find the zeros of the following polynomial p(x) = 3x³ + 9x² - 12x​

After multiplying by the LCD, the denominators are eliminated, resulting in the equation (x-2)(x+2) - 3x = (x-2)(x-3). Further simplifying this equation, we obtain x^2 - 3x - 4 = x^2 - 5x + 6 which can then be solved with algebraic methods.

To solve the given equation by multiplying each term by the lowest common denominator (LCD), which is 3x(x-2), we need to eliminate the fractions first.

The given equation is:

(x+2)/(3x) - 1/(x-2) = (x-3)/(3x)

After multiplying each term in the equation by the LCD, we have:

Now, we can write the new equation without denominators:

(x-2)(x+2) - 3x = (x-2)(x-3)

Next, we simplify it:

x^2 + 2x - 2x - 4 - 3x = x^2 - 3x - 2x + 6

x^2 - 3x - 4 = x^2 - 5x + 6

This equation can now be simplified or solved using algebraic methods such as combining like terms or moving all terms to one side in preparation for factoring or applying the quadratic formula.

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Answer:

(x-2)(x+2) - 3x = (x-2)(x-3)

Step-by-step explanation:

Answer: 10 square units

Answer:6 square units

Step-by-step explanation: count the top its 6 plus i did the test for my brother

Answer:

As a proper fraction  - 39/51 = 13/17

As a decimal number:  39/51 ≈ 0.76

As a percentage:  39/51 ≈ 76.47%

Step-by-step explanation:

Calculate the greatest (highest) common factor (divisor), gcf (gcd).

13/17 =

13 ÷ 17 =

0.764705882353 ≈

0.76

By precentage

0.764705882353 =

0.764705882353 × 100/100 =

76.470588235294/100 =

76.470588235294% ≈

76.47%

Answer:

Step-by-step explanation:

The graph has a relative minumum.  TRUE   Actually, I'd call it an absolute minimum, since 5 is the smallest y value and the graph opens up.

The graph shown has a vertex at (0, 5)  TRUE.  This point is also the absolute minimum of the function.

The graph opens up.  TRUE

The graph has neither one nor two x-intercepts.  The graph never crosses or touches the x-axis.  

Answer:

A,B,C,F

Step-by-step explanation:

everything above was right except that there were more answers! For Algebra Nation the photo is incomplete and doesnt show the last two questions. I just took the test

For this case, I should find the unit cost per pound of orange.

[tex]\frac {4} {2} = 2 \frac {dollars} {libra}[/tex]

Zack wants to buy at the same price per pound.

Then, you can buy peaches:

[tex]\frac {6} {3} = 2 \frac {dollars} {pound}[/tex]

Answer:

Option C

Peaches at $ 6.00 for 3 pounds

Answer:

[tex]a_{n}[/tex] = 8 - 11n

Step-by-step explanation:

These are the terms of an arithmetic sequence with n th term

[tex]a_{n}[/tex] = a + (n - 1)d

where a is the first term and d the common difference

here a = - 3 and

d = - 14 - (- 3) = - 14 + 3 = -11, thus

[tex]a_{n}[/tex] = - 3 - 11(n - 1)

                        = - 3 - 11n + 11

                        = 8 - 11n

The explicit formula for the sequence -3, -14, -25, -36, ... is An = -11n + 8.

The student asked for an explicit formula for the sequence -3, -14, -25, -36, and so forth. We notice that each term decreases by 11 from the previous term. To find an explicit formula, we can use the arithmetic sequence formula which is given by An = A1 + (n - 1)d, where An is the n-th term, A1 is the first term, n is the term number, and d is the common difference between the terms.

For the given sequence, the first term A1 is -3 and the common difference d is -11. Substituting these values into the formula, we get An = -3 + (n - 1)(-11). We can simplify this to An = -3 - 11n + 11, which simplifies further to An = -11n + 8. Hence, the explicit formula for the given sequence is An = -11n + 8.

