Find the value of z.

Answer:

[tex]180\ in.^2[/tex]

Step-by-step explanation:

The area of a rectangle can is defined as [tex]A = wl[/tex] where w is the width and l is the length. The width in this case is 12 and the length is 15. Also it doesn't really matter what order you put it in. This gives you an area of [tex](15\ in.) (12\ in.) = 180\ in.^2[/tex]

Answer:

Find total surface area. Multiply material unit cost by the total surface area.

Step-by-step explanation:

To find the cost of a container, you must first find the total surface area of the container. Then since you are given the unit cost for the material, you multiply the total surface are by the unit cost ($0.0015/in.²).

The diagonal matrix that has these values would be:

16 0 0 0 0

0 -8.7 0 0 0

0 0 5.4 0 0

0 0 0 1.3 0

0 0 0 0 -6.9

This is the type of matrix that is written in the form where all of the entries that are outside the diagonal are zeros.

The diagonal is a line that divides a triangle into two halves. The diagonal here has all of the digits. Outside it are all zero elements.

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Answer:

C is the correct answer

Explanation:

Hope you have a great day!

Answer:

OB. (2, 4), (3, 9), (4, 16), (5, 25)

Step-by-step explanation:

none of the points in this ordered pair have the same x-pos. In all the other options, at least 2 of the points have the same x-pos, preventing them from being functions. Therefore, OB is the only right answer.

Answer:

It would take 1.5 hours for all three to finish the work if they worked together.

Step-by-step explanation:

Elon and Jeff can complete the work in 3 hours.

Jeff and Bruce can complete the work in 6 hours.

Elon and Bruce can complete the work in 4 hours.

3 + 6 + 4 = 13

13 / 3 = 4.33

4.33 / 3 = 1.44

The area of square LMNP is 50

A circle is the locus of points equidistant from a fixed point which is known as the center of the circle.

A circle is defined if the center and the radius is known.

Analysis:

Perimeter of a circle = 2πr

Given perimeter = 10π

2πr = 10π

2r = 10

r = 10/2 = 5

r = MO

so the diagonal of the square is actually the diameter of the circle = 5+5 = 10

To find the side, x of the square the diagonal and the sides form a right-angled triangle, by  Pythagoras, [tex]10^{2}[/tex] = [tex]x^{2}[/tex] + [tex]x^{2}[/tex]

2[tex]x^{2}[/tex] = 100

[tex]x^{2}[/tex] = 100/2 = 50

Also area of square is [tex]x^{2}[/tex] = 50

In conclusion, the area of square LMNP is 50

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A perpendicular line to PQ must have a slope equal to 1/3, then the correct options are B and C.

Two lines are perpendicular if the slope of one is equal to the opposite of the inverse of the other line's slope.

We know that PQ passes through (-8, 7) and (-4, 5), then the slope of PQ is:

[tex]s = \frac{-5 - 7}{-4 - (-8)} = -3[/tex]

A perpendicular line to PQ must have a slope equal to:

[tex]s' = -(\frac{1}{-3} ) = (\frac{1}{3})[/tex]

So we have two correct options (two lines with that slope) which are options B and C.

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Answer:

A, B and D

Step-by-step explanation:

Answer:

Answer B , D , E

Step-by-step explanation:

The simplified expression for the following expression are:

7a + 3a - 2a + 5a

= 15a - 2a

= 13a

0.7 - 0.3g - 0.02g + 5

= 5.7 - 0.32g

5g² + 3g - 4g + 5g²

= 10g² - g

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The solution to the division of the given polynomial expression is:

k = (x+3)(x-4)

The division of the given polynomial can be determined by using the rational root theorem which is a method that is popularly used in determining the solutions to a polynomial equation.

From the information given:

[tex]\mathbf{\dfrac{x^3 -3x^2 - 10x +24}{x-2}}[/tex]

Using the rational root theorem;

[tex]\mathbf{\dfrac{(x-2) \dfrac{x^3 -3x^2 - 10x +24}{x-2} }{x-2}}[/tex]

[tex]\mathbf{\dfrac{(x-2)(x^2 -x-12)}{x-2} }}[/tex]

Factor: x² - x - 12

[tex]\mathbf{\dfrac{(x-2)(x+3)(x-4)}{x-2} }}[/tex]

Cancel out the common factor (x-2)

[tex]\mathbf{=(x+3)(x-4) }}[/tex]

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An interval to estimate the true average tip is  (14.62,13.78).

According to statement is

we know that the

confidence interval = sample mean ± standard deviation /(n)^1/2

substitute the values in it then

confidence interval = 14.2  ± 2.5/(35)^1/2

confidence interval = 14.2 ± 2.5/5.91

confidence interval = 14.2 ± 0.42

confidence interval = 14.2 + 0.42 , confidence interval = 14.2 - 0.42

confidence interval = (14.62,13.78)

So, an interval to estimate the true average tip is  (14.62,13.78).

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Similarity transformations involve two types of transformations required to map a  given object onto a similar object without a change in its dimensions. Thus the answers required are:

a. Similarity transformations - translation and dilation.

b. The first transformation is translation.

c. The second transformation is dilation.

Transformation is a process required to change the size or orientation of a given shape to form an image. The types are reflection, translation, rotation, and dilation.

i. Reflection is a type of rigid transformation in which a given shape is flipped about a given point or line.

ii. Translation involves moving a given shape in a certain direction without a change in its initial orientation.

iii. Rotation is a type of rigid transformation where a shape is turned about a given point or line at a required angle.

iv. Dilation is a process that requires either increasing or decreasing the dimension of a given shape.

Also, similarity transformations involve two types of transformations required to map a  given object onto a similar object without a change in its dimensions.

The appropriate answers to the given question are:

a. similarity transformations - translation and dilation

b. The first transformation is translation.

c. The second transformation is dilation.

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Call the hidden variable here "x"

3x = 30 + x
3x - (30 + x) = 0
3x - 30 - x = 0
2x - 30 = 0
x = 30 : 2 = 15

Recheck : 3 x 15 = 30 + 15 -> 45 = 45 (true)

Answer:

x=5[tex]\sqrt{2\\[/tex]

Step-by-step explanation:

Answer:

5 sqrt 2

Step-by-step explanation:

Log 2x + log x = 2

log ( 2x * x ) = 2

log (2x^2) = 2

2x^2 = 100

x^2 = 50

x = sqrt (50) =  5 sqrt 2

The correct options are:

a) g(x) = 8*x - 6

b) g(x) = 2x - 10

c) g(x) = 2x - 14

d) g(x) = 8x - 24

Here we have the function:

f(x) = 2x - 6

The proposed transformations are:

a) Stretch by a factor of 4 along the x-axis.

A horizontal stretch of scale factor k is written as:

g(x) = f(x*k).

Then, in this case, we have:

g(x) = 2(x*4) - 6 = 8*x - 6

b) Shift f(x) 4 units down.

A vertical shift of N units is written as:

g(x) = f(x) + N

A shift of 4 units down is written as:

g(x) = f(x) - 4 = 2x - 6 - 4 = 2x - 10

c) Shift f(x) 4 units right.

An horizontal shift of N units is written as:

g(x) = f(x + N).

For a shift of 4 units to the right, we write:

g(x) = f(x - 4) = 2(x - 4) - 6 = 2x - 8 - 6 = 2x - 14

d) A vertical compression of scale factor 1/4.

A vertical compression of scale factor K is written as:

g(x) = f(x)/K

In this case, we will have:

g(x) = f(x)/(1/4) = 4*f(x) = 4*(2x - 6) = 8x - 24

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Answer:

[tex]x = \frac{-1 \pm \sqrt{33}}{4}[/tex]

Step-by-step explanation:

Hello!

We can solve the quadratic by using the Quadratic Formula.

Standard form of a Quadratic: [tex]ax^2 + bx +c = 0[/tex]

Quadratic Formula: [tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

Given our equation: [tex]2x^2 + x - 4 = 0[/tex]

Plug in the values into the quadratic formula to solve.

The solution to the quadratic is [tex]x = \frac{-1 \pm \sqrt{33}}{4}[/tex].

Answer: 130

Step-by-step explanation:

Let the measure of arc DB be x.

