A farmhouse shelters 10 animals. Some are pigs and some are ducks. Altogether there are 36 legs. How many of each animal are there?

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:

Final answer:

The simplified product of the square root of 8 and the square root of 98 is determined by multiplying the numbers under the square roots to get √784, which is a perfect square. Hence, the product simplifies to 28.

Explanation:

To find the simplified product of the square root of 8 and the square root of 98, we can use the property of square roots that allows us to multiply the numbers under the radicals first, before taking the square root of the resultant product. This is a form of simplifying square roots when dealing with exponentials.

Firstly, multiply the numbers inside the square roots:

√8 × √98 = √(8 × 98)

Calculate the product:

8 × 98 = 784

Now we have:

√8 × √98 = √784

By squaring of exponentials, we know that the square root of a perfect square is the base number:

√784 = 28 (since 28 × 28 = 784)

Therefore, the simplified product is 28.

The simplified product of the square root of 8 and the square root of 98 is 28, achieved by using the property of radicals and simplifying the exponents within the radical.

To find the simplified product of the square root of 8 and the square root of 98, we can use the property of radicals where the product of two radicals can be combined into one radical, such that √(a) * √(b) = √(ab). To simplify further, we factor each number into its prime factors: 8 = 2³ and 98 = 2 * 7². We then combine the radicals: √(8) * √(98) = √(2³) * √(2 * 7²) = √(2´ * 7²).

Based on the properties of exponents and radicals, we can take the square roots of exponentials by finding which factors have exponents that are multiples of 2. In our case, we have 2´, which simplifies as 2², and 7², which is already a perfect square. Thus, √(2´ * 7²) simplifies to 2² * 7 = 4 * 7 = 28. So the simplified product of √(8) * √(98) is 28.

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

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

To find the required square feet of wood for the back of a shed, multiply the height by the width of the back wall to calculate its area.

To determine how many square feet of wood are needed to build the back of a shed, you need to know the height and width of the back wall of the shed. Assuming you have these measurements, you calculate the area in square feet by multiplying the height by the width.

For example, if the back of the shed is 10 feet high and 12 feet wide, you would calculate the area as follows: 10 feet (height) x 12 feet (width) = 120 square feet. This calculation gives you the total area in square feet of the wood needed for the back of the shed. Remember, the area of a flat surface is calculated by the formula length x width.

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:
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.

Answer:

5 7/12

Step-by-step explanation:

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

Answer:

A,C,F

Step-by-step explanation:

Which phrases can be represented by the expression 60w? Check all that apply.

the product of sixty and a number

sixty times a number

the difference of a number and sixty

the quotient of a number and sixty

a number divided by sixty

the sum of a number and sixty

Answer:

Phrases 2) a number plus 14, 4) fourteen more than a number and 7)  a number increased by 14 can be represented by the given algebraic expression.    

Step-by-step explanation:

We are given an algebraic expression:

[tex]x + 1`4[/tex]

1) the quotient of a number and 14

2) a number plus 14

Let x be the number then, it can be written as x + 14

3) fourteen less than a number

4) fourteen more than a number

Let x be the number, then, it can be written as x + 14

5) fourteen taken away from a number

6) the product of fourteen and a number

7)  a number increased by 14

Let x be the number, then, it can be written as x + 14

Phrases 2) a number plus 14, 4) fourteen more than a number and 7)  a number increased by 14 can be represented by the given algebraic expression.

The Distributive Property: a(b + c) = ab + ac.

To find an equivalent expression to 6(m + 3) using the Distributive Property, multiply 6 by each term inside the parentheses.

6 · m = 6m

6 · 3 = 18

The expression becomes 6m + 18.

The error the student made was not multiplying 6 by 3.

Answer:

6 was not multiplied by 3 (the last option).

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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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).

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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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.

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.