1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kifflom [539]
2 years ago
12

Please solve each of the following by factoring!

Mathematics
1 answer:
Oxana [17]2 years ago
6 0

Answer:

see explanation

Step-by-step explanation:

(a)

x² - 36 = 0 ← is a difference of squares and factors as

(x - 6)(x + 6) = 0

equate each factor to zero and solve for x

x + 6 = 0 ⇒ x = - 6

x - 6 = 0 ⇒ x = 6

(b)

x² - 5x + 4 = 0

consider the product of the factors of the constant term (+ 4) which sum to give the coefficient of the x- term (- 5)

the factors are - 1 and - 4 , since

- 1 × - 4 = + 4 and - 1 - 4 = - 5 , then

(x - 1)(x - 4) = 0 ← in factored form

equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

x - 4 = 0 ⇒ x = 4

(c)

x² - 2x = 3 ( subtract 3 from both sides )

x² - 2x - 3 = 0 ← in standard form

consider the product of the factors of the constant term (- 3) which sum to give the coefficient of the x- term (- 2)

the factors are + 1 and - 3 , since

1 × - 3 = - 3 and 1 - 3 = - 2 , then

(x + 1)(x - 3) = 0 ← in factored form

equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

x - 3 = 0 ⇒ x = 3

(d)

6x² - 11x - 10 = 0

consider the product of the factors of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 6 × - 10 = - 60 and sum = - 11

the factors are + 4 and - 15

use these factors to split the x- term

6x² + 4x - 15x - 10 = 0 ( factor the first/second and third/fourth terms )

2x(3x + 2) - 5(3x + 2) = 0 ← factor out (3x + 2) from each term

(3x + 2)(2x - 5) = 0

equate each factor to zero and solve for x

3x + 2 = 0 ⇒ 3x = - 2 ⇒ x = - \frac{2}{3}

2x - 5 = 0 ⇒ 2x = 5 ⇒ x = \frac{5}{2}

You might be interested in
Barba can walk 3200 meters in 24 minutes.How far can she walk on 3 mins
SashulF [63]

Answer:

400 meters in 3 minutes

Step-by-step explanation:

First find  how far she can walk in 1 minute.

3200/24 = 133 1/3.

She can walk 133 1/3 meters in 1 minute. If we want to find out how far she can walk in 3 minutes. Multiply that number by 3.

133 1/3 * 3 = 400.

Hope that helps.

8 0
2 years ago
Jared made 12 3/4 cups of snack mix for cups of snack mix for a party. His guests are 2/3 of the mic. How much snack mix did his
Rufina [12.5K]

Answer:

8  1 /2

For this we need to determine what  

2 /3 of 12 3/4 is, so we multiply the fractions together.

4 0
2 years ago
Algebra 2, please help asap and don't guess!<br><br> √−100 = ____ + ______ i
Gnesinka [82]

√−100 = ____ + ______ i

0 and 10

6 0
3 years ago
What is the measure of the angle ?
Roman55 [17]

Answer:

Answer → C) 121°

Step-by-step explanation:

» Let the wanted angle be x

{ \tt{x = 121 \degree}} \\  { \tt{ \{alternate \: angles \}}}

4 0
2 years ago
Two spinners are spun. One has 5 sections labeled Red, Orange, Purple, Yellow, and Green. The other has three sections labeled 1
quester [9]

Answer:

S = 15 possible outcomes

Step-by-step explanation:

For any experiment, the sample space of this experiment is the set of all the possible results of the experiment.

In this case we have two spinners. The first has 5 colors, by spinning the spinner you can get up to 5 different results. Therefore the sample space is S_1 = 5

For the second spinner there are 3 possible results. By spinning the spinner you can get the numbers 1, 2 or 3. Then S_2 = 3.

Then, if the two spinners are rotated, the sample space would be:

S = 5*3

S = 15 possible outcomes.

The tree diagram shown in the attached image shows the 15 possible results

{R, 1} {R, 2} {R, 3} {O, 1} {O, 2} {O, 3} {Y, 1} {Y, 2} {Y, 3} {P, 1} {P, 2} {P, 3} {G, 1}

{G, 2} {G, 3}

4 0
3 years ago
Other questions:
  • Write the expression in exponential form: logb c=a
    15·2 answers
  • I require assistance once again.​
    6·2 answers
  • The ratio of boys to girls is 4 to 3.The team has 35 members.How many are girls?
    15·1 answer
  • Darby is playing a game on her mom's phone. You can get 3 points each time you score, and you can only score up to 12 times per
    15·1 answer
  • Determine whether line AB and line CD are parallel, perpendicular, or neither. A( 4, 2), B(-3, 1), C(6, 0), D(-10, 8)
    14·1 answer
  • Type the correct answer in the box. x y 3 10 20 In the table, the relation (x, y) is not a function if the missing value of x is
    10·2 answers
  • Question 27 <br> Find the length of the hypotenuse. Leave answer in simplest radical form.
    11·1 answer
  • Write the equation of the line in slope-intercept form that passes through the point (-3, 5) and is parallel to y=-2/3x
    15·1 answer
  • SOMEONE HELP<br> Find sinD, sinE, cosD, and cosE. Write each answer as a fraction in simplest form.
    5·1 answer
  • What is the mean of the measures of the three exterior angles of a triangle if two of the interior angles have measures of 63 an
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!