Find the vertex of the function given below.
y = 3x² + 6x +1
A. (1,7)
B. (-1,-2)
C. (-4,9)
D. (-1,-1)

The equations that has the same value as x in 2/3(6x+12)=-24 are 4x+8 = -24 and 4x = -32 , option(a) and (e) are correct .

In the question ,

the equation 2/3(6x+12)=-24 is given

on solving for x ,we get

4x+8 = -24

4x = -24-8

4x = -32

x = -8 .

Solving option(a)

4x+8 = -24

4x = -24-8

4x = -32

x = -8

Solving for option(b)

9x+18 = -24

9x = -24-18

9x = -42

x = -42/9

solving for option(c)

4x = -16

x = -4

solving for option(d)

(18x+36)/2 = -24

18x + 36 = -48

18x = -48-36

18x = -84

x = -84/18

solving for option(e)

4x = -32

x = -32/4

x = -8

we can see that only option (a) and option(e) , given the value of x as -8 .

Therefore , the equations that has the same value as x in 2/3(6x+12)=-24 are 4x+8 = -24 and 4x = -32 , option(a) and (e) are correct .

The given question is incomplete , the complete question is

Which equation has the same value as X 2/3(6x+12)=-24 ?

Select two options

(a) 4x+8 = -24

(b) 9x+18 = -24

(c) 4x = -16

(d) (18x+36)/2 = -24

(e) 4x = -32

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Powell believe that the inflation rate will be  4.46% over the next year .

In the question ,

it is given that

total return offered by the investment((nominal rate) = 17% = 0.17

return according to Powell Arms(real rate) = 12% = 0.12

let the inflation rate be x.

The inflation rate over the next year can be calculated using the formula .

(1+Real rate ) = (1+nominal rate )/ (1+ inflation rate )

Substituting the values , we get

(1+0.12) = (1+0.17)/(1+x)

1.12 = 1.17/(1+x)

1+x = 1.17/1.12

1 + x = 1.0446

x = 1.0466-1

x = 0.0446

x = 4.46%

Therefore , Powell believe that the inflation rate will be  4.46% over the next year .

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Answer: Jenny = 6 | Kim = 7 | (Unknown Sister because no name) = 44

Step-by-step explanation:

Jenny = 6 years (that we already know)

6 x 2 = 12 - 5 = 7 years for Kim

7 + 6 = 13

To find the unknown age of the last sister, we will subtract 57 - 13 = 44

So the last sister is 44.

(I am very sorry if this is wrong, I am only in Middle School).

400 yards of fence = total fencing

400 = 2 widths + 2 heights

Since one side (width) is along the river, and the river bank acts as one side of the rectangle, the fence will be used in 3 sides:

400 = w+2h

Solving for h:

400-w=2h

(400-w)/2 = h

h= (400-w)/2 (a)

h= 200-1/2w (simplified)

To express the area:

Area of a rectangle : height x width

Since h = 200-1/2w

A = (200-1/2w) w

A = 200w-1/2w^2 (b)

Answer: -35

Step-by-step explanation:

set the every x in the equation to (-6)

g(-6) = 5(-6)-5

g(-6) = -30-5

g(-6) = -35

The volume of a sphere is given by the following formula:

Where r is the radius of the sphere r=5.8m.

Replace this value and solve for V:

The volume of the sphere is 816.9 cubic meters.

Answer:

200 in³

Explanation:

The lengths of the sides of the constructed tetrahedron are twice the length of the side of the small tetrahedron of 50 in³. It means that the scale factor for the solid is 2. So, the complete volume of the constructed tetrahedron is equal to

Vn = 2³(50 in³)

Vn = 8(50 in³)

Vn = 400 in³

However, we only use 4 small tetrahedrons, so the volume of these four solids is

4(50 in³) = 200 in³

Then, the volume of the gap is the difference between the volume of the constructed tetrahedron and the volume of the 4 small tetrahedrons

400 in³ - 200 in³ = 200 in³

So, the answer is 200 in³

Given data:

The given figure of the triangles.

In triangle STH and triangle GFH.

Thus, yes the triangles are similar by angle-angle (AA) property.

We are given the following function:

Part A. We are asked to draw the graph of the function. This is an exponential function with a negative sign, this means that the graph is reflected across the x-axis. Therefore, the graph is:

Part B. The domain of a function is the values that the fuction can take as an input. Since the function is an exponential function, it can take any value of "x" therefore, the domain is all the real numbers, we write this as follows:

Part B. The range of a function is the values that the function outputs, The range of an exponential function are the values that are greater than zero, but since the given function is reflected across the x-axis, this means that the rage is the negative real numbers, therefore, the range is:

Part D. For an exponential function of the form:

The asymptote is x-axis, since zero is never an output of the function. Therefore the equation of the asymptote is:

Part E. The y-intercept is the value of the function when "x = 0", therefore, substituting in the function we get:

Solving the operations:

Therefore, the y-intercept is -1

From the graph, the range of the function in the graph is; 0 ≤ M ≤ 6.5

The range of a function is the set of all possible output values for which the function still exists.

