What multiplies to make 12 and adds up to 16

Answers

Answer 1

Answer: To solve Q.15, remember to multiply the first numerical coefficient, in this case 3 to -12, to find the numbers to multiply and get that product. The middle term represents the sum the same two numbers must add to.

For example:

3r^2 - 16r - 7 = 5
3r^2 - 16r - 12 = 0

What 2 numbers multiply to give you -36, and add to give you -16, are -18 and +2, since -18 • 2 = -36, and -18 + 2 = -16.

3r^2 - 18r + 2r - 12 = 0
Factor
3r(r - 6) + 2(r - 6) = 0
(3r + 2)(r - 6) = 0
r = 6

3r + 2 = 0
3r = -2
r = -2/3.

Your 2 solutions for r are -2/3 and 6.

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Which choice represents the simplified form of the expression below and the values of x for which it is defined?√7x^3 divide by √x

A.x√2x when x>0
B.x√7 when x<0
C.x√7 when x>1
D.x√7 when x>0

Answers

$√(7x^3):√(x)=\sqrt(7x^3)/(x)=√(7x^2)=x\sqrt7\n\n√(7x^3)\to x^3\geq0\to x\geq0\ \wedge\ √(x)\to x > 0\n\nAnswer:D.\ x\sqrt7\ when\ x > 0$

If the zeroes of the polynomial x² + px + q are double in value to the zeroes of 2x² - 5x - 3, find the value of and .

Answers

Answer:

The values of "p" and "q" are p = -5 and q = -6

Step-by-step explanation:

Let's start by finding the zeroes of the polynomial 2x² - 5x - 3, and then we'll determine the relationship between these zeroes and the zeroes of x² + px + q.

The zeroes of a quadratic polynomial of the form ax² + bx + c can be found using the quadratic formula:

For the polynomial 2x² - 5x - 3, a = 2, b = -5, and c = -3. So, the quadratic formula becomes:

x = [-b ± √(b² - 4ac)] / (2a)

Substitute the values:

x = [-(-5) ± √((-5)² - 4(2)(-3))] / (2(2))

Simplify:

x = (5 ± √(25 + 24)) / 4

x = (5 ± √49) / 4

x = (5 ± 7) / 4

Now, we have two possible values for x:

x₁ = (5 + 7) / 4 = 12/4 = 3

x₂ = (5 - 7) / 4 = -2/4 = -1/2

So, the zeroes of 2x² - 5x - 3 are x₁ = 3 and x₂ = -1/2.

Now, we need to find the relationship between these zeroes and the zeroes of x² + px + q.

If the zeroes of x² + px + q are double in value to the zeroes of 2x² - 5x - 3, it means that for each zero "x" of 2x² - 5x - 3, there will be a corresponding zero "2x" for x² + px + q.

So, for x² + px + q, the zeroes will be 2 times the zeroes of 2x² - 5x - 3:

For x₁ = 3, the corresponding zero for x² + px + q is 2x₁ = 2(3) = 6.

For x₂ = -1/2, the corresponding zero for x² + px + q is 2x₂ = 2(-1/2) = -1.

Now, we have the zeroes of x² + px + q: 6 and -1.

To find "p" and "q," we can use Vieta's formulas. Vieta's formulas state that for a quadratic polynomial of the form ax² + bx + c with zeroes α and β:

α + β = -b/a

α * β = c/a

In our case, for x² + px + q with zeroes 6 and -1:

α + β = 6 - 1 = 5

α * β = 6 * (-1) = -6

Now, let's match these with the coefficients of x² + px + q:

α + β = 5, which corresponds to -p (since there's an "x" term in the middle)

α * β = -6, which corresponds to q (the constant term)

So, we have the following equations:

-p = 5

q = -6

Solve for "p" and "q":

p = -5

q = -6

So, the values of "p" and "q" are p = -5 and q = -6.

If the zeroes of the polynomial x² + px + q are double in value to the zeroes of 2x² - 5x - 3, find the value of p and q

Answer:

p and q are -5 and -6 respectively.

Step-by-step explanation:

factor

2x²-5x-3=0

(x-3) (2x + 1) = 0

x = 3, -1/2

multiply both by 2 = "double in value to the zeroes"

x = 6, -1

reverse factor them

(x-6)(x+1)

multiply

x2−5x−6

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The product of (a + b)(a − b) is a perfect square trinomial.
A. Sometimes b. Always c. Never

Answers

never
perfect squre trinomial is in form
(a+b)(a+b) or (a-b)(a-b)
that is not equal to (a+b)(a-b)

never

Answer:

C. Never

Step-by-step explanation:

it acost andrea $50 per day to rent a moving truck and an additional $3 every mile that she drove it if andrea

Answers

the answer is B. 50+3x=104. andrea drove 18 miles, because 104-50= 54 and 54 divided by 3=18

Need help with function

Answers

The answer is B, according to the Rules / Laws of Functions.

B is a function because it is the only one that has 4 different x values, therefore passing the vertical line test.

Evaluate.
5 P 3 x 6 C 4

a. 150
b. 300
c. 900

Answers

Answer:

Option (c) is correct.

$^5P_3*^6C_4$ is 900

Step-by-step explanation:

Given :Expression $^5P_3*^6C_4$

We have to find the value of given expression $^5P_3*^6C_4$

Consider the given expression $^5P_3*^6C_4$

The possibility of choosing an ordered set of r object from n object is given by

$nPr=(n!)/(\left(n-r\right)!)$

and The number of subset of r elements from n elements $nCr=(n!)/(r!\left(n-r\right)!)$

Thus, $^5P_3=(5!)/(\left(5-3\right)!)==(5!)/(2!)=5\cdot \:4\cdot \:3=60$

and $^6C_4=(6!)/(4!\left(6-4\right)!)==(6!)/(4!\cdot \:2!)==(6\cdot \:5)/(2!)=15$

Thus, $^5P_3*^6C_4=60* 15=900$

Thus, $^5P_3*^6C_4$ is 900

The answer is 300 because if u x the 5x3=15 and divide 6 and 4 is 1.5 then multipy that 22 then you put the letters in the equations