What is the simplified form of x plus 4 over x squared minus 3x minus 10⋅x minus 3 over x squared plus x minus 12? (6 points)


1 over the quantity x minus 3 times the quantity x plus 4


1 over the quantity x minus 3 times the quantity x plus 2


1 over the quantity x plus 4 times the quantity x minus 5


1 over the quantity x plus 2 times the quantity x minus 5

Answer:

volume of sphere if radius is divided by 2 is 1/8 of volume of sphere with r radius.

Step-by-step explanation:

The formula to find volume of sphere is:

Volume of sphere  = 4/3 π r^3

if radius is divided by 2 i.e r/2

Volume of sphere if r/2 = 4/3 π (r/2)^3

                                      = 4/3 π r^3/8

                                      =  (4/3 π r^3) / 8

                                      = (Volume of sphere 1)/8

So, volume of sphere if radius is divided by 2 is 1/8 of volume of sphere with r radius.

Answer:

The volume become 1/8 th of the initial volume

Step-by-step explanation:

Points to remember

Volume of sphere V = 4/3(πr³)

Where r is the radius of sphere

It is given that radius of sphere is r/2

To find the effect in volume

Here r = r/2

V = 4/3(πr³)

V = 4/3(π(r/2)³)

  = 4/3(πr³/8)

  = 1/8( 4/3(πr³)

New volume = 1/8(V)

Answer:

10(512) = 5,120

8f = 5,120

f = 640 cycles per second

The answer is:

Anna will need 27 posts.

To calculate how many post does she need to place at the corners and every 2 feet around, we need to calculate the perimeter of the garden plot.

So, we can calculate the perimeter of the garden plot (rectangle) using the following formula:

[tex]Perimeter=2height+2width[/tex]

We know that:

[tex]height=9ft\\width=18ft[/tex]

Then, calculating the perimeter of the garden plot, we have:

[tex]Perimeter=2height+2width[/tex]

[tex]Perimeter=2*9ft+2*18ft=18ft+36ft=54ft[/tex]

Now, calculating how many post she will need, we have:

[tex]No.Post=\frac{Perimeter}{DistanceBetweenPost}\\\\\frac{54feet}{2feet}=27posts[/tex]

Hence, we have that Anna will need 27 posts.

Answer:

the answer is 14 cents

Step-by-step explanation:

12 time 4 equal 48 ( this is converting the feet into inches)

48 divided by 6.72  to get 0.14

Answer:

$0.14

Step-by-step explanation:

There are 12 inch in 1 foot.

You are given 4 foot. Find the amount of inch in 4 feet.

1 ft x 12 in/ft = 12 in

4 ft x 12 in/ft = 48 in

There are 48 in. in 4 ft. Divide 48 from $6.72

(6.72)/48 = $0.14

$0.14 is the price per inch.

~

Answer:

16.6 in³

Step-by-step explanation:

Given the ratio of similarity = 2 : 3, then

the ratio of volumes = 2³ : 3³ = 8 : 27

let the volume of prism A be x then by proportion

[tex]\frac{x}{8}[/tex] = [tex]\frac{56}{27}[/tex] ( cross- multiply )

27x = 448 ( divide both sides by 27 )

x = 448 ÷ 27 ≈ 16.6 ( to 1 dec. place )

Prism A has a volume of approx 16.6 in³

Answer:

x=3

Step-by-step explanation:

25x+57+x=45x

26x+57=45x

57=19x

x=57/19

x=3

ANSWER

x=3

EXPLANATION

Use the exterior angle theorem:

25x°+(57+x)°=45x°

Group similar terms,

57=45x-25x-x

19x=57

Divide both sides by 19.

x=3

Answer:

A. Obtuse

F. Scalene

Step-by-step explanation:

There are two ways to classify a triangle:

by angles:

Obtuse - has one angle that is greater than 90°

Right - has one angle that is 90°

Acute - has all angles less than 90°

and by side lengths:

Equilateral - all sides are equal

Isosceles - two sides are equal

Scalene - no sides are equal

In this triangle, there is an obtuse angle (A. Obtuse).

∡ = 132°, which is greater than 90°.

There are no equal sides (F. Scalene).

6 ≠ 7 ≠ 11.9

Answer:

≈ 2.1 m

Step-by-step explanation:

Given

v = [tex]\sqrt{9.8d}[/tex] ← substitute v = 4.5

4.5 = [tex]\sqrt{9.8d}[/tex] ← square both sides

4.5² = 9.8d

20.25 = 9.8d ← divide both sides by 9.8

d = 2.0663 ≈ 2.1 m ( nearest tenth )

Answer:

±(√35 i)

Step-by-step explanation:

[tex]\pm\sqrt{-35}[/tex]

We need to solve the above equation using the imaginary unit i.

We know i= √-1

Solving

±√-35 =±( √-1 √35)

         = ±(√35 i)Since 35 = 5*7 or 35*1 it cannot be further simplified

So our answer is ±(√35 i).

Answer:

Step-by-step explanation:

Sigma notation is:

n

∑ ak

k=1

The n on top is the number of terms.  ak is the expression for the kth term.

Let's look at the first one.  The series is:

-2+4+-8+...+64+-128

There's two things to notice.  One, the sign changes back and forth between + and -.  Two, the magnitude doubles with each next term.  Therefore:

ak = (-2)ᵏ

Next we need to find the number of terms.  -128 is the last term, so:

128 = 2ⁿ

n = 7

So the answer is:

7

∑ (-2)^k

k=1

Now the second one.  Notice the numerators are all 1 and the denominators are all perfect squares.  Therefore:

ak = (1/k)²

The last term is 1/100, so n = 10.

So the answer is:

10

∑ (1/k)²

k=1

Now the last one.  Notice that each term is 5 plus the previous term.  This is an arithmetic series.  So we can say:

ak = 4 + 5(k-1)

ak = 4 + 5k - 5

ak = 5k - 1

The last term is 49, so:

49 = 5n - 1

n = 10

So the answer is:

10

∑ (5n-1)

k=1

Answer:

B.

Step-by-step explanation:

If you look at the graph carefully, the graph/line is starting to fall at (0,45) which is the starting point or dropping point.

I hope this helped =)

Answer:

There is not an outlier

Step-by-step explanation:

All the numbers are close together and do not have a big difference from each other

The outlier in the given series of numbers (20, 21, 23, 23, 25, 29, 32, 33) is the number 20, as it deviates significantly from the rest of the data points.

In the series given (20, 21, 23, 23, 25, 29, 32, 33), the term that appears to be an outlier is the number 20. An outlier in a number series is a number that is significantly different from the other numbers in that series. It deviates significantly from the rest of the data points. Most of the numbers in the series are in the twenties or thirties, but 20 is distinctly less than the rest. Therefore, in the given number series, 20 is the outlier.

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Answer:

The last expression is correct

Step-by-step explanation:

We have been given the following expression for simplification;

[tex]4^{4}*4^{-9}[/tex]

The bases of the two expressions are the same. They are both equal to 4. When multiplying numbers with the same base, we simply add their exponents. In this case our exponents are;

4 and -9

adding them we have;

4 + (-9) = -5

The simplified expression thus becomes;

[tex]4^{-5}=\frac{1}{4^{5}}[/tex]

Answer:

equal angles and vertical angles

Step-by-step explanation:

we know that

Vertical Angles are the angles opposite each other when two lines cross. They are always equal

In this problem

∠14=∠16 -----> by vertical angles

therefore

The answer is

equal angles and vertical angles

Answer:

Vertical angles, equal angles

Step-by-step explanation:

when a transversal passes through two lines, then,

Angles formed in the same side and inside the two lines are same side interior angles.

Angles that are formed on opposite sides of the transversal and inside the two lines are alternate interior angles.

Angles formed on opposite sides of the transversal and outside the two lines are alternate exterior angles.

Angles with the same relative position at each intersection are corresponding angles,

While, when two lines intersect each other then the opposite angles formed called vertical angles,

supplementary angles : When the sum of two angles are 180°,

Right angles : angle that has the measurement of 90°,

Equal angles : angles with the same measurement.

Now, vertical angles are always equal angles,

Also, when two parallel lines are cut by the same transversal then the pair of alternate interior angles, alternate exterior angles, corresponding angles are always equal.

Hence, by above definitions it is clear that,

∠16 and ∠14 are vertical and equal angles.

Answer: The answer is B the second option. I just took the test.

Step-by-step explanation:

Answer:

2nd Option  is correct.

Step-by-step explanation:

Given Functions:

[tex]y=\frac{-1}{2}x^2+4[/tex]

[tex]y=\frac{-1}{2}x^2-2x+2[/tex]

We need to find which conclusion supported by graph.

From the given, it is clear that both graph intersecting only at one point.

Also, One graph is translation of another graph.

So, the equation [tex]\frac{-1}{2}x^2+4=\frac{-1}{2}x^2-2x+2[/tex] has only one solution.

Therefore, 2nd Option  is correct.

Answer:

25

Step-by-step explanation:

The absolute value function always returns a positive result which represents the magnitude of the input.

The magnitude of -25 is 25.  The magnitude of 25 is 25.

Thus, |−25| = 25.

ANSWER: 25

Every time you see that sign ( | | )is the number without a sign example: |-56|= 56 ; |-37282|=37282.

Answer:

Step-by-step explanation:

378,903,970.

Answer:

The dot will land on red 74.8% of the time

Step-by-step explanation:

To start off we need to find the Area of the whole circle. We can calculate this by using the Area of a Circle Formula on the larger circle measurement.

[tex]A = \pi r^{2}[/tex]  .... A is Area, and r is radius.

[tex]A = \pi 8.01^{2}[/tex]

[tex]A = \pi *64.1601[/tex]

[tex]Aw = 201.56in^{2}[/tex] .... rounded to the nearest hundredth

So now we know that the area of the WHOLE circle is [tex]201in^{2}[/tex]. Now we need to find the area of the inner white circle.

[tex]Aw = \pi 4.02^{2}[/tex]

[tex]Aw = \pi *16.1604[/tex]

[tex]Aw = 50.77in^{2}[/tex] .... rounded to the nearest hundredth

Now that we have the area of the whole circle and the area of the smaller inner circle we subtract them to find the area in red.

[tex]Ar = 201.56in^{2} - 50.77in^{2}[/tex]

[tex]Ar = 150.79in^{2}[/tex]

Lastly, we divide the Area in Red by the total Area to get the percentage of time the dot will land on red.

[tex]d = \frac{150.79in^{2} }{201.56in^{2} }[/tex]

[tex]d = 0.748 * 100[/tex] .... multiply by 100 to turn decimal into a percent.

[tex]d = 74.8[/tex]

Finally, we can see that the dot will land on red 74.8% of the time.

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

To find the percent of the time that the point will be in the shaded region of the larger circle, we need to find the ratio of the area of the shaded region to the area of the larger circle and convert it to a percentage.

To find the percent of the time that the point will be in the shaded region, we need to find the ratio of the area of the shaded region to the area of the larger circle. Let's say the radius of the larger circle is R, and the radius of the smaller shaded circle is r. The area of the larger circle is πR2 and the area of the shaded circle is πr2. So the ratio is πr2 / πR2 = r2 / R2. The percentage is then (r2 / R2) * 100. Round this to the nearest tenth of a percent to get the final answer.

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Answer: x = 75.7 cm

Step-by-step explanation:

In the given picture, we are given a right triangle.

The length of hypotenuse = 85 cm

Angle opposite to x= [tex]63^{\circ}[/tex]

Using trigonometry,

[tex]\sin\theta=\dfrac{\text{Side opposite to }\theta}{\text{Hypotenuse}}\\\\\Rightarrow\ \sin63^{\circ}=\dfrac{x}{85}\\\\\Rightarrow\ x=85\times\sin63^{\circ}\\\\\Rightarrow\ x=85\times0.89100652418\\\\\Rightarrow\ x=75.7355545553\approx75.7\ cm[/tex]

Hence, the value of x = 75.7 cm

Answer:

x=1

y=2

Step-by-step explanation:

Hope this helps (3

Answer:

Table 2

For every input, there is one output.

Why table 1 is not a function:

The input 5 has two outputs, 3 and 2

Why table 3 is not a function:

The input 1 has two outputs, 2 and 3

Why table 4 is not a function:

The input 4 has three outputs, 2, 3, and 4

Hope this helps!

Answer: Hey i am single and ready to mingle

Step-by-step explanation:

I need someone

The 18-inch wrench will generate more torque and make it easier for Marge to loosen the lug nuts because torque is the product of the force applied and the lever arm, and the longer wrench provides a larger lever arm.

The wrench that Marge should use to generate more torque and make her job easier when changing a flat tire is the one that is 18 inches long. This is because torque (au) is calculated as the product of the force (F) applied and the distance (r) from the pivot point, with the equation torque (au) = force (F) × lever arm (r). Since the wrenches provide the lever arm and assuming the same force is applied to both, the longer wrench will provide greater torque due to a larger r.

For example, if Marge exerts a force of 100 newtons, the torque generated by each wrench would be:

12-inch wrench: au = 100 N × 0.305 m = 30.5 N.m (since 12 inches is approximately 0.305 meters)

18-inch wrench: au = 100 N × 0.457 m = 45.7 N.m (since 18 inches is approximately 0.457 meters)

The 18-inch wrench generates 45.7 N.m of torque, compared to 30.5 N.m with the 12-inch wrench, thus the 18-inch wrench will make loosening the lug nuts easier.

Answer:

  - 52/15 your welcome

Step-by-step explanation:

Answer:

28 biscuits.

Step-by-step explanation:

Belinda has 10 cups of flour

She uses 3 cups to make a loaf of bread

She uses [tex]\frac{1}{4}[/tex] cup of the remaining flour for each biscuit she wants to make.

There are 10 - 3 = 7 cups of flour remaining

[tex]\frac{1}{4}[/tex] cup of flour makes -> 1 biscuit

7 cups of flour will make;

7 × 1 ÷  [tex]\frac{1}{4}[/tex]  = 7 × 4 = 28 biscuits

Answer:

Step-by-step explanation:

The formula of a midpoint:

[tex]\left(\dfrac{x_1+x_2}{2};\ \dfrac{y_1+y_2}{2}\right)[/tex]

We have (2, 3) and (12, 3).

Substitute:

[tex]x=\dfrac{2+12}{2}=\dfrac{14}{2}=7\\\\y=\dfrac{3+3}{2}=\dfrac{6}{2}=3[/tex]

Answer: (7,3)

Step-by-step explanation:

See the paper attached. (:

Answer:

3x10^4/2x10^0

Step-by-step explanation:

just took the test!!

The expression that Jenna should use in the process is area of floor/area of sticker

The surface area is defined as the sum of area of the faces.

Area of rectangle = lengh * width

Determine the area of the rectangular sticker

The area of the rectagular sticker = 2in * 1in

The area of the rectagular sticker = 2 square inches

Determine the area of the bedroom floor

Area of the floor = 20ft * 10ft

Area of the floor = 200 square feet = 28800 square in

Determine the number of stickers needed

Number of stickers needed = area of floor/area of sticker

Number of stickers needed = 28800/2
Number of stickers needed = 14400 stickers

The expression that Jenna should use in the process is area of floor/area of sticker

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Answer:

160

Step-by-step explanation:

e.g. 5×8 --> 10×16 =160

4×10 --> 8×20 =160

2×20 --> 4×40 =160

160

When you double both the length and width, you are multiplying by 2 twice. Whatever you do to one side of an equation, you have to repeat on the other.

l * w = 40; This is the original equation.

2l * 2w = 40 * 2 * 2; This is when you double the length and the width.

The 2 * 2 on the end can be simplified.

2l * 2w = 40 * 4

Now, simplify 40 * 4.

2l * 2w = 160

So, when you double both the length and the width, you multiply the area by 4, making the area 160.

Answer:

D. 20%

Step-by-step explanation:

percent change = (new number - old number)/(old number) * 100%

The new number is the increased price, $42, and the old number is the original price, $35.

percent change = ($42 - $35)/($35) * 100%

percent change = ($7)/($35 min) * 100%

percent change = 0.20 * 100%

percent change = 20%

Since the percent change is a positive number, it is a percent increase.

The percent increase was 20%.

Answer: D. 20%

Answer:

1650

Step-by-step explanation

1320/12=110

110x15=1650

Answer:

m = 6.57 and n = -2

Step-by-step explanation:

To answer this question you will covert the thickness of a dollar to standard notation and then compare the two values.

0.07 =compared to 0.0043 = 0.0657

0.0657 = 6.57 x 10^-2

A quarter is thicker than a dollar by 6.57 x 10^-2.

m = 6.57 and n = -2

m = 6.57 and n = -2

Step-by-step explanation:

To answer this question you will covert the thickness of a dollar to standard notation and then compare the two values.

0.07 =compared to 0.0043 = 0.0657

0.0657 = 6.57 x 10^-2

A quarter is thicker than a dollar by 6.57 x 10^-2.

m = 6.57 and n = -2