Given that a is a multiple of 456, find the greatest common divisor of 3a^3+a^2+4a+57 and a.

Answers

Answer 1

Answer: 57

Step-by-step explanation:

Given: a is a multiple of 456

Let [tex]a = 456 x[/tex]

Then, expression [tex]3a^3+a^2+4a+57 =3(456x)^3+(456x)^2+4(456x)+57[/tex]

Since 456 = 57 x 8

Then, [tex]3(456x)^3+(456x)^2+4(456x)+57=3(57\times 8x)^3+(57\times 8x)^2+4(57\times 8x)+57[/tex]

[tex]=3(57)^3\times (8x)^3+(57)^2\times (8x)^2+4(57)\times (8x)+57[/tex]

Taking 57 out as common

[tex]=57[3(57)^2\times (8x)^3+(57)\times (8x)^2+4\times (8x)+1][/tex]

Now, the greatest common divisor of [tex]a = 456 x[/tex] and [tex]3a^3+a^2+4a+57=57[3(57)^2\times (8x)^3+(57)\times (8x)^2+4\times (8x)+1][/tex] is 57.

Hence, the greatest common divisor of 3a^3+a^2+4a+57 and a is 57.


Related Questions

A) Which of triangle A, B, C and D is congruent to triangle E.? B) Which other two triangles (from A, B, C and D) are congruent to each other? Please help!

Answers

Answer:

c is congruent to e congruent means to be the same

Step-by-step explanation:

8. When dividing polynomials using factorization, cancelling identical factors in the denominator and the numerator will give the _______.
A. remainder
B. dividend
C. quotient
D. divisor

Answers

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When dividing polynomials using factorization, cancelling identical factors in the denominator and the numerator will give the remainder.

A. remainder

B. dividend

C. quotient

D. divisor

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

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Hope this helped you.

Could you maybe give brainliest..?

❀*May*❀

Answer:

a. remainder

Step-by-step explanation:

took the test

dont leave your house without a vest

or you will get hit in the vital organs in your chest

Will mark the brainliest
And thank you:)

Answers

[tex]\sf{\implies Range = Highest \: - lowest }[/tex]

→ Range of Lewistown = 74 - 64

Range of Lewistown = 10 .

Range of Hamersville = 71 - 55

Range of Hamersville = 16 .

Range of Hamersville - Range of Lewistown

→ 16 - 10

6

Answer The range for Hamersville is 6 more than the range for Lewistown .

Patios can be made by mixing cubic meters of ash, stone, and wood chips in the ratio 5:7:3. How much stone is needed to make 45 cubic meters of patio?

Answers

Answer:

21 m^3

Step-by-step explanation:

5 + 7 + 3 = 15

The ratio of stone to the total is

7:15

If the total needed is 45 m^3, then we multiply both parts of the ratio by 3.

7 * 3 : 15 * 3

21:45

Answer: 21 m^3

Find an equation for the surface consisting of all points P in the three-dimensional space such that the distance from P to the point (0, 1, 0) is equal to the distance from P to the plane y

Answers

Answer:

x^2 +4y +z = 1

Step-by-step explanation:

Surface consisting of all points P to point (0,1,0) been equal to the plane y =1

given point, p (x,y,z ) the distance from P to the plane (y)

| y -1 |

attached is the remaining part of the solution

Solve systems of equations 15 points NOT CLICKBAIT!!! -6y+11y= -36 -4y+7x= -24

Answers

Answer:

x = -264/35

y = -36/5

Step-by-step explanation:

-6y + 11y = -36

-4y + 7x = -24

Solve for y in the first equation.

-6y + 11y = -36

Combine like terms.

5y = -36

Divide both sides by 5.

y = -36/5

Plug y as -36/5 in the second equation and solve for x.

-4(-36/5) + 7x = -24

Expand brackets.

144/5 + 7x = -24

Subtract 144/5 from both sides.

7x = -264/5

Divide both sides by 7.

x = -264/35

Answer: -264/35

Step-by-step explanation:

i did my work on a calculator

State the value of the expression (4.1x10^2)(2.4x10^3) over (1.5x10^7) in scientific notation?

Answers

Answer:

[tex]6.56 * 10^{-2}[/tex]

Step-by-step explanation:

:| I would just start bashing this one.

[tex]((4.1 * 10^2 ) (2.4 * 10^3))/(1/5 * 10^7) =[/tex]

[tex]((410)(2400))/(15000000) =[/tex]

[tex]984000/15000000 =[/tex]

[tex]984/15000 =[/tex]

[tex]123/1875 =[/tex]

[tex]0.0656 =[/tex]

[tex]6.56 * 10^{-2}[/tex]

Help Quick Please. Will give brainliest.

Answers

Answer:

72[tex]\sqrt{3}[/tex] units²

Step-by-step explanation:

The area (A) of the triangle is calculated as

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

Here b = ST = a = 12 and h = RS

To calculate RS use the tangent ratio in the right triangle and the exact value

tan60° = [tex]\sqrt{3}[/tex] , thus

tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{RS}{ST}[/tex] = [tex]\frac{RS}{12}[/tex] = [tex]\sqrt{3}[/tex] ( multiply both sides by 12 )

RS = 12[tex]\sqrt{3}[/tex]

Thus

A = [tex]\frac{1}{2}[/tex] × 12 × 12[tex]\sqrt{3}[/tex] = 6 × 12[tex]\sqrt{3}[/tex] = 72[tex]\sqrt{3}[/tex] units²

(G1) The distance from Flagstaff Arizona to
Tucson Arizona is 260 miles. Express this
distance in meters.
A. 418,418 meters
B. 419,000 meters
C. 126,200 meters
D. 260,000 meters

Answers

Answer:

A. 418, 418

Step-by-step explanation:

The formula to convert miles to meters is the following:

1 = 1,609.34

so for every 1 mile, you have 1,609.34 meters

so you take your distance in miles and multiply it by 1,609.34

d= 260 x 1,609.34

d = 418, 428.4

You sell tickets at school for fundraisers. You sold car wash tickets, silly string fight tickets and dance tickets – for a total of 380 tickets sold. The car wash tickets were $5 each, the silly sting fight tickets were $3 each and the dance tickets were $10 each. If you sold twice as many silly string tickets as car wash tickets, and you have $1460 total. Write the matrix in the box below. Write the solution set for this system and include any necessary work.

Answers

Answer:

Matrix :

[tex]\begin{bmatrix}1&1&1&|&380\\ 5&3&10&|&1460\\ -2&1&0&|&0\end{bmatrix}[/tex]

Solution Set : { x = 123, y = 246, z = 11 }

Step-by-step explanation:

Let's say that x represents the number of car wash tickets, y represents the number of silly sting fight tickets, and z represents the number of dance tickets. We know that the total tickets = 380, so therefore,

x + y + z = 380,

And the car wash tickets were $5 each, the silly sting fight tickets were $3 each and the dance tickets were $10 each, the total cost being $1460.

5x + 3y + 10z = 1460

The silly string tickets were sold for twice as much as the car wash tickets.

y = 2x

Therefore, if we allign the co - efficients of the following system of equations, we get it's respective matrix.

System of Equations :

[tex]\begin{bmatrix}x+y+z=380\\ 5x+3y+10z=1460\\ y=2x\end{bmatrix}[/tex]

Matrix :

[tex]\begin{bmatrix}1&1&1&|&380\\ 5&3&10&|&1460\\ -2&1&0&|&0\end{bmatrix}[/tex]

Let's reduce this matrix to row - echelon form, receiving the number of car wash tickets, silly sting fight tickets, and dance tickets,

[tex]\begin{bmatrix}5&3&10&1460\\ 1&1&1&380\\ -2&1&0&0\end{bmatrix}[/tex] - Swap Matrix Rows

[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{2}{5}&-1&88\\ -2&1&0&0\end{bmatrix}[/tex] - Cancel leading Co - efficient in second row

[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{2}{5}&-1&88\\ 0&\frac{11}{5}&4&584\end{bmatrix}[/tex] - Cancel leading Co - efficient in third row

[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{11}{5}&4&584\\ 0&\frac{2}{5}&-1&88\end{bmatrix}[/tex] - Swap second and third rows

[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{11}{5}&4&584\\ 0&0&-\frac{19}{11}&-\frac{200}{11}\end{bmatrix}[/tex] - Cancel leading co - efficient in row three

And we can continue, canceling the leading co - efficient in each row until this matrix remains,

[tex]\begin{bmatrix}1&0&0&|&\frac{2340}{19}\\ 0&1&0&|&\frac{4680}{19}\\ 0&0&1&|&\frac{200}{19}\end{bmatrix}[/tex]

x = 2340 / 19 = ( About ) 123 car wash tickets sold, y= 4680 / 19 =( About ) 246 silly string fight tickets sold, z = 200 / 19 = ( About ) 11 tickets sold

I need some help with simplifying expressions, please. 8y - 9y =

Answers

As your first step to this problem, change the minus sign to plus a negative.

