What is the original price

What is the sum of 20x^2-10x-30

ivann1987 [24]

Answer:

The sum of the roots is 0.5

Step-by-step explanation:

The correct question is

What is the sum of the roots of 20x^2-10x-30

we know that

In a quadratic equation of the form

$ax^{2} +bx+c=0$

The sum of the roots is equal to

$-\frac{b} {a}$

in this problem we have

$20x^{2} -10x-30=0$

so

$a=20\\b=-10\\c=-30$

substitute

$-\frac{(-10)} {20}=0.5$

Verify

Find the roots of the quadratic equation

The formula to solve a quadratic equation is equal to

$x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}$

$a=20\\b=-10\\c=-30$

substitute

$x=\frac{-(-10)\pm\sqrt{-10^{2}-4(20)(-30)}} {2(20)}$

$x=\frac{10\pm\sqrt{2,500}} {40}$

$x=\frac{10\pm50} {40}$

$x=\frac{10+50} {40}=1.5$

$x=\frac{10-50} {40}=-1$

The roots are x=-1 and x=1.5

The sum of the roots are

$-1+1.5=0.5$ ----> is ok

5 0

3 years ago

Find the value of x and y so that both proportions will be correct:

andrew11 [14]

The values of x and y are 0.2 and 0.4 respectively.

Explanation

The given proportions are.....

$x: 1\frac{2}{3}=y: 3\frac{1}{3}$ and $y:1.5=0.2:0.75$

From the second proportion, we will get....

$y:1.5=0.2:0.75\\ \\ \frac{y}{1.5}=\frac{0.2}{0.75} \\ \\ 0.75y=0.2*1.5\\ \\ 0.75y=0.3\\ \\ y=\frac{0.3}{0.75}=0.4$

Now, we will plug this $y=0.4$ into the first proportion. So we will get....

$x: 1\frac{2}{3}=y: 3\frac{1}{3}\\ \\ x: \frac{5}{3}=0.4:\frac{10}{3} \\ \\ \frac{x}{\frac{5}{3}}= \frac{0.4}{\frac{10}{3}}\\ \\ \frac{3x}{5}=\frac{1.2}{10}\\ \\ 30x=6\\ \\ x= \frac{6}{30}=0.2$

So, the values of x and y are 0.2 and 0.4 respectively.

6 0

3 years ago

For the equation, decide if it is always true or never true. x + 1/2 = x − 1/2

Lorico [155]

Answer:

Step-by-step explanation:

its false

3 0

3 years ago

Read 2 more answers

A piece of a chain's length and weight are in proportion. If 320 cm of chain weighs 8 kg, then

Dafna11 [192]

Answer:

B. 80 cm of chain weighs 2 kg.

Step-by-step explanation:

In order to choose the correct answer, we need to define the comparative relation between the length and weight of the chain. We will do this by performing the simple operation of division.

It is easier to divide the larger number by the smaller and that is what we will show here (although you can do as you wish and still get the same result - it's math!):

320 ÷ 8 = 40

The result we got is 40. This means that the length of the chain is equal to the value of forty of its weights! And this will be the operation we will perform in order to determine the right answer:

A) Does 2 (kg) multiplied by 40 equal 40 (cm)? No, therefore, it is incorrect.

B) Does 2 (kg) multiplied by 40 equal 80 (cm)? Yes, this answer is correct!

Just in case, we will perform this action with the rest of the possible choices:

C) 4 kg × 40 = 160 and NOT 80 cm.

D) 2 kg × 40 = 80 and NOT 160 cm.

5 0

3 years ago

Type the correct answer in each box. Use numerals instead of words.

Hatshy [7]

Answer:

$(4,-3)$ and $(-2,5)$

Step-by-step explanation:

It was given that the points $(-3,4)$ and $(5,-2)$ are on the graph of the function $f$ .

If $g$ is the inverse function of $f$ , then $g$ will take the y-values as inputs and give the x-values as outputs.

Hence we will have the ordered pairs $(4,-3)$ and $(-2,5)$

on g.

In other words, f and g are symmetric about the line $y=x$ . This implies that when we reflect the points $(-3,4)$ and $(5,-2)$ in the line $y=x$ we will obtain $(4,-3)$ and $(-2,5)$ .

This point must lie on g.

8 0

3 years ago

Read 2 more answers