What is the parity of the sum of 80 consecutive natural numbers?

Rational equations can be used to solve a variety of problems that involve rates, times and work. Using rational expressions and equations can help you answer questions about how to combine workers or machines to complete a job on schedule.

Answer:

Question 1: [tex]x=4[/tex]

Question 2: [tex]x= \pm7[/tex]

Question 5: The dimensions of one face of the container are 6 by 6 inches.

Step-by-step explanation:

Hi there!

Question 1

[tex]x^3=64[/tex]

Rewrite 64 as a power of 3:

[tex]x^3=4^3[/tex]

(We could find that 4³ = 64 through trial and error)

This above equation makes it true that x=4. If aⁿ = bⁿ, then a=b:

[tex]x=4[/tex]

Question 2

[tex]x^2=49[/tex]

Rewrite 49 as a power of 2:

[tex]x^2=7^2[/tex]

Again, we could have found this through trial and error, or by looking at our multiplication tables.

[tex]x=7[/tex]

However, remember that positive and negative numbers will all square to be a positive number. So, therefore, x can be -7 OR 7 (since both, when squared, equal 49):

[tex]x= \pm7[/tex]

Question 5

Let x be equal to the length of one edge of the cube.

Volume of a cube formula: [tex]V=x^3[/tex]

Plug in the given information, when V is the volume:

[tex]216=x^3[/tex]

Rewrite 216 as a power of 3:

[tex]6^3=x^3[/tex]

^ We could have found this through trial and error.

[tex]x=6[/tex]

Therefore, the dimensions of one face of the container are 6 by 6 inches.

I hope this helps!

Answer:

20

Step-by-step explanation:

40 x 50% = 20

So 50% of 40 equals to 20. Now, since it says decreased by 50%, we have to subtract 20 from 40 because we already know that 20 is the 50%. So 40 - 20 gives you 20.

Answer:

16 times

Step-by-step explanation:

Membership cost:

C = 135 + 2x

Non-members:

C = 11x

____

135 + 2x = 11x

135 = 9x

x = 15

The cost would be the same after renting 15 times, so after 16 times the cost would be cheaper for a member.

Answer:

A

Step-by-step explanation:

A. is the answer I'm sure

Answer:

3 slices of pizza.

Step-by-step explanation:18/6=3

Answer:  hope this helps    i didnt see any  A, B, C, D etc  options to choose from

each point of the given figure has to be changed from (x, y) to (-y, x)

Step-by-step explanation:

When we rotate a figure of 90 degrees counterclockwise, each point of the given figure has to be changed from (x, y) to (-y, x) and graph the rotated figure.

Example 1 :  

Let F (-4, -2), G (-2, -2) and H (-3, 1) be the three vertices of a triangle. If this triangle is rotated 90° counterclockwise, find the vertices of the rotated figure and graph.

Solution :  

Step 1 :

Here, triangle is rotated 90° counterclockwise. So the rule that we have to apply here is

(x, y) -------> (-y, x)

Step 2 :

Based on the rule given in step 1, we have to find the vertices of the rotated figure.

Step 3 :

(x , y) -----> (-y , x)

F(-4 , -2) -------> F'(2, -4)

G(-2, -2) -------> G'(2, -2)

H (-3, 1) -------> H'(-1, -3)

Step 4 :

Vertices of the rotated figure are        

F'(2, -4), G'(2, -2) and H'(-1, -3)  

The measure of m∠14 is 110 degrees and the angle relationship is a supplementary angles

Let us assume that angle m∠10 and m∠14 are supplementary, this means that the sum of both angles will be 180 degrees.

Since the angles are supplementary, hence the required expression will be:

m∠10 + m∠14 = 180

Given that m∠10 = 70 degrees

70 + m∠14 = 180

m∠14 = 180 - 70

m∠14 = 110 degrees

Hence the measure of m∠14 is 110 degrees and the angle relationship is a supplementary angle.

