MATHEMATICS MIDDLE SCHOOL

URGENT!! The difference between the roots of the quadratic equation x2−12x+q=0 is 2. Find q

Answers

Answer 1

Answer:

Answer:

q=35

Step-by-step explanation:

x2 - 12x + q = 0

Let the two roots be r and r+2.

Factor the quadratic expression:

(x - r)[x - (r + 2)] = 0

Expand, simplify, group like terms, and get

x2 - 2(r + 1)x + r(r + 2) = 0

Compare to

x2 - 12x + q = 0

and set equal the coefficients of like terms:

Coefficient of x:

-2(r + 1) = -12 ⇒ r + 1 = 6 ⇒ r = 5

(Then the other root is r + 2 = 5 + 2 = 7)

Constant term:

r(r + 2) = q ⇒ 5(5 + 2) = q

q = 35

Test the solution:

(x - 5)(x - 7) = x2 - 12x + 35

With two roots differing by 2, you get an equation of the form

x2 - 12x + q = 0

with q = 35.

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Is a triangle with the side lenths of 4mm, 11mm, 15mm a right triangle

Answers

The triangle with side lengths 4,11,15 does not even exist.
According to the Triangle Inequality Theorem, in order for the triangle to even exist, the sum of the two shorter lengths must be strictly greater than the length of the third side.
4 + 11 = 15.
15 is not greater than 15.

Someone help me on this

Answers

remember you can do antying to an equaitn as long as you do it to both sides
treat as equaiton, but flip sign when dividng or muliplying by negaitve

isolate x
first distribute
7+3x<8(3+x)
7+3x<24+8x
minus 3x both sides
7<24+5x
minus 24 both sides
-17<5x
divide both sides by 5
-17/5<x

Choose the correct simplification of the expression (4a^4b)^2.

Answers

(4a^4b)^2

= 4^2a^8b^2

= 16a^8b^2

Hope it helps.

$\sf Hello!$

$\sf (4a^(4)b)^(2)$

⇒ $\sf 4^(2).a^(4 × 2).b^(2)$

⇒ $\sf 16.a^(8).b^(2)$

⇒ $\sf 16a^(8)b^(2)$

$\sf Hence,$
$\sf Simplified\: expression \:is\: obtained$

~ $\sf iCarl$

Blank divided by 7>800

Answers

Hi there

Replace the blank space by x

so x/7 > 800
All you have to do is cross-multiply

x > 7*800
x> 5600

I hope that's help !

the answer Is 114.29

In another problem in my homework, it says look at problem 4, problem 4 has to do with the question about seans team when it had the numbers 0.37 and 0.31. I need to know will three soccer balls weigh more than 1 kilogram

Answers

Yes I will guess or no maybe

List all of the prime numbers less than 20 in numerical order

Answers

a prime number is a number only divisible by itself and 1 (this excludes decimals and fractions)

surprise, 1 is not prime because it must be divisible by itself and 1 and the factors of 1 are 1 and 1 so 1 is not prime

2 is prime because it is the first even counting number and since all even numbers after 2 are divisble by 2 you can cross out all odd numbers after 2
3 is prime because it is the first odd counting number that satisfies the condition
4 is not because it is even
5 is prime
6 is not because it is even
7 is prime
8 is not because it is even
9 is not
10 is not because it is even
11 is prime
12 is not because it is even
13 is prime
14 is not because it is even
15 is not
16 is not because it is even
17 is prime
18 is not because it is even
19 is prime
20 is not because it is even

so the numbers are 2,3,5,7,11,13,17,19

19, 17, 13, 11, 7, 5, 3, 2

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What is 155.43 rounded to the nearest whole number ?

How many tens are in the number 359

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A cone has a diameter of 24 in. and a slant height of 15 in.What is the approximate volume of the cone? Use 3.14 to approximate the value of straight pi. Round your answer to the nearest tenth, if necessary. (Hint: V equals 1 third straight pi r squared h ) A. 1248.6 in3 B. 1356.5 in3 C. 2260.8 in3 D. 5425.9 in3