So we have 8y + -9y.

8y + -9y simplifies to -1y which is our final answer.

Note that if you wrote -y instead, it means the same thing.

However, use the 1 to help avoid confusion if you need it.

the answer to 8y-9y= -1y

g If A and B are disjoint events, with P( A) = 0.20 and P( B) = 0.30. Then P( A and B) is: a. .00 b. .10 c. .50 d. 0.06

Answers

Answer: A) 0

P(A and B) = 0 when events A and B are disjoint, aka mutually exclusive.

We say that two events are mutually exclusive if they cannot happen at the same time. An example would be flipping a coin to have it land on heads and tails at the same time.

Suppose a vine maple grows in height linearly. Four weeks after it is planted it stands 10.67 inches, and after seven weeks it is 15.67 inches tall. Write an equation that models the growth, in inches, of the vine maple as a function of time, in weeks. 1. What is the slope of the function? 2. How tall was the tree when it was first planted? 3. Write the function 4. How tall will the vine maple be after 16 weeks?

Answers

Answer:

Height (z)= 4+(5/3)(z)

Where z is the number of weeks

1). Slope = 4

2). Height= 5.67 inches

3).Height (z)= 4+(5/3)(z)

4).Height= 30.67 inches

Step-by-step explanation:

At week four

10.67= x+4y

Week 7

15.67= x+7y

Solving both equation simultaneously

3y= 5

Y= 5/3

15.67= x+7y

15.67= x+7(5/3)

15.67-35/3= x

15.67-11.67= x

4= x

The modeled equation is

Height (z)= 4+5/3(z)

Where z is the number of weeks

Slope of the function as compared to y= mx+c is 4

The first week of it's plantation

Height (z)= 4+5/3(z)

Height (1)= 4+5/3(1)

Height= 5.67 inches

After 16 weeks

Height (z)= 4+(5/3)(z)

Height (16)= 4+(5/3)(16)

Height= 30.67 inches

What is 2 cm converted to feet?

Answers

Answer:

0.065617 ft

Step-by-step explanation:

Answer:

0.0656168 feet.

Step-by-step explanation:

If x to the 2nd power equal 60, What is the value of x

Answers

Answer:

7.745

Step-by-step explanation:

Square root of 60 equals X.

Find interval of increase and decrease of f(x) = 8 sin(x) + cot(x), −π ≤ x ≤ π

Answers

Answer:

Given f(x)=8sin(x)+cot(x) for -pi<x<pi :

Note that:

f'(x)=8cos(x)-csc^2(x)

f''(x)=-8sin(x)+2csc^2(x)cot(x)

(1) To find the intervals where f(x) is increasing or decreasing we use the first derivative test; if the first derivative is positive on an interval the functio is increasing, negative implies the functio is decreasing.

Using technology we find the approximate zeros of f'(x) on -pi<x<pi :

x~~-1.443401

x~~-.3752857

x~~.3752857

x~~1.443401

Plugging in test values on the intervals yields:

f'(x)<0 on (-pi,-1.443401)

f'(x)>0 on (-1.443401,-.3752857)

f'(x)<0 on

Plz correct me if wrong

The table shows the probability distribution of student ages in a high school
with 1500 students. What is the expected value for the age of a randomly
chosen student?
Age
13
14
15
16
17
18
Probability 0.01 0.23 0.26 0.28 0.20 0.02

Answers

Answer:

Exoected age is 15.49 years

Step-by-step explanation:

Expected age

= E(x)

= sum (p(i)*i)

= 13*0.01+14*0.23+15*0.26+16*0.28+17*0.20+18*0.02

= 15.49

Find the area of the shaded region under the standard normal curve. If​ convenient, use technology to find the area. z -2.13 0 A normal curve is over a horizontal z-axis and is centered at 0. Vertical line segments extend from the horizontal axis to the curve at negative 2.13 and 0. The area under the curve between negative 2.13 and 0 is shaded. The area of the shaded region is nothing.​(Round to four decimal places as​ needed.)

