At a college, the cost of tuition increased by 10%. Let b represent the former cost of tuition. Use the expression b+0.10b for the new cost of tuition.

a. Write an equivalent expression by combining like terms.



b. If the cost increases by 10%, you can multiply the former cost by %.

The exterior angle of the given triangle is X. The value of the angle X is 55°.

Triangle -

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes.

types of triangle

The exterior angle of a triangle is equal to the sum of two interior opposite angles.

X = 21° + 34°

X = 55°

The exterior angle of the given triangle is X. The value of the angle X is 55°.

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Answer:

The measures of <2 and <8 are 124 degrees

Step-by-step explanation:

<2 is congruent to <4 by the Vertical Angles Theorem, and <4 is congruent to <8 by the corresponding angles theorem. <2 is congruent to <8 by the Transitive Property so we get <2 is congruent to <8, and it follows that m<2 equals m<8 by the definition of congruence. We can substitute <2 and <8 with 11x+3 and 13x-19 respectively, so we get 11x+3=13x-19. Solve for x, and we get that x=11, and plug in 11 for x into 11x+3, 11(11)+3=121+3=124.

The measure of angle ∠2 is 124.

The measure of angle ∠8 is 124.

The angles that are in the same position on a given two parallel lines intersected by a transversal line are called the corresponding angles.

Corresponding angles are always equal.

We can also have alternate angles which are always equal.

We can also have alternate interior and exterior angles which are equal.

The angles on the same side make upto 180 degrees

We have,

∠2 and ∠8 are alternate exterior angles.

This means,

∠2 = ∠8

We can write it as,

11x + 3 = 13x - 19

3 + 19 = 13x  - 11x

22 = 2x

x = 11

Now,

∠2 = 11x + 3 = 11 x 11 + 3 = 121 + 3 = 124

∠8 = 13x - 19 = 143 - 19 = 124

Thus,

The measures of ∠2 and ∠8 are 124.

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Answer:

1. EFG= 90°

2.GDH=90/2=45°

3.FEG=90/2=45

4.DHG=90°

Answer:

The difference is 10$

Step-by-step explanation:

tell me if you need an explanation

Answer:

y = -4/5x + 2 & y = -2/7x - 4/7

Step-by-step explanation:

(4x) - 5y = -10                                             (2x) - 7y = 4

Move 4x on the same side as -10            Move 2x on the same side as 4

-5y = 4x -10                                                -7y = 2x + 4

Divide -5 to both sides                              Divide -7 by both sides

That should isolate the y for both equations.

4x/-5 = -4/5x....-10/-5 = 2                            2x/-7 = -2/7x....4/-7 = -4/7

y = -4/5x + 2                                                y = -2/7x - 4/7

If that wasn't the answer to your question, I'm sorry.

But if it did, then your welcome.

Answer:

I would have to say that the length of AC is 22.5

We need to check if lines ℓ and k are parallel. For two lines to be parallel, they must have the same slope and different y-intercepts.Let's compare the given lines:Line ℓ: y = 34x + 6Slope of line ℓ = 34Line k: y = 34x - 7Slope of line k = 34We see that the slope of lines ℓ and k is the same (34), which means that they could be parallel.

However, we still need to check if they have different y-intercepts. Line ℓ: y = 34x + 6 has a y-intercept of 6.Line k: y = 34x - 7 has a y-intercept of -7.So, lines ℓ and k have different y-intercepts, which means they are not parallel. Therefore, the correct answer is b) No.In slope-intercept form, the equation of a line is y = mx + b, where m is the slope of the line and b is its y-intercept. In this case, both lines have the same slope of 34 (the coefficient of x). The y-intercepts are different (+6 for line l and -7 for line k). Thus, the lines are not parallel.

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The answer is option a) Yes. Lines ℓ and k are parallel to each other.

The two distinct lines defined by the following two equations in slope-intercept form are:

Line ℓ: y = 34x + 6

Line k: y = 34x - 7

To determine if the lines are parallel, we need to compare their slopes since two non-vertical lines are parallel if and only if their slopes are equal.

Both lines are in slope-intercept form, so we can immediately read off their slopes:

Line ℓ has a slope of 34, and line k has a slope of 34.

Both the lines ℓ and k have the same slope of 34.

Hence, the answer is option a) Yes. Lines ℓ and k are parallel to each other.

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The term that best describes the analysis conducted by the researcher is trend analysis.

We have,

Trend analysis involves studying data over time to identify patterns or trends.

In this case,

The researcher recorded the lengths of fish caught in the lake over several years and observed that the average length has been decreasing by approximately 0.25 inches per year.

By recognizing this consistent decrease over time, the researcher has conducted a trend analysis to understand the long-term pattern in the data.

Thus,

The term that best describes the analysis conducted by the researcher is trend analysis.

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A. Another way to find the area of a trapezoid is by summing the areas of two triangles.
B. Area is the measurement of the amount of space occupied by a 2-dimensional shape.

A. Yes, there is another way to conceptualize the formula for the area of a trapezoid. Instead of using the formula A = (b1 + b2) * h / 2, you can think of it as the sum of the areas of two triangles. First, you find the area of the top triangle by multiplying the base by the height and dividing by 2.

Then, you find the area of the bottom triangle using the same method. Finally, you add the two triangle areas together to get the total area of the trapezoid. This approach helps visualize how the trapezoid can be divided into simpler shapes.

B. The concept of area refers to the measure of the amount of space occupied by a 2-dimensional shape. It quantifies the extent or size of a region or surface. Area is typically measured in square units, such as square inches, square feet, or square meters. It helps us compare and analyze the sizes of different shapes or regions.

For example, when calculating the area of a rectangle, we multiply the length by the width. Understanding the concept of area is important in various fields, including mathematics, physics, architecture, and design.

