2. Use the Pythagorean Theorem
5 in
11 in​

To solve the system of equations x − y = 5 and 2x − 3y = 4, we can use the method of substitution or elimination. By substituting the value of x from the first equation into the second equation, we can find the value of y. Then, substitute the value of y back into the first equation to find the value of x. The solution to the system of equations is (11, 6).

To solve the system of equations x − y = 5 and 2x − 3y = 4, we can use the method of substitution or elimination. Let's use the method of substitution:

From the first equation, we can rearrange it to x = y + 5. Now substitute this value of x into the second equation:

2(y + 5) − 3y = 4

Simplify and solve for y:

2y + 10 - 3y = 4

-y + 10 = 4

-y = -6

y = 6

Now substitute this value of y back into the first equation to find x:

x − 6 = 5

x = 11

Therefore, the solution to the system of equations is (11, 6). So, the correct answer is option D.

Answer:

Pay period, taxable allowances, and dividends

Step-by-step explanation:

Answer: Pay period, taxable allowances, and dividends

Explanation:

  Paycheck stub is the type of document which include the total paid amount to the employees. It is also known as pay slip and pay stub. The pay stub is basically received by the each pay slip and period.

This pay check stub document basically show the total earnings, deductions and the net pay after the all deductions.

We can also save the paycheck stub in our records so that we can easily access it in future. In case of the employees and employer, the paycheck stub prove that the payment and the income are both consistent.

Answer:

Area of a pyramid = (1/3) x (base area) x (height)

Answer:I know that more than half of the students did not score more than 75 because the median (the middle number) is 68.

Step-by-step explanation:

Answer:

-5

Step-by-step explanation:

-3 x 3 - 4x

x=-1

-3 x 3 - 4(-1)

-3 x 3 + 4

-9 + 4

-5

Hope This Helps! :D

Answer:

-3-4x

=-3(-1

=-3*(-1)+4

=3+4

=7

Step-by-step explanation:

that should be all you need to know

Answer: x=62

Step-by-step explanation:

A triangle is 180 degrees. When you add 71 and 47, it equals 118. Then subtract 118 from 180 and you are left with 62 degrees.

Hope this helps!

Answer: x = 62°

Remember: the interior angles of a triangle add up to 180°.

47 + 71 = 118

180 - 118 = 62

$0.13 per ounce.  5 pounds of birdseed cost $10.40, then the price per ounce is $0.13.

The easiest way to solve this problem is using arithmetic operations and unit conversion.

We have to calculate the price per pound. Let's divide $10.40 by 5 pounds.

10.40/5 = 2.08

The price per pound is $2.08

To calculate the price per ounce, with 1 pound = 16 ounces. Let's divide $2.08 by 16 ounces.

2.08/16 = 0.13

The price per ounce is $0.13

Answer:

Option C. [tex]42\ yd^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the triangular prism is equal to

[tex]V=BH[/tex]

where

B is the area of the triangular base

H is the height of the prism

Convert 9 ft to yd

Remember that

1 ft=1/3 yd

9 ft=9*(1/3)=3 yd

Find the area of the base B

[tex]B=\frac{1}{2}(3)(4)=6\ yd^{2}[/tex]

we have

[tex]H=7\ yd[/tex]

substitute the values in the formula

[tex]V=BH[/tex]

[tex]V=(6)(7)=42\ yd^{3}[/tex]

Answer:

The answer is 42 yards! Sry im late. :(

Answer:

32 unit³

Step-by-step explanation:

Length of the crate has been given as 4 units

width of the crate = 2 units

Height of the crate = 4 units

Since the crate has been packed packed with the unit cubes.

Therefore, shape of the crate will be in the form of a rectangular prism.

Volume of the prism = Length × width × height

                     crate     = 4 × 2 × 4

                                   = 32 unit³

Volume of the shipping crate is 32 unit³.

Answer:

32 Units

Step-by-step explanation:

If u do 4x2x4=32 that is your answer all you got to do is x Lxwxh and U will find the volume

Answer: The answer to your question is 4 ft

Step-by-step explanation: we know that the formula to find the area of a rectangle is

A=LW

In this problem, we have:

[tex]A= 30 ft^{2}[/tex]

[tex]L= 7.5ft[/tex]

Substitute the values and solve for W

30=7.5W

Divide by 7.5 on both sides

W= 30/ 7.5= 4ft

Answer:

The width of the tablecloth is 4 ft

Answer:

The height of the triangular pyramid is [tex]27\ cm[/tex]

Step-by-step explanation:

we know that

The volume of a triangular pyramid is equal to

[tex]V=\frac{1}{3}BH[/tex]

where

B is the area of the triangular base

H is the height of the pyramid

Find the area of the base B

[tex]B=\frac{1}{2}(15)(4)=30\ cm^{2}[/tex]

we have

[tex]V=270\ cm^{3}[/tex]

substitute and solve for H

[tex]270=\frac{1}{3}(30)H[/tex]

[tex]270=10H[/tex]

[tex]H=270/10=27\ cm[/tex]

Answer:

87380

Step-by-step explanation:

The sum to n terms of a geometric sequence is

[tex]S_{n}[/tex] = [tex]\frac{a(r^n-1)}{r-1}[/tex]

where a is the first term and r the common ratio

r = [tex]\frac{16}{4}[/tex] = 4 and a = 4, hence

[tex]S_{8}[/tex] = [tex]\frac{4(4^8-1)}{4-1}[/tex] = [tex]\frac{4(65535)}{4}[/tex] = 87380

Answer:

x= 8.5 or 9, or deciding if u adding or subtracting the problem, x= 9.5 or 10

Step-by-step explanation:

If you're meaning 4x+2=36 or 4x-2=36

                                  -2   -2          +2   +2

                              4x=34          4x=38

                              4     4            4     4

                               x= 8.5 or 9     x= 9.5 or 10

Hope i have helped you! :)

Answer:No assoication

Step-by-step explanation:

because they are not parellell with each other

Answer: No  association.

Step-by-step explanation: They aren't parallel with each other. So, it has to be no association.

Answer:

a)

The probability that an individual distance is greater than  210.00 cm is 0.1056

b)

The probability that the mean for  25  randomly selected distances is greater than  198.70 cm is 0.7917

c)

The normal distribution be used in part​ (b), even though the sample size does not exceed​ 30 since the parent population from which the sample has be obtained is Normal.

Step-by-step explanation:

a)

We let the random variable X denote the overhead reach distances of individual adult females. This implies that X is normally distributed with a mean of 200 cm and a standard deviation of 8 cm.

The probability that an individual distance is greater than 210 can be written as;

Pr(X>210)

We standardize the value to obtain the associated z-score;

[tex]P(X>210)=P(Z>\frac{210-200}{8})=P(Z>1.25)[/tex]

Using the standard normal tables, the area to the right of 1.25 is 0.1056. Therefore, the probability that an individual distance is greater than  

210.00 cm is 0.1056.

b)

The first step will be to determine the sampling distribution of the sample mean given that the variable overhead reach distance is normally distributed with a mean of  200 cm and a standard deviation of  8 cm.

In this case, the sample mean will also be normally distributed with a mean of 200 cm and a standard deviation of;

[tex]\frac{sigma}{\sqrt{n} }=\frac{8}{\sqrt{25} }=1.6[/tex]

The probability that the mean for  25  randomly selected distances is greater than  198.70 cm;

Pr(sample mean >198.70)

We standardize the value to obtain the associated z-score;

[tex]=P(Z>\frac{198.70-200}{1.6})=P(Z>-0.8125)[/tex]

Using the standard normal tables, the area to the right of -0.8125 is 0.7917. Therefore, the probability that the mean for  25  randomly selected distances is greater than  198.70 cm is 0.7917.

c)

The normal distribution be used in part​ (b), even though the sample size does not exceed​ 30 since the parent population from which the sample has be obtained is Normal.

Answer:

8/5 or 1 3/5

Step-by-step explanation:

2 2/5 = 12/5

1 1/2 = 3/2

Now that we have fractions that are easier to divide, one must understand that the opposite of dividing is multiplying. So if you multiply 12/5 by the reciprocal* of 3/2, which would be 2/3, you would get your answer so...

12     3         12    2        24     8             3

—  ÷ —   =   — × —    =  —  = —   or  1  —

5       2         5     3        15      5             5

*the reciprocal is the opposite of the fraction you have. So the denominator would become the numerator, and vise versa.

The answer is (-6,5)

Answer:

Your answer will be (-6,5).  

Step-by-step explanation:

You multiply the first equation by 3 and the second equation by 2. You will then cancel out the x's and find your y which is 5. You plug y back into your first equation to find your x which is -6. You then have your solution set.

Check the picture below.

so then, let's use the pythagorean theorem to find "x" and "y", and the distance is just x+y.