Answers

Answer:

The area of the shaded region under the standard normal curve is 0.4834.

Step-by-step explanation:

A random variable X is said to have a normal distribution with mean, µ and variance σ².

Then [tex]Z=\frac{X-\mu}{\sigma}[/tex], is a standard normal variate with mean, E (Z) = 0 and Var (Z) = 1. That is, Z [tex]\sim[/tex] N (0, 1).

The distribution of these z-variates is known as the standard normal distribution.

Compute the area under the curve between -2.13 and 0 as follows:

[tex]P(-2.13<Z<0)=P(Z<0)-P(Z<-2.13)[/tex]

                           [tex]=0.50-0.01659\\=0.48341\\\approx 0.4834[/tex]

Thus, the area of the shaded region under the standard normal curve is 0.4834.

Using the normal distribution, it is found that the area of the shaded region is of 0.4833.

In a normal distribution, our test statistic is the z-score, which measures how many standard deviations a measure is from the mean. Each z-score has an associated p-value,  which is given at the z-table, and represents the percentile of a measure or or the z-score, which is the area to the left under the normal curve.The area between two z-scores is the subtraction of their p-values.

In this problem, we want the area between Z = -2.13 and Z = 0.

Z = 0 has a p-value of 0.5.Z = -2.13 has a p-value of 0.0166.

0.5 - 0.0166 = 0.4833

The area of the shaded region is of 0.4833.

A similar problem is given at https://brainly.com/question/22940416

If mowing burns average $115 over 20 minutes how many calories are you burning in one hour

Answers

Answer:

345

Step-by-step explanation:

20*3 = 60 there's 60 minutes in one hour

115*3 = 345

Brian needs to paint a logo using two right triangles. The dimensions of the logo are shown below. What is the difference between the area of the large triangle and the area of the small triangle? ​

Answers

Answer:

7.5 cm²

Step-by-step explanation:

Dimensions of the large ∆:

[tex] base (b) = 3cm, height (h) = 9cm [/tex]

[tex] Area = 0.5*b*h = 0.5*3*9 = 13.5 cm^2 [/tex]

Dimensions of the small ∆:

[tex] base (b) = 2cm, height (h) = 6cm [/tex]

[tex] Area = 0.5*b*h = 0.5*2*6 = 6 cm^2 [/tex]

Difference between the area of the large and the small ∆ = 13.5 - 6 = 7.5 cm²

5. If W(-10, 4), X(-3,-1), and Y(-5, 11) classify AWXY by its sides. Show all work to justify your
answer.​

Answers

Answer:

  an isosceles right triangle

Step-by-step explanation:

The square of the length of a side can be found from the distance formula:

  d^2 = (x2-x1)^2 +(y2-y1)^2

The square of the length of WX is ...

  WX^2 = (-3-(-10))^2 +(-1-4)^2 = 49+25 = 74

The square of the length of XY is ...

  XY^2 = (-5-(-3))^2 +(11-(-1))^2 = 4 +144 = 148

The square of the length of YW is ...

  YW^2 = (-10-(-5))^2 +(4 -11)^2 = 25 +49 = 74

The sum of the squares of the short sides is equal to the square of the long side, so this is a right triangle. The squares of the short sides are equal, so this is an isosceles right triangle.

Solve 5(2x + 4) = 15. Round to the nearest thousandth.

Answers

[tex]5(2x + 4) = 15\\10x+20=15\\10x=-5\\x=-\dfrac{5}{10}=-0,5[/tex]

Answer:

[tex]\huge\boxed{x=-0.5}[/tex]

Step-by-step explanation:

[tex]5(2x+4)=15\qquad\text{divide both sides by 5}\\\\\dfrac{5\!\!\!\!\diagup(2x+4)}{5\!\!\!\!\diagup}=\dfrac{15\!\!\!\!\!\diagup}{5\!\!\!\!\diagup}\\\\2x+4=3\qquad\text{subtract 4 from both sides}\\\\2x+4-4=3-4\\\\2x=-1\qquad\text{divide both sides by 2}\\\\\dfrac{2x}{2}=\dfrac{-1}{2}\\\\\boxed{x=-0.5}[/tex]

Write "six and thirty-four thousandths" as a decimal

Answers

Answer:

6.034

Step-by-step explanation:

6 is a whole number.

