(b-1)2+2a; use a=6, and b=1

Answers

Answer 1

Answer: um i’m gonna go with 14 bc (1-1) is 0 and then 2+2(6) is 14. i could be wrong sorry

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Find the greatest common factor of the following monomials: 20a3 and 8a2

Answers

GCF of given monomials are $4a^2$

Solution:

Given that we have to find the greatest common factor

Given monomials are:

$20a^3 \text{ and } 8a^2$

When we find all the factors of two or more numbers, and some factors are the same, then the largest of those common factors is the Greatest Common Factor

Let us first find the GCF of 20 and 8 and then find GCF of variables and then multiply them together

GCF of 20 and 8:

The factors of 8 are: 1, 2, 4, 8

The factors of 20 are: 1, 2, 4, 5, 10, 20

Then the greatest common factor is 4

$GCF\ of\ a^3 \text{ and } a^2\n\na^3 = a^2 * a\n\na^2 = a^2$

Thus GCF is $a^2$

Therefore GCF of monomials are:

$\text{GCF of } 20a^3 \text{ and } 8a^2 = 4 * a^2 = 4a^2$

Thus GCF of given monomials are $4a^2$

Match the terms to their definition. 1. consistent equations the determinant found when column 1 consists of the constants and column 2 consists of the y-coefficients of a linear system 2. equivalent equations the determinant found when column 1 consists of the x-coefficients and column 2 consists of the constants of a linear system 3. inconsistent equations equations having a common solution in a system 4. linear inequality equations having no common solutions in a system 5. substitute replace a quantity with its equal 6. system determinant equations having all common solutions 7. x-determinant an open sentence of the form Ax By C < 0 or Ax By C > 0 8. y-determinant the determinant found when column 1 consists of the x-coefficients and column 2 consists of the y-coefficients of a linear system

Answers

Answer:

1-----3

2-----6

3------4

4------7

5-------5

6-------8

7--------1

8--------2

step-by-step explanation:

consistent equation: equations having a common solution in a system.

Equivalent equation: equations having all common solutions.

Inconsistent equations: equations having no common solutions in a system

Linear inequality: an open sentence of the form Ax+By+C < 0 or Ax+By+C > 0.

substitute: replace a quantity with its equal.

system determinant: the determinant found when column 1 consists of the x-coefficients and column 2 consists of the y-coefficients of a linear system.

x-determinant: the determinant found when column 1 consists of the constants and column 2 consists of the y-coefficients of a linear system.

y-determinant: the determinant found when column 1 consists of the x-coefficients and column 2 consists of the constants of a linear system.

Final answer:

The terms are matched with their respective definitions, providing clarity about equations, linear inequality, substitution, and determinants in the context of a system of linear equations.

Explanation:

Let's go ahead and match these terms to their correct definitions:

Consistent equations are equations having a common solution in a system.
Equivalent equations refer to equations having all common solutions.
Inconsistent equations are equations having no common solutions in a system.
Linear inequality is an open sentence of the form Ax + By < C or Ax + By > C.
To Substitute means to replace a quantity with its equal.
System determinant for this instance, since specific definition is not provided, could be considered as a determinant that serves as a pivotal element in the solution of system of linear equations.
X-determinant is the determinant found when column 1 consists of the x-coefficients and column 2 consists of the constants of a linear system.
Y-determinant is the determinant found when column 1 consists of the x-coefficients and column 2 consists of the y-coefficients of a linear system.

Learn more about Mathematical Terms here:

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The base of a solid in the xy-plane is a circle with a radius of 3. cross sections of the solid perpendicular to the x-axis are squares. set up the integral to arrive at the volume of the solid and solve.

Answers

Answer:

$\large \boxed{144}$

Step-by-step explanation:

1. Set up the integral.

The equation for the circle is

x² + y² = 9

The bottom corners of the square are at

$(x, \sqrt{9 - x^(2)})\text{ and } (x, -\sqrt{9 - x^(2)})$

The length (a) of a side is

$a = 2\sqrt{9 - x^(2)}$

and the area (A) of the square cross-section is

A = a² = 4(9 - x²)

The volume (V) of the solid is

$V = \displaystyle \int_(-3)^(3) {4(9 - x^(2))} dx$

2. Solve the integral

$\displaystyle \int_(-3)^(3) {4(9 - x^(2))} dx = 4\begin{bmatrix}9x - (1)/(3)x^(3)\end{bmatrix}_(-3)^(3)= 4[(27 - 9) - (-27 +9)] = 4[18 - (-18)]\n= 4[18 + 18] = 4 *36 = \mathbf{144}\n\n\text{The volume of the solid is $\large \boxed{\mathbf{144}}$}$

Need help solving problem number 41

Answers

ok rmemeber
√(a/b)=(√a)/(√b)
and
√ab=(√a)(√b)
and
(a^m)/(a^n)=a^(m-n)
so

ignore 11 for now, we will get to that at end

$\sqrt{ (49a^(5))/(4a^(3))}$ =
$\frac{\sqrt{49a^(5))}{\sqrt{4a^(3)}}$ =
$\frac{(√(49))(\sqrt{a^(5)})}{(\sqrt{4)(\sqrt{a^(3)}}$ =
$((7)(a^(2) √(a)) )/((2)(a √(a)) )$ =
$(7a^(2) √(a) )/(2a √(a) )$ =
$(7a)/(2)$

1. Which of the following is an arithmetic sequence?a. 2, 5, 9, 14, 20
b. 1, 3, 6, 10, 15
c. -5, -2, 1, 4, 7
d. -3, 0, 4, 9, 15

2. Which of the following is a geometric sequence?
a. 1, 2, 3, 4, 5
b. 7, 12, 17, 22, 27
c. 1, 3, 9, 27, 81
d. -4, 0, 4, 8, 12
e. -6, -4, -2, 0, 2

Answers

i say C. -5, -2, 1, 4, 7 is your answer for question 1.

and for question 2 i think is E. -6, -4, -2, 0, 2.

Factor completely and then place the factors in the proper location on the grid.a 2 - a - 20

Answers

Answer:

The correct answer is (a+4)(a-5)

Step-by-step explanation:

We have the polynomial $a^2-a-20$

For the polynomials of the form $ax^2+bx+c$ we have to rewrite the middle term as a sum of two terms whose product is, in this case, a.c=-20 and whose sum is b=(-1).

$a^2-a-20=\na^2+(-5+4)(a)-20=\n=a^2-5a+4a-20$

Because b=(-5)+4=(-1) and a.c=(-5).4=(-20)

Now we have to factor by grouping:

$a^2-5a+4a-20=\n(a^2+4a)-(5a+20)=\na(a+4)-5(a+4)=\n=(a-5)(a+4)$

Then, the correct answer is (a+4)(a-5)

The fully factored form of this expression would be
(A-5)(A+4).

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