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3 years ago

Use the zero product property to find the solutions to the equation x2 – 13x + 30 = 0?

Mathematics

1 answer:

aksik [14]3 years ago

7 0

X^2 -13x +30 = 0

x*x - 15x +2x +15*2 = 0

x(x -15) -2(x -15) = 0

(x -2)(x -15) = 0

x -2 = 0

x =2

x -15 =0

x = 15

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Solve for x<br>a.81<br>b.41<br>c.1681

Jlenok [28]

A=9 , b=40

Pythagorean theorem
$a^2+b^2=x^2 \\\\ x=\sqrt{a^2+b^2}=\sqrt{9^2+40^2}=\sqrt{81+1600}=\sqrt{1681}=\sqrt{41^2}=41$

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3 years ago

Given f(x) = –3x – 7, what is f(–4)?

lyudmila [28]

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3 years ago

Read 2 more answers

Given the original number n. Multiply the number by 9. Add 99. Divide this sum by 9. Subtract the original number, n, from the q

tangare [24]

Answer:

Step-by-step explanation:

Hello,

Given the original number n.

$\large \boxed{n}$

Multiply the number by 9.

$\large \boxed{9n}$

Add 99.

$\large \boxed{9n+99}$

Divide this sum by 9.

$\large \boxed{\dfrac{9n+99}{9}=n+11}$

Subtract the original number, n, from the quotient.

$\large \boxed{n+11-n=11}$

Thank you.

4 0

3 years ago

2. Given a quadrilateral with vertices (−1, 3), (1, 5), (5, 1), and (3,−1):

zlopas [31]

<h2>Explanation:</h2>

In every rectangle, the two diagonals have the same length. If a quadrilateral's diagonals have the same length, that doesn't mean it has to be a rectangle, but if a parallelogram's diagonals have the same length, then it's definitely a rectangle.

So first of all, let's prove this is a parallelogram. The basic definition of a parallelogram is that it is a quadrilateral where both pairs of opposite sides are parallel.

So let's name the vertices as:

$A(-1,3) \\ \\ B(1,5) \\ \\ C(5,1) \\ \\ D(3,-1)$

First pair of opposite sides:

<u>Slope:</u>

$\text{For AB}: \\ \\ m=\frac{5-3}{1-(-1)}=1 \\ \\ \\ \text{For CD}: \\ \\ m=\frac{1-(-1)}{5-3}=1 \\ \\ \\ \text{So AB and CD are parallel}$

Second pair of opposite sides:

<u>Slope:</u>

$\text{For BC}: \\ \\ m=\frac{1-5}{5-1}=-1 \\ \\ \\ \text{For AD}: \\ \\ m=\frac{-1-3}{3-(-1)}=-1 \\ \\ \\ \text{So BC and AD are parallel}$

So in fact this is a parallelogram. The other thing we need to prove is that the diagonals measure the same. Using distance formula:

$d=\sqrt{(y_{2}-y_{1})^2+(x_{2}-x_{1})^2} \\ \\ \\ Diagonal \ BD: \\ \\ d=\sqrt{(5-(-1))^2+(1-3)^2}=2\sqrt{10} \\ \\ \\ Diagonal \ AC: \\ \\ d=\sqrt{(3-1)^2+(-5-1)^2}=2\sqrt{10} \\ \\ \\$

So the diagonals measure the same, therefore this is a rectangle.

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3 years ago

A coin is to be spun 25 times. Let x be the number of spins that result in heads (H). Consider the following rule for deciding w

larisa [96]

Answer:

0.0433

Step-by-step explanation:

Since we have a fixed number of trials (N = 25) and the probability of getting heads is always p = 0.05, we are going to treat this as a binomial distribution.

Using a binomial probability calculator, we find that the probability of obtaining heads from 8 to 17 times is 0.9567 given that the con is fair. The probability of obtaining any other value given that the coin is fair is going to be:

1 - 0.9567 = 0.0433

Since we are going to conclude that the coin is baised if either x<8 or x>17, the probability of judging the coin to be baised when it is actually fair is 4.33%

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3 years ago