12 triangles outlined in blue are shown. A red square is drawn around 8 of the triangles.

The area of one of the small right triangles outlined in blue is A cm2, while the area of the square outlined in red is B cm2. Which expressions show the area of the shaded region in terms of A and B? Check all that apply.
4A + B
8A + B
2A + B
1.5B
12A

**Disclaimer** Hi there! I am not fully sure what [ T ] represents. From the answer that I got [ 38π / 3 ], it does not match any one of them, so I choose none of the above. If there's a specific meaning of [ T ] and I am incorrect, please let me know and I will modify my answer.

Answer: None of above

Step-by-step explanation:

Given formula

S = r θ

Given information

radius = 19 ft

Angle = 2π / 3

Substitute values into the formula

S = r θ

S = (19) (2π / 3)

Simplify by multiplication

[tex]\Large\boxed{S=\frac{38\pi}{3} }[/tex]

Hope this helps!! :)

Please let me know if you have any questions

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's solve ~

[tex]\qquad \sf  \dashrightarrow \: (h - g)(x) [/tex]

[tex]\qquad \sf  \dashrightarrow \: h(x) - g(x) [/tex]

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} + 2x - 6 - (2 {x}^{2} + 3x - 9)[/tex]

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} + 2x - 6 - 2 {x}^{2} - 3x + 9[/tex]

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} - 2 {x}^{2} + 2x - 3x - 6 + 9[/tex]

[tex]\qquad \sf  \dashrightarrow \: - {x}^{2} - x + 3[/tex]

For, (h - g)(2.1), put x = 2.1

[tex]\qquad \sf  \dashrightarrow \: - {(2.1)}^{2} - (2.1) + 3[/tex]

[tex]\qquad \sf  \dashrightarrow \: - 4.41 - 2.1 + 3[/tex]

[tex]\qquad \sf  \dashrightarrow \: - 6.51 + 3[/tex]

[tex]\qquad \sf  \dashrightarrow \: - 3.51[/tex]

Answer:

Resistance

Step-by-step explanation:

Answer:

Step-by-step explanation:

Convert 2y=-3x+2 into y=mx+b form

[tex]\frac{2y}{2} =\frac{-3x+2}{2}[/tex]

[tex]y=\frac{-3x}{2} +1[/tex]

Y intercept is 1, slope is -3/2

Graph looks like this:

Answer:

Step-by-step explanation:

part A:   when you graph both y=7x-9 and y=3x-1 the two lines will intersect this is how you solve the graphing part of the system of equations.

Both of these lines are in slope form (y=mx+b) where m is the slope which is 7 and 3 and b is the y-intercept which is -1 and -9.

part B

7x-9=3x-1

subtract 3x from both sides

4x-9=-1  

add 9 to both sides

4x=8  

divide both sides by 4

x=2,

making y=3x-1 become:

y=3(2)-1=6-1=5,  

the answer is (2,5)

The term that must be added to the equation x2+4x=1 to make it into a perfect square is 4.

Any equation that can be rewritten in standard form as where x represents an unknown, a, b, and c represent known numbers, and where a 0 is true is a quadratic equation. Since there is no ax2 term, the equation is linear if a = 0, not quadratic.

This is true because the Latin word quadratum, which means "square," plus the fact that the area of a square with side length x is equal to x2, make up what is known as the quadratic (or "square-like") definition of a polynomial equation with exponent two.

x²+4x=1

as, the x has coefficient 4.

so,

half the coefficient of x and add and subtract the square of the remaining.

x²+4x + 2 ² - 2² =1

Now,

make the whole square term

x²+4x + 2 ² - 4 - 1=0

( x + 2)² -5= 0

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The predicted value (in dollars) for maintenance expenses when a truck is 7 years old is $626.3.

In this question,

The equation for least regression line to this data set is

y' = 76.82x + 88.56 ------- (1)

Number of years, x = 7

The general form of equation for least regression line is

y' = a + bx

where y is the dependent variable, x is the independent variable, a is the intercept of regression line and b is the slope of regression line.

