proportionality.

While in the given equation the place of m in standard equation number 5 is presented.

Therefore, 5 is the constant of proportionality.

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Answer:

A

Step-by-step explanation:

using the sine ratio and the exact values

sin30° = [tex]\frac{1}{2}[/tex] and sin60° = [tex]\frac{\sqrt{3} }{2}[/tex]

calculate the height of the wall below x , call it h

the hypotenuse is the length of the ladder

using the sine ratio in the lower right triangle.

sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{h}{18}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

2h = 18 ( divide both sides by 2 )

h = 9

lower part of the wall is 9 meters

using the sine ratio in the right triangle on the right

sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{9+x}{18}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )

2(9 + x) = 18[tex]\sqrt{3}[/tex] ( divide both sides by 2 )

9 + x = 9[tex]\sqrt{3}[/tex] ( subtract 9 from both sides )

x = 9[tex]\sqrt{3}[/tex] - 9 = 9([tex]\sqrt{3}[/tex] - 1)

Answer:

[tex]\textsf{A)} \quad x=9(\sqrt{3}-1)[/tex]

Step-by-step explanation:

Interior angles of a triangle sum to 180°.  Therefore, if the ladder makes an angle of 30° with the ground, the angle it makes with the wall is 60°.

Therefore, the two triangles are congruent as their corresponding angles are the same and the length of their longest side (hypotenuse) is the same.

30-60-90 Triangle Theorem

A 30-60-90 triangle is a special right triangle where the measures of its angles are in the ratio 1 : 2 : 3 and the measure of its sides are in the ratio 1 : √3 : 2.

The formula for the sides is  b : b√3 : 2b  where:

Therefore, as the length of the hypotenuse is 18:

[tex]\implies 2b=18[/tex]

[tex]\implies b=9[/tex]

[tex]\implies b\sqrt{3}=9\sqrt{3}[/tex]

To find x, subtract the length of the shortest leg of the right triangle from the length of the other leg of the right triangle:

[tex]\implies x=9\sqrt{3}-9[/tex]

[tex]\implies x=9(\sqrt{3}-1)[/tex]

Answer:

3.2

Step-by-step explanation:

→ State Pythagoras theorem

x² + y² = z²

→ Substitute in

3² + 1²

→ Simplify

10 = z²

→ Evaluate

√10 = 3.2

Answer:

3.2

Step-by-step explanation:

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

a = 3

b = 1

[tex]3^{2}[/tex] + [tex]1^{2}[/tex]  = 9 + 1 = 10

[tex]c^{2}[/tex] = 10

c = [tex]\sqrt{10}[/tex]

c = 3.16227766017

Round to the nearest tenth

c = 3.2

The surface area and the volume of solid prism are 432in² and 576in³ respectively.

A rectangular prism is simply a three-dimensional solid shape which has six faces that are rectangles

The surface area of a rectangular prism is expressed as;

A = 2( wl + hl + hw )

The volume of a rectangular prism is expressed as;

V = w × h × l

Where w is the width, h is height and l is length.

Given the data in the question;

The surface area of the solid is;

A = 2( wl + hl + hw )

A = 2( (8in × 12in) + (6in × 12in) + (6in × 8in) )

A = 2( 96in² + 72in² + 48in² )

A = 2( 216in² )

A = 432in²

Therefore, surface area of the rectangular prism is 432in²

The volume of the solid is;

V = w × h × l

V = 8in × 6in × 12in

V = 576in³

Therefore, volume of the rectangular prism is 576in³

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Answer:

x-0.5,1,2,3,4,5,6

y-12,6,3,2,1.5,1

Step-by-step explanation:

Substitute the x value inside the formula. E.g. y=6 over 0.5, then solve.

Plot the points on the graph and join the up.

Answer:

Step-by-step explanation:

The amount by which an apple is more expensive than a pear is; D: 4p

We are told that  5 apples and 3 pears costs 8p more than 3 apples and 5 pears.

Let the cost of apples be x and let the cost of pears be y. Thus, the equation that represents the sentence is;

5x + 3y = 3x + 5y + 8

Rearrange to get;

5x - 3x + 3y - 5y = 8

2x - 2y = 8

divide both sides by 2 to get;

x - y = 4

Thus;

x = 4 + y

Which means it costs 4p more

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The weight of the twelve people on the elevator is 1,825 pounds.

And the weight of the thirteen person is given by the inequality:

x ≤ 175

We have an elevator with 12 people in it, such that the weights of these 12 people are:

175, 140, 135, 155, 170, 190, 125, 160, 150, 150, 130, 145

To find the total weight we just need to add these numbers, we will get:

175 + 140 + 135 + 155 + 170 + 190 + 125 + 160 + 150 + 150 + 130 + 145 = 1,825

So the 12 people in the elevator have a total weight of 1,825 pounds.

Now, the weight limit is 2,000 pounds.

So if we define x as te weight of the 13 th person, we can write the inequality:

1,825 + x ≤ 2,000

x ≤ 2,000 - 1,825

x ≤ 175

So the person can weight at mos 175 pounds.

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Option (B) Yes, it is proportional because the ratios for miles per hour are all equivalent to 1.25 miles per hour is correct.

It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.

It is given that:

A group of hikers tracked how long it took to hike a 10-mile trail. They hiked 2.5 miles in 2 hours, 7.5 miles in 6 hours, and 8.75 miles in 7 hours.

From the data given:

Ratio = distance/time

2.5 / 2 = 1.25 miles per hour

7.5 / 6 = 1.25 miles per hour

8.75 / 7 = 1.25 miles per hour

Thus, option (B) Yes, it is proportional because the ratios for miles per hour are all equivalent to 1.25 miles per hour is correct.

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No. there is no rigid transformation taking Rectangle A to Rectangle B. See the explanation below.

The type of transformation that is taking place in the attached image from Rectangle A to Rectangle B is a non-rigid transformation. This is is because A rigid transformation (or isometry) is a transformation that DOES NOT change the size or shape of a geometric figure.

As it is easily observed, rectangle A is no longer the same shape and size as B. This means that the change or transformation that has occurred is non-rigid.

It is to be noted that dilation is a transformation that keeps the figure's geometry and orientation but alters its size. A dilation's scale factor is the factor by which each linear measure of the figure (such as a side length) is multiplied.

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The possible values of the number will be -62/4 or -31/2.

Multiplication of numbers may be defined as the tool or arithmetic operation which can be used to increase the count of a number. For example, if there is a number 4, then in order to increase the number it will be multiplied with some other number like 9. Now, the number will be 4×9 = 36. We are given that the product of -4 with a number gives the answer as 62. Let us assume the number as x and form the equation in accordance with the data given in the question.

-4×(x) = 62

Now, to find x we divide -4 on both the sides and we get

x = -62/4

This number can also be simplified by dividing both numerator and denominator with 2 and we get

x = -31/2.

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The value of n is 1/2 and it is not an even number or odd number

From the question, the steps are given as

n + n + 1 = 2n + 1

n + n + 1 = 2n+2-1

n + n + 1 = 2(n+1) -1

Also, from the question, we have the result of the expression to be

2

This means that

n + n + 1 = 2

Substitute n + n + 1 = 2(n+1) -1 in the equation n + n + 1 = 2

So, we have

2(n + 1) - 1 = 2

Add 1 to all sides of the equation

So, we have

2(n + 1) = 3

Divide both sides of the equation by 2

So, we have

n + 1 = 3/2

Subtract 1 from all sides

n = 1/2

The above implies that the number n is neither an even number, nor an odd number

This is so because the result is a fraction

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Answer:60°

Step-by-step explanation:the whole thing equals 180° since it is a straight line. 30°+90°=120°   180°-120°=60°

Answer:

15

Step-by-step explanation:

40/100×25

=10

25-10=15