15 foot ladder leaning agaisnt a building touches the wall 12 feet above the ground how far from the building is the bottom of the ladder

Answers

Answer 1

The bottom of the ladder is 9 feet from the wall.

Using the Pythagorean Theorem, we can calculate the distance from the wall. The Pythagorean Theorem states that for a right triangle, the sum of the squares of the sides is equal to the square of the hypotenuse. In this case, the hypotenuse is 15 feet and the side adjacent to the wall is 12 feet.

The formula for the Pythagorean Theorem is a^2 + b^2 = c^2.

We can solve for the distance from the wall (a). a^2 = c^2 - b^2, so a^2 = 15^2 - 12^2, which equals a^2 = 225 - 144, so a^2 = 81. Taking the square root of both sides, a = 9 feet.

Therefore, the bottom of the ladder is 9 feet from the wall.

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Related Questions

After how many years will the loan be half-paid?
A. 15 years
B. 18 years
C. 21 years
D. 24 years

Answers

After 21 years it should be half paid
Good luck hope this helps
The answer is C.

Explanation: The question is how many years will the loan be paid in half (half priced). The current loan balance is 500,000. 500,000 divided by two is 250,000, so we're looking at the dots that’s is closer to 250,000. After carefully estimating throughout the 4 possible answers. Answer C is the most correct because it is closest to 250,000.

Sofia is making a batch of slime using a recipe that includes glue, water, and a salt solution. She uses 7. 5 fl oz of glue. The amount of glue is 12. 5 times the amount of salt solution. There are 4. 2 less fluid ounces of salt solution than water.

How many fluid ounces of water does Sofia use to make the batch of slime?

Answers

Total amount of fluid ounces of water used by Sofia to make proportionate amount of slime is equal to 4.8 fluid ounces.

Let us consider 'x' amount of salt solution.

Amount of glue used by Sofia = 7.5 fluid ounces

Amount of glue = 12.5 times of salt solution

⇒ 7.5 = 12.5x

⇒ x = 7.5 / 12.5

⇒ x = 0.6

Fluid ounces of water used by Sofia to make the required batch of slime is:

Now, Amount of salt solution = Fluid ounces of Water - 4.2

Fluid ounces of Water = x + 4.2

⇒ Fluid ounces of Water = 0.6 + 4.2

⇒ Fluid ounces of Water = 4.8 fluid ounces

Therefore, the fluid ounces of water used by Sofia with salt solution and glue to make a slime is equal to 4.8 fluid ounces.

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Explain in words how to solve an equation with a variable on both sides of the equation.

Answers

To solve an equation that has the same variable on both sides of it, you need to get the variables together on one side of the equation, and then get the numbers together on the other side of the equation.


The graph of y = In(x) was transformed by shifting 8 units left and 12 units up. Write an equation( please help!!)

Answers

The parent function and transformed function will be y = ln x and y = ln (x + 8) + 12, respectively.

What is a function?

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The function is given below.

y = ln x

The function is transformed by shifting 8 units left and 12 units up. Then replace x with (x + 8) and y with (y - 12). Then we have

y - 12 = ln (x + 8)

y = ln (x + 8) + 12

The parent function and transformed function will be y = ln x and y = ln (x + 8) + 12, respectively. The graph of the function is given below.

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i dont understand this

Answers

The given expression has sin A = BC/AC=36/85, cos A = AB/AC=77/85, tan A = BC/AB=36/77

How to find sin cos tan?

In trigonometry, the values of sin, cos, and tan are the main functions we consider when solving trigonometric problems. Using these trigonometric values, the angles and sides of a right-angle triangle are calculated. In addition to sine, cosine, and tangent values, the other three significant values are cotangent, secant, and cosecant.

Normally, when calculating the sin, cos, and tan values for a triangle, the angles of 0°, 30°, 45°, 60°, and 90° are taken into consideration. These specific angles' values are easy to remember. What the trigonometric values are all about is knowing the standard angles for a specific triangle according to the trigonometric ratios (sine, cosine, tangent, cotangent, secant and cosecant).

We have, AB = 77 , BC = 36.and CA=85

When we consider the t-ratios of ∠A, we have

Base = AB = 77, Perpendicular = BC = 36, Hypotenuse = AC =85.

∴sin A = BC/AC=36/85 , cos A = AB/AC=77/85 , tan A = BC/AB=36/77

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A chef made a blend of cooking oil. 1/5 of his mix was olive oil and 4/5 was corn oil. Write this blend as a ratio of corn oil to olive oil

Answers

1 :1 is the blend as a ratio of corn oil to olive oil.

Now, According to the question:

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls)

"Information available from the question"

A chef made a blend of cooking oil.

1/5 of his mix was olive oil

and 4/5 was corn oil.

To find the blend as a ratio of corn oil to olive oil.

Now, Blend Ratio will be:

olive ratio + corn ratio

1/5 + 4/5

= 5/5 = 1/1

Hence, 1:1 is the blend as a ratio of corn oil to olive oil.

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in how many different ways can the 8 letters a, b, c, d, e, f, g, and h be arranged if the letters a and b must be next to one another, the letters c and d must be next to one another, the letters e and f must be next to one another, and the letters g and h must be next to one another?

Answers

There are 384 ways to arrange these given letters as per the given situation.

What are permutation and combination?

A permutation is an orderly arrangement of things or numbers. Combinations are a means to choose items or numbers from a collection or set of items without worrying about the items' chronological order.

Given, different ways can the 8 letters a, b, c, d, e, f, g, and h be arranged if the letters a and b must be next to one another, the letters c and d must be next to one another, the letters e and f must be next to one another, and the letters g and h must be next to one another.

In this question, we have 2 ways where A and B (AB, BA) are next to each other and 2 ways where C and D (CD, DC) are next to each other.  2 ways where g and h (gh, hg) are next to each other and 2 ways where e and f (ef, fe) are next to each other.

The total number of arrangements is = 4! * 2 * 2 *2*2

The total number of arrangements is = 24 * 16

The total number of arrangements is = 384

Therefore, the Different ways to arrange these letters are 384.

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Classify the sequence {1, 6, 11, 16, 21, …}.

Answers

Answer:

Classify the sequence {1, 6, 11, 16, 21, …}.

The pattern is +5:

1 + 5 = 6

6 + 5 = 11

11 + 5 = 16

16 + 5 = 21

21 + 5 = 26

And so on

Step-by-step explanation:

You're welcome

The middle school has 24 students less than 3 times the number of students at one of
the elementary schools.

Answers

The required equation is y=3x-24, where x is the number of elementary school students and y is the number of middle school students.

What is equation?

An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =. In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical equation that depicts the relationship between two expressions on opposite sides of the sign. It mostly consists of one variable and one equal to symbol. 2x - 4 = 2 is an example.

Here,

Let x be the number of students in elementary school and y be the number of students in middle school.

y=3x-24

The required equation is y=3x-24 where x be the number of students in elementary school and y be the number of students in middle school.

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peacock premium tv charges $5.00 per month plus a set-up fee. the total cost after 10 months was $65.00. write an equation in point-slope form to model this situation.

Answers

A point-slope form is an equation for a line, using a point and the slope of the line. So we have to find one x-coordinate and y-coordinate and write it in the form of (y-y₁) = m(x-x₁).

Here the total after 10 months is said to be 65 and number of months = 10. So we can calculate the set-up fee.

5 ×10 + x = 65

  x = 65-50 = 15.

The only constant here is the set-up fee, 15.

Lets the number of months be x and total amount be y.

 y- 5x = 15

Lets calculate the y intercept. x-term will be 0.

  y+0 = 15

  y = 15

Lets calculate the x-intercept. y term will be 0

-5x = 15

x = -3

Two points on the line are (-3,0) and (0,15)

slope = (15-0)/(0--3)

         =15/3 = 5

So lets find out one point in the equation

If y=10,

10-5x = 15

  -5x = 15-10

    x = 5/-5 =-1

So a point on the line is (-1,10)

Point slope form,

(y-10) = 5 (x- ⁻1)

(y-10) = 5 (x+1)

So this is the point slope form.

y = 5x+15

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Given the following data, fill out the table for V* n and V/n
(give your answers to 3 sig figs).

Answers

The table for V* n and V/n shows the various answers as

What is multiplication and Division?

Multiplication is when you take one number and add it together a number of times.

The table appears as follows

Volume(V)       Moles(n)          V*n               V/n

3                       0.145              0.435           20.7

4                        0.193             0.773            20.7

5                        0.242            1.210             20.7

6                       0.290             1.740             20.7

These figures are gotten by the multiplication and division of the numbers in the tables as given by the formulae

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Simplify this to help me out

Answers

When we simplify the expression (4x⁴y⁵ / 3xy²)⁵, the result obtained is 1024x¹⁵y¹⁵ / 243

How do I simplify (4x⁴y⁵ / 3xy²)⁵?

To simplify the expression (4x⁴y⁵ / 3xy²)⁵, the laws of indices must be applied as illustrated below:

(4x⁴y⁵ / 3xy²)⁵

Recall

(Aᵐ)ⁿ = Aᵐⁿ

Thus,

(4x⁴y⁵ / 3xy²)⁵ = 1024x²⁰y²⁵ / 243x⁵y¹⁰

Recall

Aᵐ / Aⁿ = Aᵐ⁻ⁿ

Thus,

1024x²⁰y²⁵ / 243x⁵y¹⁰ = (1024 / 243)x²⁰⁻⁵y²⁵⁻¹⁰

1024x²⁰y²⁵ / 243x⁵y¹⁰ = (1024 / 243)x¹⁵y¹⁵

1024x²⁰y²⁵ / 243x⁵y¹⁰ = 1024x¹⁵y¹⁵ / 243

Therefore,

(4x⁴y⁵ / 3xy²)⁵ = 1024x¹⁵y¹⁵ / 243

From the above illustration, we can conclude that the simplified form of (4x⁴y⁵ / 3xy²)⁵ is 1024x¹⁵y¹⁵ / 243

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What is the solution of the system of equations
Y=1/8x-1
-5x+4y= - 13

Answers

Answer:

(2.57, -0.07)

Step-by-step explanation:

To solve the system of equations, we can substitute the expression for y in the second equation:

-5x + 4(1/8x - 1) = -13

We can then simplify and solve for x:

-5x + (1/2)x - 4 = -13

-3.5x = -9

x = 2.57

We can then substitute this value of x back into the first equation to find the value of y:

y = 1/8(2.57) - 1

y = -0.07

So the solution of the system of equations is (x, y) = (2.57, -0.07)

Mrs. Soriano baked 7 5/9 dozens of chocolate cookies. She gave 3 1/3 dozens to her friends. How many dozens of chocolate cookies were left ?
A. 4 3/9
B. 4 2/9
C. 4 5/9
D. 4 1/9

Answers

Answer:

4 2/9

Step-by-step explanation:

7 5/9 -3 1/3

68/9 -10/3

(68-30)/9

38/9

4 2/9

Find the smallest pair of 4-digit numbers such that the difference between them is 303 and their HCF is 101. Show your steps.


Please give answer immediately

Answers

Based on the information provided, the two numbers whose HCF is 101 are 1010 and 1313.

What is the HCF?

The HCF is the highest common factor or in other words, the highest number by which two numbers can be divided. Let's start by listing the four digits numbers that can be the HCF related to 101.

101 x 10 = 1010

101 x 11 = 1111

101 x 12 = 1212

101 x 13 = 1313

Now, from these numbers, there are two numbers whose difference is 303.

1313 - 1010 = 303

Based on this, the two numbers are 1010 and 1313

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If you were to sketch a circle graph for the data shown in the table below, approximately what
fraction of the circle would represent food?
Vacation Expenses Budget
Expense Amount Budgeted

Activities=600
Food= 450
Souvenirs=270

Answers

The fraction of the circle that would represent food is given as 34.09

How to solve for the fraction that would represent food

The data we have here is given as

Activities = 600

Food = 450

Souvenirs = 270

We would have to sum this up

600 + 450 + 270 = 1320

The proportion that represents food is given as 450

= 450 / 1320

= 0.3409

Then we would have to convert this to percentage

0.341 * 100

= 34.09

34.09 x 360 = 123 degrees

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Is 13,14,15 a pythagonrean triples

Answers

Answer:

milk

Step-by-step explanation:

milk store is where your dad went

Find the height of the figure.

12. A = 12 m²
4.8 m

13. A 11.0625 m²
3.75 m

Answers

The height of the figure is 66 m².

How to find height?

Finding the triangle's height can be done in a variety of ways. There are numerous other formulas, but the one that uses a triangle's area is the one that is most widely used. You can determine the triangle's area given its sides using an equation known as Heron's formula. Once you are aware of the region, you can use the fundamental equation to determine the triangle's altitude.

You multiply 27.5 and 4.8. Which gets you 132. And because your finding the area of a triangle you have to divide 132 by 2 which gets you 66.

27.5 × 4.8

= 132

132/2

= 66

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Question 32:
Write an equation in Slope-Intercept form for the
line that passes through (1,-3) and is parallel to
y+2 = 4(x-1)

Answers

The equation y+2 = 4(x-1) is already in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. In this equation, the slope is 4 and the y-intercept is -2.

For a line that is parallel to y+2 = 4(x-1), the slope (m) will be the same, which is 4.

To find the equation of a line that passes through a specific point (1,-3), we can use the point-slope form of a linear equation: y - y1 = m(x - x1)

So, using the point (1,-3) and the slope (4), we can write the equation as:

y - (-3) = 4(x - 1)

Simplifying this equation gives:

y + 3 = 4x - 4

Finally, we can write the equation in slope-intercept form by adding 4 to both sides and dividing both sides by 4:

y = 4x - 1

So the equation for the line that passes through (1,-3) and is parallel to y+2 = 4(x-1) is y = 4x - 1

Tell whether the two rates form a proportion.

-0. 4 kilometer for every 15 minutes

-0. 6 kilometer for every 20 minutes

Answers

As the value of the ratio of both the quantities are NOT same so the given values .

No, The two rates not form a proportion.

Now, According to the question:

Two ratios are equivalent, if the fractions corresponding to them are equivalent. Four quantities are said to be in proportion, if the ratio of the first and the second quantities is equal to the ratio of the third and the fourth quantities.

A proportion is an equation that sets two ratios at the same value. For instance, you might express the ratio as follows:

1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls. 0.25 are male (by dividing 1 by 4)

Now,

0. 4 kilometer for every 15 minutes equals to (0.4/15) = 0.026

So for every minute they travel 0.026km.

0. 6 kilometer for every 20 minutes equals (0.6/20) =  0.03

So for every minute they travel 0.03km.

Here, as the value of the ratio of both the quantities are NOT same so the given values .

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:)))))))))))))))))))))))))))))

Answers

The answer is 226.19
V= 3.14x2^2x18
The volume is found using Base X height. I dont have a calculator so you can finish it but the base is (pi X 4) then multiply it by 18 to find the volume as ft^3

Find five consecutive odd integers whose sum is 85.

Answers

Answer:

13+15+17+19+21 = 85

Step-by-step explanation:

Hope you got it !

Answer:

The five consecutive odd integers whose sum will be 85 are 13, 15, 17, 19, and 21.

Step-by-step explanation:

To solve this problem, let's assume the first number is n.

Then the consecutive odd integers will be n+2, n+4, n+6, n+8

Thus we can write,

n+(n+2)+(n+4)+(n+6)+(n+8) = 85

In the next step add all the n's,

5n+20 = 85

Then transfer '20' from LHS to RHS,

5n = 85 - 20

5n = 65

Then in the next step '5' needs to be transferred to RHS,  

n = 65÷5

n = 13

Therefore, n = 13

n+2 = 15

n+4 = 17

n+6 = 19

n+8 = 21

Thus the five consecutive odd integers are 13, 15, 17, 19, and 21.

There's a 1/6 chance that a student will be in Miss Jones math class if there are 30 students in her class how many students are there at all

Answers

If there is a 1/6 chance that a student will be in Miss Jones's math class, if there are 30 students in her class, then 180 students will be there at all.

Probability is a method to know how likely something is going to happen. Whenever we're uncertain about the outcome of an event, we can talk about the probabilities of certain outcomes. The analysis of events overseen by probability is called statistics.

Total number of students present in the miss jones class = 30

The chance that a student will be in Miss Jones's math class = 1/6

Let x be the students are there at all

According to the question,

1/6 × x = 30

⇒x = 30 × 6

⇒x = 180

Hence, 180 students are there at all.

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How much money would you need to deposit at 7% annual interest compounded yearly to have $10,000 in the account at the end of 5 years? Round to the nearest cent.

Answers

The account balance after five years will be $10355.

What is compound interest?

The interest that is paid on the principal and interest at regular intervals is known as compound interest. The difference between compound interest and simple interest starts to show after the first year, though.

The formula to calculate the compound interest is given below;-

[tex]A = P ( 1+\dfrac{R}{n})^{nt}[/tex]

Given that deposit at 7% annual interest compounded yearly to have $10,000 in the account at the end of 5 years.

The account balance after five years will be:-

[tex]A = P ( 1+\dfrac{R}{n})^{nt}[/tex]

[tex]A = 10000 ( 1+\dfrac{0.07}{1})^{5}[/tex]

A = 10000 x ( 1.07)⁵

A = $10355

Hence, the amount will be $10355.

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PLEASE HELPPP



You are the grade 10 representative on the student council and you have been assigned the
task of finding a location to host a dance for the students of CISE. You have narrowed it down
to three options which are outlined below:
Ancient Abyss is a location that charges a $200 flat fee and $4 per person.
Beautiful Babylon is a location that charges a $99 flat fee and $6 per person.
Crazy Cleopatra is a location that charges a $280 flat fee and $3 per person.

Task:
You will analyze the three options and put together a proposal to submit to the student
council outlining your recommendations.

Answers

Based on the information provided, I have analyzed the three options for hosting a dance for the students of CISE, and have come to the following recommendations:

Ancient Abyss: This location charges a flat fee of $200 and $4 per person. This option may be suitable for smaller events with less than 50 attendees, as the flat fee is relatively high. However, for larger events with more than 50 attendees, the per person cost will become more significant and may make this option less cost-effective.

Beautiful Babylon: This location charges a flat fee of $99 and $6 per person. This option may be more cost-effective for larger events with more than 50 attendees, as the per person cost is lower than Ancient Abyss. However, for smaller events with less than 50 attendees, the flat fee may be relatively high.

Crazy Cleopatra: This location charges a flat fee of $280 and $3 per person. This option has the highest flat fee but the lowest per person cost. This option may be more cost-effective for larger events with more than 50 attendees, as the per person cost is lower than Beautiful Babylon. However, for smaller events with less than 50 attendees, the flat fee may be relatively high.

Based on the above analysis, I recommend that the student council consider Beautiful Babylon as the most cost-effective option for hosting the dance. However, I also recommend that the council consider the number of attendees expected at the event and adjust their decision accordingly.

In summary, The council should consider the number of attendees expected, Beautiful Babylon is a good option for larger events, for smaller events, Crazy Cleopatra is the better option.

What percent of 1 3/5 is 0.2? (im stu pid, sorry)

Answers

Answer: 12.5%

(Don't worry!)

The two similar rectangles shown below have a scale factor of 3:10




If the perimeter of the larger rectangle is 90 centimeters, what is the perimeter of the smaller rectangle?

Answers

The perimeter of the smaller rectangle would be 27 cm.

What is scale factor? How it is used in Dilating sides?Scale factor tells us by how much one quantity is greater than the other. It is denoted by K. Mathematically : K = a/b.Rewriting, we get : a = KbIf a side length [a] of any 2 - D figure is dilated by a scale factor of [k], then the length of new side will be [Ka].

Given is that two similar rectangles shown below have a scale factor of

3 : 10.

Since the two rectangles are similar, then the ratio of their corresponding perimeters will be constant.

We can write -

P{1}/P{2} = 3/10

P{1}/90 = 3/10

P{1} = (3 x 90)/10

P{1} = 27

Therefore, the perimeter of the smaller rectangle would be 27 cm.

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an engineer has designed a valve that will regulate water pressure on an automobile engine. the valve was tested on 100 engines and the mean pressure was 5.5 lbs/square inch. assume the standard deviation is known to be 0.7 . if the valve was designed to produce a mean pressure of 5.3 lbs/square inch, is there sufficient evidence at the 0.05 level that the valve performs above the specifications? state the null and alternative hypotheses for the above scenario.

Answers

There is sufficient evidence that the valve performs above the specifications.

Null Hypothesis (H0): The mean pressure of the valve is equal to 5.3 lbs/square inch

Alternative Hypothesis (H1): The mean pressure of the valve is greater than 5.3 lbs/square inch

To test whether the valve performs above the specifications, a hypothesis test can be used. The test statistic used will be a t-test since the sample size is below 30. The critical value at the 0.05 level is 1.645. The formula for the t-test is: t = (X-μ)/(s/√n) , where X is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size.

Plugging in the known values, the t-test is calculated as: t = (5.5-5.3)/(0.7/√100) = 2.571. Since this value is greater than the critical value at the 0.05 level (1.645), we can reject the null hypothesis and conclude that there is sufficient evidence that the valve performs above the specifications.

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PLEASE HELP I WILL GIVE BRAINLIEST

For the set of triangle vertices, find the coordinates of the vertices of the image after a dilation by the given scale
factor and center of dilation.
D(2,-2), E(4, -2), F(1, -4)
k = 1.5,, E(4,-2), centered at E

Answers

The image of the triangle DEF are formed by the following coordinates: D'(x, y) = (1, - 2), E'(x, y) = (4, - 2) and F'(x, y) = (- 0.5, - 5).

How to dilate a triangle centered at a given point

In this problem we need to apply a rigid transformation known as dilation, whose definition is introduced below:

P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)]

Where:

O(x, y) - Center of dilationP(x, y) - Original pointP'(x, y) - Resulting pointk - Dilation factor

We need to determine the image of triangle DEF. If we know that D(x, y) = (2, - 2), E(x, y) = (4, - 2), F(x, y) = (1, - 4) and k = 1.5, then the images of the vertices of the triangle:

D'(x, y) = (4, - 2) + 1.5 · [(2, - 2) - (4, - 2)]

D'(x, y) = (4, - 2) + 1.5 · (- 2, 0)

D'(x, y) = (4, - 2) + (- 3, 0)

D'(x, y) = (1, - 2)

E'(x, y) = (4, - 2) + 1.5 · [(4, - 2) - (4, - 2)]

E'(x, y) = (4, - 2)

F'(x, y) = (4, - 2) + 1.5 · [(1, - 4) - (4, - 2)]

F'(x, y) = (4, - 2) + 1.5 · (- 3, - 2)

F'(x, y) = (4, - 2) + (- 4.5, - 3)

F'(x, y) = (- 0.5, - 5)

The coordinates of the image of triangle DEF are D'(x, y) = (1, - 2), E'(x, y) = (4, - 2) and F'(x, y) = (- 0.5, - 5)

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fred has ten feet of wire.he decides to cut it into equal length pieces. how many pieces will he get if each piece is 4 feet long?

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I don't know

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