The predicted value (in dollars) for maintenance expenses when a truck is 7 years old can be calculated as

y' = 76.82x + 88.56

Substitute the value of x in the above equation, we get

y' = 76.82(7) + 88.56

y' = 537.74 + 88.56

y' = 626.3

Hence we can conclude that the predicted value (in dollars) for maintenance expenses when a truck is 7 years old is $626.3.

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Answer:

-6

Step-by-step explanation:

Additive inverse is the number that when added to A gives a result of zero

A + inverse = 0

6 + inverse = 0

inverse = -6

The Option A is correct. The Numbers of Miles Driven for A Truck That Cost a Total Of $42.50 To Rent for One Day $25m + 0.35m = $42.50

According to the statement

we have given that the  Rental Truck Is Company Charges $25 Per Day Plus A Fee Of $0.35 For Every Mile (m) Driven. and a Truck That Cost A Total Of $42.50 To Rent For One Day.

And we have to find the equation for this.

So, for given purpose,

we know that the A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

And from the given values the equation formed that the

In the equation the charges per mile is added to the original charges is equal to the total charges per day.

So, The equation become

$25m + 0.35m = $42.50

And by this equation we represent the all given conditions related charges.

So, The Option A is correct. The Numbers of Miles Driven for A Truck That Cost a Total Of $42.50 To Rent for One Day $25m + 0.35m = $42.50

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The solution to the system of equations is x = 1, y = 10 and z = 4

The system of equations is given as:

3x +2y +4z = 11

2x -y +3z = 4

5x -3y +5z = -1

Multiply the second equation by 2

So, we have

4x - 2y + 6z = 8

Add this equation to the first equation

3x + 4x + 2y - 2y + 4z + 6z = 11 + 8

Evaluate the like terms

7x + 10z = 19

Multiply the second equation by 3

So, we have

6x - 3y + 9z = 12

Subtract this equation from the third equation

6x - 5x - 3y + 3y + 9z - 5z = 12 + 1

Evaluate the like terms

x + 4z = 13

Make x the subject

x = 13 - 4z

Substitute x = 13 - 4z in 7x + 10z = 19

7(13 - 4z) + 10z = 19

Expand

91 - 28z + 10z = 19

Evaluate the like terms

-18z = -72

Divide

z = 4

Substitute z = 4 in x = 13 - 4z

x = 13 - 4 * 4

Evaluate

x = 1

We have:

2x -y +3z = 4

This gives

2(1) - y + 3 * 4 = 4

Evaluate

2 - y + 12 = 4

This gives

y = 10

Hence, the solution to the system of equations is x = 1, y = 10 and z = 4

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The correct statements about the solids are:

To find which statements are correct:

Congruent base: This is used to indicate that the triangles' bases are the same and that they have the same shape.

The volume of the first triangle is: [tex]2x^{2} h[/tex]

The volume of the second triangle is: [tex]x^{2} h[/tex]

Therefore, the correct statements about the solids are:

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The complete question is given below:
One rectangular solid with a square base has twice the height of another rectangular solid with a square base with the same side length. Which statements about the two rectangular solids are true? Check all that apply.

A) The bases are congruent.

B) The solids are similar.

C) The ratio of the volumes of the first solid to the second solid is 8:1.

D)The volume of the first solid is twice as much as the volume of the second solid.

E) If the dimensions of the second solid are x by x by h, the first solid has 4xh more

surface area than the second solid.

Answer:

c. 3  

yes you are right, good job!!

Step-by-step explanation:

18 divided by what equals 2?

18 / 2 = 9 so 18 / 9 = 2

so 27 / 9 = y which y = 3

check: 9 x 3 = 27

Answer:

Yes, C

Step-by-step explanation:

18/2 = 9 so you need to divide 27 by 9 to get 3

Answer:

  s = -24

Step-by-step explanation:

This is a 2-step linear equation, so can be solved the way all 2-step equations are solved.

Step 1

Identify the constant term on the side of the equation with the variable term, and add its opposite to both sides.

