Using synthetic division, what is the quotient (3x^3 + 4x − 32) ÷ (x − 2)?

Answer:

13.1

Step-by-step explanation:

yes

Answer:

c -2 -1 0 1 and 2

Step-by-step explanation:

abs (x) < 3

Absolute value equations have 2 solutions, one positive and one negative ( remember to flip the inequality when taking the negative solution).

x<3 and x>-3

-3 <x<3

The integer solutions are -2,-1,0,1-2

We do not include 3 because there is no equals sign on the inequality.

Answer:

32291999

Step-by-step explanation:

Step 1

We will use the fundamental counting principle to work out the total number of possible plates. The fundamental principle of counting states that if a process can be completed in k steps, and that there are [tex]n_1[/tex] steps to complete the first step, [tex]n_2[/tex] steps to complete the second step and [tex]n_k[/tex] stepts to finish the kth step, then there are [tex]n_1\times n_2 \times ....\times n_k[/tex] ways to complete the steps.

Step 2

In this step we figure out the number of ways to complete each step given that no repetitions are allowed. Note that this will include the plate that has I,O,W,A.

The first step can be carried out in 10 ways because there are 10 digits.

The second step can be carried out in 9 ways because we are not allowed to repeat any digits.

The third step can be carried out in 26 ways as there are 26 letters of the alphabet.

The fourth step can be carried out in 25 ways because no repeats are allowed.

the fifth step can be carried out in 24 ways because two of the letters will already have been used.

The sixth step can be carried out in in 23 ways because three letters have been used already.

Step 3

The third step is to use the fundamental counting principle with the values listed in step 3. We will also subtract 1 from whatever value we get because we would have counted the combination with I,O,W,A in it. This calculation is shown below,

[tex]10\times 9\times 26\times 25\times 24\times 23-1=32291999[/tex]

To calculate the total number of available license plates in Iowa based on specific formats and restrictions.

License Plate Combination Calculation:

Since the format is 2 numbers followed by 4 letters, with restrictions on certain letters and repeat use, we calculate the possibilities step by step:

For numbers: 10 choices for each position, so 10×10 = 100 possibilities.

For letters: After considering the restrictions, we have 22 choices for the first letter, 21 for the second, 20 for the third, and 19 for the fourth, resulting in 22×21×20×19 = 155,760 possibilities.

Finally, multiplying the possibilities for numbers and letters gives us the total number of available license plates: 100 × 155,760 = 15,576,000.

let's say that number is "x", so that is then the 100%.

if 150 is 25%, what is "x"?

[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} x&100\\ 150&25 \end{array}\implies \cfrac{x}{150}=\cfrac{100}{25}\implies \cfrac{x}{150}=4\implies x=600[/tex]

Answer:

The answer is 19.4322

Step-by-step explanation:

The probability of Felipe winning a specific prize in the charity raffle is 1/9 or approximately 0.111.

The subject of the question is Mathematics and the grade level is Middle School.

To determine the probability of Felipe winning a specific prize from the 9 prizes, we need to divide the number of desired outcomes (one specific prize) by the total number of possible outcomes (9 prizes in total). Therefore, the probability of Felipe winning a specific prize is 1/9, or approximately 0.111.

For example, if Felipe wants to calculate the probability of winning the first prize, he has 1 desired outcome (winning the first prize) out of 9 possible outcomes (9 prizes in total). Thus, the probability of winning the first prize is 1/9.

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Answer:

associative property of multiplication

Step-by-step explanation:

Associative property of multiplication states that (a x b) x c = a x (b x c).

5 * (sqrt(9) *4) = (5* sqrt(9) ) *4

Answer:

What is the numerical sum of the degree measures of ∠DEA and ∠AEB?

✔ 180

What are the numerical measures of the angles?

x =

✔ 14.5

m∠DEA =

✔ 39.5

°

m∠AEB =

✔ 140.5

°

Step-by-step explanation:

Answer: 100 cents making it 1 dollar

Answer:

91 Cents

Step-by-step explanation:

The next and lowest coin is a penny.

