can someone help me with this factoring problem? I forgot how to factor.

Factor completely −3x2 + 6x − 9.

−3(x2 − 2x + 3)
−1(x2 − 6x + 9)
−3x(x2 − 2x + 3)
−3(x2 + 2x − 3)

Answer:

Option: B is correct.

The factorization of the polynomial graphed below is:

f(x)=(x-2)(x-2)

Step-by-step solution:

Clearly from the graph we could see that the graph of the function touches x=2.

that means that x=2 is a root of the function

Also when the graph touches the point of x-axis and does not pass that point than that zero is the repeated zero of the function.

That means that x=2 is a repeated zero of the function f(x).

Hence,

The factorization of the polynomial graphed below is:

f(x)=(x-2)(x-2)

Hence, option B is correct.

( Also in first option:

A) x(x+2)

x=0 must also be an zero but in the graph we could see that x=0 is not a solution.

Hence option A is false.

C)

x(x-2)

again as in option: A x=0 must be a solution.

Hence, option C is false.

D)

(x+2)(x+2)

x=-2 must be a solution but the graph does not touches x=-2.

Hence, option D is incorrect )

Answer:

-_- Answer is -3

Step-by-step explanation:

Doing the instruction vidio.

Answer:

x = −3, 3, −4

Step-by-step explanation:

If all three guesses for the number of jelly beans 98, 137, and 164 were off by 12, 27, and 39 the correct guess for the number of jelly beans is 125.

The number of jelly beans was 125.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division. 

Example:

2x + 3 is an expression

2x  - 3 = 4 is an expression

We have,

Three guesses for the number of jelly beans:

98, 137, and 164.

These three guesses were all wrong.

The three guesses were off by:

12, 27, and 39.

The correct guess is 125 because,

98 + 27 = 125

137 - 12 = 125

164 - 39 = 125

Thus,

The number of jelly beans was 125.

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Answer:

$1,056,000 ≤ x ≤ $1,344,000

Step-by-step explanation:

took test

When [tex]\(x = 6\)[/tex], the expression [tex]\(4x - 7\)[/tex] simplifies to 17 following the order of operations.

To evaluate the expression [tex]\(4x - 7\)[/tex] when [tex]\(x = 6\)[/tex], substitute the value of [tex]\(x\)[/tex] into the expression and simplify using the order of operations.

[tex]\[4x - 7\][/tex]

Replace [tex]\(x\)[/tex] with 6:

[tex]\[4(6) - 7\][/tex]

Following the order of operations (PEMDAS), perform the multiplication first:

[tex]\[24 - 7\][/tex]

Now, perform the subtraction:

[tex]\[17\][/tex]

Thus, when \(x = 6\), the value of [tex]\(4x - 7\)[/tex] is 17.

In this expression, the variable [tex]\(x\)[/tex] is multiplied by 4, and then 7 is subtracted from the result. By substituting the value of [tex]\(x\)[/tex], which is 6 in this case, and simplifying according to the order of operations, we obtain the final result of 17.

The value of dimensions of rectangle are 5 and 7.

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

A rectangular table top has a perimeter of 24 inches and an area of 35 square inches.

Let the dimensions of rectangle are;

Length = L

Width = W

So, We can formulate;

⇒ 2 ( L + W ) = 24

⇒ L + W = 12   ..(i)

And,

⇒ L × W = 35

⇒ L = 35 / W  ... (ii)

Substitute the value from (ii) in (i), we get;

⇒ L + W = 12

⇒ 35/W + W = 12

⇒ 35 + W² = 12W

⇒ W² - 12W + 35 = 0

⇒ W² - (7W + 5W) + 35 = 0

⇒ W² - 7W - 5W + 35 = 0

⇒ W (W - 7) - 5 (W - 7) = 0

⇒ (W - 5) (W - 7) = 0

⇒ W = 5

And, W = 7

And, We get;

⇒ L = 35 / W

Put W = 5;

⇒ L = 35 / 5

⇒ L = 7

And,

⇒ L = 35 / W

Put W = 7;

⇒ L = 35 / 7

⇒ L = 5

Thus, The possible values of dimensions are;

⇒ 5 and 7.

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the first 4 would be rounded up tot he nearest dollar and the last one rounded down to the nearest dollar

 doing that I estimate $23.00

Answer is C

Answer:

8 half-lives of polonium-210 occur in 1104 days.

0.1174 g of polonium-210 will remain in the sample after 1104 days.

Step-by-step explanation:

Initial mass of the polonium-210 = 30 g

Half life of the sample, = [tex]t_{\frac{1}{2}}=138 days[/tex]

Formula used :

[tex]N=N_o\times e^{-\lambda t}\\\\\lambda =\frac{0.693}{t_{\frac{1}{2}}}[/tex]

where,

[tex]N_o[/tex] = initial mass of isotope

N = mass of the parent isotope left after the time, (t)

[tex]t_{\frac{1}{2}}[/tex] = half life of the isotope

[tex]\lambda[/tex] = rate constant

[tex]\lambda =\frac{0.693}{138 days}=0.005021 day^{-1}[/tex]

time ,t = 1104 dyas

[tex]N=N_o\times e^{-(\lambda )\times t}[/tex]

Now put all the given values in this formula, we get

[tex]N=30g\times e^{-0.005021 day^{-1}\times 1104 days}[/tex]

[tex]N=0.1174 g[/tex]

Number of half-lives:

[tex]N=\frac{N_o}{2^n}[/tex]

n =  Number of half lives elapsed

[tex]0.1174 g=\frac{30 g}{2^n}[/tex]

[tex]n = 7.99\approx 8[/tex]

8 half-lives of polonium-210 occur in 1104 days.

0.1174 g of polonium-210 will remain in the sample after 1104 days.

Final answer:

After using the compound interest formula with an initial deposit of $25,000, an annual interest rate of 11%, and a time period of 16 years, the balance rounds to $120,034.10, which does not match any of the provided answer choices.

Explanation:

To find out how much is in the account when the child turns 16 years old, we can use the formula for compound interest: an = a1(1 + r)n, where a1 is the original amount deposited, r is the annual interest rate (expressed as a decimal), and n is the number of years the money is invested. In this case, a1 is $25,000, r is 0.11 (11%), and n is 16.

Using the formula, we calculate the account balance as follows:

Account Balance = 25,000(1 + 0.11)16

Account Balance = 25,000(1.11)16

Account Balance = 25,000(4.801364)

Account Balance = $119,999.10

However, this result is not in the given answer choices, so let's ensure we are rounding to the nearest cent:

Account Balance = $120,034.09 (before rounding)

Account Balance = $120,034.10 (after rounding to the nearest cent)

None of the answer choices matches this amount, so it is possible there has been a mistake in the provided choices or in our calculations. We should double-check the interest rate, time period, and the formula used.

there are 13 diamonds per deck

26 black cards

4 aces

 so a 13/52 chance for a diamond

 a 26/52, reduced to 1/2 chance for a black card

 and a 4/52 chance for an ace

13/52 x 1/2 x 4/52 = 52/5408 = 1/104 probability

The transformation of the function f(x) to g(x) is a horizontal stretch.

The parent function f(x) is given by:

             [tex]f(x)=\sqrt{x}[/tex]

and the transformed function g(x) is given by:

              [tex]g(x)=\sqrt{0.5x}[/tex]

Now we know that the transformation of the type:

       f(x) → f(bx)

is a horizontal stretch if 0<b<1

and is a horizontal shrink if b>1

Here we have:

[tex]b=\dfrac{1}{2}=0.5[/tex]

i.e.

[tex]0<b<1[/tex]

This means that the transformation of the function f(x) to g(x) is a horizontal stretch by a factor of 2.

Answer: Option 'C' is correct.

The perimeter will be 10 times the original .

Step-by-step explanation:

Since we have given that

Length of the rectangle = 6 cm

Breadth of the rectangle = 3 cm

As we know the formula for "Perimeter of rectangle "

[tex]\text{Perimeter of original rectangle }=2(Length+ Breadth)\\\\\text{Preimeter of rectangle }=2(6+3)\\\\\text{Perimeter of rectangle }=18\ cm[/tex]

According to question, each side is increased by a factor of 10

so, Perimeter of new rectangle is given by

[tex]10\times 2\times (6+3)\\\\=180\ cm[/tex]

Hence, Option 'C' is correct.

So, the perimeter will be 10 times the original .

Answer:  The equivalent expression in degrees is 60°.

Step-by-step explanation:  We are given to find the equivalent of the following expression in degrees.

[tex]E=\dfrac{\pi}{3}~\textup{radians}.[/tex]

We will be using the UNITARY method the solve the given problem.

We know that

[tex]\pi~\textup{radians}=180^\circ\\\\\\\Rightarrow 1~\textup{radian}=\left(\dfrac{180}{\pi}\right)^\circ\\\\\\\Rightarrow \dfrac{\pi}{3}~\textup{radians}=\left(\dfrac{\pi}{3}\times\dfrac{180}{\pi}\right)^\circ=60^\circ.[/tex]

Thus, the equivalent expression in degrees is 60°.

To find the number, we set up the equation 7 - 1/(3x) = 1/(2x) and solve for x.

To find the number, we need to set up an equation based on the given information.

Let's assume the number is 'x'.

According to the problem, the reciprocal of three times the number is subtracted from 7 and is equal to the reciprocal of twice the number. We can write this as:

7 - 1/(3x) = 1/(2x)

To solve this equation, we can multiply both sides by the common denominator, which is 6x. This will eliminate the fractions.

6x * 7 - 6x * 1/(3x) = 6x * 1/(2x)

42x - 2 = 3

Subtracting 2 from both sides, we get:

42x = 1

Dividing both sides by 42, we find:

x = 1/42

Therefore, the number is 1/42.

The length of longest side of the triangle is 20 ft .

The perimeter of a triangle is defined as the total length of its boundary.

The basic formula used to calculate the perimeter of a triangle is:

Perimeter = sum of the three sides

According to the question

The lengths of the sides of a triangle are in the extended ratio 1 : 2 : 5 .

Let  common constant factor within ratio = x

Therefore,

Sides of triangle = x , 2x , 5x

and the perimeter of the triangle = 32 ft  

i.e

according to the formula of perimeter of a triangle:

Perimeter = sum of the three sides  

Now,

Substituting the value in formula

[tex]32 = x + 2x + 5x[/tex]

[tex]32 = 8x[/tex]

[tex]x = 4[/tex]  

The sides of triangle is  : 4 ft  , 2*4 , 5*4

                                       : 4 ft   , 8 ft  , 20 ft    

Hence, the length of longest side of the triangle is 20 ft

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Answer:

A. r^n=a

B. a^1/n=r

Step-by-step explanation:

ape x

The true statements about the equation [tex]\sqrt[n]a = r[/tex] are (a) r^n=a and (b) a^1/n=r

The equation is given as:

[tex]\sqrt[n]a = r[/tex]

Take the power of n on both sides of the equation

[tex](\sqrt[n]a)^n = r^n[/tex]

This gives

a = r^n

Rewrite as:

r^n = a

Also, we have:

[tex]\sqrt[n]a = r[/tex]

Apply the law of indices

a^1/n = r

Hence, the true statements about the equation [tex]\sqrt[n]a = r[/tex] are (a) r^n=a and (b) a^1/n=r

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