List a value of b that will cause 4x2 + bx + 25 = 0 to have one real solution

Jim and Jackie are married with three children at home and a mortgage. Jim’s net pay per year is $67,000 and Jackie does not hav

Darya [45]

The answer is A. they should work on their plan for managing income.

4 0

3 years ago

Read 2 more answers

A man invests his savings in two accounts, one paying 6% and the other paying 10% simple interest per year. He puts twice as muc

Masteriza [31]

Let x represent amount invested in the higher-yielding account.

We have been given that a man puts twice as much in the lower-yielding account because it is less risky. So amount invested in the lower-yielding account would be $2x$ .

We are also told that his annual interest is $6600 dollars. We know that annual interest for one year will be principal amount times interest rate.

$I=Prt$ , where,

I = Amount of interest,

P = Principal amount,

r = Annual interest rate in decimal form,

t = Time in years.

We are told that interest rates are 6% and 10%.

$6\%=\frac{6}{100}=0.06$

$10\%=\frac{10}{100}=0.10$

Amount of interest earned from lower-yielding account: $2x(0.06)=0.12x$ .

Amount of interest earned from higher-yielding account: $x(0.10)=0.10x$ .

$0.12x+0.10x=6600$

Let us solve for x.

$0.22x=6600$

$\frac{0.22x}{0.22}=\frac{6600}{0.22}$

$x=30,000$

Therefore, the man invested $30,000 at 10%.

Amount invested in the lower-yielding account would be $2x\Rightarrow 2(30,000)=60,000$ .

Therefore, the man invested $60,000 at 6%.

8 0

2 years ago

Could someone pls explain this step by step? Really simplify it pls because I don't understand it at all.

Lunna [17]

Answer:

y = 2x -6
y = -x +2
y = 4/5x -2
y = -3/2x +4

Step-by-step explanation:

The slope-intercept form of the equation for a line is ...

y = mx +b . . . . . where m is the slope, and b is the y-intercept

For these equations, writing them in slope-intercept form means "solve for y." You always do any "solve for ..." problem by undoing the operations that are done to the variable. Addition is undone by adding the opposite. Multiplication is undone by division.

As always, whatever operation we perform on one side of the equal sign must also be performed on the other side. That is how the equal sign remains valid.

__

1/2y = x -3

All we need to do is get rid of the coefficient of y. We can do that by dividing by 1/2, or multiplying by 2. The latter is easier to see, perhaps.

2(1/2y) = 2(x -3)

y = 2x +2(-3)

y = 2x -6

__

x +y = 2

Here, we need to undo the addition of x. We do that by adding (-x) to both sides of the equation.

-x +x +y = -x +2

y = -x +2

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4x -5y -10 = 0

This is a combination of the above operations. We can separate the y-term from the others by either subtracting the others, or adding the opposite of the y-term. We choose the latter, because that will give a positive coefficient for y. Adding 5y to both sides gives ...

4x -5y +5y -10 = 5y

5y = 4x -10 . . . . . . . . simplify and put y on the left

Now, we need to divide by the coefficient of y. We do that to both sides of the equation.

5y/5 = (4x -10)/5

y = 4/5x -10/5

y = 4/5x -2

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3x = -2y +8

We have a constant with the y-term. To get rid of it, we add its opposite to both sides.

3x -8 = -2y +8 -8

3x -8 = -2y

As before, we divide by the coefficient of y: