A set of equations is given below: Equation E: c = 2d + 1 Equation F: c = 3d + 7 Which statement describes a step that can be used to find the solution to the set of equations? (1 point)


Equation F can be written as c = 3(c – 1) + 7.
Equation F can be written as c = 2(c – 7) + 1.
Equation F can be written as d + 1 = 3d + 7.
Equation F can be written as 2d + 1 = 3d + 7.

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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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

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 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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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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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:

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 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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The answer would be B

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: 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

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]

Answer:

c 4.47

Step-by-step explanation:

got it right on my test

The distance from (−3, 1) to (−1, 5) is 4.47

Slope of line is defined as the angle of line.  

The distance between two points is found by

[tex]d = \sqrt{( (x_2-x_1)^2 + (y_2-y_1)^2)}[/tex]

[tex]d = \sqrt{ ( (-1--3)^2 + (5-1)^2)}[/tex]

[tex]d=\sqrt{( (2)^2 + (4)^2)}[/tex]

[tex]d=\sqrt{(4+16)}[/tex]

[tex]d=\sqrt{(20)}[/tex]

d = 4.472135955

Rounding to the nearest hundredth

d = 4.47

Hence,  the distance from (−3, 1) to (−1, 5) is 4.47

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