Which term describes the red curve in the figure below?
• A. Hyperbola
B. Circle
C. Parabola
• D. Ellipse

Answer: 8th graders should be encouraged to read more. This is because they have the least read pages on average. If you calculate the average number of pages read, the 6th-grade students have a total of 25 pages, the 7th-grade students have a total of 34 and the 8th-grade students have a total of 23. It is because of their lowest total number of pages read that the 8th graders would have the most and should be encouraged to read more.

Answer:

Length = Width = 55

Step-by-step explanation:

Perimeter of rectangle = 2(length + width)

Let x = length; let y = width.

perimeter = 2(x + y)

The perimeter must be 220.

2(x + y) = 220

x + y = 110

y = 110 - x

length = x

width = 110 - x

area = length × width

area = x(110 - x)

area = 110x - x²

A = 110x - x²

Take the first derivative of the area function and set equal to zero. Then solve for x.

A' = 110 - 2x

110 - 2x = 0

2x = 110

x = 55

y = 110 - x = 110 - 55 = 55

Answer: Length = Width = 55

The equation that has the solution x = -1 is D. 7x+8 = -6x - 5

To find the solution of an equation, we need to find the value of the variable that makes the equation true. In this case, we need to find the value of x that makes the equation 7x+8 = -6x - 5 true.

We can start isolating the x variable by adding or subtracting the same terms on both sides of the equation.

D. 7x+8 = -6x - 5

13x = -13

x = -1

So the solution of the equation is x = -1

We can check if this is the solution by substituting it back in the equation. If the equation is true, both sides will be equal when x is -1.

7x+8 = -6x - 5

7*-1 + 8 = -6*-1 -5

-7+8 = 6 -5

1 = 1 (true)

Therefore, D. 7x+8 = -6x - 5 has x = -1 as the solution.

The approximate side length of the square is 4.2 units. Hence option B is the correct option.

What is a square?

A square is a regular quadrilateral in Euclidean geometry, which means it has four equal sides and four equal angles. It can alternatively be defined as a rectangle having two neighboring sides of identical length.

Given that the length of half of the diagonal is 3 units.

The diagonals of the square cut each other at a right angle.

The length of OB is 3 units and OC is 3 units.

The △BOC is a right triangle at O.

The hypotenuse of △BOC is BC. The legs of △BOC are OB and OC.

According to the Pythagorean theorem,

OB² + OC² = BC²

3² + 3² = BC²

BC² = 9 + 9

BC² =  18

BC = 3√2

BC ≈ 4.2

The approximate side length of the square is 4.2 units.

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Answer:

b: 59 houses

Step-by-step explanation:

50 + 18% of 50 =

= 50 + 0.18 × 50

= 50 + 9

= 59

Answer:

b

Step-by-step explanation:

Answer:51.96 dollars total

Step-by-step explanation:

go to a smart cauculator and add 8.25%  to 48

Answer:

$56.00

Step-by-step explanation:

8(5 + 2)  Distribute the 8

8(5) + 8(2)

40 + 16

56

Answer:

36

Step-by-step explanation:

The probability of landing on yellow is less than the probability of landing on blue

Probability is the likelihood of a desired event happening.

Since there are one orange, two purple, two yellow, and three blue and the spinner divided into eight equal colored sections.

Thus, we can write the probabilities as follow:

probability of orange = 1/8

probability of purple = 2/8 = 1/4

probability of yellow = 2/8 = 1/4

probability of blue = 3/8

Therefore, the probability of landing on yellow is less than the probability of landing on blue is the true statement

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The diagram relating to the scatterplot for the data is attached.

I put the height of people on the x-axis because this is what I am trying to correlate the arm span to. I put the arm span on the y-axis because it is dependent on height.

I used point (60,61) and (70,72) to draw the line of best fit and to get the equation. First, to get the slope I would use the slope formula of m = 72-61/70-60 or 11/10 to get a slope of approximately 1.1. Then I used (60,61) to get the rest of the equation by plugging it in: y-61 = 1.1(x -60). This becomes y-61 = 1.1x - 66. Add 61 to both sides and the final equation is y = 1.1x – 5.

