solve for x if 2(5x + 2)^2 = 48

Where a and b are determined by the value of D.

A parabola is a type of graph, or curve, that is represented by an equation of the form y = ax² + bx + c. The vertex of a parabola is the point where the curve reaches its maximum or minimum point, depending on the direction of the opening of the parabola. In this case, the vertex of the parabola is at (-4,-1).
To find the equation of the parabola, we need to know two more points on the graph. We are given that when the y-value is 0, the x-value is 10-D. We can use this information to find another point on the graph.
When the y-value is 0, we have:
0 = a(10-D)² + b(10-D) + c
Simplifying this equation gives:
0 = 100a - 20aD + aD² + 10b - bD + c
Since the vertex is at (-4,-1), we know that:
-1 = a(-4)² + b(-4) + c
Simplifying this equation gives:
-1 = 16a - 4b + c
We now have two equations with three unknowns (a,b,c). To solve for these variables, we need one more point on the graph. Let's use the point (0,-5) as our third point.
When x = 0, y = -5:
-5 = a(0)² + b(0) + c
Simplifying this equation gives:
-5 = c
We can now substitute this value for c into the other two equations to get:
0 = 100a - 20aD + aD² + 10b - bD - 5
-1 = 16a - 4b - 5
Simplifying these equations gives:
100a - 20aD + aD² + 10b - bD = 5
16a - 4b = 4
We now have two equations with two unknowns (a,b). We can solve for these variables by using substitution or elimination. For example, we can solve for b in the second equation and substitute it into the first equation:
16a - 4b = 4
b = 4a - 1
100a - 20aD + aD² + 10(4a-1) - D(4a-1) = 5
Simplifying this equation gives:
aD² - 20aD - 391a + 391 = 0
We can now use the quadratic formula to solve for D:

D = [20 ± sqrt(20² - 4(a)(391a-391))]/2a
D = [20 ± sqrt(400 - 1564a² + 1564a)]/2a
D = 10 ± sqrt(100 - 391a² + 391a)/a
There are two possible values for D, depending on the value of a. However, since we don't have any information about the sign of a, we cannot determine which value of D is correct. Therefore, the final equation of the parabola is:
y = ax² + bx - 5

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The area of the sidewalk is total area of the square and the two semicircles, and then subtract the area of the garden itself i.e 2.25 square meters.

To find the area of the sidewalk surrounding the garden, we need to calculate the total area of the square and the two semicircles, and then subtract the area of the garden itself.

Let's break down the steps to calculate the area of the sidewalk:

Area of the square:

The side length of the square is equal to the diameter of the semicircle, which is 2 * 10 = 20 meters.

The area of the square is given by the formula: side length * side length = 20 * 20 = 400 square meters.

Area of the two semicircles:

The radius of each semicircle is 10 meters, so the area of one semicircle is (1/2) * π * radius² = (1/2) * π * 10² = 50π square meters.

Since there are two semicircles, the total area of the semicircles is 2 * 50π = 100π square meters.

Area of the garden:

The area of the garden is the combined area of the square and the two semicircles, which is 400 + 100π square meters.

Area of the sidewalk:

The width of the sidewalk is 1.5 meters, and it surrounds the garden along its edge. To find the area of the sidewalk, we subtract the area of the garden from the area of the garden plus the sidewalk.

Area of the sidewalk = (400 + 100π) - (400 + 100π - 1.5 * 1.5) square meters.

Simplifying the equation, we have:

Area of the sidewalk = 1.5 * 1.5 square meters.

Therefore, the area of the sidewalk is 2.25 square meters.

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Answer: 266256π

Step-by-step explanation:

♡ Hope this helps ♡

Answer:

bdhdbhdjndjxbdixn,jzhhdhuu,ubxhsjxjnx

The algebraic statement that is true is (c) (x²y - xz)/x² = (xy - z)/x

From the question, we have the following parameters that can be used in our computation:

The algebraic statements

Next, we test the options

A/B + A/C = 2A/(B + C)

Take the LCM and evaluate

(AC + AB)/(BC) = 2A/(B + C)

This means that

A/B + A/C = 2A/(B + C) --- false

Next, we have

(a²b - c)/a² = b - c

Cross multiply

a²b - c = a²b - a²c

This means that

(a²b - c)/a² = b - c --- false

Lastly, we have

(x²y - xz)/x² = (xy - z)/x

Factor out x

x(xy - z)/x² = (xy - z)/x

Divide

(xy - z)/x = (xy - z)/x

This means that

(x²y - xz)/x² = (xy - z)/x --- true

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Answer:

One of them must be a mirror image of the other

Step-by-step explanation:

Two shapes are congruent if one is a mirror shape of the other or if both have the same size.

Identity properties of addition are known to commutative in nature.

Given A and B, A and B are commutative or possess identity property of addition if;

A+B = B+A

For identity property, the two integers you are summing must include zero. For exmaple, a+0 = 0+a = a

The answer must always give the non-zero integer. Let us use 8 and 0 for example. This two possess the identity property of addition because;

8+0 = 0+8 = 8 (identity property of addition)

Answer: well about 3

Step-by-step explanation:

father(youngest)mom(middle child)oldest

oldest(youngest)mom(middle child)father

father(middle child)mom(youngest)oldest

hope this helps:)

Answer:

18-6×10=-42

Step-by-step explanation:

all i did was put it in my calculator

Thus, the correct options are C, D, and E.

Given: Anna bought 8 tetras and 2 rainbow fish for her aquarium.

To Find: Which option is correct?

Solution: Let's say that the price of tetras is x, which means the price of a rainbow fish will be (x + 6).

Here, we get the equation,

8x +2(x + 6)=37

Now, after simplifying the above equation, we get

10x + 12 =37

By adding -12 on both sides of the equation, we get

10x = 37 - 12 =25

Now, we will divide the equation with 10

x = 25/10

After simplifying the equation, we get

x = 5/2 = 2.5

So, the cost of a tetra will be $2.5, and the cost of a rainbow fist will be $2.5 + $6 = $8.5

Here, option B is false because the cost of each rainbow fish is greater by $6, and here 6 is only taken once.

Option A is false because 4(2.5) is not equal to 8.5.

Option E is true because 37 - 8.5 = 28.5.

Option D is true because the equation that is being used has only one difference which is the selection of variable.

Option C is true because 5(2.5) + 8.5 = 12.5 + 8.5 = 21.

Thus, the correct options are C, D, and E.

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Answer:

k = 10

Step-by-step explanation:

given y varies inversely as x then the equation relating them is

y = \(\frac{k}{x}\) ← k is the constant of variation

to find k use the condition that y = 5 when x = 2

5 = \(\frac{k}{2}\) ( multiply both sides by 2 )

10 = k

Answer: 30 feet

Step-by-step explanation:

10 / 2.5 = 4

7.5 * 4 = 30

Answer:

Step-by-step explanation:

To find the mean absolute deviation (MAD) of the number of newspapers delivered, we first need to calculate the mean. Adding up all the numbers and dividing by the total number of values gives us a mean of 18. Next, we calculate the absolute difference between each number and the mean, which gives us the following values: 1, 4, 1, 3, 1. Finally, we average these values by adding them up and dividing by the total number of values, which is 5. Therefore, the MAD of the number of newspapers delivered is 2.

Answer:

The mean absolute deviation (MAD) is calculated by averaging the absolute differences between each data point and the mean. In this case, the data points are the number of newspapers delivered: 19, 14, 19, 21, and 17. The mean of these numbers is 18.

The absolute differences between each data point and the mean are: |19-18| = 1, |14-18| = 4, |19-18| = 1, |21-18| = 3, and |17-18| = 1.

The sum of these absolute differences is 1 + 4 + 1 + 3 + 1 = 10. Dividing this sum by the number of data points (5) gives us the MAD: 10/5 = 2.

So the MAD for this data set is 2.

Answer:

acute and equilateral

Explanation:

The red lines on each side means that all three sides have the same length. It means that this triangle is an equilateral triangle.

The interior angles of equilateral triangle are all the same and are equal to 60 degrees. Since 60 degrees is lower than 90 degrees, the triangle is acute.

Therefore, the answer is;

acute and equilateral.

A) Function is increasing on (-∞, -1) and (7/2, ∞), and decreasing on (-1, 7/2).

b)  The local minimum value of f is; 5608/2197 at x = -42/13, and the local maximum value of f is 139/8 at x = 7/2.

(a) To determine the intervals on which f is increasing or decreasing, we need to determine the critical points and then check the sign of the derivative on the intervals between them.

f(x)=8x³-42x-48x + 4

f'(x) = 24x² - 90

Setting f'(x) = 0, we get

24x² - 90 = 0

24x² = 90

x =±  √3.75

So, the critical points are;

x = -1 and x = 7/2.

We can test the sign of f'(x) on the intervals as; (-∞, -1), (-1, 7/2), and (7/2, ∞).

f'(-2) = 72 > 0, so f is increasing on (-∞, -1).

f'(-1/2) = -25 < 0, so f is decreasing on (-1, 7/2).

f'(4) = 72 > 0, so f is increasing on (7/2, ∞).

Therefore, f is increasing on (-∞, -1) and (7/2, ∞), and decreasing on (-1, 7/2).

(b) To determine the local maximum and minimum values of f, we need to look at the critical points and the endpoints of the interval (-1, 7/2).

f(-1) = -49

f(7/2) = 139/8

f(-42/13) = 5608/2197

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Answer: X=74

if you want to be shown step by step comment below

Answer:

113

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

f(x) = 5ˣ - 12

f(3) is x = 3

Step 2: Evaluate

Answer:

Option (3)

Option (3)

Option (2)

Step-by-step explanation:

(3x² + 2x - 2)×(x² - 2) = x²(3x² + 2x - 2) - 2(3x² + 2x - 2) [By distributive law]

                                  = \((3x^{4}+2x^{3}-2x^2)-(6x^{2}+4x-4)\)

                                  = \(3x^4+2x^3-2x^2-6x^2-4x+4\)

                                  = \(3x^4+ 2x^3-8x^2-4x+4\)

Therefore, Option (3) will be the answer.

\(-\frac{75x^3y^2}{-5x^2y}=\frac{75}{5}\times \frac{x^3}{x^2}\times \frac{y^2}{y}\)

             = 15xy

Therefore, Option (3) is the answer.

-3x²y) 12x³y² + 9x²y³(-4xy - 3y²

          12x³y²

               0 + 9x²y³

                  + 9x²y³

                        0

Therefore, (-4xy - 3y²) will be the quotient.

Option (2) will be the answer.

Answer:

positive

Step-by-step explanation:

x^59/2.3x × 4/5 = x^58 × 10/23 × 4/5 = x^58 × 8/23

x has even power so, it will have positive sign regardless of value of x

Answer:

y = 1

Step-by-step explanation:

Note the line passes through (1, 1 ) and (4, 1 ) both with a y- coordinate of 1

This indicate the line is horizontal and parallel to the x- axis with equation

y = c

where c is the value of the y- coordinates the line passes through, then

y = 1 ← equation of line

Complete question :

A 12-foot by 15-foot patio is increased by placing a stone border around the patio. The width of the border is the same all around the patio.The perimeter of the patio after it is expanded is 74 feet. The equation which represents x, the width of the border is 2[(12+2x)+15+2x)]=74. What is the width of the border?

1) 2 1/2 feet

2) 3 feet

4) 5 feet

5) 8 1/2 feet

Answer:

2.5

Step-by-step explanation:

Solving for X in the perimeter equation :

2[(12+2x)+15+2x)]=74

Open the bracket

2[(12 + 2x + 15 + 2x)] = 74

2(27 + 4x) = 74

54 + 8x = 74

8x = 74 - 54

8x = 20

x = 20/8

x = 2.5

Hence, width fo border = 2.5

The three general approaches to valuing an asset, such as a sports franchise, are the market approach, the income approach, and the cost approach.

(a) Market Approach:

The market approach determines the value of an asset by comparing it to similar assets that have been recently sold in the market. This approach relies on the principle of supply and demand, considering the prices at which comparable sports franchises have been bought or sold. It involves analyzing factors such as market trends, recent transactions, and the financial performance of similar franchises. By comparing the sports franchise to comparable market transactions, an estimate of its value can be derived.

(b) Income Approach:

The income approach values an asset based on the income it is expected to generate in the future. For a sports franchise, this approach considers factors such as revenue streams from ticket sales, broadcasting rights, merchandise, and sponsorships. It involves forecasting future cash flows and discounting them to their present value using an appropriate discount rate. By estimating the future income potential and risks associated with owning the franchise, the income approach provides a valuation based on the expected returns the asset can generate.

(c) Cost Approach:

The cost approach determines the value of an asset by considering the cost required to replace or reproduce it. In the case of a sports franchise, this approach evaluates the expenses that would be incurred to establish a similar franchise from scratch, taking into account factors such as team development, stadium construction, player acquisition, marketing, and administrative costs.

It considers the principle of substitution, assuming that a buyer would not pay more for an asset when an equivalent could be obtained at a lower cost.

The cost approach provides an estimate of the value based on the expenses associated with creating a similar sports franchise.

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The speed of the kayak in component form is approximately 3.112 meters per second in the east-west direction and 7.368 meters per second in the north-south direction.

The speed of the kayak can be represented in component form, which consists of two perpendicular components: one in the east-west direction (x-component) and the other in the north-south direction (y-component).

Given that the kayak is traveling at a speed of 8 meters per second in the direction of S 67 degrees W, we can use trigonometry to determine the x-component and y-component of the speed.

The x-component represents the east-west direction and can be calculated using the cosine function. The y-component represents the north-south direction and can be calculated using the sine function.

