what is a rational number?

V=1 /4*h*sqrt(﹣a^4+2(ab)^2+2(ac)^2﹣b^4+2(bc)^2﹣c^4)

h = sqrt(3^2 + 5^2) = 5.80

Answer:  43.63 units^3

Final answer:

The turkey weighs 12 pounds, and the ham weighs 6 pounds. This was determined by setting up an equation based on the given cooking times per pound, converting the total cooking time to minutes, and solving for the weight of the ham, which was then used to find the turkey's weight.

Explanation:

Calculating the Weights of Turkey and Ham

Ella is cooking a turkey and a ham for Thanksgiving. The turkey takes 15 minutes per pound to cook, while the ham takes 23 minutes per pound. Altogether, the cooking time is 5 hours and 18 minutes, which converts to 318 minutes (5 hours x 60 + 18). We are told the turkey weighs twice as much as the ham.

Let's define x as the weight of the ham in pounds. Then the turkey's weight is 2x pounds. The total cooking time for the ham is 23x minutes, and for the turkey, it is 2x multiplied by 15, which is 30x minutes. Adding both cooking times gives us the total cooking time:
23x + 30x = 318
53x = 318
x = 6

Therefore, the ham weighs 6 pounds, and the turkey weighs 12 pounds (twice the weight of the ham).

i think your answer is 22.5 because if you divide 15 by 8 to find out how each one works you get 1.875 and take that and multiply it by 12 because 3 stopped, you would have 22.5

Final answer:

Karen's mother picked 51 pears. The ratio of pears to apples picked was 3:7, and using the total number of items (170), we set up and solved two equations to find the number of pears.

Explanation:

The question is about determining how many pears were picked if Karen's mother picked 3 pears for every 7 apples, with a total of 170 items picked. Let's let P represent the number of pears and A represent the number of apples. We know the following ratios and totals:

We can use these ratios to set up two equations:

By substituting the first equation into the second, we get:

(3/7 * A) + A = 170

This simplifies to:

(10/7) * A = 170

Dividing both sides by (10/7) we find:

A = 170 * (7/10)

A = 119

Substituting A back into the P + A equation:

P + 119 = 170

P = 170 - 119

P = 51

So, Karen's mother picked 51 pears.

We cannot calculate the percentage reduction in price because the question does not provide enough information. We need the sale price, as well as the original price, to determine the percentage reduction. The formula used is Percentage Reduction = ((Original Price - Sale Price) / Original Price) * 100.

To determine the percentage by which the total cost of the two books is reduced during the sale, we first need to know the original price and the sale price of the books. The original price for two books, according to Jim, is $10 each which means the total cost is $20. However, we are not given the information about the sale price of the books, hence we cannot calculate the percent reduction.

We use the formula: Percentage Reduction = ((Original Price - Sale Price) / Original Price) * 100. Despite having the original price, without information on the sale price, solving the problem is impossible.

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Answer:

By comparison, 2x = 4 and x + y = -5.

2x = 4 implies that x = 4/2 = 2

x + y = -5 implies that y = -5 - x = -5 - 2 = -7.

Step-by-step explanation:

If I am correct, I think you have to subtract 121 degrees from 79 degrees, and the answer would be:

B. 48 degrees

The quadratic equation for this would be f(x) = 5x^2 - 10x - 120.

In order to find that, we need to start by taking our x intercept values and setting them equal to zero.

x = 6 ----> subtract 6 from both sides

x - 6 = 0

x = -4 ----> add 4 to both sides

x + 4 = 0

Now that we have both of these zero terms, we can multiply them to get a standard form.

f(x) = (x - 6)(x + 4)

And while this will give us the zeros we need, it will no give us the lead coefficient. So we must multiply by the desired lead coefficient.

f(x) = 5(x - 6)(x + 4)

f(x) = 5(x^2 - 6x + 4x - 24)

f(x) = 5(x^2 - 2x - 24)

f(x) = 5x^2 - 10x - 120

The quadratic equation whose roots are 6 and -4, and leading coefficient is 5 is 5x^2 - 10x - 120 = 0.

To write the quadratic equation whose roots are 6 and -4 with a leading coefficient of 5, we make use of the general form of a quadratic equation ax^2 + bx + c = 0. Knowing that the roots can be represented as (x - root1)(x - root2) = 0, we can form the equation as x^2 - (root1 + root2)x + root1*root2 = 0. Here, root1 is 6 and root2 is -4.

Plugging these values into the equation, we get:x^2 - (6 - 4)x + 6*-4 = x^2 - 2x - 24 = 0. Finally, we multiply this entire equation by the leading coefficient of 5 to get 5x^2 - 10x - 120 = 0.

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It is given in the question that a parade traveled 9 miles in 3 minutes.

Here distance is 9 miles and time is 3 minutes.

We have to find how many miles travelled per minute. It means , we have to find the speed, and the formula of speed is

[tex]speed = \frac{distance}{time}[/tex]

Substituting the values of distance and time, we will get

[tex]speed = \frac{9}{3} miles/minutes[/tex]

[tex]speed = 3 miles/minutes[/tex]

Therefore the parade travelled 3 miles per minute .

Answer:

B. The sum of three products; there are three terms.

Step-by-step explanation:

We have been given an expression [tex]3x+2y+8z[/tex]. We are asked to choose the sentence which best describes our given expression.

We can see that our given expression has three variables and each of them is multiplied by a number. Therefore, there are three terms is our given expression.

We can see that each term is product of a number and variable and all terms are being added, therefore, our expression represents the sum of three products and option B .

Answer:

5 7/12

Step-by-step explanation:

28/12 + 39/12 = 67/12 = 5 7/12

The mean distance ran by all four of them is 30.

Given is that during one week, Josh ran 36 miles, Corey ran 26 miles, Rhona ran 30 miles, and Lyndsay ran 28 miles.

       [tex]${\displaystyle {\bar {x}}={\frac {1}{n}}\left(\sum _{i=1}^{n}{x_{i}}\right)={\frac {x_{1}+x_{2}+\cdots +x_{n}}{n}}}[/tex]

We can write the mean as -

m = (36 + 26 + 30 + 28)/4

m = 120/4

m = 30

Therefore, the mean distance ran by all four of them is 30.

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Answer:
6) x = 16°, scalene triangle
7) x = 45°, right triangle

Explanation:
The sum of all angles within a triangle is 180 degrees so if given two angles, we can set up an equation to solve for the missing third angle.

For question 6, our equation is 39 + 125 + x = 180. Let's solve and then classify:
39 + 125 + x = 180
164 + x = 180
164 - 164 + x = 180 - 164
0 + x = 180 - 164
x = 16

Because no two angles within the triangle have the same measure and no two legs on its edges have the same length, its classification is a scalene triangle.

For question 7, the triangle has a box that indicates one of its known angles is 90 degrees. So our equation is 90 + 45 + x = 180. Let's solve and then classify:
90 + 45 + x = 180
135 + x = 180
135 - 135 + x = 180 - 135
0 + x = 180 - 135
x = 45

Because the triangle contains a right angle indicated by that same box we used to derive that one of the angles measured 90 degrees, we can determine that this classification is a right triangle.

Final answer:

To find the total length that 5 pairs of size 8 shoes will cover, multiply the length of one pair by the number of pairs. The total length will be 48 1/3 inches.

Explanation:

To find the total length that 5 pairs of size 8 shoes will cover, we need to multiply the length of one pair by the number of pairs. Since a size 8 kids shoe measures 9 2/3 inches, we can multiply this by 5 to find the total length.

Step 1: Convert the mixed number,16/3, to an improper fraction:  9 2/3 = (9*3 + 2)/3 = 29/3 inches.

Step 2: Multiply the length of one pair by the number of pairs: (29/3) * 5 = 145/3 inches.

Step 3: Simplify the fraction: 145/3 = 48 1/3 inches.