Find GH in each trapezoid.

The solution to the system of equations is: x = -4, y = -15.

Given the equations of a system as:

y = 3/4x - 12 --> eqn. 1

y = -4x - 31 --> eqn. 2

Substitute y = (-4x - 31) into eqn. 1 to find x:

-4x - 31 = 3/4x - 12

-4x - 3/4x = 31 - 12

-19/4x = 19

Multiply both sides by -4/19

x = 19(-4/19)

x = -4

Substitute x = -4 into eqn. 2

y = -4(-4) - 31

y = 16 - 31

y = -15

The solution is: x = -4, y = -15.

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The solutions to the given quadratic equation are x = -6 and x = -2

From the question, we are to solve the given quadratic equation

The given equation is

y = x² + 8x + 12

To solve the equation, we will set it equal to 0

That is,

x² + 8x + 12 = 0

Solving

x² + 8x + 12 = 0

x² + 2x + 6x + 12 = 0

x(x +2) +6(x + 2) = 0

(x +6)(x + 2) = 0

x +6 = 0 OR x +2 = 0

x = -6 OR x = -2

Hence, the solutions to the given quadratic equation are x = -6 and x = -2

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Doubling the lengths of the sides of a rectangle quadruple the area

Let the dimension of the rectangle be L and W.

So, the area is

A = LW

When the lengths are doubled, we have:

A2 = 2L * 2W

This gives

A2 = 4LW

This means that the initial area is multiplied by 4

Hence, doubling the lengths of the sides of a rectangle quadruple the area

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The lowest carrier frequency at which each modulated wave S(t) component may be uniquely defined by m(t) is

Fc,Fc+w,Fc-w =>1.5k,2.5k,0.5kHz

-Fc,-Fc+w,-Fc-w =>-1.5k,-0.5k,-2.5kHz

"-w,w -1kHz,1kHz" are the frequency components of the detector output in this case.

Fc,Fc+w,fc-w =>0.75k,1.75k,-0.25kHz

-Fc,-Fc+w,-Fc-w =>-0.75k,0.25k,-1.75kHz

This is further explained below.

For a modulated wave with frequency components, the equation looks like this:

Fc,Fc+w,Fc-w =>1.5k,2.5k,0.5kHz

-Fc,-Fc+w,-Fc-w =>-1.5k,-0.5k,-2.5kHz

"-w,w -1kHz,1kHz" are the frequency components of the detector output in this case.

b)

In conclusion, we may state that the modulated wave has frequency components as well.

Fc,Fc+w,fc-w =>0.75k,1.75k,-0.25kHz

-Fc,-Fc+w,-Fc-w =>-0.75k,0.25k,-1.75kHz

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Answer: Option (1)

Step-by-step explanation:

[tex]3x^3 - 6x^2 + 30x-20=-20\\\\3x^3 - 6x^2 + 30x=0\\\\3x(x^2 - 2x+10)=0\\\\[/tex]

So, either [tex]x=0[/tex] or [tex]x^2 -2x +10=0[/tex]

For the second case, we know x=0.

For the second case, we can use the quadratic formula.

[tex]x=\frac{2 \pm \sqrt{(-2)^2 - 4(1)(10)}}{2}\\\\x=1 \pm 3i[/tex]

Angle L: 70°

The trigonometric ratio used to solve for NM is the tangent ratio.

NM = 57.7 [nearest tenth]

Using the triangle sum theorem, find angle L.

Angle L = 180 - 90 - 20 = 70°

Using the tangent ratio, we can use  ∠M and LN to solve for NM

Tan 20 = 21/NM [tan ∅ = opposite/adjacent]

NM = 21/tan 20

NM = 57.7 [nearest tenth]

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Answer:

70, tangent, 57.7

Step-by-step explanation:

Answer:

m∠B > m∠C > m∠A

Step-by-step explanation:

The angle opposite the largest side in a triangle is the largest, and the angle opposite the shortest side is the smallest.

Option C. The statement that describes the graph of the equation y + 2 ≥ –4(x – 3)2 is a a parabola opening down, with shading above the vertex.

To do this you have to create a graph of the equation as seen in the attachment.

From the attachment we can see that the parabola is shaped downwards while we have the shading to be at the top of the vertex.

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The equation of a line parallel to the given line and passing through the point (0, 8) is 5y - 3x = 40

The equation of a line in point-slope form is expressed as;

y - y0 = m(x -x0)

where

m is the slope

(x0, y0) is the point on the line

Given the following parameters

Point (0,8)

Slope from the equation = 3/5

Substitute

y - 8 = 3/5(x - 0)
5(y -8) =3x

5y - 40 = 3x

5y - 3x = 40

Hence the equation of a line parallel to the given line and passing through the point (0, 8) is 5y - 3x = 40

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Answer:

f(x + 3) = 2(x + 7)

Step-by-step explanation:

Now lets find out what does f(x + 3) means.

f(x + 3) means shifting the entire function 3 units to the left. Which also means, all x values will be shifted to the left by that number of units. (Excluding the constant that is multiplied or divided by x, eg. 5x + 6 shifted by 7 units to the left is 5(x + 7) + 6 and not 5x + 7 + 6.)

