What identity can be used to rewrite the expression 27x^3-64?

Answer: (3x-2)(x+5)

Hope this helps.

The correct answer for the factorization of   [tex]3x^{2} +13x -10[/tex]   is  [tex](3x-2)(x+5)[/tex].

Given expression:

[tex]3x^{2} +13x -10[/tex]

a: The coefficient  of [tex]x^{2}[/tex]

b: The coefficient of linear term variable.

c: The constant term.

In given question:

a= [tex]3x^{2}[/tex]  ,   b =[tex]13x[/tex]  ,   c = [tex]-10[/tex]

To factorize,
Split the middle term:

Find two numbers that multiply to ac (product of the coefficients of [tex]x^{2}[/tex] and the constant term) and add up to b (coefficient of [tex]x[/tex]).

ac = [tex]3*-10 = -30[/tex]

b = [tex]13[/tex]

The two numbers are:

[tex]15[/tex] and [tex]-2[/tex] because [tex]15 * -2[/tex] = [tex]-30[/tex] and [tex]15+(-2) = 13[/tex].

Rewrite the middle term using the two numbers found:

[tex]3x^{2} +15x-2x -10[/tex]

Simplify:

[tex]3x(x^{} + 5x)-2(x+5)[/tex]

[tex](x+5)(3x-2)[/tex]

The factored term of equation [tex]3x^{2} +13x -10[/tex]  is  [tex](3x-2)(x+5)[/tex].

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Answer:

answer is attached in the image below

(a) Jason arrives at the factory first

(b) It takes 5 minutes until the other person arrives

Step-by-step explanation:

Jason and Jeremy work together at a juggling-ball factory

We need to know who arrives at the factory first and how long it is until the other person arrives

Time = Distance ÷ speed

∵ Jason lives 25 miles away from the factory

∴ The distance = 25 miles

∵ He drives at 60 miles per hour

∴ The speed = 60 miles per hour

- Use the rule above to find the time

∵ Time = 25 ÷ 60 = [tex]\frac{5}{12}[/tex] hour

∵ 1 hour = 60 minutes

∴  [tex]\frac{5}{12}[/tex] hour =  

∴ Jason arrives to the factory in 25 minutes

∵ Jeremy lives 35 miles away from the factory

∴ The distance = 35 miles

∵ He drives at 70 miles per hour

∴ The speed = 60 miles per hour

- Use the rule above to find the time

∵ Time = 35 ÷ 70 = [tex]\frac{1}{2}[/tex] hour

∵  [tex]\frac{1}{2}[/tex] hour =  

∴ Jeremy arrives to the factory in 30 minutes

∵ They leave their houses at the same time

∵ 25 minutes < 30 minutes

∴ Jason arrives first

(a) Jason arrives at the factory first

∵ Jason arrives to the factory in 25 minutes

∵ Jeremy arrives to the factory in 30 minutes

∵ 30 - 25 = 5 minutes

∴ Jeremy arrives after Jason by 5 minutes

(b) It takes 5 minutes until the other person arrives

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Final answer:

Jason arrives at the factory first, taking approximately 25 minutes, while Jeremy arrives 5 minutes later, taking around 30 minutes to reach.

Explanation:

The question involves calculating time taken for different scenarios involving motion and relative speed. In the given scenario, Jason lives 25 miles away from the factory and drives at 60 miles per hour, while Jeremy lives 35 miles away and drives at 70 miles per hour. To find out who arrives at the factory first, we calculate the time each person takes to reach the factory.

For Jason: Time = Distance / Speed = 25 miles / 60 mph = 0.4167 hours.
For Jeremy: Time = Distance / Speed = 35 miles / 70 mph = 0.5 hours.
Clearly, Jason will arrive first.

The difference in arrival time between Jeremy and Jason is:
Jeremy's time - Jason's time = 0.5 hours - 0.4167 hours = 0.0833 hours, which is 5 minutes.

