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MrMuchimi
3 years ago
14

Which equation is a point-slope form of the equation of this line?

Mathematics
1 answer:
tigry1 [53]3 years ago
3 0
The y-intercept is easily read:  it is (0,5).  The slope, m, is m = rise / run

       7-1
= ----------- = 6/3 = 2
      1-(-2)

Thus, the eqn of the line is y = 2x + 5.  In point-slope format, y-5=2(x-0).
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Kelly has a rock garden with a length of 6 feet. She constructs a scale model of the rock garden using the
Annette [7]

Answer:

  • (a) 3 inches

  • (b)  Her scale model drawing will not fit on a piece of paper that is 8.5 inches by 7 inches because the dimensions are not proportional to the scale.

Explanation:

(a) What is the length of the garden in her model? Show your work, including your proportion

<u>1. Scale</u>:

  • model length / real length = 1 inch / 2 feet

<u>2. Proportion</u>:

Naming x the model length:

  • 1 inch / 2 feet = x / 6 feet

Cross multiply:

  • 1 inch × 6 feet = 2 feet × x

Divide both sides by x:

  • x = 1 inch × 6 feet / 2 feet = 3 inch.

Answer: 3 inches

(b) If the width is 5 inches for the scale model and the scale is still 1 inch to 2 feet, will her scale model drawing fit on a piece of paper that is 8.5 inches by 7 inches? Why or why not?​

Both the width and the length must use the same scale, thus the corresponding sides of the scale model and the drawing must be proportional.

In the model the ratio of the length to the width is 3 inch / 5 inch

In the paper the ratio of the length to the width is 8.5 inch / 7 inch

Hence, you can see that in the model the length (mumerator of the fraction) is less than the width (denominator) while in the paper it is the opposite. Bieng the two ratios different, they are not proportional, and you conclude that her scale model drawing will not fit on a piece of paper that is 8.5 inches by 7 inches.

8 0
3 years ago
What does y= 3x - 2 equal?<br><br><br>​
cestrela7 [59]
THE ANSWER WOULD BE X=2/3
8 0
3 years ago
Read 2 more answers
Lisa is performing a study regarding the average height of roses grown using an organic fertilizer. Her population
GuDViN [60]

Answer:

Every fifth rose in each row of roses

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Find two consecutive whole numbers such that 4/7 of the larger exceeds 1/2 of the smaller by 5
Darina [25.2K]

Answer:

The consecutive numbers are 62 and 63

Step-by-step explanation:

Let the larger number be represented by x and the smaller number by y,

Provided they are consecutive numbers;

x = y + 1 --- Equation 1

From the question; we have that

\frac{4x}{7} = \frac{y}{2} + 5 --- Equation 2

Required

Find x and y

Multiply both sides of equation 2 by 14

14 * \frac{4x}{7} = 14 * \frac{y}{2} + 14 * 5

2 * 4x = 7 * y + 70

8x = 7y + 70 ---- Equation 3

Substitute y + 1 for x in equation 2

8(y + 1) = 7y + 70

Open bracket

8y + 8 = 7y + 70

Collect like terms

8y - 7y = 70 - 8

y = 62

x = y + 1

So,

x = 62 + 1

x = 63

Hence, the consecutive numbers are 62 and 63

8 0
3 years ago
Kristen has 64 coins in her bank. She has $9.25 in dimes and quarters. How many dimes and quarters does she have?
Stella [2.4K]
D= # of dimes
q= # of quarters

QUANTITY EQUATION:
d + q= 64

COST EQUATION:
0.10d + 0.25q= $9.25


STEP 1:
multiply quantity equation by -0.10 to be able to eliminate the d term in step 2

(-0.10)(d + q)= (-0.10)(64)
-0.10d - 0.10q= -6.40


STEP 2:
add equation from step 1 to cost equation to eliminate the d term and solve for q

Add
0.10d + 0.25q= $9.25
-0.10d - 0.10q= -6.40

0.15q= 2.85
divide both sides by 0.15

q= 19 quarters


STEP 3:
substitute q value in step 2 into either original equation to find d value

d + q= 64

d + 19= 64
subtract 19 from both sides

d= 45 dimes


CHECK:
0.10d + 0.25q= $9.25
0.10(45) + 0.25(19)= 9.25
4.50 + 4.75= 9.25
9.25= 9.25


ANSWER: There are 45 dimes and 19 quarters.

Hope this helps! :)
7 0
3 years ago
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