Then,

[tex]80=\frac{x+30}{2}\\\\160=x+30\\\\x=130[/tex]

Step-by-step explanation:

L = 10W

L + W = 132/2 = 66

---

10W + W = 66

W = 6

L = 60

[tex] \sf{\red{Answer}} [/tex]

[tex] \sf{\purple{Step \: \: By \: \: Step \: \: Explanation}} [/tex]

Perimeter = 2(L + W)

132 = 2(L + L/10)

132 = 2(10L/10 + L/10)

132 = 2(11L/10)

132 : 2 = 11L : 10

66 = 11L : 10

66 : 11 = L : 10

6 = L : 10

The height of the smallest tank if the larger is 300cm tall will be 240cm.

Similar figures are those figures which are identical in shape, but not necessarily in size.

Two squares with sides of 10 and 5 are similar because their shape is exact but the size is different.

We can utilize scale factors because the tanks have comparable shapes.

The scale factor for volume will be given as,

The volume of small tank/volume of big tank = 512000/1000000 = 0.512

Since volume, if the cube so,

Scale factor = [tex](0.512)^{1/3}[/tex] = 0.8

With this scale factor the height of the smaller tank = 300 x 0.8 = 240cm

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The coordinates of the image after a reflection over the x-axis are A(-2,3) ,B(0,3), and (-1,1).

Given The coordinates of the triangle ABC are A(-2,3) B (0,3) and C(-1,-1).

We know that the coordinates of x axis used to be positive in first and fourth quadrant. The coordinates of y axis used to be positive in second and first quadrant. The coordinates of x axis are to be negative in second and third quadrant. The coordinates of y-axis used to be negative in third and fourth quadrant.

We have to reflect the triangle over x-axis so the values of y-axis needs to be positive. So we need to just convert the coordinates of y to positive numbers which will make the coordinates as under:

A (-2,3) will not change because it is already positive.

B(0,3) will not change as it is is also positive.

C(-1,-1) will change to (-1,1)

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Answer: a (-2,-3) b (0,-3) c (-1,1)

Step-by-step explanation: how is the other person verified if there wrong.

Answer:

When the volume of a gas in a container varies inversely with the pressure on the gas and a container of nitrogen has a volume of 29.5 litres with 2000 psi. So, if the tank has a 14.7 psi pressure, then the volume of the tank would be 4013.6 litres.

Step-by-step explanation:

Step 1 of 2

Write the inversely proportionality relation between the volume and pressure of a gas in container.

[tex]$v \propto \frac{1}{p}$[/tex]

Where volume is represented by v and pressure is represented by p.

Remove the proportionality and place a constant say k.

[tex]$v=\frac{k}{p}$[/tex]

Substitute the given values of nitrogen that v=29.5 and

p=2000 and calculate the value of k from above equation.

[tex]$$\begin{aligned}&29.5=\frac{k}{2000} \\&\Rightarrow k=29.5 \times 2000 \\&\Rightarrow k=59000\end{aligned}$$[/tex]

Step 2 of 2

Substitute the value p=14.7 and above calculated k value in the equation

[tex]$$\begin{aligned}&v=\frac{k}{p} . \\&v=\frac{59000}{14.7} \\&\Rightarrow v=4013.6\end{aligned}$$[/tex]

Answer:

Step-by-step explanation:

Solution

Start with the product

The product is 7*x where x is a number but not specified.

Now add 6

Answer: 7x + 6      

This cannot be simplified any more than what it is now.

Represent the following sentences as an algebraic expression:

Assuming:

6 is added to the product of 7 and a number.

Product : 7 × x = 7x

Now we will add 6.

Add : 7x + 6.

Final Answer:

7x + 6.

[tex] \star\tiny\pmb{spbankingandsscseries} \small\star [/tex]

The value of x which is the missing angle of the triangles is; x = 30°

We know that Alternate angle theorem states that when two parallel lines are cut by a transversal, then the resulting alternate interior angles or alternate exterior angles are congruent.

Thus, if we label the vertex with the unknown angle in the smaller triangle as A, then by the alternate angle theorem, we can say that;

∠A = 2x

Thus, from sum of angles in a triangle equals to 180°, we can say that;

x + 2x + 90 = 180

3x + 90 = 180

3x = 180 - 90

3x = 90

x = 90/3

x = 30°

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Answer:

Step-by-step explanation:

You did not post any question and I just retrieved all possible information from whatever is given.

The measure of angle ABD (m∠ABD) is 104°

From the question, we are to determine the measure of angle ABD

In the diagram,

∠ABC = ∠ABD + ∠DBC

Thus,

m∠ABC = m∠ABD + m∠DBC

From the given information,

m∠ABC = 140°

m∠DBC = 36°

∴ 140° =  m∠ABD + 36°

m∠ABD = 140° - 36°

m∠ABD = 104°

Hence, the measure of angle ABD (m∠ABD) is 104°

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The length of one leg of the right triangle is h = 12√2 inches

The length of a right triangle can be found as follows;

sin 45 = opposite / hypotenuse

Therefore,

hypotenuse = 24 inches

Hence,

sin 45 = h / 24

h = 24 sin 45

h = 24 × 1 / √2

Therefore,

h = 24 / √2 × √2 / √2

h = 24√2 / 2

h = 12√2 inches

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Answer: B. 12√2 inches

Step-by-step explanation: TRUST ME!!! Answer correct on Edge!!! :)

Answer:

(0,-2)

Step-by-step explanation:

the answer is (0,-2) because -2 is where the line crosses over the y-axis. If we looked at a graph you would see that the line goes over 0 on the X-axis, which causes the line to touch the y-axis and intercept it at the -2 mark.

An easy way to find the answer for these sorts of questions is to draw out a graph and mark the coordinates on it and draw the line conecting them. Once you've done that you can easily see where the line intercepts on both the y and x axis.

Answer:

(0,-2)

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The solution of the equation is x=±i or x=±i√2.

Given that the equation is x⁴+3x²+2=0 and use u substitution method to solve.

We can rewrite our given equation as:

(x²)²+3x²+2=0

Let's assume that the (x²)=u.

The given equation is rewritten as u²+3u+2=0.

Factorize the quadratic equation by adding or subtracting two number that gives the sum of 3u and product 2u² as

u²+2u+u+2=0

u(u+2)+1(u+2)=0

Taking out (u+2) as common and get

(u+2)(u+1)=0

Compare each equation with 0 and get

u+2=0 or u+1=0

u=-2 or u=-1

Performing back substitution by substituting the values of u in x²

when u=-1 then x is

x²=-1

x=±√(-1)

As we know that √(-1)=i.

So, we get

x=±i

And when u=-2 then x is

x²=-2

x=±√(-2)

As we know that √(-1)=i.

So, substituting this, we get

x=±i√2

Hence, the solutions of the x⁴+3x²+2=0 is x=±i and x=±i√2.

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Step-by-step explanation:

So you can check for extraneous solutions by plugging in the 5 and -2 as x.

Plug 5 in as x

[tex]5=\sqrt{3(5)+10}\\5=\sqrt{15+10}\\5=\sqrt{25}\\5=5[/tex]

I'm not sure if this is exactly considered an extraneous solution, but I'm assuming it is, since technically the radical doesn't have a plus/minus in front of it, so it's the principle square root which means it only outputs the positive values. This would mean that the -2 wouldn't be a solution, since the principle square root doesn't output negative values, so it's a function, since if it outputted 2 values, then it wouldn't be a function by definition.

Answer:

  about 1.56637 radians ≈ 89.746°

Step-by-step explanation:

The reference angle in radians can be found by the formula ...

  ref angle = min(mod(θ, π), π -mod(θ, π))

Equivalently, it is ...

  ref angle = min(ceiling(θ/π) -θ/π, θ/π -floor(θ/π))×π

When we divide 11 radians by π, the result is about 3.501409. The fractional part of this quotient is more than 1/2, so the reference angle will be ...

  ref angle = (1 -0.501409)π radians ≈ 1.56637 radians ≈ 89.746°

__

Additional comment

For calculations such as this, you need to use the most accurate value of pi available. The approximations 22/7 or 3.14 are not sufficiently accurate to give good results.