7n2 + 8n − 12
A) (7n + 6)(n − 2)
B) (5n − 8)(n + 10)
C) Not factorable
D) (7n − 6)(n + 2)

The student took 28 classes at the dance academy.

The question is asking us to find out the number of dance classes the student took. This is a problem of linear equation where the total cost is the sum of the one-time registration fee and the total cost for the classes attended.

We are given the total amount paid, $687, and we know that $24 is charged per class plus a one-time fee of $15. We can represent this information in a linear equation [tex]687 = $15 + $24x[/tex], where x is the number of classes the student took.

Subtract the one-time fee from both sides of the equation you get $672 = $24x. Finally, solve for x by dividing by 24 you get x = 28. This means the student took 28 classes at the dance academy.

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Final answer:

To express 42 + 24 differently, one might use the commutative property (24 + 42), break the numbers into tens and ones (40 + 20 + 2 + 4), or use rounding to aid mental addition (60 + 6). Each method simplifies the problem while reaching the same correct answer.

Explanation:

Another way to express 42 + 24 could be by rearranging the numbers to use commutative property of addition or by changing one or both of the numbers into a sum that makes mental addition easier. For example:

24 + 42 - Which uses the commutative property of addition, meaning that numbers can be added in any order and the result will be the same.

40 + 20 + 2 + 4 - Here we break down both numbers into tens and ones and add them separately.

60 + 6 - By rounding 42 up to the nearest ten (40) and adding 20, you get 60 plus the remaining 2 and 4 to add up to 6.

Each method provides a different way of reorganizing the original problem to potentially simplify the adding process or to suit mental math strategies. Remember, arithmetic has specific rules, but there's flexibility in how we apply them to reach the same correct answer. This shows the beauty and versatility of mathematics.

Final answer:

To express 42 + 24 differently, one can use the commutative property (24 + 42), factor out common numbers (2(21 + 12), or round and adjust (60 + 6), showcasing the variety of methods mathematics provides to reach the same answer.

Explanation:

The question asks for an alternative way to express the sum 42 + 24. One strategy is to use properties of numbers and operations to simplify and find patterns that make it easier to perform calculations in our head. For instance, using commutative property of addition, we can restate 42 + 24 as 24 + 42. Moreover, we can utilize the distributive property by factoring out a common number to make the addition easier, such as expressing it as 2(21 + 12) since both 42 and 24 are divisible by 2, or 6(7 + 4) if you notice that both numbers are divisible by 6. It's also possible to round numbers up, perform the addition, and then adjust back, for example: (40 + 20) + (2 + 4) which simplifies to 60 + 6. Each of these methods provides a different path to the same correct answer, exemplifying that mathematics offers numerous ways to solve a problem, which ultimately reinforces our understanding.

The reason for statement 2 of the two-column proof is : Definition of bisect ( optionC).

Since angle RPS is bisected, the two angles in which are formed will be equal. Bisecting an angles means dividing the angle into two equal part.

line PQ bisects RPS into two;

angle QPS = 61°

this means that RPQ is also 61°. Thus it is an acute angle. This is because 61° is an acute angle.

An acute angle is an angle that is less than 90°

Therefore, The reason for statement 2 of the two-column proof is : Definition of bisect

Answer:- A) is the right answer.[tex]7\times10^{10}[/tex] is 50 times larger than [tex]13\times10^{8}[/tex]

Explanation:-

To estimate the number of times [tex]7\times10^{10}[/tex] is larger than [tex]13\times10^{8}[/tex]

Let [tex]7\times10^{10}[/tex] is larger than [tex]13\times10^{8}[/tex]  by n times.

then [tex]7\times10^{10}[/tex]  [tex]=n\times13\times10^{8}[/tex]

[tex]\Rightarrow\ n=\frac{7\times10^{10}}{13\times10^{8}}\\\\\Rightarrow\ n=\frac{7\times10^{10-8}}{13}.......[by\ law\ of\ exponents\ \frac{a^m}{a^n}=a^{m-n}]\\\\\Rightarrow\ n=\frac{7\times10^2}{13}\\\\\Rightarrow\ n=\frac{7\times100}{13}\\\\\Rightarrow\ n=\frac{700}{13}=53.84\approx50[/tex]

[as 53.84 is near to 50 by rounding off it to the nearest ten it becomes 50]

Thus [tex]7\times10^{10}[/tex] is 50 times larger than [tex]13\times10^{8}[/tex]

The linear equation for the axis of symmetry for the parabola y = -2x² - 16x - 27 is x = -4.

A parabola is a U-shaped curve this is drawn for a quadratic function,

f(x) = ax² + b x + c. The graph of the parabola is downward (or opens down), when the price of a is much less than 0, a < 0. The graph of the parabola is upward (or opens up) when the value of a is more than 0, a > 0.

Consider the parabola: y=−2x²−16x−27.

The axis of symmetry of a parabola is a line that divides the parabola into two mirror images.

For a parabola in the form y = ax² + b x + c, the axis of symmetry is a vertical line that passes through the vertex of the parabola.

The x-coordinate of the vertex is given by -b/(2a), so the equation of the axis of symmetry for the given parabola is :

x = -(-16)/(2×-2) = -4.

Therefore, the required axis of symmetry for the parabola is x = -4.

Learn more about the parabola here:

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Answer:

Option D correctly describes the key features of the graph of the function.

Explanation:

To analyze the given function [tex]\( f(x) = 4(0.5x) + 1 - 3 \)[/tex], let's break it down:

1. The function is in the form [tex]\( f(x) = mx + b \)[/tex], where [tex]\( m \)[/tex] represents the slope and [tex]\( b \)[/tex] represents the y-intercept.

2. The coefficient of [tex]\( x \), \( 0.5 \)[/tex], represents the slope of the line. Since it's positive, the line is increasing from left to right.

3. The y-intercept occurs when [tex]\( x = 0 \)[/tex]. Substituting [tex]\( x = 0 \)[/tex] into the function, we find [tex]\( f(0) = 4(0.5 \times 0) + 1 - 3 = 1 - 3 = -2 \).[/tex] So, the y-intercept is (0, -2).

Now, let's consider the options:

A. Y-intercept of (0, −1), starts up on the left, gets closer to y = −3 on the right - Incorrect.

B. Y-intercept of (0, −1), starts down on the left, gets closer to y = −3 on the right - Incorrect.

C. Y-intercept of (0, 1), starts up on the left, gets closer to y = −3 on the right - Incorrect.

D. Y-intercept of (0, 1), starts down on the left, gets closer to y = −3 on the right - Correct.

The expected value of buying a $1 ticket out of a lottery of 1000 tickets where the prize for the one winning ticket is $1000 is approximately -$0.999. This means that, on average, you can expect to lose about $0.999 for each ticket you buy.

To calculate the expected value, we need to multiply each possible outcome by its probability and then sum them up. In this case, the possible outcomes are winning $1000 with probability 1/1000 and losing $1 with probability 999/1000. So, the expected value is: ($1000 × 1/1000) + (-$1 × 999/1000) = -$0.999

Therefore, the expected value is approximately -$0.999. This means that, on average, you can expect to lose about $0.999 for each ticket you buy.

To find the fifth number in a sequence of 5 consecutive integers with a sum of 265, you can use the formula for the sum of an arithmetic series. The fifth number is 53.

To find the fifth number in a sequence of 5 consecutive integers where the sum is 265, we can use the formula for the sum of an arithmetic series. The formula is: Sum = (n/2)(2a + (n-1)d), where n is the number of terms, a is the first term, and d is the common difference. In this case, we have n = 5, so:

Since we are looking for the fifth term, we can use the formula a + (n-1)d = 53 to solve for the fifth number:

Substituting the value of d back into the equation a + 4d = 53, we can find the value of a:

Therefore, the fifth number in the sequence is a + 4d = 0 + 4(13.25) = 53.

11

Scientific and standard notation conversion for a variety of numbers.

1. The number 2,000 can be written in scientific notation as 2 × 103. In standard notation, it remains as 2,000.

2. The number 91,007,500 can be written in scientific notation as 9.10075 × 107. In standard notation, it remains as 91,007,500.

3. The number 1.0395 × 109 is already in scientific notation. In standard notation, it would be 1,039,500,000.

4. The numbers 4, 100, and 5 are already in standard notation. In scientific notation, 4 can be written as 4 × 100, 100 can be written as 1 × 102, and 5 can be written as 5 × 100.

0.026 can be written in scientific notation as 2.6 × 10-2. In standard notation, it remains as 0.026.

0.0007017 can be written in scientific notation as 7.017 × 10-4. In standard notation, it remains as 0.0007017.

8.9 × 106 is already in scientific notation. In standard notation, it would be 8,900,000.

4.41 × 102 is already in scientific notation. In standard notation, it would be 441.

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it is false for APEX

Answer:

The given statement is False.

Step-by-step explanation:

We have been given the function [tex]f(x)=(\frac{1}{2})^x[/tex] and the domain of this function is all real numbers greater than 1.

We know that the domain is the set of x values for which the function is defined.

We can see that for any real values of x, the function is defined. Therefore, the domain of the given function is the set of all real numbers.

Therefore, the given statement is False.

Final answer:

To convert the compound statement into symbolic form using propositional logic, we assign P to 'You work out', Q to 'You practice your free throws', and R to 'You are a starting player', resulted in the symbolic representation \((P \land Q) \rightarrow R\).

Explanation:

To write the compound statement 'If you work out and practice your free throws in basketball, then you will be a starting player.' in symbolic form, you can use propositional logic symbols. Let's define the simple statements first:

P: You work out.

Q: You practice your free throws in basketball.

R: You are a starting player.

The compound statement combines these simple statements using the logical connective 'and', symbolized by \(\land\), and the implication 'then', symbolized by \(\rightarrow\). The symbolic form of the compound statement is:

\((P \land Q) \rightarrow R\)

This reads as 'If P and Q are true, then R will also be true.'

9 minutes / 12 customers = 0.75 minutes per customer

4 customers x 0.75 minutes per customer = 3 minutes total for 4 customers

To find the standard form of a line with a given slope and a point, use the point-slope formula, plug in the values, and rearrange into Ax + By = C.

To enter an equation in standard form using the given information that the slope is -6 and the point (7, 5) is on the line, we start by using the point-slope formula:

y - y1 = m(x - x1)

Where (x1, y1) is the given point and m is the slope. Plugging in the values, we have:

y - 5 = -6(x - 7)

Now we distribute the slope on the right side:

y - 5 = -6x + 42

Adding 5 to both sides to solve for y gives us:

y = -6x + 47

To get the standard form, Ax + By = C, we add 6x to both sides:

6x + y = 47

This is the equation in standard form

divide  4 1 /4 cups by 2

4/2 = 2

1/4 / 2 = 1/8

 so 2 1/8 cups are needed

an  x intercept is where the blue line meets both the x and y coordinates given

 in this graph the only one of the 4 answers that the blue line meets is (-1,0)

Denise is constructing A square.

Note: A square has all sides equal.

We already given two vertices M and N of the square.

And another edge of the square is made by from N.

Because a square has all sides of equal length, the side NO should also be equal to MN side of the square.

Therefore, Denise need to place the point of the compass on point N and draw an arc that intersects N O, using MN as the width for the opening of the compass. That would make the NO equals MN.

Therefore, correct option is :

D) place the point of the compass on point N and draw an arc that intersects N O, using MN as the width for the opening of the compass.