What is the volume of the solid?
A. 12 yd³
B. 14 yd³
C. 22 yd³
D. 5 yd³

The solution to the system of inequalities 2x − y < 4 and x + y < −1 is the intersection of the shaded regions below the lines 2x - y = 4 and x + y = -1, labeled AB on the graph. Regions A and B represent the solutions to each individual inequality.

To solve the system of inequalities 2x − y < 4 and x + y < −1, we can use the following steps

Solve each inequality for y in terms of x

2x - 4 < y

-x - 1 < y

Plot the boundary lines for each inequality as dotted lines. To do this, we can use the equality signs instead of the inequality signs.

2x - 4 = y

-x - 1 = y

Shade the region that satisfies each inequality. To do this, we can test a point that is not on the boundary line in each inequality. For example, we can test (0,0) in the first inequality

2(0) - 0 < 4

0 < 4

Since (0,0) satisfies the first inequality, we shade the region below the line 2x - y = 4. Similarly, we can test (0,-2) in the second inequality

(0) + (-2) < -1

-2 < -1

Since (0,-2) satisfies the second inequality, we shade the region below the line x + y = -1.

The solution to the system of inequalities is the intersection of the shaded regions, which is labeled AB in the graph. The shaded region labeled AB is the region that satisfies both inequalities, which is the region below both lines.

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Step-by-step explanation:

in what form do you need the equation ?

I assume it is the slope-intercept form :

y = ax + b

"a" being the slope of the line, "b" being the y-intercept of the line.

the slope of a line is the ratio

y-coordinate difference / x-coordinate difference

when going from one point on the line to another.

and the y-intercept (y-axis intercept, to be precise) is the y-value when x = 0.

so, starting with the slope, we go for example from (1, 6) to (6, 1) :

x changes by +5 (from 1 to 6).

y changes by -5 (from 6 to 1).

so, the slope is

-5/+5 = -1

so, we know, our equation looks like

y = -x + b

to get "b" we use one of the points, e.g. (1, 6) :

6 = -1 + b

b = 7

and our final equation is

y = -x + 7

The photographer should set the tripod at an angle of approximately 75.96 degrees to get a picture of the rocket at its maximum altitude.

We have,

We can use trigonometry to solve this problem.

          C

        /   \

       /     \

      /θ     \

     /         \

    /           \

   A-------------B

          50 ft

In this diagram, A represents the launch pad, B represents the maximum altitude of the rocket, C represents the position of the photographer, and θ represents the angle at which the tripod should be set.

We want to find θ.

First, we can find the height of the triangle ABC using the Pythagorean theorem:

AB² = AC² + BC²

200² = AC² + 50²

AC² = 200² - 50²

AC = √(200² - 50²)

AC = 190.526 ft

Next, we can use the tangent function to find θ:

tan(θ) = opposite/adjacent = AB/BC = 200/50 = 4

Taking the arctangent of both sides, we get:

θ = [tex]tan^{-1}(4)[/tex]

θ = 75.96 degrees

Therefore,

The photographer should set the tripod at an angle of approximately 75.96 degrees to get a picture of the rocket at its maximum altitude.

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Writing the correct number relies on what our number system calls the place value system. The 9, the 3, and the 1 are all located in different spots in the larger number, and each of them is called a digit.

Putting the digits in the wrong locations could result in disaster when dealing with money and in many other situations.

The value of x after solving the given equation (6x+30) = 2x is equal to -7.5.

To solve for x in the equation (6x+30) = 2x, we need to isolate x on one side of the equation.

First, we can simplify the equation by subtracting 2x from both sides:

(6x+30) - 2x = 0

Simplifying this further gives:

4x + 30 = 0

To isolate x, we can subtract 30 from both sides:

4x = -30

Finally, we can solve for x by dividing both sides by 4:

x = -7.5

Therefore, the value of x in the equation (6x+30) = 2x is -7.5.

In general, when solving linear equations such as this, we want to manipulate the equation in such a way that we can isolate the variable on one side of the equation.

This can involve adding or subtracting terms, multiplying or dividing by constants, or taking square roots, among other techniques. The goal is to get the equation into a form that allows us to solve for the variable by itself.

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Complete question is:

What is the value of x? (6x+30) = 2x

The distance from (-18, -5) and (-18, 24) is 29 units which is calculated with  the formula of shortest distance between two coordinates.

Hence option d is the correct option.

The coordinates are given as, say P is (-18, -5) and Q is (-18, 24).

