Solve each equation using the Zero Product Property and the Distributive Property (as necessary)

11. f(x)=3x(2x-6)

12. f(x)=3x(x+7)-2(x+7)

Answers

Answer 1

Answer:

11) x=1 or x=3.

12) x=2/3 or x=-7.

Step-by-step explanation:

So we have two equations:

[tex]f(x)=3x(2x-6)\\f(x)=3x(x+7)-2(x+7)[/tex]

And we want to solve them. To do so, make each of them equal 0 and then solve for x:

11)

[tex]f(x)=3x(2x-6)\\0=3x(2x-6)[/tex]

Using the Zero Product Property, either one or both of the factor must be zero for this to be true. Therefore, make each factor equal to zero and solve:

[tex]3x=0 \text{ or } 2x-6=0[/tex]

Divide the left by 3. On the right, add 6 and then divide by 2:

[tex]x=0\text{ or } 2x=6\\x=0 \text{ or } x=3[/tex]

Therefore, the solutions to the first equation is:

x=1 or x=3.

12)

[tex]f(x)=3x(x+7)-2(x+7)[/tex]

First, use the distributive property to group the terms together. The equation is equivalent to:

[tex]f(x)=(3x-2)(x+7)[/tex]

Now, set the function to zero and solve:

[tex]0=(3x-2)(x+7)[/tex]

[tex](3x-2)=0 \text{ or } x+7=0\\3x=2 \text{ or } x=-7\\x=2/3 \text{ or } x=-7.[/tex]

Therefore, the answer is:

x=2/3 or x=-7.

Answer 2

Answer:

[tex]\large \boxed{{\bold{11.} \ x=0, \ x=3}} \\ \\ \large \boxed{{\bold{12.} \ x=-7, \ x=2/3}}[/tex]

Step-by-step explanation:

We will set the outputs of the functions to 0 and solve for x.

0 = 3x(2x - 6)

Set factors equal to 0.

First possibility:

3x = 0

x = 0

Second possibility:

2x - 6 = 0

2x = 6

x = 3

0=3x(x+7)-2(x+7)

Take (x+7) as a common factor.

0 = (3x-2)(x+7)

Set factors equal to 0.

First possibility:

x + 7 = 0

x = -7

Second possibility:

3x - 2 = 0

3x = 2

x = 2/3


Related Questions

WILL MARK BRAINLIEST IF CORRECT!!!!!!!!!!! :) (IMAGE ATTACHED)

Answers

Answer:

B

Step-by-step explanation:

just did it

Answer:

[tex]\huge\boxed{Option \ B: 5\sqrt[3]{10} + 4\sqrt[3]{10} }[/tex]

Step-by-step explanation:

[tex]\sf 9\sqrt[3]{10} \\We \ can \ split \ 9 \ into\ 5 \ and \ 4\\(5 + 4)\sqrt[3]{10} \\Applying distributive property\\5\sqrt[3]{10} + 4\sqrt[3]{10}[/tex]

Kamal prepares 2 kilograms of dough every hour he works at the bakery. Write an equation that shows the relationship between the hours worked x and the dough prepared y. *

Answers

Answer:

2 into x into y

Step-by-step explanation:

you move left 1 unit and up 1 unit. you end at (-5, 5) where did you start?​

Answers

Answer:-4,4

Step-by-step explanation:

Because, -4 plus -1 is -5 and 4+1 is 5, hope this helps

>~<

Step-by-step explanation:

(-6,1)

Factorise:
8 x 3 + 729 +10800² + 486X.

Answers

Answer:

(2x+9)  ^3

Step-by-step explanation:

 (((8 • (x3)) +  729) +  (22•33x2)) +  486x

 ((23x3 +  729) +  (22•33x2)) +  486x

Factoring:  8x3+108x2+486x+729  

 8x3+108x2+486x+729  is a perfect cube which means it is the cube of another polynomial  

 In our case, the cubic root of  8x3+108x2+486x+729  is  2x+9  

 Factorization is  (2x+9)3

Hope this helped

HELP ME ASAP PLEASE!!!

Answers

Answer:

idk

Step-by-step explanation:

What is the image point of (3,1) after a translation left 3 units and up 3 units?