90 + 1 = 91

ANSWER: [tex]y=9x-23[/tex]

EXPLANATION:

We can use the slope-formula to find the slope.

[tex]\text{Slope Formula:} \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\\frac{4+5}{3-2} =m\\\\\frac{9}{1} = m\\\\9=m[/tex]

Now that we have the slope, we can plug in one of the x and y values into the slope-intercept formula to find b.

[tex]\text{Slope-Intercept Formula}:y=mx+b\\\\4=9(3)+b\\\\4=27+b\\\\-23=b[/tex]

The equation of the line that passes through (3, 4) and (2, -1) is [tex]y=9x-23[/tex]

Answer:

(3v5+8v3+10v2)+(-12v5+4v3+14v2)

Final result :

 -3v2 • (3v3 - 4v - 8)

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 (((3•(v5))+(8•(v3)))+(10•(v2)))+(((0-(12•(v5)))+(4•(v3)))+(2•7v2))

Step  2  :

Equation at the end of step  2  :

 (((3•(v5))+(8•(v3)))+(10•(v2)))+(((0-(12•(v5)))+22v3)+(2•7v2))

Step  3  :

Equation at the end of step  3  :

 (((3•(v5))+(8•(v3)))+(10•(v2)))+(((0-(22•3v5))+22v3)+(2•7v2))

Step  4  :

Equation at the end of step  4  :

 (((3•(v5))+(8•(v3)))+(2•5v2))+(-12v5+4v3+14v2)

Step  5  :

Equation at the end of step  5  :

 (((3•(v5))+23v3)+(2•5v2))+(-12v5+4v3+14v2)

Step  6  :

Equation at the end of step  6  :

 ((3v5 +  23v3) +  (2•5v2)) +  (-12v5 + 4v3 + 14v2)

Step  7  :

Step  8  :

Pulling out like terms :

8.1     Pull out like factors :

  -9v5 + 12v3 + 24v2  =   -3v2 • (3v3 - 4v - 8)

Polynomial Roots Calculator :

8.2    Find roots (zeroes) of :       F(v) = 3v3 - 4v - 8

Polynomial Roots Calculator is a set of methods aimed at finding values of  v  for which   F(v)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  v  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  3  and the Trailing Constant is  -8.

The factor(s) are:

of the Leading Coefficient :  1,3

of the Trailing Constant :  1 ,2 ,4 ,8

Let us test ....

  P    Q    P/Q    F(P/Q)     Divisor

     -1       1        -1.00        -7.00    

     -1       3        -0.33        -6.78    

     -2       1        -2.00        -24.00    

     -2       3        -0.67        -6.22    

     -4       1        -4.00        -184.00    

     -4       3        -1.33        -9.78    

     -8       1        -8.00       -1512.00    

     -8       3        -2.67        -54.22    

     1       1        1.00        -9.00    

     1       3        0.33        -9.22    

     2       1        2.00        8.00    

     2       3        0.67        -9.78    

     4       1        4.00        168.00    

     4       3        1.33        -6.22    

     8       1        8.00        1496.00    

     8       3        2.67        38.22    

Polynomial Roots Calculator found no rational roots

Final result :

 -3v2 • (3v3 - 4v - 8)

Step-by-step explanation:

If the rectangle a × b and the rectangle c × d are similar, then

a : b = c : d.

Check:

[tex]A)\ \dfrac{6}{8}=\dfrac{6:2}{8:2}=\dfrac{3}{4}\qquad\text{CORRECT}\\\\B)\ \dfrac{6}{8}=\dfrac{6:2}{8:2}=\dfrac{3}{4}\neq\dfrac{2}{4}\\\\C)\ \dfrac{6}{15}=\dfrac{6:3}{15:3}=\dfrac{2}{5}\neq\dfrac{3}{8}\\\\D)\ \dfrac{9}{15}=\dfrac{9:3}{15:3}=\dfrac{3}{5}\neq\dfrac{3}{4}[/tex]

The problem is that Bob cannot evenly distribute his 24 fish and 18 plants across 5 tanks due to left over quantities when the numbers are divided.

