If [tex]\frac{w}{y} = \frac{y}{z} then what is the value of x?[/tex]

Answer:

198 [m²].

Step-by-step explanation:

1) required area can be calculated as four area of the triangle PQT:

A=4*A(ΔPQT);

2) A(ΔPQT)=0.5*PT*QT, then

3) A=4*0.5*PT*QT; ⇔

A=2*PT*QT; ⇒

4) finally,

A=2*11*9=198 [m²].

The area of the rhombus PQRS is 198 m².

A rhombus is a quadrilateral with four vertices, four sides and four angles with all four sides are equal. It has basically a diamond shape. Rhombus will become square if all the angles of the rhombus equals 90°.

Given that, PT = 11 m and QT = 9 m.

We know that diagonals of a rhombus are perpendicular bisectors.

Therefore, RT = 11 m and ST = 9 m.

Area of a rhombus can be found using diagonals as,

Area = [tex]\frac{1}{2}[/tex] × D₁ × D₂

where D₁ and D₂ are the length of two diagonals of the rhombus.

D₁ = PT + RT = 11 + 11 = 22 m

D₂ = QT + ST = 9 + 9 = 18 m

Area = [tex]\frac{1}{2}[/tex] × 22 × 18

        = 22 × 9

        = 198 m²

Hence the area of the rhombus given is 198 m².

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The second option is the correct answer

[tex]16x^{4}+40x^{3} -24x^{2}[/tex]

The expression given to us is:

[tex]8x^{2} (5x+2x^{2}-3 )[/tex]

Herein, we can simplify it by opening up the bracket and multiplying each term inside the bracket by the term which is outside the bracket.

Thus, we get:

[tex]8x^{2} (5x+2x^{2}-3 )=8*5x^{2+1} +8*2x^{2+2}-8*3x^{2}[/tex]

[tex]40x^{3} +16x^{4}-24x^{2}[/tex]

Rearranging the above expression in descending order of power we get:

[tex]16x^{4}+40x^{3} -24x^{2}[/tex]

From the given options we can see this is the second option. Hence the second option is the correct answer.

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Part 1

Each floor is [tex](28)(56)=1568[/tex] square feet. Since there are 2 floors, the total square footage is [tex]2(1568)=3136[/tex] square feet.

Part 2

[tex](3136)(93)=\$291648[/tex]

142,506 different five-member committees can be made.

If we have a set of N elements, the number of different subsets of K elements that we can make out of these N elements is:

[tex]C(N, K) = \frac{N!}{K!*(N - K)!}[/tex]

In this particular case, the set has 30 elements which are the students. And the committee has 5 members, so K = 5 and N = 30, then we get:

[tex]C(30, 5) = \frac{30!}{(30 - 4)!*5!} = \frac{30*29*28*27*26}{5*4*3*2*1} = 142,506[/tex]

This means that 142,506 different five-member committees can be made.

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Option B. The correct answer to this question is that The mixture has less than the intended volume and has more than the intended percent of butterfat.

From the graph that we have here, the point L is under the blue line of the graph.

x + y = 500

From here we have

0.18x + 0.04y = 500(0.12)

Continuing on trhe graph the solution is given as x = 285.7 and y = 214.3

From the explanation here we can conclude that option B is correct.

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Answer:

The mixture has the intended volume and has more than the intended percent of butterfat.

Step-by-step explanation:

Answer: A

Step-by-step explanation:

This is a fact.

The absolute value parent or modulus function is f ( x ) = | x |

Regardless of the sign, a modulus function returns the magnitude of a number. The absolute value function is another name for it.

It always gives a non-negative value of any number or variable. Modulus function is denoted as y = |x| or f(x) = |x|, where f: R → (0,∞) and x ∈ R.

The value of the modulus function is always non-negative. If f(x) is a modulus function , then we have:

If x is positive, then f(x) = x

If x = 0, then f(x) = 0

If x < 0, then f(x) = -x

Given data ,

Let the function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = | x |

The absolute value parent function is f(x) = |x|, which represents the absolute value of x.