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hijab day of doing a great day of doing a little bit more about the way for me the ch-2 ex is a very good time to be able to get the day of doing a great day when mother speaks it happens to be a good time to be a good time to be a good day please anyone who is in the day and in the way for me the way

Answer:

c

Step-by-step explanation:

edge 2022

Answer:

1. Yes and for 2. I don't know

Step-by-step explanation:

1. is a monomial because 21/27 is one group

Answer:66  dollars

Step-by-step explanation:110 - 44 = 66

Answer:

Length = 30

Width = 5

Step-by-step explanation:

So the formula for perimeter is

P = 2L+2W

And we know that:

L = 6W

So then we put in all the information that we do know

70 = 2(6W)+2W

And pop that into a calculator and you get W=5

So now we put that information into L = 6W to get:

L = 6×5

L = 30

Answer:

Step-by-step explanation:

Remember PEMDAS

1-1:5=

1-0.2=

0.8

Answer: x = 60°

Step-by-step explanation:

The rest of the question is the attached figure.

Given: A rhombus inside a regular hexagon, work out the angle x.

As shown

ABCDEF is a regular hexagon.

The regular hexagon have 6 congruent angles, and the sum of the interior angles is 720°

So, the measure of one angle of the regular hexagon = 720/6 = 120°

So, ∠F = ∠BAF = 120°

AFEG is a rhombus.

The rhombus have 2 obtuse angles and 2 acute angles.

∠F is one of the obtuse angles of the rhombus = 120°

∠F and ∠FA G are supplementary angles

So, ∠F + ∠FA G = 180°

∴ ∠FA G = 180° - ∠F = 180 - 120 = 60°

∴ x = ∠GAB = ∠BAF - ∠FA G = 120 - 60 = 60°

So, the measure of the angle x = 60°

Answer:

16 inches after one year

Step-by-step explanation:

in 3/4 a year tree grew 12 inches

divide by 3

multiply by 4

16 inches

8x² - 24 = 8 (x² - 3)

Answer:

10

Step-by-step explanation:

y=(x=3)+7

y=3+7 add

y=10

Answer:

b

Step-by-step explanation:

Answer: 52.288.802.199

Answer:

The missing side would be 6.

And the area would be 54.

Step-by-step explanation:

The perimeter equals 30, that's the outside of the rectangle. They give you a part of the perimeter, 9ft. So 9ft and there's another 9ft on the bottom line, (because it is equal to the top width) Which equals 18. To get the other sides you need to subtract 18 from the whole perimeter, 30. Which gives you 12. And there's two sides left, so divide by 2, and you have 6 on each side(left and right sides) Perimeter is adding all the sides up.

And the Area formula is Area=Length times Width. Area=9ft×6ft Which equals 54.

Answer:

[tex]x = 5[/tex]

Step-by-step explanation:

Find the side length of the square. The formula is for area is

[tex]a = {s}^{2} [/tex]

So take the square root to find the side length.

[tex] \sqrt{121} = \sqrt{ {s}^{2} } [/tex]

[tex]s = 11[/tex]

Now find the perimeter of the square.

[tex]11 \times 4 = 44[/tex]

setup the equation to solve for x. The left side is the perimeter of the rectangle and the right is the perimeter of the square.

[tex]3x + 3x + x - 2 + x - 2 = 44[/tex]

Collect like terms

[tex]8x - 4 = 44[/tex]

subtract 4 from both side

[tex]8x = 40[/tex]

divide both side by 8

[tex]x = 5[/tex]

Answer:

[tex]x=61[/tex]

Step-by-step explanation:

We can find the angle directly above the [tex]2x+8[/tex].

We know that because they both lie on a straight line, the other angle is [tex]180-(2x+8)=172-2x[/tex].

Aha! We have a path to the solution!

[tex]172-2x=x-11[/tex] because of the parallel line angle theorem(I forget what it's called).

We then add [tex]2x[/tex] and [tex]11[/tex] to both sides to get [tex]183=3x[/tex].

Lastly, we divide by [tex]3[/tex] to get [tex]61=x[/tex].

So, [tex]\boxed{x=61}[/tex] and we're done!

Answer:

The hundred thousands place

Step-by-step explanation:

The value of k so that the two given lines are parallel is; k = 22.5

First, the correct question is;

In line segment geometry;

First, we must determine the slope of the lines by rewriting the equations to resemble the equation of a line in the slope-intercept form; y = mx + c

Therefore, we have;

.

And since the slope of parallel lines are equal;

By cross product;

k = 22.5

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Answer:

[tex]y = \frac{1}{5} x - \frac{7}{5} [/tex]

Step-by-step explanation:

Look at graph above⤴⤴⤴

Hope this helps :)