1) Solve by using the perfect squares method. x2 + 8x + 16 = 0 2) Solve. x2 – 5x – 6 = 0

3) What value should be added to the expression to create a perfect square? x2 – 20x

4) Solve. x2 + 8x – 8 = 0

5) Solve: 2x2 + 12x = 0

6) Solve each problem by using the quadratic formula. Write solutions in simplest radical form. 2x2 – 2x – 1 = 0

7) Calculate the discriminant. x2 – x + 2 = 0

8) Calculate the discriminant and use it to determine how many real-number roots the equation has. 3x2 – 6x + 1 = 0

9) Without drawing the graph of the equation, determine how many points the parabola has in common with the x-axis and whether its vertex lies above, on, or below the x-axis. y = 2x2 + x – 3

10) Without drawing the graph of the equation, determine how many points the parabola has in common with the x-axis and whether its vertex lies above, on, or below the x-axis. y = x2 – 12x + 12

Answers

Answer 1

Answer: 1)
$x^2+8x+16=0 \n(x+4)^2=0 \nx+4=0 \n\boxed{x=-4}$

2)
$x^2-5x-6=0 \nx^2-6x+x-6=0 \nx(x-6)+1(x-6)=0 \n(x+1)(x-6)=0 \nx+1=0 \ \lor \ x-6=0 \nx=-1 \ \lor \ x=6 \n\boxed{x=-1 \hbox{ or } x=6}$

3)
$\hbox{a perfect square:} \n (x-a)^2=x^2-2xa+a^2 \n \n 2xa=20x \n a=(20x)/(2x) \n a=10 \n \n a^2=10^2=100 \n \n \hbox{the expression:} \n x^2-20x+100 \n \n \boxed{\hbox{100 should be added to the expression}}$

4)
$x^2+8x-8=0 \n \na=1 \n b=8 \n c=-8 \n \Delta=b^2-4ac=8^2-4 * 1 * (-8)=64+32=96 \n√(\Delta)=√(96)=√(16 *6)=4√(6) \n \nx=(-b \pm √(\Delta))/(2a)=(-8 \pm 4√(6))/(2 * 1)=(2(-4 \pm 2√(6)))/(2)=-4 \pm 2√(6) \n\boxed{x=-4-2√(6) \hbox{ or } x=-4+2√(6)}$

5)
$2x^2+12x=0 \n2x(x+6)=0 \n2x=0 \ \lor \ x+6=0 \nx=0 \ \lor \ x=-6 \n\boxed{x=-6 \hbox{ or } x=0}$

6)
$2x^2-2x-1=0 \n \na=2 \n b=-2 \n c=-1 \n \Delta=b^2-4ac=(-2)^2-4 * 2 * (-1)=4+8=12 \n√(\Delta)=√(12)=√(4 * 3)=2√(3) \n \nx=(-b \pm √(\Delta))/(2a)=(-(-2) \pm 2√(3))/(2 * 2)=(2 \pm 2√(3))/(2 * 2)=(2(1 \pm √(3)))/(2 * 2)=(1 \pm √(3))/(2) \n\boxed{x=(1-√(3))/(2) \hbox{ or } x=(1+√(3))/(2)}$

7)
$x^2-x+2=0 \n \na=1 \n b=-1 \n c=2 \n\Delta=b^2-4ac=(-1)^2-4 * 1 * 2=1-8=-7 \n \n\boxed{\hbox{the discriminant } \Delta=-7}$

8)
$3x^2-6x+1=0 \n \na=3 \n b=-6 \n c=1 \n \Delta=b^2-4ac=(-6)^2-4 * 3 * 1=36-12=24 \n \n\boxed{\hbox{the discriminant } \Delta=24} \n \n\hbox{if } \Delta\ \textless \ 0 \hbox{ then there are no real roots} \n\hbox{if } \Delta=0 \hbox{ then there's one real root} \n\hbox{if } \Delta\ \textgreater \ 0 \hbox{ then there are two real roots} \n \n\Delta=24\ \textgreater \ 0 \n\boxed{\hbox{the equation has two real roots}}$

9)
$y=2x^2+x-3 \n \n a=2 \n b=1 \n c=-3 \n \Delta=b^2-4ac=1^2-4 * 2 * (-3)=1+24=25 \n \n \hbox{the function has two zeros} \n \boxed{\hbox{the parabola has 2 points in common with the x-axis}} \n \n a\ \textgreater \ 0 \hbox{ so the parabola ope} \hbox{ns upwards} \n \boxed{\hbox{the vertex lies below the x-axis}}$

10)
$y=x^2-12x+12 \n \na=1 \n b=-12 \n c=12 \n \Delta=b^2-4ac=(-12)^2-4 * 1 * 12=144-48=96 \n \n \hbox{the function has two zeros} \n \boxed{\hbox{the parabola has 2 points in common with the x-axis}} \n \n a\ \textgreater \ 0 \hbox{ so the parabola ope} \hbox{ns upwards} \n \boxed{\hbox{the vertex lies below the x-axis}}$

Related Questions

Write the quadratic equation in general form. (x - 3)^ 2 = 0
Jesse collected 42 football cards and 28 basketball cards simpfly the ratio of baseball cards to football cards in his collection
Multiply. Enter your answer in scientific notation.(7 x 10^*13) (3.39 x 10^*5)=
What is the decimal equivalent for a meter and a centimeter?
Consider the function f(x) = 4x2 + 5. Find the value of f(x) when x = 2 and select the correct answer below.

Can you please take a look at these 3 problems?1. A carpentry shop makes dinner tables and coffee tables. Each week the shop must complete at least 9 dinner tables and 13 coffee tables to be shippeed to furniture stores. The shop can produce at most 30 dinner tables and coffee tables combined each week. If the shop sells dinner tables for $120 and coffee tables for $150, how many of each item should be produced for a maximum weekly income? What is the maximum weekly income?

Answers

Shop has to produced 30 furnitures.
It must be at least 9 dinner tables for 120$ and 13 coffe tables for 150$.
We noticed that income will be greater when shop will produce as much is possible coffe tables.
So if sum of furnitures is 30, shop should produce 9 (minimum) of dinner tables and the rest of cofee tables.
There are 9 dinner tables and 30-9=21 coffe tables.
Income is equal:
120*9+21*150=4230$

Holly wants to add an odd number to 659. Which number could possibly be the sum?

Answers

1 is an odd number, therefore 660 (since 659+1=660) could possibly be the sum.

Which of the following statements contain a variable? Check all that apply.A. The number of different colors on the page.
B. They scored 27 points.
C. Eighty miles per hour.
D. Half the speed of the car.

Answers

A. The number of different colors on the page.

D. Half the speed of the car.

These statements contain variables representing unknown quantities or values.

Variables in mathematics and science are symbols that represent unknown values or quantities. Let's analyze each statement to identify the ones containing variables:

A. "The number of different colors on the page."

This statement contains a variable because it represents an unknown quantity, the number of colors.

B. "They scored 27 points."

This statement does not contain a variable as it explicitly states a specific value (27 points).

C. "Eighty miles per hour."

This statement does not contain a variable as it provides a specific constant value (80 miles per hour).

D. "Half the speed of the car."

This statement contains a variable because it represents an unknown value, which would depend on the actual speed of the car.

In summary, the statements containing variables are:

A. The number of different colors on the page.

D. Half the speed of the car.

These statements represent quantities that can vary, making them suitable for mathematical or scientific analysis where variables are used to express relationships and solve equations.

For more such questions on speed

brainly.com/question/553636

#SPJ6

The correct answers are:

A) the number of different colors on the page; and
D) half the speed of the car.

Explanation:

A variable represents an unknown amount.

For A, we do not know how many colors are on the page; this means we would use a variable to represent it.

For D, while we know we want half of the speed of the car, we do not know what the speed of the car actually is; therefore we would use a variable to represent it.

Find 3 consecutive even numbers where the product of the smaller two numbers is 40 less than the square of the largest number.

Answers

$3\ consecutive\ even\ numbers:\ 2x,2x+2,2x+4\n\n2x(2x+2)+40=(2x+4)^2\n\n 4x^2+4x+40=4x^2+16x+16\n\n 4x^2-4x^2+4x-16x=16-40\n\n-12x=-24\ \ |:(-12)\n\nx=(24)/(12)=2\n\n2x=2=4\n\n2x+2=6\n\n2x+4=8\n\nNumbers\ are\ 4,6,8.$

the total weight of 3 tables is 16.9 pounds. the first table is twice as heavy as the second table. The weight of the third table is 1/3 the weight of the second table. What is the weight of the first table?

Answers

2x + x + 1/3x =16.9
31/3x=16.9

x = 5

the first table is 10 pounds

Six friends share 4 pears. how much will each person get when shared equally

Answers

6 divided by 4 is 1 1/2. So they would each one and a half pears.

Other Questions

Which set of lengths might be used to represent the sides of a right triangle? A. (6, 7, 10) B. (7, 15, 17) C. (9, 12, 16) D. (7, 24, 25)

What is the 2x2 identity matrix?

A field in the shape of a square has an area of 8,100 square feet. How can you determine the length of one side of the field?

What is the value of j in the equation j + j + 14 = 3 j + 10?a. 2 b. 16 c. 2 d. 4