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The distance between the 1st and the 3rd poles is 140 meters.

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.

ESB poles are placed along a road 70 meters apart.

So the distance between two poles is 70 meters.

So the distance between 1 and 3rd will be = 2*70 =140metets

Hence, the distance between the 1st and the 3rd poles is 140 meters.

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Complete Question:
Esb poles are placed along a road 70 metres apart. What is the distance between the 1st and the 3rd poles?

By using the given domain and range, we will see that the false statements are:

What we know about the function f(x) is:

The domain is: -10 ≤ x ≤ 20

The range is: -40 ≤ f(x) ≤ -10

Which statements are false:

1)  f(0)= 0

This is false, because the maximum value of the range is -10, so f(0) can't be equal to zero.

2. f(1) = 13

Same reasoning than above, 13 is outside of the range.

3. f(-15) =- 20

The smallest value on the domain (possible inputs) is -10, so the input -15 is not in the domain.

4)  f(-9) = 88

88 is outside the range of the function, so this is false.

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Therefore the solution for this question is  the unit price of each pair of gloves is $7.99.

One of the four fundamental arithmetic operations, or the process by which two or more numbers are added together to create a new number, is division. Multiplication, addition, and subtraction round out the list of operations.

Here,

The cost of 6 pairs of gloves  = $47.94

Now, the unit price = Price per unit of the given item

Let x be the unit price of the glove

thus

x=47.94/6

x=7.99

or it can be written as price of glove=$7.99

Therefore, Unit price of the glove = $7.99

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Scales on a wall, change of units conversion

1 inch = 4 1/2 feets

7 1/8 inches = ?

First convert to fractions

(4 + 1/2) • ( 7 + 1/8) =

apply distributive law ( a+b)•(c+d)= ac + ad + bc + bd

then length of wall= 4•7 + 4/8 + 7/2 + 1/16

= 28 + 8/16 + 56/16 + 1/16

= 28 + 64/16 + 1/16

= 28 + 4 + 1/16

= 32 + 1/16

lenght is 32 and 1/16 feet

Answer:

35

Step-by-step explanation:

15-5+(5^2)

10+25

35

Answer:

50 percent

Step-by-step explanation:

100 percent divided by 6 (the amount of data) is 16 2/3.

Each number represents 16 2/3 percent.

3 of the numbers are either 2 or 9.

16 2/3x3=50.001

The final answer is a 50% probability.

I think

On solving the provided question, we can say that the required probability is = 13/204.

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

probability of 1st card =  1/4

since the card is not replaced

total number remaining cards = 51

second card 13/51

the required probability is = 13/204

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The cost of one pair of shoes is $8.

The cost of one shirt is $12.

2a + b = 32 equation 1

2a + 3b = 48 equation 2

Where:

Subtract  equation 1 from  equation 2

2b = 16

b = 16/2

b = $8

Substitute for b in equation 1

2a + 8 = 32

2a = 32 - 8

2a = 24

a = 24 / 2

a = $12

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The Future Value after 7 years of the vending machine that produces a constant annual income of 6000 dollars and is invested at an annual rate of 5% compounded continuously is approximately 50,292 dollars.

How we can determine future value?

To find the Future Value (FV) after 7 years of a vending machine that produces a constant annual income of 6000 dollars and is invested at an annual rate of 5% compounded continuously, follow these steps:

The Future Value after 7 years of the vending machine that produces a constant annual income of 6000 dollars and is invested at an annual rate of 5% compounded continuously is approximately 50,292 dollars.

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Answer:

42.875

Step-by-step explanation:

V=BxHxW

3 1/2 =3.5

3.5 x 3.5 x 3.5

=42.875 cubic in.

The total cost for 10 hours of work would be 25 + 50(10) = 525.

Cost is the monitorial associated with the purchase of production of food or service if can include the prices of material of which is over it and other expenses that are related to the production of the code of service cost is a major fraction of when deciding whether to purchase a product something as it is and indicator of the value of the product of sound service.
The marginal cost of producing 5 items can be calculated using the equation C(x)=1300+4x/10. The marginal cost is the cost associated with producing one additional item. To calculate the marginal cost, we can plug in x=5 into the equation.

The equation in slope-intercept form for cost, c, after h hours of service is c = 25 + 50h.

The total cost for 8 hours of work would be 25 + 50(8) = 425.

The total cost for 10 hours of work would be 25 + 50(10) = 525.

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Answer:

\(f(x)=x^3-7x^2-6x+72\)

Step-by-step explanation:

\(f(x)=a(x-p)(x-q)(x-r)\\\\f(x)=1(x-6)(x+3)(x-4)\\\\f(x)=(x^2-3x-18)(x-4)\\\\f(x)=x^3-4x^2-3x^2+12x-18x+72\\\\f(x)=x^3-7x^2-6x+72\)

This is because \(x=6\) is the solution to \(x-6=0\), \(x=-3\) is the solution to \(x+3=0\), and \(x=4\) is the solution to \(x-4=0\).

Answer:

false

true

true

false

Step-by-step explanation:

The probability of a majority of the advisory board opposes to funding is 0.352

Two events are said to be independent of each other if the probability that one event occurs in no way affects the probability of the other event occurring .If A and B are independent events then the probability that they all occur is given by P(A) x P(B)

Here, the opinions of the three students on the board are independent the probability is 0.4 that each opposes the funding of interest groups

Mjority of the board opposes can be when two or more members oppose it.

P(ABC) = P(A) x P(B) x P(C)

P(ABC) = 3 (0.6) x 0.4 x 0.4 + 0.4 x 0.4 x 0.4

= 0.288 + 0.064

= 0.352

Therefore, the probability of a majority of the advisory board opposes to funding is 0.352

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