A 12 ft ladder leans against the side of a house. The top of the ladder is 11 ft off the ground. Find x , the angle of elevation of the ladder. Round your answer to the nearest tenth of a degree.

Answer: The sum of the numbers from 1 to 400 that are divisible by 11 is equal to $11 \cdot 666 = 7326$.

Step-by-step explanation:

To find the sum of all the natural numbers from 1 to 400 that are not divisible by 11, we can first find the sum of all the natural numbers from 1 to 400, and then subtract the sum of all the natural numbers from 1 to 400 that are divisible by 11.

The sum of the natural numbers from 1 to 400 is equal to $\frac{400 \cdot 401}{2} = 80150$.

There are 400/11 = 36 numbers that are divisible by 11 between 1 and 400, inclusive. The sum of these numbers is equal to $11 + 22 + 33 + \dots + 396 = 11(1 + 2 + 3 + \dots + 36)$. The sum of the first 36 natural numbers is equal to $\frac{36 \cdot 37}{2} = 666$. Therefore, the sum of the numbers from 1 to 400 that are divisible by 11 is equal to $11 \cdot 666 = 7326$.

Subtracting the sum of the numbers that are divisible by 11 from the sum of all the numbers from 1 to 400 gives us a final answer of $80150 - 7326 = 72824$. This is not equal to 35840, as stated in the problem.

Answer:

--------------------------------

Use the sum of the first n terms formula for an AP:

The sum of all natural numbers from 1 to 400:

The greatest natural number less than 400 but divisible by 11:

Sum of the numbers divisible by 11:

Sum of the numbers not divisible by 11:

Answer:3.8

Step-by-step explanation:

Answer:

[tex]S_{1000}=500500[/tex]

Step-by-step explanation:

[tex]\displaystyle S_n=\frac{n(a_1+a_n)}{2}=\frac{1000(1+1000)}{2}=500*1001=500500[/tex]

The simplified form of the expression [tex]\sqrt[5]{1215}[/tex] is [tex]3\sqrt[5]{5}[/tex].

We know there are two types of radicals one is surds when the number has been raised by such power that it is greater than zero and less than one,

The other type of radicals are indices where a number is raised to such power that is greater than one.

Given, A radical [tex]\sqrt[5]{1215}[/tex].

Now we'll prime factor 1215.

= [tex]\sqrt[5]{5\times243}[/tex]

= [tex]\sqrt[5]{5\times3\times81}[/tex].

= [tex]\sqrt[5]{5\times3\times3\times3\times3\times3}[/tex].

= [tex]3\sqrt[5]{5}[/tex].

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Answer:1.5 inches

Step-by-step explanation:

Answer:

x = 6[tex]\sqrt{2}[/tex]

Step-by-step explanation:

using the cosine ratio in the right triangle and the exact value

cos45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then

cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{6}{x}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )

x = 6[tex]\sqrt{2}[/tex]

This is the exact value for x. It may be rounded if you wish

Answer:

[tex]x=6\sqrt{2}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9.4 cm}\underline{Trigonometric ratios} \\\\$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

From inspection of the given right triangle:

Substitute the given values into the cosine trigonometric ratio and solve for x:

[tex]\implies \cos(45^{\circ})=\dfrac{6}{x}[/tex]

[tex]\implies \dfrac{\sqrt{2}}{2}=\dfrac{6}{x}[/tex]

[tex]\implies x\sqrt{2}=6 \cdot 2[/tex]

[tex]\implies x\sqrt{2}=12[/tex]

[tex]\implies x=\dfrac{12}{\sqrt{2}}[/tex]

[tex]\implies x=\dfrac{12}{\sqrt{2}}\cdot \dfrac{\sqrt{2}}{\sqrt{2}}[/tex]

[tex]\implies x=\dfrac{12\sqrt{2}}{2}[/tex]

[tex]\implies x=6\sqrt{2}[/tex]

630,000

Step-by-step explanation:

350x60=21,000

21,000x30=630,000

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

to get the slope of any straight line, we simply need two points off of it, let's use those provided

[tex]R(\stackrel{x_1}{5}~,~\stackrel{y_1}{7})\qquad S(\stackrel{x_2}{15}~,~\stackrel{y_2}{31}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{31}-\stackrel{y1}{7}}}{\underset{\textit{\large run}} {\underset{x_2}{15}-\underset{x_1}{5}}} \implies \cfrac{ 24 }{ 10 } \implies \cfrac{12 }{ 5 }[/tex]

keeping in mind that perpendicular lines have negative reciprocal slopes

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{12}{5}} ~\hfill \stackrel{reciprocal}{\cfrac{5}{12}} ~\hfill \stackrel{negative~reciprocal}{ {\Large \begin{array}{llll} -\cfrac{5}{12} \end{array}} }}[/tex]

Step-by-step explanation:

the slope of a line is the ratio

y coordinate change / x coordinate change

when going from one point on the line to another.

the perpendicular slope is simply turning that ratio fraction upside down and flips the sign.

(5, 7) to (15, 31)

x changes by +10 (from 5 to 15).

y changes by +24 (from 7 to 31).

the slope (or gradient) is therefore

+24/+10 = 12/5

the perpendicular slope or gradient is then

-5/12

The graph of the system of linear equations is attached with the answer.

The general equation of a straight line is -

y = mx + c

{m} - slope.

{c} - intercept along the y - axis.

Given is the system of linear equations as given -

- 2x + y = 10

x + 2y = 5

The given system of linear equations is -

- 2x + y = 10

x + 2y = 5

Refer to the graph of the system of linear functions attached. The point (-3, 4) is the solution set of this system of equation.

Therefore, the graph of the system of linear equations is attached with the answer.

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The expression is factorized to give (x + 7) and (x + 7)

Factorization described a mathematical methods that consists of writing a number or mathematical object as a product of several other factors that are mostly simpler or smaller objects of the same kind.

Given the quadratic equation;

x² + 14x +49

Find the pair factors of 49 that sum up to 14, the numbers are 7 and 7

Now, substitute the numbers in the expression

x² + 7x + 7x + 49

Make into two expressions, we have;

(x² + 7x) + (7x + 49)

factor out the common terms, we get;

x(x + 7)+ 7(x + 7)

Then, we have;

(x + 7)

(x + 7)

Hence, the factorized form is (x + 7) and (x + 7)

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Answer:

a^4b^24

Step-by-step explanation:

We know, (xy)^n = x^ny^n. So,

(ab^6)^4 = a^4b^(6×4)

= a^4b^24

Check the picture below.

so let's start with 34, well a centroid is the point where all "medians" meet, well a median is half of the segment, the heck does that mean?  well, it means that CG = GD, and since CD is 34, that means that GD = 17.

let's keep in mind that a centroid cuts all medians in a 2 : 1 ratio, meaning one cut-side is twice as along as the other, that said

[tex]\stackrel{\textit{keeping in mind that BG=57}}{\cfrac{BH}{HG}=\cfrac{2}{1}\implies \cfrac{BH}{HG}=\cfrac{2\cdot \frac{57}{2+1}}{1\cdot \frac{57}{2+1}}}\hspace{10em} \cfrac{BH=38}{HG=19} \\\\\\ \cfrac{HD}{EH}=\cfrac{2}{1}\implies \cfrac{HD}{15}=\cfrac{2}{1}\implies HD=30\hspace{5em}\stackrel{15~~ + ~~30}{ED=45} \\\\\\ \stackrel{\textit{keeping in mind that CF=39}}{\cfrac{CH}{HF}=\cfrac{2}{1}\implies \cfrac{CH}{HF}=\cfrac{2\cdot \frac{39}{2+1}}{1\cdot \frac{39}{2+1}}}\hspace{10em}\cfrac{CH=26}{HF=13}[/tex]

Given,

To Find : Amount the customer needs to pay for the discounted book

In order to convert Discount % to Discount we use the formula

[tex]D = \frac{25}{100} X36\\D = 9[/tex]

SP = 36 - 9

SP = $27

The domain and range of the function on the table are the ones in options B and C.

Domain: {-3, 1, 5, 7}

Range: {2, 4, 5, 9}

For a function y = f(x), we define the domain as the set of the inputs, this is, the set of the possible values of x.

On the other hand, the range is the set of the outputs, this is, the set of the possible values of y.

Then the domain is just the set of the values of x on the table:

Domain: {-3, 1, 5, 7}

And the range is the set of the values of y on the table:

Range: {2, 4, 5, 9}

Then the correct options are C and B.

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Therefore, the number of stickers David has in terms of d is d+10 and the number of stickers Matt has in terms of d is 2d-10.

A term is a phrase or statement that is used to convey a certain meaning. Rap, punk, grunge, and heavy metal are examples of words used to characterize certain musical genres. To the majority of people, at least, "sweetie" is a word of affection.

A phrase is a collection of words with significance but which is not usually a complete sentence. A set of words that form a sentence must have a topic.

We know that Matt has twice as many stickers as David, so if David has d stickers, then Matt has 2d stickers.

When Matt gives David 10 stickers, David has d+10 stickers and Matt has 2d-10 stickers.

So the number of stickers David has in terms of d is d+10 and the number of stickers Matt has in terms of d is 2d-10.

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Answer: To solve a quadratic equation of the form ax^2 + bx + c = 0, there are several steps that Inga could use. Here are three options:

She could complete the square to rewrite the equation in the form (x + p)^2 = q.

She could use the quadratic formula: x = (-b +/- √(b^2 - 4ac)) / (2a).

She could factor the equation to rewrite it in the form (x + r)(x + s) = 0.

Option 1: Completing the square

To complete the square, Inga could add and subtract (b/2)^2 to the equation to get:

a(x^2 + bx + (b/2)^2) - (b/2)^2 = 0

Then, she could rewrite the equation in the form:

a(x + (b/2))^2 = (b/2)^2

Option 2: Using the quadratic formula

To use the quadratic formula, Inga could substitute the values of a, b, and c into the formula to get:

x = (-12 +/- √(12^2 - 4 * 2 * -3)) / (2 * 2)

= (-12 +/- √(144 + 24)) / 4

= (-

Step-by-step explanation:

Using division operation, since Benjamin jogs at a pace of 16 minutes per mile, in 45 minutes he will jog 2.8 miles.

The division operation is one of the basic mathematical operations, including addition, subtraction, and multiplication.

The division operation involves dividing the dividend (the numerator) by the divisor (the denominator) to obtain the quotient (the result).

The distance between Benjamin and Felix = 35 miles

Benjamin's jogging pace or speed = 16 minutes per mile

Felix's jogging pace or speed = 10 minutes per mile

The number of miles that Benjamin can jog in 45 minutes = Time/Speed

= 2.8125 miles (45/16)

Thus, Benjamin will jog 2.8 miles in 45 minutes.

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a) The function is continuous in it's entire domain.

b) The increasing and decreasing intervals for the function are given as follows:

A function f(x) is continuous at x = a if it is defined at x = a, and the lateral limits are equal, that is:

[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]

In this problem, we have a piece-wise function which has the definition changing at x = 2, hence the continuity must be studied at x = 2.

The lateral limits for the function in this problem are defined as follows:

The second limit is also equals to the numeric value at x = 2, due to the equal sign in the definition, hence the function is continuous at x = 2 and for all other values in the domain.

The intervals of increase and decrease are given as follows:

The function for this problem is the piece-wise function A(x).

Item a asks if the function is continuous.

Item b asks when the function is increasing and when it is decreasing.

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Answer:

Step-by-step explanation:

( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )

Slope "m"

y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex] )

~~~~~~~~~~~~~~

( 4 , - 7 )

m = [tex]-\frac{1}{2}[/tex]

y - ( - 7 ) = [tex]-\frac{1}{2}[/tex] ( x - 4 )

y + 7 = [tex]-\frac{1}{2}[/tex] ( x - 4 )

Answer:

To find the range of flight times, you need to find the difference between the shortest and longest flight times. The shortest flight time was on Monday at 314 minutes, and the longest flight time was on Friday at 407 minutes. The range is 407 - 314 = 93 minutes. The correct answer is therefore (b) 93 min.

Step-by-step explanation:

The fraction of the original passengers remaining on the bus is 11/21.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, A crowded bus makes several stops along a city street, with no passengers boarding the bus at any stop.

.At the 1st stop 1/3 of the passengers exit.

At the 2nd stop, 3/7 of the remaining passengers exit the bus.

Therefore, The fraction of the original passengers who remain on the bus is,

= [(1 - (1×1/3) - (1)×(1/3)×(3/7)].

= [ 1 - (1/3) - (3/21)].

= [ (2/3) - (3/21)].

= [(14 - 3)/21].

= 11/21.

So, 11/21 remains on the bus.

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Answer:

Step-by-step explanation:

1 in a tenth of a million. I did the math with all the cards and how many are kinds diamonds or red or queens yk.

Answer: solve the same variables

Step-by-step explanation:

1. 3y + 4.1

2. 4x +

3. 5x + 22½

4. 4y²

5. + 25

6. 0



The solution to the equation log₇343 = 3 is 7³ = 343

An equation is used to show the relationship between numbers and variables.

The logarithm can be defined as the exponent that raises a base to get a particular number. The law of logarithm states:

logₓm = n is the same as xⁿ = m

Given the equation:

log₇343 = 3

Applying the law of logarithm gives:

7³ = 343

The solution to the equation is 7³ = 343

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Answer: “Rate of change” just means “slope”. All of calculus is just ways to find the slope for curves. Find y at -5 and at -4 and calculate the slope.

Step-by-step explanation:

On solving the provided question, we can say that we can assume that it is a rectangular backyard. Since no dimensions are provided therefore, neither volume nor area can be calculated.

A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.

here,

we can assume that it is a rectangular backyard.

since no dimensions are provided therefore, neither volume nor area can be calculated.

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Answer:

y=3x+13

2x=y-9

Step-by-step explanation:

i need to know :(

Answer:

Step-by-step explanation:

Substitute 1 in 2 and solve for x.

2x=y-9

2x=3x+13-9

2x = 3x+4

-x = 4

x = -4

Then use equation 1 to solve for x.

y = 3x+13

y = -12+13

y= 1