Option B, f(x) = 13x1, does not represent the absolute value function, as it has a coefficient of 13, which scales the function vertically.

Option C, f(x) = x-− 1|, represents a translation of the absolute value function. The "-1" shifts the function one unit to the right, and the vertical bar denotes the absolute value of the expression within the bar. While it is related to the absolute value function, it is not the parent function itself.

Option D, f(x) = x+2, represents a linear function with a slope of 1, which is not the absolute value function.

Hence , the absolute value parent function is f ( x ) = | x |

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Answer:

x = 0 or x = 1

Step-by-step explanation:

f(x) = |x| - 4

g(x) = x³ - 4

f(x) = g(x)

|x| - 4 = x³ - 4

Add 4 to both sides.

|x| = x³

x = x³  or  -x = x³

x³ - x = 0   or   x³ + x = 0

x(x² - 1) =   or  x(x² + 1) = 0

x = 0 or x + 1 = 0 or x - 1 = 0

x = 0 or x = -1 or x = 1

x = -1 does not work, so we discard that solution.

Answer: x = 0 or x = 1

Answer:

values of x: x = 1 and x = 0

Step-by-step explanation:

Given:

Want: x - values when f(x) = g(x)

|x| - 4 = x³ - 4, the 4 cancel out on both sides

|x| = x³

|x| - x³ = x³ - x³

|x| - x³ = 0, x ≥ 0

-x - x³ = 0, x < 0

x = 0

x = -1, x ≥ 0

x = 1

x = 0, x < 0

The intersections are x = 0 and x = 1 and no solution

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Answer:

it's ax+b form answer is Q(x-2)=4x-6

Step-by-step explanation:

ax+b=Q(x),Q(x-2)=a(x-2)+2

Q(3x)=a(3x)+b=12x+2, 3a=12 =>a=4,b=2

the original q of x is 4x+2

Q of x-2 =4(x-2)+2=4x-8+2=4x-6

There are 120 different ways the people can line up

The number of people that arrived is:

n = 5

Take the factorial to calculate the number of ways they can line up

n! = 5!

Expand

n! = 5* 4 * 3 * 2 * 1

Evaluate

n! = 120

Hence, there are 120 different ways the people can line up

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Answer:

g(f(-2)) = -15

Step-by-step explanation:

• f(x) = x³

Then

f(-2) = (-2)³ = -8

• When x = -2 → g(f(x)) = g(f(-2)) = g(-8)

Since -8 ≤ 0 then g(-8) = 2×(-8) + 1 = -16 + 1 = -15

Conclusion:

g(f(-2)) = -15

Answer:

Vertical shift up 2, horizontal shift left 2 reflection over x-axis then reflection over the y-axis.

Step-by-step explanation:

One can Identify the differences between the rise in prices due to inflation and the rise in prices in microeconomic markets by?

The difference that exist between a rise in price due to the inflation and a rise in price due to microeconomic markets is based on the price changes that has occurred in terms of demand and supply model.

Note that this is said to be the price in a given market but the price rise as a result of to inflation tells that the price rise is one that reaches a lot of markets and not only just one market.

Hence, One can Identify the differences between the rise in prices due to inflation and the rise in prices in microeconomic markets by?

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The expression 3/16 of 200 expression as a percentage is; 6.25%.

The value of the expression given in the task content can be evaluated as follows;

3/16 × 200 = 12.5

Hence, the value 12.5 expressed as a percentage of 200 is;

(12.5/200) × 100%.

= 6.25%.

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Rhe polynomial is P(x) = x³ -2x² + 9x - 18 if the zeros are 2 and 3i and a lead coefficient of 1

What is polynomial?

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

We have:

The zeros of a polynomial are 2 and 3i and a lead coefficient of 1.

