Rewrite 302+40=342 in a different way, using the commutative of addition

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.

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!

Answer:

1

Step-by-step explanation:

6=2y+4

2=2y

y=1

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]

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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The slope of the function is which describes the direction and steepness and the slope for the equation will be m = (-30)

This is the process of finding the rate of change of the value y (dependent variable) of the function changes with respect to that of the variable x (independent variable). The slope itself describes the direction and steepness of the line.

slope = m = rise / run = [tex]\frac{y2 - y1}{x2 - x1}[/tex],

To find the slope , In the case of a straight line y=mx+b, the slope m=Δy/Δx measures the change in y per unit change in x. This can be interpreted as a measure of "sensitivity''; for example, if y=100x+5, a small change in x corresponds to a change one hundred times as large in y, so y is quite sensitive to changes in x.

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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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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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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]

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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There are 7 packs of candy, but only two people can share it equally. 7/2= 3.5. If each person gets 3.5 bags, they both have an equal amount.

Credit to: primebunny24

Answer:

3.1429

Step-by-step explanation

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

The range of Sanders support among millennials in within 90% confidence interval is between 53% and 57%.

Percentage is defined as "out of 100." Similar to fractions and decimals, percentages are being used in mathematics to represent subsets of a whole. When expressing a sum as a percentage, 100 equal components are regarded to make up the entire.

In order to answer this question, a statistical power (90% CI) must be calculated for the percentage of millennials who had a favorable impression of Sanders.

The sample size is n=1,754.

The p-hat, taken from the poll, is

[tex]$\hat{p}=0.55$[/tex]

The estimated standard deviation is equal to:

[tex]$$\sigma_p=\sqrt{\frac{p(1-p)}{N}}=\sqrt{\frac{0.55 * 0.45}{1754}}=0.012$$[/tex]

For a 90% CI, the z-value is z = 1.645.

Then, the confidence interval is

[tex]$$\begin{aligned}& \hat{p}-z * \sigma_p \leq p \leq \hat{p}-z * \sigma_p \\& 0.55-1.645 * 0.012 \leq p \leq 0.55-1.645 * 0.012 \\& 0.55-0.02 \leq p \leq 0.55+0.02 \\& 0.53 \leq p \leq 0.57\end{aligned}$$[/tex]

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The complete question is-

Throughout the 2016 Presidential election primaries, Millennials (those aged 20 t 36 years) consistently supported Senator Bernie Sanders over Secretary Hillary Clinton. According to the 2016 Gallup poll of 1,754 Millenials, 55% had a favorable opinion of Sanders than Hillary Clinton (38%). Calculate the 90% confidence interval for Bernie Sanders. *round to two decimals (Please read the rules for rounding in the preface page xvi. If the number you are rounding is followed by 5, 6, 7, 8, 9 round the number up. If the number is followed by 0,1,2,3,4, you are rounding down, meaning you do not change the number). The 90% confidence interval for Bernie Sanders is to

Answer:

E

Step-by-step explanation:

Yes, the system of inequalities in the graph may be solved using the point (2,4).

A relationship that compares two numbers or other mathematical expressions in an unequal way is known as an inequality in mathematics.  To indicate various types of inequalities, a variety of notations are used:

A > B indicates that an is greater than b.

A and b are not equivalent in either scenario. an is strictly less than or strictly greater than b in certain relations, which are referred to as strict inequalities. Equivalence is disregarded.

An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way, per definition.

The points (4,2) are among the parameters provided.

y<2x+3

y≥-4x+1

By solving these inequalities:

y<2x+3

Let y<0

0<2x+3

-3<2x

x<-3/2

(-3/2,0)

when x<0

y<2(0)+3

y<3

(0,3)

y≥-4x+1

x≥0

y≥0+1

y≥1

(0,1)

y≥0

0≥-4x+1

x≥-1/4

(-1/4,0)

The graphs are drawn using coordinates, and the lines intersect at specific locations (4,2)

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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).

