Given: ZF and ZG are right angles.

(08.07 HC)

andreev551 [17]

Answer:

$\textsf{A)} \quad x=-2, \:\:x=\dfrac{5}{2}$

$\textsf{B)} \quad \left(\dfrac{1}{4},-\dfrac{81}{8}\right)=(0.25,-10.125)$

C) See attachment.

Step-by-step explanation:

Given function:

$f(x)=2x^2-x-10$

To factor a <u>quadratic</u> in the form $ax^2+bx+c$ <em> , </em>find two numbers that multiply to $ac$ and sum to $b$ :

$\implies ac=2 \cdot -10=-20$

$\implies b=-1$

Therefore, the two numbers are -5 and 4.

Rewrite $b$ as the sum of these two numbers:

$\implies f(x)=2x^2-5x+4x-10$

Factor the first two terms and the last two terms separately:

$\implies f(x)=x(2x-5)+2(2x-5)$

Factor out the common term (2x - 5):

$\implies f(x)=(x+2)(2x-5)$

The x-intercepts are when the curve crosses the x-axis, so when y = 0:

$\implies (x+2)(2x-5)=0$

Therefore:

$\implies (x+2)=0 \implies x=-2$

$\implies (2x-5)=0 \implies x=\dfrac{5}{2}$

So the x-intercepts are:

$x=-2, \:\:x=\dfrac{5}{2}$

The x-value of the vertex is:

$\implies x=\dfrac{-b}{2a}$

Therefore, the x-value of the vertex of the given function is:

$\implies x=\dfrac{-(-1)}{2(2)}=\dfrac{1}{4}$

To find the y-value of the vertex, substitute the found value of x into the function:

$\implies f\left(\dfrac{1}{4}\right)=2\left(\dfrac{1}{4}\right)^2-\left(\dfrac{1}{4}\right)-10=-\dfrac{81}{8}$

Therefore, the vertex of the function is:

$\left(\dfrac{1}{4},-\dfrac{81}{8}\right)=(0.25,-10.125)$

Plot the x-intercepts found in Part A.

Plot the vertex found in Part B.

As the <u>leading coefficient</u> of the function is positive, the parabola will open upwards. This is confirmed as the vertex is a minimum point.

The axis of symmetry is the <u>x-value</u> of the <u>vertex</u>. Draw a line at x = ¹/₄ and use this to ensure the drawing of the parabola is <u>symmetrical</u>.

Draw a upwards opening parabola that has a minimum point at the vertex and that passes through the x-intercepts (see attachment).

5 0

1 year ago

What is the gcf of 23 and 50

valkas [14]

Answer:

The greatest common factor of 23 and 50 is 1

Step-by-step explanation:

7 0

3 years ago

5. A hairstylist charges $15 for an

Rashid [163]

Answer:

you cut off some of the problem

Step-by-step explanation:

6 0

2 years ago

The sum of the digits of a 2-digit number is 10. If 18 is added to the number, the digits of the new number are those of the ori

Aliun [14]

Answer:

46

Step-by-step explanation:

Let $(ab)$ represent a number with $a$ in the ten's position and $b$ is the one's position.

This means $(ab)$ actually has value of $10a+b$ .

We are given the sum of those digits of $(ab)$ is 10; this means $a+b=10$ .

It says if 18 is added to the number $(ab)$ , then the result is $(ba)$ .

So $(ab)$ has value $10a+b$ and

$(ba)$ has value $10b+a$ .

We are given then:

$(ab)+18=(ba)$

$10a+b+18=10b+a$

Subtract $10a$ on both sides:

$b+18=10b+a-10a$

Simplify:

$b+18=10b-9a$

Subtract $b$ on both sides:

$18=10b-b-9a$

$18=9b-9a$

Divide both sides by 9:

$2=b-a$

Rearrange by commutative property:

$2=-a+b$

So the system of equations we want to solve is:

$a+b=10$

$-a+b=2$

-------------------------Add equations together (this will eliminate the variable $a$ and allow you to go ahead and solve for $b$ :

$0+2b=12$

$2b=12$

Divide both sides by 2:

$b=\frac{12}{2}$

Simplify:

$b=6$

If $b=6$ and $a+b=10$ , then $a=4$ . $a=4$ since 4+6=10.

So the original number is (46).

18 more than 46 is 18+46=(64) which is what we wanted.

We also have the sum of 4 and 6 is 10 as well.

7 0

3 years ago

A student scored in the 60th percentile on her math exam. What does this student's score mean in relation to those of the other

Andrei [34K]

Answer:

The correct option is;

c. Her score was better than those of 60% of all test takers

Step-by-step explanation:

Percentile Score is the score of an exam or test candidate with regard to the relative performance of the other persons that took part in the exam or test.

The percentile score is calculated by converting candidates scores into a scale consisting of the scores of all candidates and ranging from 0 to 100

A 60th percentile score means that the student performed better than 60% of all the candidates of the test and 40% of the test takers scored the same as or better than the student.

5 0

3 years ago