find the values of a and b such that x^4 +ax^3 -7x^2 - 8x +b is exactly divisible by(x+2) and (x+3)

Yo sup??

6x^2+5x is a polynomial

-x^2+52 is also a polynomial

-7x^2+5/3x is not a polynomial as power of x is negative

x^2+5x^1/5 is not a polynomial as power of x is fraction

Hope this helps.

Answer:

  392

Step-by-step explanation:

You want the value of the square of the length XY, given X and Y are outside and symmetrically opposite the center of a 10-unit square and each is 6 units and 8 units from the two nearest vertices.

The attached drawing shows the positions of points X and Y. Each is 4.8 units horizontally and 3.6 units vertically from the nearest vertex of the square. That means their locations relative to each other are ...

  horizontally: 2×4.8 +10 = 19.6 units

  vertically: 6.4 -3.6 = 2.8 units

The square of the distance between X and Y will be given by the Pythagorean theorem:

  XY² = 19.6² +2.8² = 384.16 +7.84

  XY² = 392

__

Additional comment

The locations of X and Y relative to the side of the square can be found using the "geometric mean" relations for a right triangle. Triangle QXP has side lengths 6, 8, 10, which are a multiple of the well-known {3, 4, 5} right triangle. So ∆QXP is a right triangle with a right angle at X.

The length QX is the geometric mean √(QA·QP), so we have ...

  6 = √(10·QA)
  36 = 10·QA
  QA = 3.6   ⇒   PA = 6.4

and

  XA = √(QA·PA) = √(3.6·6.4)
  XA = 4.8

The value of [tex]\( XY^2 \)[/tex] is 100.

Let's begin by visualizing the problem. We have a square PQRS with side length 10. Points X and Y are outside the square such that XQ = YS = 6 and XP = YR = 8. We need to find the square of the distance between X and Y, denoted as [tex]\( XY^2 \)[/tex].

To solve this, we can use the Pythagorean theorem. Let's consider triangle XPQ. Since PQRS is a square, angle PQX is a right angle. Therefore, triangle XPQ is a right-angled triangle with PQ as the hypotenuse and XQ and XP as the other two sides.

Using the Pythagorean theorem for triangle XPQ, we have:

[tex]\[ 8^2 = 6^2 + XQ^2 \][/tex]

[tex]\[ 64 = 36 + XQ^2 \][/tex]

[tex]\[ XQ^2 = 64 - 36 \][/tex]

[tex]\[ XQ^2 = 28 \][/tex]

Now, we have found the square of the distance XQ, which is [tex]\( 28 \)[/tex].

Similarly, for triangle YRQ, which is also a right-angled triangle with YR as one leg and YS as the other leg, and RQ as the hypotenuse, we can write:

[tex]\[ 8^2 = 6^2 + RQ^2 \][/tex]

[tex]\[ 64 = 36 + RQ^2 \][/tex]

[tex]\[ RQ^2 = 64 - 36 \][/tex]

[tex]\[ RQ^2 = 28 \][/tex]

We have found that [tex]\( RQ^2 = 28 \)[/tex], which is the same as [tex]\( XQ^2 \)[/tex].

Now, to find [tex]\( XY^2 \)[/tex], we need to consider the distance between points X and Y. Since X and Y are outside the square and their distances to the square are equal (XQ = YS and XP = YR), the line segment XY is parallel to side PQ of the square and is also equal to the side length of the square, which is 10.

Therefore, [tex]\( XY^2 \)[/tex] is simply the square of the side length of the square PQRS:

[tex]\[ XY^2 = PQ^2 \][/tex]

[tex]\[ XY^2 = 10^2 \][/tex]

[tex]\[ XY^2 = 100 \][/tex]

Answer:

[tex]\log 2-\log 8=\log\frac{1}{4}\\\\\log 2-\log 8=-\log 4[/tex]

Step-by-step explanation:

[tex]\log 2-\log 8=\log\frac{2}{8}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \log\frac{a}{b}=\log a-\log b\\\\\log 2-\log 8=\log\frac{1}{4}\\\\\log 2-\log 8=\log 1-\log 4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \log\frac{a}{b}=\log a-\log b\\\\\log 2-\log 8=-\log 4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \log 1=0[/tex]

Answer:

log(1/4)

log(2) + log (1/8)

(A)  4 sec the ball is in the air.

(B) Height of the ball = 49 ft.

(C) Yes, the ball is at its maximum height at 1.5 seconds.

