Factor completely.

a^3x-a^2x

Answer:

(h+9)(h-3)

Step-by-step explanation:

The 6 can be made from factoring -27 into -3 and 9

Answer:

y = 4x - 3

Step-by-step explanation:

The values in the x column increase by 1 each time.

The values in the y column increase by 4 each time.

Therefore, the slope of your equation should be 4.

The y-intercept is -3 when x = 0.

The final equation would be:

y = 4x - 3

I believe that the answer should be 5/6

Answer:

e=-2

Step-by-step explanation:

9e-7e=-11+7

2e=-4

e=-2

The distance covered is. 90 miles

Speed is the distance an object travels in a given time.

This is represented as

Speed = Distance ÷ Time

We can also use the speed formula to calculate the distance or time by substituting the known values in the formula for speed and further evaluating,

Distance = Speed × Time or,

Time = Distance/Speed

To find the distance covered, we find the total speed

= 5 + 10(twice as fast on the trip back)

= 15

Distance = speed x time

= 15mph x 6hours

= 90miles

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We are given the polynomial

Find the roots:

To find the roots of this polynomial, we want to solve the following equation

On the left side, we can factor the polynomial as follows

This leads to the following two equations

with solution x=0, and the equation

by subtracting -2 from both sides , we get

Finally, by dividing both sides by -7, we get

So, the roots of this polynomial are x=0 and x=2/7.

Describe the end behavior:

To describe the end behavior of a polynomial we should first see how the polynomial is written

In here, we see that we have a power of 4 and a power of 3. Consider that the power of 4, as x grows bigger and bigger (or smaller and smaller) the power of 4 will dominate the behavior of the polynomial as x⁴ grow bigger and bigger than x³. So, we can forget the other part and focus on the polynomial

Note that as x is a positive number, then x^4 is also a positive number. So as x grows bigger and bigger, we would get a more negative number, since we are multiplying -7 (a negative number) with a really big positive number (x^4). Then this polynomial will go to - infinity as x grows bigger and bigger.

Also, to understand the end behaviour, we should see how the polynomial behaves as x becomes a really negative number. As before, we can only focus on the polynomial

note that if x is a negative number, x^4 is again a positive number. So, as x becomes more negative (approaching - infinity) the number -7x^4 would once again be a negative number. So, the end behavior as x goes - infinity is also - infinity.

Sketch:

For the sketching, we will use a sketchin software, so the polynomial would look like this

Answer:

Option D

Step-by-step explanation:

Given the function \(g(x)=\frac{-7(x-5)^2(x+6)}{(x-5)(x+5)}\), we see that \((x-5)\) appears in both the numerator and denominator which cancel out to be \(\frac{-7(x-5)(x+6)}{(x+5)}\). This means that there's a vertical asymptote at \(x=-5\) for the denominator to be 0.

Additionally, the limit of the function g(x) as x approaches -5 from the left side is -∞. The limit of the function g(x) as x approaches -5 from the right side is ∞. See the attached graph for a visual of these limits.

In conclusion, option D is correct.

Slack represents the buffer or flexibility available in the project schedule, allowing for adjustments and potential delays without affecting the project's critical path.

In project network analysis, slack refers to the difference between the latest start and earliest start times of an activity. It represents the amount of time that an activity can be delayed without affecting the overall project duration.

The latest start time (LS) is the latest point in time an activity can start without delaying the project completion. It is determined by considering the dependencies and constraints of the project schedule. The earliest start time (ES) is the earliest possible point in time an activity can start based on its dependencies and the project schedule.

By subtracting the earliest start time from the latest start time, we calculate the slack or float of an activity. If an activity has positive slack, it means there is flexibility in its start time, and it can be delayed without impacting the project's critical path or completion date. On the other hand, if the slack is zero or negative, it indicates that any delay in the activity will affect the project's overall duration, making it critical.

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For the given parallelogram \(ABCD\) the measure  \(\angle DAC\) is 29 degrees.

Use the concept of quadrilateral defined as:

A quadrilateral is a four-sided shape, with four vertices, and four angles that are only two-dimensional. The two primary types are concave and convex. There are several subgroups into which convex quadrilaterals can be subdivided, such as trapezoids, parallelograms, rectangles, rhombuses, and squares.

Given that,

ABCD is a parallelogram.

The diagonal of the parallelogram is AC.

The measure of angle CAB is 24°.

The measure of angle ADC is 127°.

To find the measure of angle DAC:

Use the fact that opposite angles in a parallelogram are congruent.

Since the angle CAB is 24°,

We know that \(\angle ADC\) is also 24° as it is an opposite angle.

Since, the sum of the interior angles in a triangle = 180°,

Then find the angle DAC by subtracting the measures of angles CAB and ADC from 180°:

DAC = 180° - CAB - ADC

DAC = 180° - 24° - 127°

DAC = 29°

Hence,

The measure of the angle DAC is 29 degrees.

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The height of prism B based on the information given will b 22cm.

Prisms are transparent optical elements that have at least two flat surfaces and refract light. They are usually made of glass or plastic and are used in a variety of optical applications, including scientific experiments, photography, and surveying. Prisms come in a variety of shapes and sizes, including triangular, rectangular, and pentagonal.

From the information, it should be noted that the surface area of prism A will be

= 60 × 2 + 7+ 384

= 576cm²

The surface area of prism A will be:

48 + 10h + 8h + 6h = 576

48 + 24h = 576

h = 528 / 24

h = 22cm

The height is 22cm

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The right triangular prisms shown have the same surface area. Find the height of prism B.

Prism A:

Height: 24 cm

Base: a right triangle with legs 3 cm and 20 cm

Depth: 6 cm

Prism B:

Height: ?

Base: a right triangle with legs 8 cm and 20 cm

Depth: 3 cm

Both prisms have the same surface area.

Answer:

18 or 9 13/34

Step-by-step explanation:

6 - 1 * 16 + 21 ÷ 3 4 ?

Remember the order of operations

6 - 1 * 16 + 21 ÷ 3/4

6 - 16 + 21  * 4/3

6 - 16 + 28

-10 + 28

18

or

6 - 1 * 16 + 21 ÷ 3 4 ?

remember the order of operations

6 - 16 + 21 ÷ 34

6 - 16 + 21/34

-10 + 21/34

9 13/34

Answer:

80.6176470588

Step-by-step explanation:

Or 80.6

Hope this helps!!

Answer:License plate numbers in certain state consists of seven characters: The first character is digit (0 through 9) The next four characters are capital letters (A through Z) and the last two characters are digits. Therefore; license plate number in this state can be any string - of the form: Digit-Letter-Letter-Letter-Letter-Digit-Digit How many license plate numbers are possible if no digit appears more than once?

Step-by-step explanation: i don't know rm

There is no answer since we cannot take the square root of a negative trigonometry value. As a result, the issue as presented cannot be resolved.

The area of mathematics called trigonometry examines how triangle side lengths and angles relate to one another. The subject first came to light in the Hellenistic era, about in the third century BC, as a result of the use of geometry in astronomical investigations. The area of mathematics known as exact techniques deals with several trigonometric functions and possible computations using them. There are six common trigonometric functions in trigonometry. These go by the designations sine, cosine, tangent, cotangent, secant, and cosecant, respectively (csc). Trigonometry is the study of triangle characteristics, particularly those of right triangles. Consequently, studying geometry entails learning about the characteristics of all geometric forms.  

Trigonometry can be used to resolve this issue. We'll abbreviate the angle between the stairs and the slide as "".

We must first determine the slide's height. The Pythagorean Theorem allows us to perform the following:

Height 2 equals (slide length)/2 - (distance from step bottom to bottom of slide)/2 Height 2 equals 4.2/2 - 4.9/2 Height 2 equals -7.55

There is no answer since we cannot take the square root of a negative value. As a result, the issue as presented cannot be resolved.

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in a stem-and-leaf display: b. one or more digits are used to define each stem, and a single digit is used to define each leaf

A stem and leaf plot, often known as a stem plot, is a method for categorizing discrete or continuous data. Data are organized as they are gathered using a stem and leaf plot. A stem and leaf plot resembles a bar graph in appearance. As each integer throughout the database is divided into a stem and a leaf, thus the name fits.

The last digit of each data point serves as the "leaf" in a stem and leaf plot, which divides the data into numerical points (the leading digit or digits).
Thus, in this case, correct option is:b

in a stem-and-leaf display: b. one or more digits are used to define each stem, and a single digit is used to define each leaf

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Answer:

40x²+2x-21

Step-by-step explanation:

4x × 10x - 4x × 7 + 3×10x - 3 × 7

40x² - 28x + 30x - 21

40x²+2x-21

Answer:

40x^2+2x-21

Step-by-step explanation:

(4x + 3) (10x - 7)

Foil

first 4x*10x = 40x^2

outer  4x*-7 = -28x

inner 3*10x = 30x

last 3 *-7 = -21

Add them together

40x^2 -28x+30x-21

Combine like terms

40x^2+2x-21

Answer: 8 1/8 in

Hope this helps, tell me if thats wrong!

Answer: 0 and -5

Step-by-step explanation:

Answer:

-5 and 0 make the inequality true.

Step-by-step explanation:

-5 and 0 are less than 1, making 1 and 5 greater than one (so 1 and 5 don't apply to this situation)

Answer:

If you use a search engine you will get the right answer.

Step-by-step explanation:

Answer:

-15g+11.1+4k

Step-by-step explanation:

5g - 10g)+4K+(-10g+11.1)

-15g+11.1+4k

add like terms together

Answer:

the answer is number 1

Step-by-step explanation:

\(\cos \theta=\cos \frac{2\pi}{3}=-\cos \frac{\pi}{3}=\boxed{-\frac{1}{2}}\\\\\\\sin \theta=\sin \frac{2\pi}{3}=\sin \frac{\pi}{3}=\boxed{\frac{\sqrt 3}{2}}\)

Calculating the likelihood of experiments happening is one of the branches of mathematics named as probability. The probability that none of the 2 vials have hairline cracks is 0.0565.

The study of probabilities, which exists defined by the ratio of favorable occurrences to probable cases, exists comprehended as probability.

The probability that there won't be any hairline cracks = 13/53

If you choose two vials at random from the delivery

Probability (avoiding hairline cracks) = 13 - 1/53 - 1

Probability (avoiding hairline cracks) = 12/52

To find the chance that neither of the two vials has a hairline crack is

(13/53) × (12/52) = 0.2452 × 0.2307

= 0.0565

The probability that none of the 2 vials have hairline cracks is 0.0565

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Using proportions, it is found that:

A proportion is a fraction of total amount.

In this problem, the total amount divided is R 4625.

For every R4 Andrew gets, both Brendan and Clair gets R3, hence the ratio is 4:3:3, which means that:

Then:

\(A = 0.4(4625) = 1850\)

\(B = C = 0.3(4625) = 1387.5\)

Hence:

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Answer:

y =-5x + 7

Step-by-step explanation:

y = -5x + 4

Slope = -5

Parallel lines have same slope

Slope of the parallel line to this line = -5

(1 , 2)

y -y1 =m(x - x1)

y - 2 = -5(x - 1)

y -2 = -5x + 5

   y = -5x + 5 + 2

  y = -5x + 7

Recalll that the general equation fo the line is of the form y=mx+b where m is the slope and b is the y intercept. Also, remember that if we have two lines y=m1x+b1 and y=m2x+b2, they are perpendicular if and only if m1*m2=-1.

Let's construct the equation of the line we want. Say y=mx+b. So we must find the value of m and b. We are given the line y=5x-4. The slope of this line is 5. Since we want them to be perpendicular, it must happen that

if we divide by 5 on both sides, we get

this means that the equation we want, so far, is

Now, since this line passes through the point (3,8) it must happen that whenever we replace x by 3, y should be replaced by 8. Then we have the equation

Then, if we add 3/5 on both sides, we get

So, the equation of our perpendicular line is

The location of the eagle's nest at 1,284 feet and the diving speed of the eagle of 88 feet/seconds gives;

First part;

The function that gives the height of the eagle after a seconds is presented as follows;

h(a) = 1,284 - 88•a

Second part;

After 7 seconds, the eagles height is; 668 feet

A function maps an input element to one output element or value

First part;

The given parameters are;

Initial height of the eagle = 1,284 feet

Speed at which the eagle can dive, v = 88 feet/second

Required; The eagles height after 7 seconds of diving

Solution;

Height reached, h, which is the same as distance traveled, is given by the equation;

Distance = Speed, v × Time, a

The height reached by the eagle is given by the difference between the initial height and the distance traveled.

Distance traveled by the eagle = 88 × a

Eagles height = Initial height - 88 × a

Therefore, the eagles height, h, after t seconds is given by the equation;

Second part;

The eagle's height reached after 7 seconds

Solution;

The height reached after 7 seconds is found by plugging in a = 7 in the function for the height as follows;

h(7) = 1,284 - 88×7 = 668

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The correct answer is option c as DE/AE=BC/AC

In Mathematics, a slope of a line is the change in y coordinate with respect to the change in x coordinate. The net change in y-coordinate is represented by Δy and the net change in x-coordinate is represented by Δx. Where “m” is the slope of a line. So, tan θ to be the slope of a line.

Given here ΔADE ≈ΔABC and thus  DE/AE=BC/AC

but tanθ = DE/AE=BC/AC where tan θ is the slope of the line thus both the lines have identical slopes.

Hence, The correct answer is option c)  ΔADE ≈ΔABC thus DE/AE=BC/AC Therefore the slope of AD is the same as the slope of AB

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Answer:

1) x=1/2-y/2-3z

2)x= 16/3- 2y/3- 5z/3

3)x= 11/7- 3y/7+ 4z/7

Step-by-step explanation:

isolate the variable, to do that divide each side by the factors that don't contain the variable

Answer:

its the second one

Step-by-step explanation:

Answer:

B. Subtract 28 from both sides

Step-by-step explanation:

2x + 28 = 40

      -28   -28

2x = 12

2x/2 = 12/2

x = 6