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Luda [366]
3 years ago
10

The graph above shows the distance Mr. Johnson drives over time.

Mathematics
1 answer:
loris [4]3 years ago
6 0
After 1 hour he has driven 40 miles
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A given line has the equation 10x + 2y = −2.
worty [1.4K]

The equation is \boxed{ \ y = - 5x + 12 \ or \ y = 12 - 5x} \ }

<h3>Further explanation </h3>

This case asking the end result in the form of a slope-intercept.

<u>Step-1: find out the gradient. </u>

10x + 2y = -2

We isolate the y variable on the left side. Subtract both sides by 10x, we get:

2y = - 10x - 2  

Divide both sides by two

y = -5x -1

The slope-intercept form is \boxed{ \ y = mx + c \ }, with the coefficient m as a gradient. Therefore, the gradient is m = -5.

If you want a shortcut to find a gradient from the standard form, implement this:  

\boxed{ \ ax + by = k \rightarrow m = - \frac{a}{b} \ }

10x + 2y = −2 ⇒ a = 10, b = 2

\boxed{m = - \frac{10}{2} \rightarrow m = -5}

<u>Step-2:</u> the conditions of the two parallel lines

The gradient of parallel lines is the same \boxed{ \ m_1 = m_2 \ }. So \boxed{m_1 = m_2 = -5}.

<u>Final step:</u> figure out the equation, in slope-intercept form, of the parallel line to the given line and passes through the point (0, 12)

We use the point-slope form.

\boxed{ \ \boxed{ \ y - y_1 = m(x - x_1)} \ }

Given that

  • m = -5
  • (x₁, y₁) = (0, 12)  

y - 12 = - 5(x - 0)

y - 12 = - 5x

After adding both sides by 12, the results is \boxed{ \ y = - 5x + 12 \ or \ y = 12 - 5x} \ }

<u>Alternative steps </u>

Substitutes m = -5 and (0, 12) to slope-intercept form \boxed{ \ y = mx + c \ }

12 = -5(0) + c

Constant c is 12 then arrange the slope-intercept form.

Similar results as above, i.e. \boxed{ \ y = - 5x + 12 \ or \ y = 12 - 5x} \ }

<u>Note: </u>

\boxed{Standard \ form: ax + by = c, with \ a > 0}

\boxed{Point-slope \ form: y - y_1 = m(x - x_1)}

\boxed{Slope-intercept \ form: y = mx + k}

<h3>Learn more </h3>
  1. A similar problem brainly.com/question/10704388
  2. Investigate the relationship between two lines brainly.com/question/3238013
  3. Write the line equation from the graph brainly.com/question/2564656

Keywords: given line, the equation, slope-intercept form, standard form, point-slope, gradien, parallel, perpendicular, passes, through the point, constant

7 0
3 years ago
Read 2 more answers
In△XYZ , XY¯¯¯¯¯¯=7in , YZ¯¯¯¯¯=5in , and XZ¯¯¯¯¯=4in . This triangle is reflected across the x-axis to result in △X'Y'Z' . Whic
ki77a [65]

Answer:

B

Step-by-step explanation:

Reflection is a transformation that preserves lengths.

Triangle XYZ, with side lengths XY = 7 in, YZ = 5 in, XZ = 4 in, is reflected across the x-axis to result in △X'Y'Z'.

This means that corresponding sides have the same lengths:

  • XY = X'Y' = 7 in;
  • XZ = X'Z' = 4 in;
  • YZ = Y'Z' = 5 in.

Find the perimeters of both triangles:

P_{XYZ}=XY+XZ+YZ=7+4+5=16\ in\\ \\P_{X'Y'Z'}=X'Y'+X'Z'+Y'Z'=7+4+5=16\ in

Hence, only option B is true.

8 0
3 years ago
Hi anybody tell me teh answer for tim and sam
Rasek [7]

Answer:

Tim gets 8 pounds and Sam gets 32 pounds

Step-by-step explanation:

Divide 40 by 5

40/5=8

Now 8 is 1 part of the ratio. Just put it in the ratio now and you get:

Tim gets 8 pounds and Sam gets 32 pounds

3 0
3 years ago
The coordinates of the vertices of △JKL are J(3, 4), K(3, 1) , and L(1, 1) . The coordinates of the vertices of △J′K′L′ are J′(−
timurjin [86]

The <em><u>correct answer</u></em> is:

A 180° rotation followed by a translation 1 unit down.

Explanation:

The points are mapped as follows:

J(3, 4)→J'(-3, -5)

K(3, 1)→K'(-3, -2)

L(1, 1)→L'(-1, -2)

A 180° rotation maps a point (x, y) to (-x, -y).  This would map

J(3, 4)→(-3, -4)

K(3, 1)→(-3, -1)

L(1, 1)→(-1, -1)

The difference between these points and the image points are that each y-coordinate of the image is 1 lower than these.  This means a translation 1 unit down would result in the image points.

7 0
3 years ago
Read 2 more answers
Save You More offers a buy one/get one free item each week. Customers who purchase only one of the items must pay the regular pr
Elis [28]
C because the relation acts as a function no mater the 2 items
3 0
3 years ago
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