Which of the following is the graph of y=1/2x^2?

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The equation X^2/2 - 8 = 2X - 2 has two solutions, X = 6 and X = -2. These are the values of X that satisfy the equation and make both equations Y = X^2/2 - 8 and Y = 2X - 2 intersect on the graph.

To find the solutions to the equation X^2/2 - 8 = 2X - 2, we need to set the two equations equal to each other and solve for X.

The equation is:

X^2/2 - 8 = 2X - 2

To simplify the equation, let's multiply both sides by 2 to eliminate the fraction:

X^2 - 16 = 4X - 4

Next, we rearrange the equation to have all terms on one side:

X^2 - 4X - 12 = 0

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Let's use factoring in this case:

(X - 6)(X + 2) = 0

Setting each factor equal to zero gives us two possible solutions:

X - 6 = 0 --> X = 6

X + 2 = 0 --> X = -2

So the solutions to the equation X^2/2 - 8 = 2X - 2 are X = 6 and X = -2.

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Answer:

Step-by-step explanation:

You have to use the quadratic formula

x = -b +/- \(\sqrt{(b^{2} -4ac)/2a\)

and then you can simplify both answers so the first one would be -13/2 and the second would be -27/2

you usually have to reject an answer but since there is no equal sign in the question, you should be fine

The sum of the interior angles of a regular polygon with 9 sides will be 1260°. The correct option is A.

An angle is defined in mathematics as the figure formed by joining two rays at their common endpoint. An interior angle is an angle that exists within a shape. Polygons are closed shapes with sides and vertices. All of the interior angles of a regular polygon are equal.

Given that the number of the sides of the polygon is 9. The sum of the interior angles of the polygons will be calculated as,

Sum = ( n - 2 ) 180°

Sum = ( 9 - 2 ) 180

Sum = 7 x 180

Sum = 1260°

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income tax = $2572

social security tax = 13.3% of the profit

= 13.3% of $22,150

= 13.3/100 * 22,150 = $2,945.95

So, the total tax =

2572 + 2,945.95 = $5,517.95

Rounding to the nearest dollar

the total tax = $5,518

The answer is option C. $5,518

Answer:

1248

Step-by-step explanation:

Surface are of a rectangular prism can be found using:

A=2(wl+hl+hw)

Plug in the given values of

l= 12m

w=12m

h=20m

to this equation and you get:

1248

The total value of the prize is $936,000.

The state will need to invest $591,498.96 now at a 5% interest rate to cover the weekly prize payments for 20 years.

The total value of the prize is calculated by multiplying the annual payment by the number of years and is equal to:

=  $900/week x 52 weeks/year x 20 years

= $936,000.

We need to use the present value formula which is: PV = PMT x [1 - (1 + r)^-n] / r

Plugging in the values:

PV = $900 x [1 - (1 + 0.00096154)^-1,040] / 0.00096154

PV = $900 x 657.221075423

PV = $591,498.968.

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Answer:

What impact did the American Revolution have on Haiti? The American Revolution occurred first and in part inspired the Haitian and French Revolutions. ... The Haitian Revolution was the first and only slave uprising that led to the establishment of a free state without slavery and ruled by non-whites and former slaves.

What impact did the Haitian Revolution have on the United States?The Haitian Revolution had many international repercussions. It ended Napoleon's attempts to create a French empire in the Western Hemisphere and arguably caused France to decide to sell its North American holdings to the United States (the Louisiana Purchase)—thus enabling the expansion of slavery into that territory.

Step-by-step explanation:

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The measure of the j of triangle ΔHIJ is given by the law of sine and is given by j = 2.3 inches

The relationship between a triangle's sides and angles is provided by the Law of Sines. Trigonometry's law of sines can be expressed as a/sinA = b/sinB = c/sinC, where a, b, and c are the lengths of the triangle's sides, and A, B, and C are the triangle's respective opposite angles.