  [tex]7 = \dfrac{1}{6}s+11\qquad\text{given}\\\\7-11=\dfrac{1}{6}s+11-11\qquad\text{add $-11$ to both sides}\\\\-4=\dfrac{1}{6}s\qquad\text{simplify}[/tex]

Step 2

Multiply both sides by the inverse of the coefficient of the variable.

  [tex](6)(-4)=(6)\left(\dfrac{1}{6}s\right)\qquad\text{multiply both sides by 6}\\\\\boxed{-24=s}\qquad\text{simplify}[/tex]

Often, when equations contain fractions, you are advised to "eliminate fractions" as a first step. That generally means you multiply both sides of the equation by a suitable common denominator.

Here, the only denominator is 6, so the fraction can be eliminated by multiplying both sides of the equation by 6.

  [tex]7=\dfrac{1}{6}s+11\qquad\text{given}\\\\6(7)=6\left(\dfrac{1}{6}s+11\right)\qquad\text{multiply both sides by 6}\\\\42=s+66\qquad\text{simplify}\\\\42-66=s+66-66\qquad\text{add the opposite of 66 to both sides}\\\\\boxed{-24=s}\qquad\text{simplify}[/tex]

You will note this requires the same number of steps, but you don't have to mess with fractions after the first step.

The value we found for the variable can be checked in the original equation.

  [tex]7=\dfrac{1}{6}(-24)+11\\\\7=-4+11\qquad\text{true}[/tex]

Answer:

A.

Sample 1 mean: 6.375

Sample 2 mean: 6.375

Sample 3 mean: 6.625

B.

Range of sample means: 0.25

C.

The first and last boxes should be checked, as they are true.

Step-by-step explanation:

To calculate the mean you must add all of the numbers together and then divide the sum by the quantity of numbers. Ex: 3+7+8+3+7+9+6+8 = 51.

51/8 = 6.375.

Step-by-step explanation:

x = 7

y = 5

[tex] = {x}^{2} + {y}^{2} [/tex]

[tex] = (7 {)}^{2} + (5 {)}^{2} [/tex]

= 7 × 7 + 5 × 5

[tex] = 49 + 25 [/tex]

[tex] = 74[/tex]

Hey there!

x^2 + y^2

= 7^2 + 5^2

= 7 * 7 + 5 * 5

= 49 + 25

= 74

Therefore, your answer should be: 74

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

its the 4th one i think

Step-by-step explanation:

The median value is 63 and Lower quartile range is 48 and Interquartile range is 80.

According to the given statement

we have given data set and we have to find the five number summary.

So, For this purpose,

the given data set is:

48, 50, 54, 56, 63, 63, 64, 68, 74, 74, 79, 80

Firstly we have to find the upper quartile means median for it.

So, Median = n /2

median = 12/2

median = 6th term.

So, Upper quartile range for this data set is 63.

And

Lower quartile for data set is the lower value of the data set.

So, That's why

Lower quartile range for this data set is 48.

And now, we have to find the Interquartile range

so, Interquartile range means maximum value of data.

So, That's why

Interquartile range of this data is 80.

So, The median value is 63 and Lower quartile range is 48 and Interquartile range is 80.

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Answer:

y = 8x+7

Step-by-step explanation:

firstly reduce the equation to an arithmetic series starting from the 0th term so:
7, 15, 23, 31, 39....

Secondly, identify the common difference: 8
we now know that the answer must contain 8x

Thirdly, form the equation 8x + c = y where y is a constant. Afterwards insert the values of any given x and y so:
8*0 + c = 7
c = 7
Thusly we now know that the series and thus equation is 8x+7 = y

Answer:

y = 8x + 7

Step-by-step explanation:

the equation of a linear function in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

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

with (x₁, y₁ ) = (1,15) and (x₂, y₂ ) = (2, 23) ← 2 ordered pairs from the table

m = [tex]\frac{23-15}{2-1}[/tex] = [tex]\frac{8}{1}[/tex] = 8

the ordered pair (0, 7 ) indicates c = 7

y = 8x + 7 ← equation of linear function

Just me:

? I will just explain what I understand

Answer:

(Think hard) If you cut a snake in half you get 1/2 but if you cut it into 4's 1/5

I tried.

