how many different roots does the polynomial function have y = (x-2)(x+3)^2 have

Answer:

f(-3) = 0

Step-by-step explanation:

The question is asking you to evaluate the function when x = -3. Therefore, substitute -3 in for x and simplify.

f(x) = x² + 7x + 12                            <---- Original equation

f(-3) = (-3)² + 7(-3) + 12                    <---- Substitute -3 for x

f(-3) = 9 + 7(-3) + 12                         <---- Square -3

f(-3) = 9 - 21 + 12                             <---- Multiply 7 x -3

f(-3) = 0                                          <---- Combine terms

The difference in sizes in real life of the two scale drawing is  10 feet.

They hired two different architect to create a blueprints for the house.

Anderson Architects uses a scale of 1 in. to represent 1.5 feet.

Therefore,

1 inches = 1.5 feet

Real life size of 12inches by 12 inches

12 inches = ?

size = 12 × 1.5 / 1 = 18 feet

Charleston Architects uses a scale of 1.5 inches to represent 1 foot.

Therefore,

1.5 inches = 1 foot

Hence,

Real life size of 12inches by 12 inches

12 inches = ?

size = 12 / 1.5 = 8 feet

Therefore, the difference in real life is 18 - 8 = 10 feet.

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Answer:

A. 9x² - 7

Step-by-step explanation:

» Concepts

A monomial is an expression that consists of only one mathematical term.

A binomial is an expression that consists of only two mathematical terms joined by an addition (+) or subtraction (-) sign.

A polynomial is an expression that consists of three or more mathematical terms joined by an addition (+) or subtraction (-) sign.

» Solution

Given these definition, we can surely determine that A. 9x² - 7 is the correct answer because it's the only answer choice with only two terms. B is a polynomial, and C and D are monomials.

Answer:

45 degrees

Step-by-step explanation:

90 - 45 = 45

Answer:

1

Step-by-step explanation:

3:3 = 1

Answer:

12/25

Step-by-step explanation:

Multiply both the numerator and denominator of each fraction by the number whom makes its denominator equal the LCD.

[tex]\left(\frac{4 \cdot 10}{10 \cdot 10} \right) + \left(\frac{8 \cdot 1}{100 \cdot 1}\right) = \frac{40}{100} + \frac{8}{100}[/tex]

[tex]= \frac{48}{100}[/tex]

Find the new LCD(4).

[tex]\frac{48/4}{100/4} = \frac{12}{25}[/tex]

Answer:  2/5

Step-by-step explanation;

Answer:

1. 55.5

2. 54.5

Step-by-step explanation:

Use division to convert the fraction to a decimal:

1/4 = 1 ÷ 4 = 0.25

Multiply by 100 to get percent value:

0.25 × 100 = 25%

Answer:

1. 0.56

percentage: 56%

2. 0.55

percentage: 55%

Step-by-step explanation:

5/9 to decimal= 0.56

to percentage multiply by 100

same for the second one

Answer:

56 days

Explanation:

[tex]\sf Half \ Life : A = A_O \ x \ (\dfrac{1}{2} )^{\dfrac{t}{h} }[/tex]

where A is final amount, Ao is initial amount, t is time taken, h is half life

Here given:

initial amount: 400 millicuries

final amount: 3.125 millicuries

half life: 8 days

time taken: ?

Hence solve for time taken:

[tex]\sf \rightarrow A = A_O \ x \ (\dfrac{1}{2} )^{\dfrac{t}{h} }[/tex]

insert values given

[tex]\sf \rightarrow 3.125 = 400 \ x \ (\dfrac{1}{2} )^{\dfrac{t}{8} }[/tex]

divide both sides by 400

[tex]\sf \rightarrow (\dfrac{1}{2})^{\dfrac{t}{8}}=0.0078125[/tex]

apply exponent rule

[tex]\sf \rightarrow {\dfrac{t}{8}}=\dfrac{ln(0.0078125)}{ln(1/2)}[/tex]

simplify

[tex]\rightarrow \sf \dfrac{t}{8}=7[/tex]

multiply both sides by 8

[tex]\rightarrow \sf t = 56[/tex]

The value of 'x' with rational denominator =

[tex] \frac{4 \sqrt{3} }{3} [/tex]

Step-by-step explanation:

cos =

[tex] \frac{adjacent \: side}{hypotenuse} [/tex]

cos 30 =

[tex] \frac{ \sqrt{3} }{2} [/tex]

given triangle is a right- angled triangle.

from the triangle,

cost 30 =

[tex] \frac{adjacent \: side}{hypotenuse} \: \: = \: \frac{2}{x} [/tex]

[tex] \frac{ \sqrt{3} }{2} \: = \frac{2}{x} [/tex]

√3x = 4

[tex]x \: = \: \frac{4}{ \sqrt{3} } [/tex]

Rationalising the denominator we get,

x =

[tex] \frac{4}{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } [/tex]

x =

[tex] \frac{4 \sqrt{3} }{3} [/tex]

Therefore, the value of 'x' =

[tex] \frac{4 \sqrt{3} }{3} [/tex]

Answer:

x^3 + 3x^2 - 16x - 48.

