Find an equation of the circle that satisfies the given conditions:

Endpoints of a diameter are P(-1,3) and Q(7,-7)

Answer:

60 my vros                

Step-by-step explanation:

Answer:D

Step-by-step explanation:

y - y1 = m (x - x1)

where m is the slope and (x1 , y1) is the point given

We are given:

m= -1

the point is (2, 4)

Then:

1 yard = 3 ft

10/3 = 3 1/3 yards

3 1/3 x 4 = 13 1/3 square yards

the length of the rectangle is either -11 inches or 40 inches.

Given the following data;

Translating the word problem into an algebraic equation, we have;

[tex]L = W + 29[/tex]

To find the length of the rectangle;

Mathematically, the area of a rectangle is given by the formula;

[tex]Area = L * W[/tex]

Substituting the values into the formula, we have;

[tex]440 = (W + 29) * W\\\\440 = W^{2} + 29W[/tex]

Rearranging the equation, we have;

[tex]W^{2} + 29W - 440 = 0[/tex]

W e would solve the quadratic equation by factorization;

[tex]W^{2} + 40W - 11W - 440 = 0\\\\W(W + 40) - 11(W + 40)\\\\(W + 40)(W- 11)[/tex]

Width, W = -40 0r 11 inches.

Next, we would find the length of the rectangle;

When Width, W = -40;

[tex]L = W + 29[/tex]

[tex]L = -40 + 29[/tex]

Length, L = -11 inches

When Width, W = 11;

[tex]L = W + 29[/tex]

[tex]L = 11 + 29[/tex]

Length, L = 40 inches

Therefore, the length of the rectangle is either -11 inches or 40 inches.

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Final answer:

To represent the relationship between Matt and Andy's ages mathematically, let x be Andy's age, and express Matt's age as 2x + 5. The inequality x + (2x + 5) < 35 simplifies to x < 10, indicating Andy's age must be less than 10.

Explanation:

The question involves creating an inequality to represent the relationship between Matt and Andy's ages, where Matt is five years older than twice Andy's age, and the sum of their ages is less than 35.

Let x represent Andy's age. The formula for Matt's age would be 2x + 5. To find the range of possible values for Andy's age, you would write the inequality  x + (2x + 5) < 35.

Solving this inequality involves combining like terms and isolating the variable x.

Step 1: Combine like terms.

x + 2x + 5 < 35

Step 2: Simplify the inequality.

3x + 5 < 35

Step 3: Subtract 5 from both sides to isolate the term with x.

3x < 30

Step 4: Divide both sides by 3 to solve for x.

x < 10

This tells us that Andy's age must be less than 10 for the conditions to be met.

The simplified form of the expression (y^8)(y^2) is y^10, found by applying the laws of exponents that dictate adding the exponents when multiplying with the same base.

The simplified form of the expression (y8)(y2) can be found using the laws of exponents which state that when multiplying two powers with the same base, you add the exponents. Here, since the base is y, and we have exponents 8 and 2, we add them together:

y8 × y2 = y8+2

This simplifies to y10, which is the compressed form of the given expression.

Final answer:

To simplify the expression (y⁸)(y²), use the rule of exponents which says that you add the exponents when multiplying powers with the same base, resulting in y¹⁰.

Explanation:

The question requires simplifying an algebraic expression with exponents. The given expression is (y⁸)(y²). To simplify this, we use the rule of exponents which states that when multiplying two powers with the same base, you add the exponents. Therefore, y⁸ × y² = y⁸₊²} = y¹⁰

The unknown number(n) is equal to - 2 satisfying asked statement.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Let the unknown number be 'n'.

Given, If 3 is added to twice a number,

and this sum is multiplied by 2​,

the result is the same as if the number is multiplied by 3

and 4 is added to the product.

∴ (2n + 3)×2 = n×3 + 4.

4n + 6 = 3n + 4.

4n - 3n = 4 - 6.

n = - 2.

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Answer:

Your answer would be A 10cm

Answer:  The required value of c that makes the given statement true is 5.

Step-by-step explanation:  We are given to find the value of c that makes the following statement TRUE :

[tex]-2x^3(cx^3+x^2)=-10x^6-2x^5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

To find the value of c, we need to equate the coefficients of the same powers of the unknown variable x.

From equation (i), we have

[tex]-2x^3(cx^3+x^2)=-10x^6-2x^5\\\\\Rightarrow -2cx^{3+3}-2x^{3+2}=-10x^6-2x^5\\\\\Rightarrow -2cx^6-2x^5=-10x^6-2x^5.[/tex]

Equating the coefficients of [tex]x^6[/tex] on both sides of the above equation, we get

[tex]-2c=-10\\\\\Rightarrow c=\dfrac{-10}{-2}\\\\\Rightarrow c=5.[/tex]

Thus, the required value of c that makes the given statement true is 5.

3x-6 = 2x+11

3x = 2x+17

x = 17

3(17)-6 = 45

2(17)+11 = 45

45+45 = 90

answer is C 90 degrees:right

Answer:

3 1/100

hope this is helpful!

Two complementary angles are given as 4x - 16 and 2x + 10. Solving for x we find x = 16. Substituting x into the expressions for the angles, we find the angles to be 48 and 42 degrees.

The task here is to find the value of two angles that are complementary. Given the expressions for the angles are 4x - 16 and 2x + 10. As complementary angles, they sum up to 90 degrees. Hence, mathematically, we can express this as (4x - 16) + (2x + 10) = 90.

Solving the equation, combine like terms to get 6x - 6 = 90. Then, add 6 to both sides to get 6x = 96. Divide each side by 6 to find x, hence x = 16.

Substitute x = 16 into 4x - 16, therefore the first angle is 4×16 - 16 = 48 degrees. Similarly, substitute x = 16 into 2x + 10, hence the second angle is 2×16 + 10 = 42 degrees. The angles are thus 48 and 42 degrees, which adds up to 90).

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To put the given equation of a sphere in standard form, complete the square for x, y, and z, and combine constant terms on the right side. The standard form of the sphere's equation is (x + 2)2 + (y - 3)2 + (z - 3)2 = 28, with a center at (-2, 3, 3) and a radius of √28.

To write the equation of the sphere in standard form, we will complete the square for the x, y, and z terms in the given equation x2 + y2 + z2 + 4x − 6y − 6z = −6.

First, we organize the variables and separate the constants:

x2 + 4x + y2 - 6y + z2 - 6z = -6

We then complete the square for each variable by adding and subtracting the square of half the coefficient of the linear term:

x2 + 4x + 4 - 4 + y2 - 6y + 9 - 9 + z2 - 6z + 9 - 9 = -6

Now we can rewrite this as:

(x + 2)2 - 4 + (y - 3)2 - 9 + (z - 3)2 - 9 = -6

Combining the constant terms on the right side we get:

(x + 2)2 + (y - 3)2 + (z - 3)2 = 4 + 9 + 9 + 6

Which simplifies to:

(x + 2)2 + (y - 3)2 + (z - 3)2 = 28

The sphere's center is located at (-2, 3, 3) and has a radius of √28. In standard form, the equation of the sphere is:

(x + 2)2 + (y - 3)2 + (z - 3)2 = 28