Solution:

Given data:

[tex]h(t)=-16t^2+48t+64[/tex]

Initial velocity = 48 ft/s

Height = 64 ft

(A)  [tex]-16t^2+48t+64=0[/tex]

a = –16, b = 48, c = 64

We can solve it by using a quadratic formula,

[tex]$\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$[/tex]

[tex]$\Rightarrow t=\frac{-48 \pm \sqrt{(48)^{2}-4 \times(-16)(64)}}{2(-16)}[/tex]

[tex]$\Rightarrow t=\frac{-48 \pm \sqrt{2304+4096}}{-32}[/tex]

[tex]$\Rightarrow t=\frac{-48 \pm \sqrt{6400}}{-32}[/tex]

[tex]$\Rightarrow t=\frac{-48 \pm 80}{-32}[/tex]

[tex]$\Rightarrow t=\frac{-48 + 80}{-32},\frac{-48 - 80}{-32}[/tex]

[tex]$\Rightarrow t=-1,t=4[/tex]

Time cannot be in negative. So neglect t = –1

t = 4 sec

Hence, 4 sec the ball is in the air.

(B) When t = 1.5 sec,

[tex]h(1.5)=-16(1.5)^2+48(1.5)+64[/tex]

h(1.5) = 49 ft

(C) The maximum height occurs at the average of zeros.

Average = [tex]\frac{(-1+4)}{2}=1.5[/tex] sec

Yes, the ball is at its maximum height at 1.5 seconds.

Answer:

y=4x+8

Step-by-step explanation:

y-y1=m(x-x1)

y-(-8)=4(x-(-4))

y+8=4(x+4)

y=4x+16-8

y=4x+8

Work is attached in the image provided.

Answer:

$278

Step-by-step explanation:

There is an endowpayment policy with face of $25,000 with the annual premium $22.24 per $1000.

So, the annual premium of the endowpayment policy with face of $25,000 will be equal to [tex]\frac{25000}{1000}\times 22.24 = 556[/tex] dollars.

And the semi annual payment for this policy will be [tex]\frac{556}{2} = 278[/tex] dollars. (Answer)

Answer: X = 27

Step-by-step explanation: The diagram shows two triangles with one triangle cut out from the other. A careful observation would reveal triangle BDR and triangle QDC.

Since line QC is parallel to line BR, that makes triangle QDC similar to triangle BDR. Also the ratio of lines QD and BQ is the same as the ratio of lines CD and RD. The same applies to lines QC and BR.

Therefore,

QD/BQ = CD/RC

Alternatively we can use the ratios,

QD/BD = CD/RD

Using the first ratios, we have

QD/BQ = CD/RC

39/26 = X/18

3/2 = X/18 {the left hand side has been reduced to it's simplest form}

If we cross multiply, we now arrive at

3 × 18 = 2X

54 = 2X

Divide both sides of the equation by 2

27 = X

Answer:

Step-by-step explanation:

40 per month + 0.20 per text(t)

40 + 0.2t....no parenthesis needed

Answer:

did it

Step-by-step explanation:

Answer:

The points are (0,-1) and (1,1)

Step-by-step explanation:

Answer:

Line A

Step-by-step explanation:

To find the total weight of the hamburger in three packages, multiply the weight of one package by three. The total weight of the hamburger is 5 1/4 pounds.

The student's question involves finding the total weight of three packages of hamburger, each weighing 1 3/4 pounds.

To solve this problem, the weight of one package must be multiplied by the number of packages.

The calculation is: 1 3/4 pounds × 3, or in improper fraction form, (7/4) pounds × 3.

Multiplying the improper fraction by 3, we have:

The fraction 21/4 is equivalent to 5 1/4 when converted into a mixed number because 21 divided by 4 is 5 with a remainder of 1.

Therefore, Mary has a total of 5 1/4 pounds of hamburger across the three packages.

Answer:

(1) Factor: a^n(1+a)

(2) Solve: x=0, x=2/3

Step-by-step explanation:

Steps to factor:

[tex]a^n+a^{n+1}[/tex]

~Apply rule of exponent ([tex]a^{b+c}=a^ba^c[/tex])

[tex]a^n+a^1a^n[/tex]

~Factor out the common term of [tex]a^n[/tex]

[tex]a^n(1+a)[/tex]

Steps to solve:

[tex]3x^3-x^2=x^2[/tex]

~Subtract [tex]x^2[/tex] to both sides

[tex]3x^3-x^2-x^2=x^2-x^2[/tex]

~Simplify

[tex]3x^3-2x^2=0[/tex]

~Factor left side of the equation

[tex]x^2(3x-2)=0[/tex]

~Set factors to equal zero

[tex]x^2=0[/tex] and [tex]3x-2=0[/tex]

~Simplify

[tex]x = 0[/tex] and [tex]x=\frac{2}{3}[/tex]

Best of Luck!