Now, from the graph, we can see that it is a linear graph that starts on the vertical axis with a coordinate of approximately (0, 1) which denotes 1 kg when the volume is 0 liters.

Now, we see that the line of the graph stops at the coordinate (7.5, 6.5) which denotes 6.5 kg when the volume is 7.5 liters.

Therefore the maximum mass is 6.5 kg while the minimum is 0 kg. Thus,;

Range; (0 ≤ M ≤ 6.5)

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Answer: According to the law of sines, we have the following:

Therefore, according to this, the answer is Option (B).

The required answer would be the inequality 4x + 2y ≥ 45, the graph has been attached which represents the given situation.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

We have been given that the price for each bucket of popcorn was $4. The price of each drink was half the price of a bucket of popcorn.

The total amount of spend is $45

As per the given condition, the required inequality would be as

4x + 2y ≥ 45

The situation's representation is in the attached graph with labels for the intercepts.

Here y-axis represents the number of drinks, and the x-axis represents the number of buckets of popcorn.

Thus, the required answer would be the inequality 4x + 2y ≥ 45, the graph has been attached which represents the given situation.

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The missing side and angle of the similar polygons are as follows:

Similar polygons are two polygons with the same shape, but not the same size.

Similar polygons have corresponding angles that are congruent, and corresponding sides that are proportional.

Therefore, polygon ABCD is similar to polygon FGHI. This means the corresponding angles are congruent and the corresponding sides are proportional.

Therefore,

∠C is corresponding angle to ∠H. This means they are both congruent.

Hence,

∠H = 90 degrees

Let's find FI,

10 / 6  = 9 / FI

cross multiply

FI = 54 / 10

FI = 5.4

Let's find IH

10 / 6 = 8 / IH

cross multiply

IH = 48 / 10

IH  = 4.8

Let's find BC

10 / 6 = BC / 4.6

cross multiply

BC = 46 / 6

BC = 7.66666666667

BC = 7.7

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Answer:

You hiked 5.3 miles yesterday

Answer:

Yes, [tex]z=-\frac{2}{3}, 6[/tex]

Step-by-step explanation:

Using the zero-product property,

[tex]3z+2=0, 6-z=0 \\ \\ \implies z=-\frac{2}{3}, 6[/tex]

Answer: 2

Step-by-step explanation:

The constant of proportionality is the same as the slope of the line. Using the slope formula with the points (0, 0) and (2, 4), [tex]\frac{4-0}{2-0}=2[/tex].

System of equations:

Using a graphing calculator we can get the graph:

As the point in which both functions meet is (2, 4), then this is the solution.

Answer: (2, 4)

The difference quotient for the given function is:

[tex]-\frac{4}{x*(x + h)}[/tex]

For the function f(x), we define the difference quotient as:

[tex]\frac{f(x + h) - f(x)}{h}[/tex]

In this case, the function is f(x) = 4/x, replacing that in the general difference quotient:

[tex]\frac{4/(x + h) - 4/x}{h}[/tex]

Now we can simplify this to get:

[tex]\frac{4/(x + h) - 4/x}{h} = 4*\frac{1/(x + h) - 1/x}{h} \\\\4*\frac{1/(x + h) - 1/x}{h} = 4*(\frac{1/(x + h)}{h} - \frac{1/x}{h})[/tex]

[tex]4*(\frac{1/(x + h)}{h} - \frac{1/x}{h}) = 4*(\frac{1}{(x + h)*h} - \frac{1}{x*h}) = 4*\frac{x - x - h}{x*h*(x + h)} = -\frac{4}{x*(x + h)}[/tex]

So the correct option is the last one.

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the answer

a perfect square is a number that when two exact same number multiply each other, it produce

example 2 * 2 = 4

4 is a square number and the square root is 2

the answer to your question is 64 and 100 which is option B and C

Solution:

Given:

Using the graphical method,

The solution is the point of intersection of the two lines.

Therefore, the solution is;

The answer is -83/2

Decimal Form: -41.5

Mixed Number Form: -41 1/2

Let:

A be the number of pairs of Jeans Amina has.

I be the number of pairs of Jeans Idris has.

T be the total of pairs of Jeans.

Then,

A = 2

I = 3

Then, the equation that represents the total of pairs of jeans is:

Substituting the values we can find T:

Answer:

The equation is: T = A + I.

And the solution is T = 5.

Answer:

16.90≤19.78

Step-by-step explanation:

The statements about the function that are true are

The equation of the graph is given as

f(x) = (x - 1)(x + 7)

The graph of the function is added as an attachment

On the graph, we have

Vertex = (-3, -16)

This is so because the graph has a minimum point of (-3, -16)

Also, the graph crosses the x-axis at x = 1 and x = -7

This means that the graph is positive at x >1 and x >-7

Because the vertex is a minimum, the graph is increasing at the left of its symmetry i.e. x > -3

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(a) The probability that exactly 4 out of 12 randomly sampled 18 to 20 year old consumes an alcoholic drink is 0.008127.

(b) The probability that exactly 8 out of 12, 18 to 20-year-olds have not consumed an alcoholic beverage is 0.231991.

(c) The probability that at most two out of four randomly sampled 18 to 20 year old have consumed alcoholic beverages is 0.35.

(d) The probability that at least one out of four randomly sample 18 to 20 years has consumed alcoholic beverages is 0.99168.

The possibility of an event happening is defined by probability. We may need to forecast an event's result in a variety of real-world circumstances. The outcomes of an event may be certain or uncertain to us.

Given that 69.8% of people of 18-20 yr old consume alcohol.

Then p=0.698

Now let X is the random variable denoting the number of people who drinks alcohol.

(a) Let the sample size, n = 12, p = 0.698

It can be seen that X follows a binomial distribution

Then,

P(X=4) = ¹²C₄p⁴(1-p)⁸

= 495 × (0.698)⁴(1-0.698)⁸

=495 × 0.2373 × 0.00006919

= 0.008127

(b) P(X=8) = ¹²C₈p⁸(1-p)⁴

= 12!/ (8!)(4!)(0.698)⁸(1-0.698)⁴

=495 × 0.05634344 × 0.0083181

= 0.231991

(c) Let sample size n=4

p= 0.698

Then,

P(X≤2) = P(X=0)+P(X=1)+P(X=2)

= ⁴C₀p⁰(1-p)⁴ + ⁴C₁p¹(1-p)³ + ⁴C₂p²(1-p)²

=1 × 1× 0.0083181 + 4× 0.698 × 0.0275 + 6× 0.4872 × 0.091204

=0.3516881

=0.35

(d)

For P(X≥1)= 1-P(X<1)

=1-P(X=0)

=1-⁴C₀ p⁰(1-p)⁴

=1-1 × 1 × 0.0083181

= 0.99168

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QS = 20.7

To get length of side QS, we will consider triangle SQR (right angle triangle)

opposite (the side opposite the angle 28°) = QS

adjacent = base = 39

We apply tangent ratio:

tan28 = opposite/adjacent

tan28 = QS/39

QS = 39 × tan28

QS = 39 × 0.5317

QS = 20.7363

To the nearest tenth, QS = 20.7

The actual distance between the two cities in kilometers is 73.8 kilometers.

Given:

The distance between two cities on a map = 4.1 centimeters

The Scale used by the map is, 1 centimeter is equivalent to 18 kilometers.

To find the actual distance between the two cities in kilometers,

We know, 1 centimeter = 18 kilometers.

For converting the distance in centimeters to kilometers we multiply the value in centimeters by the value of 1 centimeter i.e.18 kilometers.

So, 4.1 centimeter = (4.1 × 18) kilometers

                              = 73.8 kilometers

Therefore, the actual distance between the two cities calculated in kilometers is 73.8 kilometers.

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The coordinates of the other endpoint Q.=(2,0)

How to calculate the coordinates of the other endpoint Q ?

Given:

Midpoint = PQ = M(4,0)

One endpoint = P = [tex](x_1,y_1)[/tex]  = (6,0)

Other endpoint Q= [tex](x_2,y_2)[/tex]

We know that,

[tex]\text{Midpoint PQ}=(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )\\\\=(\frac{6+x_2}{2} ,\frac{0+y_2}{2} )=(4,0)\\\\= > \frac{6+x_2}{2} =4\\\\= > 6+x_2= 8\\\\= > x_2=2[/tex]

[tex]\text{Similarly},\\\\\frac{0+y_2}{2} =0\\\\= > y_2=0[/tex]

So, the Other endpoint Q=(2,0)

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To find the hypotenuse we going to use the Pythagorean theorem

being c the hypotenuse and a and b the other two sides

Replacing

Solving

Answer: hypotenuse = 13