Select the correct answer. What is the solution to the equation? 3(x + 9)^3/4 = 24​

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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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:

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.

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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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 formula for the squirrel population is P(t) = 400 e^0.5t and the doubling time of the population is 17. 68 years

The growth constant k can be defined as the frequency or also known as the number of times per unit time of growing by a factor

it is also called the logarithmic return, compounded return, or the force of interest.

Note that the general formula for growth rate is given as;

[tex]P(t) = P0 e^k^t[/tex]

Where,

Po =  Initial value = 400 squirrels

r = Rate of growth

k = constant of proportionality = 0. 5 per year

t = time = 1 year

The function P(t) is given as;

P(t) = 400 e^0.5t

Note that the formula for doubling time is given as;

[tex]TD = t \frac{In 2}{In 1 + r/ 100}[/tex]

r = 4

t = 1

substitute into the formula

[tex]TD = 1 \frac{0. 693}{0. 0392}[/tex]

Doubling time  = 1 × 17. 68

Doubling time = 17. 68 years

Thus, the formula for the squirrel population is P(t) = 400 e^0.5t and the doubling time of the population is 17. 68 years

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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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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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The missing side in the given triangle is x = √193 km

The Pythagoras theorem is expressed as;

x^2 = a^2 + b^2

where

x is the longest side

Substitute the given side

x^2 = 12^2 + 7^2

x^2 = 144 + 49

x = √193 km

Hence the missing side in the given triangle is x = √193 km

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Answer:

(4,-5)

Step-by-step explanation:

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 sum accumulated by 31st December 2018 is Rs 4,163,060.00

What is future value?

Future value is the accumulated amount that investments would yield in future period when the amounts invested are added with the total interest earned.

Note in this case that Rs500,000  would be invested subsequently for 4 years( 2015-2018 , January 1st of each year)

We can determine the future value of each investment using the future value formula shown below:

FV=PV*(1+r)^N

PV=amount invested

r=interest=10%

N=number of years that an amount is invested(for instance, the amount invested on 1st January 2014 will earn interest in 2014,2015,2016, 2017 and 2018 i.e. for 4 years)

Total FV=1,000,000*(1+10%)^5+500,000*(1+10%)^4+500,000*(1+10%)^3+500,000*(1+10%)^2+500,000*(1+10%)^1

Total FV=Rs 4,163,060.00

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Answer:

$160

Step-by-step explanation:

115% = $184

100% = X

let X be the original salary

(X is unknown)

115% = $184

100% = X

cross mutiply

115 x X = 100 x 184

115X = 18400

X = 18400 divided by 115

X = $160

therefore,Mr Black's original salary before increased by 15% was $160

hope am helpful.

Answer:

y=-2x+12

Step-by-step explanation:

First, subtract 1/2 from each side

1/4y = -1/2x + 3 --> multiply each side by 4

y = -2x + 12 is your final answer

Answer:

hey its me again so the answer is 11.

I'm sure because I did this.

The composition of transformation that maps ABCD to EHGF is reflect over the y-axis, then translate (x - 1, y + 1)

Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, rotation, translation and dilation.

Translation is the movement of a point either up, left, right or down in the coordinate plane.

The composition of transformation that maps ABCD to EHGF is reflect over the y-axis, then translate (x - 1, y + 1)

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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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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

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:

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

Answer:

Step-by-step explanation:

1 Answer

1=12.

4=22.

9=32.

16=42.

25=52.

36=62.

49=72.

64=82 .

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:

Based on the graph which depicts the United States domestic market for  corn at different prices, we can logically deduce the following information:

Assuming France is the only other corn-producing nations at a domestic price of $4, we can reasonably infer that the United States will export corn while France will import it.

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Answer:

the difference between them is zero cause on first year simple interest and compound interest are equal

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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[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.

Given that, Nathan shares out 12 sweets, if he gives Yasmin 1 sweet for 3 sweets he buys, Nathan will get 9 sweets.

Given that, Nathan shares out 12 sweets, he gives Yasmin 1 sweet for 3 sweets he buys.

Let the sweet be represented by x

For each x sweet for Yasmin, Nathan gets 3x sweets

Hence

x + 3x = 12

We solve for x

4x = 12

x = 12/4

x = 3

Hence;

Yasmin gets x sweet = 3

Nathan gets 3x sweets = 3 × 3 = 9

Given that, Nathan shares out 12 sweets, if he gives Yasmin 1 sweet for 3 sweets he buys, Nathan will get 9 sweets.

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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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