Item 11
A 10-foot ladder leans against a wall so that it is 6 feet high at the top. The ladder is moved so that the base of the ladder travels toward the wall twice the distance that the top of the ladder moves up. How much higher is the top of the ladder now? (Hint: Let 8−2x be the distance from the base of the ladder to the wall.)

Answers

Answer 1

Answer:

4 ft higher

Step-by-step explanation:

Since the ladder is 10 ft long and its top is 6 feet high(above the ground), we find the distance of its base from the wall since these three (the ladder, wall and ground) form a right angled triangle. Let d be the distance from the wall to the ladder.

So, by Pythagoras' theorem,

10² = 6² + d²  (the length of the ladder is the hypotenuse side)

d² = 10² - 6²

d² = 100 - 36

d² = 64

d = √64

d = 8 ft

Since the ladder is moved so that the base of the ladder travels toward the wall twice the distance that the top of the ladder moves up.

Now, let x be the distance the top of the ladder is moved, the new height of top of the ladder is 6 + x. Since the base moves twice the distance the top of the ladder moves up, the new distance for our base is 8 - 2x(It reduces since it gets closer to the wall).

Now, applying Pythagoras' theorem to the ladder with these new lengths, we have

10² = (6 + x)² + (8 - 2x)²

Expanding the brackets, we have

100 = 36 + 12x + x² + 64 - 32x + 4x²

collecting like terms, we have

100 = 4x² + x² + 12x - 32x + 64 + 36

100 = 5x² - 20x + 100

Subtracting 100 from both sides, we have

100 - 100 = 5x² - 20x + 100 - 100

5x² - 20x = 0

Factorizing, we have

5x(x - 4) = 0

5x = 0 or x - 4 = 0

x = 0 or x = 4

The top of the ladder is thus 4 ft higher


Related Questions

If m varies directly as n and inversely as the square of p then m=n/kp
true or flase​

Answers

It’s true :) no problem

please helpp will mark brainlyist

Answers

I’m pretty sure it’s (3.63)


3.631923997916374

which one is greater 3/10 or 2/5

Answers

Answer:

2/5

Step-by-step explanation:

2/5=4/10

Answer:

2/5 is great because it's 40%

3/10 is 30%

so 2/5 is greater

Currently I have separators on my molars so I can have enough space for an expander. But I noticed that one of my molars has shifted a lot to the side where it’s uncomfortable to eat or bite down. And I’m not sure if it’s suppose to shift to the side or not

Is that normal?-

Answers

Answer:

Yes I think

Step-by-step explanation:

I went through the braces process a few years ago and I got an expander. Your separator is probably making room for something meaning your teeth will probably move. Im no professional so Id say call into the office tomorrow or asap. And for the pain use whatever pain meds they allow (normally ibprophen ot tylenol) (sorry for spelling)

PLEASE HELP GEOMETRY IM STUCK!!! SHOW WORK

Answers

Answer:

N

Step-by-step explanation:

Since C is 48 you minus 6 from it since 6 is on the side so thus 48 - 6 = 42

Happy I can help

Answer:

48

Step-by-step explanation:

We are going to use trigonometry to solve for the wanted angle

Remember these are the trigonometric functions

( Remember SOH CAH TOA )

Sine = Opposite over Hypotenuse (SOH)

Cosine = Adjacent over Hypotenuse (CAH)

Tangent = Opposite over Adjacent (TOA)

For angle Ф

we are given its adjacent side length (6) and the hypotenuse (9)

Adjacent and hypotenuse corresponds with the trig function Cosine

So we will use cosine to solve for the missing angle

( let x = missing angle )

( remember cosine = adjacent over hypotenuse )

[tex]cosX=\frac{6}{9} \\\frac{6}{9} =.66\\cos(x)=.66[/tex]

now we want to get rid of the "cos" on the x

To do so we take the inverse of cos ( arc cos ^-!1 ) and apply it to each side

so...

[tex]arcos(cos(x))=x\\arccos(.66)=48.1[/tex]

we're left with x = 48.1

A triangle has two sides measuring 8 and 15. The included angle is 33°. What is the length of the side opposite the 33° angle?

Answers

Answer:

Measure of the side opposite to the angle measuring 33° is 9.37 unit

Step-by-step explanation:

If a, b and c are the sides of a triangle,

And 'a' = 8

b = 15

Measure of the Included angle C = 33°

By applying cosine rule in the given triangle,

c² = a² + b² - 2abcos(C)

c² = 8² + (15)² - 2(8)(15)cos(33°)

   = 64 + 225 - 201.28

   = 87.72

c = √87.72

c = 9.266

  ≈ 9.27

Therefore, measure of the side opposite to the angle measuring 33° is 9.37 units

Can you please help me?

Answers

Question 3: y=25000(.94)^t
Question 4: c

Can anyone help me wit this please, with an explanation

Answers

Answer:

ΔABC → ΔA'B'C'

7 up and 6 right

(x - 6, y + 7)

ΔA'B'C' → ΔA''B''C''

Reflection over the x-axis

(x, -y)

pls help ASAP WILL MARK BRAINLIEST

Answers

Answer:

[tex](4w + 4) + < de + (2w + 11) = 180 \\ < de = 180 - 4w - 4 - 2w - 11 \\ < de = (165 - 6w)[/tex]

Where is the blue dot on the number line?

Answers

Answer:

-15

Step-by-step explanation:

Answer:

On -15.

Step-by-step explanation:

So, the common difference seems to be 5.

Therefore, the point before -5 will be -10 and the point before -10 is -15.

Yo guys help pls.pls pls

Answers

Answer:

A rectangle is a parallelogram because parallelograms have to have exactly 2 pairs of parallel sides. A rectangle has 2 parallel sides, therefore it is considered a parallelogram.

Step-by-step explanation:

Algebra 2 will mark brainliest. 4 pictures 4 questions

Answers

Answer:

decreasing because x is negative.

Write the inequality that represents the number line

Answers

Answer:

C)

Step-by-step explanation:

2. Which of the following expressions has a simplified
value of 2a + 2?
A. -6a + 9a + 4-2
B. -a + 4 + 5a-a-6
C. -8 + 3a + 10 - a
D. -10 -5a + 12 + 8a

Answers

Answer:

C) -8 + 3a + 10 -a = 2a + 2

Step-by-step explanation:

I think the answer might be C.

Step-by-step explanation:

That is because if you look at C, it is -8 + 3a + 10 - a. Since it says -a, it means you have to subtract 3a - a = 2a, since a variable equals one in algebra.  Then all that is left is -8 + 10, which will give you 2, which will give you 2a + 2. Hope this helps.

In 0.46, in which place is the 6?

Answers

Answer:

hundredths

Step-by-step explanation:

the 4 is in the tenth place therfore the 6 is in the hundredth place because it is 46/100

It is Hundredths
That place 6

Please help ASAP!!!!

Answers

Answer:

m<CAO = 56°

Step-by-step explanation:

Same-side interior angles are supplementary to each other, so take their sum and set them equal to 180 and solve for x:

2x + 3x + 40 = 180

5x + 40 = 180

5x = 140

x = 28

Plug x=28 into angle CAO:

CAO = 2(28) = 56°

-4(w+1) = -24−4(w+1)=−24minus, 4, left parenthesis, w, plus, 1, right parenthesis, equals, minus, 24 w =w=w, equals

Answers

Answer:

W=5

Step-by-step explanation:

-4(w+1}=-24

-4w-4=-24

-4w=-20

w=5

Answer:

its 5

Step-by-step explanation:

i got i correct ;)

Please help
The price of a sweater decreased from 29.99 to 24.49. Find the percent decrease.

Answers

Answer:

The answer is 5.45%.

Step-by-step explanation:

29.99 - 24.49 = 5.5 which is the amount the price decreased.

Then, we divide the amount of decrease from the initial amount:

29.99 / 5.5 = 5.45

The answer is 5.45%

Someone please help!! I’ll give brainliest:))

Answers

I’ve attached my work...
Hope it helps! Have a nice day :)

what is the value of [(-3)^3]^2+2^4?

Answers

745!

Hope this helped :)



I need help take your time and think you

Answers

(X-4)(x+1) this is what I found

A point at (-7, -6) is reflected over the x-axis. What is the distance between the point and its reflection?

6 units
7 units
12 units
14 units

Answers

Answer:

It Would be 14 units.

Step-by-step explanation:

Have a Great Day.

:)

Will accept Brainliest

Marco has 2 bags of flour with 6
cups of flour in each bag. He makes 6 batches of muffins and uses 1 2/3
cups of flour for each batch.
How many more batches of muffins can Marco make with the flour he has left?

Answers

Answer:

2 batches

Step-by-step explanation:

Find the missing side.

Need help please. Need explanation, please.

Answers

This is basic trigonometry. First use SOH CAH TOA. Now look, you are finding opposite and adjacent so you use tangent. Now heres the equation - x/11 = tan48 now isolate the x. 11(tan48) = x.
Now plug into calculator and you get 12.2167

Answer:

x ≈ 12.22

Step-by-step explanation:

SOH CAH TOA(Tangent = opposite side/adjacent side)

tan (48°) = x/11

=> x = tan (48°) × 11

=> x ≈ 12.22

Help!!! I need this asap!

Answers

Answer:

x= 14.8

Step-by-step explanation:

√12²+8²= 4√13

56.3= sin-¹(12/4√13)

tan56.3= 21.6/4√13

x+8= √21.6²+4√13²

x= 14.8

do the following conditions make a unique triangle more than one triangle or no triangle possible​

Answers

C no rectangle possible

Answer:

No triangle possible.

Step-by-step explanation:

3 + 6 < 10 so no triangle can be drawn with these lengths.

solve each of the following equations show solution set on a number line 3x-1=8

Answers

Answer:

x=3

Step-by-step explanation:

here u go!!! :)

answer

Steffie makes a scale drawing for a crate with a scale factor of 1 to 3 the dimensions of her scale drawing are 15 inches long by 12 inches wide. The builder creates a scale drawing of the crate with a scale factor of 1 to 9

Answers

Answer:

The length is 5 inches and the width is 4 inches

Step-by-step explanation:

Steffie makes a scale drawing for a crate with a scale factor of 1:3. The dimensions of her scale drawing are 15 inches long by 12 inches wide. The builder creates a scale drawing of the crate with a scale factor of 1:9. What are the dimensions of the builder's scale drawing? A. The length is 4 inches and the width is 5 inches B. The length is 45 inches and the width is 36 inches. C. The length is 5 inches and the width is 4 inches. D. The length is 36 inches and the width is 45 inches

A scale drawing is a reduced form in terms of dimensions of an original image / building / object

the scale drawing is usually reduced at a constant dimension

scale of the drawing = original dimensions / dimensions of the scale drawing

dimensions of the image steffie scaled = (15 x 3) by (12 x 3) = 45 by 36

Builders scaled image = (45 / 9) by (36 /9) = 5 by 4

Helpppp asapppp I’ll give you a lot of points

Answers

Answer:

[tex]x = \frac{5a-2} {7+5a}\\[/tex]

Step-by-step explanation:

Given the expressions

[tex]x = \frac{5}{9y+5}....1\\y = \frac{5}{5a-2} ...2[/tex]

Substitute 2 into 1

[tex]x = \frac{5}{9(\frac{5}{5a-2} )+5} \\x = \frac{5}{(\frac{45}{5a-2} )+5} \\x = \frac{5}{\frac{45+5(5a-2)}{5a-2} } \\x= \frac{5}{\frac{35+25a}{5a-2} }\\x = \frac{5(5a-2)} {35+25a}\\x = \frac{5(5a-2)} {5(7+5a})\\\\x = \frac{5a-2} {7+5a}\\[/tex]

PLEASSE HELP!!! find the midpoint

Answers

The answer is B

-5 is between -2 and -8.

If you are unable to do this problem, make a graph and see where the midpoint is. Even imagine the graph if necessary.

Have a great day :)

Answer:

Option B --> (8, -5)

Step-by-step explanation:

To find the midpoint, we use the equation-

[tex]\frac{x1 + x2}{2} , \frac{y1 + y2}{2}[/tex]

The coordinates given were (8, -2) (8, -8)

x1= 8,

x2 = 8

y1 = -2

y2= -8

Substituting these values in the equation:-

[tex]\frac{8+ 8}{2} , \frac{-2 + -8}{2}[/tex]

[tex]\frac{16}{2} , \frac{-10}{2}[/tex]

Coordinates of midpoint will be ---> (8, -5)

Other Questions
Which of the following are most likely to cause erosion? Choose more than one answer. What natural disasters are caused by the water cycle? 14. Rewrite the sentence to correct the dangling modifier: Climbing into the car, my camera dropped and broke. PLEASEEEE HELP THIS IS SPANISH QuizActive23610TIME REMAINING01:55:50Read the introduction to an outline of a narrative essay.Introduction: My positive experiences planting a victory garden during WWIIWhich of the following is the best thesis to include in the introduction to this outline? Working with my family to plant a victory garden made me feel that I was doing something helpful to win the war.O I helped my family plant fruits and vegetables in our victory garden during World War II.O Working with my family to plant a victory garden during World War II was a good thing to do.I liked helping plant a large victory garden during World War II because gardening is fun.Mark this and returnSave and ExitNextSubmit HELPPPPZ WORTH 30 POINTS AND BRAINLIEST When entering numbers that start with a zero, apply the _____ number format.A. TextB. ContextC. ZeroD. Zero decimal sine of z if the opp=5 hyp=6 What is the five-digit number, no zeroes, in which the second digit is three times the first, the third is one more than the second, the fourth is four times the first, and the last is one-half more than the second? HI I NEED HELP I WILL GIVE BRAINLIEST NEED IT NOW ITS 8TH GRADE HISTORY FLVS LESSON 3.06 In a recent poll, less than 10 percent of American adults knew why the Bill of Rights was written! Something must be done to inform people, and you are just the person to do it. You will take on the role of someone who has recently been granted U.S. citizenship. Use your imagination to create your own name and story.As a new citizen, you are excited about the freedoms and rights that your new government protects. You would like to help other citizens, including immigrants like you, understand what these rights mean. Explore the tab box below to learn more about this assessment.Remember to select each tab below so you do not miss any necessary information.ResearchPreparePresentResearch:To share your knowledge of the Bill of Rights with others, you will create a public service announcement that will appear around your community. Review the 10 amendments and explore examples of public service announcements to get started!Prepare:Remember that you need to attract peoples attention with a catchy phrase or title. Then you need to keep their attention by being direct and creative. Reading or watching a PSA should take only a minute of peoples time. The public service announcement should include:Your imaginary nameAn explanation, in your own words, of one of the first 10 amendments to the ConstitutionAn explanation, in your own words, of why it is important for a person to know the amendment you choseAn example of how the amendment would be used todayPresent:You can choose to present your public service announcement in many different formats. Here are a few suggestions to get you started.Brochure: Create a brochure about the Bill of Rights. Your brochure should be made on paper folded in thirds. You may use a computer program to create the brochure and use photos or drawing tools for illustrations.Television spot: Create a television spot about the Bill of Rights. Consider what images and information will best inform your viewers. Your television spot should be one to two minutes long.Podcast: Create a podcast about the Bill of Rights. Your podcast should be one to two minutes long. Consider how your tone of voice and possible sound effects might enhance your content.Poster: Create a poster about the Bill of Rights. Consider using photos or drawing tools to illustrate your poster.Your public service announcement announcement must be typed. If you choose to create a video or podcast, the script should be typed and submitted as well. Someday, as a result of space exploration and travel, scientists may be able to solve the mysteries of the universe. Their discoveries may also change our view of life on Earth and of our planet's role in the universe.What kind of argument is used in this paragraph? A sugar cube was placed into a beaker containing 100 mL of water at room temperature and completely dissolved into the water. This process is represented by the series of diagrams labeled A, B, and C below. Describe one way that the dissolved sugar at C could be separated from the water. What is likely to happen to the trees if the trend continues? Semester 2 Exam Review Part 1Quiz: Teen Detective 36.0 (Practice)Because of all of their adventures, what class did Summer say they would be ahead in?GeometryGeographyHistorySocial StudiesFor what purpose are the works of art being kept safe?for future art classesfor future generationsfor future history classesfor future museumsWhat happened at the end of the story?Jake and Summer were awarded the "Teen Detective of the Year".Dr. Sabato became Jake and Summer's history teacher.Jake's and Summer's teleportation devices activated.Jake and Summer go to Disneyland. Question ProgressHomework Progress20/32 Marksa) Write 375 as the product of prime factors.Give your answer in index form.b) Work out the Highest Common Factor of 375 and 150. Mr. Cooper purchased a night standat the furniture store. It came in arectangular-prism-shaped box. Thevolume of the box is 31,050 cubicinches. The box is 36 inches deep and284 inches wide. What is the height ofthe box? Using the Hex color system in web design, which pair of numbers and letters relates to the amount of blue in the color #8b31c9? 11 to the power of negative 4 / 11 to the power to 8 Compare the decline or fall of the ancient Greek empire to the Mongol Empire when it fell? Think of the similarities or differences between the two empires.Please help me out, this is due tomorrow :,) The school office is located at the origin (0,0) of the coordinate grid. Which describes a path thatcould be followed to walk from the school library to the school office?(1 Point)A. walk 2 units north, then 3 units westB. walk 3 units west, then 9 units southC. walk 8 units east, then 2 units northD. walk 9 units north, then 3 units east