Combine like terms to make a simpler expression:
5k+(−2k)−(−1)

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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The answer would equal 1/2x.

9 minutes / 12 customers = 0.75 minutes per customer

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

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.

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.

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

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.

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 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:

Shane's statement is not correct.

Step-by-step explanation:

Shane said that he could write related multiplication and addition sentences for 6+4+3.

No, Shane's sentence does not make any sense as if we add the digits we get = [tex]6+4+3=13[/tex]

But when we multiply the digits we get = [tex]6*4*3=72[/tex]

So, how can he relate these two different things.

Hence, i guess no is the answer.

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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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: The value of x must be 7 units.

Step-by-step explanation:

Since we have given that

ABCD is a parallelogram.

Suppose that AC and BD intersect at o.

So, AO = OC.

And we have given that

AO = 5x

OC = 6x-7

According to question,

[tex]5x=6x-7\\\\5x-6x=-7\\\\-x=-7\\\\x=7[/tex]

Hence, the value of x must be 7 units.

In geometry, for ABCD to be a parallelogram, certain conditions must hold true, such as equal opposite sides or equal opposite angles. The specific value of x would be determined based on the specific properties or relations outlined in your question.

In Mathematics, specifically in geometry, a quadrilateral ABCD is a parallelogram if opposite sides are equal in length (i.e., AB = DC and BC = AD), or if opposite angles are equal (i.e., ∠A = ∠C and ∠B = ∠D), or if one pair of opposite sides are both parallel and equal (i.e., AB || DC and AB = DC).

The value of x would be determined based on the specific properties or relations given in your problem. You would have to set up the equations based on these properties or relations, and solve for x.

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