The vertices of a rectangle are at (-4,2),(3,2),(3,-2), and (-4,-2). What is the length of the longer side of the rectangle?

The area of the triangle is equal to half the product of the two base lengths (6) multiplied by the height (6), or 18.

Area is a quantity that measures the size of a two-dimensional surface or shape. It is expressed in square units such as square centimetres (cm2), square metres (m2) or square kilometres (km2). Area is used to describe the size of a garden, a house, a room, a city and much more. It can also be used to calculate the amount of material required for a project, such as paint, carpet or tiles. Knowing the area of a shape can help to calculate costs, and to make sure that enough materials are ordered.

The area of the triangle can be determined by using the midpoint formula, which states that the area of an isosceles triangle is equal to half the product of the two base lengths multiplied by the height.

In this case, the midpoint of the triangle is (3,0). This means that the triangle's base lengths are equal to 6 (the difference between the x coordinates of the midpoint and the two endpoints, 3-(-3)) and the height is equal to 6 (the difference between the y coordinates of the midpoint and the two endpoints, 3-(-3)).

Therefore, the area of the triangle is equal to half the product of the two base lengths (6) multiplied by the height (6), or 18.

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The value of sin -1(square root 2/2) is π/4 or 45 degrees.

Inverse sine, also known as arcsine, is a trigonometric function that is the inverse of the sine function. It is denoted as sin^-1(x), where x is a number between -1 and 1.

The inverse sine function is used to find the angle in a right triangle that has a given sine value. In other words, if we know the ratio of the length of the side opposite an angle to the length of the hypotenuse in a right triangle, we can use the inverse sine function to find the measure of that angle.

The inverse sine function returns an angle in radians, which can be converted to degrees if needed. It has a domain of -1 ≤ x ≤ 1 and a range of -π/2 ≤ sin^-1(x) ≤ π/2.

Like other inverse trigonometric functions, the inverse sine function is a multivalued function. This means that for a given value of x, there can be multiple angles that satisfy sinθ = x. To address this, the principal value of the inverse sine function is defined as the angle between -π/2 and π/2 that satisfies sinθ = x.

The inverse sine function has many applications in mathematics, physics, engineering, and other fields. It is used in the calculation of angles in a variety of contexts, such as in the design of structures and in the analysis of wave phenomena. It is also used in calculus and other advanced mathematics courses to solve integrals and differential equations.

To see why, we can use the definition of the inverse sine function, which gives us the angle whose sine is equal to the input value. In this case, we have:

sin -1(square root 2/2) = θ

where sin(θ) = square root 2/2.

We know that the sine of 45 degrees (or π/4 radians) is also equal to square root 2/2. Therefore, we have:

sin(45 degrees) = square root 2/2

Taking the inverse sine of both sides gives us:

sin -1(square root 2/2) = 45 degrees = π/4

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The equation of rational function is f(x) = 3 - (5/2)(x - 5)(x + 1) / ((x + 2)(x + 6))

One possible equation for a rational function with the given properties is:

f(x) = 3 + (k(x + 5)(x - 5)) / ((x + 2)(x + 6))

Here, k is a constant that determines the vertical scale of the function. We choose the factor (x + 5)(x - 5) in the numerator to make the x-intercepts at x = 5 and x = -5. We choose the factors (x + 2) and (x + 6) in the denominator to make the vertical asymptotes at x = -2 and x = -6. We choose the constant term 3 in the equation to make the horizontal asymptote at y = 3.

To determine the value of k, we can use one of the x-intercepts, say x = 5. Substituting x = 5 into the equation and setting the result to 0 (since the function has an x-intercept at x = 5) gives:

0 = 3 + (k(5 + 5)(5 - 5)) / ((5 + 2)(5 + 6))

Simplifying the right-hand side, we get:

0 = 3 + 0 / (7 * 11)

0 = 3

This equation is not true, which means that we have made a mistake somewhere. The mistake is in assuming that the x-intercepts occur at x = 5 and x = -5. Instead, we should have x-intercepts at x = 5 and x = -1, which are the roots of the numerator (x - 5)(x + 1). So we need to adjust the numerator in the equation to (x - 5)(x + 1) in order to get the correct x-intercepts.

The correct equation for the rational function is:

f(x) = 3 + (k(x - 5)(x + 1)) / ((x + 2)(x + 6))

To determine the value of k, we can use the other x-intercept, x = -1. Substituting x = -1 into the equation and setting the result to 0 gives:

0 = 3 + (k(-1 - 5)(-1 + 1)) / ((-1 + 2)(-1 + 6))

Simplifying the right-hand side, we get:

0 = 3 + 6k / 5

Multiplying both sides by 5, we get:

0 = 15 + 6k

Solving for k, we get:

k = -15 / 6 = -5/2

So the final equation for the rational function is:

f(x) = 3 - (5/2)(x - 5)(x + 1) / ((x + 2)(x + 6))

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Answer: Sherry wants to buy at least 2 movies and at least 8 songs, and her gift card has a value of $25. To represent this information as a system of inequalities, we can use the following:

Let x be the number of movies Sherry buys, and y be the number of songs she buys.

