MATHEMATICS HIGH SCHOOL

A quadratic equation is shown below:x2 − 8x + 13 = 0

Which of the following is the first correct step to write the above equation in the form (x − p)2 = q, where p and q are integers?
Subtract 5 from both sides of the equation

Add 3 to both sides of the equation

Add 5 to both sides of the equation

Subtract 3 from both sides of the equation

Answers

Answer 1

Answer:

The given quadratic equation can be represented in the form $(x-p)^2 = q$

by adding 3 to both sides of the equation.

What is a quadratic equation?

The polynomial equation whose highest degree is two is called a quadratic equation. The equation is given by

$ax^2 + bx + c = 0$

where $a\neq 0$ .

The given quadratic equation is

$x^2 - 8x + 13 = 0$

Case 1: Subtract 5 from both sides of the equation

i.e. $x^2 - 8x + 13 - 5 = 0 - 5$

⇒ $x^2 - 8x + 8 = -5$

The LHS of the above equation can not be expressed in $(x-p)^2$ form. Hence, it is not the correct step.

Case 2: Add 3 to both sides of the equation.

i.e. $x^2 - 8x + 13 +3 = 0 + 3$

⇒ $x^2 - 8x + 16 = 3$

⇒ $x^2 - 2* x * 4 + (4)^2 =3$

⇒ $(x - 4)^2 = 3$

The above equation is expressed in $(x-p)^2 = q$ form where p = 4 and q = 3.

Case 3: Add 5 to both sides of the equation

i.e. $x^2 - 8x + 13 + 5 = 0+5$

⇒ $x^2 - 8x + 18 = 5$

The LHS of the above equation can not be expressed in the $(x-p)^2$ . Hence, it is not the correct step.

Case 4: Subtract 3 from both sides of the equation

i.e. $x^2 - 8x + 13 - 3 = 0-3$

⇒ $x^2 - 8x + 10 = -3$

The LHS of the above equation can not be expressed in the $(x-p)^2$ . Hence, it is not the correct step.

Hence, "Add 3 to both sides of the equation" is the correct step.

Learn more about quadratic equations here:

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Answer 2

Answer: Add 3 to both sides, so you will have

x^2 - 8x + 13 + 3 = 3
x^2 -8x + 16 = 3

And now the left side is a perfect square trinolmial: (x-4)^2.

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What is the name of the relationship between ∠1
and
∠5
?

alternate exterior angles

alternate interior angles

corresponding angles

adjacent angles

Answers

Corresponding angles.

Answer:

It is corresponding angles.

Step-by-step explanation:

I took the test and this is the correct answer.

You can tell what the answer is without the picture as well.

What is times plus 4

Answers

Answer:

you forgot the number before times

Step-by-step explanation:

Please help i don’t understand this it would mean a lot :(

Answers

Answer:

send the pic

Step-by-step explanation:

in japan, farmers have created watermelons in the shape of rectangular prisms. find the volume of a prism-shaped watermelon in cubic inches if its length is 10 inches, its width is 2/3 foot, and its height is 9 inches

Answers

Given:
rectangular prism.
length = 10 inches
width = 2/3 foot
height = 9 inches

convert width from foot to inches. 1 foot = 12 inches
2/3 foot * 12inches/ft = 2/3 * 12 inches = 2*12/3 = 24/3 = 8 inches

Volume of rectangular prism = length * width * height
V = 10 inches * 8 inches * 9 inches
V = 720 in³

Two sides of a right triangle have the lengths 4 and 5. What is the product of the possible lengths of the third side? Express the product as a decimal rounded to the nearest tenth.

Answers

Answer:

19.2

Step-by-step explanation:

1st Case:

4 and 5 are legs of the right triangle.

Using the pythagorean therom: a^2+b^2=c^2

We can say that 4^2+5^2=x^2

16+25=x^2

41=x^2

x=√41

√41 is about 6.4

x=6.4

2nd Case

5 is the hypotenuse of the right triangle and 4 is the legs.

Using the pythagorean therom: a^2+b^2=c^2

We can say that 4^2+x^2=5^2

16+x^2=25

x^2=9

x=3

Final Step

We need to multiply the two possible lengths for x. So for case 1 the length of x was 6.4 and for case two the length was 3. 6.4*3=19.2

Anwser: 19.2

Each equation given below describes a parabola. Which statement best compares their graphs? y = -3x2 y= -7x2

A. Both parabolas open downward, and y = -7x2 is wider than y = -3x2.
B. Both parabolas open downward, and y = -3x2 is wider than y = -7x2.
C. Both parabolas open to the left, and y = -3x2 is wider than y = -7x2.
D. Both parabolas open to the left, and y = -7x2 is wider than y = -3x2.