Solve for the dimensions of the area model below and then write an equation showing how the area as a sum is equivalent to the area as a product.

Answer:

Original position: base is 1.5 meters away from the wall and the vertical distance from the top end to the ground let it be y and length of the ladder be L.

Step-by-step explanation:

By pythagorean theorem, L^2=y^2+(1.5)^2=y^2+2.25 Eq1.

Final position: base is 2 meters away, and the vertical distance from top end to the ground is y - 0.25 because it falls down the wall 0.25 meters and length of the ladder is also L.

By pythagorean theorem, L^2=(y -0.25)^2+(2)^2=y^2–0.5y+ 0.0625+4=y^2–0.5y+4.0625 Eq 2.

Equating both Eq 1 and Eq 2: y^2+2.25=y^2–0.5y+4.0625

y^2-y^2+0.5y+2.25–4.0625=0

0.5y- 1.8125=0

0.5y=1.8125

y=1.8125/0.5= 3.625

Using Eq 1: L^2=(3.625)^2+2.25=15.390625, L=(15.390625)^1/2= 3.92 meters length of ladder

Using Eq 2: L^2=(3.625)^2–0.5(3.625)+4.0625

L^2=13.140625–0.90625+4.0615=15.390625

L= (15.390625)^1/2= 3.92 meters length of ladder

hope it helps...

correct me if I'm wrong...

Answer:

4.8 feet

Step-by-step explanation:

Use the cosine ratio, since we are given the length of the hypotenuse (the ladder) and are asked to find the horizontal distance between it and the ground.

Let x represent the horizontal distance (the adjacent leg)

cosine θ = adjacent / hypotenuse

cosine 76° = x / 20

(20)(cosine 76°) = x

4.8 = x

So, the horizontal distance is approximately 4.8 feet

Answer:

Angle a = 80°, Angle b = 55°, Angle c = 45°, Angle d = 80°

Step-by-step explanation:

To find the measure of Angle a, we add 55 and 45, then subtract the sum from 180.

180 - 100 = 80

Angle a is 80°.

Then, we solve for Angle b. Line segment CD is congruent to Line AB, so Angle b is congruent to 55°.

After that, we find Angle c. Line segment AC is congruent to Line segment BD, so Angle c is congruent to 45°.

Lastly, we solve for Angle d using the same method we used for Angle b and Angle c. Angle d is congruent to Angle a, so it measures 80°.

So, Angle a = 80°, Angle b = 55°, Angle c = 45°, Angle d = 80°.

Answer:

c = 24

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

5x + 10y = 800

y = 50

5x + 10(50) = 800

5x + 500 = 800

5x = 300

x = 60

Answer: 60

Step-by-step explanation:

If x = small vehicles and if y = large vehicles and y = 50, then substitute and solve for x. So,

5x + 10(50) = 800

5x + 500 = 800

5x = 300

x = 60

So, the number of small vehicles is 60.

Answer:

1..9.9

2....23.9

3...106.9

4....21.8

Step-by-step explanation:

1-9.9

2-23.9

3-106.9

4-21.8

5-95.01

6-715.8

Answer:

D

Step-by-step explanation:

f(x)=x²+3x+5

put x=a+h

f(a+h)=(a+h)²+3(a+h)+5

=a²+2ah+h²+3a+3h+5

Answer:

2a(b+c)

Step-by-step explanation:

Find HCF (2a)

Then factorise

Answer:

2a(b+c)

.............

Answer:

x = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Given

[tex]\frac{4}{5}[/tex] x - [tex]\frac{1}{10}[/tex] = [tex]\frac{3}{10}[/tex]

Multiply through by 10 ( the LCM of 5 and 10 ) to clear the fractions

8x - 1 = 3 ( add 1 to both sides )

8x = 4 ( divide both sides by 8 )

x = [tex]\frac{4}{8}[/tex] = [tex]\frac{1}{2}[/tex]

Answer:

500 kilowatt-hours.

Step-by-step explanation:

Let k = number of kilowatt-hours.

[tex]0.15k+30=105\\0.15k=75\\k=500[/tex]

Therefore, Dalton used 500 kilowatt-hours of electricity.

Answer:

I think the answer is option C

Answer:

110 marbles

side 14

Step-by-step explanation:

Draw triangles using marbles as the sides.

If the side is 2 marbles long, the triangle uses 3 marbles. 1 + 2 = 3

If the side is 3 marbles long, the triangle uses 6 marbles. 1 + 2 + 3 = 6

If the side is 4 marbles long, the triangle uses 10 marbles. 1 + 2 + 3 + 4 = 10

If the side is n marbles long, the triangle uses n(n + 1)/2 marbles.

These numbers are called triangular numbers.