The cost of buying x movies is 5.99x dollars, and the cost of buying y songs is 0.99y dollars. Since Sherry's gift card is worth $25, we have the inequality:

5.99x + 0.99y ≤ 25

In addition, Sherry wants to buy at least 2 movies, which means x must be greater than or equal to 2. She also wants to buy at least 8 songs, which means y must be greater than or equal to 8. This gives us the inequalities:

x ≥ 2

y ≥ 8

Therefore, the system of inequalities that represents the number of movies and songs that Sherry can download is:

x ≥ 2

y ≥ 8

5.99x + 0.99y ≤ 25

The answer is (A).

Step-by-step explanation:

The value of A n (B U C) = {q, s, w, y} for the given sets.

A set is a clearly defined group of things in mathematics. We may define several operations on sets and look at their attributes, unlike numbers. An operation in set theory is a task that involves combining different sets in order to create a new set with unique attributes.

The set containing all elements shared by sets A and B is the intersection of the two sets.

The given sets are:

U= {q,r,s,t,u,v,w,x,y,z}, A={q,s,u,w,y}, B={q,s,y,z}, and C= {v,w,x,y,z}

The value of (B U C) depicts all the terms in B and C:

(B U C) = {q, s, y, z, v, w, x}

The value of A n (B U C) depicts all the common terms in set A and B U C:

A n (B U C) = {q, s, w, y}

Hence, the value of A n (B U C) = {q, s, w, y} for the given sets.

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Kevin's error is that he incorrectly identified the vertex of the parabola as (3, 2) instead of (2, 3), which resulted to the parabola opens downward. The correct vertex is at (2, 3) and the parabola opens upward.

You are correct that the vertex of the parabola can be determined using the equation f(x) = a(x - h)² + k, where the vertex is at (h, k). In this case, we have f(x) = -(x-2)² + 3, so the vertex can be found by setting x - 2 = 0, which gives x = 2. Plugging this value into the equation,

we get f(2) = -(2-2)² + 3 = 3, so the vertex is at (2, 3).

However, your reasoning for why h is positive is not correct. The expression x - h represents the horizontal distance from the vertex to any point on the parabola. So if x is greater than h, then the expression x - h will be positive, and if x is less than h, then the expression x - h will be negative. In this case, the vertex is at (2, 3), so we have h = 2. This means that any point to the right of the vertex will have a positive value of x - h, while any point to the left of the vertex will have a negative value of x - h.

Therefore, the correct explanation of Kevin's error is that he incorrectly identified the vertex as (3, 2) instead of (2, 3), and as a result, he also incorrectly concluded that the parabola opens downward. In fact, the parabola opens upward because the coefficient of the x² term, -1, is negative.

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Answer:

90  berries

Step-by-step explanation:

On dividing 153 by 4, we get the value as 38[tex]\frac{1}{4}[/tex].

An algebraic expression is a combination of terms both constants and variables. For example -

2x + 3y + z

3x + y

Given is to find the equivalent value for the division as -

"153 ÷ 4"

On dividing 153 by 4, we can write the result as follows -

{x} = 153/4

{x} = 38.25

{x} = 38[tex]\frac{1}{4}[/tex]

Therefore, On dividing 153 by 4, we get the value as 38[tex]\frac{1}{4}[/tex].

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{Question in english -

What is the remainder when 153 is divided by 4?}

Answer:

A.35°, 114°, 31°.

B.61°,119°,153°,27° and 92°

A. alternates angles are equal;

35°=35°

Vertically opposites angles are equal;

114°=114°

Sum of interior angles of a triangle is 180;

114+35+x=180

x=180-(114+35)

x=31

Picture B.

Corresponding angles are equal;

61°=61°

Sum of angles on a straight line is 180°

61+x=180

x=180-61

x=119°

Corresponding angles are equal;

153°=153°

Sum of angle on straight line is 180;

153+x=180

x=180-153

x=27

Sum of interior angle of a triangle is 180;

27+61+X=180

x=180-(27+61)

x=92

The correct equation of the table is John's

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

John: y = -6x + 510

Jim: y = 6x + 51

From the table (see below), we have the following x and y values

x = 0, 1, 2, 3, 4

y = 510  504  498 492 486

Next, we test the equations:

John: y = -6x + 510

Substitute the known values in the above equation, so, we have the following representation

y = -6(0) + 510 = 510

y = -6(1) + 510 = 504

y = -6(2) + 510 = 498

y = -6(3) + 510 = 492

y = -6(4) + 510 = 486

Jim: y = 6x + 51

y = 6(0) + 51 = 51

y = 6(1) + 51 = 57

y = 6(2) + 51 = 63

y = 6(3) + 51 = 69

y = 6(4) + 51 = 75

The above shows that John's y values corresponds to the table of values added at the end of the equation.

Jim would be correct if the table of values is:

x = 0, 1, 2, 3, 4

y = 51  57  63 69 75

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Complete question

Given the table of values

x    y

0   510

1    504

2   498

3   492

4   486

John says that the function representing the table is y = -6x + 510

Jim says that the function representing the table is y = 6x + 51

Who’s is correct?

0.06 can be expressed as literally 0.06%

Oh okay I see now, as a fraction you would multiply by 100, so it would be 6 / 100

Answer: 6%

Step-by-step explanation:

if you multiply 0.06 by 100 it gets you 6%

The correct statements are -

In statistics, an outlier is a data point that differs significantly from other observations. An outlier may be due to a variability in the measurement, an indication of novel data, or it may be the result of experimental error; the latter are sometimes excluded from the data set.

Given is to identify which of the following statements is most accurate with respect to outliers in this example.

The correct statements are -

Therefore, the correct statements are -

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Answer:

Step-by-step explanation:

18% of $3200.80 = $576.144.

$576.144 is for one month. So, for a year is 12 * $576.144 = $6913.728.

The length of the base of the given isosceles triangle is 18.

What is an isosceles triangle?

A triangle with two equal sides is known as an isosceles triangle in geometry. Both having exactly two sides of equal length and having at least two sides of equal length are acceptable specifications, with the latter version containing the equilateral triangle as an exception. The theorem that describes the isosceles triangle is, "if the two sides of a triangle are congruent, then the angle opposite to them is likewise congruent."

Given the sides of the triangle as 2x+4, x+8 and 5x-2

∠A and ∠B are given as same.

So this is an isosceles triangle.

One of the properties of an isosceles triangle is that the opposite angle of an isosceles triangle will also be equal if the sides are equal. As a result, if two sides are equal, so will the two angles that are across from them.

So 2x + 4 = x + 8

Solving, we get x as

x = 4

So now substituting this value in 5x -2, which is the base of the triangle.

5 * 4 -2 = 20 - 2 = 18

Therefore the length of the base of the given isosceles triangle is 18.

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Answer:

No

Step-by-step explanation:

The y intercept is 7. For it to be proportional it has to go through (0,0).

Answer:

Yes

Step-by-step explanation:

Answer:

y = (-1/5)x + b

Step-by-step explanation:

The given line is y = 5x. To find a line perpendicular to it, we need to use the fact that the slopes of perpendicular lines are negative reciprocals of each other.

The slope of the given line y = 5x is 5, so the slope of the line perpendicular to it is -1/5.

Let (x1, y1) be any point on the line L. Then the point-slope form of the equation of L is:

y - y1 = m(x - x1)

where m is the slope of the line, which in this case is -1/5.

So the equation of line L in point-slope form is:

y - y1 = (-1/5)(x - x1)

To find the equation of line L in slope-intercept form, we need to solve the point-slope equation for y. First, we can simplify the equation to:

y = (-1/5)x + (1/5)x1 + y1

This equation can be rearranged to the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept. In this case:

m = -1/5

b = (1/5)x1 + y1

Therefore, the equation of line L in slope-intercept form is:

y = (-1/5)x + b, where b = (1/5)x1 + y1.

The correct conclusions about the triangle reflections are -

        {y} - axis.

        {x} - axis.

Reflections of graphs involve reflecting a graph over a specific line.

Given is a triangle along with their reflections.

We can conclude the following points regarding the reflected triangles -

        {y} - axis.

        {x} - axis.

Therefore, the correct conclusions about the triangle reflections are -

        {y} - axis.

        {x} - axis.

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Answer:

Step-by-step explanation:

If 20% of the test is made up of 10 open-ended questions, we can set up a proportion to find the total number of questions on the test.

Let x be the total number of questions on the test.

We can write the proportion as:

open-ended questions/total questions = 20%/100%

or

10/x = 20/100

To solve for x, we can cross-multiply to get:

10 * 100 = 20 * x

1000 = 20x

x = 50

Therefore, there are 50 total questions on the test.

Answer:

Step-by-step explanation:

First 3 + 4 is 7. Then for the red paint ( 3 ) , this is written.

= [tex]\frac{3}{7}[/tex] * 1400

Then calculated.

= [tex]\frac{3}{7}[/tex] * [tex]\frac{1400}{1}[/tex] = [tex]\frac{4200}{7}[/tex] = 600 ml for the red paint.