From the above,

f(x + 3) = 4(x + 3) + 2 = 4x + 12 + 2 = 4x + 14 = 2(x + 7)

Answer:

(4,-5)

Step-by-step explanation:

Considering that the graphs have two intersection points, the two lines are equal.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In a graph, the solution of two linear equations is the intersection of the two lines. Hence, if there are two solutions, as is the case in this problem, the two lines are equal.

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Answer:

Step-by-step explanation:

Purchase price (A) : $12,500

Down Payment (B): $3,000

Loan Taken (C = A - B):  $9500

D :  Interest calculation for $9,500 for 3 years P(1 + rt)

= 9500(1 + (14.5/100) * 3)

= 9500(1 + 0.145 * 3)

= 9500 * 1.435

= $13632.5

E : Interest calculation for $9,500 for 2 years P(1 + rt)

= 9500(1 + (14.5/100) * 2)

= 9500(1 + 0.145 * 2)

= 9500 * 1.29

= $12,255

Difference between D - E

= $13632.5 - $12,255

= $1377.5

Hence the answer is B i.e. $1377.5 less interest for same amount of load for 2 years vs 3 years

Answer:

Step-by-step explanation:

1 Answer

1=12.

4=22.

9=32.

16=42.

25=52.

36=62.

49=72.

64=82 .

The number of ways when the choice is not relevant is 1716

The number of letters are:

Letter, n = 13

The letter to choose are:

r = 6

Relevant choice

When the choice is relevant, we have:

[tex]Ways = ^nP_r[/tex]

This gives

[tex]Ways = ^{13}P_6[/tex]

Evaluate

Ways = 241235520

Hence, the number of ways when the choice is relevant is 1235520

Not relevant choice

When the choice is not relevant, we have:

[tex]Ways = ^nC_r[/tex]

This gives

[tex]Ways = ^{13}C_6[/tex]

Evaluate

Ways = 1716

Hence, the number of ways when the choice is not relevant is 1716

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From the information given about the square pyramid, the maximum base length of the building is 67.42 cm.

We are given the following  details  are:

Base = b

Slant height (l) = 5b

The lateral surface area is calculated using:

L = 2bl

So, we have:

L = 2 * b * 5b

Evaluate the product

L = 10b²

The total surface area is calculated using:

T = L + b²

So, we have:

T = 10b² + b²

Evaluate the sum

T = 11b²

Recall that the maximum surface area is 50,000 square feet

So, we have:

11b² = 50000

Divide both sides by 11

b² = 50000/11

Taking the square root of both sides, we have

b = 67.42

Hence, the maximum base length of the building is 67.42 cm

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Answer:

1/4

Step-by-step explanation:

Chances of getting tails out of all the numbers (including heads)

Totals numbers (including heads & tails): 12

Tails & Even Number: 3

3/12 simplified to 1/4

Answer:

14

Step-by-step explanation:

The equation would be R = 5(4) - 6. Multiply 5 by 4 to get 20, then subtract 6 to get 14.

Answer:

The temperature was 3 degrees colder in the afternoon

Step-by-step explanation:

numbers on the left of zero on the number line are arranged in decreasing order and as such -2 is greater than -5.

The true statement is The temperature was 3 degrees colder in the afternoon.

Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer.

Given that, Darcy read her thermometer in the morning and the temperature was -2° C. In the afternoon, the same thermometer showed a temperature of -5° C.

-2-3 = -5

We see, that, the temperature is falling from -2 to -5, that means, there was a fall in temperature from morning to afternoon.

Hence, the temperature was 3 degrees colder in the afternoon.

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The vertex form of the equation is y = 3(x + 2)^2 - 5

The equation is given as:

y = 3x^2 + 12x + 7

Set to 0

3x^2 + 12x + 7 = 0

Subtract 7 from both sides

3x^2 + 12x = -7

Divide through by 3

x^2 + 4x = -7/3

-------------------------------------------------------------------

Take the coefficient of x

k = 4

Divide by 2

k/2 = 2

Square both sides

(k/2)^2 = 4

-------------------------------------------------------------------

So, we add 4 to both sides of x^2 + 4x = -7/3

x^2 + 4x + 4 = -7/3 + 4

Express as perfect square

(x + 2)^2 = -7/3 + 4

Multiply through by 3

3(x + 2)^2 = -7 + 12

Evaluate

3(x + 2)^2 = 5

Subtract 5 from both sides

3(x + 2)^2 - 5 = 0

Rewrite as

y = 3(x + 2)^2 - 5

Hence, the vertex form of the equation is y = 3(x + 2)^2 - 5

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Answer:

  A.  $56

Step-by-step explanation:

The markup is added to the cost price to find the selling price.

The markup is 75% of the cost price:

  markup = 75% × $32 = $24

The selling price is the cost price plus the markup:

  selling price = cost + markup

  selling price = $32 +24 = $56

The selling price of shoes in the athletic store is $56 per pair.

The selling price for shoes in the athletic store with 75% mark up is [tex]\$56[/tex]

Selling price of the item is sum of Markup and cost price.

The cost of shoes is [tex]\$32[/tex]. The company decides Markup by [tex]75\%[/tex] of cost price.

Markup = [tex]\frac{75}{100}\times 32[/tex]

Markup = [tex]\$24[/tex]

Selling price = Markup + Cost price

Selling price = [tex]24+32[/tex]

Selling price = [tex]\$56[/tex]

The selling price for the shoes in the athletic store is [tex]\$56[/tex].

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The description of the box plots are as follows:

IQR = 25 - 2

= 23

The difference between the median values

= 20 - 6

= 14

That female admires those movie stars and has a large group of pals with whom she goes out on a regular basis to keep them company.

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Answer:

When t = 4

Step-by-step explanation:

The phone will hit the ground when h = 0.

[tex]16t^2 + 32t + 384 =0 \\ \\ t^2 + 2t + 24=0 \\ \\ (t+6)(t-4)=0 \\ \\ t=-6, 4[/tex]

However, as time cannot be negative, we know the answer is when t = 4.

The solution to the system of equations is (3, 2)

Give the system of equation below

y = -x + 5

y=x-1

Equate both expression

-x+5 =x - 1

Equate

-x - x = -1 - 5

-2x = -6

x = 3

Since y = x - 1

y = 3 - 1

y = 2

Hence the solution to the system of equations is (3, 2)

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Bearing is a topic that can be used to locate the position of an object at a given time. Therefore, the blimp is 80 m far away from its starting point. And in the North-East direction.

The speed of an object relates the distance it covers to the time taken to cover the said distance.

i.e speed = [tex]\frac{distance}{time taken}[/tex]

⇒ distance = speed x time taken

In the given question, the initial distance covered can be determined as;

distance = 40 mph x 3 h

              = 120 m

The final distance covered can be determined as;

distance = 40 mph x 1 h

              = 40 m

Let the distance from its starting point to its final location be represented by x.

Thus applying the Cosine rule, we have:

[tex]c^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex] - 2abCos C

[tex]x^{2}[/tex] = [tex]120^{2}[/tex] + [tex]40^{2}[/tex] - 2(120 x 40) Cos 90

   = 14400 + 1600 - 9600

[tex]x^{2}[/tex] = 16000 - 9600

   = 6400

x = [tex]\sqrt{6400}[/tex]

 = 80

x = 80 m

Therefore, the distance of the blimp from its starting point to its final destination is 80 m.

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Answer:

min = a_1

for i:= 2 to n:

      if [tex]a_i[/tex] < min then min = [tex]a_i[/tex]

return min

Step-by-step explanation:

We call the algorithm "minimum" and a list of natural numbers [tex]a_1, a_2, \cdot\cdot\cdot, a_n.[/tex]

So lets first set the minimum to [tex]a_1[/tex]

min = a_1

now we want to check all the other numbers.

We can use a simple for loop, to find the minimum

min = a_1

for i:= 2 to n:

      if [tex]a_i[/tex] < min then min = [tex]a_i[/tex]

return min

Answer:

The sequence of natural numbers is a_1, a_2, a_3, ..., a_n.

Use min as the variable that will contain the minimum value.

Set min = a_1

In a loop, compare min to each number from a_2 to an.

If min > a_i, then let min = a_i

min = a_1

for i = 2 to n

  if min > a_i, then min = a_i

[tex]\begin{gathered} 9 - 4\sqrt{5} \\ \\ = 4 + 5 - 4\sqrt{5} \\ \\ = (- 2)^2 + (\sqrt{5})^2 + (2 \times - 2 \times \sqrt{5}) \\ \\ = (- 2 + \sqrt{5})^2 \\ \\ = (\sqrt{5} - 2)^2 \\ \\ \\ \therefore \sqrt{9 - 4\sqrt{5}} = \sqrt{5} - 2 \end{gathered}[/tex]

Hope this may be helpful.

Answer:

sorry the drawing is messy, not used to drawing with just a finger haha! hope this helps<<3

The best model for the package is a cone and the approximate surface area is 258 square inches.

From the information given, it was stated that the diagram shows a shape with circular base and curved surface meeting at a point. The diameter of the base is labeled 9 inches and the height of the shape is labeled 13 inches.

In this case, the information given about the diagram shows that it's a cone.

Also, given the information, the total surface area of the cone that has a slant height and diameter is given as:

= π(d/2)(d/2 + l)

In such a situation, it should be noted that d represents the diameter in the question. The surface area is the total area that's covered by its surface.

Therefore, the best model for the package is a cone and the approximate surface area is 258 square inches.

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