Solve the system of equation using ELIMINATION (solve for x)
x + 3y = 14
-x + y = 10

The geometry is defined by the combination of rectangular prism and half-cylinder. Then the volume of the composite geometry will be 796.94 cubic mm.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

The graph is given below.

The geometry is defined by the combination of rectangular prism and half-cylinder. Then the volume of the composite geometry will be

Volume = [(πr²/2) + a x b] x h

Volume = [(π x 4.5²/2) + 9 x 2] x 16

Volume = [10.125π + 18] x 16

Volume = 48.808 x 16

Volume = 796.938

Volume ≅ 796.94 cubic mm

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Answer:

True

Step-by-step explanation:

A relation is a function when each input has exactly one output. Looking at the coordinates given, none of the inputs(x-values) are repeated. Therefore, the relation is a function.

Day 6/11 = $6,920

Day 6/15 = $6,505

Day 6/20 = $6,305

She withdrew $279 to buy clothes

Therefore her final balance= $6,920

Therefore, her balance is

= $6,920 - $415

= $6,505

Therefore her balance is

= $6,505 - $200

= $6,305

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Answer:

a. Solve the System of Equations. Show your work

Answer:

straight line on 2 on the y axis

Step-by-step explanation:

Its just a straight line on 2 on the y axis

Answer: 20 sq ft

Step-by-step explanation: The base is AB = 5 ft because AB = CD. Recall that opposite sides in a parallelogram are congruent and parallel.

area of parallelogram = base * height = 5*4 = 20

note: the base is always perpendicular to the height

[tex]\text{L.H.S}\\\\=(1 - \cot \theta )^2 + (1 + \cot \theta)^2 \\\\=(1-\cot \theta + 1 + \cot \theta)^2 - 2(1 -\cot \theta)(1 + \cot \theta)\\\\=2^2 - 2(1 - \cot^2 \theta)\\\\=4-2+2 \cot ^2 \theta\\\\=2+2 \cot^2 \theta\\\\=2(1 + \cot^2 \theta)\\\\=2 \csc^2 \theta\\\\=\text{R.H.S}\\\\\text{Proved.}[/tex]

Answer:

[tex]\huge\boxed{\sf x = \pm \sqrt{7} }[/tex]

Step-by-step explanation:

Given function:

[tex]f(x)=x^2-7[/tex]

We can also write it as:

[tex]y =x^2-7[/tex]

x-intercept is the point where y = 0

Put y = 0 in the above equation

[tex]0=x^2-7\\\\Add \ 7 \ to \ both\ sides\\\\7 = x^2\\\\Take \ sqrt \ on \ both \ sides\\\\\pm \sqrt{7} =x\\\\x = \pm \sqrt{7} \\\\\rule[225]{225}{2}[/tex]

Answer:

polynomial

Step-by-step explanation:

because poly=more than 1

mono=1

bi= 2

tri=3

Answers:

[tex](f \circ g)(x) = 2x^2-5x\\\\(g \circ f)(x) = 2x^2+7x\\\\[/tex]

The domain is "all real numbers" which you could type in (-infinity, infinity) or [tex](-\infty, \infty)[/tex] when doing interval notation. This applies to both.

=========================================================

Explanation:

See the attached image for the steps of each.

The domain is the set of all real numbers because each result is a polynomial. We don't have to worry about dividing by zero, taking a square root of a negative number etc. There are no restrictions on x. Any real number can replace x to get some real number result for y. This applies to both composite functions.

The coordinates of the new triangle's vertices are (0, -1), (-4, -3), and

(-2, -1). Hence option A is true.

Used the rule of a point (x, y) when rotated over the y-axis of 90° clockwise rotation from point (0, 0),

(x, y) → (y, - x)

Given that the triangle BCD is shown in the image.

Here, the coordinates of the vertices of BCD are,

B = (1, 0)

C = (3, - 4)

D = (1, - 2)

Now apply the rotation rule, the coordinates of the new triangle's vertices are;

B' = (0, - 1)

C' = (- 4, - 3)

D' = (- 2, - 1)

Therefore, the option A is true.

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Answer:

[tex]x=-72[/tex]

Step-by-step explanation:

[tex]-\frac{x}{8}-11=-2\\ -\frac{x}{8}=9\\ -x=72\\x=-72[/tex]

Answer:

260 cm^2

Step-by-step explanation:

Area of rectangle = 20 x 10 = 200 cm^2

Area of triangle = 6 x 20 /2 = 60 cm ^2

Area of figure = 200 + 60 = 260 cm^2

The difference between the two polynomials is 11x²3y³ - 4xy².

The difference between two polynomials is the result you get by subtracting one from the other.

Thus:

= (4x²2y³ + 2xy² – 2y) – (–7x²y³ + 6xy² – 2y)

= 4x²2y³ + 2xy² – 2y + 7x²y³ - 6xy² + 2y

= 11x²3y³ - 4xy²

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Answer:308

Step-by-step explanation:Multiply 4*7*11

Answer:

98

Step-by-step explanation:

b(c(3))

b(3(3)-2)

2(3(3)-2)^2

2(9-2)^2

2(7)^2

2(49)

98

Answer:

5 hours and 42 mins

Step-by-step explanation:

Answer:

8 hours

Step-by-step explanation:

12/2= 6
He grades 6 exams per hour
48/6= 8
it would take 8 hours to grade 48 exams

Bonus:
it takes him 10 minutes to grade an exam. That doesnt matter for this question but it's good 2 know

Answer:

8 hours

Step-by-step explanation:

To solve this it seems you need to set up a proportion.

12/2=48/x

cross multiply the 2 and 48.

2•48=96.

divide by the remaining number to get x.

96/12=8.

Answer:

30600

Step-by-step explanation:

Answer/Step-by-step explanation:

Given:

A gas station offers a lucky draw to customers. Each time you spend more than $20 on gas, you can make a draw to win a prize. The probability of winning a prize is 1/12 suppose you buy gas 4 times.

To Find:

what is the probability of you winning a prize each time?

Solve:

Since, it given that you buy gas 4 times. Thus that means:

1/12 × 1/12 × 1/12 × 1/12 or  1/12⁴

Now solving it:

1/12 × 1/12 × 1/12 × 1/12 = 1/20736

Which also means (0.0048%) in decimal form since, 1 divide by 2076 equal to 0.0048%

Kavinsky

Answer:

Graph B

Step-by-step explanation:

Point-line graphs are usually used to compare data over a course of time, and bar graphs are more commonly used to compare statistics between different data sets (in this case it is between different countries)

Answer:

908

Step-by-step explanation:

879+29=908

Answer:

64

Step-by-step explanation:

The equation that has exactly one solution will be 2x + 31 = - 2x - 31. Then the correct option is B.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

The linear equations are given.

Check whether the equation is linear or not.

1.   2x + 31 = 2x - 31, this is not a linear equation.

2.  2x + 31 = - 2x - 31, this is a linear equation.

Then the solution of the linear equation will be

4x = - 62

 x = - 15.5

3.  2x + 31 = 2x - 31, this is not a linear equation.

4.    2x - 2 = 2x - 31, this is not a linear equation.

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Let's solve this problem step by step:

 ⇒ on one side, I solve the equaiton

    ⇒ on the other side, I give you the property that I use to solve the

        equation

         ⇒ you don't need to write down those properties if your teachers

             didn't ask you for it

  [tex]4(5x-2)=2(9x+3)\\[/tex]      |   Given equation

  [tex]20x-8=19x+6[/tex]           |    Distributive Multiplication over subtract/add

  [tex]x=14[/tex]                             |    Subtraction Property of Equality

Answer: x = 14

Definition of Properties:

If the width of peter's garden is 32 yards, the ratio of the areas is 47: 32

area of rectangle = lw

where

Therefore,

Peter rectangular garden

Jorge is planting a square garden. The sides of Jorge's garden are equal to the width of Peter's garden.

Therefore,

The ratios are as follows;

(15 + x)x : x²

Therefore, if the width of peter's garden is 32 yards, the ratio of the areas is as follows:

(15 + 32)32 : 32²

1504: 1024

752: 512

376: 256

94:64

47: 32

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Answer:

(x+15)/x; 47/32

Answer:

Answer In this Picture.

The graph represents a polynomial graph, and the equation of the polynomial graph is f(x) = -(x + 5)³(x - 2)²

From the graph, we have the following observations:

This means that the graph has a multiplicity of 2 at x = 2 and a multiplicity of 3 at x = -5

So, we have:

f(x) = a(x + 5)³(x - 2)²

The curve is inverted,

This means that a < 0

Assume a = -1.

Then, we have:

f(x) = -(x + 5)³(x - 2)²

Hence, the equation of the polynomial graph is f(x) = -(x + 5)³(x - 2)²

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Answer:

root of 15 or in decimal form 3.87 (rounded)

Step-by-step explanation:

You just multiply both together