Then its easy to find the blue paint, either the long way ( above ) or...

= 1400 ml - 600 ml = 800 ml for blue paint.

Have a wonderful day! :-)

With Scale factor=4, the area of bigger square is 2304 and perimeter is 192 and for smaller square area=144 unit and perimeter=48.

What is the definition of scaling factor?

The Scale Factor is used to scale shapes of different sizes. Geometry teaches us about different geometrical shapes in two and three dimensions. The scale factor is a statistic that is used to compare statistics that appear comparable but have distinct scales or metrics. Consider two circles with the same shape but different radii.

The scale factor indicates how much bigger or smaller a figure is in comparison to the original figure. You may create an extended or reduced version of any original form by using a scale factor.

Now,

side of smaller square=12

area=12²=144

perimeter=12*4=48

For bigger square, as scaling factor=4

then side=12*4=48

area=48²=2304

perimeter=4*48=192

Hence,

            the area of bigger square is 2304 and perimeter is 192 and for smaller square area=144 unit and perimeter=48.

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Answer:

(2x-1)(3x-4)

Step-by-step explanation:

6x²-11x+4

Now we will split the middle term so when we add the digits it will give the original number back but when we multiply them, it will give the sum of the first and the last digit

6x²-11x+4

6x²-3x-8x+4

Now you can that if we add -3 and -8, we get -11 back but if we multiple them, we get the sum of 6 and 4 (the first and the last digits), which is 24

Now we will simplify the values

3x(2x-1) - 4(2x-1)

Simplifying further, we get

(2x-1) (3x-4) which is the answer

Answer:

-$32

Step-by-step explanation:

Credited = Positive Change

Debited = Negative Change

48-80 = -32

-$32

Distance reading at the start of journey = 12468

Distance reading at the end of the journey = 12845

Distance traveled in the journey = 12845 - 12468 = 377 miles

Cost of petrol per mile = 13p

Cost of petrol for the journey = 13 × 377 = 4901p

Since one pound is one hundred pence, 4901p in pounds will be 4901/100 = 49.01 pounds

Cost of petrol used in the journey is 49.01 pounds

The $500,000 and $350,000 invested by Mario and Luigi, and the $3 million profit from the business in the first year indicates;

a) The amount Luigi made a day is about $3,384.4

b) The amount Luigi made per hour is about $141

Profit is the revenue, less costs, expenses and tax.

The amount Mario invests = $500,000

Amount Luigi invests = $350,000

The ratio in which the profit was split after their first year = Within the same ratio of their initial investments

The amount of profit made by the business = $3 million

The ratio of their initial investment = 500,000 : 350,000 = 10 : 7

Therefore, the ratio in which the profit is split = 10 : 7

The amount Luigi received in a year = (7/(10 + 7)) × 3 = 1235294 2/17

The time unit conversion from year to day is presented as follows;

Number of days in a year = 365 days

The amount Luigi received peer day = (1235294 2/17)/365 = 3384 456/1241

3384 456/1241 ≈ 3384.4

b) The number of hours in a day = 24 hours

Amount Luigi received per hour = (3384 456/1241)/24 = 141 19/1241

141 19/1241 ≈ 141

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Answer:

it depends on how many students?

Step-by-step explanation:

For the given percenatge of total cost, the total value of Gabe's health care coverage for the year is $9,984.

What is percentage?

Percentage is a way of expressing a fraction or a part of a whole as a portion out of 100. It is represented by the symbol "%".

We can start by using the information given to determine the total cost of the health care coverage. Let's call this cost "C". Since Gabe contributes 15% of this cost and pays $28.80 per week, we can write:

0.15C = 28.80

To solve for C, we can divide both sides by 0.15:

C = 28.80 / 0.15

= 192

So the total cost of the health care coverage is $192 per week. To find the total value of Gabe's health care coverage for the year, we need to multiply this weekly cost by the number of weeks in a year.

Assuming there are 52 weeks in a year, we have:

Total value of Gabe's health care coverage = 192 x 52

= 9984

Therefore, the total value of Gabe's health care coverage for the year is $9,984.

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Answer:

it dude

Step-by-step explanation:

use internet

Answer:

Step-by-step explanation:

175

The value of the expression 3 (x - y) is 12

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

x - y = 4

Multiply both sides of the equation by 3

So, we have the following representation

3 * (x - y) = 4 * 3

Evaluate the products

This gives

3 (x - y) = 12

Hence, the soluton of 3 (x - y) is 12

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Answer: Obtuse Triangle

Step-by-step explanation:

63 + 22 = 85

180 - 85 = 95

Since the unknown angle is over 90 degrees, it is an obtuse triangle.