Answers

Answer:

0,4

Step-by-step explanation:

When yo go  3 to the left for x you get back to 0 and when you go up 3 for 1 you go up to 4.

Answer:

(0,4)

Step-by-step explanation:

its right

Solve: -5 + 7 - 6 - (-4) *

Answers

Answer:

0

Step-by-step explanation:

-5 + 7 - 6 - (-4)

-11 + 7 - (-4)

-11 + 7 +4

-11 + 11

= 0

Answer: 0

Step-by-step explanation:

-5 + 7 -6-(-4)    

-5 + 7 -2

-5+ 5 = 0

8+(-3) full work thx If u can help

Answers

Answer: 5

Step-by-step explanation:

 8+(-3)

=8-3 ⇔ you don't need to change signs when it is positive(+) outside the parenthesis

=5 ⇔ subtraction

#CarryOnLearning

Negative +positive =a negative number
+(-)= -
8+(-3) =8-3
=5

12x+4(x-1)=60
solve please

Answers

Answer:

Hey there!

12x+4(x-1)=60

12x+4x-4=60

16x-4=60

16x=64

x=4

Let me know if this helps :)

Answer:

x=4

Step-by-step explanation:

The product of this number and 10 is equal to the square of this number

Answers

Answer:

___ x 10 = ____^2

Step-by-step explanation:

The number is 10. 10 times 10 equals 100. 10 squared is 100.

how many centimetre square are there in a rectangle of 10cmby5cm

Answers

Answer:

30cm²

Step-by-step explanation:

Since there are two 10 centimeter sides, this can be shown as 10cm×2=20cm. Since there are two 5 centimeter sides, this can be shown as 5cm×2=10cm. 20cm+10cm=30cm².

This diagram is a straightedge and compass construction. A is the center of one
circle, and B
is the center of the other. Select all the true statements.

Answers

Answer:

True choices are 1, 2, 5

Step-by-step explanation:

As per diagram, the circles are equal.

Since the distance AB is the radius of both circles:

AB = AC = BC = BD = AD = r

So the answer choices:

1. AC = BC

Correct, both equal to r

2. AC = BD

Correct, both equal to r

3. CD = AB

Incorrect. Half of CD is the leg of 30-60-90 triangle and is equal to  r√3/2, so CD = AB√3

4. ABCD is a square

Incorrect. ACBD is rhombus

5. ABD is an equilateral triangle

Correct, all three sides are equal to r

6. CD = AB + AB

Incorrect as CD = AB√3

Chloe wants to net 50000 on her house. Her closing costs will be 8000 plus 7% commission. She owes 200000 on her loan . What is the minimum contract price that she can accept for the property?

Answers

Answer:

$277,419

Step-by-step explanation:

Relevant Data provided as per the question is

Net amount = 50,000

Closing cost = 8,000

Loan amount = 200,000

Commission percentage = 7%

According to the given situation, the calculation of the minimum contract price is shown below:-

[tex]Minimum\ contract\ price = \frac{(Net\ amount\ +\ Closing\ cost\ +\ Loan\ amount) }{Remaining\ percentage}[/tex]

[tex]= \frac{(50,000 + 8,000 + 200,000)}{(100\% - 7\%)}[/tex]

[tex]= \frac{258,000}{93\%}[/tex]

= $277,419

Therefore for calculating the minimum contract price we simply applied the above formula.

A person ran 300 yards ran how many feet did he run

Answers

Answer:

900 feet

Step-by-step explanation:

300 yards converted to feet is 900 ft.

Which of the following is true given that 2.1 < 2.8?
A.
2.1 is to the right of 2.8 on a horizontal number line
B.
2.1 is at the same place as 2.8 on a horizontal number line
a.
2.1 is to the left of 2.8 on a horizontal number line
KDD
2.1 is the opposite of 2.8 on a horizontal number line

Answers

Answer:

[tex]\large \boxed{\mathrm{2.1 \ is \ to \ the \ left \ of \ 2.8 \ on \ a \ horizontal \ number \ line}}[/tex]

Step-by-step explanation:

[tex]2.1<2.8[/tex]

[tex]\sf 2.1 \ is \ lesser \ than \ 2.8.[/tex]

[tex]\sf A \ number \ that \ is \ lesser \ than \ another \ number \ is \ to \ the \ left \\ \ of \ that \ number \ on \ a \ horizontal \ number \ line.[/tex]

Answer:1 is to the left of 2.8 on a horizontal number line

Step-by-step explanation:

Joshua sold his bike for 10% less than payed for it. If he sold the bike for $585, how much did he pay for it.

