Given that y varies directly as x when y = 8 and x=5.
(a) express y in terms of x, and hence
(b) find y when x=30

Answer:

solution,

[tex]a. \: 3(x + 5) \\ \: \: = 3 \times x + 3 \times 5 \\ \: \: = 3x + 15[/tex]

[tex]b. \: 4(x - 4) \\ \: \: = 4 \times x - 4 \times 4 \\ \: \: = 4x - 16[/tex]

[tex]c. \: 2(5x + 1) \\ \: = 2 \times 5x + 2 \times 1 \\ \: \: = 10x + 2[/tex]

[tex]d . \: 7(x - 9y) \\ \: = 7 \times x - 7 \times 9y \\ \: \: = 7x - 63y[/tex]

Hope this helps..

Good luck on your assignment..

Answer:

a) 3(x + 5)  =

= 3x + 15

b) 4(x-4)  =

= 4x - 16

c) 2(5x + 1)  =

= 10x + 2

d) 7(x-9y) =

= 7x - 63y

Answer:

[tex]1 \frac{2}{3} - 2\frac{2}{3} = -1[/tex]

Step-by-step explanation:

[tex]1\frac{2}{3} - 2 \frac{2}{3\\} \\\\\frac{5}{3} - \frac{8}{3} = \frac{-3}{3} \\ \\\frac{-3}{3} = -1[/tex]

Hope this helps! :)

oooooooooooooooooooooooooooooooo

Answer:

The approximate area of the hexagon is 42 in²

Now, the length of one side is 4 inches.

Answer:

B. 42 in.^2

Step-by-step explanation:

Just took the Unit Test on Edg (2020-2021)!!

Answer: 50

Step-by-step explanation:

I am rounding it to 1 significant figure.

9.8 = 10 (round up when the last digit is 5, 6, 7, 8 or 9)

5.2 = 5 (round down when the last digit end with 0, 2, 3 or 4)

So it now is 10 x 5 = 50

Rounding to 1 significant figure, we get the product of 9.8 * 5.2 is 50. Thus, option B is correct.

Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility.

Rounding to some place keeps it accurate on the left side of that place but rounded or sort of like trimmed from the right in terms of exact digits.

Given product is 9.8 * 5.2

Now we are rounding it to 1 significant figure.

Round up when the last digit is 5, 6, 7, 8 or 9

9.8 = 10

Round down when the last digit end with 0, 2, 3 or 4

5.2 = 5

So, 10 x 5 = 50

Thus, option B is correct.

Learn more about rounding numbers  here:

https://brainly.com/question/1285054

#SPJ2

Answer:

They made 36 three-point field goals

Step-by-step explanation:

For free throws , we have one point each.

So here, the total points they made from free throws is 22 * 1 = 22 points

So the number of points made from field goals would be 184-22 = 162 points

So the issue we have now is knowing the number of 3-point field goals that was made.

How can we get this?

Remember they made 85 baskets? so if we subtract the number of free throws, then we can have the number of field throws and that is 85-22 = 63

Now, let the number of 2 points throws be x and the number of 3 points throws be y

From our earlier analysis;

x + y = 63 ••••••••• (i)

Now the total number of three pointers would be 3 * y = 3y and the total number of two pointers would be 2 * x = 2x

Adding both gives a total of 162

Thus;

2x + 3y = 162 •••••••• (ii)

So we have two equations to solve simultaneously.

From equation 1, we can say that;

x = 63-y

Let’s substitute this into equation 2

2(63-y) + 3y = 162

126 -2y + 3y = 162

126+y = 162

y = 162-126

y = 36

This means that they made 36 three-point field goals

Answer:

They made 36 three-point field goals during the game

Step-by-step explanation:

Answer: 10

Step-by-step explanation:

AB = 2EB

AB=CD

Due to that

Cd = 2EB therefore

CD = 10

The value of CD is 10.

Perpendicular lines are lines that intersect at a right (90 degrees) angle.

Given:

EB= 5

As, OE is perpendicular to AB  

AB = 2EB

Also, AB=CD

so, CD= 2 EB

CD = 2*5

CD= 10

Learn more about perpendicular here:

https://brainly.com/question/18271653

#SPJ2

Answer:

y<3

Step-by-step explanation:

It is  y<3 because all areas below y=3 are shaded.

In addition, the line y=3 is dotted, which means it is not part of the inequality (i.e. strict inequality).

If it had been a full line, then it would be y<=3.

Answer:

Step-by-step explanation:

r = 15 ft

h = 22 ft

Volume of cylinder = πr²h

                                = π * 15 * 15 * 22

                                = 4950π

                                = 4950 * 3.14

                               = 15543 cubic ft

Answer:

y = -2/9 |X| - 8

Step-by-step explanation:

I'm not certain whether the -7 is part of the |X| or it's just out of the equation. But shifting an equation up or down is very intuitive.

If you want to move an equation up a certain unit, you just add that many units (positive) onto the end of an equation. The same goes for moving a unit down, where you subtract that many units you want to go down.

Answer:

y=-2/9 |x| -8

Step-by-step explanation:

y = f(x) + C  C < 0 moves it down

y=-2/9 |x| -7 Shift down 1 by subtracting 1

y=-2/9 |x| -7-1

y=-2/9 |x| -8

Respuesta: 19; 19,89

B) 19 C) No

Explicación paso a paso:

Dados los datos:

15, 25, 17, 19, 16, 26, 18, 19, 24

Reorganizando los datos:

15, 16, 17, 18, 19, 19, 24, 25, 26

Mediana de los datos:

(N + 1) / 2

Donde N = número de observaciones

Mediana = (9 +1) / 2 = 10/2 = 5 a observación = 19.

Media = suma de valores observados / número de observaciones

Media = (15 + 16 + 17 + 18 + 19 + 19 + 24 + 25 + 26) / 9

Media = 179/9 = 19.89

B) mediana si se agrega otro niño que pese 43 kg

Los nuevos datos se convierten en:

15, 16, 17, 18, 19, 19, 24, 25, 26, 43

Mediana = (N + 1) / 2

Mediana = (10 + 1) / 2 = 11/2 = 5.5 Como tenemos un decimal:

La mediana será el promedio de la quinta y sexta observación: (19 +19) / 2 = 38/2 = 19

C) No, la media aritmética no parece ser un buen representante de la observación de 10 datos con el valor de peso recién agregado de 43 kg, ya que el valor parece considerablemente más alto que el conjunto de los 9 valores anteriores. Con el peso recién agregado, la media aritmética se convierte en: Media = (15 + 16 + 17 + 18 + 19 + 19 + 24 + 25 + 26 + 43) / 10 Media = 222/10 = 22.2

Answer:

In a 45 - 45 - 90 triangle, the legs are equal and the ratio of sides from shortest to longest is 1 : 1 : √2 where 1 are the legs and √2 is the hypotenuse. In this case the leg is 10 / √2 = 5√2.

Answer:

-20x -5

Step-by-step explanation:

3x + (-7) – 23x - (-2)

Subtracting a negative is like adding

3x -7 -23x +2

Combine like terms

3x-23x   -7+2

-20x -5

Answer:

-20x - 5

Step-by-step explanation:

Simplify the expression

3x - 7 - 23x + 2

Combine like terms

-20x - 5

Answer: Part 1: 111.24

Part 2: 9.27

Part 3: 54 minutes

Step-by-step explanation:

Part 1: Since you already know that the total bill increases by 3%, you just have to find 103% of 180.

1.03*108= 111.24; your answer would be 111.24 pounds

Part 2: Since you already know yearly, 111.24 divided by 12= 9.27 per month

Part 3: First find 73% of 200 which is 146. Then subtract that from 200 which is 54. So you have 54 minutes left.

Answer:

Yes,planner has met the minimum height, as minimum height was 9 feet and maximum height of arc is 9.6 feet

Step-by-step explanation:

The question is incomplete as all the details have not been given in the question.I have attached the complete question and its options at the bottom. Consult in for better understanding.

As we can see that at the mid value, for x=4, the value of f(x)=9.4

It means that the maximum height occurs at mid of the arc where it is height is 9.6 feet above the ground.

It means that the planner has met the minimum height, as minimum height was 9 feet and maximum height of arc is 9.6 feet

Answer:

B on Edge

Step-by-step explanation:

yes, because the width of the arch is 9.6 feet

Answer:

The pressure decreased by 18%

Step-by-step explanation:

Given two scenarios:

Step 1: Find the initial pressure

Initial force = 90 Newtons

Initial surface force is applied on = 20 cm²

Initial pressure = initial force/initial surface

*Note: the SI unit for pressure is N/m²

We need to convert cm² to m²

1 cm² = 0.0001 m²

20 cm² = 0.002 m²

Initial pressure = 90/0.002 m²

Initial pressure = 45,000 N/m²

Step 2: find new pressure

New force = 90+5 = 95N

New area = 20+5 = 25 m² = 0.0025m²

New pressure = 95/0.0025 = 38,000

Step 3: find the outcome of the increases by calculating the % change in pressure

% change in pressure = (new pressure - initial pressure)/initial pressure × 100

Thus,

% change in pressure = (38,000 - 45,000)/38,000 × 100

= -7,000/38,000 × 100

= -18.42 ≈ -18%

The outcome of the increase resulted in a decrease in pressure. Thus,

The pressure decreased by 18%

Answer:

The pressure is decreased by 15.56%

Answer:

Choice C.

Step-by-step explanation:

There are students listening to music for 6.5 hours. So, the students will be in a range where the numbers on the x-axis go to 9.

According to the table, there are 11 students who listen to music for 0 to 3 hours. There are 3 students who listen to music for 3 to 6 hours. There is 1 student listening to music from 6 to 9 hours. This data matches up with the histogram from Choice C.

Hope this helps!

Answer:

The answer to c is an arc

Answer:

it's an arc of the circle.

Step-by-step explanation:

An arc of a circle is a "portion" of the circumference of the circle.

Answer:6 √3

Step-by-step explanation:

Length of a side of an equilateral triangle inscribed in a circle =

r

√

3

where r is the radius of the circle

Therefore, Area =

√

3

a

2

4

a

=

6

√

3

Answer:

27√3

Step-by-step explanation:

Length of a side of an equilateral triangle inscribed in a circle =

r√3, where r is the radius of the circle

Therefore, Area =

√3 a^2/4

a=6√3

a/Asin = b/Bsin = c/Csin

c = a * sin C/sin A = 6(sin 120/sin 30) = 6√3

Answer:

the most accurate argument is (C) The transportation and brokerage costs that Suriland's farmers would face if they sold their wheat outside Suriland could amount to almost a dollar per bushel.

Step-by-step explanation:

The cost of transportation and other logistics is being covered by the government that is why the government pay less than dollar per bushel.

so the price of the wheat would have to decrease at home so that the cost of the transportation can be covered by the government who are buying directly from the farmers.

Answer:

The faucet has turned a total distance of 3 25/28

Step-by-step explanation:

To know the total distance turned by the faucet, what we need to do is to add together the distances to which it has turned.

Mathematically, that would be;

2 1/7 + 1 3/4

which is;

15/7 + 7/4 = (60 + 49)/28 = 109/28 = 3 25/28

Answer:

Factor GCF: 3x(2x⁴ - 5x + 4)

Step-by-step explanation:

Simply take out the greatest variable first and then take out the GCF of the numbers to find out factored GCF.

The supplementary angles are:

<1 and <3

<1 and <4

<2 and <3

<2 and <4

Angles that add up to 180 degrees are referred to as supplementary angles. For instance, angle 130° and angle 50° are complementary angles since the sum of these two angles is 180°. The sum of complimentary angles is 90 degrees.

Given:

As, the supplement angles forms 180 angles.

So, from the angles that are supplementary are

<1 and <3

<1 and <4

<2 and <3

<2 and <4

Learn more about supplementary angles here:

https://brainly.com/question/13045673

#SPJ5

Answer:

b

Step-by-step explanation:

A line sloping upwards from left to right has a positive gradient.

A line sloping downwards from left to right has a negative slope

If the line crosses the y- axis above the x- axis then y- intercept is positive.

If the line crosses the x- axis below the x- axis then y- intercept is negative.

The line shown slopes downwards from left to right, thus negative gradient

The line crosses the y- axis above the x- axis thus y- intercept is positive

Answer:-12=-24 FALSE

Step-by-step explanation:

6-18= -12

18-42= -24

The statement is false

<!> Brainliest is appreciated! <!>

[tex]\text{Solve:}\\\\6(1-3) = 2(9-21)\\\\\text{Use the distributive property}\\\\6-18 = 18-42\\\\-12=-24\\\\\text{This would make the equation False, since -12 doesn't equal -24}[/tex]

Answer:

Step-by-step explanation:

(1-3)/(5-1)= -2/4 = -1/2

y - 3 = -1/2(x - 1)

y - 3 = -1/2x + 1/2

y - 6/2 = -1/2x + 1/2

y = -1/2x + 7/2

Answer:

30%

Step-by-step explanation:

Since its 10 marbles we can just add 1 zero to each number

5 marbles = 50%

3= 30%

2= 20%

Answer:

Step-by-step explanation:

P=3/5 ×1/6=1/10