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3 years ago

Solve the quadratic equation below for the exact values of x: 4x^2-5=75

Mathematics

1 answer:

grandymaker [24]3 years ago

6 0

Step-by-step explanation:

$4 {x}^{2} - 5 = 75 \\ 4 {x}^{2} = 75 + 5 \\ 4 {x}^{2} = 80 \\ {x}^{2} = \frac{80}{4} \\ {x}^{2} = 20 \\ x = \pm \sqrt{20} \\ x = \pm 2 \sqrt{5}$

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Write the formula for the parabola that has x- intercepts (3,0) and (8,0), and y- intercept (0,−2)

alexira [117]

Answer: $x^2-5x=-12(y+2)$

Step-by-step explanation:

Given

Parabola has x-intercept has $(3,0)$ and $(8,0)$

and Y-intercept as $(0,-2)$

Now the general equation of parabola is

$y=ax^2+bx+c\quad \ldots(i)$

Substitute $(0,-2)$ in $(i)$ we get

$-2=c$

Now substitute $(3,0)$ in equation $(i)$

$0=a(3)^2+3b-2\quad \ldots(ii)$

Now substitute $(8,0)$ in equation $(i)$

$0=a(8)^2+8b-2\quad \ldots(iii)$

Solving $(ii)$ and $(iii)$ we get

$a=\frac{-1}{12}\ \text{and}\ b=\frac{5}{12}$

therefore

$y=\frac{-x^2}{12}+\frac{5x}{12}-2$

$12y=-x^2+5x-24$

5 0

3 years ago

I need help with this question!!

Veronika [31]

Answer:

right

Step-by-step explanation:

4 0

3 years ago

Please Answer ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Veronika [31]

Answer:

6/3=2/1

Step-by-step explanation:

6/3 is the same as 2/1 because if we divide the common denominator, 3, on both sides, your answer will be 2/1.

7 0

2 years ago

Hayden is organizing his assets and liabilities in the table below. If his net worth is $17,550, then how much does he have in h

77julia77 [94]

Answer: His checking account balance is $2,800.

Step-by-step explanation: What Hayden is doing is comparing his assets against his liabilities. This will determine his net worth. His assets ideally are those that increase his net worth such as landed properties, etc while his liabilities in the simplest language are those debts he is paying off either right away, or that he must pay off eventually.

In other words, to determine his net worth, Hayden has to add up all his assets and from the total derived, deduct his liabilities.

Consider the calculations below;

NET WORTH: $17,550

Add ASSETS

Automobile 13600

Retirement Account 6700

Checking Account XX

Less LIABILITIES

Student Loan 4800

Credit card debt 750

Net Worth <u>17550</u>

The above table can be simplified as follows;

Net worth = Assets - Liabilities

17550 = 20300 + XX - 5550

Collecting like terms, you now have;

17550 -20300 +5550 = XX

2800 = XX

The Checking Account represented by XX is now calculated as $2,800

7 0

2 years ago

How many ways can an employer send 3 employees to a job fair if she has 11 employees?

algol13

We have to find the number of ways an employer send 3 employees to a job fair if she has 11 employees.

This is the problem from combination.

The formula for combination is given by

$^nC_r= \frac{n!}{r!(n-r)!}$

Here, n= 11, r= 3

Therefore, total number of ways is given by

$^{11}C_3= \frac{11!}{3!(11-3)!}\\
\\
=\frac{11!}{3!8!}\\
\\
=\frac{8!\times 9 \times 10 \times 11}{3!8!}\\
\\
=\frac{9 \times 10 \times 11}{6}\\
\\
=165$

A is the correct option.

6 0

2 years ago