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lozanna [386]
2 years ago
9

Write a quadratic equation with -4 and 3/2 as it’s roots. Write the equation in the form ax^2 + bx + c = 0, where a, b, and c ar

e integers.
Mathematics
1 answer:
jonny [76]2 years ago
5 0

9514 1404 393

Answer:

  2x² +5x -12 = 0

Step-by-step explanation:

When p and q are roots of a quadratic, its factored form can be written as ...

  (x -p)(x -q) = 0

Here, the roots are given as -4 and 3/2, so the factored form would be ...

  (x -(-4))(x -(3/2) = 0

Multiplying by 2 gives us ...

  (x +4)(2x -3) = 0

Expanding the product, we find the desired quadratic is ...

  2x² +5x -12 = 0

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According to a survey of adults, 64 percent have money in a bank savings account. If we were to survey 50 randomly selected adul
zheka24 [161]

Answer:

The mean number of adults who would have bank savings accounts is 32.

Step-by-step explanation:

For each adult surveyed, there are only two possible outcomes. Either they have bank savings accounts, or they do not. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

E(X) = np

In this problem, we have that:

p = 0.64

If we were to survey 50 randomly selected adults, find the mean number of adults who would have bank savings accounts.

This is E(X) when n = 50.

So

E(X) = np = 50*0.64 = 32

The mean number of adults who would have bank savings accounts is 32.

6 0
3 years ago
in a AP the first term is 8,nth term is 33 and sum to first n terms is 123.Find n and common difference​
allsm [11]

I believe there is no such AP...

Recursively, this sequence is supposed to be given by

\begin{cases}a_1=8\\a_k=a_{k-1}+d&\text{for }k>1\end{cases}

so that

a_k=a_{k-1}+d=a_{k-2}+2d=\cdots=a_1+(k-1)d

a_n=a_1+(n-1)d

33=8+(n-1)d

21=(n-1)d

n has to be an integer, which means there are 4 possible cases.

Case 1: n-1=1 and d=21. But

\displaystyle\sum_{k=1}^2(8+21(k-1))=37\neq123

Case 2: n-1=21 and d=1. But

\displaystyle\sum_{k=1}^{22}(8+1(k-1))=407\neq123

Case 3: n-1=3 and d=7. But

\displaystyle\sum_{k=1}^4(8+7(k-1))=74\neq123

Case 4: n-1=7 and d=3. But

\displaystyle\sum_{k=1}^8(8+3(k-1))=148\neq123

8 0
3 years ago
A picture has a height that is 2 times it’s width . It is to be enlarged to an area of 128 in 2
morpeh [17]

9514 1404 393

Answer:

  8 in by 16 in

Step-by-step explanation:

In your equation, we presume that x represents the width. Solving for x, we have ...

  2x² = 128 . . . . . . given equation

  x² = 64 . . . . . . . . divide by 2

  x = √64 = 8 . . . . square root

The enlargement will be 8 inches by 16 inches.

8 0
2 years ago
What is the value of x? <br><br> Enter your answer in the box.<br><br> x =___
Zanzabum

Answer:

x = 12

Step-by-step explanation:

The diagram shows an equilateral triangle (because all angles are congruent). All sides in equilateral triangle are congruent, so

4x-10=5x-22=3x+2

Solve the equation

4x-10=5x-22\\ \\4x-10-4x=5x-22-4x\\ \\-10=x-22\\ \\-10+22=x-22+22\\ \\12=x

Check this value:

4x-10=4\cdot 12-10=48-10=38\ units \\ \\5x-22=5\cdot 12-22=60-22=38\ units\\ \\3x+2=3\cdot 12+2=36+2=38\ units

Thus, x=12

8 0
3 years ago
9e^x-240=6e^x+270 what is the solution
zmey [24]

e^x=170

because you subtract like terms (or add, it depends) then simplify (im bad at explaining)

4 0
3 years ago
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