Find the area of the figure shown below and choose the appropriate result.

"The sum of two numbers is 20" can be translated mathematically into the equation:

x + y = 20.

"... and their difference is 10" can be translated mathematically as:

x - y = 10

We can now find the two unknown numbers, x and y, because we now have a system of two equations in two unknowns, x and y. We'll use the Addition-Subtraction Method, also know as the Elimination Method, to solve this system of equations for x and y by first eliminating one of the variables, y, by adding the second equation to the first equation to get a third equation in just one unknown, x, as follows:

Adding the two equations will eliminate the variable y:

x + y = 20

x - y = 10

-----------

2x + 0 = 30

2x = 30

(2x)/2 = 30/2

(2/2)x = 15

(1)x = 15

x = 15

Now, substitute x = 15 back into one of the two original equations. Let's use the equation showing the sum of x and y as follows (Note: We could have used the other equation instead):

x + y = 20

15 + y = 20

15 - 15 + y = 20 - 15

0 + y = 5

y = 5

CHECK:

In order for x = 15 and y = 5 to be the solution to our original system of two linear equations in two unknowns, x and y, this pair of numbers must satisfy BOTH equations as follows:

x + y = 20 x - y = 10

15 + 5 = 20 15 - 5 = 10

20 = 20 10 = 10

Therefore, x = 15 and y = 5 is indeed the solution to our original system of two linear equations in two unknowns, x and y, and the product of the two numbers x = 15 and y = 5 is:

xy = 15(5)

xy = 75

Answer:

B

Step-by-step explanation:

We can substitute the x value given, -3, into our equation, y = x^2, to get what the y would be:

y = x^2

y = (-3)^2

When a negative number is squared, it is positive, so (-3)^2 = 9, and:

y = 9

This is option b

Answer:

B) 9

Step-by-step explanation:

We are given the equation y = x^2 for the table, and a x value.

To find the y value that corresponds to that x value, we must plug the x value in the equation.

Y =x^2

Y= -3^2

Y=9

Answer:

− 0.85 y + 10.26

Step-by-step explanation:

The multiplication of the expression (5.23y + 3.8) and (2.7 - 1.6y) will be 8.041y + 10.26 - 8.368y²

When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ (5.23y + 3.8) · (2.7 - 1.6y)

Simplify the expression, then we have

⇒ (5.23y + 3.8) · (2.7 - 1.6y)

⇒ 14.121y + 10.26 - 8.368y² - 6.08y

⇒ 8.041y + 10.26 - 8.368y²

More about the value of the expression link is given below.

https://brainly.com/question/23671908

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Answer:

2b + 10

Step-by-step explanation:

Answer:

G. 25%

Step-by-step explanation:

given : The price of a video game was reduced from $60 to $45 .

$60 - $45 = $15

then, the percentage was the price of the video game reduced :-

reduction in price/previous price x 100 = 15/60 x 100 = 25%

the percentage was the price of the video game reduced = 25%

Answer:

m∡ZA = 51°

m∡ZB = 39°

Step-by-step explanation:

∡ZB = 'b'

∡ZA = '12 + b'

b + 12 + b = 90

2b + 12 = 90

2b = 78

b = 39

12 + 39 = 51

Answer:

The surface area of the ball is of 29 square inches.

The volume of the ball is of 15 cubic inches.

Step-by-step explanation:

The ball has an spherical format:

Circumference of a sphere:

The circumference of a sphere is 6.2832 times the radius.

Surface area

[tex]A = 4\pi r[/tex]

In which r is the radius.

Volume:

[tex]V = \frac{4\pi r^3}{3}[/tex]

The circumference of the ball is 9.4 inches.

So the radius is:

[tex]6.2832r = 9.4[/tex]

[tex]r = \frac{9.4}{6.2832} = 1.53[/tex]

Surface area

[tex]A = 4\pi(1.53)^2 = 29.3[/tex]

Rounding to the nearest unit, the surface area of the ball is of 29 square inches.

Volume:

[tex]V = \frac{4\pi (1.53)^3}{3} = 14.9[/tex]

Rounding to the nearest unit, the volume of the ball is of 15 cubic inches.

Answer:

The margin of error is multiplied by 4.

Step-by-step explanation:

Margin of error is:

[tex]M = \frac{zs}{\sqrt{n}}[/tex]

In which z is related to the confidence level, s is elated to the standard deviation and n is the sample size.

From this, we have that the standard deviation is inversely proportional to the square root of the sample size.

If you cut the sample size in half:

The margin of error is inversely proportional to the square root of the sample size, so if you cut the sample size by [tex]\frac{1}{2}[/tex], the margin of error will be multiplied by [tex]2^2 = 4[/tex]

So

The margin of error is multiplied by 4.

Answer:

A. 45°

Step-by-step explanation:

I calculated it logically

Answer:

The answer is (A) decreases

Answer:

x = 2

Step-by-step explanation:

Inverse variation between x and y can be represented as:

xy = k

Where k is the constant of proportionality.

If x = 1 when y = 11, the constant of proportionality, k, would be:

1*11 = k

k = 11

To find x when y = 5.5, substitute y = 5.5 and k = 11 into xy = k

Thus:

x*5.5 = 11

Divide both sides by 5.5

x = 11/5.5

x = 2

Answer:

4 children

Step-by-step explanation:

Let the number of children = c.

The cost of the pizza place for c children (without the fee) = 8c

The cost of the pizza place for c children (with the fee) = 8c+30

The cost of the taco place for c children (without the fee) = 12c

The cost of the taco place for c children (with the fee) = 12c+14

To find c when the totals are equal, set 8c+30 equal to 12c+14 and solve:

8c+30=12c+14

8c-12c=14-30

-4c=-16

c=4

Answer:

HI!!

