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3 years ago

11

On a regional map, the scale shows that 2 cm on the map = 10 actual miles. The actual distance from Forest Hills to Plainville i

s 74 miles. How far apart are these cities on the map?
A.)5 cm
B.)7.4 cm
C.)8 cm
D).14.8 cm

1 answer:

Gelneren [198K]3 years ago

4 0

Answer:

D

Step-by-step explanation:

if every 2 cm on the map=10 miles, I can use my basic knowledge to find out how many cm will equal 70, in this case I can multiply 7 on both sides to find out how many cm on the map will equal 70, so 2(7)cm=10(7)mi will result as 14cm=70mi. Even though the answer seems pretty clear I can round my answer closer to 2 or I can double check by dividing 74 by 10=7.4 times the 2 cm which gets me 14.8.

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WHICH IS BIGGER 3/10 OR 3/5

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Find the equation for the line that passes through the point (5,-3), and that is perpendicular to the line with the equation y-1

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Answer:

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Explanation:

Part A

Given the line:

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First, determine the slope of the perpendicular line.

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By definition, two lines are perpendicular if the product of their slopes is -1.

Let the slope of the perpendicular line = n

$\begin{gathered} \implies\frac{1}{4}n=-1 \\ n=-4 \end{gathered}$

Thus, using a slope of -4 and a point (5,-3), we find the equation of the line.

$\begin{gathered} y-y_1=m(x-x_1) \\ y-(-3)=-4(x-5) \\ y+3=-4(x-5) \end{gathered}$

The equation of the perpendicular line in the slope-point form is:

$y+3=-4(x-5)$

Part B

In order to graph the line, first, find two points on the line.

When x=0

$\begin{gathered} y+3=-4(0-5) \\ y+3=20 \\ y=20-3=17 \\ \implies(0,17) \end{gathered}$

When y=1

$\begin{gathered} 1+3=-4(x-5) \\ 4=-4(x-5) \\ \frac{4}{-4}=x-5 \\ -1=x-5 \\ x=5-1=4 \\ \implies(4,1) \end{gathered}$

Join the points (0,17) and (4,1) as shown in the graph below:

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1 year ago

Which of the following graphs is described by the function given below? y = 2x 2 + 6x + 3

Alla [95]

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

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This is the equation of a vertical parabola open up

The vertex is a minimum

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$y-3=2x^{2}+6x$

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Rewrite as perfect squares

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square root both sides

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Find the y-intercept

For x=0

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The y-intercept is the point (0,3)

therefore

The graph in the attached figure

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