The first five terms of the given arithmetic sequence are:

54, 45, 36, 27, 18 (First option)

The arithmetic sequence is given as follows,

f(n) = f(n-1) - 9 ............ (1)

Also, f(1) = 54 .............. (2)

Now, for finding the first five term of this arithmetic sequence, we will substitute n as 1, 2, 3, 4, and 5 one by one. Using the above formula for the arithmetic sequence, we can deduce the first five terms.

f(1) is the first term of the sequence which is already provided as 54.

Now, putting n=2 in equation (1), we get,

f(2) = f(2-1) - 9

f(2) = f(1) - 9

Substitute f(1) = 54 from equation (2)

⇒ f(2) = 54 - 9

f(2) = 45

To find the third term of the arithmetic sequence, put n = 3 in equation (1)

f(3) = f(3-1) - 9

f(3) = f(2) - 9

⇒ f(3) = 45 - 9

f(3) = 36

Similarly, we can find the fourth and fifth terms of the arithmetic sequence by substituting n = 4 and n = 5 respectively.

∴ f(4) = f(3) - 9

⇒ f(4) = 36 - 9

f(4) = 27

Likewise, f(5) = f(4) - 9

⇒f(5) = 27 - 9

f(5) = 18

Thus, using the recursive formula, the first five terms of the arithmetic sequence are deduced to be:

54, 45, 36, 27, 18

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Answer:

Option 2

Step-by-step explanation:

Using the quadrstic formula,

[tex]\tan \theta=\frac{-2 \pm \sqrt{2^2 - 4(\sqrt{3})(-\sqrt{3})}}{2\sqrt{3}} \\ \\ =\frac{-2 \pm 4}{2\sqrt{3}} \\ \\ =\frac{-1 \pm 2}{\sqrt{3}} \\ \\ = -\sqrt{3}, \frac{1}{\sqrt{3}}[/tex]

Case 1

[tex]\tan \theta=-\sqrt{3} \implies \theta=\frac{2\pi}{3}, \frac{5\pi}{3}[/tex]

Case 2

[tex]\tan \theta=\frac{1}{\sqrt{3}} \implies \theta=\frac{\pi}{6}, \frac{7\pi}{6}[/tex]

Answer:

The graph of g(x) has a y-intercept at (0,0) and a slope of -2.

Answer: 4/10, 6/15, 8/20

Hope this helps!

The number of additional days she wants to rent the car for the two specials are equivalent is 5 days.

Compact car:

y = 50 + 6x

Another special:

y = 40 + 8x

let

x = number of additional days

50 + 6x = 40 + 8x

50 - 40 = 8x - 6x

10 = 2x

x = 10/2

x = 5 days

Therefore, the number of additional days she wants to rent the car for, the two specials are equivalent is 5 days.

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The difference in mail handled between 195 and 1965 is -5.4 x 10

The data on the pieces of mail handled by the United States Postal Service is written in scientific notation. Scientific notation is used to compress larger numbers into smaller numbers.

In order to write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10. For example, 1 x 10² is equivalent to 100

Difference in mail handled = mail handled in 1995 - mail handled in 1965

(1.8 x [tex]10^{11}[/tex]) - (7.2 x [tex]10^{10}[/tex])

(1.8 - 7.2)  x [tex]10^{11 - 10}[/tex]

-5.4 x 10

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Answer:

y = 3x + 6

Step-by-step explanation:

We are given a line.

We know this line is parallel to the line y=3x+2, and passes through (1, 9).
We want find the equation of this line.

Parallel lines have the same slopes.

So, let's find the slope of y=3x+2.

The line is written the format y=mx+b, where m is the slope and b is the value of y at the y intercept.

As 3 is in the place of where m (the slope) is, the slope of the line is 3.

It is also the slope of the line parallel to it.

We should write the equation of the line parallel y=3x+2 in slope-intercept form as well, however, before we do that, we can write the line in point-slope form, and then convert it to slope-intercept form.