Answer:

Width = 16cm length = 24cm; Draw up to larger dimensions.

Step-by-step explanation:

Scale factor of 4 means the new shape is 4 times the size of the original.

Answer:

20%

Step-by-step explanation:

30-24=6

6/30=.2=20%

Answer:

Decrease by 6

Step-by-step explanation:

20%

At the same rate, the bakery would sell approximately 10 loaves of bread for every 7 rolls.

The bakery sells 25 rolls for every 35 loaves of bread. To find out how many loaves of bread will be sold for every 7 rolls of bread, we need to use a simple proportion based on the given ratio. This can be set up as a fraction, 25 rolls/35 loaves = 7 rolls/x loaves, where x represents the number of loaves sold for every 7 rolls.

We can solve for x by cross-multiplying:

(25 rolls/35 loaves) = (7 rolls/x loaves),

so 25x = 35*7.

The next step is to divide both sides of the equation by 25 to solve for x:

x = (35*7)/25 = 9.8 loaves.

Therefore, the bakery would sell approximately 10 loaves of bread for every 7 rolls, given the same rate.

8x + -4 > 12

8x > 16

x > 2

Hope this helps! ;)

Answer:8x + -4 > 12

8x > 16

x > 2

Step-by-step explanation:

4 pints of strawberries and 2 pints of blueberries are bought

Solution:

Let "a" be the pints of strawberries bought

Let "b" be the pints of blueberries cost

Cost per pint of strawberry = $ 1.60

Cost per pint of blueberry = $ 2.30

A shopper bought twice as many pints of strawberries as pints of blueberries

Therefore,

a = 2b --------- eqn 1

They spent a total of $11.00. Therefore we frame a equation as:

pints of strawberries bought x Cost per pint of strawberry + pints of blueberries cost x Cost per pint of blueberry = 11

[tex]a \times 1.60 + b \times 2.30 = 11[/tex]

1.6a + 2.3b = 11 --------- eqn 2

Substitute eqn 1 in eqn 2

1.6(2b) + 2.3b = 11

3.2b + 2.3b = 11

5.5b = 11

Divide both sides by 11

b = 2

Substitute b = 2 in eqn 1

a = 2(2)

a = 4

Thus 4 pints of strawberries and 2 pints of blueberries are bought

Answer:

3.45

Step-by-step explanation:

Its right on the quiz

Answer:

-1, 8, 17, 26

Step-by-step explanation:

35 - (-10) = 45

45/5 = 9

-10 + 9 = -1

-1 + 9 = 8

8 + 9 = 17

17 + 9 = 26

Final answer:

The four arithmetic means between -10 and 35 are -1, 8, 17, and 26.

Explanation:

To find the four arithmetic means between -10 and 35, we want to divide the interval evenly into six equal parts (because there will be five intervals with four means and two endpoints). First, calculate the total interval size:

35 - (-10) = 45

Then divide this interval by the total number of segments (which is one more than the number of means):

45 / (4 + 1) = 9

This gives us the common difference. Starting from -10 and adding the common difference of 9 each time, the four arithmetic means would be:

Thus, the four arithmetic means between -10 and 35 are -1, 8, 17, and 26.

Answer:

Explanation:

I will rewrite the table to understand how the process of solving using succesive approximations is.

Table:

x        f(x)      g(x)

0        - 5      - 6

1         - 3       - 5

2        - 1       - 2

3          1          3

Those are the points shown in the table.

Now you must continue the process of solving using successive approximations until you find the positive solution to the nearest tenth.

You need to determine whether a "guess" is closer or farther away of the solution.

The first row shows that g(x) is less than f(x) in 1 unit when x = 0 ( -6 - (-5) ) = -1.

The second raw shows that g(x) is less than g(x) in 2 units when x = 1 ( - 5 - (-3) ) = - 2

The third row shows that g(x) is is less than f(x) in 1 unit when x = 2 ( - 2 - (-1) ) = - 1.

The fourth row shows that g(x) is than f(x) in 2 units when x = 3 ( 3 - 1 = 2).