The problem presented is a math problem requiring the use of division and balance. It involves Bob trying to evenly distribute his 24 fish and 18 plants across 5 tanks. An effective way is to divide the quantities of fish and plants by the number of tanks. Therefore, if there are 5 tanks, 24 fish would be divided by 5, giving 4 fish with 4 left over, and 18 plants divided by 5 gives 3 plants each with 3 left over. This indicates that an even distribution is not possible with these numbers, because there would always be a excess quantity of fish and plants beyond what can be put in the 5 tanks.

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To distribute the fish and plants without any leftover, divide the total number of fish and plants by the number of tanks.

To distribute the fish and plants without any leftover, Bob needs to divide them equally among the tanks. To find out how many fish and plants should be in each tank, we need to divide the total number of fish and plants by the number of tanks.

Number of fish in each tank = 24 fish / 5 tanks = 4 fish per tank.

Number of plants in each tank = 18 plants / 5 tanks = 3.6 plants per tank. Since we can't have a fraction of a plant, we can round it up to 4 plants per tank or distribute the leftover plant evenly among the tanks.

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Answer:

7.10

Step-by-step explanation:

163.25- 106.45

divided by 8

7.10

The cost c of one baseball if, baseball bat and 8 baseballs cost $163.25, and the bat cost $106.45 is $11.36.

It is a mathematical statement that says, "this is equivalent to that," in other words. There appears to be an equal sign in the middle, a mathematical expression on the right, and a mathematical expression on the left.

Given:

The total cost of a baseball bat and 8 baseballs cost is $163.25,

The cost of one bat is $106.45,

Write the equation for the statement as shown below,

106.45 × 1 + 8c = 163.25

Here c is the cost of one baseball,

Solve the above equation as shown below,

106.45  + 8c = 163.25

8c = 163.25 - 106.45

c = 56.8 / 8

c = 11.36

Thus, the cost of one baseball is $11.36.

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Answer:

Take wholesale cost and multiply it by 95%, then add to the original value

another way, just multiply by 1.95

Retail cost:  1.95*($99.50) = $194.03

Answer:

y = -3x-9

Step-by-step explanation:

To solve for y, we need to subtract 7 from each side

7-7 + y = -2-7 -3x

y = -3x-9

For x:

[tex]-2-3x=7+y[/tex]             add 2 to both sides

[tex]-3x=9+y[/tex]          divide both sides by (-3)

[tex]\boxed{x=-3-\dfrac{1}{3}y}[/tex]

For y:

[tex]7+y=-2-3x[/tex]      subtract 7 from both sides

[tex]\boxed{y=-9-3x}[/tex]

Using the scale factor 1/4 inch equals 1 foot to convert Julie's actual bedroom dimensions to the blueprint scale, the bedroom measures 3 inches by 4 inches on the blueprint.

To find the dimensions of Julie's bedroom on the architect's blueprint when the scale drawing is 1/4 inch equals 1 foot, we first need to establish the unit scale as a ratio. Given that the actual dimensions of her bedroom are 12 feet by 16 feet, we convert these measurements to inches on the blueprint using the provided scale.

We use the ratios:

By cross-multiplying and dividing, we can find the blueprint measurements:

For length:

For the width:

Therefore, the dimensions of her bedroom on the blueprint are 3 inches by 4 inches.

To find the blueprint dimensions of Julie's bedroom using the scale 1/4 inch = 1 foot, the actual dimensions of 12 ft by 16 ft are converted to 48 inches by 64 inches respectively by multiplying each dimension by the inverse of the scale ratio (4 feet / 1 inch).

To find the dimensions of Julie's bedroom on the blueprint, we must use the scale given which is 1/4 inch = 1 foot. This means that for every foot in actual size, it is represented by 1/4 inch on the blueprint. To convert Julie's actual bedroom dimensions, 12 feet by 16 feet, to blueprint dimensions, we multiply each by the inverse of the given scale.