Point-slope form is given as [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1,y_1)[/tex] is a point.

We can substitute 3 as m in the formula, as we know that is the slope of the line

[tex]y-y_1=3(x-x_1)[/tex]

Recall that we were given the point (1, 9), which also belongs to (it passes through) the line.

Therefore, we can use its values in the formula.

Substitute 1 as [tex]x_1[/tex] and 9 as [tex]y_1[/tex].

y - 9 = 3(x-1)

We can now convert the equation into slope intercept form.

Notice how y is by itself in slope-intercept form; this means we'll need to solve the equation for y.

Start by distributing 3 to both x and -1.

y - 9 = 3x - 3

Now add 9 to both sides.

y = 3x + 6

Answer:x=5

Step-by-step explanation: 73+73+6x+4=180

150+6x=180

6x=30

x=5

Answer:

PQ = 10 units

Step-by-step explanation:

to find where the lines cross the x- axis let y = 0 and solve for x , that is

2x + 8 = 0 ( subtract 8 from both sides )

2x = - 8 ( divide both sides by 2 )

x = - 4 ← point P

and

2x - 12 = 0 ( add 12 to both sides )

2x = 12 ( divide both sides by 2 )

x = 6 ← point Q

the lines cross the x- axis at x = - 4 and x = 6

using the absolute value of the difference , then

PQ = | - 4 - 6 | = | - 10 | = 10 units

or

PQ = | 6 - (- 4) | = | 6 + 4 | = | 10 | = 10 units

Answer: [tex]\Huge\boxed{Distance=10~units}[/tex]

Step-by-step explanation:

Given expression

y = 2x + 8

Substitute 0 for the y value to find the x value

This is the definition of x-intercepts

(0) = 2x + 8

Subtract 8 on both sides

0 - 8 = 2x + 8 - 8

-8 = 2x

Divide 2 on both sides

-8 / 2 = 2x / 2

x = -4

[tex]\large\boxed{P~(-4,0)}[/tex]

Given expression

y = 2x - 12

Substitute 0 for the y value to find the x value

(0) = 2x - 12

Add 12 on both sides

0 + 12 = 2x - 12 + 12

12 = 2x

Divide 2 on both sides

12 / 2 = 2x / 2

x = 6

[tex]\large\boxed{Q~(6,0)}[/tex]

Given information

[tex](x_1,~y_1)=(-4,~0)[/tex]

[tex](x_2,~y_2)=(6,~0)[/tex]

Substitute values into the distance formula

[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]Distance=\sqrt{(6-(-4))^2+(0-0)^2}[/tex]

Simplify values in the parenthesis

[tex]Distance=\sqrt{(10)^2+(0)^2}[/tex]

Simplify values in the radical sign

[tex]Distance=\sqrt{100}[/tex]

[tex]\Huge\boxed{Distance=10~units}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The missing length of given right triangle is equal to 1500.

A triangle is classified as a right triangle when it presents one of your angles equal to 90º.  The greatest side of a right triangle is called hypotenuse. And, the other two sides are called cathetus or legs.

The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean  Theorem.

The Pythagorean Theorem says: [tex]hypotenuse^2=(leg_1)^2+(leg_2)^2[/tex] . And the main trigonometric ratios are: sin (x),  cos (x) and tan (x) , where:

[tex]sin(x)=\frac{opposite\ side}{hypotenuse} \\ \\ cos(x)=\frac{adjacent\ side}{hypotenuse} \\ \\ tan (x)= \frac{opposite\ side}{adjacent\ side}[/tex]

There is another important property, where h²=m*n. See the attached image.

From the previous informations presented, you can solve the given question.

Thus, if h²=m*n. You can write:

h²=900*1600

[tex]h=\sqrt{1440000}\\ \\ h=1200[/tex]

If h=1200, you can find x from Pythagorean  Theorem.

x²=1200²+900²

x²=1440000+810000

x²=2250000

x=[tex]\sqrt{2250000}[/tex]

x=1500

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