As we know, zeros of a polynomial are occurs in pairs

So the zeros are 2,3i,-3i

The factor form of a polynomial:

P(x) = (x- 2)(x - 3i)(x + 3i)

[tex]\rm P(x) =\left(x-2\right)\left(x^2+\left(-3\right)^2\right)[/tex]

[tex]\rm P(x) =\left(x-2\right)\left(x^2+9\right)[/tex]

[tex]\rm P(x) =x^3+9x-2x^2-18[/tex]

Thus, the polynomial is P(x) = x³ -2x² + 9x - 18 if the zeros are 2 and 3i and a lead coefficient of 1

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Triangle RST was transformed by using the rule (x,y) → (-x,-y) and the transformation is described by the transformation of 180° rotation about the origin.

Transform the shapes on a coordinate plane by rotating, reflecting, or translating them. Here we have transformed the triangle using the rotation method.

Rotation is the geometric transformation that revolves each point in a shape a predetermined number of degrees around that point. When the number of degrees is positive, the shape spins counterclockwise; when the number of degrees is negative, it rotates clockwise. The following is a broad description of how rotation about the origin can be transformed.

Here the points change to R'(-1,-1) , S'(-3,-1) and T'(-1,-6).

A 180° rotation about the origin will be the transformation.

The triangles RST and R'S'T' are first plotted on a graph. The graph is provided for your reference below.

The original triangle RST, which was in quadrant 1, has changed to triangle R'S'T', which is in quadrant 3, as shown in the graph. The rotation around the origin is 180° from quadrant 1 to quadrant 3.

Your question was incomplete. Please check below for full content.

Triangle RST was transformed using the rule (x, y) → (–x, –y). The vertices of the triangles are shown.

R (1, 1)

S (3, 1)

T (1, 6) R' (–1, –1)

S' (–3, –1)

T' (–1, –6)

Which describes the transformation?

The transformation was a 90° rotation about origin.

The transformation was a 180° rotation about origin.

The transformation was a 270° rotation about origin.

The transformation was a 360° rotation about origin.

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Using the trigonometric ratios, the measures are:

a. z = 222.5 ft

b. h = 38.6 ft.

c. b = 10.4 ft

d. B = 219.1 ft.

The ratios of trigonometry that can be used to solve a right triangle are:

sin ∅ = opp/hyp

cos ∅ = adj/hyp

tan ∅ = opp/adj.

a. Find h using the sin ∅ = opp/hyp:

sin 75 = opp/hyp = h/40

h = (sin 75)(40) = 38.6

Find z using the sin ∅ = opp/hyp

sin 10 = opp/hyp = 38.6/z

z = 38.6/sin 10

z = 222.5 ft. (length of the zip line)

b. Height of the tree = h = 38.6 ft.

c. Using sin ∅ = opp/hyp, find b (distance between the base of the ladder and the base of the tree):

sin 15 = b/40

b = (sin 15)(40)

b = 10.4 ft

d. Using sin ∅ = opp/hyp, find B as shown in the image:

sin 80 = opp/hyp = B/222.5

B = (sin 80)(222.5)

B = 219.1 ft.

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The volume of the octagonal pyramid is 1302 cubic m if the length of the apothem is 7 m.

The pyramid has an octagonal base with 8 isosceles triangular faces, known as an octagonal base pyramid.

The length of the apothem = 7 m

Side length = 9 m

The area of the one triangle = (1/2)×7×9 = 63/2 square m

The area of the octagonal base = 8(63/2) = 252 square m

The volume of the pyramid = (1/3)(base area)(height)

The volume of the pyramid = (1/3)(252)(15.5)

= 1302 cuibc m

Thus, the volume of the octagonal pyramid is 1302 cubic m if the length of the apothem is 7 m.

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Answer:

You need to know what 3 u - 9 is equal to, in order to solve the equation for the variable u. Please post the entire equation. As this stands, it is just an algebraic expression and cannot be "solved".

Step-by-step explanation:

The equation of a parabola that has intercepts of x=-2 and x=6 and passes through point (8,6) is f(x) = 3/10(x+2)(x-6)

The standard equation of a parabola is in the form f(x) = (x-a)(x-b)

where a and b are the intercepts of the graph. Given the parabola that has intercepts of x=-2 and x=6, the resulting equation will be:

f(x) = a(x-(-2))(x-6)

f(x) = a(x+2)(x-6)

If the parabola passes through (8, 6), then;

6 = a(8+2)(8-6)

6 = a(20)

a = 6/20

a = 3/10

Substitute

f(x) = 3/10(x+2)(x-6)

Hence the equation of a parabola that has intercepts of x=-2 and x=6 and passes through point (8,6) is f(x) = 3/10(x+2)(x-6)

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Answer:

$30.60

Step-by-step explanation:

So when a problem says some price is x% off, it means the current price is now (100-x)% of the original value. So if the shirt is 15% off, the current price is 85% the original value. To find 85% of a number you simple convert the percentage into a decimal, by dividing it by 100 and multiply that decimal by the value. So in this case 85/100 = 0.85. And then 0.85 * 45 = 38.25. Now that it reduces its price by 20%, it's 80% the original value. 38.25 * 0.8 = 30.60.

The slope of the given line according to the table is -8

The slope of a function is also defined as the rate of change of the function.

Using the coordinate points (-3, 8) and (-2, 0) from the table

Slope = 0-8/-2-(-3)

Slope = -8/-2+3
Slope = -8/1

Slope = -8

Hence the slope of the given line according to the table is -8

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Answer:

[tex]q^2+7q+2[/tex]

Step-by-step explanation:

Check the attachment I added, hope it helps!

The new graphs would make it more difficult to estimate the price of a book.

To do this, we simply combine the frequencies on Felix and Tyler's table.

When this is done, we have the following dataset

3,3,3,3,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7, 8,8,8,8,9,9,9,9,9,9,9,9,9,11,11,13,13,13,13,15,15,15,16,16,18,18,18,18,18,19,19,19,19,19,19,29,32,32,36,36,36,38,38,64,64,66,66,66,68,68,69,75,75,76,76,76,76,76,78,78,79,82,82,86,86,86,89,96,96,97,97,99

Next, we create the box & whisker plot and the histogram using the new dataset

(see attachment for the graphs)

The new graphs would make it more difficult to estimate the price of a book.

This is so because the dataset used to create the graphs do not come from the same source

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Answer:

simple interest

Step-by-step explanation:

this is because r is interest rate, p is principal, and t is time

Answer:

simple interest

Step-by-step explanation:

Simple interest rate is defined as: I = p * r * t. So you're taking the principle amount (initial amount loaned) and multiply it by the interest rate. This gives you the interest rate in a year (usually, depends on time unit of t). Generally speaking, it gives you the interest over a specific amount of time. Now multiply it by the amount of time that's passed. So you're just calculating the total amount of interest. So the I stands for the simple interest.

Answer:

Third option(double circle)

Step-by-step explanation:

Isometry (iso meaning same and metry meaning measure)

preserves the length and overall mass/size of a shape during a transformation. The 3rd option is the only shape that changes size in the examples, making it a non isometric transformation.

Answer:

20percent

Step-by-step explanation:

First we will find the value of k.

Given

White + Black + Blue + Red = Total

8k+30+(30-2k)+k+5 = 100

8k+30+30-2k+k+5=100

7k+65=100

7k+65-65=100-65

7k=35

k = 35/7 = 5

Now given number of blue cell phone sold is 30-2k = 30 - 2(5) = 30 - 10 = 20,

Percentage of Blue cell phones = [tex]\frac{Blue}{Total} *100\\=\frac{20}{100} *100\\=20%[/tex]percent

Answer:

-x-2<y<-x-10

Step-by-step explanation: