It is given that -3 is one of the roots of the quadratic equation x square -4x-h=0.find the value of h

Answers

Answer 1

Answer: Since -3 is one of the roots, that means it would satisfy the equation.

x^2 - 4x - h = 0, substitute x = -3.

(-3)^2 -4(-3) - h = 0
9 + 12 - h = 0
21 - h = 0
21 = h.
h = 21.
That's the value of h. Cheers.

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What is 2×10to the 3rd power subtract from 1.9×10to the 2nd power equal

Answers

(2x10)^3-(1.9x10)^2
(8000)-(361)=7639

Lisa invests $4,000 in two types of bonds, bond A and bond B. Bond A offers a 10% return, and bond B offers a 6% return. Lisa invests $x in bond A and $y in bond B. Her total return on the investment is $340. The system of linear equations defining the situation is x+y=4,000 and .1x=.06y=340. The amount Lisa invested at the rate of 10% is ___ , and the amount she invested at the rate of 6% is ___ .

Answers

Lisa invests $4,000 in two types of bonds, bond A and bond B. A + B = 4000 Bond A offers a 10% return, and bond B offers a 6% return. .10 A + .06 B = 340 Her total return on the investment is $340. since the relationship A+B=4000 must satisfy the setup for all values A and B we can state that A = 2000 + n, and B = 2000 -n afterall: 2000 +n + 2000 - n = 4000 for all n .10(2000+n) + .06(2000-n) = 340, once we know n we know A and B

Use Pascal's triangle or the Binomial theorem to expand the binomials. 1. (3c-2d)^4
2. (2n+3)^5
3. (x^2+4)^3

Answers

$(3c-2d)^4=(3c)^4-4(3c)^3\cdot2d+6\cdot(3c)^2\cdot(2d)^2-4\cdot3c\cdot(2d)^3-(2d)^4\n\n=81c^4-216c^3d+216c^2d^2-96cd^3-16d^4\n-------------------------------\n(2n+3)^2\n=(2n)^5+5(2n)^4\cdot3+10(2n)^3\cdot3^2+10(2n)^2\cdot3^3+5\cdot2n\cdot3^4+3^5\n\n=32n^5+240n^4+720n^3+1080n^2+810n+243\n-------------------------------\n(x^2+4)^3=(x^2)^3+3(x^2)^2\cdot4+3x^2\cdot4^2+4^3\n\n=x^6+12x^4+48x^2+64$

What is the value of the expression 2z + 2w when z=7 and w=5

Answers

Answer:

The solution is 24

Step-by-step explanation:

z = 7

w = 5

2z + 2w

we enter the numbers

2(7) + 2(5)

= 14 + 10

= 24

Factor the GCF out of the following expression to create a multiplication problem.-72n^5 +81n³

Answers

Answer:For 9n^3: (9n^3) * (-8n^2+9)

For -9n^3: (-9n^3) * (8n^2-9)

Step-by-step explanation:

The GCF is the greatest common factor.

The great common factor between 72 and 81 is 9 as 72=9*8 and 81=9*9

the GCF between n^5 and n^3=n^3.

SO the GCF is 9n^3.

But I would like to keep that leading coefficient positive, so i will factor -9n^3. It doesn't matter which one you choose, ill do both so u will have both ready.

For 9n^3: (9n^3) * (-8n^2+9)

For -9n^3: (-9n^3) * (8n^2-9)

If 5x + x² > 100, then x is not 10 8 7 9

Answers

We will solve the equation:
x^2+5x-100≥0 $x_(12) = (-5\pm √(25+400) )/(2)= (-5\pm20.6)/(2)$ x1≈-12.8 x2≈ 7.8
It means that x∈ (-∞, -12.8 ) ∪ (7.8, +∞ ).
Answer: C) x ≠ 7
Thank you.

If inequality 5x + x² > 100, then x is not equal to 7.

The given inequality looks like you have a quadratic inequality that we have to solve,

5x + x² > 100

To determine which values of x will not satisfy this inequality,

We can use algebraic manipulation.

We can rewrite the inequality as,

x² + 5x - 100 > 0

Then, we can use the quadratic formula to find the roots of the equation, which are x = (-5 ± √(425)) / 2.

x ≈ -12.8 or 7.8

It means that x∈ (-∞, -12.8 ) ∪ (7.8, +∞ ).

Hence, x ≠ 7

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