Step-by-step explanation:

Answer:

[tex](g\ o\ f)=-20x+10[/tex]

Step-by-step explanation:

One is given the following functions:

f(x) =5x + 2

g(x) = 4x + 2

One is asked to find the following:

[tex](g\ o\ f)(x)[/tex]

One can rewrite this operation as the following:

g(f(x))

In essence, one substitutes in function (g) in place of the parameter (x), and solves to find the new function formed.

[tex]g(f(x))\\\\=g(-5x+2)\\\\=4(-5x+2)+2[/tex]

Simplify, distribute, multiply every term in the parenthesis by the term outside of it, then simplify,

[tex]=-20x+8+2\\\\=-20x+10[/tex]

Answer:

She has to get a score of 88 on that test

Step-by-step explanation:

Take the average of the other grades, and that gives you 84.25. So she has to think about what rating she gives it is 85, and the rating is 88.

Hailey needs to score an 88 on the last exam in order to get an average of 85.

The overall average is the mean and the mean is calculated by adding up all the scores and then dividing by the number of exams.

There are 5 exams but only 4 scores. The 5th score will be denoted, "x" and the average we are looking for is 85.

The fifth score should therefore be:

Overall score = Sum of 5 exams / 5

85 = (86 + 94 + 76 + 81 + x) / 5

85 x 5 = 337 + x

425 = 337 + x

x = 425 - 337

= 88

In conclusion, Hailey needs a score of 88 on the fifth exam.

Find out more at https://brainly.com/question/17031271.

Answer:

36 meters

Step-by-step explanation:

A square has equal side lengths, and a total of 4 sides, so

9 times 4 is equal to 36.

Remember your units!

Answer:

1. 0

2. a/ a + b

3. a + b/ a - b

Answer:

y = x - 3

Step-by-step explanation:

Slope = Rise / run

Slope = 4/4 = 1

y-intercept = -3

y = x - 3

Answer:

The slope represents the change/rise is the yearly imcome based on age. The y-intercept is the amount that they make when they first get a job.

Step-by-step explanation:

Answer:

the mean of those numbers is 17.1

Answer:

The M.A.D (mean absolute deviation) is 2.3

Bonus (Just in case you need it): The Mean is 17.1

Have a good day!

9514 1404 393

Answer:

  10.  A) 120°

  11.  D) 40°

  12.  D) 54°

  13.  A) 101°

Step-by-step explanation:

The applicable rules of angles and arcs are ...

__

10) Angles C and L intercept the same arc (DE) so will have the same measure.

  15x = 16x -4

  4 = x . . . . . . . . add 4-15x

  arc DE = 2(15x) = 30(4) = 120 . . . degrees

__

11) Arc VW is twice the measure of angle X, so ...

  9x +8 = 2(5x)

  8 = x . . . . . . . . . subtract 9x

  ∠VXW = 5x = 5(8) = 40 . . . degrees

__

12) Arc EFG is twice the measure of angle W, so ...

  70° +FG = 2(88°)

  FG = 106° . . . . . . . . . subtract 70°

Arc FGW is twice the measure of angle E, so ...

  106° +GW = 2(80°)

  GW = 54° . . . . . . . . . . subtract 106°

__

13) Arc ST is twice the measure of angle R. The sum of arcs is 360°.

  RS +ST +TR = 360°

  119° +2(70°) +TR = 360°

  TR = 101° . . . . . . . . subtract 259°

Answer:

The area of the trapezium is 18 ft²

Step-by-step explanation:

Given;

Two parallel sides of the polygon as  follows;

The first parallel side = 1 ft + 4 ft = 5 ft

The second parallel side = 4 ft

If this polygon is rotated 90 degrees, it forms a trapezium with a height of 4 ft.

The area of a trapezium is calculated as;

[tex]A rea= \frac{1}{2} (sum \ of \ parallel \ sides) \times height\\\\Area = \frac{1}{2} (5 \ + \ 4) \times 4\\\\Area = 18 \ ft^2[/tex]

Therefore, the area of the trapezium is 18 ft²

Answer:

[tex]h=5.11ft[/tex]

Step-by-step explanation:

[tex]S=12+6+14/2=16[/tex]

[tex]area ~A= \sqrt{s(s-14)(5-12)(5-6)}[/tex]

[tex]area=\sqrt{16(16-14)(16-12)(16-6)}[/tex]

[tex]A=\sqrt{16×2×4×10}[/tex]

[tex]A=35.70[/tex]

[tex]A=1/2× base~×height[/tex]

[tex]35.70=1/2×14×h[/tex]

[tex]h=2×35.75/14[/tex]

[tex]h=5.11ft[/tex]

｡･:*:･ﾟ★,｡･:*:･ﾟ☆

hope it helps...

have a great day!!

Answer:

4.15

Step-by-step explanation:

the radius is half the diameter so 8.3/2

=4.15mm

Answer:

4.15

Step-by-step explanation:

radius is the half of the diameter so 8.3/2 is 4.15

Answer:

49.2%

Step-by-step explanation:

Answer:

0.9929 = 99.29% probability that the carbon fiber composite material can withstand pressure less than 2.45 standard deviations above the mean when compared to the individual materials

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

What is the probability that the carbon fiber composite material can withstand pressure less than 2.45 standard deviations above the mean when compared to the individual materials?

2.45 standard deviations above the mean is Z = 2.45, so this probability is the p-value of Z = 2.45.

Looking at the z-table, Z = 2.45 has a p-value of 0.9929.

0.9929 = 99.29% probability that the carbon fiber composite material can withstand pressure less than 2.45 standard deviations above the mean when compared to the individual materials

Answer:

0.375

Step-by-step explanation:

510 male out of a total of 1360

510/1360 = 0.375