.034 because it is 34 thousandths, not 34 hundredths.

Simplify to create an equivalent expression. 4(-15-3p)-4(-p+5)

Answers

Answer:

- 8p - 80

Step-by-step explanation:

Given

4(- 15 - 3p) - 4(- p + 5) ← distribute both parenthesis

= - 60 - 12p + 4p - 20 ← collect like terms

= - 8p - 80

Answer:

-8p -80

Step-by-step explanation:

4(-15-3p)-4(-p+5)

Distribute

-60 -12p +4p -20

Combine like terms

-60-20 -8p +4p

-80-8p

-8p -80

Which property of equality was used to solve this equation?
X-5 = -14
X-5 + 5 = -14 + 5
x= -9

OA. addition property of equality

OB. subtraction property of equality

OC. multiplication property of equality

OD.division property of equality

Answers

Answer:

OA. addition property of equality

Step-by-step explanation:

In the second step of the problem, you can see they add 5 to both sides of the equation. So, it is the addition property of equality.

Answer:

addition property of equality

Step-by-step explanation:

X-5 = -14

Add 5 to each side using the addition property of equality

X-5 + 5 = -14 + 5

x= -9

what is the number if 4 is subtracted from the sum of one fourth of 5 times of 8 and 10

Answers

Answer=16. Hope this helps

Answer:18.5

Step-by-step explanation:

10+8=18

18*5=90

90/4

22.5-4=18.5

If the coefficient of correlation is 0.8, the percentage of variation in the dependent variable explained by the variation in the independent variable is

Answers

Answer:

The percentage of variation in the dependent variable explained by the variation in the independent variable is 80 %.

Step-by-step explanation:

A coefficient of correlation of 0.8 means that dependent variable changes in 0.8 when independent variable changes in a unit. Hence, the percentage of such variation ([tex]\%R[/tex]) is:

[tex]\%R = \frac{\Delta y}{\Delta x}\times 100\,\%[/tex]

Where:

[tex]\Delta x[/tex] - Change in independent variable, dimensionless.

[tex]\Delta y[/tex] - Change in dependent variable, dimensionless.

If [tex]\Delta x = 1.0[/tex] and [tex]\Delta y = 0.8[/tex], then:

[tex]\%R = 80\,\%[/tex]

The percentage of variation in the dependent variable explained by the variation in the independent variable is 80 %.

What is the diameter of the base of the cone below, to the nearest foot, if the volume is 314 cubic feet? Use π = 3.14.

Answers

This question is incomplete because it lacks the required diagram. Please find attached the diagram required to answer the question.

Answer:

14 feet

Step-by-step explanation:

The volume of a cone = 1/3 πr²h

In the above question, we are given the volume = 314 cubic feet

the height is given in the attached diagram = 6ft

Step 1

We find the radius.

From the formula for the volume of a cone, we can derive the formula for radius of the cone.

Radius of the cone = √(3 × V/π × h

π = 3.14

Radius of the cone = √( 3 × 314 /3.14 × 6

Radius of the cone = √942/3.14× 6

Radius = √50

= 7.0710678119feet

Step 2

Diameter of the cone = Radius of the cone × 2

= 7.0710678119 × 2

= 14.142135624 feet

Approximately to the nearest foot = 14 feet

Therefore, the diameter of the cone to the nearest foot = 14 feet.

-4-(-1) answer the question

Answers

Answer:

-3

Step-by-step explanation:

Since you are subtracting a negative, it turns positive so it will be.

-4+1

-3

Answer:

-3

Step-by-step explanation:

-4-(-1) = -4 + 1 = -3

A bag of 100 hard candies included 30 butterscotch, 40 peppermint, 15 strawberry, 10 orange, and 5 banana. The probability that the first candy pulled out of the bag will be butterscotch or strawberry is .45
a) true
b) false

Answers

Answer:

true

Step-by-step explanation:

there is 100 candies. That means we can easily turn the amount of each type of candy into a percent. there was 30 butterscotch which means that is 30 percent. There was 15 strawberry which means that is 15 percent. add that and you get 45. This is a shortcut and i advise you use the way your teacher taught you.

[tex]|\Omega|=100\\|A|=30+15=45\\\\P(A)=\dfrac{45}{100}=0.45[/tex]

So TRUE

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