To calculate the x-component:

x-component = speed * cosine(angle)

x-component = 8 * cosine(67 degrees)

x-component ≈ 8 * 0.389

x-component ≈ 3.112 meters per second (rounded to three decimal places)

To calculate the y-component:

y-component = speed * sine(angle)

y-component = 8 * sine(67 degrees)

y-component ≈ 8 * 0.921

y-component ≈ 7.368 meters per second (rounded to three decimal places)

Therefore, the speed of the kayak in component form is approximately 3.112 meters per second in the east-west direction and 7.368 meters per second in the north-south direction.

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Answer: M=2

y-intercept = (0,7)

x-intercept = (-7/2,0)

Step-by-step explanation:

The slope is already given in the equation, which is 2

M=2

y-intercept = (0,7)

x-intercept = (-7/2,0)

The inner product of two vectors A = (2, -3,0) and B = (-1,0,5) is -2 / √(13×26).

Solving the given system of equations using Gaussian elimination:

2x + 3y + z = 2 y + 5z = 20 -x+2y+3z = 13

Matrix form of the system is

[A] = [B] 2 3 1 | 2 0 5 | 20 -1 2 3 | 13

Divide row 1 by 2 and replace row 1 by the new row 1: 1 3/2 1/2 | 1

Divide row 2 by 5 and replace row 2 by the new row 2: 0 1 1 | 4

Divide row 3 by -1 and replace row 3 by the new row 3: 0 0 1 | 5

Back substitution, replace z = 5 into second equation to solve for y, y + 5(5) = 20 y = -5

Back substitution, replace z = 5 and y = -5 into the first equation to solve for x, 2x + 3(-5) + 5 = 2 2x - 15 + 5 = 2 2x = 12 x = 6

The solution is (x,y,z) = (6,-5,5)

Therefore, the solution to the given system of equations using Gaussian elimination is (x,y,z) = (6,-5,5).

The given two vectors are A = (2, -3,0) and B = = (-1,0,5). The inner product of two vectors A and B is given by

A·B = |A||B|cosθ

Given,A = (2, -3,0) and B = (-1,0,5)

Magnitude of A is |A| = √(2²+(-3)²+0²) = √13

Magnitude of B is |B| = √((-1)²+0²+5²) = √26

Dot product of A and B is A·B = 2(-1) + (-3)(0) + 0(5) = -2

Cosine of the angle between A and B is

cosθ = A·B / (|A||B|)

cosθ = -2 / (√13×√26)

cosθ = -2 / √(13×26)

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Answer:

64

Step-by-step explanation:

The volume of rectangular prisms is measured by l*w*h

And by counting the units of the length, width, and height are all 4 units long.

So take the numbers and plot them into the formula

4*4*4 = V

16 * 4 = V

64 = V

The prism is 64 cubic units.

Answer:

(x - 1, y + 1 )

Step-by-step explanation:

Consider the reflection in the y- axis

A point (x, y ) → (- x, y )

Consider the reflection of point A

A(- 5, 2 ) → A'(5, 2 )

Now A → E after the transformations

E = (4, 3 ), thus

A'(5, 2 ) → E(4, 3 )

(x, y ) → (x + (- 1), y + 1 ) = (x - 1, y + 1 )

The translation rule is (x, y ) → (x - 1, y + 1 ).

In mathematics, translation is a transformation that moves every point of a figure or a graph the same distance and in the same direction. The object being translated retains its size and shape, but its position changes.

Consider the reflection in the y- axis

A point (x, y ) → (- x, y )

Consider the reflection of point A

A(- 5, 2 ) → A'(5, 2 )

Now A → E after the transformations

E = (4, 3 ), then

A'(5, 2 ) → E(4, 3 )

Thus, the translation rule is (x, y ) → (x + (- 1), y + 1 ) = (x - 1, y + 1 )

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Among the options provided, historical data can be used to guide the choice of the probability distribution for a random variable.

Historical data provides information about past occurrences and can be analyzed to understand the distribution of the variable in question. By examining the frequency and patterns of past observations, one can gain insights into the underlying probability distribution that best represents the random variable.

Forecasting results can also play a role in selecting a probability distribution, as it involves predicting future outcomes based on available data.

The forecasting process may involve evaluating different probability distributions and selecting the one that aligns with the observed patterns and is most suitable for predicting future events.

Likelihood factors and an objective function are not directly related to the choice of a probability distribution. Likelihood factors typically refer to the factors that influence the likelihood of a particular outcome, while an objective function is a measure used to optimize a certain goal or objective.

While these factors may indirectly inform the choice of a probability distribution, they are not specific guidelines for selecting the distribution itself.

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Answer:

m<GEF = 32 degrees

Step-by-step explanation:

<EGF = 180-64=116

116 + 32 + 32 = 180 degrees

64/2 = 32 degrees

Answer:

40 mph (miles per hour)

Step-By-Step Explanation:

Tom

40 miles per 2 hours

or

20 miles per hour

Sam

80 miles per 2 hours

or

40 miles per hour

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