Linear relationships are important to understand because they are common in the world around you. For example, all rates and ratios are linear relationships. Miles per gallon is a common rate used to describe the number of miles a car can travel on one gallon of gasoline. Dollars per gallon, or the price of gas, is a linear relationship as well. What other relationships can you think of that are linear? How do they affect your everyday life?

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The length of arc of the given circle, to the nearest hundreth, is: 2.41 units.

Length of arc = ∅/360 × 2πr, where the radius of the circle is r, and the reference angle is ∅.

We are given the following:

Radius (r) = 3 units

Reference angle (∅) = 46°

Plug in the values into the length of arc formula:

Length of arc = 46/360 × 2π(3)

Length of arc = 2.41 units.

Therefore, the length of arc of the given circle, to the nearest hundreth, is: 2.41 units.

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Answer:

Step-by-step explanation:

21/5*2000=  21*400= 8,400 pounds

Answer:

[tex]\displaystyle 8400\:lbs.[/tex]

Explanation:

On United States Imperial [Customary] System, there is one ton in two thousand pounds. So, because we are going from a bigger unit of measurement to a smaller unit of measurement, we multiply the quantity of tons by two thousand:

[tex]\displaystyle \boxed{8400} = 2000[4\frac{1}{5}][/tex]

I am joyous to assist you at any time.

Answer:

Step-by-step explanation:

Basic propotionality theorem: If a line is drawn paralle to one side of a triangle and intersect other two sides in distinct points, then the line segment divide the two linesin same ratio.

[tex]\sf \dfrac{LP}{PN}=\dfrac{LO}{OM}\\\\\dfrac{x+12}{5}=\dfrac{22}{8}\\\\\text{cross multiply,}\\\\[/tex]

8*(x + 12) = 22*5

8x + 8*12 = 110

 8x + 96 = 110

        8x = 110 - 96

        8x = 14

          x = 14/8

          x = 1.75

It has a ratio of 1:4, meaning for every x, you'd get 4 from your y

Answer:

it is option B that is correct

Step-by-step explanation:

use BODMAS

B- Brackets

O-order

D-division

M-multiplication

Addition

Subtraction

Answer:

True

Step-by-step explanation:

I always remember it, over then up

Answer:

option 3

Step-by-step explanation:

6(3√5)

Subtract to find how much was spent on coffee:

90 - 47.65 = 42.35

Divide what was spent by the price per pound:

42.35 / 8.47 = 5

They bought 5 pounds of coffee

Answer:

The smallest number by which 256 must be divided so that the quotient is a perfect cube is 4.

Step-by-step explanation:

Answer: 13.5 in

Step-by-step explanation:

The formula for the volume of a cone is: V = π*r^2*(h/3).

Therefore, when the given numbers are plugged in, it becomes:

1144.53 = (3.14)(9^2)(h/3).

Solving this for h, we get the answer of 13.5 in

Answer:

1.5hours

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

2a + 2 / a = 4

2a + 2 = 4a

4a - 2a = 2

2a = 2

a = 1

2a² + 2 / a²

a = 1

2(1²) + 2 / 1²

2 + 2 / 1

4

Answer:

step by step solution:

(r/p)(9) = (9+1)²/(9-4) = 100/5 = 20

(q.s)(3) = (-2(3)+7).(3(3)² - 5(3)) = 1×12 = 12

(q/r)(-1) = (-2(-1) + 7)/(-1+1)² = 9/0 = Undefined

(t + s)(4) = -(4)² + 4(4) + 9 + 3(4)² -5(4) = -16 + 16 +9 + 48 - 20= 37

(s o p)(8) = s(p(8)) = s(8-4) = s(4) = 3(4)² -5(4) = 48 - 20 = 28

(q o t)(7) = q(t(7)) = q(-(7)² + 4(7) + 9) = q(-12) = -2(-12) + 7= 24+7 = 31

(r o u)(1) = r(u(1)) = r(1+6) = r(7) = (7+1)² = 64

(t o s)(0) = t(s(0)) = t(0) = 9

(u-p)(-3) = (-3)³ + 6(-3) - (-3) + 4 = -27 -18 + 3 + 4 = -38

(u o r)(-2) = u(r(-2)) = u((-2+1)²) = u(1) = 1 + 6 = 7

(q o q)(6) = q(q(6)) =q (-2(6) + 7) = q(-5) = -2(-5) + 7 = 17

END

Answer:

Step-by-step explanation:

as i think it is triangle which means the sum of interior angle 180

14x+13+4x+13+6x+2=180

24x+28=180

24x=152

x=6.2

Answer:

The answer is no

*View the attached graph to check your answer graphically.*

Step-by-step explanation:

y = 4x + 9

y = 2x + 5

For this problem, I will be using substitution, since the both equations are already in the slope-intercept form, and it's a little easier than the elimination method.

First, I will substitute the first equation, for y, into the second equation:

y = 4x + 9

y = 2x + 5

4x + 9 = 2x + 5

Next, subtract 2x from both sides to isolate x:

4x + 9 = 2x + 5

-2x      -2x

2x + 9 = 5

Then, subtract 9 from both sides:

2x + 9 = 5

     - 9  - 9

2x = -4

Now, divide both sides by 2:

2x = -4

/2    /2

x = -2

Now, we find the value of y, by substituting -2 for x:

y = 2x + 5

y = 2(-2) + 5

y = -4 + 5

y = 1

(x, y) ==> (-2, 1)

Check your answer using (-2, 1):

y = 2x + 5

1 = 2(-2) + 5

1 = -4 + 5

1 = 1

This statment is correct

y = 4x + 9

1 = 4(-2) + 9

1 = -8 + 9

1 = 1

This statment is also correct

Check your answer using  (-6, -7):

y = 2x + 5

-7 = 2(-6) + 5

-7 = -12 + 5

-7 = -7

This statment is correct

y = 4x + 9

-7 = 4(-6) + 9

-7 = -24 + 9

-7 = -15

This statment is NOT correct

Therefore, no (-6,-7) is NOT a solution to this system of equations.

*View the attached graph to check your answer graphically.*

Hope this helps!

Answer:

no

Step-by-step explanation:

Yosef should have multiplied the x-values by 80 to get the y-values.

Tables are told used to arrange ungrouped data.

From the given table, we can find the equation by using the coordinate points (1, 80) and (1, 160)

The standard equation of a line is  y = mx + b

m is the slope

b is the y-intercept

Slop = 160-80/2-1

Slope = 80

For the y-intercept

160 = 80(2) + b

b = 0

The required equation is y = 80x

This means that Yosef should have multiplied the x-values by 80 to get the y-values.

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Answer:

A

Step-by-step explanation:

The total number of nickles that Alice has got for this case is 14. The total amount of money from those nickle and dimes that Alice hold is $1.9

A dollar is further divided into some majorly used parts as:

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

For this case, we're specified that:

Suppose that she has got 'x' nickles.

Then, as it is given that she has 2 more nickles than dimes, therefore, we get:

number of nickles = 2 + number of dimes

x = 2 + 12 = 14

Thus, Alice has got  12 dimes and 14 nickles.

Similarly, we have:

Thus, the total amount of money she got is $1.2 + $0.7 = $1.9

Thus, the total number of nickles that Alice has got for this case is 14. The total amount of money from those nickle and dimes that Alice hold is $1.9

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#SPJ4

The scale factor used for scaling the actual rectangular pool was 4/15 and the length of the scaled rectangle is 9.6 feet.

Suppose the initial measurement of a figure was x units.

And let the figure is scaled and new measurement is of y units.

Since the scaling is done by multiplication of some constant, that constant is called scale factor. Let that constant be 's'.

Then we have:

[tex]s \times x = y\\s = \dfrac{y}{x}[/tex]

Thus, scale factor is the ratio of the new measurement to the old measurement.

For this case, we're specified that:

Dimensions of the original pool = 24 feet wide by 36 feet long

The scaled rectangle's dimension: 6.4 feet width and L feet length (we assume the length be L units).

So, in scale drawing, 24 feet was converted to 6.4 feet. Let the scale factor be 's', then:

[tex]6.4 = s \times 24\\\\s = \dfrac{6.4}{24} = \dfrac{4}{15}[/tex]

Thus, since length is also scaled by same factor(as the whole figure is scaled by constant scale factor assumingly), we get:

Scaled length = s times original length

[tex]L = \dfrac{4}{15} \times 36 = 9.6 \: \rm feet[/tex]

Thus, the scale factor used for scaling the actual rectangular pool was 4/15 and the length of the scaled rectangle is 9.6 feet.

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Answer:

hai

Step-by-step explanation:

Pak Awi mau beli jam tangan Rolex hulk submarine dengan harga 300jt. Dia mau beli 2 tahun lagi

dengan asumsi harga jam naik 2% / tahun. Future Value

Uang pak awi sekarang hanya 100jt, berapa yang harus pak awi tabung tiap bulan nya agar 2 tahun lagi

dia bisa beli jam tangan tersebut, jika bunga tahunan adalah 15% / tahun (pajak = 10%) ??? Present

value. Future value. Present value annuity.

Bunga di terima per bulan, dan tetap di gulung.

Ya Berapa yang dia tabung tiap bulan

-pakai tabel

Answer:

Step-by-step explanation: 5.6 would be the add on to 27 so since it included the key word '' left'' you'd substract the two and you'd get your answer, just use calculator. You got this!!!

Go sub to clan fbib !!!!!

Answer:

2.744 cubic milimeters

Step-by-step explanation:

Here,

Length ( l ) = 1.4 mm

Base ( b ) = 1.4 mm

Height ( h ) = 1.4 mm

l = b = h = 1.4 mm = a

To find : Volume

This shape is a cube.

Formula : -

Volume of cube = a³

Volume of cube

= 1.4³

= 1.4 x 1.4 x 1.4

= 2.744 cubic milimeters

[tex] \huge\fbox\orange{ANSWER} [/tex]

[tex] \mathsf \purple{v = l \times w \times h}[/tex]

[tex] \mathsf \pink{v = 1.4 \times 1.4 \times 1.4}[/tex]

[tex] \mathsf \purple{v = 2.744 {mm}^{3} }[/tex]

2.74 cubic millimeters

Pythagorean Theorem: a^2 + b^2 = c^2

a = 23 m

b = 11 m

c^2 = (23 m)^2 + (11 m)^2 = 650 m^2

c = sqrt(650 m^2) = 25.5 (rounded to nearest tenth)

Answer: yes it would change my answer for what is a better buy

Step-by-step explanation: if you buy a $1.98 large soda for 50¢ off you’ll have a $1.48 soda that is only 30¢ more but the size is significantly larger

The volume of a triangular right prism whose area is 15.2 inches and height is 9.7 inches is  147.44 in³

Volume is the amount of space occupied by a three dimensional shape or object.

The volume of a triangular prism is given by:

Volume = Area of triangular base * height.

Hence, for a triangular right prism whose area is 15.2 inches. If its height is 9.7 inches:

Volume = 15.2 * 9.7 = 147.44 in³

The volume of a triangular right prism whose area is 15.2 inches and height is 9.7 inches is  147.44 in³

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Answer:

Step-by-step explanation:

If i is 300 times as much as k, then i=300k.

So we have k(something)=300k -> that something is 300

Answer:

b no.is the correct answer.

Answer:

No

Step-by-step explanation:

If you simplify 17/8;

You'd get 2 1/8, and that is not proportional to 1/2.

Answer:NO

Step-by-step explanation:

17 is a prime number hence can't be simplified.

⇒ 17/8 can't be simplified

Answer:

12.5 years = 216 months

Step-by-step explanation:

4% of 2000= $80

1000/80=12.5

It will take 12.5 years to make $1000 on its own without adding additonal funds.