Which shows one way to determine the factors of x3 – 9x2 + 5x – 45 by grouping?

x2(x – 9) – 5(x – 9)
x2(x + 9) – 5(x + 9)
x(x2 + 5) – 9(x2 + 5)
x(x2 – 5) – 9(x2 – 5)

Answer: [tex]x=76\°[/tex]

Step-by-step explanation:

By definition the angle formed by the intersection of two chords inside a circle is:

[tex]Angle\ formed\ by\ two\ Chords=\frac{sum\ of\ intercepted\ Arcs}{2}[/tex]

You can observe in the figure that  the angle formed by the intersection of the two chords measures 94°, and the intercepteed arcs are: x° and 112°.

Therefore, you need to substitute these values into the formula and solve for "x to find its value. Then:

[tex]94\°=\frac{x+112\°}{2}\\\\(94\°)(2)=x+112\°\\\\188\°-112\°=x\\\\x=76\°[/tex]

Answer:

The experimental probability is 3% greater than the theoretical probability.

Step-by-step explanation:

We are given the results of flipping two coins with their outcomes and number of times they were tossed.

We are to compare the experimental and theoretical probability of getting HH.

The theoretical Outcomes are: HH HT TH TT

So theoretical probability of getting HH = [tex]\frac{1}{4} \times 100[/tex] = 25%

Total number of outcomes = [tex]28+22+34+16[/tex] = 100

So experimental probability of getting HH = [tex]\frac{28}{100} \times 100[/tex] = 28%

Therefore, the experimental probability is 3% greater than the theoretical probability.

Answer:

B

Step-by-step explanation:

The image is a reflection of the original in the y- axis

The equation of the y- axis is x = 0 → B

Answer:

The correct option is B.

Step-by-step explanation:

The coordinates of polygon ABCDE are A(-2,2), B(-1,2), C(1,1), D(0,-1) and E(-2,1).

The coordinates of polygon A'B'C'D'E' are A'(2,2), B'(1,2), C'(-1,1), D'(0,-1) and E'(2,1).

The relation between preimage and image is

[tex]P(x,y)\rightarrow P'(-x,y)[/tex]

From the given figure it is clear that the figure ABCDE reflected across the y-axis.

If a figure reflected across the y-axis, then

[tex](x,y)\rightarrow (-x,y)[/tex]

The equation of y-axis is x=0, so the given figure reflected across x=0.

Therefore the correct option is B.

Answer:

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

(x₁, y₁) - point

We have the equation:

[tex]y-4=5(x-2)[/tex]

Therefore

m = 5

(x₁, y₁) = (2, 4)

Answer:B The slope is 5 and (2,5) is on the line

Step-by-step explanation:

.

Answer:

V = 18 pi unit ^3

Step-by-step explanation:

Volume of a cylinder is given by

V = pi r^2 h

where r is the radius and h is the height

V = pi * (3)^2 *2

V = pi *9(2)

V = 18 pi unit ^3

The volume of a cylinder is

(Pi) x (radius squared) x (height) .

Using this, you can FIND the volume of any cylinder, even when you don't know it. This one is 18 pi cubic units.

Answer:

6.4

Step-by-step explanation:

8.9 - 2.5 = 6.4

8 - 2 = 6

9 - 5 = 4

there you have it your answer 6.4

Answer:

Raquel should adjust the number of rotations  to 115.81 rotations

Step-by-step explanation:

step 1

Find the circumference of the wheels that are 2.5 cm in diameter

The circumference is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=2.5/2=1.25\ cm[/tex]

assume

[tex]\pi =3.14[/tex]

substitute

[tex]C=2(3.14) (1.25)[/tex]

[tex]C=7.85\ cm[/tex]

step 2

Find the number of rotations

Divide 10 meters by the circumference

[tex]10\ m=1,000\ cm[/tex]

[tex]1,000/7.85=127.39\ rotations[/tex]

step 3

For a diameter of 2.75 cm find how should she adjust the number of rotations so that the robot travels the same distance

Find the circumference of the wheels

The circumference is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=2.75/2=1.375\ cm[/tex]

assume

[tex]\pi =3.14[/tex]

substitute

[tex]C=2(3.14) (1.375)[/tex]

[tex]C=8.635\ cm[/tex]

step 4

Find the number of rotations

Divide 10 meters by the circumference

[tex]10\ m=1,000\ cm[/tex]

[tex]1,000/8.635=115.81\ rotations[/tex]

The answer to this question is 2.

Answer:

4.75

Step-by-step explanation:

Given

f(x)=  (x^2-1)/(x-4)

The average rate of change for the interval a≤x≤b is given by:

Rate of change=  (f(b)-f(a))/(b-a)

In our question,

a=2

and

b=6

So,

f(2)=  ((2)^2-1)/(2-4)

=(4-1)/(-2)

= -3/2

And

f(6)=  ((6)^2-1)/(6-4)

=(36-1)/2

=  35/2

Rate of change=  ( 35/2-(-3/2))/(6-2)

=(35/2+3/2)/(6-2)

=  ((35+3)/2)/4

=(38/2)/4

=19/4

=4.75

The average rate of change is 4.75 ..

Answer:

Average rate of change =4.75.

Step-by-step explanation:

Given function is [tex]f\left(x\right)=\frac{x^2-1}{x-4}[/tex].

Now we need to find the average rate of change of f(x) for [tex]2\le x\le6[/tex].

So plug these values into average rate of change  (ARC) formula.

[tex]ARC=\frac{f\left(b\right)-f\left(a\right)}{b-a}[/tex]

[tex]ARC=\frac{f\left(6\right)-f\left(2\right)}{6-2}[/tex]

[tex]ARC=\frac{\frac{6^2-1}{6-4}-\frac{2^2-1}{2-4}}{4}[/tex]

[tex]ARC=\frac{\frac{36-1}{6-4}-\frac{4-1}{2-4}}{4}[/tex]

[tex]ARC=\frac{17.5-\left(-1.5\right)}{4}[/tex]

[tex]ARC=\frac{19}{4}[/tex]

[tex]ARC=4.75[/tex]

So the final answer is average rate of change =4.75.

Answer:

The correct answer option is 192.

Step-by-step explanation:

We are given the results of a random survey about the preferred service for streaming movies.

We are to find the number of people we would expect to prefer Company B.

Number of people using service B = 32

Total number of people = 125

Number of people expected to prefer Company B = [tex] \frac{32}{125} \times 7 5 0 [/tex] = 192

Answer: Option A

192 people[

Step-by-step explanation:

From the participation survey

[tex]n =75+32+18=125[/tex] people

Among these 125 people, only 32 preferred the company B

Now assuming that this sample is representative of the total population, then the probability that a randomly selected person prefers company B is:

[tex]P =\frac{X_B}{n}[/tex]

Where

[tex]X_B=32[/tex]

[tex]n=125[/tex]

[tex]P =\frac{32}{125}[/tex]

[tex]P =0.256[/tex]

Finally, the expected number of people who prefer company B is:

[tex]E = P * m[/tex]

Where m is the number of people in the total population. [tex]m = 750[/tex]

[tex]E=0.256*750[/tex]

[tex]E=192\ people[/tex]

Answer:

See picture attached below

Step-by-step explanation:

We can easily find the answer to your question, if we plot the equation with a graphing calculator or any plotting tool.

The equation is

y = 3 cos (θ + 20) - 4

See attached picture below

phase_shift = 20

max_amplitude = -1

min_amplitude = -7

Period = 2π

Answer:

The graph is shifted 3 units to the left

Step-by-step explanation:

Answer:

The parent graph will shift 3 units to the right.

Step-by-step explanation:

We are given that there is this parent graph with the equation [tex] y = | x | [/tex] and if we graph [tex] y = | x + 3 | [/tex], what are the changes that will be made to the parent graph to get this.

Since there is addition of 3 units in x, therefore the parent graph will shift 3 units to the right side.

Answer:

The recursively-defined function to describe this situation is:

Step-by-step explanation:

To solve the number of birds that there will be after three years, you must recognize that the function f(0) means the number of birds at time zero, in which the birds are complete (that is, the 14,000 birds), by their part, following the equation provided below we have the following calculation:

So:

Therefore, the final number of birds after three years in decline is 10206.

ANSWER

[tex]y = - \frac{1}{3} x -\frac{4}{3} [/tex]

EXPLANATION

The given line is

[tex]y = 3x + 3[/tex]

The given point is

[tex](-1,-1)[/tex]

The slope of the given line is

[tex]m = 3[/tex]

We found this by comparing

[tex]y = 3x + 3[/tex]

to

[tex]y = mx + b[/tex]

If two lines are perpendicular, then one is the negative reciprocal of the other.

Hence the slope of the required line is

[tex] - \frac{1}{3} [/tex]

Using the point-slope formula or otherwise, we can find the required equation.

[tex]y-y_1=m(x-x_1)[/tex]

We substitute the slope and point to get:

[tex]y + 1 = - \frac{1}{3} (x + 1)[/tex]

[tex]y = - \frac{1}{3} x -\frac{4}{3} [/tex]

Answer:

The definition of present value is the current value of a future sum of money.

Choice A

Step-by-step explanation:

Present value (PV) is the current value of a future streams of cash flows or sum of money at a given expected rate of return by the investor. Future payment streams are discounted at the rate of return. The present value increases with the decrease in the rate of return or the discount rate and vice versa.

Option A is correct,  the definition of present value is the current value of a future sum of money.

Present value refers to the concept of determining the value of a future sum of money in terms of its current worth.

It takes into account factors such as the time value of money and discounting to calculate the value of future cash flows in today's terms.

By discounting future cash flows, the present value represents the amount of money that would need to be invested or received today to achieve the same value as the future sum of money.

Hence, the definition of present value of the current value of a future sum of money.

To learn more on Present value click:

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Answer:

3.3 hours

Step-by-step explanation:

10/3≈3.3

Answer:

You just have to divide 10 by 3 since John takes 10 hours to paint the fence

it would take 3.3 hours for john and his friends to finish painting the fence

Step-by-step explanation:

Answer:

Answer:

x = 2

Step-by-step explanation:

A vertical line has the equation x = a.  This line passes through points with x-coordinate of 2, so the equation is x = 2.

Answer:

5/28 (Decimal: 0.178571)

Step-by-step explanation:

(−2/7) (5/−8)

= −2/7 (5/−8)

=−2/7 (−5/8)= 5/28

Answer: -1 1/2 < -1/4

Explanation: Since the number is negative, -1 1/2 is further to the left on the number line, meaning it has less value.

The relationship between -1 1/2 and -1/4 can be expressed as an inequality. In this case, -1 1/2 is less than -1/4, so the inequality is -1 1/2 < -1/4.

The relationship between -1 1/2 and -1/4 may be written as an inequality. Remember, an inequality indicates that one number is larger or smaller than another. In this case, it shows which negative number, either -1 1/2 or -1/4, is larger. On the number line, a negative number situated to the right is larger than a number situated to the left. So, in terms of value, -1/4 is larger than -1 1/2 as it's less negative. This can be written as:

-1 1/2 < -1/4

.

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Step-by-step explanation:

ΔADG - NO (it's an equilateral triangle)

ΔAFH - NO (it's an equilateral triangle)

ΔBCH - NO (it's an equilateral triangle)

ΔBEH - NO (it's an equilateral triangle)

ΔBFG - YES

ΔCDG - YES

ΔEFG - YES

ΔDFG - NO (it's an equilateral triangle)

All equilateral triangles have the sides equal a√2 (a - length of edge).

ΔBFG has sides a, a√2 and a√3.

From Inverse Pythagorean Theorem:

a² + (a√2)² = (a√3)²

a² + 2a² = 3a²

3a² = 3a²     CORRECT :)

ΔCDG and ΔEFG have sides a, a and a√2.

From Inverse Pythagorean Theorem:

a² + a² = (a√2)²

2a² = 2a²        CORRECT :)

Answer:

Maybe a C if the grade is summative

Step-by-step explanation:

F's are not hard to raise, you're gonna need more than 2 A's to get a "passing grade." Try extra credit!

Answer:

360 km

Step-by-step explanation:

we know that

The scale of the map is

1:1,500,000

That means

1 cm on a map ------> represent 1.500.000 cm in the actual

or

1 cm on a map ------> represent 15,000 m in the actual

or

1 cm on a map ------> represent 15 km in the actual

therefore

In this problem

24 cm on a map-------> represent 24*15=360 km actually

The actual length of the river Severn is 360 kilometers.

To determine the actual length of the river Severn, we need to apply the map scale to the map length. The scale given is 1:1,500,000, which means that 1 unit of measurement on the map corresponds to 1,500,000 of the same units in reality.

The map length of the river Severn is given as 24 cm. To find the actual length, we multiply the map length by the scale factor:

[tex]\[ \text{Actual length} = \text{Map length} \times \text{Scale factor} \] \[ \text{Actual length} = 24 \, \text{cm} \times 1,500,000 \][/tex]

Since the scale is in centimeters to kilometers, we need to convert the map length from centimeters to kilometers before multiplying by the scale factor. There are 100,000 centimeters in a kilometer, so:

[tex]\[ 24 \, \text{cm} = \frac{24}{100,000} \, \text{km} \] \[ 24 \, \text{cm} = 0.00024 \, \text{km} \][/tex]

Now, we multiply this by the scale factor:

[tex]\[ \text{Actual length} = 0.00024 \, \text{km} \times 1,500,000 \] \[ \text{Actual length} = 360 \, \text{km} \][/tex]

Therefore, the actual length of the river Severn is 360 kilometers.

Answer: a=4 or a= −3, so you can use anyone of the answers.

Step-by-step explanation:

Solve Absolute Value.

|2a−1|=7

We know either 2a−1= 7or 2a−1 = −7

2a−1=7(Possibility 1)

2a−1+1=7+1(Add 1 to both sides)

2a=8

[tex]\frac{2a}{2} = \frac{8}{2}[/tex] (Divide both sides by 2)

a=4

OR,

2a−1=−7 (Possibility 2)

2a−1+1= −7+1 (Add 1 to both sides)

2a= −6

[tex]\frac{2a}{2} =\frac{-6}{2}[/tex] (Divide both sides by 2)

a= −3

Therefor the answers are a=4 or a= −3

* Hopefully this helps:) Mark me the brainliest:)!!

Answer:

answerbis 2.25

Step-by-step explanation:

f(x)=9/4

f(x)=2.25

it would be a because of the -4

Answer:

There are two inputs for which the output is 5.

The vertex of its graph is at (0,-2)

Step-by-step explanation:

ANSWER

2nd

4th

5th

EXPLANATION

The given function is

[tex]y = |x| - 2[/tex]

The value of this function cannot be negative: False.

y = |1| - 2=-1

Its graph has a V-shape. This is true because it is the graph of y=|x| shifted downwards by 2 units.

There is only one input for which this function is zero. False

both -2 and 2 will make this function zero.

There are two inputs for which this function is 5. True, x=7 and x=-7

The vertex is (0,-2). This is true because it is the graph of y=|x| shifted downwards by 2 units.

Answer:

1. y=0.35x+35

2. If 979 minutes are used, the total cost will be $377.65 dollars.

Step-by-step explanation:

1. Let $x be the flat monthly fee and $y be the amount of money paid per minute used on the phone.

If a customer uses 210 minutes, the monthly cost will be $108.5, thus

[tex]x+210y=108.5[/tex]

If the customer uses 620 minutes, the monthly cost will be $252, then

[tex]x+620y=252[/tex]

Subtract from the second equation the first one:

[tex]x+620y-(x+210y)=252-108.5\\ \\x+620y-x-210y=143.5\\ \\410y=143.5\\ \\y=0.35[/tex]

Substitute it into the first equation

[tex]x+210\cdot 0.35=108.5\\ \\x=108.5-73.5\\ \\x=35[/tex]

We get the flat fee is $35 and the amount of money per minure used is $0.35. So, the equation of the function is

[tex]y=35+0.35x,[/tex]

where x is the number of monthly minutes used and y is the total monthly of the NextFell plan.

2. When x=979, then

[tex]y=35+0.35\cdot 979=377.65[/tex]

Answer:

50 miles per hour

Step-by-step explanation:

Answer:

Option D. angle S apostrophe

Step-by-step explanation:

we know that

The transformation of the figure is a translation

The rule of the translation is

(x,y)-----> (x-3,y-7)

That means ----> left 3 units and down 7 units

Remember that a translation does not modify the internal angles of the figure as neither the length of their sides

so

∠S=∠S'

Answer:

I believe the answer is C. Point

Step-by-step explanation:

Hope my answer has helped you!

Answer:

The correct answer is option C - point

Step-by-step explanation:

The definition of an angle uses the undefined term : POINT

An angle has two rays that share a common endpoint.

This common point is also referred to as the vertex.

Angles that meet at 90 degrees are called right angles.

Angles that are less than 90 degrees are called acute angles.

Angles that are exactly 180 degrees are called straight angles.