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
otez555 [7]
3 years ago
12

Solve each quadratic equation by factoring and using the zero product property.

Mathematics
2 answers:
zepelin [54]3 years ago
8 0

Answer:

x  = 5 or x  = 6

Step-by-step explanation:

Given equation is :

x²-8x+30   = 3x

adding -3x to both sides of above equation, we get

x²-8x+30-3x  = 3x-3x

add like terms

x²-11x+30  = 0

we solve this equation by factoring.

split the middle term so that the product of two numbers should be 30 and the sum is -11.

x²-6x-5x+30  = 0

make two groups

x(x-6)-5(x-6)  = 0

take (x-6) as common

(x-6)(x-5)  = 0

Applying Zero-Product Property to above equation,we get

x-6  = 0 or x-5  = 0

first solve x-6  = 0

adding 6 to both sides of above equation,we get

x-6+6  = 0+6

x+0  = 6

x  = 6

secondly, solve this x-5 = 0

adding 5 to above equation , we get

x-5+5  = 0+5

x +0  = 5

x  = 5

Hence, the solution of x²-8x+30  = 3x  is {6,5}.

Iteru [2.4K]3 years ago
7 0

Answer:

x=5                            x=6

Step-by-step explanation:

x^2 - 8x + 30 = 3x

Subtract 3x from each side

x^2 - 8x-3x + 30 = 3x-3x

x^2 - 11x + 30 = 0

What 2 numbers multiply to 30 and add to -11

-5*-6 = 30

-5+-6 = -11

(x-5) (x-6) =0

Using the zero product property

x-5 = 0  and x-6 =0

x-5+5 =0+5   and x-6+6 =0+6

x=5                            x=6

You might be interested in
Evaluate.<br><br> 10^2 + 6 ⋅ 7 + 8<br><br> A. 70<br><br> B. 142<br><br> C. 150<br><br> D. 190
Kaylis [27]
I hope this helps you




100+42+8



100+50


150
8 0
3 years ago
Suppose a population is growing by 8% each year. How many years will it take the population to double?
Doss [256]

ANSWER

\text{9 years}

EXPLANATION

We want to find the number of years that it will take the population to double.

To do this, we have to apply the exponential growth function:

y=a(1+r)^t

where y = final value

a = initial value

r = rate of growth

t = time (in years)

For the population to double, it means that the final value must be 2 times the initial value:

y=2a

Substitute the given values into the function above:

\begin{gathered} 2a=a(1+\frac{8}{100})^t \\ \frac{2a}{a}=(1+0.08)^t=1.08^t \\ 2=1.08^t \end{gathered}

To solve further, convert the function from an exponential function to a logarithmic function as follows:

\log _{1.08}2=t

Solve for t:

\begin{gathered} \frac{\log _{10}2}{\log _{10}1.08}=t \\ \Rightarrow t=9\text{ years} \end{gathered}

It will take 9 years for the population to double.

4 0
1 year ago
1. The weekly ad for a local grocery store advertises a 5 pound bag of organic apples for $13.95. Round each rate to the nearest
olga_2 [115]

Answer:

a)

$2.79 per pound.

$0.93 per apple.

b)

Unit price per pound is typically used because weight and size of every      apple is not same.

Step-by-step explanation:

5 pound bag of organic apples = $13.95

1 pound bag of organic apples = $13.95/5

                                                   = $2.79

The unit price of apples that cost $13.95 for 5 pounds is $12.79 per pound.

<em>As a general rule, 1 pound of apples is equal to: 4 small apples. 3 medium apples. 2 large apples. So, here we assume that apples are of medium size.</em>

3 apples cost = $2.79

<em>The unit price means 'what is the cost of 1 apple'</em>

1 apple cost    =$2.79/3

                       =$0.93

The unit price of apples that cost $2.79 for 3apples is $0.93 per apple.

<em />

4 0
3 years ago
Read 2 more answers
Find the sum. A. 4x2 – x – 5 B. 10x2 + 7x – 5 C. –10x2 + 7x + 11 D. 4x2 + x – 11
Kobotan [32]

Answer:

A

Step-by-step explanation:

7x² - 4x - 8 - [ -3x² - 3x - 3]

In subtraction, flip the sign of all terms in the minuend

   7x² - 4x - 8

  <u> 3x² + 3x + 3</u>

   4x² - x - 5

7 0
3 years ago
PLEASE HELP WILL MARK BRAINLIEST Determine the value of h. Round your answer to the nearest hundredth if necessary.
jarptica [38.1K]

Answer:

<h2><u>Answer</u><u> </u><u>:</u><u>-</u></h2>

Here,

At first we know that parallel line cut transversal lines. They make them in a proportion.

h/10 = 9/13

h = 10 × 9/13

h = 90/13

h = 6.92

\\

5 0
3 years ago
Read 2 more answers
Other questions:
  • The sides, top, and bottom of a storage bin are made of wood. The storage bin measures 2 meters wide, 3 meters long, and 2 meter
    11·2 answers
  • Each interior angel of a regular polygon has measure 2x+4 degrees. What is x?
    12·1 answer
  • A <br> B <br> C or D please help
    6·1 answer
  • Please help need help
    8·1 answer
  • Order the numbers from least to greatest 3/8, 19/24, 2/3<br>EASY
    14·1 answer
  • Find the sum of the following infinite geometric series, if it exists.
    13·2 answers
  • Help please!!! as part of a summer job, you stack crates. the crates have the same length and width but have heights of 1 or 2 f
    10·1 answer
  • Drag the expressions to show the order of their quotients from least to greatest
    9·1 answer
  • What does i^16 equal and how do you get the answer​
    6·1 answer
  • For 20 points. Which point is a reflection of Z(5 1/2, 3) across the x-axis? Point A point B point C point D point E
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!