While flying against the wind, the plane covered 1800 km in 2 hours and 40 minutes. On the return flight it spent 16 minutes less because the plane was moving on the direction of the wind. What was the speed of the wind and the speed of the plane?

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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Step-by-step explanation:

PT=2QS = 2×8 = 16m

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

hope this helps you.

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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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 :>

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

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

Answer:

Option D is correct

Step-by-step explanation:

First, let's find side BC by using Pythagoras theorem.

Given:

=> 9² = 7.8² + x²

=> 81 = 60.84 + BC²

=> BC² = 20.16

=> √BC² = √20.16

=> BC = √20.16

=> BC = 4.48998886413 (Using calculator)

=> BC ≈ 4.49 (Estimated)

Therefore, side BC ≈ 4.49 units. Now, let's find the area by using hero's formula.

=> 1/2(Perimeter) = S

=> Perimeter: Hypotenuse + Side 1 + Side 2

=> 7.8 + 9 + 4.49

=> 21.29 = Perimeter

=> 1/2(21.29) = S

=> 10.645 = S

=> √s(s - a)(s - b)(s - c) = Area of triangle

=> √10.645(10.645 - 9)(10.645 - 4.49)(10.645 - 7.8)

=> √10.645(1.645)(6.155)(2.845)

=> √10.645 x 1.645 x 6.155 x 2.845

=> √306.635120999 (Using calculator)

=> √306.64 (Estimated)

=> 17.5111393119 (Using Calculator)

=> 17.51 units² (Estimated)

We can see that option D is the closest option. Therefore, Option D is correct.

If Option D was incorrect, then my second opinion is A.

If both are wrong, I deeply apologize for the inconvenience caused by me. Hoped this helped.

Answer:

answer is d) 18.6

Step-by-step explanation:

area = 1/2ab sin ∅

a= 9

b = 7.8

so it's

1/2 ×7.8 × 9 sin 32

use your calculator to get 18.600 unit squared

*we can also use the heroes formula*...

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%.

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.

NEW ANSWER

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.

thanks for brainly (:

glad I could help!

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

Using it's formula, it is found that the mean of the data set is of 4.1 shirts.

In this problem, the 12 observations are: 3, 4, 8, 5, 2, 5, 0, 5, 3, 4, 3, 7

Hence:

[tex]M = \frac{3 + 4 + 8 + 5 + 2 + 5 + 0 + 5 + 3 + 4 + 3 + 7}{12} = 4.1[/tex]

The mean of the data set is of 4.1 shirts.

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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.

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

2:1

Answer:

It is approximately 0.13 grams.

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

Answer:

a = 2

Step-by-step explanation:

I hope this helps!

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! :)

Answer:

x=65

Step-by-step explanation:

Based on the given conditions, formulate: 157+3.75 X x=400.75

Rearrange unknown terms and Calculate the sum:

3.75x = 400.75 - 157

3.75x = 243.75

x=243.75 / 3.75

x=65

The cost of labour per hour is $65.

Given that, the technician at the store worked on the computer for 3.75 hours and charged her $157 for parts. The total was $400.75.

We need to write and solve an equation which can be used to determine x, the cost of the labour per hour.

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.

Now, according to question 157+3.75×x=400.75

⇒3.75x=400.75-157

⇒3.75x=243.75

⇒x=243.75/3.75

⇒x=65

Therefore, the cost of labour per hour is $65.

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3(x + 7) = 57 |÷3

x + 7 = 57/3

x + 7 = 19 |-7

x = 19 - 7

x = 12

[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:

$57.45

Step-by-step explanation:

102.45=2x-12.45

2x= 102.45+12.45

2x=114.90

x= 114.90/2

x=$57.45

Answer:

tans=0.8770580193

Step-by-step explanation:

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.

[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]

____________________________________________

Have a great day ♡

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.