Law of Sines :

a / sin A = b / sin B = c / sin C

Given data ,

Let the triangle be represented as ΔHIJ

Now , the equation will be

The measure of i = 2.8 inches

The measure of ∠I = 68°

The measure of j = j

The measure of ∠J = 50°

Now , from the law of sines , we get

a / sin A = b / sin B

Substituting the values in the equation , we get

2.8 / sin ( 68 )° = j / sin ( 50 )°

On simplifying the equation , we get

2.8 / 0.92718 = j / 0.766044

Multiply by 0.766044 on both sides of the equation , we get

j = 3.0198972 x 0.766044

On further simplification , we get

j = 2.3 inches

Hence , the measure of j of triangle is 2.3 inches

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Answer:

28.3

Step-by-step explanation:

A=3.14*3*3=28.27433 rounded to 28.3

Answer:

0.025

Step-by-step explanation:

Mean = 79 ; Standard deviation = 7

P(x ≥ 93)

We obtain the ZSCORE :

Zscore = (x - mean) / standard deviation

x = 93

Zscore = (93 - 79) / 7 = 2

P(Z ≥ 2) = 0.02275

Answer:

Mean, median, mode is 7 and the range is 4

Using proportions, the ratios are given as follows:

a) 9:196.

b) 27:2744.

c) 3:14.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Considering the standard ratio of 3:14 units, we have that:

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Answer:

B) \(4i\sqrt{2}\)

Step-by-step explanation:

\(\sqrt{-2}=i\sqrt{2}\\\sqrt{-18}=i\sqrt{18}=i\sqrt{9*2}=3i\sqrt{2}\\\\\sqrt{-2}+\sqrt{-18}=i\sqrt{2}+3i\sqrt{2}=4i\sqrt{2}\)

Answer:

K=27

Step-by-step explanation:

the answer is 27

Answer:

0.2

Step-by-step explanation:

Answer:

3/8

Step-by-step explanation:

Given that:

Work required to stretch a string:

3 ft = 6ft - lb

The work required to stretch it 9 inches

Given that :

Work(W) = kx

Take the integral of W at 3 fts beyond its natural length;

W = ∫kx dx at 0 to 3

W = k ∫xdx at 0 to 3

W = 6

W = k[x²/2] at x =0 to x = 3

6 = k[3² /2] - 0

6 = k[9/2]

12 = 9k

k = 12/9 = 4/3 = 1.333

Converting inches to feet:

1 inch 0.0833 ft

9 inches = 0.75 ft

W = ∫kx dx at 0.75 to 0

W = 4/3 ∫xdx at 0 to 0.75 = 3/4

W = 4/3[x²/2] at x =0.75 to 0

W = 4/3[(3/4)²/2] at 0.75 to 0

W = 4/3[(9/16) / 2]

W = 4/3 * (9/16 * 1/2)

W = 36/96

W = 6/16 = 3/8 ft - lbs

The perimeters of ABCDE and PQRST are 65 and 91, respectively, and their respective scale factors are 5/7.

The perimeter of a form is its circumference. The interior space of a form is measured by area. The perimeter is the space around a shape's edge. Discover how to calculate the perimeter of various forms by multiplying their side lengths. The whole length of a shape's boundary is referred to in geometry as the perimeter of that shape. The length of each side and edge that surrounds a shape is added to find its perimeter. It is measured in linear distances such as centimeters, meters, inches, or feet.

given

the scale factor in the following format: a: b = 5/7 for ABCDE and PQRST

ABCDE's perimeter is equal to the total of its sides,

which is 65 (10 + 10 + 10 + 20 + 15).

the sum of all the sides of PQRST equals 91.

The perimeters of ABCDE and PQRST are 65 and 91, respectively, and their respective scale factors are 5/7.

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Answer:

B is the answer for the question

The radius of the circle is determined as r = 5.

option B.

The radius of the circle is determined by applying the general formula for circle equation.

(x - h)² + (y - k)² = r²

where;

The given circle equation;

4x² + 4y² = 100

Simplify the equation by dividing through by 4;

x² + y² = 25

x² + y² = 5²

So from the equation above, the radius of the circle corresponds to 5.

r = 5

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If segment Ab I segment BC and m<3=36, m<4 is 72°.

A segment is a part of a line that is defined by two distinct endpoints. It is a set of points that are between two specific points on a line, called the endpoints. The endpoints are also included in the segment. It can be represented by an ordered pair of points (A, B) where A and B are the endpoints of the segment. The length of a segment can be found using the distance formula between the endpoints.

In order to find the measure of angle 4 (m<4), we can use the information given in the problem and some basic angle relationships.

We know that segment AB is congruent to segment BC (Ab = BC) and that angle 3 (m<3) measures 36 degrees.

From this information, we can deduce that triangle ABC is an isosceles triangle. In an isosceles triangle, the base angles are congruent (congruent to each other). Therefore, we know that angle 1 (m<1) and angle 2 (m<2) are congruent.

We can also use the sum of the angles in a triangle. The sum of the angles in a triangle is always 180 degrees. We know that m<1 + m<2 + m<3 = 180 degrees. If we substitute the value of m<3, we get:

m<1 + m<2 + 36 = 180

m<1 + m<2 = 180 - 36

m<1 + m<2 = 144

Now we know that m<1 + m<2 = 144, and that m<1 and m<2 are congruent, so we can write:

m<1 + m<1 = 144

2(m<1) = 144

m<1 = 72

Since m<1 and m<2 are congruent, we know that m<2 = 72.

Finally, we can use the information that angle 4 is the angle opposite to the congruent side. Using the congruent side, we can find the measure of angle 4:

m<4 = m<1 = 72

Therefore, angle 4 measures 72 degrees.

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Answer:

Factor of GCF(Greatest common factor) of given expression = [2 × 3 × m]

Step-by-step explanation:

Given expression;

24m³ + 54m

Find:

The factor of GCF(Greatest common factor) of the given expression.

Computation:

24m³ + 54m

Step 1 :

Write in factor form;

[2 × 2 × 2 × 3 × m × m × m] + [2 × 3 × 3 × 3 × m]

Step 2 :

By taking [2 × 3 × m as common]

[2 × 3 × m][(2 × 2 × m × m) + (3 × 3)]

Step 3 :

[2 × 3 × m][(4m²) + (9)]

Factor of GCF(Greatest common factor) of given expression = [2 × 3 × m]

Answer: the first one is 7/9 and the second one is option 2

Step-by-step explanation:

4+7 = 11

< or> = open dot

The 55th term of the arithmetic sequence is 131.

An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same. The general form an arithmetic sequence is aₙ=a+(n-1)d.

Given that, the nth term of the sequence is aₙ= -1+3(n−1)

Here, the 55th term in the sequence is

a₅₅= -1+3(55-1)

= -1+132

= 131

Therefore, the 55th term is 131.

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Answer:

6/8

Step-by-step explanation:

1/8+1/4+3/8

1/8+2/8+3/8

The length of each side of the wood is 5 centimetres.

Doug has 8 square pieces of wood. Each piece of wood have a side length of s cm. The total area of all 8 pieces of wood is 200 cm².

Hence, using quadratic equation let's find the length of each side of the wood.

Therefore,

8s² = 200

Hence,

8s² = 200

divide both sides of the equation by 8

s² = 200 / 8

s² = 25

s = √25

s = 5 centimetres

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When y = -x² + 15x - 56 then coordinates are is (c) (-7, 0); (8, 0).

Quadratic functions are a type of polynomial function of degree 2, which can be expressed in form f(x) = ax² + bx + c, where a, b, and c are constants, and x is the variable.

The graph of the given quadratic equation y = -x² + 15x - 56 can be plotted using a graphing calculator or any graphing tool. The x-intercepts are the points on the x-axis where the graph intersects the x-axis, i.e., the points where y = 0. By plotting the graph, we can determine the x-intercepts to be (-7, 0) and (8, 0), which correspond to option (c) (-7, 0); (8, 0).

Option (a) and (b) have incorrect x-coordinates for the x-intercepts, and option (d) has both positive x-coordinates for the x-intercepts, which is not correct based on the graph of the given quadratic equation.

Hence, option (c) is the correct answer.

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