(2%)Find the solution set ofx^2+4x-21≤0.

The division of the given polynomial would be (x^4) + 81.

What is the synthetic division?

Synthetic division is a method for dividing polynomials that allows you to divide a polynomial by a linear factor (a factor in the form of (x-c) where c is a constant) without actually performing the long division process. It is a short cut method that simplifies the process of dividing polynomials.

To divide the polynomials using synthetic division, we will use the following steps:

Write the polynomials in descending order of exponents. In this case, the given polynomials are already in descending order:

(x^4+ 81) / (x + 3)

Create a grid with the dividend on the left and the divisor on the right.

x^4 81

x 3

Bring down the leading coefficient of the dividend, which is x^4 in this case. Write it in the next row of the grid.

x^4 81

x^4 x 3

Multiply the divisor (x + 3) by the leading coefficient (x^4) and write the result in the next row.

x^4 81

x^4 x 3

x^5 x^5 3x^4

Subtract the second row from the third row and write the result in the next row.

x^4 81

x^4 x 3

x^5 x^5 3x^4

0 81-3x^4

Bring down the next coefficient of the dividend (81) and write it in the next row of the grid.

x^4 81

x^4 x 3

x^5 x^5 3x^4

0 81-3x^4

81

Now we repeat the steps 4-6 for the rest of the coefficients of the dividend, but there is no more coefficients in this example.

The quotient is x^4 and the remainder is 81

So the final answer is:

(x^4)+(81)

Hence, the division of the given polynomial would be (x^4) + 81.

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Answer:

y>\frac{2}{3} x+4

Step-by-step explanation:

Graph the inequality by finding the boundary line, then shading the appropriate area.

Hope this helps :)

Answer:

Step-by-step explanation:

Your first step should be to use the Distributive property to simplify the part where it says: -2(a+b). Then you need to put in the numbers given to you for a=2 and b=4  

[tex]\begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \log_{3}(y+5)+\log_3(6)~~ = ~~\log_3(66) \\\\[-0.35em] ~\dotfill\\\\ \log_3[(y+5)\cdot 6]=\log_3(66)\implies (y+5)6=66 \\\\\\ y+5=\cfrac{66}{6}\implies y+5=11\implies \boxed{y=6}[/tex]

A decaying exponential function is modeled as follows:

y = a(1 - r)^t.

In which the parameters are given as follows:

For this problem, the function is defined as follows:

y = 476000(0.81)^t.

Hence the values of the parameters are given as follows:

a = 476000, r = 0.19, meaning that the percent decay is of 19%.

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N'O' is a transformation of NO. The measurement of  N'O' is 30.

What is a line segment?

A line segment is a section of a straight line that is bounded by two distinct end points and contains every point on the line between them. The Euclidean distance between the endpoints of a line segment determines its length.

A scale factor is defined as the ratio of the scale of a given original object to the scale of a new object that is its representation but of a different size (bigger or smaller). For example, we can enlarge a rectangle with sides of 2 cm and 4 cm by multiplying each side by a number, say 2.

Given that NO is dilated by a scale factor of 3/4 to form N'O'.

The length of NO is 40.

To find the length of N'O', multiply the scale factor by the length of NO.

Thus the length of N'O is 3/4 ×40 =30

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N'O' is a transformation of NO. The measurement of  N'O' is 30.

What is a line segment?

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Explore all similar answers

The complex number in rectangular form is z = √2 - i√2

The rectangular form of of a complex number is given by z = a + ib where

where

Given the complex number

z = 2[cos(- π/4) + isin(- π/4)] , we desire to find the rectangular form of the complex number. We proceed as follows.

z = 2[cos(- π/4) + isin(- π/4)]

z = 2cos(- π/4) + i2sin(- π/4)]

z = 2cos(π/4) - i2sin(-π/4)]

Since cos(π/4) = sin(π/4) = 1/√2, we have that

z = 2cos(π/4) - i2sin(-π/4)]

z = 2 × 1/√2 - i2 × 1/√2

z = 2/√2 - i2/√2

Rationalizing the denominators, we have that

z = 2/√2 × √2/√2 - i2/√2 × √2/√2

z = 2√2/2 - i2√2/√2

z = √2 - i√2

So, we have the number in rectangular form as z = √2 - i√2

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Step-by-step explanation: angle on a straight line equals=180

