If f(x)= -x²+3x+5, find f(-3), f(0), f(2), f(5), and f(8).

12) 10.77 + 2.09 + 0.75 = 13.61

13.61 x 1.07 = $14.56

 total amount = $14.56

14) C shows the possible combinations

Answer:

Option A is correct.

Step-by-step explanation:

Given: A 6-sided cube is rolled.

To find: Probability of getting a number greater than 3.

Total number of outcome when a 6-sided cube is rolled = 6

Favorable outcome = { 4 , 5  6 }

Number of favorable outcome = 3

Theoretical Probability is a probability based on reasoning written as a ratio of the number of favorable outcomes to the number of possible outcomes.

[tex]Probability=\frac{Number\:of\:favorable\:outcome}{Number\:of\:Total\:outcome}[/tex]

[tex]Probability=\frac{3}{6}=\frac{1}{2}[/tex]

Therefore, Option A is correct.

The solutions to the given quadratic equation are x=4 and x= -3/2.

The given quadratic equation is 2x²-5x-12=0.

By splitting the middle term, we get

2x²-8x+3x-12=0

2x(x-4)+3(x-4)=0

(x-4)(2x+3)=0

(x-4)=0 and (2x+3)=0

x=4 and 2x=-3

x=4 and x= -3/2

Therefore, the solutions to the given quadratic equation are x=4 and x= -3/2.

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Answer:

t = d/r

Step-by-step explanation:

In order to solve an equation for another term from which is initally solved by another term you just have to leave the term you want to solve the equation for, in this case the "t" and to do so since in this formula it is multiplying the "r" we haec to divide both sides of the equation by "r":

[tex]d=rt[/tex]

[tex]\frac{d}{r} =\frac{rt}{r}[/tex]

Now we eliminate the since they are in both sides of the fraction:

[tex]\frac{d}{r} =\frac{rt}{r}[/tex]

And the function is solved for t.

[tex]t=\frac{d}{r}[/tex]

Final answer:

To solve for b in the equation 4a = 2b - 7, you need to add 7 to both sides and then divide by 2. The solution is b = (4a + 7)/2.

Explanation:

To solve the equation 4a = 2b - 7 for b, you want to isolate b on one side of the equation. This means we need to perform operations that will move all other terms away from b.

First, let's add 7 to both sides of the equation to get rid of the -7 that's subtracted from b:

4a + 7 = 2b

Next, we will divide both sides of the equation by 2 to solve for b:

(4a + 7)/2 = b

So, b equals to the expression (4a + 7)/2.

Answer:

9.98 + 25.01p ≤ 60, so p ≤ 2

Step-by-step explanation:

I took a test and had this question got the answer you were told wrong

The number of cubes should be 1.440.

Calculate the volume of each shape is as follows:

Volume of rectangle = [tex]6 \times 5\div 6 \times 1\ 2\div 6 = 6\ 2\div 3[/tex] cubic inches.

And,

Volume of cube =[tex] 1\div6 \times 1\div6 \times 1\div6 = 1\div216[/tex] cubic inch.

Now

divide the volume of the rectangle by the volume of the cube:

So,

[tex]= (6\ 2\div 3) \div (1\div 216)[/tex]

= 1.440

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With whole life insurance, the insured agrees to pay a specific premium each year until death.

Whole life insurance is a plan that requires you to pay premiums for you entire life, thus it is known as "whole life."

The weight of each tire in pounds is approximately:

Full steel bead tire: 1.76 pounds.

Lighter wheel: 1.54 pounds.

Given that the weight of a full steel bead tire is approximately 800 grams, while a lighter wheel weighs only 700 grams.

We need to convert the weights into pound.

To convert the weight of each tire from grams to pounds, we'll use the conversion factor that there are 453.592 grams in one pound.

Weight of a full steel bead tire in pounds:

800 grams x (1 pound / 453.592 grams) ≈ 1.76 pounds

Weight of a lighter wheel in pounds:

700 grams x (1 pound / 453.592 grams) ≈ 1.54 pounds

Rounded to 2 decimal places:

Weight of a full steel bead tire = 1.76 pounds

Weight of a lighter wheel = 1.54 pounds

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Answer: [tex]n^4[/tex]

Step-by-step explanation:

The given division problem is [tex]n^7\div n^3[/tex]

The law of exponents says that [tex]a^{m+n}=a^ma^n[/tex]

Therefore, [tex]n^7=n^{3+4}=n^3n^4[/tex]

Now, the division problem becomes

[tex]n^7\div n^3\\\\=\frac{n^7}{n^3}\\\\=\frac{n^3n^4}{n^3}\\\\\text{Cancel }n^3\text{ as common from numerator and denominator, we get}\\\\n^7\div n^3=n^4[/tex]

hence, the quotient of the given problem = [tex]n^4[/tex]

Value of x is 1 + 5√2

Given that;

(x - 1)² = 50

Find:

Value of x

Computation:

(x - 1)² = 50

By taking square root both side

x - 1 = √50

x - 1 = 5√2

x = 5√2 + 1

x = 1 + 5√2

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Answer: Simplifying the square roots and adding the similar square roots the answer is option c. 6 square root of 5 end root minus 4 square root of 7

Solution:

3√5-2√7+√45-√28

45=9*5 and 28=4*7. Replacing in the equation above:

3√5-2√7+√(9*5)-√(4*7)

Using √(a*b)=√a√b

3√5-2√7+√9√5-√4√7

√9=3 and √4=2. Replacing in the equation above:

3√5-2√7+3√5-2√7

Adding similar square roots:

(3+3)√5+(-2-2)√7=

(6)√5+(-4)√7=

6√5-4√7

The correct conversion from scientific notation to standard notation are:

            b)   [tex]8.05\times 10^5[/tex]

            e)   [tex]7.09\times 10^{-6}[/tex]

We know that when we have  a power of 10 as positive then the decimal is shifted to the right and if the power of 10 is negative then we shift the decimal to the left.

a)

         [tex]1.71\times 10^3[/tex]

As the power of 10 is positive hence we shift the decimal to the right 3 places.

Hence, the conversion is:

         [tex]1.71\times 10^3=1710[/tex]

b)

           [tex]8.05\times 10^5[/tex]

Again the power of 10 is positive and hence we will shift the decimal 5 places to the right and the conversion is done as follows:

        [tex]8.05\times 10^5=805000[/tex]

c)

       [tex]2.4\times 10^4[/tex]

Since, the power of 10 is positive and hence we will shift the decimal 4 places to the right and we convert the number to standard notation as:

      [tex]2.4\times 10^4=24000[/tex]

d)

           [tex]8.25\times 10^{-3}[/tex]

Since, the power of 10 is negative and hence we will shift the decimal 3 places to the left and we convert the number to standard notation as:

        [tex]8.25\times 10^{-3}=0.00825[/tex]

e)

             [tex]7.09\times 10^{-6}[/tex]

Since, the power of 10 is negative and hence we will shift the decimal 8 places to the left.

Hence, we convert our number to standard notation:

[tex]7.09\times 10^{-8}=0.00000709[/tex]

It is accurate to convert scientific notation to standard notation in the following ways:

B [tex]8.05x10^5=805,000[/tex]

C [tex]2.4x10^4= -24,000[/tex]

E [tex]7.09x10^-^6=0.0000070[/tex]

Firstly, Let's evaluate each conversion one by one:

[tex]1.71x 10^3=0.00171[/tex]

This conversion is not true. The correct value of[tex]1.71x 10^3[/tex] is 1710.

[tex]8.05x10^5=805,000[/tex]

This conversion is true.

[tex]2.4x10^4= -24,000[/tex]

This conversion is true.

[tex]8.25x10^-^3=-8,250[/tex]

This conversion is not true. The correct value of [tex]8.25x 10^-^3[/tex] is 0.00825.

[tex]7.09x10^-^6=0.0000070[/tex]

This conversion is true.

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Answer:

STep by step

Step-by-step explanation: