A triangular prism and two nets are shown:

A right triangular prism is shown with two nets. The triangular base of the prism has height 5 inches, base 12 inches, and hypotenuse 13 inches. The length of the prism is 18 inches. Net A has 3 rectangles having dimensions 5 by 18, 18 by 12, and 18 by 13, and two triangles having legs 12 inches and 5 inches. Net B has 3 rectangles having dimensions 5 by 13, 13 by 12, and 13 by 18, and two triangles having legs 5 inches and 12 inches.

Which is the correct net of the prism and what is the surface area of the prism?

Answer:

the value of x is 115

Step-by-step explanation:

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Answer:

x = 4  &  x = -2

Step-by-step explanation:

For rational functions (functions which themselves are a fraction, with polynomial pieces in the numerator and polynomial pieces in the denominator), these functions have "discontinuities" anywhere the denominator is equal to zero.  Usually, those discontinuities are "vertical asymptotes".  Occasionally, those discontinuities are "holes".

A discontinuity is a "hole," only if both the numerator AND the denominator are zero for that same value of x.  If that value of x doesn't make the numerator zero (it only makes the denominator zero), the discontinuity is just a vertical asymptote.

To find the discontinuities, we'll be making an entirely separate equation.  It's not the function, it's not using algebra to change both sides of the equation/function we started with ... it's pretty much just like scratch work to figure out something that you can use later (although, your teacher may want to see your work on how you found them).

The equation we need for this is the denominator of our rational function set equal to zero:

[tex](x-4)(x+2)=0[/tex]

Note, this equation doesn't have a denominator.  It's not the original function.  It's like scratch work.  This equation is designed as if we want the denominator of our function to be zero, and to find the values of x that will make us divide by zero in the original function.

There are many ways to solve this equation.  The easiest is remembering the zero product property.  The Zero Product property states that if the product of two things is equal to zero, then at least one of the original things had to be zero:  [tex]\text{If }a*b=0,\text{ then }a=0\text{ or }b=0 \text{ (or both)}[/tex]

Noting that our equation is a product of two things, and is equal to zero, the zero product property allows us to separate our equation into two equations:

[tex]x-4=0, \text{ or } x+2=0[/tex]

Solving each equation by isolating x, by adding or subtracting the relevant number from both sides of the equations:

[tex]x=4, \text{ or } x=-2[/tex]

So these values of x will make the denominator of the original function zero.  These are both discontinuities of the function, so while when we were solving for values of x that would make the denominator zero, it was appropriate to say "or", we know that both of these values are discontinuities and now we list them both saying "and":

Discontinuities: [tex]x=4 \text{ and } x=-2[/tex]

But wait!  Are they holes, or are they just vertical asymptotes?  Do we have one of each?

Testing to see if the discontinuities are asymptotes:

To test and see if the discontinuities we've found are holes, we need to substitute them into the numerator of the original function, and see the result.... but just the numerator (we already know they will make the denominator zero, and we can't divide by zero)

Since the numerator is just x, we're checking to see if 4=0, or if -2=0.  They don't.  So, for this function, both of the discontinuities are vertical asymptotes.

Listing the asymptotes

Vertical asymptotes at [tex]x=4 \text{ and } x=-2[/tex]

The median of books to a box is 9 and The mean of books to a box is 11

The complete question is

Garth is packing boxes with books. The list shows how many boxes are in each of 10 boxes. 6,14,6,18,9,9,12,10,11,15

Which statement is true about the number of boxes packed to a box?

A) The median # of books to a box is 8

B) The median # of books to a box is 9

C) The mean # of books to a box is 11

D) The mean # of books to a box is 12

Mean is the average of the data given while the median is the middle point of the data.

It is given that

The data is

6, 14, 6, 18, 9, 9, 12, 10, 11, 15

The mean is

(6 + 14 + 6 + 18 + 9 + 9 + 12 + 10 + 11 + 15)/10 = 11

and the median is 9

Therefore Option B and C is the correct answer.

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Answer:

A

Step-by-step explanation:

Reflection over the x axis means that for points A, B, and C, the sign of the y value would change. Since point A is (1, 1), a reflection over the x axis means that it would become (1, -1). We can do the same for points B and C and therefore the answer is graph A

Answer: D for me at least

Step-by-step explanation: hope this helps :3

Answer: 3

Reason:

Going from x^2 to (x+5)^2 means we shift the graph 5 units to the left.

The +3 at the end shifts the parabola up 3 units. This is because we add 3 to each y value. For instance a point like (0,25) moves to (0,28)

Answer:

Should have ended with "at most -15, not "at least -15."

Step-by-step explanation:

[tex]\leq[/tex] -15 means less than or equal to -15

So it can be -15, but also anything less than -15.  The phrase "at most -15, not "at least -15" says exactly that.

Answer:

-12

Step-by-step explanation:

x = 12-3a

When a=8:

x = 12-3(8)

x = 12 - 24

x = -12

Answer:

x < 9

Step-by-step explanation:

Our original inequality:

[tex]9(4x-8) < 4(6x+9)[/tex]

Firstly, let's expand the brackets on both sides:

[tex]36x - 72 < 24x + 36[/tex]

Now, we add the 72 over to isolate the [tex]x[/tex]:

[tex]36x < 24x + 108[/tex]

Next, we take away the [tex]24x[/tex] to isolate the [tex]x[/tex]:

[tex]12x < 108[/tex]

Finally, we divide both sides by 12 to convert the [tex]12x[/tex] to [tex]x[/tex]:

[tex]x < 9[/tex]

This means our final answer is [tex]x < 9[/tex].

So

[tex]\\ \rm\Rrightarrow r=\sqrt{a^2+b^2}[/tex]

[tex]\\ \rm\Rrightarrow r=\sqrt{(-3)^2+(\sqrt{3})^2}[/tex]

[tex]\\ \rm\Rrightarrow r=\sqrt{9+3}[/tex]

[tex]\\ \rm\Rrightarrow r=\sqrt{12}[/tex]

[tex]\\ \rm\Rrightarrow r=2\sqrt{3}[/tex]

Find theta

[tex]\\ \rm\Rrightarrow \theta=tan^{-1}(\dfrac{y}{x})[/tex]

[tex]\\ \rm\Rrightarrow \theta=tan^{-1}(\dfrac{\sqrt{3}}{3})[/tex]

[tex]\\ \rm\Rrightarrow \theta=tan^{-1}(\dfrac{-1}{\sqrt{3}})[/tex]

[tex]\\ \rm\Rrightarrow \theta=\dfrac{5\pi}{6}[/tex]

Polar form

[tex]\\ \rm\Rrightarrow r(cos\theta+isin\theta)[/tex]

[tex]\\ \rm\Rrightarrow 2\sqrt{3}(cos\dfrac{5\pi}{6}+isin\dfrac{5\pi}{6})[/tex]

[tex](x)(x^{2} +9x+8)[/tex]

GCF is a way to simplify a polynomial by separating out one factor.

GCF

GCF stands for greatest common factor. This means the GCF is the largest number that is a factor of each term.

For example, the GCF of 15 and 25 is 5 because that is the greatest common factor between the 2 numbers.

Finding the GCF

To find the GCF, first look at the coefficients of each term.

These numbers have no shared factors besides 1, which doesn't help because factoring out 1 does nothing.

However, next, we can move on to the variables. You can factor out variables the same way you do constants.

Factoring Out X

The question states that we only need to do GCF to solve. So, we can just factor out x. Remember that factoring is like dividing each term by x.

The completely factored expression is:

Here we have divided each term by x and then added x as a new factor in the expression.

Answer:

X(x+1)(x+8)

Step-by-step explanation:

U just have to find the comment number

Answer:

Step-by-step explanation:

   1) -4 + 3x = 4x - 8

        Add 4 to both sides

      -4 + 3x + 4 = 4x - 8 +  4

               3x     = 4x - 4

Subtract 4x from both sides,

        3x - 4x = -4x + 4x - 4

              -x   = -4

                [tex]\sf \boxed{\bf x = 4}[/tex]

2) -5x - 8 = 2

Add 8 to both sides

 -5x - 8 + 8 = 2 + 8

            -5x  = 10

Divide both sides by (-5)

            [tex]\sf \dfrac{-5}{-5}x =\dfrac{10}{-5}[/tex]

                 [tex]\sf \boxed{\bf x = -2}[/tex]

3) 12r - 14 = 5(2-r)

    12r - 14 = 5*2 - 5*r

     12r - 14 = 10 - 5r

Add 14 to both sides

 12r - 14 + 14 = 10 - 5r + 14

             12r  = 24 - 5r

Add 5r to both sides

        12r + 5r = 24

               17r = 24

Divide both sides by 17

                 r = 24/17

4) 3x - 8 = -(17 + 2x)

  3x - 8 = -17 - 2x

Add 8 to both sides

3x - 8 + 8 = -17 - 2x + 8

           3x = -9 - 2x

Add 2x to both sides

      3x + 2x = -9

            5x  = -9

Divide both sides by 5

              [tex]\sf \dfrac{5}{5}x=\dfrac{-9}{5}\\\\\boxed{x = \dfrac{-9}{5}}[/tex]

Answer:

1) x = 4

2) x = -2

3) [tex]r= \frac{24}{7}[/tex]   [tex](1\frac{7}{17})[/tex]

4) [tex]x=-\frac{9}{5}[/tex]  [tex](-1\frac{4}{5})[/tex]

Step-by-step explanation:

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(work shown in photo :)  )

The graph that accurately shows the velocity of the park or at any time is as shown in the attached image.

Velocity is defined as the rate of change of position of object with respect to time. Velocity is also defined as the speed of an object moving in a definite direction.

Velocity is a vector quantity and so it has both magnitude and direction. Its' SI unit is in meters per second.

The velocity of a particle is modeled by the function;

v(t) = ¹/₁₀(3t - 8)³ + 2

The given velocity function is cubic function and as such the attached graph shows the velocity of the particle at any time.

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The inverse function will be h⁻¹(x) = {(–5, 3), (–7, 5), (–9, 6), (–12, 10), (–16, 12)}. Then the correct option is B.

Suppose that the given function is

f:X → Y

Then the inverse of the considered function will be

f⁻¹: Y → X

The function h(x) is given below.

h(x) = {(3, –5), (5, –7), (6, –9), (10, –12), (12, –16)}

Then the coordinate of the inverse function gets swapped.

h⁻¹(x) = {(–5, 3), (–7, 5), (–9, 6), (–12, 10), (–16, 12)}

Then the correct option is B.

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Answer:

...

Step-by-step explanation:

Answer:

20 counters/box

Step-by-step explanation:

Missing counters(m)= 8

Total number of counters available (t-m)= 132

Required number of counters(t):

=(t-m) + m

= 132 + 8 = 140

Total number of boxes(tB) = 7( 6 full and one with eight missing)

Total Counters/Boxes= t/tB

= 140/7

= 20

Answer:

The answer will be 38° + 32° = 70°

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Answer:

Yellow Brass with a Density of 8.47 g/cm^3

Step-by-step explanation:

That's the answer on the website

Answer:

21/428 or 0.04 906542056074...

Step-by-step explanation:

The total area of the given composite figure is 84.8 ft²

We are given;

Area of Triangle = 5.6 ft²

Thus, area of 2 triangles = 2 * 5.6 = 11.2 ft²

Area of rectangles = 2(3.6 * 2) + 2(2 * 4) + 3(4 * 3.6)

Area of rectangles = 14.4 + 16 + 43.2

Area of rectangles = 73.6 ft²

Total area of composite figure = 73.6 ft² + 11.2 ft²

Total area of composite figure = 84.8 ft²

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The explicit rule for the arithmetic sequence is a(n) = 7n + 8 if the arithmetic series is 15, 22, 29,...

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

We have:

In the first week, only 15 shirts were sold. In the next week, 22 shirts were sold and in the third week, 29 shirts were sold.

15, 22, 29,...

The first term a = 15

The common difference d = 22 - 15 = 7

a(n) = 15 + (n - 1)7

a(n) = 7n + 8

Thus, the explicit rule for the arithmetic sequence is a(n) = 7n + 8 if the arithmetic series is 15, 22, 29,...

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Answer:

Continuous

A continuous random variable has infinitely many values, and those values can be associated with measurements on a continuous scale in such a way that there are no gaps or interruptions.

Answer:

[tex]\sf C) \ x = -1\dfrac{2}{5} , \ y = \ 1\dfrac{3}{5}[/tex]

Given equations:

Make x the subject in equation 1:

Substitute this into equation 2:

2(y - 3) - 7y = -14

2y - 7y = -14 + 6

-5y = -8

  y = -8/-5

  y = 1.6

Then x = y - 3

           = 1.6 - 3

           = -1.4

Solution: (x, y) ⇒ (-1.4, 1.6)

Answer:

A. 1

Step-by-step explanation:

To find the x-intercept, substitute 0 for y and solve for x.

x-intercept(s): (-5,0)

Considering (-5,0) is the only intersection on the x-axis, 1 is your answer.

If you want a visual of this, I recommend you use the Desmos graphing calculator to input your equation. It will show you what the curved line looks like.

2400 - 40x = 600

As she has not studied 600 flashcards still, we subtract unit rate from total.

40x - 600 = 2400

Here 'x' represent per hour. As he rents studio space for 600, subtracting this from total he earns by charging his students gives us the profit.

(600 + 40)x = 2400

Here 'x' represent mass. As masses are same for both. They can be joined.

Answer:

XY = 6

Step-by-step explanation:

using the sine ratio in the right triangle and the exact value

sin30° = [tex]\frac{1}{2}[/tex] , then

sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{XY}{XZ}[/tex] = [tex]\frac{XY}{12}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

2 XY = 12 ( divide both sides by 2 )

XY = 6

The length of the side XY in ΔXYZ is 6 units.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

In reference to the angle of 30° opposite side is XY and the hypotenuse is 12 units.

We know, sin = opposite/hypotenuse.

Therefore, sin30° = XY/12.

1/2 = XY/12.

XY = 12/2.

XY = 6 units.

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Answer:

y = 139

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

110° is an exterior angle of the triangle , then

3x + 2x - 5 = 110

5x - 5 = 110 ( add 5 to both sides )

5x = 115 ( divide both sides by 5 )

x = 23

then

2x - 5 = 2(23) - 5 = 46 - 5 = 41

y and 2x - 5 are a linear pair and sum to 180° , so

y = 180 - 41 = 139

Answer:

I got 139

Someone correct me if I'm wrong.

Step-by-step explanation:

(2x-5) + 3x + 70 = 180

Collect liketerms. Take away 70 from both sides and add 5.

5x=115

x=23

2(23) -5 = 41

180-41 = 139

y = 139

Answer:

cheesefnekeeorknfdndndndn

[tex]x^2+4x-7=x^2+4x+4-11=(x+2)^2-11[/tex]

The measure of arc BEC is 134°. The correct option is the first option 134°

From the question, we are to determine the measure of arc BEC

In the given diagram,

Measure of angle C = 1/2 (measure of arc AB)

Reason: The measure of an inscribed angle is half the measure of the intercepted arc

∴ Measure of angle C = 1/2 (76°)

Measure of angle C = 38°

m∠A + m∠B + m∠C = 180° (Sum of angles in a triangle)

m∠A + 75° + 38° = 180°

m∠A + 113° = 180°

m∠A = 180° - 113°

m∠A = 67°

Measure of arc BEC = 2 × m∠A (Angle at the center is twice the angle at the circumference)

Measure of arc BEC = 2 × 67°

Measure of arc BEC = 134°

Hence, the measure of arc BEC is 134°. The correct option is the first option 134°

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Answer:

In order to make the function continuous, the first and second pairs of lines should have common points.

1. Intersection of the first two lines:

This determines the value of a:

2. Intersection of the second two lines:

This determines the value of b:

See the graph attached