(a) x+2x+3x =180

(b) 6x=180 (divide both sides by the coefficient of x i.e 6)x

    x=180divide by 60

    x =30

(c) now we know the value of x substitute it to get the largest value

      x+2x+3x =180

30+2(30)+3(30)=180

30+60+90=180

therefore the largest angle is 90 degrees

Answer:

19

Step-by-step explanation:

8 = 1/3 (a+5)

24 = a + 5

=> a = 19

Answer:

[tex]a=19[/tex]

Step-by-step explanation:

[tex]8=\frac{1}{3} (a+5)[/tex]

To find the answer we have to find the value of the variable. In order to find the value of the variable we need to isolate it from the equation.

[tex]8=\frac{1}{3} (a+5)[/tex]
[tex]\frac{1}{3} (a+5)=8[/tex]
Multiply 3 on both sides:
[tex]8\times3=24[/tex]
[tex](a+5)=24[/tex]
Subtract both sides by 5:
[tex]24-5=19[/tex]
[tex]a=19[/tex]

Therefore your answer is "a = 19."

Hope this helps.

Answer:

Step-by-step explanation:

When the plane landed in Las Vegas it was 4:30PM Pacific time - this converts to 730 PM Eastern time.

The entire trip lasted from 9:45 am to 7:30 pm.  This is a total of 9 hours and 45 minutes.

Subtract 2 hours and 20 minutes for the layover and the plane was flying

for 7 hours and 25 minutes.

9 - 2 = 7 hours and 45 minutes - 20 = 25 minutes

The slope of the given  linear relationship is; 4/5

Slope tells us that a unit change in x, which  is the independent variable will result in a change in y by the amount of b. Thus;

slope = change in y/change in x

Slope = rise/run.

In terms of two coordinates, the slope can be  expressed as;

slope = (y₂ - y₁)/(x₂ - x₁)

From the graph attached, we are given the two coordinates as;

(-3, -2) and (2,2)

Thus;

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

Slope = 4/5

This is the slope of the linear relationship.

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Answer:

1) Quadrilateral ABCD is translated 5 units and 4 units down, then reflected in the y-axis. This will result in congruent figures. Translation only moves the figure without changing the size or shape, and reflection in the y-axis will mirror the figure across the y-axis without altering its size or shape. Since both operations preserve the size and shape of the figure, the resulting figure will be congruent to the original.

2) ΔJKL is dilated by a scale factor of 2 and then rotated 180° about the origin. This will result in congruent figures. Dilation by a scale factor of 2 will double the size of the triangle while maintaining its shape, and rotation by 180° about the origin will flip the triangle over the origin while maintaining its shape. Since both operations preserve the size and shape of the figure, the resulting figure will be congruent to the original.

3) Line segment XY is rotated 90° about the origin, dilated by a scale factor of -1/2, and then reflected in the line x = 5. This will result in similar figures. Rotation by 90° about the origin will rotate the line segment by 90 degrees, dilated by a scale factor of -1/2 will shrink the size by half but with a change in direction and reflection in the line x = 5 will mirror the figure across the x=5 line without altering its size or shape. Since all the operations maintain the shape of the figure but the size changes, the resulting figure will be similar to the original one.

Translation and reflection doesn't change the shape or size of the figure, therefore the resulting figure is congruent to the initial one.

Rotation doesn't change the shape of the figure, but dilation changes the size, therefore the resulting figure is similar to the initial one.

Rotation and reflection don't change, but dilation changes the size, therefore the resulting segment is similar to the initial one.

Answer:

First choice

y = 3ˣ

Step-by-step explanation:

It is easier if you examine the obviously wrong choices

Choice 2, y = 9x is incorrect because at x = 0, y = 9x should be 0, instead it is 1

Choice 3 , y = 3x is incorrect for the same reason

Choice 4 y = x³ is incorrect because at x = 0, x³ should be 0, instead it is 1

Correct choice is the first one: y = 3ˣ

Let's check:

x = 0,  y = 3⁰  = 1 because any number raised to the power 0 is 1

x = 1, y = 3¹ = 3; because any number raised to the power 1 is 1itself

x = 2; y = 3² = 9 ; so fts

You can test out the rest of the entries yourself

Answer:

The equation that can be used to find y, the height of the first bounce, in inches, when the ball is dropped from a height of x inches is y=x/2. This can be determined by analyzing the data in the table:

-When the ball is dropped from a height of 10 inches, the height of the first bounce is 5 inches (y=5).