Answer:

4(x-2 +y) = 4x-8+4y

Step-by-step explanation:

You have to apply the distributive law

4(x-2+y) = 4x + 4 (-2) + 4y

Then solve it which equals

4 x +4 (-2) + 4y

Then multiply the numbers

4 (-2) = -8

Which gets you 4x-8+4y

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

a) The range of values that the game operator can use to represent a winner getting a basketball is of: 50 to 100.

b) The percentage of the 10 simulated winners who got a basketball is of: 40%.

The range of values is the set that contains all possible values that can result in a person getting a basketball.

There is a 51% probability of the winner getting a basketball, hence supposing that the last 51 values represent the winner getting a basketball, the range of values is given as follows:

50 to 100.

From the 10 simulated winners, 4 had numbers ranging from 50 to 100, hence the percentage of them who won a basketball is calculated as follows:

p = 4/10 x 100% = 40%.

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

Answer:

It sounds like you want to use the equation h = "-5" - 2 t + 36 to calculate how many seconds it will take for a coin to fall from a balcony to a fountain below. The only problem is that the equation you provided is not correct. The correct equation for the height of an object in free fall is h = -16t^2 + vt + h0, where t is the time in seconds, h0 is the initial height of the object, and v is the initial velocity of the object.

To solve for the time it will take for the coin to fall to a height of 12 feet, you need to know the initial height of the balcony and the initial velocity of the coin. Assuming the initial height of the balcony is 36 feet and the initial velocity of the coin is 0 (since it is not moving when it is released), you can plug these values into the equation to solve for t:

h = -16t^2 + 0 + 36

12 = -16t^2 + 36

-24 = -16t^2

t^2 = 1.5

t = sqrt(1.5)

t = approximately 1.22 seconds

So it will take approximately 1.22 seconds for the coin to fall from the balcony to a height of 12 feet.

Answer:

45 pounds of meat.

Step-by-step explanation:

= 120 ( 3/8)

= 360 / 8

= 45

The least amount possible is $25 and the number of miles is 25 miles

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

Yellow Taxi service charges a $15 flat fee plus $2.50

This means that

Yellow Taxi: y = 15 + 2.5x

For the graph, we have

y-intercept = 10

(x, y) = (0, 10) and (2, 16)

So, the slope is

slope = (y₂ - y₁)/(x₂ - x₁) = (16 - 10)/(2 - 0) = 3

So, we have

Black and White Taxi service: y = 10 + 3x

Yellow Taxi: y = 15 + 2.5x

When he travels for 5 miles, we have

Black and White Taxi service: y = 10 + 3 * 5 = 25

Yellow Taxi: y = 15 + 2.5 * 5 = 27.5

Hence, the least amount possible is $25

This means that we equate the above equations

So, we have

15 + 2.5x = 10 + 3x

Evaluate the like terms

0.5x = 5

Divide

x = 25

Hence, the distance is 25 miles

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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:

Refer to the photo taken.

Step-by-step explanation:

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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The area of the right triangle is 27,000 square units. The result is obtained by using the determinant method.

The area of a triangle in coordinate geometry can be found by using the determinant formula.

[tex]Area \: of \Delta ABC = \frac{1}{2} \left[\begin{array}{ccc}x_{1} &y_{1}&1\\x_{2}&y_{2}&1\\x_{3}&y_{3}&1\end{array}\right][/tex]

The vertices of a right triangle are:

Using the determinant formula, the area of the triangle is

[tex]Area \: of \Delta ABC = \frac{1}{2} \left[\begin{array}{ccc}525 &260&1\\725&260&1\\525&-10&1\end{array}\right][/tex]

Area of ΔABC = 1/2 |525(260-(-10)) - 725(260-(-10)) + 525(260-260)|

Area of ΔABC = 1/2 |525(270) - 725(270) + 0|

Area of ΔABC = 1/2 |141,700 - 195,750|

Area of ΔABC = 1/2 |-54,000|

Area of ΔABC = 27,000 unit square

Hence, the area of ΔABC is 27.000 square units.

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