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Elis [28]
3 years ago
11

The coordinates of point a are 30 units of x and 70 units of y. the coordinates of point b are 28 units of x and 76 units of y.

with x on the horizontal axis and y on the vertical axis, the slope of the line between points a and b is
Mathematics
1 answer:
Leni [432]3 years ago
6 0
The first thing you should know is that the slope of the line that passes through two points, by definition is given by:
 m = (y2-y1) / (x2-x1)
 Substituting the values we have:
 m = (76-70) / (28-30)
 m = -3
 answer:
 the slope of the line between points a and b is
 m = -3
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The diagram shows the dimensions of a teepee. Find the volume of the building to the nearest cubic unit. Use 3.14 for pi.
LekaFEV [45]
The volume of a cone uses the following formula:

V =  \pi r^{2} \frac{h}{3}

Our diameter is 20 feet, so divide this by 2 to find the radius:

20 \div 2 = 10

We now have all of our values need to fill in the formula. Plug in these values:

\pi = 3.14, r = 10, h = 17

3.14 * 10^{2} *  \frac{17}{3}

3.14 * 100 * 5.67

314 * 5.67 = 1780.38

The volume of the cone is 1780 cubic feet.
7 0
3 years ago
Each of the line segments in the word MATH are numbered in the graph below. Find the slope (as a ratio of rise over run) of each
emmasim [6.3K]

Answer/Step-by-step explanation:

7. Line 1 = undefined.

Slope of a vertical line is always undefined. The run is zero as x-coordinate remains the same.

8. Line 2 = \frac{4}{3}

slope = \frac{y_2 - y_1}{x_2 - x_1}

slope = \frac{8 - 4}{-5 -(-8)}

slope = \frac{8 - 4}{-5 + 8}

slope = \frac{4}{3}

9. Line 3 = \frac{4}{3}

slope = \frac{y_2 - y_1}{x_2 - x_1}

slope = \frac{8 - 4}{-2 -(-5)}

slope = \frac{8 - 4}{-2 + 5}

slope = \frac{4}{3}

10. Line 4 = undefined (slope of a vertical line is always undefined)

11. Line 5 = \frac{7}{3}

slope = \frac{y_2 - y_1}{x_2 - x_1}

slope = \frac{8 - 1}{5 - 2}

slope = \frac{7}{3}

12. Line 6 = -\frac{7}{3}

slope = \frac{y_2 - y_1}{x_2 - x_1}

slope = \frac{8 - 1}{5 - 8}

slope = \frac{7}{-3}

slope = -\frac{7}{3}

13. Line 7 = 0

An horizontal line has no rise.

14. Line 8 = 0 (slope of horizontal line is always zero)

15. Line 9 = undefined (slope of a vertical line is always undefined)

16. Line 10 = undefined (slope of a vertical line is always undefined)

17. Line 11 = 0 (slope of horizontal line is always zero)

18. Line 12 = undefined (slope of a vertical line is always undefined)

5 0
3 years ago
Find the area of the surface. The part of the surface z = xy that lies within the cylinder x2 + y2 = 36.
rewona [7]

Answer:

Step-by-step explanation:

From the given information:

The domain D of integration in polar coordinates can be represented by:

D = {(r,θ)| 0 ≤ r ≤ 6, 0 ≤ θ ≤ 2π) &;

The partial derivates for z = xy can be expressed  as:

y =\dfrac{\partial z}{\partial x} , x = \dfrac{\partial z}{\partial y}

Thus, the area of the surface is as follows:

\iint_D \sqrt{(\dfrac{\partial z}{\partial x})^2+ (\dfrac{\partial z}{\partial y})^2 +1 }\ dA = \iint_D \sqrt{(y)^2+(x)^2+1 } \ dA

= \iint_D \sqrt{x^2 +y^2 +1 } \ dA

= \int^{2 \pi}_{0} \int^{6}_{0} \ r  \sqrt{r^2 +1 } \ dr \ d \theta

=2 \pi \int^{6}_{0} \ r  \sqrt{r^2 +1 } \ dr

= 2 \pi \begin {bmatrix} \dfrac{1}{3}(r^2 +1) ^{^\dfrac{3}{2}} \end {bmatrix}^6_0

= 2 \pi \times \dfrac{1}{3}  \Bigg [ (37)^{3/2} - 1 \Bigg]

= \dfrac{2 \pi}{3} \Bigg [37 \sqrt{37} -1 \Bigg ]

3 0
2 years ago
Is it <br> a.x = _<br> b. the solution is all real numbers <br> c. there is no solution
Zielflug [23.3K]

The solution to the given algebraic equation 1000(7x - 10) = 50(292 + 100x) is; x = 12.3

<h3>How to simplify algebraic equations?</h3>

We want to simplify the algebraic equation;

1000(7x - 10) = 50(292 + 100x)

The first step is to use distributive property of equality to expand the bracket to get;

7000x - 10000 = 14600 + 5000x

7000x - 5000x = 14600 + 10000

2000x = 24600

Use division property of equality to divide both sides by 2000 to get;

x = 24600/2000

x = 12.3

Thus, we can conclude that the solution to the given algebraic equation 1000(7x - 10) = 50(292 + 100x) is; x = 12.3

Read more about algebraic equations at; brainly.com/question/723406

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7 0
1 year ago
Charlie wants to buy new carpet for his living room floor the floor is in the shape of a rectangle its length is 15 feet and the
sdas [7]

Answer:

135 square ft.

Step-by-step explanation:

To solve this equation, you need to find the area of this rectangle. Area is always base x height, or in this case, length x width. Now you multply your length, 15', by your width, 9', to get your answer, 135 square feet. When you multiply two measurments of the same unit together, you get square (units), which simply means that you multiplied two of the same unit of measurment together.

8 0
3 years ago
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