-When the ball is dropped from a height of 20 inches, the height of the first bounce is 10 inches (y=10).

-When the ball is dropped from a height of 30 inches, the height of the first bounce is 15 inches (y=15).

In all these cases, the height of the first bounce is half the height of the drop, meaning that the equation y=x/2 is the correct one

Answer:

B) y = x/2

Step-by-step explanation:

When the ball is dropped 10 inches, the ball bounces 5 inches

5 = 10/2

When the ball is dropped 20 inches, the ball bounces 10 inches.

10 = 20/2

When the ball is dropped 30 inches, the ball bounces 15 inches.

15 = 30/2

Answer: 69

Step-by-step explanation:

In the equation 692 = 4,761, we can see that 692 is being multiplied by some number to get 4,761. To find that number, we can divide 4,761 by 692:

4,761 / 692 = 69.

So, 4,761 / 69 = 69

In this case, 692 is being multiplied by 69 to get 4,761, so 69 is the value we get when we divide 4,761 by 69.

The probability that -2 < x < 2 is given as follows:

P(-2 < x < 2) = 0.16.

From the table given in this problem, the probability distribution is defined as follows:

The desired interval in this problem is given as follows:

-2< x <2.

It is an open interval, meaning that the only outcome that satisfies this interval is X = 0, and thus the probability is given as follows:

P(-2 < x < 2) = 0.16.

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Answer:

Step-by-step explanation:

First, we will use the property of radicals that states that (a √b) * (c √d) = (ac) √(bd). Since the expression has both multiplication and addition, we will break the expression down into its components and simplify each component separately.

6√x+7√(54) = 6√x + 7√(27*2) = 6√x + 7√27 * 7√2 = 6√x + 7√27 * (2*√2) = 6√x + 14√27 * √2 .

Next, we will simplify the second component of the expression: 12√(6) = 12√(2*3) = 12√2 * 6√3 = (4*3)√2 * 6√3 = 12√2 * 6√3.

Finally, we can combine the two separate parts of the expression to get the simplified version: 6√x + 14√27 * √2 - 12√2 * 6√3 = 6√x + 14√27 * √2 - 12√6.

The simplified version of the expression is 6√x + 14√27 * √2 - 12√6, in exact terms (no decimals).

The equation of a circle in general form is (x-a)^2 + (y-b)^2 = r^2, where (a,b) is the center of the circle and r is the radius.

To put the equation of circle in standard form x2+y2−4x+5y−3=0 you need to complete the square and

bring the equation to the form (x-a)^2 + (y-b)^2 = r^2

so the center of the circle is (-2,2) and the radius is 3

Answer:

a)  The product of any two odd integers is an odd integer.

b)  The sum of two negative integers is always smaller than the smallest negative integer.

Step-by-step explanation:

Given:

Carry out a few examples to find a pattern:

Pattern:

Write the conjecture based on the found pattern.

Conjecture:  

Test the conjecture for accuracy using at least three sets of numbers.

Test:

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Given:

Carry out a few examples to find a pattern:

Pattern:

Write the conjecture based on the found pattern.

Conjecture:  

Test the conjecture for accuracy using at least three sets of numbers.

Test:

The linear function graphed is defined as follows:

B. y = 3x + 2.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The line in this problem crosses the y-axis at y = 2, hence the intercept b is given as follows:

b = 2.

When x increases by one, y increases by three, hence the slope m of the function is given as follows:

m = 3.

This means that the function is defined as follows:

y = 3x + 2.

Meaning that the correct option is given by option B.

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Answer:

130°

Step-by-step explanation:

Since QS bisects ∠PQR, the measures of angles PQS and SQR must be the same

m ∠PQS = 3x + 5

m ∠SQR= 2x + 25

Setting these expressions equal to each other:
3x + 5 = 2x + 25

Subtract 2x from both sides

3x - 2x + 5 = 25

x + 5 = 25

Subtract 5 from both sides

x = 20

Therefore m ∠PQS which is  3x + 5:

m ∠PQS = 3(20) + 5 = 65°

m ∠SQR = ∠PQS =65°  also

Adding the two together we get

m ∠PQR = 65 + 65 = 130°

Answer:

152

Step-by-step explanation:

8*10+12*6 =80+72 =152

The transformation of graph f (x) = x and h (x) = x - 4 is a translation 4 units to the left

The term transformation is used in mathematics to refer to the movements made by objects.

Translation refers to a type of transformation that involve a linear movement.

Movements as seen in translation includes

up

down

left

right

The y coordinate governs movements in the vertical direction that are up and down.

While the x coordinate controls the horizontal movement in the left and right directions.

The movement as described in the graphs f(x) and h(x) is translation 4 units to the left

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Answer:

the police tactic of charging a crowd with lathis or batons in order to disperse it

the interest the bond paid off is $7507.8125.

What is simple interest?

A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount. Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest. Now, before exploring the idea of basic curiosity in further detail,

The formula for simple interest is:

S = p*t*r/100

where P is the principal amount of money, R is the interest rate as a decimal, T is the time.

a bond that paid 7.75% simple interest earned $3,875 interest.

S = (3875*7.75*25)/100 = $7507.8125

Hence the interest the bond paid off is $7507.8125.

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Answer:

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

The distance is the product of the speed and time.

Given:

Find the distance:

Answer: Tina has read 16 pages and reads 22 pages per day until the book is finished.

Zuri has read 24 pages and reads 18 pages per day until the book is finished.

We can use this information to set up an equation to represent the number of pages read by each student over a certain number of days.

Let's call the page number they are on when they read the same amount of the book "p"

We can set up the equation as follows:

16 + 22d = 24 + 18d = p

Now we can solve for p by combining like terms:

16 + 22d = 24 + 18d

4d = 8

d = 2

Now we know that it takes 2 days for Tina and Zuri to read the same amount of the book.

Now we can use this value of d to find out what page they are on when they read the same amount of the book.

p = 16 + 22*2 = 16 + 44 = 60

So Tina and Zuri are on page 60 when they have read the same amount of the book.

Step-by-step explanation:

Let x be the first day's ride.The second ride will then be equal to 1.5 times.The third day's journey will cost 1.5 (1.5x)The ride on the fourth day will cost 1.5*1.5. (1.5x)

The length of the line that connects two places serves as the unit of measurement for distance.

By subtracting the different coordinates from the pair if the two points are on the same horizontal or vertical line, the distance can be calculated.

Let x be the first day's ride.

The second ride will then be equal to 1.5 times.

The third day's journey will cost 1.5 (1.5x)

The ride on the fourth day will cost 1.5*1.5. (1.5x)

Consequently, the distance traveled over the four days is

65=x+1.5x+1.5*1.5x+1.5*1.5*1.5x

65=x+1.5x+2.25x+3.375x

65=8.125x

by multiplying both sides by 8.125, we get

x=65/8.125

x=8mile

the initial ride be x miles long.

The second day's ride will be 12 miles long (=1.5 x =1.5*8).

The third day's ride will be 18 miles (1.5 x 1.5).

The fourth day's ride will be 27 miles, or 1.5*1.5(1.5x).

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Answer:

  7:48 p.m.

Step-by-step explanation:

You want to know when lights with periods 36 s, 64 s, and 110 s will change simultaneously again if they do so at 11 a.m..

The lights will change simultaneously after a time that is the least common multiple (LCM) of the periods of the lights.

The least common multiple is the product of the unique factors in each of the numbers:

  36 = 2² · 3²

  64 = 2⁶

  110 = 2 · 5 · 11

The unique factors are 2⁶, 3², 5, and 11. Their product is 31680. The lights will change simultaneously again after 31680 seconds.

We can convert this to hours, minutes, and seconds by repeated division by 60:

  31680 / 60 = 528 r 0

  528 / 60 = 8 r 48

31680 seconds is 8 hours, 48 minutes, and no seconds.

Adding that time to 11 a.m. gives a clock time of ...

  11:00 +8:48 = 19:48 = 7:48 p.m.

The lights will change simultaneously again at 7:48 p.m..

__

Additional comment

The lights will change simultaneously at 11 a.m. again after 11 days.