The perimeter of a square is 109.8 square inches. what is the length of one square? A 2.74 in B 10.98 in C 25 in D 27.45 in

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Elina [12.6K]

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4 0

3 years ago

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Write the equation of each line using the given information.

Marat540 [252]

A. The equation of the line is y = -0.2 x + 1.9

B. The equation of the line is y = 4 x + 3

C. The equation of the line is y = -8

D. The equation of the line is y = 2 x + 4

Step-by-step explanation:

The slope-intercept form of the equation of a line is y = m x + b, where

m is the slope of the line and b is the y-intercept

The formula of the slope of a line which passes through points $(x_{1},y_{1})$ and $(x_{2},y_{2})$ is $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$
The slope of a horizontal line whose equation y = b is zero
The y-intercept means the line intersect the y-axis at point (0 , b)

A.

∵ The line passes through points (2 , 1.5) and (-5 , 36.5)

∴ $x_{1}$ = 2 and $x_{2}$ = -5

∴ $y_{1}$ = 1.5 and $y_{2}$ = 36.5

∵ $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

∴ $m=\frac{-5-2}{36.5-1.5}=\frac{-7}{35}=\frac{-1}{5}$

∴ m = -0.2

∵ y = m x + b

∵ m = -0.2

∴ y = -0.2 x + b

- To find b substitute x and y in the equation by the coordinates of

one of the two given points

∵ x = 2 and y = 1.5

∴ 1.5 = -0.2(2) + b

∴ 1.5 = - 0.4 + b

- Add 0.4 to both sides

∴ 1.9 = b

∴ y = -0.2 x + 1.9

The equation of the line is y = -0.2 x + 1.9

B.

∵ m = 4

∵ y = m x + b

∴ y = 4 x + b

∵ Point (3 , 15) lies on the line

- To find b substitute x and y in the equation by the coordinates

of the given point

∵ x = 3 and y = 15

∴ 15 = 4(3) + b

∴ 15 = 12 + b

- Subtract 12 from both sides

∴ 3 = b

∴ y = 4 x + 3

The equation of the line is y = 4 x + 3

C.

∵ The line has the same slope of line y = 1

- The line whose equation y = 1 is a horizontal line

∵ The slope of the line y = 1 is zero because it is a horizontal line

∴ m = zero

∵ y = m x + b

∴ The equation of the line is y = (0)x + b

∴ y = b

∵ The line passes through point (3 , -8)

- In the horizontal line the y-coordinates of all point lie on the line

are equal

∴ The line intersect the y-axis at point (0 , -8)

∴ b = -8

∴ y = -8

The equation of the line is y = -8

D.

∵ m = 2

∵ y-intercept is at point (0 , 4)

∴ b = 4

∵ y = m x + b

∴ y = 2 x + 4

The equation of the line is y = 2 x + 4

Learn more:

You can learn more about the linear equations in brainly.com/question/4326955

#LearnwithBrainly

6 0

3 years ago

A cylinder shaped bucket is used as a sand container. The bucket has a height of 2.5 ft and a radius of 0.5 ft.

kaheart [24]

I'm late but your answer would be 1.96 $ft^3$ :D

8 0

3 years ago

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Choose all of the expressions that are equal to 61. |−61| the opposite of −61 the opposite of 61 the distance from zero to −61 −

igomit [66]

Step-by-step explanation:

We need to choose all the expressions that are equal to 61.

(i) |−61| : It is true. Modulus of any negative number gives positive number. |-61|=61.

(ii) The opposite of −61 ; It is true. Opposite of negative is positive.

(iii) The opposite of 61 : It is false. The opposite of 61 gives -61.

(iv) distance from zero to −61 : It is true. Distance is positive always.

(v) −|61| : False. It remains negative.

(vi) −|−61| : False. It remains negative.

(vii) -(-61) : True. Double negative makes positive .

Hence, the correct options are : (i), (ii), (iv), (vii).

8 0

3 years ago

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A newsletter publisher believes that below 68% of their readers own a Rolls Royce. Step 1 of 1 :State the null and alternative h

Vanyuwa [196]

The null hypothesis is p = 0.68 while the alternative hypothesis will be that it's below that is p < 0.68.

First, let us understand the Null and Alternative hypotheses:

The null hypothesis is simply to predict that there is no effect of the relationship between the variables.

The alternative hypothesis is to state the research prediction of a relationship or effect. In this case, the newsletter publisher believes that below 68% of their readers own a Rolls Royce.

The null hypothesis is that the proportion of readers who own a Rolls Royce is equal to 0.68.

Null hypotheses = H₀: p = 0.68

The alternate hypothesis is that the proportion of readers who own a Rolls Royce is below 0.68.

Alternate hypotheses = H₁: p < 0.68.

Thus, the null hypothesis is p = 0.68 while the alternative hypothesis will be that it's below that is p < 0.68.

To learn more about the Null and Alternative hypotheses visit:

brainly.com/question/25263462

#SPJ9

4 0

1 year ago