On the first day of summer a rainstorm brought 2.29 inches of rain to the area. During the rest of the summer there was 3 times as much rain as on the first day. What was the total number of inches of rainfall for the summer?

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

The equation of a line parallel to y = -7x + 15 that passes through the point (9,-6) is y = -7x + 57.

The question asks for an equation of a line parallel to y = -7x + 15 that passes through the point p(9,-6). Parallel lines have the same slope. Thus, the slope of our new line is also -7. In the form y = mx + b, 'm' represents the slope and 'b' is the y-intercept.  We know the slope and a point on the line, but we don't know the y-intercept. We can plug the point p' s coordinates (9,-6) into the equation and solve for 'b'.

Therefore, -6 = -7(9) + b results in b = 57. So, the equation of the requested line is y = -7x + 57.

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Answer:

-20

Step-by-step explanation:

The two negatives will cancel each other out, so you will have -35 + 15 =  f. If you add 15 to -35, you will have a smaller negative number since you are getting closer to 0.

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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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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In right triangle LMN are given the lenghts of two legs. You can find the value of  [tex]\tan x[/tex] and [tex]\tan y[/tex] and then estimate the difference y-x.

1.

[tex]\tan x=\dfrac{LM}{LN}=\dfrac{14.1}{19.1}=\dfrac{141}{191},\\ \\x=\arctan \dfrac{141}{191}\approx 36.4^{\circ}.[/tex]

2.

[tex]\tan y=\dfrac{LN}{LM}=\dfrac{19.1}{14.1}=\dfrac{191}{141},\\ \\y=\arctan \dfrac{191}{141}\approx 53.6^{\circ}.[/tex]

Then

[tex]y-x=53.6^{\circ}-36.4^{\circ}=17.2^{\circ}.[/tex]

Answer: correct choice is D

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.

To multiply the given radicals, first simplify the radicals to get like terms, then multiply coefficients and like radicals separately. The result of multiplying 4√3 × 10√12 × √6 × √2 is 480√3.

The task is to multiply the following radical expressions: 4√3 × 10√12 × √6 × √2.

First, let's simplify the radicals where possible. We know that √12 can be broken down into √4×√3, because 4 is a perfect square and 4×3=12. Thus, √12 simplifies to 2√3. Now, our expression looks like: 4√3 × 10×2√3 × √6 × √2.

Next, we multiply the coefficients (numbers outside the radicals) and the like radicals separately:

Simplifying further, we can pair √6 and √2 to get √12, which we already simplified earlier into 2√3. Thus, 3 × 2√3 = 6√3.

Finally, we multiply the coefficient we got from our first step (80) by the simplified radical (6√3) to get the final answer: 480√3.

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.

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

Final answer:

The two trains traveling towards each other at 85 mph and 95 mph respectively, will meet after 1.2 hours, as they have a combined approach rate of 180 mph.

Explanation:

To find out how long it will take for two trains to meet when they start 216 miles apart, moving toward each other at speeds of 85 miles per hour and 95 miles per hour, respectively, we can add their speeds to determine their approach rate. The sum of their speeds is the relative speed at which they are moving towards each other. Therefore, we calculate:

85 mph + 95 mph = 180 mph.

This means that the two trains cover 180 miles of the distance between them in one hour. To find the total time until they meet, we divided the total distance by their approach rate.

216 miles ÷ 180 mph = 1.2 hours.

Therefore, it will take 1.2 hours for the two trains to meet.

9 minutes / 12 customers = 0.75 minutes per customer

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

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.'

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.