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alekssr [168]
2 years ago
11

A line passes through the points (0, –7) and (5, –10). What is its equation in slope-intercept form?

Mathematics
1 answer:
ankoles [38]2 years ago
5 0
<h2>Answer: Step-by-step explanation</h2><h3>STEP 1</h3>

slope = \frac{rise}{run}\\\\m = \frac{y2 - y1}{x2 - x1}

<h3 /><h3>STEP 2</h3><h3>Substitute point values into the slope equation.</h3><h3>m = \frac{10 - 7}{5 - 0} = \frac{3}{5}</h3><h3></h3><h3>STEP 3</h3><h3>Point-slope form.</h3><h3>y - y1 = m (x - x1)</h3><h3></h3><h3>STEP 4</h3><h3>Substitute any point on the line and the slope for x1, y1, m</h3><h3>y - 7 = \frac{3}{5} (x - 0)</h3><h3></h3><h3>Result</h3><h3>\\y - 7 = \frac{3}{5}x</h3>

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Find the area of the shaded region
kogti [31]

Answer:

  7. 183 in^2

  8. 192.42 m^2

  9. 239.4 ft^2

Step-by-step explanation:

7. The figure seems most easily seen as a trapezoid with a triangle removed. The trapezoid has bases of 26 and 14, and a height of 15. So, its area is ...

  A = (1/2)(b1 +b2)(h) = (1/2)(26+14)(15) = 300 . . . . . . square inches

The triangle has a base of 26 and a height of 9, so an area of ...

  A = (1/2)bh = (1/2)(26)(9) = 117 . . . . . . square inches

Then the shaded area is ...

  300 in^2 -117 in^2 = 183 in^2

__

8. The area of the donut can be found different ways. One way is to multiply the width of the shaded area (3.5 m) by the circumference of its centerline.

The centerline diameter is 21 m - 3.5 m = 17.5 m, so the circumference of that circle is ...

  C = πd = π(17.5 m) = 17.5π m

Then the area of the shaded part is ...

  (3.5 m)(17.5π m) = 61.25π m^2 ≈ 192.42 m^2

__

9. As in problem 7, this can be treated as a parallelogram less a triangle. Here, we need to do a little work to find the area of the triangle.

The triangle of interest is a right triangle with hypotenuse 23.8 ft and one leg 21 ft. The Pythagorean theorem can be used to find the other leg:

  h = √(23.8^2 -21^2) = √125.44 = 11.2

Then the area of the triangle is ...

  A = (1/2)bh = (1/2)(21)(11.2) = 117.6 . . . ft^2

The area of the parallelogram (including the triangle) is ...

  A = bh = (23.8 ft)(15 ft) = 357 ft^2

So, the shaded area is the difference ...

  357 ft^2 -117.6 ft^2 = 239.4 ft^2

_____

<em>Comment on significant digits</em>

The area in problem 8 may be considered to be 192.325 m^2 if you are required to use 3.14 as the value for pi. Since that value is only good to 3 significant digits, it is quite pointless to report the answer to 6 significant digits when using that value. It is quite reasonable to use 192 m^2 for the answer, especially if you're required to round to whole numbers.

8 0
3 years ago
Andrea made a replica of the Empire State Building. The surface area of the model is 45 ft2. What is the surface area of the act
melamori03 [73]

Answer:

<u>87,120 ft²</u>

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Surface area of the Empire State building replica = 45 square feet

Scale factor = 44

2. What is the surface area of the actual Empire State Building in square feet?

For answering the question, we will make the following calculations:

45 square feet = 9 feet * 5 feet or,

45 square feet = 10 feet * 4.5 feet, or,

45 square feet = 20 feet * 2.25 feet.

Now, let's apply the scale factor to all of these probable lengths of the sides of the surface area of the replica, as follows:

(9 *44) * (5 * 44) = 396 * 220 = 87,120 ft²

(10 * 44) * (4.5 * 44) = 440 * 198 = 87,120 ft²

(20 * 44) * (2.25 * 44) =  880 * 99 = 87,120 ft²

<u>As we proved, no matter what are the lengths of the sides of the surface area of the replica. after applying the scale factor, the result is the same: 87,120 ft²</u>

6 0
3 years ago
How does knowing the slope and y-intercept help you graph and write the equation of a line?
IgorLugansk [536]

Answer:

It allows to to know y-intercept formula which is used to graph a line.

Step-by-step explanation:

Y-intercept formula:

y=mx+b

  M: slope (keep in fraction if it is fraction, to help you graph)

  B: y-interecept

8 0
3 years ago
Write as a decimal fraction of a cm (a) 5 mm (b) 8mm
lys-0071 [83]
1 mm = 0.1 cm

(a) 5 mm

5 × 0.1 = 0.5 

Fraction :- 5/0.5
5 ÷ 0.5 =10
Decimal:- 10

(b) 8 mm

8 × 0.1 = 0.8

Fraction:- 8/0.8
8 ÷ 0.8 = 10
Decimal:- 10
8 0
3 years ago
Read 2 more answers
What is the measure of m?
Tanya [424]
(6+18)^2 = m^2 + m^2
=> 2m^2 = (24)^2
=> m = 24/sqrt(2)
8 0
3 years ago
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