We are looking for the side, n.

n(n + 1)/2 + 5 = (n + 1)(n + 2)/2 - 10

n^2 + n + 10 = n^2 + 3n + 2 - 20

n + 10 = 3n - 18

-n = -14

n = 14

For n = 14

n(n + 1)/2 =

= 14(15)/2

= 105

For n = 15

n(n + 1)/2 =

= 15(16)/2

= 120

105 + 5 = 120 - 10

You have 110 marbles. If you had 5 fewer, 105, you'd have a triangle with sides 14. If you had 10 more, 120, you'd have a triangle with sides 15. Since you have 110, you have 5 too many for side 14 and 10 too few for side 15.

The sides of the triangle is 14.

Answer:

the square of hypotenuse rs eqaul to the sum of the square of the legs

Answer:

V=1/3(pi)*r^2*h

Step-by-step explanation:

Think about a cylinder. If you combine 3 cones, you get a cylinder. Find the volume of a cylinder

Answer:

Step-by-step explanation:

V = 1/3 r^2 * π * h

3V = r^2 *π * h

3V/π = r^2 * h

h = 3V/(r^2 * π)

Answer:

B

Step-by-step explanation:

B was missed. You have to convert this from hours into minutes before you can deal with seconds.

9514 1404 393

Answer:

  (a)  y = 2/x

Step-by-step explanation:

The vertical and horizontal asymptotes are the axes, so there is neither a vertical nor a horizontal offset to the parent function y = 1/x. There is a vertical stretch by a factor of 2, so the describing function is ...

  y = 2/x

Answer:

Answer:[tex]13c = 65 \ \ c = \frac{65}{13} \ \ c = 5[/tex]  More

Answer:

12 nickels and 9 dimes

Step-by-step explanation:

1/ We have: n + d = 21 <=> d = 21 - n or opposite (n = 21 - d)

2/ We have: 0.05n + 0.10d = 1.50 and then we will put 1/ into 2/

=> 0.05n + 0.10(21 - n) = 1.50

=> 0.05n + 2.1 - 0.1n = 1.5

=> -0.05n = -0.6

=> n = 12

Nevertheless, d = 21 - n = 21 - 12 = 9

Explanation:

Angles 4 and 8 are corresponding angles since they are both in the southwest corner of their respective 4 corner configuration.

Corresponding angles are congruent when we have parallel lines like this.

Set the expressions equal to each other and solve for x

angle 4 = angle 8

x+20 = 2x+5

x-2x = 5-20

-x = -15

x = 15

Use this x value to find the two angles to help confirm we have the correct x value, and to finish up to answer the question.

So that's why the answer is B) 35 degrees

Step-by-step explanation:

(1/2) / (1/3) = (1/2)(3/1) = 3/2 miles per hour = 1.5 miles per hour

Answer:

Step-by-step explanation:

to find the unit rate, which is what we are looking for, we have to divide the number of miles by the number of hours. Specifically:

[tex]\frac{\frac{1}{2} }{\frac{1}{3} }[/tex] and to work this out, we bring up the bottom fraction and flip it to multiply, giving us:

[tex]\frac{1}{2}[/tex] × [tex]\frac{3}{1}[/tex] which is [tex]\frac{3}{2}[/tex] miles per hour (which is the same thing as walking a mile and a half every hour). The choice you're looking for is the one that reflects 3/2 miles per hour. (I can't see which choice it is; they're too small!)

Answer:

B. (negative infinity, -1)

Answer:

1.

avg time = total time/ 3

for big car :-

= 4.46/ 3

= 1.48

for small car :-

= 5.14/ 3

= 1.71

2.

avg speed = total distance/ total time

for big car:-

= 2/ 4.46

= 0.45

for small car :-

= 2/ 5.14

= 0.4

Answer: 16,200 Seconds

Step-by-step explanation:

Data: 4.5 hours(h)=x seconds(s)

Step One, Convert Hours Into Minutes

4.5h=4h and 30 minutes(m)

1h=60mx4=240m+30=270m

Reason: Since to convert to seconds, minutes are needed, you have to convert everything to minutes. And with 60 minutes in an hour you have to multiply 60 by 4 to get 240 and add 30 minutes to it(since it's 4.5 hours) to find ourselves at 270 minutes.

Step two, Convert Minutes Into Seconds

1m=60s

270mx60=16,200s

Reason: Since we are ultimately trying to get 4.5 hours into seconds, we have to convert the minutes we have into seconds by multiplying 270 minutes by 60(since 60 seconds are in a minute) to get our final answer of 16,200 seconds.

I hope this helps!

Answer:

None of the above

Step-by-step explanation:

Distance is the difference between two positions. That is x1- x2  Since both numbers were negative, you would want the absolute value of one plus the other, because subtracting a negative results in a positive. For this example the distance would look more like this:

| -4.7 - ( -3.9 ) | = .8

Answer:

[tex]32 \frac{2}{3 }miles- - - - 3 \frac{1}{ 2} minutes \\ \frac{98}{3} miles - - - - \frac{7}{2} minutes \\ \frac{2}{7} \times \frac{98}{3} miles - - - - 1minute \\ 60 \times \frac{2}{7} \times \frac{98}{3} miles - - - - 1 \: hour \\ 560 \: miles - - - - 1hour[/tex]

Answer:

the first one

Step-by-step explanation: