The senior classes at high school A and high school B planned separate trips to the county fail. The senior class at high school A rented and filled 7 vans and 12 busses with 640 student. High school B rented and filled 12 vans and 6 busses with 456 students. Each van and each bus carried the same number of students. Find the number of students in each van and each bus.

For any triangle created by points u, v, and any point on the line r t other than s, it will be an isosceles triangle.

Isosceles triangle, in geometry, refers to a triangle that has at least two equal length sides. The isosceles triangle sometimes is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length. The triangle which has at least two sides of equal length includes the equilateral triangle as a special case. An isosceles triangle has two sides that are congruent to each other and the third side which is unequal to the other two sides is called the base of the isosceles triangle. The two angles opposite to the equal sides are congruent to each other. Hence, in the given situation, any triangle created by  u, v, and any point on the line r t other than s, will be an isosceles triangle as the sides UR and UV will always be equal.

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(3⁴)² can be written as 3² × 3⁶.

Exponentiation is the operation of doing multiplication repeatedly and it is written in the form aᵇ.

We have to write the given expression (3⁴)² as product of two numbers.

Now, (3⁴)² = 3⁸

We have the property of exponentiation,

aⁿ × aˣ = a^(n + x)

Thus 3⁸ = 3^(2+6) = 3² × 3⁶

Hence, (3⁴)² can be expressed as 3² × 3⁶.

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Answer: -1/32

Step-by-step explanation:

Use the slope formula: y2-y1/x2-x1

Apply that:

9-8/-17-15 = 1/-32 = -1/32

The value of 2[tex]\sqrt{12xy^{2} }[/tex] is 4y[tex]\sqrt{3x}[/tex].

According to the question,

We have the following expression:

[tex]2\sqrt{12xy^{2} }[/tex]

Now, we know that the square root of [tex]y^{2}[/tex] is y.

And the square root of 12 is [tex]2\sqrt{3}[/tex].

(More to know: we have the perfect square root of numbers. For example, the perfect square root of 36 is 6 and the perfect square root of 100 is 10. In the same way, there are perfect cube roots of numbers. For example, the perfect square root of 27 is 3.)

So, by putting the values of these terms in the square root, we have the following expression:

2*y*2[tex]\sqrt{3x}[/tex]

4y[tex]\sqrt{3x}[/tex]

Hence, the value of the given expression after solution is 4y[tex]\sqrt{3x}[/tex].

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Answer:

17/10 (1.7)

Hope this helps!

The reflection of the point (8,0) across the x-axis is (8, 0)

From the question, the point is given as:

Point = (8, 0)

Rewrite this point as

(x, y) = (8, 0)

The transformation is given as

Reflection across the x-axis

Mathematically, we have

(x, y) = (x, -y)

So,we have

Image = (8, 0)

Hence, the image of the reflection is (8, 0)

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Answer:

Step-by-step explanation:

The visitor might be exactly 54 inches or above 54 inches.

The correct property is used to prove the two expressions are equivalent is;

''Commutative property''

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Lara writes the expression 1.5x + 2.75y + 3.

And, Maria writes the expression 3 + 1.5x + 2.75y.

Now,

Since, The commutative property states that;

a + b = b + a

So, Clearly, Here the commutative property used to prove the two expressions are equivalent, as;

⇒ 1.5x + 2.75y + 3 = 3 + 1.5x + 2.75y.

Thu, The correct property is used to prove the two expressions are equivalent is;

''Commutative property''

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Answer: D

Step-by-step explanation: The part of the lawn that receive the new lawn food may also get more shade than other parts of the lawn. And the shade might also cause fewer weeds

Answer:

(4.5 , 6)

Step-by-step explanation:

Finding the midpoints of segment when endpoints are given:

      To find the midpoints, add the x-coordinates and divide by 2 and add the y-coordinates and divide by 2.

(8 , 2) ⇒  x₁ = 8 ; y₁ = 2

 (1 , 10) ⇒ x₂ = 1 ; y₂ = 10

[tex]\sf Mipoint\left(\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2}\right)[/tex]

           [tex]\sf = \left(\dfrac{8+1}{2},\dfrac{2+10}{2}\right)\\\\\\=\left(\dfrac{9}{2},\dfrac{12}{2}\right)\\\\\\=(4.5,6)[/tex]

Answer:

A. 20 + 6L < 60

Step-by-step explanation:

It can't be B. or D. because 20L, not a thing in this problem. That leaves us with A. and C. being our only reasonable answers.