Jason arrives at the factory first, and Jeremy arrives 5 minutes later.

Answer:

A rule of polygons is that the sum of the exterior angles always equals 360 degrees. Since it is a regular octagon, so each of the interior angles of octagon are equal. ((n-2)*180)/n where n is the number of sides of the polygon.for example in case n=8 for an octagon, so we get:

((8-2)*180)/8 => (6*180)/8 => 1080/8 = 135 degrees. This means that each interior angle of the regular octagon is equal to 135 degrees.  

Each exterior angle is the supplementary angle to the interior angle at the vertex of the polygon, so in this case each exterior angle is equal to 45 degrees. (180 - 135 = 45). Remember that supplementary angles add up to 180 degrees.  

And since there are 8 exterior angles, we multiply 45 degrees * 8 and we get 360 degrees.

This technique works for every polygon, as long as you are asked to take one exterior angle per vertex.

The sum of the exterior angles of any polygon, including an octagon, is always 360 degrees. This is true regardless of the polygon's number of sides, because when one traces around the polygon, the point will have made one full revolution, or 360 degrees.

In mathematics, the sum of the exterior angles of any polygon, not just an octagon, is always 360 degrees. This applies regardless of the number of sides the polygon has. The concept comes from observing how a point moves as one traces around the polygon: during the complete circuit, it will have made exactly one full revolution, which is 360 degrees in total. Just as a circle consists of 360 degrees, this concept applies to polygons and their exterior angles as well.

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Answer:

slope: 0

Step-by-step explanation:

y=6

no matter what x is, y is always going to equal 6

Answer:

d=60t

Step-by-step explanation:

Use the equation speed = distance / time

To get distance you do speed X time

D =60t shows that

The distance traveled  = 60t.

Distance exists defined to be the magnitude or extent of displacement between two positions. Distance traveled exists the entire length of the path traveled between two positions. Distance traveled exists not a vector.

The independent variable exists as t (hours) and the dependent variable exists as d (distance). The total distance (d) depends on the number of hours (t). As the hours increase, the distance will rise. The distance relies on the amount of time traveling.

Speed = distance / time

Therefore, Distance = speed [tex]*[/tex] time

Distance = 60t

Therefore, the correct answer is option A. d = 60t.

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Stephanie worked for 33 hours 20 minutes.

Explanation:

Step 1; Stephanie works and earns $4.50 an hour. Her last paycheck was for $150. So to find the number of hours she has worked we divide the total money earned by the money she earns every hour.

Total hours worked = Total money earned / Money earned for an hour

                                  = $150 / $4.50 = 33.33 hours.

Step 2; We need to convert the 33.33 hours into hours and minutes.

We multiply the 0.33 hours with 60 to convert it into minutes. 0.33 × 60 = 20 minutes. So Stephanie worked for 33 hours and 20 minutes to get her last paycheck.

Answer:

20 hours

Step-by-step explanation:

She receives $60 regardless of the number of hours she works for. Per hour, she earns $4.50. In t hours, she earns:

60 + 4.50t

For some t, the total is $150

150 = 60 + 4.50t

90 = 4.50t

t = 20

Answer:

Therefore the x-coordinate of the solution to this system is 2.4.

Step-by-step explanation:

Given system of equation is

      3x-y=6............(1)

and 2x+y=6...........(2)

Adding equation (1) and (2)

3x -y+2x-y=6+6

⇔5x =12

[tex]\Leftrightarrow x=\frac{12}{5}[/tex]

⇔x = 2.4

Putting the value of x in equation (1)

3×2.4 - y =6

⇔7.2 -y = 6

⇔y = 7.2-6

⇔y=1.2

Therefore the x-coordinate of the solution to this system is 2.4.

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

recall that the point-slope form of a linear equation is given by

y = mx + c

Rearranging so that it is in the same form as the answer choices, we get

y = c + mx

where m is the slope and c is the y-intercept

we note the following observations

1) The line goes from top left to bottom right, this means that the slope is negative, hence m has to be negative. (in our case, all the choices have negative x)

2) The line crosses the y-axis at y = 4, this means the y-intercept is 4 and hence c = 4.

If we look at the choices, only choice B satisfies both observations (that m is negative and c = 4)

Answer:

B)

Step-by-step explanation:

Answer:

x=120°

Step-by-step explanation:

Let us draw a third horizontal line through x, parallel to the two parallel lines.

This line divides angle X into A and B as shown.

By alternate interior angle theorem, angle B=50°

and

angle A=70°

We know that: A+B=x

Therefore x=70°+50°=120°

Answer:

x=120 degrees

Step-by-step explanation:

1. 70+50=120

I get it its simple but its correct i do RSM

Answer:

$50

Step-by-step explanation:

Simple math

Extended warranty don’t count so gotta take that out that’s be 20x18=360 1260-360=900 now divide 18 tvs from that and u get 900/18=50

To determine the fixed amount Gi earns for each television, a simple algebraic equation is set up and solved to find that he earns $ 50 per television without the extended warranty.

To solve for the fixed amount Gi earns for each television without the extended warranty, we can set up an equation.

Let's call the fixed amount $F. Each television with an extended warranty earns Gi an additional $ 20, so for each of those televisions, he earns $F + $20. If he sells 18 televisions with extended warranties,

the total amount he earns can be represented by 18($F + $ 20), which equals $ 1,260 according to the question.

We can create the following equation to find the fixed amount $F:

18($F + $ 20) = $ 1,260

To solve for $F, divide both sides of the equation by 18:

$F + $ 20 = $ 70

Then, subtract $ 20 from both sides to isolate $F:

$F = $ 50

So, the fixed amount Gi earns for each television is $ 50.

Answer:

0.785398163 rad

Step-by-step explanation:

The value of arctan(1) is equal to π/4 or 45 degrees.

The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle.

For the angle whose tangent is 1, we can visualize a right triangle where the length of the side opposite to the angle is 1 and the length of the adjacent side is also 1.

Using the Pythagorean theorem, we can calculate the length of the hypotenuse:

hypotenuse² = opposite² + adjacent²

hypotenuse² = 1² + 1²

hypotenuse² = 1 + 1

hypotenuse² = 2

hypotenuse = √2

Now, we can use the definition of the arctan function to find the angle whose tangent is 1:

arctan(1) = angle whose tangent is 1 = angle whose opposite side is 1 and adjacent side is 1

This angle is a well-known special angle in trigonometry.

It is a 45-degree angle (π/4 radians) or a quarter of a full circle.

Therefore, arctan(1) is equal to π/4 or 45 degrees.

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Answer:

72 cubic ft

Step-by-step explanation:

To find volume you multiply length × width × height

Length is 4, width is 6 and height is 3

4×6×3= 72

Answer:

72 cubic ft

Step-by-step explanation:

Use the formula v= lxwxh

1. Write 6x4x3

2. 6x4=24

3. 24x3=72

***or***

1. 3x4=12

2. 12x6=72

Either way both equal 72 cubic ft

Answer:11/12

Step-by-step explanation:

Answer:

Period =½

Equation of midline, y=0

Maximum =2

Minimum=-2

Step-by-step explanation:

The given function is

[tex]f(x) = - 2 \cos(4 \pi \: x) [/tex]

The period is given by:

[tex] \frac{2\pi}{b} = \frac{2\pi}{4\pi} = \frac{1}{2} [/tex]

The equation of the midline is y=0 since there is no vertical shift

The amplitude of this function is 2 so the range is -2≤y≤2.

Hence the maximum value is 2 and minimum value is -2

n(AxB) = 25

Step-by-step explanation:

AxB in sets is called Cartesian product. And is defined as a set of ordered pairs (a,b) where a belongs to A and b belongs to B.

Given

A = {a,b,c,d,e}

B = {1,2,3,4,5}

The number of elements for Cartesian product of two sets is determined by:

[tex]n(AxB) = n(A) * n(B)[/tex]

Here

[tex]n(A) = 5\\n(B) = 5[/tex]

So,

[tex]n(AxB) = 5*5 = 25[/tex]

Hence,

n(AxB) = 25

Keywords: Sets, Cartesian Product

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The value of n(AxB) is 25

Given the following sets

A= {a,b,c,d,e} and let B= {1,2,3,4,5}, we are to determine n(AxB)

n(A) = 5 (number of elements in the set)

n(B) = 5

Get the cardinality of n(AxB)

Hence the value of n(AxB) is 25

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Step-by-step explanation:

The numbers which are multipe of 3:

3, 6, 9, 12, 15, 18, 21, 24, ......

The numbers which are multipe of 12:

12, 24, 36, 48, ......

The number is multiple of 12 is also multiple of 3 but the number is multiple of 3 the number may be multiple of 12 or may not be multople of 12.

Thus, If a number is a multiple of 3, it is not necessary to a multiple of 12.

Final answer:

Explaining how to create an equation for a specific scenario where 12 is subtracted from a certain number to equal 19.

Explanation:

An equation for 12 less than a number x is 19:

Define the variable: Let x be the number.

Set up the equation: x - 12 = 19.

Solve for x: x = 19 + 12 = 31.

Answer:

-8

Step-by-step explanation:

if its 2 more then [tex]-6-2=-8[/tex]

so if you think the opposite negative 8 plus 2 is -6

Answer:

1. a. 72/100 = 324/x

72x = 32,400

b. 450 students are in Math 6

2. a. o = 3b

b. o = 3 pounds

3. a. Most popular animals:

A. Dogs - 67%

B. Cats - 20%

C. Other - 8%

D. None - 4%

E. Horses - 1%

b.  20 students

c. If 75 students have cats, the estimate of 250 students isn't correct.

The actual number of students interviewed is 375.

Step-by-step explanation:

1. a. Let's use the following equation to solve the question:

x = Students that are in Math 6

72/100 = 324/x

72 * x = 324 * 100

72x = 32,400

b. Let's solve the equation, as follows:

x = 32,400/72

x = 450

450 students are in Math 6

2. a. The equation is:

o = 0.15 *20b

o = 3b

where, o = weight of oats in pounds and b = number of dog food bags

b. Let's find out the weight of the oats in one dog food bag, using our equation:

o = 0.15 *20b

o = 0.15 *20 * 1

o = 3 pounds

3. a. Most popular animals:

A. Dogs - 67%

B. Cats - 20%

C. Other - 8%

D. None - 4%

E. Horses - 1%

b. If 250 students were interviewed, the 8% who answered "other" are:

8% of 250 = 0.08 * 250 = 20 students

c. If 75 students have cats, the estimate of 250 students isn't correct.

The 20% of 250 is 50, not 75.

0.2 * 250 = 50

The actual number of students interviewed is:

x = Actual number of students interviewed

75/x = 20/100

20x = 7,500

x = 7,500/20

x = 375

The actual number of students interviewed is 375.

The radius of a circle with center at  [tex]C (0, 4)[/tex] and point [tex]P(-2, -1)[/tex] will be [tex]\sqrt{29}[/tex].  

Equation of a circle is written in the form of [tex](x-h)^2+(y-k)^2=r^2[/tex]  where [tex](h,k)[/tex]  represents the center and  [tex]r[/tex]  is the radius.

We have,

Center at  [tex]C (0, 4)[/tex]

i.e. [tex]h=0,\ k=4[/tex]

And,

Point  [tex]P(-2, -1)[/tex]

i.e. [tex]x=-2,\ y=-1[/tex]

Now,

To determine Radius of the circle;

[tex]r^2=(x-h)^2+(y-k)^2[/tex]

[tex]r^2=(-2-0)^2+(-1-4)^2[/tex]

[tex]r^2=(-2)^2+(-5)^2[/tex]

[tex]r=\sqrt{4+25}[/tex]

[tex]r=\sqrt{29}[/tex]

So, radius of the circle is [tex]\sqrt{29}[/tex] , which is find out using equation of a circle.

Hence, we can say that the radius of a circle with center at  [tex]C (0, 4)[/tex] and point [tex]P(-2, -1)[/tex] will be [tex]\sqrt{29}[/tex].

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The length of the radius of the circle is sqrt(29) or approximately 5.39 units.

To find the length of the radius of a circle, we can use the distance formula. The distance between the center of the circle (0, 4) and the point on the circle (-2, -1) is given by:

d = sqrt((x2-x1)^2 + (y2-y1)^2)

Plugging in the values, we get:

d = sqrt((-2-0)^2 + (-1-4)^2)

d = sqrt((-2)^2 + (-5)^2)

d = sqrt(4 + 25)

d = sqrt(29)

Therefore, the length of the radius of the circle is approximately sqrt(29) or 5.39 units.

Answer:

15-(6-3) = 12

Step-by-step explanation:

15 - (6-3) =

Solve inside the parenthesis

15-3=12

Answer:

The percent of the apartment that is unoccupied = (21/ 175) [tex]\times[/tex] 100 = 12%

Step-by-step explanation:

i.) the apartment complex has a total of 175 units.

ii.) 154 units are occupied.

iii.) therefore the number of unoccupied units is = 175 - 154 = 21 units.

iv.) the percent of the apartment that is unoccupied = (21/ 175) [tex]\times[/tex] 100 = 12%

Answer:

-1

Step-by-step explanation:

Answer:

Step-by-step explanation:

(-1 - 4)/(2 + 3) = -5/5 = -1

answer is -1

Answer:

(-4,17)

Step-by-step explanation:

2x-3y=-11

2x+y=9

solve the equation

x=-4

2x+y=9

substitute the value of x into an equation

2×(-4)+y=9

solve the equation

y=17

A possible solution is

(-4,17)

check the solution

2×(-4)-3=-11

2×(-4)+17=9

simplify

-11=-11

9=9

the order pair is a solution

answer is (-4,17)

To solve the given system using the substitution method, solve the second equation for y, substitute into the first equation, and solve for x. Substituting x back into the expression for y gives the solution x = 2 and y = 5.

To solve the system of equations using the substitution method, we have to express one variable in terms of another from one of the equations and then substitute it into the other equation. For the given system of equations:

First, we solve the second equation for y:

y = 9 - 2x

Now we substitute this expression for y into the first equation:

2x - 3(9 - 2x) = -11

2x - 27 + 6x = -11

8x - 27 = -11

8x = 16

x = 2

After finding x, we can substitute x back into y = 9 - 2x to find the value of y:

y = 9 - 2(2)

y = 9 - 4

y = 5

The solution to the system of equations is x = 2 and y = 5.

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Answer:

23.44%

Step-by-step explanation:

The probability of getting a 4 on the first 2 throws and different numbers on the last 5 throws = 1/6 * 1/6 * (5/6)^5

= 0.01116

There are 7C2 ways of the  2 4's  being in different positions

= 7*6 / 2 = 21 ways.

So the required probability =  0.01116 * 21

= 0.2344 or 23.44%.

Answer:

C. a 90° counterclockwise rotation about the origin and then a translation 10 units left.

Step-by-step explanation:

See the diagram attached to the question.

We have to select the sequence of transformations confirms congruence by mapping the shape I onto shape II.

The correct option is Option C.

C. a 90° counterclockwise rotation about the origin and then a translation 10 units left. (Answer)

Answer:

x < 21

Step-by-step explanation:

Given

12x < 252 ( divide both sides by 12 )

x < 21