Answer:

the answer is

The surface area of Figure 1 is 10.2 square centimeters Less than the surface area of Figure 2.

Step-by-step explanation:

Figure 1

area of a square = s2

=9squared

=81 sq cm

area of triangle = 1/2 bh

=1/2 (9cm) (14cm)

=63 sq. cm

find surface area

SA = 81 sq. cm + 4(63 sq. cm)

SA = 81 sq. cm + 252 sq. cm

SA = 333 sq. cm

Figure 2 Calculation

area of rectangle = lw

a = (12cm) (8 cm)

a = 96 sq. cm

area of triangle = 1/2 bh

=1/2 (8 cm) (6.9 cm)

= 27.6 sq. cm

total surface are of figure 2

SA = 3 (96 sq.cm) + 2 (27.6 sq. cm)

SA = 288 sq. cm + 55.2 sq. cm

SA = 343.2 sq. cm

find the difference between figure 1 and figure 2

343.2 sq. cm - 333 sq. cm = 10.2 sq. cm

Final answer:

We cannot complete the statement definitively about the surface area comparison between the square pyramid and the triangular prism without specific measurements. However, if we knew the dimensions, we could use the principle that surface area scales with the square of the linear dimensions to compare the two.

Explanation:

To complete the statement about the surface areas of Figure 1 (a square pyramid) and Figure 2 (a right triangular prism), we need to consider how areas scale with the dimensions of the shapes. Salviati's example illustrates that surface areas scale with the square of the linear dimensions, which is an important concept in geometry. Applying this concept to two triangles where one is larger than the other with linear dimensions twice as long, the larger triangle will have an area four times greater (area scales with the square of the linear dimensions).

Correct solution #1: Since the larger triangle's sides are twice as long, its area is 22 = 4 times more than the smaller triangle. If we applied similar reasoning and knew the dimensions of Figure 1 and Figure 2, we could compare their surface areas. However, with the provided information, we cannot definitively complete the given statement about the surface area of the pyramid relative to the prism without the specific measurements of each figure.

By understanding that the surface area of shapes scales with the square of their dimensions and using examples like cutting the larger triangle into four smaller ones (correct solution #2), we can tackle the surface area comparison confidently, provided we have the necessary dimensions.

Answer: that would be 112 oz

Step-by-step explanation:

Answer:

I believe the correct answer is  112 Ounces

Step-by-step explanation:

: 16 (1 lb = 16 oz)

which means you would do 7 times 16

Including Billy's score of 80% will lower the class average from 93% because his score is below the initial average.

When including Billy's test score of 80% into the class average that was previously 93%, the class average will definitely go down. This is because Billy's score is lower than the class average, so when it is factored into the overall calculation, it will decrease the average. Hence, the correct answer to the question is: C. The class average will go down.

Answer:

Derek delivers 10 magazines per hour.

Step-by-step explanation:

derek delivers ten magazines per hr

Answer:

Step-by-step explanation:

Put x = -15 to the equation y = 2x - 3:

y = 2(-15) - 3 = -30 - 3 = -33

Answer:

y = 27

Step-by-step explanation:

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

[tex]y=2(15)-3[/tex]

[tex]y=30-3[/tex]

[tex]y=27[/tex]

Answer:

it will be less than

Step-by-step explanation:

Answer:less than

Step-by-step explanation:

Answer: 26in

s=r*theta

r=s/theta

d=r*2

136ft=r*40pi

r=136/40pi=1.082ft

d=1.082*2=2.1645ft*(12in/1ft)=25.97in

Rounded to nearest in is 26in diameter

The diameter of the bike's tire is calculated by dividing the total distance traveled by the number of revolutions to find the circumference and then dividing the circumference by pi (π) to find the diameter, which is approximately 26 inches.

To find the diameter of the bike’s tire, given that it completes 20 revolutions and travels 136 feet, we can use the relationship between the circumference of a circle (in this case, the tire) and its diameter.

First, we calculate the circumference of the tire by dividing the total distance traveled by the number of revolutions:

Circumference = Total Distance ÷ Number of Revolutions

Total Distance = 136 feet (1 foot = 12 inches, so convert feet to inches for precision)

Total Distance in inches = 136 feet × 12 inches/foot = 1632 inches

Circumference = 1632 inches ÷ 20 = 81.6 inches

Now, we use the circumference to find the diameter:

Circumference = π × Diameter

Diameter = Circumference ÷ π

Diameter ≈ 81.6 inches ÷ π ≈ 26 inches

Therefore, the diameter of the bike’s tire, rounded to the nearest inch, is approximately 26 inches.

Answer:

View the picture please!

Step-by-step explanation:

Answer:

20.6

Step-by-step explanation:

Use the trig function Cosine to find the length of the ramp. The cosine function is defined as the ratio adjacent side over hypotenuse. The base 20 is the adjacent side to the angle 14 while the length of the ramp is the hypotenuse. Using the function we write, cos 14 = 20 / x. Solve for x.

Cos 14 = 20 / x

x*Cos 14 = 20

x = 20 / cos 14

x = 20.6

Answer:

Your can times them all up

Step-by-step explanation:

Answer: it is (-2,2)

Step-by-step explanation:

You go on the -2 point on the x axis and 2 block up from that point to get (-2,2).

Answer:

The answer .03 is 10 times greater than .003

Step-by-step explanation:

.003 x 10= .03

Final answer:

The value of 0.03 is ten times greater than the value of 0.003. This is evident by observing that 0.03 is expressed as 3 x 10^-2 while 0.003 is expressed as 3 x 10^-3, showing 0.03 is one decimal place to the left of 0.003.

Explanation:

The value of 0.03 is ten times greater than the value of 0.003. This conclusion is reached by observing the placement of the decimal point. For each power of ten we move to the right, the number becomes 1/10 the size of the previous number. Conversely, moving one place to the left (making the number ten times bigger), we increase the value of the number by a factor of 10.

Expressing these numbers with negative exponents, we have:

As illustrated above, since 10-3 is one factor of 10 smaller than 10-2, the value 0.03 is ten times greater than 0.003.

Answer:

see explanation

Step-by-step explanation:

Using the rule of logarithms

• [tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]

Hence

with b = 4 and n = - 2

[tex]log_{4}[/tex] [tex]\frac{1}{16}[/tex] = - 2, then

[tex]\frac{1}{16}[/tex] = [tex]4^{-2}[/tex] ← in exponential form

ANSWER

The exponential form is

[tex] \frac{1}{16} = {4}^{ - 2} [/tex]

EXPLANATION

The given logarithm is

[tex] log_{4}( \frac{1}{16} ) = - 2[/tex]

We want to write the given logarithm in exponential form:

We take the antilogarithm of both sides to obtain:

[tex] {4}^{log_{4}( \frac{1}{16} )} = {4}^{ - 2} [/tex]

We simplify the left hand side to obtain:

[tex] \frac{1}{16} = {4}^{ - 2} [/tex]

Hence the exponential form is

[tex] \frac{1}{16} = {4}^{ - 2} [/tex]

Answer:

see explanation

Step-by-step explanation:

This is an arithmetic sequence with n th term

• [tex]a_{n}[/tex] = a + (n - 1)d

where a is the first term and d the common difference

d = 2 - 7 = - 3 - 2 = - 5 and a = 7, hence

[tex]a_{n}[/tex] = 7 - 5(n - 1) = 7 - 5n + 5 = 12 - 5n

[tex]a_{n}[/tex] = 12 - 5n ← n th term formula

False, The claim that the range of the data set (16, 8, 16, 14, 10, 9, 8, 11, 12, 13, 18) is 97 is false. The actual range is the difference between the largest and smallest values, which is 10.

The task is to determine whether the statement that the range of the provided data set is 97 is true or false. First, let's define the range. It is the difference between the smallest and largest numbers in a data set. Looking at the data provided: 16, 8, 16, 14, 10, 9, 8, 11, 12, 13, 18, we find the smallest value to be 8 and the largest to be 18.

To calculate the range, we subtract the smallest number from the largest: 18 - 8 = 10. Consequently, the initial claim that the range is 97 is false. The correct range of this data set is, in fact, 10.

The given statement the range of the set of data below is 9 is false.

The correct answer is False.

To find the range of a set of data, we subtract the smallest value from the largest value.

Step 1: Identify the smallest and largest values in the data set.

  Smallest value: 7

  Largest value: 18

Step 2: Calculate the range.

  Range = Largest value - Smallest value

  Range = 18 - 7

  Range = 11

Step 3: Compare the calculated range with the given range.

  Given range = 9

  Calculated range = 11

Since the calculated range (11) does not match the given range (9), the statement "The range of the set of data below is 9" is False.

The range of a data set measures the spread or dispersion of the data. It is calculated by finding the difference between the largest and smallest values in the data set. In this case, the smallest value is 7 and the largest value is 18. Therefore, the range is 18 - 7 = 11. This contradicts the given range of 9, making the statement false. In summary, the correct answer is False, and the range of the given data set is 11.

Complete question:

The range of the set of data below is 9

7. 16, 8, 16, 14, 10, 9, 8, 11, 12, 13, 18

True

False

Answer:

Step-by-step explanation:

Since the questions are about which numbers are positive or negative and which have the largest magnitude, it is convenient to arrange them in order from least to greatest:

  -3.00 (E), -2.25 (A), -1.50 (C), 1.00 (B), 3.25 (D)

Nearsighted patients are those with negative prescriptions: E, A, C.

Farsighted patients are those with positive prescriptions: B, D.

The most nearsighted patient has the most negative prescription: E

The most farsighted patient has the most positive prescription: D

(5,3)

1. Determine the rule for this rotation

(x,y) ---> (-y,x)

2. Plug in

(3, -5) ----> (5,3)

Answer

(5,3)

Answer:

( -5, -3) .

Step-by-step explanation:

Given : A pre-image point is rotated 90° clockwise. If the pre-image point had the coordinates (3, -5).

To find : what are the coordinates of its image point.

Solution : We have given that

Parent coordinates (3, -5)

If the  point is rotated 90° clockwise.

By the rotation rule of 90° clockwise (x ,y) →→ ( y , -x) .

Then  (3 ,-5) →→ ( -5, -3)

Therefore, ( -5, -3) .

∠R = ∠Q, AS = AT       Given

∠5 = ∠6                        Base ∠'s of isosceles triangle are =

∠4, ∠5 are supplementary and ∠6, ∠7 are supplementary           Exterior sides in opposite rays

∠4 = ∠7                         Two ∠'s supplementary to equal ∠'s are =

Triangle RAS congruent to Triangle QAT          AAS

RS = QT                          CPCTE

Answer:

∠R = ∠Q, AS = AT       Given

∠5 = ∠6                        Base ∠'s of isosceles triangle are =

∠4, ∠5 are supplementary and ∠6, ∠7 are supplementary           Exterior sides in opposite rays

∠4 = ∠7                         Two ∠'s supplementary to equal ∠'s are =

Triangle RAS congruent to Triangle QAT          AAS

RS = QT                          CPCTE

Step-by-step explanation:

Micha's scale model of the Empire State Building is 7.62 centimeters tall

To determine the height in centimeters of Micha's scale model of the Empire State Building, we use the given scale where 1 cm represents 50 meters.

First, we find the scale factor for the actual height of the Empire State Building, which is 381 meters.

Using the scale, the calculation is as follows:

Actual height of Empire State Building = 381 m.