Step-by-step explanation:

(x - 4)(x + 3)(x + 4)

= (x - 4)(x + 4)(x + 3)

= (x^2 - 16)(x + 3)

= x^3 + 3x^2 - 16x - 48.

The number of customer you expect to pay with a credit card will be 51 customers.

Binomial distributions consist of n independent Bernoulli trials.

The expected value will be

E(X) = np

Ian owns a small business selling used books.

He knows that in the last week 122 customers paid cash, 14 customers used a debit card, and 4 customers used a credit card.

If next week, he is expecting 1800 customers.

Then the number of the customer you expect to pay with a credit card will be

n = 1800

The probability of the customer who pays with a credit card will be

p = 4/140

p = 0.02587

Then the expected value will be

E(x) = 1800 x 0.02587

E(x) = 51.42

E(x) ≅ 51

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Answer:

b. 4 inches by 3inches.

Step-by-step explanation:

Length on the paper = 100/25 = 4 inches

Width  on the paper = 75/25 = 3 inches.

Each scatter plot with the description of its association are matched as:

A scatter plot refers to a type of graph which is used to graphically represent the values of two (2) variables, with the resulting points showing any association (correlation) between the data set.

Generally, there are four types of association in a scatter plot scatter plot and these include the following:

In this exercise, we would match each scatter plot with the description of its association as follows:

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Answer:

2.192

Step-by-step explanation:

Answer:

what do you need help with

Step-by-step explanation:

Answer:

[tex] {144in}^{3} [/tex]

Step-by-step explanation:

The formula for the volume of a pyramid is

1/3(b*h)

b = base area

h = height

1/3(36*12)

1/3(432)

144

Volume is always cubed, so answer is

[tex] {144in}^{3} [/tex]

Answer:

The answer is a

Step-by-step explanation:

If the triangles are congruent, then angle K will be the same as angle N

The triangles are congruent and the measures of angle  ∠K ≅ ∠N

Transformations change the size or position of shapes. Congruent shapes are identical, but may be reflected, rotated or translated. Scale factors can increase or decrease the size of a shape. Congruent Triangles simply mean the triangles that possess the same size and shape

The three sides are equal (SSS: side, side, side)

Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)

Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)

A right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)

Given data ,

Let the first triangle be ΔJKL

Let the second triangle be ΔMNP

Now , the triangles are congruent

So , ΔJKL ≅ ΔMNP ( given )

And , Congruent Triangles simply mean the triangles that possess the same size and shape

The three sides are equal (SSS: side, side, side)

So , the measures of angles are also similar

Hence , the angles are similar ( ∠K ≅ ∠N )

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Answer:

it's 68...............

Answer:

68

Step-by-step explanation:

so 25% of x=17

17*4=68

Answer:

5 to the power of 9

Step-by-step explanation:

You have 5^7 over 5^-2.

The 5^-2 on the bottom can be handled by moving the whole thing UP across the fraction bar. This makes the -2 exponent into a positive 2 exponent.

5^7 / 5^-2

= 5^7• 5^2

Now, to multiply these, ADD the exponents.

5^7•5^2

= 5^9

Answer:

D. They will always agree

Step-by-step explanation:

Correct me if I'm wrong

Answer:

Angle 1= 63°

Angle 2 = 21°

Angle 3 = 96°

Answer:

Positive

Step-by-step explanation:

As the "y" value of the coordinates increases from 3 to 5, the slope must be positive as the "x" value increases.

Given equations:

To find :

Put value of y of second equation (i.e y = 4x) in equation one (i.e x + y = 15)

➞ x + y = 15

➞ x + 4x = 15

➞ 5x = 15

Divide both LHS and RHS by 5

➞ (5x)/5 = 15/5

➞ x/1 = 3/1

➞ x = 3

Now put value of x in equation 2

{Note : value of x can be inserted both in equation 1 and 2}

➞ y = 4x

➞ y = 4 × 3

➞y = 12

Verification :

put value of x and y in equation 1 :

LHS = RHS

hence verified !

put value of x and y in equation 2 :

LHS = RHS

hence verified !

∴ Value of x and y is 3 and 12 respectedly .

REQUIRED ANSWER :

(x , y) = (3 , 12)

Answer:

(3, 12)

Step-by-step explanation:

Given equations:

Substitute Equation 2 into Equation 1 and solve for x:

⇒ x + 4x = 15

⇒ 5x = 15

⇒ x = 15 ÷ 5

⇒ x = 3

Substitute the found value of x into Equation 2 and solve for y:

⇒ y = 4(3)

⇒ y = 12

Therefore, the solution of the system is (3, 12)