The distance between P and Q can be calculated with the formula of shortest distance between two coordinates as,

Shortest distance between P and Q, PQ = [tex]\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2 }[/tex]  units

⇒ PQ = [tex]\sqrt{((-18) - (-18))^2 + ((24) - (-5))^2 }[/tex]  units

⇒ PQ = [tex]\sqrt{(-18 +18)^2 + (24 +5)^2 }[/tex]  units

⇒ PQ = [tex]\sqrt{(0)^2 + (29)^2 }[/tex]  units

⇒ PQ = [tex]\sqrt{29^2}[/tex] units

⇒ PQ = 29 units

Hence option d 29 units is the correct option.

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Answer:20

Step-by-step explanation:

40/2=20

20 days of giving away 2 tickets

The value of Y is givan as y = 2 * 3^x

The general form is of

y = ab^x

where we have to define the terms as

'a' is the initial value, 'b' is the base, and 'x' is the exponent

Point (0, 2):

y = ab^x

2 = a * b^0

Since any non-zero number raised to the power of 0 is 1, we have:

2 = a * 1

a = 2

Point (1, 6):

y = ab^x

6 = 2 * b^1

6 = 2 * b

b = 6 / 2

b = 3

From the values that we have solve we would have

y = 2 * 3^x

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Answer:

1(.1) + 2(.2) + 3(.3) + 4(.4)

= .1 + .4 + .9 + 1.6 = 3.0

Answer:

Step-by-step explanation:

To calculate the weighted mean, first multiply each number by its corresponding weight, then add-up the products and divide by the sum of the weights-

weighted mean = (1 x 0.1 + 2 x 0.2 + 3 x 0.3 + 4 x 0.4) / (0.1 + 0.2 + 0.3 + 0.4)

Then simplifying the numerator:-

weighted mean = (0.1 + 0.4 + 0.9 + 1.6) / (0.1 + 0.2 + 0.3 + 0.4)

Then adding up the numerator:-

So the weighted mean of the numbers 1, 2, 3, and 4 with weights 0.1, 0.2, 0.3, and 0.4 respectively is 3.

The function given in the table is an exponential function.

The function given in the table is clearly not linear, since the y value is changing rapidly.

Here we can see that the function value is changing as the multiplication of 7.

y = 7⁰ = 1, when x = 1

y = 7¹ = 7, when x = 2

y = 7² = 49, when x = 3

y = 7³ = 343, when x = 4

y = 7⁴ = 2401, when x = 5

So here the equation of the function can be written as,

y = 7ˣ⁻¹

Here the variable x is in the exponent.

So it is an exponential function.

Hence the given function is an exponential function.

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There are 6 different possible arrangements as obtained using the factorial method and they are :

DMC, CMD, DCM, MDC, CDM, MCD

Given that:

DETECTIVE STORY = D

MYSTERY STORY = M

COMIC BOOK = C

Now, To use the factorial method, we find the factorial value of the number of books to be arranged

Number of different possible arrangements = (number of books)!

Number of books = 3

Hence,

3! = 3 x 2 x 1 = 6 ways

The sample space :

DMC

CMD

DCM

MDC

CDM

MCD

Therefore, there are 6 different samples on the SAMPLE SPACE.

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Complete question is,

Leena is arranging 3 different books in a row on a shelf. Create a sample space for the arrangement of a detective story (D), a mystery story (M), and a comic book (C).

Source

StylesNormal

The surafce area of the cone with a slant height of 14 in and a diameter of 6 in is 160.2 in².

A cone is simply a 3-dimensional geometric shape with a flat base and a curved surface pointed towards the top.

The surface area of a cone can be expressed as;

SA = πrl + πr²

Where r is radius of the base, l is the slant height of the cone and π is constant pi.

Given that:

Slant height l = 14 in

Diameter d = 6 in

Radius r = diameter/2 = 6/2 = 3in

S.A = ?

Plug the given values into the above formula and solve for the surface area.

SA = πrl + πr²

SA = ( π × 3in × 14in ) + ( π × (3in)² )

SA = 160.2 in²

Therefore, the surface area is 160.2 in².

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One pound of spice mix will have 1 1/9 cups of cinnamon.

Given that in 3/4 pound of a spice mix there are 5/6 cups of cinnamon,

we need to find the amount of cinnamon in a pound,

Since, 3/4 pound = 5/6 cinnamon

So,

1 pound = 5/6 x 4/3

= 20/18 = 10/9

= 1 1/9 cups

Hence, one pound of spice mix will have 1 1/9 cups of cinnamon.

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The volume of the shape to the nearest tenth is equal to 138.4π m³.

In Mathematics and Geometry, the volume of a sphere can be calculated by using the following mathematical equation (formula):

Volume of a sphere = 4/3 × πr³

Where:

r represents the radius.

By substituting the given parameters into the formula for the volume of a sphere, we have the following;

Volume of a sphere = 4/3 × π × 4.7³

Volume of a sphere = 138.4π m³

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Answer:

To find the amount included in the Other Items section of Miller's income statement, we need to add up all the expenses and losses that are not related to advertising, interest, rent, cost of goods sold, depreciation, and prepaid insurance. These expenses and losses fall under the category of "Other Expenses" or "Other Items" in the income statement.

From the given information, the expenses and losses that are not included in the above categories are:

- Loss on sale of property and equipment = $11,400

Therefore, the amount included in the Other Items section of Miller's income statement is $11,400.

Step-by-step explanation:

The mass of a piece of metal that has a volume of 12.4 cubic centimeters.

We can set up a proportion with the given masses and volumes:

Mass ₁ / Volume ₁ = Mass ₂ / Volume ₂

We can choose any two sets of masses and volumes from the table to use in the proportion. Let's use the first set of masses and volumes:

2.5 / 2.5 = Mass₂  / 12.4

We can solve for Mass 2 by cross-multiplying and simplifying:

2.5 x 12.4 = 2.5 Mass ₂

31 = Mass ₂

Therefore, the mass of a piece of metal with a volume of 12.4 cubic centimeters is 31 grams. We can round this answer to the nearest tenth of a gram, which gives us 31.0 grams.

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Answer:

a) y = -2x + 3

b) y = -3x + 7

c) y = -1/2x + 4

d) y = 2

Step-by-step explanation:

Gradient is also known as slope

a) y = mx + b

3 = (-2)0 + b

b = 3

y = -2x + 3

b) y = mx + b

1 = (-3)(2) + b

1 = -6 + b

b = 7

y = -3x + 7

c) Slope m = (y2 - y1)/(x2 - x1)

m = (2 - 3)/(4 - 2) = -1/2

y = mx + b

3 = -1/2(2) + b

3 = -1 + b

b = 4

y = -1/2x + 4

d) The x‐axis or any line parallel to the x‐axis has a slope of 0.

y = mx + b

2 = -3(0) + b

b = 2

y = 2

Answer:

a) The equation of this line is y = -2x + 3

b) The equation of this line is y = -3x + 7

c) The equation of this line is y = -1/2x + 4 or y = -0.5x + 4

d) The equation of this line is y = 2

Step-by-step explanation:

The equation of a line can be written in the form y = mx + c, where m is the gradient and c is the y-intercept.

a) The equation of the line with a gradient of -2 and cutting the y-axis at 3 can be found using the point-slope form of a linear equation. The point-slope form is given by y - y1 = m(x - x1), where m is the gradient and (x1, y1) is a point on the line. Substituting m = -2 and (x1, y1) = (0, 3), we get:

y - 3 = -2(x - 0)

Simplifying the right-hand side gives:

y - 3 = -2x

Adding 3 to both sides gives the final equation:

y = -2x + 3

b) The equation of the line with a gradient of -3 and passing through the point (2, 1) can be found using the point-slope form again. Substituting m = -3 and (x1, y1) = (2, 1), we get:

y - 1 = -3(x - 2)

Simplifying the right-hand side gives:

y - 1 = -3x + 6

Adding 1 to both sides gives the final equation:

y = -3x + 7

c) To find the equation of the line passing through the points (2, 3) and (4, 2), we first need to find its gradient. The gradient is given by:

m = (y2 - y1)/(x2 - x1)

Substituting the coordinates of the two points, we get:

m = (2 - 3)/(4 - 2) = -1/2 or -0.5

Now, we can use the point-slope form again, this time with (x1, y1) = (2, 3) and m = -1/2:

y - 3 = (-1/2)(x - 2)

Simplifying the right-hand side gives:

y - 3 = (-1/2)x + 1

Adding 3 to both sides gives the final equation:

y = (-1/2)x + 4 or y = -0.5x + 4

d)The line is parallel to the x-axis and passes through the point (-3 ; 2). A line parallel to the x-axis has a gradient of 0. The general equation of a line is y = mx + c, where m is the gradient and c is the y-intercept. Since the gradient is 0, the equation becomes y = c. Since the line passes through the point (-3 ; 2), we can substitute y = 2 into the equation to find that c = 2. Therefore, the equation of this line is y = 2.

The statement that is not true on the cube - shaped box is C. The volume of the box is 1 square foot.

The possible dimensions for the bottom layer would be :

In answer to the rectangular prism inquiry, we know that the prism is made of 36 cubic units and has a height of 3 units. To discover all potential bottom layer dimensions, divide the total number of cubic units (36) by the height (3 units):

36 / 3 = 12

The possible dimensions of the bottom layer:

1 x 12 = 12

2 x 6 = 12

3 x 4 = 12

This means that the possible dimensions would be:

Length = 1 unit , Width = 12 units

Length = 2 units , Width = 6 units

Length = 3 units , Width = 4 units

A square foot is a unit of area, not volume. The volume should be measured in cubic feet.

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Answer:

Ryan: (100/13)(1/1,609.34)(3,600) =

17.21 miles per hour

Ryan is faster than Juan, by about 2.21 miles per hour

Answer:

y = - [tex]\frac{1}{2}[/tex] x + 6

Step-by-step explanation:

the equation of a line 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 ) = (- 4, 8 ) and (x₂, y₂ ) = (6, 3 )

m = [tex]\frac{3-8}{6-(-4)}[/tex] = [tex]\frac{-5}{6+4}[/tex] = [tex]\frac{-5}{10}[/tex] = - [tex]\frac{1}{2}[/tex] , then

y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (- 4, 8 )

8 = - [tex]\frac{1}{2}[/tex] (- 4) + c = 2 + c ( subtract 2 from both sides )

6 = c

y = - [tex]\frac{1}{2}[/tex] x + 6 ← equation of line

The resistance of 1800 feet of the same sort of wire with a 0.45in diameter is roughly 15037.45 ohms.

Let R be the resistance of the wire,

L be the length of the wire,

d be the diameter of the wire, and

k be a constant of variation.

Then we have the equation:

R = k * L / d^2

Solving for k to find the resistance of a wire of varying length and diameter.

We can create an equation using the information provided:

15611 = k * 700 / 0.2^2

Solving for k, we get:

k = 15611 * 0.2^2 / 700

k ≈ 0.1799

Using k to calculate the resistance of a wire with a length of 1800 feet and a diameter of 0.45 inches:

15037.45 ohms = 0.1799 * 1800 / 0.452 R

As a result, the resistance of 1800 feet of the same sort of wire with a 0.45in diameter is roughly 15037.45 ohms.

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The linear function with the greatest rate of change is f(x) = 2x

The general linear function can be written in the following way.

y = ax + b

a is the slope or rate of change, and b is the y-intercept.

From the given options, the line with the greatest rate of change is the one that grows the fastest, and we can see that the equation for that line is:

y = 2x

So that is the correct option.

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The correct options are:

[tex]8(x^2 + 2x) = -3\\\\8(x^2 + 2x + 1) = -3 + 8[/tex]

x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot

Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax2 + bx + c = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where 'a' is called the leading coefficient and 'c' is called the absolute term of f (x).

Now, We have the quadratic equation is:

[tex]8x^2 + 16x + 3 = 0[/tex]

We separate variables from constants

[tex]8x^2+16x = -3[/tex]

Taking the common factor  8

[tex]8(x^2+2x)=-3[/tex]

Completing squares in the brackets and balancing the equation in the right side

[tex]8(x^2+2x+1)=-3+8[/tex]

Factoring the perfect square

[tex]8(x+1)^2=5[/tex]

[tex](x+1)^2=\frac{5}{8}[/tex]

[tex](x+1)=[/tex] ± [tex]\sqrt{\frac{5}{8} }[/tex]

x = -1 ± [tex]\sqrt{\frac{5}{8} }[/tex]

The correct options are:

[tex]8(x^2 + 2x) = -3\\\\8(x^2 + 2x + 1) = -3 + 8[/tex]

x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot

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The given question is incomplete, complete question is:

Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options.

8(x2 + 2x + 1) = –3 + 8

x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot

x = –1 Plus or minus StartRoot StartFraction 4 Over 8 EndFraction EndRoot

8(x2 + 2x + 1) = 3 + 1

8(x2 + 2x) = –3

The volumes of the image for each given value of k are computed below

From the question, we have the following parameters that can be used in our computation:

Volume = 8

Scale factor = k

The volume of the image  is calculated as

Volume = 8k^3

Using the values of k, we have

Volume = 8(1/2)^3 = 1

Volume = 8(0.6)^3 = 1.728

Volume = 8(1)^3 = 8

Volume = 8(1.5)^3 = 27

Hence, the volumes are calculaed above

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The area inside the polar curve R = 2cos(3θ) for three full rotations is 6π.