I chose A. because Jenny can't spend more than 60

The probability that tails appears on the next toss is 0.5

Given,

In the question:

If I toss a fair coin five times and the outcomes are TTTTT,

To find the probability that tails appears on the next toss is.

Now, According to the question:

The possible ordered outcomes are listed as elements in a sample space, which is commonly indicated using set notation.

A sequence of five fair coin flips has a sample space that contains all potential outcomes. [tex]2^3[/tex] {H, T}  is the sample of a fair coin toss. {HHHHH, HHHHT, HHHTH, HHTHH, HTHHH,...…TTTTT} .

The probability of a tails result on the next flip is always equal to 0.5 It makes no difference if previous outcomes were {TTTTT} , {HHHHH}  or {THTHT} In each of these and all other circumstances, the probability of the next being tails is still 0.5

Hence,  the probability that tails appears on the next toss is 0.5

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Answer:

C. -10

Step-by-step explanation:

Using the average rate of change formula,

[tex]\frac{-37-(-17)}{6-4}=-10[/tex]

Answer:

Step-by-step explanation:

Tips: All of the figures are prisms so always add prism to end.

2. Rectangular prism. Since it is a rectangle with the 3d dimensions added to it.

3. Hexagonal Prism. Since it is a hexagon with 3d dimensions added to it.

6. Triangular prism. Since it is a triangle with 3d dimensions added to it.

8. Also Triangular prism. Look above.

9. Rectangular prism. Since it is a rectangle with the 3d dimensions added to it.

10. Another Rectangular prism.Since it is a rectangle with the 3d dimensions added to it.

Ps. All the answers you created are correct!

Answer: slope = 0

Step-by-step explanation:

The equation of straight line can be expressed in the form y = mx + b, which is referred to as slope intercept form.

In this equation, m represents the slope of the line, y is the y-coordinate of an arbitrary point along the line and x is the x-coordinate of the same point, and b is the location where the line intercepts the y-axis of the graph.

if y = 16, then the slope of the line, m, must be 0.

y = mx + b

y = (0)x + b

y = b

In other words, the line described by the equation y = 16 is a horizontal line that passes through the y-axis at the point (0,16).

In a group of 50 people, 20 are vegetarian. If two people are selected at random, the expected number of vegetarians is 0.8.

In mathematics, the mean is the average of a set of data, which is calculated by adding all the numbers together and then dividing the result by the total number of numbers. There are various mean types in mathematics, particularly in statistics. Each mean helps to summarize a certain set of data, frequently to help determine the overall significance of a specific data set.

Given,

In a group of 50 people, 20 are vegetarian. If two people are selected at random,

For proportion,

p = x/n

p = 20/50

p = 0.4

n = 2

Mean:

x = np

x = 2 × 0.4

x = 0.8

In a group of 50 people, 20 are vegetarian. If two people are selected at random, the expected number of vegetarians is 0.8.

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x = 1

Step-by-step explanation:

[tex]{ \orange{ \tt{ - 4(x + 1) + 6x}}}[/tex]

Multiply -4 with (x+1) then the Eqⁿ becomes

[tex]{ \orange{ \tt{ - 4x - 4 + 6x}}}[/tex]

Step (1):- [tex]{ \red{ \sf{combine \: like \: terms}}}[/tex]

You can see the like terms i.e. -4x and 6x. Now, add this like terms.

[tex]{ \orange{ \tt{ - 4x + 6x - 4}}}[/tex]

[tex]{ = \orange{ \tt {2x - 4}}}[/tex]

Step (2):- [tex]{ \red{ \sf{ common \: factor}}}[/tex]

Take 2 as common in 2x-4 then,

[tex]{ \orange{ \tt{2(x - 2)}}}[/tex]

[tex]{ \orange{ \tt{2x - 2 = 0}}}[/tex]

[tex]{ \orange{ \tt{2x = 2}}}[/tex]

[tex]{ \blue{ \boxed{ \purple{ \sf{x = 1}}}}}[/tex]

Answer:

Line W's equation is y= 1/2x - 8

Step-by-step explanation:

Answer:

128 square feet

Step-by-step explanation:

2(4)^2 + 4 * 4 * 6 =

= 2 * 16 + 16 * 6 =

= 32 + 96 =

= 128 square feet

The measure of angle KJL from the given figure is 84°.

Given that, 3(m∠LJM)=2(m∠KJL) and m∠KJM=140°.

An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.

Here, m∠KJM=m∠LJM+m∠KJL

Now, (m∠LJM)=2/3 (m∠KJL)

140°= 2/3 (m∠KJL) + m∠KJL

⇒ [2(m∠KJL)+3(m∠KJL)]/3 = 140°

⇒ 5m∠KJL=420°

⇒ m∠KJL=420°/5

⇒ m∠KJL=84°

Hence, the measure of angle KJL from the given figure is 84°.

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A quadrilateral that has 2 separate pairs of equal length sides but is NOT a parallelogram is called a KITE.

What is a quadrilateral?

A quadrilateral is any polygon that has four sides and four vertices. They include;

Properties

What is a kite?

A quadrilateral is a polygon with four sides, commonly known as a kite. Four points on the plane must be "independent" in order for the kite to have four corners. As a result, none of the three are parallel to one another.

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If the store's cost for the incentives was $103.The amount of  each incentive that were given away is: Free Rental  5, Box of popcorn 54.

Let Free Rental = r

Let Box of popcorn  = p

Total incentives:

r+p=59

r= 59-p Equation 1

r×1+p×2=103

r+2p=103 Equation 2

Put the value of r in (eq 2) from (eq 1)

r+2p=103  (eq 2)

59-p+2p=103

59+p=103

p=103-59

p=44

Put the value of p in (eq 1)

r=49-p...........(1)

r=49-44

r= 5

Free Rental = 5

Box of popcorn = 59 -5

Box of popcorn = 54

Therefore 5 and 54 incentive were given.

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Answer: 3 hours 36 minutes

Step-by-step explanation:

You can find out that the cold pipe fills up the pool by 1/4 every hour from the question. if you turn on the cold pipe for 3 hours, the pool would be filled 3/4 before you turn on the hot water. you also can find out that the hot pipe fills up the pool 1/6 every hour. so the next hour will continue to fill up the pool 5/12 until you turn off the water. you only need to fill up the pool 1/4 more so it will take a total of 3 hours and 36 minutes to fill up.

The value of x at which the tangent line approximation will result in an overestimate is given by:

Point of tangency near x = 0.

The possible results for the tangent line approximation are given as follows:

The underestimate or underestimate depend on the second derivative of the function, as follows:

Hence, regarding the concavity, we have that the definitions are listed as follows:

On the graph given by the image at the end of the answer, the concave down point is given as follows:

x = 0.

Hence the correct option is:

Point of tangency near x = 0.

The graph is given by the image at the end of the answer.

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Answer:

3n+9

Step-by-step explanation:

The constant of variation of the distance is 13.5 miles

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

Distance cycled = 9 miles

Number of hours = 2/3 of an hour

From the above parameter, we can calculate the constant of variation

The constant of variation is calculated as

Constant of variation = Distance cycled/Number of hours

Substitute the known values in the above equation

So, we have the following equation

Constant of variation = 9/(2/3)

Evaluate the quotient

Constant of variation = 13.5

Hence, the constant of variation is 13.5 miles per hour

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Step-by-step explanation:

convert equation to y = mx+c:

3x-2y= - 6

3x+6=2y

y=3/2x+6/2

y=3/2x+3

gradient/slope=3/2

y intercept = 3

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Answer:

Step-by-step explanation:

y = mx + b , where "m" is a slope and "b" is a y-intercept

~~~~~~~~~~~~~~

3x - 2y = - 6

3x - 3x - 2y = - 3x - 6

- 2y = - 3x - 6

[tex]\frac{-2}{-2}[/tex] y = [tex]\frac{-3}{-2}[/tex] x + [tex]\frac{-6}{-2}[/tex]

y = [tex]\frac{3}{2}[/tex] x + 3

Slope: [tex]\frac{3}{2}[/tex]

y-intercept: 3

The required solution will be -30 which is expressed as an integer.

To represent this in a general context, we may utilize functions that are referred to in terms of the number tossed.

We know that if the number he gets is an even number, he will get 5 times the number.

As a result, the function for when the integer x is even is f(x) = 5x.

If the number is an odd number, he will lose 10 times the number.

As a result, the function for when the integer x is odd is f(x)=-10x.

Finally, Joe tosses a 3, which is an odd integer, hence the function we will represent is f(x) = - 10x.

⇒ f(3) = -10(3) = -30

Thus, the required solution will be -30 which is expressed as an integer.

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Answer:

Step-by-step explanation:

decrease by 10

Answer:

Step-by-step explanation:

increased by thirty tickets