The length of a rectangle is 4 times the width. The rectangle width is 8 m what is the area of the rectangle

Maleek rested a 15.5-foot ladder against a building. The base of the ladder is 8.2 feet from the building. How far up the buildi

Whitepunk [10]

The ladder creates a right triangle with the building and the ground. The horizontal leg is 8.2 ft, the hypotenuse is 15.5 ft, and we need to find the vertical leg.
To do this, we use the Pythagorean Theorem:
${a}^{2} = \sqrt{ {b}^{2} + {c}^{2} } \\ a = 15.5 \\ b = 8.2 \\ c = \: ?$
First, we solve for c without adding numbers:
${( {a} ) }^{2} = {( \sqrt{ {b}^{2} + {c}^{2} } )}^{2} \\ {a}^{2} = {b}^{2} + {c}^{2} \\ {a}^{2} - {b}^{2} = {c}^{2} \\ \sqrt{ {a}^{2} - {b}^{2} } = c$
We square both sides, then subtract b^2 from both sides. Then we square root both sides to find c.
Now we plug in the numbers:
$c = \sqrt{ {(15.5)}^{2} - {(8.2)}^{2} } \\ c = \sqrt{ 240.25 - 67.24} \\ c = \sqrt{173.01} \\ c = 13.1533$
We plug in for a and b, then simplify. C, the distance from the ground to where the ladder rests against the wall, is about 13.2 ft.

7 0

3 years ago

Read 2 more answers

Select the correct answer.

Tanya [424]

Answer:

A. Yes they do. Both equations have their opposing set of y-intercept. Where equation one has a y-intercept of +7, and equation two, +7.

B. No they do not. Equation one has a slope of +3, while equation 2 has a slope of -4.

C. Yes they do. Equation one represents that of a positive increasing graph, while equation two the opposite, decreasing.

Step-by-step explanation:

You can use the slope formula to identify and graph each equation simply by using y = mx + b. Where y is the the y coordinate, x is the x coordinate, m is the slope, and b is the y-intercept. With this you can start plotting by marking the y-intercept by putting the x as zero and seeing what number you get. In this case, 3x0-7 = -7. Meaning that would be the y-intercept. For the slope, depending on what the x coordinate is, that's how much the graph will increase or decrease whenever the x coordinate changes. Say the x coordinate is 1, so 3x1-7 = 3-7 = -4. Meaning your coordinate would be (1, -4) where you can keep doing this formula on and on to find the y coordinate for what x coordinate you want to find, or make it easier to graph with a ruler on paper once you have enough points.

3 0

2 years ago

in trapezium abcd diagonals ac and bd intersect at o ar(COD) = 24cm² ar( AOB) = 96 cm² find the area of trapezium

irina1246 [14]

Answer:

The area of the trapezium is 216 cm²

Step-by-step explanation:

The parameters of the trapezium are;

The point of intersection of the diagonals ac and bd = point o

The area of ΔCOD = 24 cm²

The area of ΔAOB = 96 cm²

Let h represent the height of the trapezium and let x represent the height of triangle ΔCOD, we have;

The height of ΔAOB = h - x

Therefore;

The area of ΔCOD = (1/2) × The length of CD × x = 24

∴ The length of CD = 24/((1/2) × x) = 48/x

The area of ΔAOB = (1/2) × The length of AB × (h - x) = 96

The length of AB = 96/((1/2) × (h - x)) = 192/(h - x)

The area of the trapezium, A = ((48/x + 192/(h - x))/2) × h

We note that ΔCOD ~ ΔAOB, therefore;

(AB)²/(CD)² = (h - x)²/x² = (arΔAOB)/(arΔCOD) = 96/24 = 4

∴ √((h - x)²/x²) = (h - x)/x = √4 = 2

∴ h - x = 2·x

h = 2·x + x = 3·x

A = ((48/x + 192/(h - x))/2) × h

∴ A = ((48/x + 192/(2·x))/2) × 3·x = ((48 + 192/(2))/2) × 3 = 216

The area of the trapezium, A = 216 cm².

8 0

3 years ago

8. The circle centered at Q is a scaled copy of the circle center

VLD [36.1K]

Answer:

scale factor is: 1:4

the value of x is: x=4

Step-by-step explanation:

to find the answer, you do

x= √5² - 3² = √25 - 9 = √16 = 4

7 0

2 years ago

I have 11 months to raise 2,700 how much would i have to make everyday to get to my goal

Ilia_Sergeevich [38]

Answer:

The average amount of days in a month is about 30 days. Among 11 months, that is 330 days.

2700 divided by 330 days = $8.18 a day to reach exactly $2700

Step-by-step explanation:

Hope this helps! Have a nice day!

4 0

3 years ago