Calculation steps for the length:

For the width, follow the same steps:

Therefore, the dimensions of Julie's bedroom on the blueprint should be 48 inches by 64 inches.

Answer:

I would combine like terms

Step-by-step explanation:

2/3x + 1/3x + =5

The first step would be to combine like terms

2/3 x + 1/3 x  = x

Answer:

- 10

Step-by-step explanation:

Wherever you see an x, put in a minus 1.

f(-1) = -3(-1)^2 + 2x - 5

f(-1) = -3(1) + 2(-1)  - 5

f(-1) = - 3 - 2 - 5

f(-1) = - 10

Answer:

  9/10 hours

Step-by-step explanation:

You want the total of 1/2 hours and 2/5 hours.

Addition of fractions is accomplished by converting them to values that have a common denominator.

  1/2 = 5/10

  2/5 = 4/10

Then the sum is ...

  1/2 +2/5 = (5/10) +(4/10) = (5 +4)/10 = 9/10

Manuel spent 9/10 hours on the two assignments.

__

Additional comment

Equivalently, you can convert the fractions to decimals and add them that way:

  1/2 +2/5 = 0.5 +0.4 = 0.9 . . . . . 9/10 hours

Your calculator can tell you what the sum is.

Answer:

The equation of the  line has a slope of -5 and passes through the point (2, 2) is  y = -5x + 12 .

Option (D) is correct.

Step-by-step explanation

The equation of the line

y = mx + c

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

As given

A line has a slope of -5 and passes through the point (2, 2).

The slope of the line is -5.

m = -5

Put in the equation of the line

y = -5x + c

Put x = 2 and y = 2

2 = -5 × 2  + c

2 = - 10  + c

2 + 10 = c

12 = c

Put the value of c in the y = -5x + c

y = -5x + 12

Therefore the equation of the  line has a slope of -5 and passes through the point (2, 2) is  y = -5x + 12 .

Option (D) is correct.

To find the equation of the line with slope -5 passing through (2, 2), use the point-slope form and simplify to get y = -5x + 12. Therefore, the correct answer is option D.

To find the equation of the line with a slope of -5 that passes through the point (2, 2), we can use the point-slope form of the equation of a line:

y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is the point the line passes through.

Substituting the given values:

y - 2 = -5(x - 2)

Simplify this equation:

Therefore, the equation of the line is y = -5x + 12, so the correct answer is option D.

The statement is true. Amir did indeed drive from Jerusalem to the Dead Sea, which holds the distinction of being the lowest point on Earth in terms of land elevation.

True. Amir drove from Jerusalem to the Dead Sea, which is indeed the lowest place on Earth in terms of land elevation. The Dead Sea is a remarkable geographical feature located in the Jordan Rift Valley and is renowned for its extreme salinity, making it one of the saltiest bodies of water on Earth. The surface of the Dead Sea lies approximately 430 meters (1,410 feet) below sea level, and its shores border both Jordan to the east and Israel and the West Bank to the west.

Jerusalem, on the other hand, is situated on a plateau in the Judaean Mountains, and the drive from Jerusalem to the Dead Sea involves descending from higher elevations down to the low-lying area where the Dead Sea is located. This journey provides travelers with a striking transition from the elevated terrain around Jerusalem to the uniquely low and buoyant waters of the Dead Sea.

The Dead Sea's remarkable location and its high salinity levels have made it a popular destination for tourists seeking the therapeutic benefits of its mineral-rich mud and the sensation of effortlessly floating on its surface. This natural wonder's status as the lowest place on Earth is well-documented and contributes to its global renown.

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The question probable may be:

Amir drove from Jerusalem to the lowest place on earth, the Dead Sea.   True or false.

Answer:  a) 278382 oz

b) 43 oz

c) 64.1 oz

Step-by-step explanation:

a) 8 T. 1,398 lb. 14 oz. × 6

First we need to change it in 'oz'.

As we know that

[tex]1\ ton=32000\ oz\\\\1\ lb=16\ oz[/tex]

so, it becomes,

[tex]8\times 32000+1398\times 16+14\ oz\\\\=278382\ oz[/tex]

8 T. 1,398 lb. 14 oz. × 6 becomes

[tex]278382\times 6\\\\=1670292\ oz[/tex]

b) 349 lb. 6 oz. ÷ 130

It becomes,

[tex]349\times 16+6\ oz\\\\=5590\ oz\\\\\text{ at last it becomes}\\\\=\frac{5590}{130}\\\\=43\ oz[/tex]

c) 6 T. 294 lb. ÷ 3,071

First it becomes,

[tex]6\times 32000+294\times 16\ oz\\\\=196704\ oz[/tex]

At last it becomes,

[tex]\frac{196704}{3071}\\\\=64.1\ oz[/tex]

Hence, a) 278382 oz

b) 43 oz

c) 64.1 oz

Answer:

A. 278382 ounces

B. 43 ounces

C. 64.1 ounces

The length of DE is 6 inches.

I can see that from the image, DE is a horizontal line segment that is 6 units long. This is because the x-axis is labeled in units, and DE spans 6 units on the x-axis.

we know that

The triangle XYZ and DEF are similar triangles

therefore

The ratio of their corresponding sides is equal

12/8 = 9/x

x = 8 * 9/12

x = 6 Units.

Therefore the length of DE is 6 inches.

Answer:

4 hours

Step-by-step explanation:

6.25X4=25 so he'll have an extra dollar

The green square is the larger square, the total area for the target would be 8 x 8 = 64 square units.

The area of the smaller yellow square would be 4 x 4 = 16 square units.

The green area would be the difference between the total target area and the yellow area: 64 - 16 = 48 square units.

The probability of hitting the green area = 48 / 64 = 0.75

The answer is C.

Answer:

(x, y) = (- 3, 3)

Step-by-step explanation:

given the 2 equations

- x + 3y = 12 → (1)

y = 6x + 21 → (2)

Substitute y = 6x + 21 into (1)

- x + 3(6x + 21) = 12 ← distribute

- x + 18x + 63 = 12

17x + 63 = 12 ( subtract 63 from both sides )

17x = - 51 ( divide both sides by 17 )

x = - 3

Substitute  x = - 3 into (2) for y

y = (6 × - 3 ) + 21 = - 18 + 21 = 3

solution is (- 3, 3 )

Answer:

C) m = -63 is your answer

Step-by-step explanation:

Isolate the variable (m). Note the equal sign, what you do to one side, you do to the other.

Multiply 3 to both sides

-21 = (m/3)

(-21)(3) = (m/3)(3)

m = (-21)(3)

Combine like terms. Simplify.

m = -21 * 3

m = -63

C) m = -63 is your answer

~

Answer:

x = 4 1/2 or 4.5 cm

Step-by-step explanation:

We know the perimeter of the rectangle is given by the formula

P =2(l+w)

19 = 2(2.5 + (2.5+x))

Simplifying

19 = 2( 5+x)

Distribute

19 = 10 + 2x

Subtract 10 from each side

19-10 = 10-10 + 2x

9 = 2x

Divide each side by 2

9/2 = 2x/2

4.5 = x

Answer:

When dealing with the area of ANY geometric shape the rule is, an increase that doubles one dimension, will equal an increase of 4 in area.

Basically, this is because 2² = 4

So, the larger cake will serve 6 * 4 = 24 people.

Step-by-step explanation:

Answer:

12 people

Step-by-step explanation:

rachel has 2 hexagonally shaped birthday cakes

Let A and B represent the two hexagonally shaped cakes.

the smaller of which serves six people.

Oh!, so Let A represent the Bigger cake;     &

B to represent the smaller cake;

SO, B serves ------- 6 people

The question proceeds by stating it that ;

If one length of one side of the larger cake is twice that of the smaller cake

If the smaller cake side B is x

and the larger cake A be 2x

An hexagonally shaped cake is definitely going to have 6 sides

So;

For B

6x = 6

x = 1

Since x =6 , For A

2x = 2(1)

= 2

Therefore, the cake is going to serve 2 × 6 people

= 12 people