[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=\stackrel{hypotenuse}{x}\\ a=\stackrel{adjacent}{9}\\ b=\stackrel{opposite}{5}\\ \end{cases} \\\\\\ x=\sqrt{9^2+5^2}\implies x=\sqrt{81+25}\implies x=\sqrt{106} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=\stackrel{hypotenuse}{y}\\ a=\stackrel{adjacent}{17}\\ b=\stackrel{opposite}{5}\\ \end{cases} \\\\\\ y=\sqrt{17^2+5^2}\implies y=\sqrt{289+25}\implies y=\sqrt{314} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{total distance}}{x+y}\implies \sqrt{106}+\sqrt{314}\qquad \approx 10.296+17.72\qquad \approx 28.016[/tex]

Final answer:

To find the distance from Carson's house to Salemburg through Pueblo 'as the crow flies', we use the Pythagorean theorem. Adding together the two legs of a right triangle formed by the given distances and solving for the hypotenuse, we find it is approximately 26.48 miles.

Explanation:

To determine the distance from Carson's house to Salemburg through Pueblo 'as the crow flies', we need to create a diagram and use the Pythagorean theorem. First, we know that Salemburg is 17 miles south of Linbrooke, Linbrooke is 5 miles west of Pueblo, and Carson lives 9 miles north of Linbrooke. Therefore, the distance directly north from Carson's to Pueblo is 9 miles (since he is directly north of Linbrooke), and from Pueblo to Salemburg the direct line would consist of 5 miles west and 17 miles south, which forms a right triangle.

Using the Pythagorean theorem to find the length of the hypotenuse (direct line from Carson's past Pueblo to Salemburg), we have:

Calculate the total distance north-south by adding Carson's 9 miles north to Salemburg's 17 miles south, which gives us 26 miles.

Since we already have the west-east distance as 5 miles, we can set up the equation a^2 + b^2 = c^2, where 'a' is 5 miles, 'b' is 26 miles, and 'c' is the hypotenuse we are looking for.

Plugging in the values gives: 5^2 + 26^2 = c^2, or 25 + 676 = c^2, resulting in c^2 = 701.

Take the square root to find 'c': c ≈ 26.48 miles.

Therefore, the distance from Carson's house to Salemburg 'as the crow flies' passing through Pueblo is approximately 26.48 miles.

Answer:

the answer would be 90

Step-by-step explanation:

100 giants fills 5/8 (100/160) of the theater leaving 3/8 of the theater for the elves.

3/8 times 240 elves is 90 elves.

If there were 150 elves that would also be 5/8 filled plus the original 5/8 filled with 100 giants! Some elves might suffer!!!

Answer:

the building strong enough to withstand the denali quake

Step-by-step explanation:

denali quake 6.7  x 70 = 469

the building in denali should be strong enough to withstand an earthquake of that magnitude  

rat island quake 7.8 x 30 = 234

the building in the rat islands  should be strong enough to withstand an earthquake of that magnitude  

Answer:

Last option: 4

Step-by-step explanation:

The quadratic equation simplified: [tex]x^2-4x=-\frac{7}{2}[/tex] has the form:

[tex]ax^2+bx=c[/tex]

In this case, you can identify that "a", "b" and "c" are:

[tex]a=1\\b=-4\\c=-\frac{7}{2}[/tex]

To solve this quadratic equation  by completing the square, Carlos should add [tex](\frac{b}{2})^2[/tex] to both sides of the equation. This is:

[tex](\frac{-4}{2})^2=(-2)^2=4[/tex]

Then:

[tex]x^2-4x+4=-\frac{7}{2}+4[/tex]

Therefore you can observe that the number he should add to both sides of the equation is: 4

Answer:

(1.5, 2.5) is the best approximate solution.

Step-by-step explanation:

According to the graph, at the point of intersection of these two lines, x is closest to 1.5 and y is simultaneously closest to 2.5.

(1.5, 2.5) is the best approximate solution.

Answer:

Step-by-step explanation:

1.5 AND 2.5

An entrepreneur is a someone who organizes and conducts a business, and taking great financial risks.

Answer:

The correct answer would be option C, A person who takes a risk to create a new product or develop a better way to operate a business.

Step-by-step explanation:

An entrepreneur is a person who starts a new business alone. An Entrepreneur is responsible for all the profits and losses of the business. He takes risks in the hope of earning profits. He introduces new products in the market and develops better ways to operate a business. He is solely liable for all his decisions and the resulting profit or losses. Entrepreneurs are usually hard working, strong decision makers, risk takers, and highly innovative people.

A decrease by 30%, means that the price is now 70% of the original price ( 100% - 30% = 70%)

To find the original price divide the new price by the percent of the original price it is now.

147 / 0.70 = 210

The original price was £210

The price before the decrease is £210.

Given that,

Based on the above information, the calculation is as follows:

[tex]= 147 \div 70\%[/tex]

=  £210

Therefore we can conclude that the price before the decrease is £210.

Learn more: brainly.com/question/6201432

Answer:

1249.37

Step-by-step explanation:

7850 = 2 pi r

r = 7850/(2pi) = 1249.37

ANSWER

The radius is approximately 1249 units.

EXPLANATION

The relation between the radius of a circle and its circumference is expressed in the formula:

[tex]C = 2\pi \: r[/tex]

The circumference is given as 7,850 .

This implies that

[tex]7850 = 2\pi \: r[/tex]

[tex]r = \frac{7850}{2 \: \pi} [/tex]

[tex]r = 1249.4[/tex]

to the nearest tenth.

Answer:

[tex]\frac{dy}{dx} = \frac{cos(x+y)}{1-cos(x+y)}[/tex]

Step-by-step explanation:

We have the function [tex]y=sin(x+y)[/tex]

We need find the derivative of y with respect to x

Note that the function [tex]y = sin (x + y)[/tex] depends on the variable x and the variable y. Therefore the derivative of y with respect to x will be equal to the derivative of [tex]sin (x + y)[/tex] by the internal derivative of  [tex]sin (x + y)[/tex]

[tex]\frac{dy}{dx}= cos(x+y)*\frac{d}{dx}(x+y)[/tex]

[tex]\frac{dy}{dx}= cos(x+y)*(1+\frac{dy}{dx})\\\\\frac{dy}{dx}= cos(x+y)+\frac{dy}{dx}cos(x+y)\\\\\frac{dy}{dx} -\frac{dy}{dx}cos(x+y)=cos(x+y)\\\\\frac{dy}{dx}(1-cos(x+y))=cos(x+y)\\\\\frac{dy}{dx} = \frac{cos(x+y)}{1-cos(x+y)}[/tex]

Answer:

Step-by-step explanation:

Note that y=sin(x+y) is an implicit function; y appears on both sides of the equation, which makes it difficult or impossible to solve for y.

However, our job here is to find the derivative dy/dx.

We apply the derivative operator d/dx to both sides.  Here are the results:

dy

---- = cos(x + y)(dx/dx + dy/dx), or

dx                                                         Note:  dx/dx = 1

dy

---- = cos(x + y)(1 + dy/dx), or  = cos(x + y) + cos(x + y)(dy/dx)

dx

We move that cos(x + y)(dy/dx) term to the left side to consolidate dy/dx terms:

dy

----  -  cos(x + y)(dy/dx) = cos(x + y)

dx

or:

 dy

[ ---- ] [ 1 -  cos(x + y) ] = cos(x + y)

  dx

Finally, we divide both sides by [ 1 -  cos(x + y) ], obtaining the derivative:

 dy            cos(x + y)

[ ---- ]  -------------------------

  dx         1 -  cos(x + y)

Answer:

Step-by-step explanation:

y2-y1/x2-x1= -3-(-3)/6-2= 0/4

2 as what he said above

For this case we must find the value of the variable "x" of the following equation:

[tex]5x (4-2) = 20[/tex]

We solve the operation within the parenthesis:

[tex]5x (2) = 20[/tex]

We multiply the left side:

[tex]10x = 20[/tex]

We divide both sides of the equation by 10:

[tex]x = \frac {20} {10}\\x = 2[/tex]

ANswer:

[tex]x = 2[/tex]

The solution of the expression given for x is 2.

Given is an expression 5x(4-2) = 20, we need to solve for x.

To solve the expression 5x(4-2) = 20 step by step, follow these steps:

Simplify the expression inside the parentheses:

5x(4 - 2) = 20

5x(2) = 20

Multiply 5x by 2:

10x = 20

Divide both sides of the equation by 10 to isolate x:

(10x)/10 = 20/10

x = 2

Therefore, the solution for x is 2.

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To find the distance of objects sighted at angles of 29 degrees and 59 degrees, use the function d = 93 sec(theta). Substituting theta values, the distances are 106.87 feet and 166.39 feet, respectively.

To find the distance of an object sighted at angles of 29 degrees and 59 degrees, we can use the function given, d = 93 sec(theta). Substituting theta = 29 degrees, we get d = 93 sec(29) = 93*(1/cos(29)) = 93/0.8714 = 106.87 feet. Similarly, substituting theta = 59 degrees, we get d = 93 sec(59) = 93*(1/cos(59)) = 93/0.5588 = 166.39 feet.