Hence, the trend changed form negative to positive, meaning that, since the functions are continous, there must be an intertemediate value of x (between x = 2 and x = 3) for which f(x) = g(x) and that is the solution.

Therefore, test x = 2.5

Test for x = 2.4

Now the difference is less than 0.1 and the solution to the nearest tenth is (2.4, - 0.2).

Answer:

answer is 2.7

Step-by-step explanation:

I got it right

Answer:

the answer is x^5

Step-by-step explanation:

add the exponents

The required expression equal to x².x³ is [tex]x^5[/tex].

Given that,
To determine the expression is equivalent to  x².x³

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
The given expression,
= x².x³
There is a property in the product if the base of the exponents is the same then their power gets added.
So, the simplification
= [tex]x^{2+3}[/tex]
= [tex]x^5[/tex]

Thus, the required expression equal to x².x³ is [tex]x^5[/tex].

Learn more about arithmetic here:

brainly.com/question/14753192

#SPJ2

Answer: 1/4

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:

i had the same question and 1/4 was right

Answer:

y =16

I have solved it . It's in the picture above. Hope it helps

A line is graphed in the x-y plane and it will follow a path of straight line and equation for that is,  Y = (-3/2)X.

So option (C) is correct.

The equation of a straight line is a relationship between x and y coordinates, The equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept.

The net change in y coordinate is written as, Δy and the net change in x coordinate is written as, Δx.

m = change in y coordinate/change in x coordinate = Δy/Δx = y2-y1/x2-x1

In given graph,

Line is passing through the points (2, -3) & (-2 ,3)

Slope = -3-3/2-(-2)

Slope = -3/2

y = (-3/2) x + c  ____(i)

by putting point (2, -3) in  equation (i)

-3 = (-3/2) 2 + c

c = 0

Hence, The equation is  Y = (-3/2)X

To know more about the equation of line check:

https://brainly.com/question/2564656

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Answer:

-8x+60

Step-by-step explanation:

3(-3x+20)+ 5(x/5)

Solve one term at a time

3(-3x+20)

-9x+60

Solve second term

5(x/5)

5x/5

X

Add both terms together

-9x+60+x

-9x+x+60

-8x+60

-8x+60

Step-by-step explanation:

3(-3x+20)+ 5(x/5)

Solve one term at a time

3(-3x+20)

-9x+60

Solve second term

5(x/5)

5x/5

X

Add both terms together

-9x+60+x

-9x+x+60

-8x+60

Answer:

Step-by-step explanation:

Simple multiply both 8 and 12 by any number and then equivalent

Answer:

3/4 or 16/24 or 2/3

Step-by-step explanation:

Answer:

not that hard sir

Step-by-step explanation:

do 7/8 x 5

Final answer:

Tarryn drives a total of 8.75 miles in a week to and from work, with each one-way trip being 7/8 mile and she works 5 days a week.

Explanation:

Calculating Total Distance Driven

Tarryn drives to and from work 5 days a week, with each trip being 7/8 mile. To calculate the total distance she drives in a week, we need to consider both the trip to work and the return trip. This will give us the daily round trip distance, which we will then multiply by the number of days she works in a week.

First, we calculate the daily round trip distance:

Round trip distance = Distance to work + Distance from work

Round trip distance = 7/8 mile + 7/8 mile

Round trip distance = 7/4 miles (or 1.75 miles)

Then, we calculate the total distance for the week:

Total weekly distance = Daily round trip distance × Number of workdays

Total weekly distance = 7/4 miles × 5 days

Total weekly distance = 35/4 miles (or 8.75 miles)

Therefore, Tarryn drives a total of 8.75 miles over the course of a 5-day workweek.

Using the negative exponent rule move x^-2 to the numerator

Answer = 5x^2/y^5

Answer:

3,-2

Step-by-step explanation:

Answer:

ITS (-3,2)

Step-by-step explanation:

Answer:

Step-by-step explanation:

So the dilation of .75.

You want to find what each point is before the dilation.

A(-10,-14)

B(-10,14)

C(12,14)

D(12,-14)

So, we multiply these by the scale factor, 0.75.

(x,y) = (X x 0.75, y x 0.75)

A  = -10 x 0.75, -14 x 0.75

B= -10 x 0.75, 14 x 0.75

C = 12 x 0.75 , 14 x 0.75

D = 12 x 0.75 , -14 x 0.75

now, the image of the figure would be

A' ( -7.5, -10.5)

B' (-7.5, 10.5)

C' (9, 10.5)

D' (9, -10.5)