The polar curve R = 2cos(3θ) is symmetric about the x-axis, with three petals that extend from θ = 0 to θ = π/3, π to 4π/3, and 5π/3 to 2π. To find the area inside the curve, we need to integrate the expression for the area element in polar coordinates over the desired region:

dA = (1/2) [tex]R^{2}[/tex] dθ

The limits of integration for θ are from α = -6π to β = 6π, since we want to find the total area inside the curve for three full rotations. Thus, the integral for the area is:

A = ∫(β=6π, α=-6π) (1/2) [tex]R^{2}[/tex]dθ

= ∫(β=6π, α=-6π) (1/2) (2cos(3θ))^2 dθ

= 2∫(β=6π/3, α=-6π/3) cos^2(3θ) d(3θ) (using the identity cos^2(3θ) = (1 +    cos(6θ))/2)

= ∫(β=6π/3, α=-6π/3) (1/2 + (1/2)cos(6θ)) d(3θ)

= (1/2)θ + (1/12)sin(6θ) ∣(β=6π/3, α=-6π/3)

= (1/2)(6π - (-6π)) + (1/12)(sin(36π) - sin(-36π))

= 6π

Correct Question :

Find The Area Inside R=2cos(3θ) (Tip: Use Α=−6π And Β=6π )

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The exact value for the trigonometric function of numbers is derived to be √3/2.

Trigonometric identities are equations that involve the trigonometric functions (such as sine, cosine, tangent, cosecant, secant and cotangent) and are true for all possible values of the variables involved. These identities can be used to simplify trigonometric expressions, solve equations, and prove other mathematical statements.

Then sum and difference identities states that:

sin(A ± B) = sinAcosB ± cosAsinB

cos(A ± B) = cosAcosB ∓ sinAsinB

so;

sin(11°) cos(49°) + cos(11°) sin(49°) = sin(11 + 49)

sin(11°) cos(49°) + cos(11°) sin(49°) = sin(60°)

sin(11°) cos(49°) + cos(11°) sin(49°) = √3/2.

Therefore, the exact value for the trigonometric function of numbers is derived to be √3/2.

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Answer:

To calculate the area of the shaded shape, we need to first find the area of the two rectangles and then subtract the overlap.

The area of the rectangle with dimensions 5m and 13m is:

Area = 5m x 13m = 65 square meters

The area of the rectangle with dimensions 9m and 11m is:

Area = 9m x 11m = 99 square meters

To find the overlap, we need to calculate the width of the shaded region. We can do this by subtracting the length of one rectangle from the other:

13m - 9m = 4m

So the width of the shaded region is 4m.

Now we can find the area of the shaded region by multiplying the width by the length:

Area = 4m x 5m = 20 square meters

Finally, we can find the total area by subtracting the overlap from the sum of the two rectangle areas:

Total Area = (65 + 99) - 20 = 144 square meters

Therefore, the area of the shaded shape is 144 square meters.

Answer: 61m^2 would be the answer

Answer:

I did the math in my head but please please trust me

It’s below

Step-by-step explanation:

C = 1 1/2

B = 2

A = 5

I’m going to try to explain as best as I can

First solve for C by subtracting the other numbers in its line going up to down from 9:

9 - 3 1/2 + 4 = C

9 - 7 1/2 = C

1 1/2 = C

now that w have C we can solve for b doing same steps:

9 - 5 1/2 + 1 1/2 = b

9 - 7 = b

2 = b

now we do A:

9 - 2 + 2 = a

9 - 4 = a

5 = a

Answer

A should be 5

B should be 2

c should be

[tex] 1\frac{1}{2 \\ } [/tex]

all should add up to 9

2+A(5)+b(2)= 9

a(5)+3 1/2+ 1/2=9

5 1/2+ b(2)+ 1 1/2= 9

3 1/2+ 1 1/2+ 4= 9

The coordinates of B'(6, 3) and C'(4, 4).

We have,

The point A (6, 8) is translated to A' (2, 5).

So, here the points are translated as

(x₁ - x₂ , y₁ - y₂)

= (6 -2, 8-5)

= (4, 3)

So, the coordinates of B'

= (8 -2, 8-5)

= (6, 3)

and, the coordinate of C'

= (6-2, 9-5)

= (4, 4)

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