The slope represents the rate of change arm span based on height. The y intercept is the arm span.

Using points (66,68) and points (70,72) I plug each into the equation y=1.1x-5 to figure each out based on the difference from the actual points and get .4 for (66,68) and 0 for point (70,72) so I would say, based on .4 and 0 for these two points that this is a good line of best fit.

Based on this data, for every inch in height, the arm span increases by 1.1 inches.

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Answer:

20

Step-by-step explanation:

4 ans ten both have 20 in common and it jas ro be the first because the next is like 40

5y is the coefficient of x² in the given polynomial 5x²y.

Polynomial coefficients are the integers preceding a word. Terms are often composed of a number and a variable (for example, 2 x 2 2x2 2x2, where 2 is the number and x is the variable). The coefficient is represented by the number portion. Simply put, it is the leading term's coefficient. The polynomial degree is the largest power of the variable that occurs in the polynomial. The leading phrase is the one with the greatest power of the variable: the term with the greatest degree. The leading coefficient is the leading term's coefficient.

Here,

The coefficient of x^2 in the above polynomial 5x^2y is 5y.

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It depends on the context and the audience. Both describing the solution of a system of linear inequalities in words and showing it using a graph have their own advantages.

An explanation graph is what?

A graph is a representation of the relationship between two variables that are normally measured along one of a pair of axes at right angles.

Describing the solution of a system of linear inequalities in words is often useful when the system is simple and the inequalities are easy to understand. It can be a more straightforward way to explain the solution, especially when the audience is not familiar with reading graphs.

On the other hand, using a graph to show the solution of a system of linear inequalities can be more efficient and effective when the system is more complex and the inequalities are harder to understand. Graphs can provide a visual representation of the solution, which can make it easier for the audience to understand the solution and see how it relates to the original problem. Additionally, it can be easier to find the exact point of intersection between the inequalities by looking at the graph.

Both methods can be useful depending on the situation, so it's best to consider your audience, the complexity of the system, and the goal of your explanation when deciding which method to use.

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On solving the provided question we can say that by percentage  40% of savings  = 40% of 20 = 40/100 X 20 = $8 140% of savings  = 140% of 20 = 140/100 X 20 = $28 his monthly allowance is =  $8 + $28 = $36

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.

Increase in savings $20

by percentage

40% of savings  = 40% of 20 = 40/100 X 20 = $8

140% of savings  = 140% of 20 = 140/100 X 20 = $28

his monthly allowance is =  $8 + $28 = $36

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the answer is  y = 16.

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.

here, we have,

E(-6, y), F(6, 5), G(14, 11), and H(8,-13),

& EF is perpendicular to GH.

now, we get,

The slope of GH is ...

G -H = (14, 11) -(8, -13) = (6, 24) = (Δx, Δy)

slope = Δy/Δx = 24/6 = 4

The perpendicular line through F will have a slope of the negative reciprocal of this, or -1/4.

The point-slope form of the equation can be written as ...

y -k = m(x -h) . . . . . line with slope m through point (h, k)

The perpendicular line through F is then ...

 y -13 = (-1/4)(x -6)

For an x-value of -6, the value of y will be ...

y = (-1/4)(-6 -6) +13 = 12/4 +13 = 16

hence, The value of y so that EF is perpendicular to GH is 16.

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The equation that represents the situation is $160.40 = $100 + $7.55h.

An equation is a statement that consists of numbers or letters and an equal to sign. The amount earned is a function  of the tip, hours worked and the pay per hour.

The form of the equation is:

Total amount earned =tip + (amount earned peer hour)

$160.40 = $100 + ($7.55 x h)

$160.40 = $100 + $7.55h

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The sum of all the internal angle is [tex]$180^{\circ}$[/tex].

The sum of all the internal angle is [tex]$180^{\circ}$[/tex].

[tex]$$\angle A+\angle B+\angle C=180^{\circ}$$[/tex]

1. 34 and 88

[tex]34+88+\angle C=180 \\[/tex]

[tex]122+\angle C=180 \\[/tex]

[tex]\angle C=180-122 \\[/tex]

[tex]\angle C=58^{\circ}[/tex]

2. 45 and 90

[tex]45+90+\angle C=180 \\[/tex]

[tex]135+\angle C=180 \\[/tex]

[tex]\angle C=180-135 \\[/tex]

[tex]\angle C=45^{\circ}[/tex]

3. 10 and 102

[tex]10+102+\angle C=180 \\[/tex]

[tex]112+\angle C=180[/tex]

[tex]\angle C=180-112 \\[/tex]

[tex]\angle C=68^{\circ}[/tex]

4. [tex]$\boldsymbol{x}$[/tex]and 50

[tex]x+50+\angle C=180 \\[/tex]

[tex]\angle C=180-50-x \\[/tex]

[tex]\angle C=(130-x)^{\circ}[/tex]

The complete question is,

Find the measure of the third angle of a triangle given the measures of two angles.

1. 34 and 88

2. 45 and 90

3. 10 and 102

4. x and 50

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Answer:

"Choices A & D": (6 x 10) + (6 x 5). &  (15 x 3) + (15 x 3) are the correct number sentences.

Step-by-step explanation:

 1. Parentheses, ie. (6 + 10) - (11 x 5).

 2. Exponents, ie. [tex]a^{c}[/tex].

 3. Division, ie. 11÷5.

 4. Addition, ie. 12+1.

 5. Subtraction, ie. 10-5.

Number Sentences:

a. (6 x 10) + (6 x 5).

  ii. 6 x 10 = 60.

  iii. 6 x 5 = 30.

  iv. Then we add the products.

  v. 60 + 30 = 90.

  vi. So this choice IS CORRECT.

b. 6 x 10 + 5.

  ii. 6 x 10 = 60.

  iii. Then we add the product to 5.

  iv. 60 + 5 = 65.

  v. 65 DOES NOT equal 90 so this is one of the incorrect number sentences.

c. (3 x 10) + (6 x 5).

  ii. 3 x 10 = 30.

  iii. 6 x 5 = 30.

  iv. Then we add the products.

  v. 30 + 30 = 60.

  vi. 60 DOES NOT equal 90 so this is one of the incorrect number sentences.

d. (15 x 3) + (15 x 3).

  ii. 15 x 3 = 45.

  iii. 15 x 3 = 45.

  iv. Then we add the products.

  v. 45 + 45 = 90.

  vi. So this choice IS CORRECT.

e. 6 + 15.

 i. 6 + 15 = 21.

ii.21 DOES NOT equal 90 so this is one of the incorrect number sentences.

Please let me know if this helped (photo also attached)!!!

Range of function is {5, 4, 3, 2, 1, 0,1} and the function is monotonous.

A function is a mathematical expression that state the relationship between an independent variable and a dependent variable. The value of independent variable is called domain and the value of dependent variable is called range.

given, a function f(x) = √ (x² - 4x +4)

now for every input value of x we will get an output value for f(x).

we select the domain of function as x = {-3, -2, -1, 0, 1, 2, 3}

when we put the x value in the function, we get f(-3) = √[(-3²) - 4×(-3)+4]

                                                                            f(-3) = √25 =5

     similarly, f( -2) = 4

                            f(-1) = 3

                             f(0) = 2

                               f(1) = 1

                            f(2) =0

                           f(3) = 1

the range of function is {5, 4, 3, 2, 1, 0,1}

The range of function indicates that it is neither increasing nor decreasing.

hence the function is a monotonous function.

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Therefore ,perimeter of square photo frame = 63.2 centimeter.

The total length of boundary of a closed geometric shape is called perimeter. Different geometric shape has different formula for determining perimeter. For a square shaped object perimeter is the four times of its side length.

Here,

Area of a square photo frame = 250 square centimeter.

We know, area of a square photo frame = square of side length

if side length = s

area = s²

it is given that area of a square photo frame = 250 cm²

250 cm² = s²

s = √250 cm

s = 15.81 cm

side length = 15.81 cm

formula for perimeter = 4× side length

perimeter of frame = 4×15.81 = 63.24 cm

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The algebraic expression known as a trinomial contains three terms then the trinomials exists a^2 + b^2 + c^2

What is meant by trinomial?

Three non-zero terms make up a trinomial, which is an algebraic expression. The algebraic expression known as a trinomial contains three terms. An mathematical equation called a trinomial has three terms with on-zero coefficients, each separated by a + or - sign. It is a trinomial if three monomials are divided by addition or subtraction.

When a polynomial has three terms, it is referred to as a trinomial. Its general expression is ax² + bx + c, where a and b are coefficients and c is a constant. In order to factor trinomials, you must follow these three easy steps: Calculate the values of b (middle term) and c. (last term).

A. 8x  

Not a trinomial because, it contains only one term.

B. 3y +5y² + y

A trinomial because, it contains three terms.

C. 6x²

Not a trinomial because, it contains only one term.

D.  + x² +1

A trinomial because, it contains three terms.

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Answer: A=16 B=14 C=34

Step-by-step explanation:

The height of the tree is 43.7 feet

Height deals with the length of the tree vertically.  

The given parameters that will help us solve the problem are

The angle of elevation = 63 degrees

The distance from the foot of the tree to the point is 22 feet

Using the trigonometrical ratio

Tan ∅ = Opposite/Adjacent

Tan63 = h/22⁰

Height of the tree = 22*tan63

The height of the tree is equal = 22*1.9626

Height = 43.7 feet

Therefore the tree has a height of 43.7 feet

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Equality means being equal in all aspects such as status, rights irrespective of caste, colour, race, gender, etc.

Now, According to the question:

What is a equality in math?

Equality is a relationship between two quantities or, more generally two mathematical expressions, asserting that the quantities have the same value, or that the expressions represent the same mathematical object. The equality between A and B is written A = B, and pronounced A equals B.

Example of Equality

Two equations that have the same solution are called equivalent equations e.g. 5 +3 = 2 + 6. And this as we learned in a previous section is shown by the equality sign =. An inverse operation are two operations that undo each other e.g. addition and subtraction or multiplication and division.

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The base of an exponent can be simplified by multiplying it by itself as many times as the exponent indicates. If you want to simplify the base of an exponent in an expression, it would be done by raising the base to the power of the exponent using the notation aᵇ = aa...*a (b times)

The base of an exponent is the number that is being multiplied by itself a certain number of times. The exponent is the number indicating how many times the base is being multiplied by itself.

For example, in the expression 2³, the base is 2 and the exponent is 3. This means that 2 is being multiplied by itself 3 times, or 2 * 2 * 2. The simplified form of this expression is 8.

In general, if the base is 'a' and the exponent is 'b' then the simplified form of the expression is 'a' raised to the power 'b' or aᵇ = aa*...*a (b times)

It's also important to note that when the exponent is 1, the expression can't be simplified anymore. For example, 2¹ = 2, where 2 is the base and 1 is the exponent.

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Sam is 25 years old, and Harry is 5 years old.

If we multiply the age of Harry (5) five times, it will give us 25:

5×5= 25

and if we multiply Harry's age three times and then add up ten, it will give us 25:

(5×3) +10 = 25

15 + 10 = 25

25 = 25

F and h, because the log of a quotient is the difference of the log. Logs work that way when you subtract one log from another you can rewrite it as a fraction. The correct is option C.

Logarithm is a power to which a range of should be raised for you to get a few different wide varieties as an example the bottom ten logarithms of a hundred is two because ten raised to the electricity of is one hundred: log a hundred = 2.

There are three common types of logarithms such as:

Therefore logarithm is the mathematical expression used to answer the question.

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Candidate A is likely to receive 8640 voters if all 18000 voters cast their ballot.

Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening is equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.

Given here: The survey results from the sample as

A -240

B-210

C-50

The total number of people surveyed is 500

Now as per the given survey results the voters likely to vote for candidate A is P(A)=240/500

              =12/25

Similarly, the probability that the voters vote for Candidate A and B are

P(A)=210/500

      =21/50

P(B)=1/10

∴ If 18000 voters vote the voters likely to vote for A are

=12/25 ×18000

=8640 voters

Hence, Candidate A is likely to receive 8640 voters if all 18000 voters cast their ballot.

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