write the quadratic function in standard form (show steps)

Intercept form: y=(x+2) (x-2)

Answer:

Therefore, the possible values of x are all numbers less than 8.

Step-by-step explanation:

To find the value of x, we need to isolate the variable on one side of the inequality.

To do this, we can subtract 36 from both sides of the inequality to get -36 + x < 8 - 36.

This simplifies to -36 + x < -28.

Next, we can add 36 to both sides to get x < -28 + 36, which simplifies to x < 8.

Therefore, the possible values of x are all numbers less than 8.

Answer:

Inequality Form:

x<44

Interval Notation:

(−∞,44)

Step-by-step explanation:

Move all terms not containing x to the right side of the inequality.

The coordinates  of the circumcenter of the triangle with the vertices H(-10, 7), J(-6, 3) and K(-2, 3) is (-4, 9).

A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.

The sum of the angles of a triangle is always 180°

The given points are H(-10, 7), J(-6, 3) and K(-2, 3)

Since, Circumcenter of triangle is equidistant from vertices,

Therefore, H(-10, 7), J(-6, 3) and K(-2, 3) are equidistant from circumcenter O,

Let the coordinate of  O be (x,y).

OH = OJ

(x + 10)² + (y - 7)² = (x + 6)² + (y - 3)²

x² + 100 + 20x + y² + 49 - 14y = x² + 36 + 12x + y² + 9 -6y

8x - 8y + 104 = 0

x - y + 13 = 0   (1)

Also, OH = OK

(x + 10)² + (y - 7)² = (x + 2)² + (y - 3)²

x² + 100 + 20x + y² + 49 - 14y  = x² + 4 + 4x + y² + 9 - 6y

16x - 8y + 136 = 0

2x - y + 17 = 0     (2)

By solving equation (1) and (2),

x = -4

y = 9

The coordinate of the circumcenter is (-4, 9).

Hence, this is the required answer.

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Answer:

  [15-√226, 1] ∪ [29, 15+√226]

Step-by-step explanation:

You want all solutions to |x^2 - 30x - 1| + |x^2 - 30x + 29| = 30.

The equation resolves to a piecewise equation whose domains are delimited by the points where the absolute value arguments are zero.

The argument of the left absolute value function will be zero where ...

  x^2 - 30x - 1 = 0

  x = (-(-30) ±√((-30)² -4(1)(-1)))/(2(1) = 15 ± √226 ≈ {-0.0332964, 30.0332964}

The argument of the right absolute value function will be zero where ...

  x^2 -30x +29 = 0

  (x -29)(x -1) = 0

  x = {1, 29}

In this domain, both absolute value arguments are positive, so the equation is ...

  x^2 -30x -1 +x^2 -30x +29 = 30

  2x^2 -60x +28 = 30 . . . . . collect terms

  x^2 -30x -1 = 0 . . . . . . . . . write in standard form

  x = {15 -√226, 15 +√226} . . . . solutions to the equation

These solutions are not in the domain we have defined for this equation.

In this domain, the left absolute value argument is negative, and the right argument is positive, so the equation is ...

  -(x^2 -30x -1) +(x^2 -30x +29) = 30

  30 = 30

All values of x in this domain (15-√226 ≤ x ≤ 1) are in the solution set.

In this domain, both absolute value arguments are negative, so the equation is ...

  -(x^2 -30x -1) -(x^2 -30x +29) = 30

  -2x^2 +60x -58 = 0 . . . . . . write in standard form

  x^2 -30x +29 = 0 . . . . . . . divide by -2

The solutions to this are x={1, 29}, neither of which is in the domain we have defined for this equation.

In this domain, the left absolute value argument is negative and the right argument is positive. The equation resolves to the same one as for the domain 15-√226 ≤ x ≤ 1: 30 = 30. Hence, all x-values in this domain (29 ≤ x ≤ 15+√226) are part of the solution set.

In this domain, both absolute value arguments are positive, so the equation is ...

  x^2 -30x -1 = 0 . . . . . . . . . write in standard form

  x = {15 -√226, 15 +√226} . . . . solutions to the equation

These solutions are not in the domain we have defined for this equation.

In interval notation, the solution set for the equation is ...

  [15-√226, 1] ∪ [29, 15+√226]

The image of the triangle ΔABC under a reflection across the line l can be obtained my making use of the laws of reflection, and the rules of a reflection transformation, to obtain the triangle ΔA'B'C', with vertices at A'(10, -5), B'(13, -6), and C'(12, -3)

Please find attached the plot of the image of the triangle ΔABC, created with MS Excel

A reflection transformation is one that forms a mirror image of the object across the line of reflection, such that lines joining corresponding points on the pre-image and the image are perpendicular to the line of reflection, and the corresponding points on the pre-image and the image are equidistant from the line of reflection.

Taking the coordinate of the vertices of the triangle ΔABC as A(10, 5), B(13, 6), C(12, 3), and the line l as coinciding with the x-axis, we get:

The coordinates of the image of a point (x, y) following a reflection about the x-axis is the point (x, -y)

Therefor, the coordinates of the vertices of the image of the triangle under a reflection across the line l are;

Please find attached the plot of the image of the triangle ABC under a reflection, across line l, created with MS Excel.

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The investment compounded annually has a higher final value than the investment you described because the annual compound interest rate is higher.

What is compound interest?

Compound interest is a type of interest that is calculated on the initial principal of an investment as well as any accumulated interest. In other words, compound interest is interest that is earned on both the original principal and on the accumulated interest from previous periods.

To compare the investment you described to an investment of the same principal at the same rate compounded annually, we need to calculate the final value of each investment after 18 years.

For the investment you described, the final value can be calculated using the formula:

FV = P(1 + r/n)^(nt)

Where FV is the final value, P is the principal, r is the annual interest rate, n is the number of interest periods per year, and t is the number of years.

Plugging in the values given in the problem, we get:

FV = $6,000(1 + 0.06/6)^(6*18) = $6,000(1.01)^108 = $12,688.80

For the investment compounded annually, the final value can be calculated using the same formula, but with n = 1:

FV = $6,000(1 + 0.06/1)^(1*18) = $6,000(1.06)^18 = $15,848.75

Hence, the investment compounded annually has a higher final value than the investment you described because the annual compound interest rate is higher. The difference in final value between the two investments is $15,848.75 - $12,688.80 = $3,159.95.

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Answer:

The graph of h(x) = 1/7×2^x will be shifted to the left and compressed compared to the graph of f(x). The y-intercept of h(x) will be 1/7, whereas the y-intercept of f(x) is 1. The graph of h(x) will also have a much smaller range than the graph of f(x).

Step-by-step explanation:

The equation of a graph is given by y=f(x). After transformation, the equation changes to y=h(x).

h(x) = 1/7×2^x

h(x) = 1/7 × (2^x)

h(x) = 1/7 * 2^x

h(x) = (1/7)2^x

=> y = (1/7)2^x

=> y = 1/7 (2^x)

Therefore, the graph of h(x) = 1/7×2^x will be shifted to the left and compressed compared to the graph of f(x). The y-intercept of h(x) will be 1/7, whereas the y-intercept of f(x) is 1. The graph of h(x) will also have a much smaller range than the graph of f(x).

Answer:

The graph of h(x) = 1/7×2^x would be the same as the graph of f(x) = 2^x, but it would be vertically scaled down by a factor of 1/7. This means that all the points on the graph of h(x) would have the same x-coordinates as the corresponding points on the graph of f(x), but their y-coordinates would be 1/7 times smaller. For example, the point (1,2) on the graph of f(x) would be located at (1,1/7) on the graph of h(x).

1.7a+0.3a=0.8

2a=0.8

a=0.4

Answer:r4r

Step-by-step explanation:

the answer to the equation is x2=4 or 2-2

Answer:

3.1429

Step-by-step explanation

`(22)/(7)=3.1429` correct to four decimal places.

The required solution is given as x = -4.32 and x = 8.32.

Given that,
To Solve (x-2)²- 40 = 0, where x is a real number.

The process in mathematics to operate and the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

(x-2)²- 40 = 0
(x - 2) = √40
x - 2 = ± 6.32
Taking plus,
x = 6.32 + 2
x = 8.32
Taking minus
x = -6.32 + 2
x = -4.32

Thus, the required solution is given as x = -4.32 and x = 8.32.

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The data set is  the data is univariate and numerical.

What is  set ?

A set comprises elements or members that can be mathematical objects of any sort, including numbers, symbols, points in space, lines, other geometric forms, variables, or even other sets. A set is the mathematical model for a collection of various things.

A set is represented by a capital letter symbol and the number of elements in the finite set is represented as the cardinal number of a set in a curly bracket {…}.

The display summarizes grades on a World History exam.

100,95,90,85,80,75,70,65,60,55, 50

The data is univariate and numerical.

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Answer:

Refer to the photo taken.

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

6=2y+4

2=2y

y=1

a) The linear function used to find the equipment rental fee is of: y = 9x + 20.

b) The cost for 6 hours of training is of: $74.

The linear function is defined considering it's slope-intercept format, given as follows:

y = mx + b.

The coefficients of the function are given as follows:

A soccer training camp charges $9.50 per hour for training, hence the slope is of:

m = 9.

The total fee for 12 hours of training was $128, hence the intercept b is obtained as follows:

128 = 9(12) + b

b = 128 - 108

b = 20.

Hence the function is defined as follows:

y = 9x + 20.

The cost for six hours of training is obtained as follows:

y = 9(6) + 20 = $54.

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Answer:

Dang this is hard

Step-by-step explanation:

Answer:

The latus rectum of an ellipse is a line segment that is perpendicular to the major axis of the ellipse and passes through one of its foci. If the ellipse has a major axis of length 2a, then the latus rectum will have a length of a. Therefore, if the latus rectum is equal to half of the major axis, then the major axis must have a length of 2a, and the latus rectum will have a length of a.

The point (√6, 1) can be the end point of the latus rectum if it lies on the ellipse. To determine if this is the case, you can substitute the coordinates of the point into the standard equation of an ellipse. If the point satisfies the equation, then it lies on the ellipse and can be the end point of the latus rectum.

The standard equation of an ellipse with major axis of length 2a and minor axis of length 2b is:

(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1

Where (h, k) is the center of the ellipse. In this case, we don't know the values of a, b, h, and k, so we can't determine if the point (√6, 1) lies on the ellipse. However, we can use the fact that the latus rectum has a length of a to find the center of the ellipse.

Since the latus rectum is perpendicular to the major axis and passes through the focus, it must also pass through the center of the ellipse. Therefore, the midpoint of the line segment defined by the coordinates (√6, 1) and the center of the ellipse must be the center of the ellipse. The coordinates of the center can be found by taking the average of the x-coordinates and the average of the y-coordinates. In this case, the center of the ellipse will have coordinates:

(x, y) = ((√6 + h) / 2, (1 + k) / 2)

Once you know the center of the ellipse, you can use the standard equation of an ellipse to find the values of a, b, h, and k. Once you have those values, you can determine if the point (√6, 1) lies on the ellipse and can be the end point of the latus rectum.

I hope this helps. Let me know if you have any other questions.

We only need to multiply by 10 to determine the length because we know the length is 10 meters longer than our width is 38.75 meters for L.

The formula for a rectangle's perimeter is

2w + 2L = P where w stands for width and l for length.

The length is 10 meters longer than the breadth, according to this dilemma. So:

L = 10 + w

In our perimeter equation, we may replace L with 10 + w and also 80 in place of P, our perimeter, to solve:

2W + 2(10 + W) = 100

2W + 20 + 2W = 100

4W + 20 = 100

-25. -20

4W = 75

75 /4 =

18.75 meters in W

We only need to multiply by 10 to determine the length because we know the length is 10 meters longer than our width:

18.75 + 10 = 38.75 meters for L.

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Elyse can select from one of 960 cities or a combination of them. if Elyse decides to purchase a round-the-world ticket. From each of the continents she will travel, she will only get to view one city.

In mathematics, there are two additional methods for dividing a set of components into subsets: combination and permutation. The elements of the subset may be mixed in any order. The subset's elements are listed in a permutation in a certain order.

Given,

Elyse is planning to purchase a round-the-world flight. From each of the continents she will travel, she will only get to view one city. The continents she will visit and the number of cities she can visit are displayed in the table below. There are options for every continent.

We utilize permutations and combinations to calculate the number of alternatives Elyse will have.

For every 10 cities in Europe, she can choose from any of the eight cities in Asia. For every eight cities in Asia, she can choose any of the four in Africa. Africa and Australia share a similar situation.

Elyse can select one of these total:

10×8×4×3

960

Elyse can choose one of 960 cities or a combination of them.

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Answer:

E

Step-by-step explanation:

Answer: it is 8 and if you need me to explain tell me.

Step-by-step explanation:

Using the points [tex](40,20)[/tex] and [tex](50,50)[/tex], [tex]m=\frac{50-20}{50-40}=3[/tex]

Answer:

340=10*340 calculated

Answer:

340

Step-by-step explanation:

i know math alot

Answer:

The answer will be 11.78

Step-by-step explanation:

The first step to dividing fractions of 412.3 and 35. Next to find the reciprocal (reverse the numerator and denominator) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. Finally, simplify the fractions if needed. You will get the answer in no time!

Given expression 60% of 25 is equivalent to 0.6 × 25.

What do you mean by percentage?

a % is a quantity or ratio that can be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

Given expression:

60% of 25

⇒ [tex]\frac{60}{100} \times[/tex] 25

⇒ 0.6 × 25

⇒ 15

Therefore, given expression 60% of 25 is equivalent to 0.6 × 25.

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Answer:Select the correct answer from each drop-down menu.

Consider the end behavior of this function, and then complete the statements.

h(x) = -x - 3| +4

As x approaches negative infinity, h (x) approaches

As x approaches positive infinity, h (x) approaches

Step-by-step explanation:

h(x) = -x - 3| +4 x311