What is the factored form of 8x24-27y6?
o (8x-27y2) (2x¹+xy+3y*)
ọ (2x³− 3y²)(4x¹6−6x³y² +9y4)
0 (2x³-3y²) (4x¹6 +6x³y² +9yª)
(8x-27y²) (2x¹6-Bxy+3y4)

Okay, here are the steps to solve this problem:

* Jen earns a weekly salary of $250

* She gets a 10% bonus on any sales

* In the past 4 weeks, she sold $312 worth of phones and accessories

* 10% of $312 is $31.20

* So in 4 weeks, her bonus would be $31.20 * 4 = $124.80

* Her weekly salary is $250

* So in 4 weeks, her salary would be $250 * 4 = $1000

* Her total income over 4 weeks is $1000 + $124.80 = $1124.80

* The choices are:

** $1,031.20 ** $562.00 ** $312.00 ** $281.20 ** $31.20

So the correct choice is $1,031.20.

the balance after 6 years is approximately $926.45.

What is Continuous compounding ?

Continuous compounding is the process of calculating interest and reinvesting it into an account's balance over an infinite number of periods.

We can use the formula for continuous compounding to find the balance after 6 years:

[tex]F = Pe^{(rt)}[/tex]

where F is the future value, P is the present value, e is the mathematical constant e (approximately 2.71828), r is the annual interest rate, and t is the time in years.

In this problem, P = $550, r = 8.5% = 0.085 (note that we need to use the decimal form of the interest rate), and t = 6 years.

[tex]F = 550e^{(0.085*6)}[/tex]

F ≈ $926.45

Therefore, the balance after 6 years is approximately $926.45.

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Answer:

The product of -6 is not a well-formed question. A product refers to the result of multiplying two or more numbers together, but there is no other number specified in the question. If you provide more information or context, I would be happy to assist you.

Step-by-step explanation:

It will take 4. 09 weeks for the tires to be rotated at the current rate.

When rotating a car's tires every 10,000 miles, each tire must complete this distance before being moved.

25, 200 rotations / day x 7 days / week = 176, 400 rotations per week

To solve this predicament, dividing 10,000 miles by the number of rotations/mile (which equates to the tire's circumference) is necessary. The formula for calculating a tire's circumference can aid in obtaining this number along with the weeks required to perform the rotation process:

C = 2πr

Rotation per mile is:

1 mile / 87.96 inches / rotation = 72.26 rotations / mile

Number of weeks:

10, 000 miles x 72. 26 rotations / mile = 722, 600 rotations

722, 600 rotations / 176, 400 rotations/week = 4.09 weeks

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The values of x are the two expressions equal to All real numbers except 2.

We are given that rational expression has been simplified below.

(x+4)(x-2)x+4

9(x-2)

WE know that X=4/9 is simplified, but we can simplify the other side by canceling out the (x-2) in the numerator and denominator.

The expression should be;

(x + 4)(x - 2)/9(x - 2)= (x + 4)/9.

After simplification by (x - 2) , the remainder will be;

(x + 4)/9.

When x = -4,  both sides equal to zero.

When x = 0 , both sides equal to 4/9

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Answer:

------------------------------

We are given three sides and need to find one of angles.

Use the law of cosines:

  [tex]cos(A) = \cfrac{ b^2 + c^2 - a^2}{2bc}[/tex]

Here we are given:

Substitute above values into the given equation:

   [tex]cos(R) = \cfrac{ 52^2 + 41^2 - 59.7^2}{2*52*41} =0.1925[/tex]

Find m∠R:

the greatest common factor of 72 and 96 is 24

Doppler Effect happens when there is shift in frequency during a realtive motion between a source and the observer of that source.

It can be calculated as:

[tex]f_o=f_s\huge \text(\dfrac{c+v_o}{c+v_s}\huge \text )[/tex]

where:

c is the speed of light (c = 332m/s)

all the subscripted s is related to the Source (frequency, velocity);

all the subscripted o is related to the Observer (frequency, velocity);

As the source is moving towards the observer and the observer is moving towards the source, the velocities of each are opposite related to direction.

So, the frequency perceived by the observer:

[tex]f_o=460\huge \text(\dfrac{332+32}{332-40}\huge \text)[/tex]

[tex]f_o=460\huge \text(\dfrac{364}{292}\huge \text)[/tex]

[tex]f_o=460(1.247)[/tex]

[tex]f_o= 573.6 \ \text{Hz}[/tex]

At this condition, the observer hears the train's horn in a perceived frequency of 573.6 Hz

Answer:

The perceived frequency of sound is the amount of sound wave that pass a point in a given amount of time

The perceived frequency you hear is

370.9 Hertz

The function is given as:

[tex]f_{o}=\frac{c+V_{o} }{c-V_{o} }[/tex] x  [tex]f_{s}[/tex]

From the question

[tex]c=332[/tex] --- speed of the sound

[tex]V_{o} =32[/tex] ---current speed of the train

[tex]V_{s} = 40[/tex] --- speed of the opposite train

[tex]f_{s} =460[/tex] --- frequency of the sound wave

This gives:

[tex]f_{o}= \frac{332-32}{332+40}[/tex]  ×[tex]460[/tex]

[tex]f_{o}= \frac{300}{372} x460[/tex]

Rewrite as:

[tex]f_{o}= \frac{300x460}{372}[/tex]

[tex]f_{o}= 370.9[/tex]

When 14,277s is converted to hr, min and hr, it gives 3 hours, 57 minutes, 7 seconds.

Conversion is the process of changing the value of one form to another. It is also the conversion between different units of measurement for the same quantity.

How to determine this

When 60 seconds makes 1 minute

60 minutes makes 1 hour

14,277 seconds to minutes

When 60 seconds = 1 minute

14,277 seconds = x

x = 14,277/60 minutes

x = 237 minutes 7 seconds

By converting 237 minutes to hour

When 60 minutes = 1 hour

237 minutes = x

x = 237/60 hours

x = 3 hours 57 minutes.

Therefore, the conversion is 3 hours 57 minutes 7 seconds

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The values of the angles will be 6.67°, 156.78° Be 29.93° and the sides will be 10.01, 34 and 43.

SSA stands for side side angle postulate. In this postulate of congruence, we say that if two sides and an angle not included between them are respectively equal to two sides and an angle of the other triangle then the two triangles are equal.

By sine rule,

Y = sin156.78 × 44 / 34

= 29

sin Y = 0.499

Y = 29.93°

By the angle sum property. The last angle will be:

180 - 156.78 - 29.93

= 6.67°

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Given

ABCΔ  is a triangle.

D is a point on [BC]

|BD|=4

|AD|=|CD|

m(CBAˆ)=α=30∘

m(ACBˆ)=β=20∘

To Find

What is |AC|=x?

Solution

Geometric approaches gave me nothing. Letting |AD|=|CD|=a, |AB|=b

and applying law of cosines to all three triangles yields;

respectively, from ACDΔ, ABDΔ and ABCΔ. Directly isolating x from these equations gives an expression involves trigonometric function(s), and i cannot find a way to annihilate trigonometric functions in these equations to reach the answer which is x=4

The complete question is -

In the given diagram find the value of x

a) 1

b) 2

c) 3

d) 4

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Measure of ∠ADB  is 240 degrees,  the area of the shaded region is 42.67π m² and arc length ADB  is 10.67π m

Given that the circle has a center O.

The radius of the circle is 8 m.

The measure of ∠AOB is 120°

We need to determine the area of the shaded region and the length of the arc ADB.

The measure of ∠ADB is given by

∠ADB = 360 - ∠AOB

= 360 - 120

=240 degrees

The area of the shaded region can be determined using the formula,

A = (θ/360) πr²

A = (θ/360) ×3.14× 8²

A = 42.67 m²

Thus, the area of the shaded region is 42.67π m²

The length of arc ADB can be determined using the formula,

Arc length =  (θ/360) 2πr

=10.67π m

Hence,  measure of ∠ADB  is 240 degrees,  the area of the shaded region is 42.67π m² and  length of arc ADB  is 10.67π m

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Answer: Area=3.125 square feet

Step-by-step explanation:

2.5x2.5=6.25

6.25/2= 3.125

Answer:

A = 50 ft²

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

given that 1 inch equals 4 feet , then

b = 2.5 in = 2.5 × 4 feet = 10 feet

h = 2.5 in = 2.5 × 4 feet = 10 feet

then

A = [tex]\frac{1}{2}[/tex] × 10 × 10 = 5 × 10 = 50 ft²

The estimated number of quarts of blood the individual with the given weight will have would be = 2.7 quarts.

The body weight of the first individual = 200 pounds

The volume of blood = 6 quarts.

Therefore a person of 90 pounds = X quarts.

That is;

200 pounds = 6 quarts

90 pounds = X quarts

make X quarts the subject of formula;

X = 90×6/200

= 540/200

= 2.7 quarts

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Answer:

D. Quadratic

Step-by-step explanation:

The vertex of the parent function y = x2 lies on the origin. It also has a domain of all real numbers and a range of [0, ∞). Observe that this function increases when x is positive and decreases while x is negative

We number of bags is 10 bags of fertilizer to complete the job.

Algebra is a branch of mathematics that deals with the study of mathematical symbols and their manipulation. It involves the use of letters, symbols, and equations to represent and solve mathematical problems.

In algebra, we use letters and symbols to represent unknown quantities and then use mathematical operations such as addition, subtraction, multiplication, division, and exponentiation to manipulate those quantities and solve equations. We can use algebra to model and solve real-world problems in various fields such as science, engineering, economics, and finance.

The total area of the football field is:

360 feet × 160 feet = 57,600 square feet

To find out how many bags of fertilizer are needed, we need to calculate how many 1000-square-foot areas there are on the field:

57,600 square feet ÷ 1000 square feet/area = 57.6 areas

So there are 57.6 areas on the football field.

We need 8 pounds of fertilizer per 1000 square feet, so to find out how many pounds we need for the whole field, we can multiply by the number of areas:

8 pounds/1000 square feet × 57.6 areas = 460.8 pounds

Therefore, we need 460.8 pounds of fertilizer to cover the football field.

Since the fertilizer comes in 50-pound bags, we can divide the total amount of fertilizer needed by 50 to find out how many bags we need:

460.8 pounds ÷ 50 pounds/bag ≈ 9.22 bags

We can't buy a fraction of a bag, so we need to round up to the nearest whole bag. Therefore, we need 10 bags of fertilizer to complete the job.

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The complete question is:

You are applying fertilizer to a football field. The field is 360 feet long and 160 feet wide. You use 8 pounds of fertilizer per 1000 square feet. The fertilizer comes in 50- pound bags. How many bags of fertilizer will you need to complete this job?

The surface area of this cylinder is 942 millimeter square

The formula for the surface area of a cylinder is expressed as;

SA = 2πr h + 2πr²

Given that the parameters are identified as;

From the information given, we have that;

Surface area = 2 × 3.14 × 10 × 5  + 2× 3.14 × 10²

Find the square values

Surface area = 2 × 3.14 × 10 × 5  + 2× 3.14 × 100

Multiply the values

Surface area = 314 + 628

Now, add the values

Surface area = 942 mm²

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As a result, the item's final price is $53.50 and the sales tax is $3.50.

The government levies a consumption tax known as sales tax on the purchase of goods and services. The seller often calculates it as a percentage of the purchase price and collects it. After then, the vendor transfers it to the government .. The funding of government services and programmers comes from sales tax

We can multiply the item's price by the applicable sales tax rate to determine the sales tax:

Price of Item  x   Sales Tax Rate equals Sales Tax

Sales Tax: $50.00 x 7% = $3.50

We can multiply the item's price by the applicable sales tax to determine the entire cost of the purchase, including tax:

Price of Item + Sales Tax = Total Cost

$50.00 plus $3.50 equals $53.50 as a total

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Answer:

hope this might help you!!

Answer: ∠EGF and/or ∠CGB

Step-by-step explanation:

Starting Angle: ∠CGE

Possible Supplements: ∠EGF and ∠CGB

23. By the diagram, the triangle is a [tex]45^\circ - 45^\circ-90^\circ[/tex] triangle. Therefore, the triangle is isosceles, so [tex]x=6.[/tex] And by the Pythagorean theorem, [tex]y^2=x^2+6^2=6^2+6^2=72,[/tex] and taking the square root yields [tex]y = 6\sqrt{2}.[/tex]

24. Notice that by the diagram, the triangle is a [tex]30^\circ-60^\circ-90^\circ[/tex] triangle. It is well known that in these special types of triangles, if [tex]a[/tex] is the side length opposite the [tex]30^\circ[/tex] angle, then the side length opposite the [tex]90^\circ[/tex] angle is [tex]2a,[/tex]  and finally the side length opposite the [tex]60^\circ[/tex]  is [tex]a\sqrt{3}.[/tex] This is shown in the image I've attached below, and can also be easily proven by the fact that two of these triangles combine to form an equilateral triangle.

So using this fact, we know that [tex]x = \frac{8}{2} = 4,[/tex] and [tex]y = x\sqrt{3} = 4\sqrt{3}.[/tex]

25. Tell whether the given side lengths can represent the sides of a right triangle: 10, 12, 20

For this question, we simply use the converse of the Pythagorean theorem. One part of its statement says that if a triangle has sides of length [tex]a, b, c[/tex] such that [tex]a^2 + b^2 = c^2[/tex], and [tex]c[/tex] is the longest side, then the angle opposite the side of length [tex]c[/tex] is a right angle.

Thus, if the triple [tex](a, b, c)[/tex] does not satisfy the equation, the triangle it forms is not a right triangle. In our case, the corresponding values for [tex](a, b, c)[/tex] are [tex](10, 12, 20),[/tex] because [tex]20[/tex] is the largest number in this triple. But [tex]10^2+12^2=244\neq 400 = 20^2,[/tex] so the triangle with side lengths [tex]10, 12, 20[/tex] is not a right triangle.

26. Another statement of the converse of the Pythagorean theorem is that if a triangle has side lengths [tex]a, b, c[/tex] such that [tex]c^2 > a^2+b^2[/tex] , with [tex]c[/tex] being the longest side, then the triangle is an obtuse triangle. So the corresponding values for [tex]a, b, c[/tex] are [tex]10, 11, 14,[/tex] and because [tex]14^2 = 196 < 221 = 10^2+11^2,[/tex] the triangle is an obtuse triangle.

The Sum of interior angles of the given polygon is: 540°

The value of the angle x is: 85°

The interior angle-sum formula for an irregular polygon is the same as the sum of interior angle in a regular polygon.

Sum of interior angles in a n-sided polygon is:

Sum = (n - 2)180

where:

n is the number of sides of the irregular polygon.

This is a 5-sided irregular polygon

Thus:

Sum = (5 - 2)180

Sum = 540°

Thus:

x + 115 + 115 + 130 + 95 = 540

x + 455 = 540

x = 540 - 455

x = 85°

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Step-by-step explanation:

We have the triple integral:

∫∫∫E x^2 + y^2 + z^2 dV

where E is the ball x^2 + y^2 + z^2 ≤ 81.

In spherical coordinates, the volume element is given by:

dV = ρ^2 sin φ dρ dθ dφ

where ρ is the radial distance, φ is the polar angle (measured from the positive z-axis), and θ is the azimuthal angle (measured from the positive x-axis).

Substituting into the integral, we get:

∫φ=0 to φ=π ∫θ=0 to θ=2π ∫ρ=0 to ρ=9 ρ^2 sin φ (ρ^2) dρ dθ dφ

= ∫φ=0 to φ=π ∫θ=0 to θ=2π ∫ρ=0 to ρ=9 ρ^4 sin φ dρ dθ dφ

= ∫φ=0 to φ=π ∫θ=0 to θ=2π (1/5)(9^5) sin φ dθ dφ

= (2π/5)(9^5)(-cos φ)|φ=0 to φ=π

= (2π/5)(9^5)(-(-1 - 1))

= (4π/5)(9^5)

≈ 114413.73

Therefore, the value of the triple integral is approximately 114413.73.

a)Traveled 0.3 miles in 1 hour.

b) The fraction representation is 3/10 miles per hour.

a) To find out how many miles the person traveled in 1 hour, we need to divide the distance traveled by the time taken.

Distance traveled = 1/5 miles

Time taken = 3/2 hours

To make it easier to divide, we can convert the time taken to a fraction with a common denominator of 10:

3/2 = 15/10

Now we can divide the distance by the time:

1/5 ÷ 15/10 = 1/5 x 10/15 = 2/15

This tells us that the person traveled 2/15 miles in one-tenth of an hour (i.e., 6 minutes).

To find out how many miles per hour they traveled, we can convert the fraction to a rate by multiplying it by the reciprocal of the time fraction (i.e., 10/3):

2/15 x 10/3 = 2/9

Therefore, the person traveled 2/9 miles per hour.

b) To write this as a model fraction representation, we can express it as a single fraction:

2/9 = 3/10 (rounded to the nearest tenth)

So the person traveled at a rate of 3/10 miles per hour.

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Answer:

The correct equation is C. d = 163t.

This equation shows a direct proportionality between the amount of time worked (t) and the amount of money earned (d). For each hour worked, Rajindri earns $163, so the total amount earned (d) is equal to the hourly rate of $163 multiplied by the number of hours worked (t).

Step-by-step explanation:

To the nearest tenth of a year, the person must leave the money in the bank for 15.5 years.

We can use the formula for compound interest:

A = P[tex](1 + r/n)^{nt}[/tex]

where A is the final amount, P is the principal (initial investment), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time in years.

We know P = 8000, r = 0.0475, and we want A = 20400. We also know that the interest is compounded daily, so n = 365.

Let's solve for t:

20400 = 8000[tex](1 + 0.0475/365)^{(365t)}[/tex]

2.55 = [tex](1.00013)^{(365t)}[/tex]

Taking the natural logarithm of both sides, we get:

after solving

Using a calculator, we find:

t ≈ 15.5

So, to the nearest tenth of a year, the person must leave the money in the bank for 15.5 years.

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