MATHEMATICS MIDDLE SCHOOL

The roots of the equation x²-kx+28=0 are alpha (a) and alpha (a) + 3.find the values of k.​

Answers

Answer 1
Answer:

The possible values of k are -11 and 11

Solution:

Given that equation is:

x^2 - kx + 28 = 0

Roots are:

\alpha\n\n\alpha + 3

To find: value of x

The general quadratic equation is:

ax^2 + bx + c = 0

\text{ Product of roots } = (c)/(a)\n\n\text{ Sum of roots } = (-b)/(a)

From given,

x^2 - kx + 28 = 0

a = 1

b = -k

c = 28

Therefore,

Product\ of\ roots = (28)/(1) = 28

Sum\ of\ roots = (-k)/(1) = -k

Given roots are:

\alpha\n\n\alpha + 3

Therefore,

The two roots are two numbers whose difference is 3 and whose product is 28

Those two roots are 4 and 7 or -4 and -7

Then, sum of roots are:

4 + 7 = 11

-4 - 7 = -11

Therefore, the possible values of k are -11 and 11

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Solve 4y-70=12y+2 explain

Answers

4y-70=12y+2
-8y=72
y=-9

4(-9)-70=12(-9)+2
-36-70=-108+2
-106=-106

Answer:

y=-9

Step-by-step explanation:

Please show you work Thankyou :)

Answers

Answer:

it would be D i cant exactly show work but if you download photo math itll show you how to get the answer and that its correct :)

Which of the following is the solution to 9|x+4|>54 ?

Answers

Answer:

x < -10, x > 2

Step-by-step explanation:

9|x+4| > 54

|x+4| > 6

Split the absolute value into two equation, positive and negative.

1.)POSITIVE

x+4 > 6

x > 2

2.)NEGATIVE

-(x+4) > 6

-x - 4 > 6

-x > 10

x < -10

Answer:

\large\boxed{x<-10\ \vee\ x>2\to x\in(-\infty,\ -10)\ \cup\ (2,\ \infty)}

Step-by-step explanation:

9|x+4|>54\qquad\text{divide both sides by 9}\n\n(9|x+4|)/(9)>(54)/(9)\n\n|x+4|>6\iff x+4>6\ \vee\ x+4<-6\n\nx+4>6\qquad\text{subtract 4 from both sides}\n\nx+4-4>6-4\n\nx>2\n\nx+4<-6\qquad\text{subtract 4 from both sides}\n\nx+4-4<-6-4\n\nx<-10

Solve the inequality and graph solution
8 |x+3/4| <2

Answers

 Answer:     x<-1

Step-by-step explanation:

8 |x+3/4| <2  

|x+3/4| <2/8  

x+3/4<+/-(plus/minus,since modulus) 2/8  

if 2/8,  

x<2/8-3/4  

x<-1/2  

if -2/8,  

x<-2/8-3/4

Answer in 5 mins get 100pt and a brainly a scale model of the status of liberty is 15 inches tall if the statue of liberty is 305 feet tall find the scale of the model

Answers

i dont know if this right, but the scale is 20.333333.... times shorter than the real statue. sorry if its wrong

Answer:

I think the answer is 20

Step-by-step explanation:

hope this helps

Is 2,359 × 1,580 even or odd?

Answers

This will be even! You don't even need to work past multiplying the ones digits in each number because 9 times 0 is 0! If you do solve it you get 3,727,220, but that'd take forever to do :)
2,359 times 1,580 is going to be even because of the ones place if the first place is and odd number u have and odd number total and if its and equation u take out the rest of wach of thenbers and you can tell if its even or odd
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