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Lupita is correct because when there is a constant of proportiantilly the line will start at the origin and it will be straight all the way. No curves, bends, etc. Another way you can tell is because when the line gets to "2" it lines up with 300 when the line gets to "4" it lines up with 600. That shows that the line is equal all the way through.

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[tex]61 + (6x - 31) = 90[/tex]

Subtract both sides 61

[tex]61 - 61 + 6x - 31 = 90 - 61[/tex]

[tex]6x - 31 = 29[/tex]

Add both sides 31

[tex]6x - 31 + 31 = 29 + 31[/tex]

[tex]6x = 60[/tex]

Divide both sides by 6

[tex] \frac{6x}{6} = \frac{60}{6} \\ [/tex]

[tex]x = 10[/tex]

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Answer:

x = 10

Step-by-step explanation:

It's a 90˚ angle so subtract 61 from 90, which is 29.

Then add 31 to that 29, which would come out to 60.

60 divided by 6 to isolate the variable would come to 10.

Check your answer by multiplying 10 by 6, subtract the 31, and lastly add the 61 to get back to your 90.

[tex] \: \: \: \: [/tex]

[tex]elipse \: \: \: with \: \: the \: \: center (3, - 4)[/tex]

The length of major axis of the ellipse 2√32.

The length of minor axis of the ellipse 2√18.

What is an ellipse?

The standard form of the ellipse is defined as;

x² / a² + y² / b² = 1

Where, a < b

Minor axis of the ellipse = 2a

And, Major axis of the ellipse = 2b

Given that;

The equation of the ellipse is,

(x−3)² / 18 + (y+4)² /32 = 1

Now,

We can compare with the standards form of an equation of ellipse, we get;

a² = 18

a = √18

And, b² = 32

b = √32

Clearly, √18 < √32

That is; a < b

So, The minor axis of the ellipse = 2a

                                                  = 2√18

And, The major axis of the ellipse = 2b

                                             = 2√32

Therefore,

The length of major axis of the ellipse 2√32.

The length of minor axis of the ellipse 2√18.

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Answer:

34.5

Step-by-step explanation:

The absolute value of -|-34.5| is -34.5. So, -34.5 is 34.5 away from 0.

Answer:

34.5 units.

Step-by-step explanation:

When we simplify -|-34.5|, we get -34.5, which is basically 34.5 units away from 0.

Hoped this helped.

Answer:

Look Below

Step-by-step explanation:

Now if you are looking what percent 15 is in 150, then it'll be 22.5%

Just Multiply 150 with 15 (add a 0. before adding the 15) then multiply 150 x 0.15, and you get 22.5, to which that is 22.5%.

The expressions that calculate the number of hours that Demetrius works in a week are [tex]5(x+1)\text{ and }5x+5[/tex]

If Latisha works [tex]x[/tex] hours each day

Demetrius works one more hour than Latisha each day. Algebraically, Demetrius works [tex](x+1)[/tex] hours each day

So for a [tex]5[/tex]-day working week, Demetrius will work

[tex](x+1)+(x+1)+(x+1)+(x+1)+(x+1)\\=5\times (x+1)\\=5(x+1)hours[/tex]

If we remove the brackets, we have the equivalent expression

[tex]5(x+1)=5x+5[/tex]

So the expressions that calculate the number of hours that Demetrius works in a week are [tex]5(x+1)\text{ and }5x+5[/tex]

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Answer:

10 dimes and 6 quarters.

Step-by-step explanation:

2.50-25-25=2.00-10 dimes = 1.00-4 0.25=0

so

10 dimes and 6 quarters.

Answer:

10 Dimes and 6 Quarters.

Step-by-step explanation:

Important info:

16 Coins

Total = $2.50

Note:

Dimes = 0.10 Cents

Quarters = 0.25 Cents

Question to answer:

How many of each type of coin does she have?

Solution:

10 Dimes = $1.00

6 Quarters = $1.50

$1.00+$1.50 = $2.50

Therefore 10 Dimes and 6 Quarters = $2.50 and = 16 Coin.

Answer:

739 x 4

2926 ft³ is your answer

Answer:

Step-by-step explanation:

radius=18/2=9 ft

[tex]V=\frac{4}{3} \pi r^3\\=\frac{4}{3} \pi (9)^3\\\approx \frac{4}{3} \times 3\times 729\\\approx 4 \times 729\\\approx 2916 ~ft^3[/tex]

Answer:

A≈653.45

Step-by-step explanation:

Solution

A=2πrh+2πr2=2·π·8·5+2·π·82≈653.45127

Answer:

Step-by-step explanation:

1. 4x° + 4x° + 4x° = 180° ( The sum of all interior angles of any triangle is equal to 180° )

[tex]4x + 4x + 4x = 180 \\ 12x = 180 \\ x = \frac{180}{12} \\ x = {15}^{o} \\ [/tex]

4x° + 4x° = y° ( An exterior angle of a triangle is equal to the sum of its two interior opposite angles. )

[tex]4x + 4x = y \\ 4(15) + 4(15) = y \\ 60 + 60 = y \\ {120}^{o} = y[/tex]

2. y° + 60° + 60° = 180° ( The sum of all interior angles of any triangle is equal to 180° )

[tex]y + 60 + 60 = 180 \\ y + 120 = 180 \\ y = 180 - 120 \\ y = {60}^{o} \\ [/tex]

All three internal angles are also congruent to each other and are each 60°. Therefore this is a equilateral triangle.

Perimeter = 4x + 4x + 4x ( An equilateral triangle is a triangle with all three sides of equal length. )

[tex]54 = 4x + 4x + 4x \\ 54 = 12x \\ \frac{54}{12} = x \\ x = 4.5[/tex]

we have: ∠A + ∠B = 90°

<=> (2x-14) + (3x-6) = 90° <=> 2x - 14 + 3x - 6 = 90°

<=> 5x + 20 = 90°

<=> 5x = 70°

<=> x = 14°

So: ∠A = 2x - 14 = 2.14 - 14 = 14°

Ok done. Thank to me :>

Answer: The slope intercept form equation is y = 25x - 100.

Answer:

Step-by-step explanation:

Hello! :p

[tex]\sqrt{-8}[/tex]  = [tex]2i\sqrt{2}[/tex]

[tex]\sqrt{-36}[/tex] = [tex]6i[/tex]

[tex]\sqrt{-5}[/tex] = [tex]i\sqrt{5}[/tex]

I hope you do well on your assignment! I also hope this helps! :)

Step-by-step explanation:

PT=2QS = 2×8 = 16m

therefore perimeter of ∆PRT = 6+16+14 = 36m

hope this helps you.

Answer:

5.4

Step-by-step explanation:

You need to use the Pythagorean theorem and if you know that the base is 2 and the height 5 then you got 5.4

the denominator has to be one so you multiply 1/4 by 4, and 4/8 by 4 also

2:1

Answer: You need to count how many squares are shaded (at least half of it), therefore the area is 32 square units.

The answer is B) Dilating a triangle does not change the measurements of the triangle's angles.

Answer:

8 laps

Step-by-step explanation:

every 8mins 4 laps are run

Maria completed a total of 8 laps in 16 minutes.

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have Maria who walks 2 laps in 5 minutes and then runs 2 laps in 3 minutes.

Assume that she completes [x] laps in 16 minutes.

x = L[walking] + L[Running]

x = (2 + 2) + (2 + 2)

x = 8

Therefore, Maria completed a total of 8 laps in 16 minutes.

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Answer: Sunday

Step-by-step explanation:

The 27th would be tuesday

The 3rd would be tuesday

The 10th would be tuesday

The 15th would be sunday

Answer:

tans=0.8770580193

Step-by-step explanation:

Answer:

a = 2

Step-by-step explanation:

I hope this helps!

3(x + 7) = 57 |÷3

x + 7 = 57/3

x + 7 = 19 |-7

x = 19 - 7

x = 12

Answer:

Plot the points (0,0) and (1,3) to make the line.

Step-by-step explanation:

We know that a linear equation is y=mx+b, m is the slope and b is the y-intercept. We can see that the slope is m=3, and there is no b meaning b=0. Since the y-intercept is 0 we can start from the origin (0,0). The slope is 3/1 or known as rise/run. You go up 3 and go right 1, making the second point (1,3). This should work.

Answer:

Proton

Step-by-step explanation:

The charge on the proton and electron are exactly the same size but opposite. Neutrons have no charge. Since opposite charges attract, protons and electrons attract each other.

Hope this helps you luv!