Scale ratio = 1 cm : 50 m.

Height of model in cm = Actual height (in meters) \/ Scale ratio (meters per cm).

Height of model in cm = 381 m / 50 m/cm.

Height of model in cm = 7.62 cm.

Therefore, the height of Micha's model is 7.62 centimeters.

Answer:

[tex]48.98\%[/tex]

Step-by-step explanation:

we know that

The probability that it will hit a point in the outer (yellow) ring is equal to divide the area of the yellow ring by the total area of the target

step 1

Find the area of the yellow ring

[tex]A=\pi [7^{2} -5^{2}][/tex]

[tex]A=24\pi\ cm^{2}[/tex]

step 2

Find the total area of the target

[tex]A=\pi [7^{2}][/tex]

[tex]A=49\pi\ cm^{2}[/tex]

step 3

Find the probability

[tex]24\pi/49\pi=0.4898[/tex]

Convert to percentage

[tex]0.4898*100=48.98\%[/tex]

Answer:

0.38468

Step-by-step explanation:

To know the probability we need to know the area of the yellow zone and the area of the rest. So, the yellow circle (that contains white, red and blue circle) has a radius of 1+2+2+2=7. Then the area is

Area yellow= [tex]\pi r^{2}= \pi *7^{2}=49\pi.[/tex]

But, the yellow zone is yellow circle - blue circle.

Area blue = [tex]\pi r^{2}= \pi *(1+2+2)^{2}=\pi *5^{2}=25\pi.[/tex]

Then, the yellow zone will be  [tex]49\pi-25\pi=24\pi.[/tex]

Area target= 14*14 = 196.

So, the probability is the yellow zone divided by the target (total area):

P = [tex]\frac{24\pi}{196}= \frac{6\pi}{49}= 0.38468.[/tex]

A. 3x+21

B. 25-5x

C.8x-16

D.x^2+6x+24

a. 3x + 21

b. 25 - 5x

c. 8x - 16

d. x^2 +6x + 8

Answer:

8 books; 4 from each shelf

Step-by-step explanation:

let x represent equal number of books from each shelf

from shelf A = 40 -x

from shelf B = 16 -x

shelf A has 3 times as many books than shelf B

3(16- x) = 40 -x

48 -3x = 40 -x

48 - 40 = -x + 3x

8 = 2x

x = 4

altogether she borrowed 4 + 4 = 8 books

[tex]\bf \begin{array}{ccll} books&price\\ \cline{1-2} 8&y\\ 3&x \end{array}\implies \cfrac{8}{3}=\cfrac{y}{x}\implies 8x=3y\implies x=\cfrac{3}{8}y[/tex]

Final answer:

To determine the price of 3 books when given the cost of 8 similar books, you divide the total cost by 8 to find the price per book, then multiply this price by 3.

Explanation:

The student asked: At a bookstore, 8 similar books cost y dollars. What is the price of 3 such books? To find the price of one book, we divide the total cost y by the number of books, which is 8. Let's call the price of one book x. So, x = y/8.

To find the price of 3 books, we multiply the price of one book by 3. Hence, the price of 3 books would be x times 3 or (y/8) times 3, which can be simplified to 3y/8.

Thus, the price of 3 such books is 3y/8 dollars.

Answer:

[tex]2(8x+3y)^2)[/tex]

Step-by-step explanation:

The given expression is [tex]128x^2+96xy+18y^2[/tex].

We factor the GCF to get:

[tex]2(64x^2+48xy+9y^2)[/tex]

This can be rewritten as:

[tex]2[(8x)^2+2(3\times8)xy+(3y)^2][/tex]

We can observe that the quadratic trinomial is a perfect square)

[tex]2(8x+3y)^2)[/tex]

Therefore the completely factored form of the given trinomial is [tex]2(8x+3y)^2)[/tex]

Answer:

What did he have before?

Step-by-step explanation:

A is the correct answer