Answers

Answer: $650

Step-by-step explanation:

If he sold the bike 10% less than the original amount which means he sold it as a 10% discount so the person has to pay 90% of the price. And 90% of the price has to equal $585  so we could set up an equation and solve for the price.

90% * x =  585

0.9 * x = 585

0.9x = 585

x = 650  

Which means he paid $650 for the bike.

2x - 3y = 16 5x - 3y = 13 solve the system of equations

Answers

Answer:

x=-1 y=-6

Step-by-step explanation:

i hope that helped

2 3/7 - 1 1/4 please give the answer as a mixed number with the fraction part in the lowest terms :))

Answers

Answer:

9/28

Step-by-step explanation:

2 3/7 - 1 1/4

2 3/7 - 1 1/4First turn the two mixed numbers into improper fraction:

2 3/7 - 1 1/4First turn the two mixed numbers into improper fraction:17/7 - 5/4

2 3/7 - 1 1/4First turn the two mixed numbers into improper fraction:17/7 - 5/4Next find the Lowest Common Denominator:

L.C.D = 28

L.C.D = 2821 - 12/28

L.C.D = 2821 - 12/28= 9/28

It won't be a mixed number because the denominator is bigger than the numerator.

5. The shape of a dome can be modeled by the equation h = - 2 d 2 + 100 where h is the height (in feet) of the dome from the floor d feet from its center. How far from the center of the dome is the height 50 feet?

6. A cab charges $0.10 per mile and a flat fee of $3.00. Write an equation to model the price y of an x-mile-long cab ride.

7. Use the discriminate to determine the number of solutions to the quadratic equation y = 3 x 2 - 4 x + 6. 8. If f ( x ) = 7 x 2 + 5, compute f ( )3 . 9. Write an equation representing the translation of f ( x ) = 7 x + 3 down 4 units.

Answers

Answer:

5. When the dome is 50 feet high, the distance from the center is 5 feet

6. The equation that model the price y of an x-mile long ride is given as follows;

y = 0.1×x + $3.00

7. The discriminant is < 0; The equation has no real root

8. f(3) = 68

9. The equation representing the translation of the line f(x) = 7·x + 3 down 4 units is f(x) = 7·x + 7

Step-by-step explanation:

5. The given equation for the shape of the dome is presented as follows;

h = -2·d² + 100

Where;

h = The height of the dome (in feet)

d = The distance from the center

Therefore, we have;

When h = 50, d is found as follows;

h = -2·d² + 100

50 = -2·d² + 100

50 - 100 = -2·d²

-50 = -2·d²

∴ 2·d² = 50

d² = 50/2 = 25

d = √25 = 5 feet

Therefore when the dome is 50 feet high, the distance from the center is 5 feet

6. The given rate the cab charges per mile, x = $0.10

The rate the cab charges as flat fee = $3.00

Therefore, the price, y a person traveling by cab for x miles is given by the straight lie equation as y = m·x + c,

Where;

m = the slope or rate which in this case = $0.1/hour

c = A constant term which in this case = $3.00

Therefore

y = 0.1×x + $3.00

The equation that model the price y of an x-mile long ride is y = 0.1×x + $3.00

7. The discriminant, b² - 4·a·c  of the quadratic equation is (-4)² - 4×3×6 = -56

which is < 0, the equation has no real root

8. Given f(x) = 7·x² + 5

f(3) = 7 × (3)² + 5 = 68

f(3) = 68

9. The equation representing the translation of the line f(x) = 7·x + 3 down 4 units is given as follows;

Down 4 units is equivalent to subtracting 4 from the y-coordinate value, therefore, we have;

f(x) - 4= 7·x + 3

f(x) = 7·x + 3 + 4

f(x) = 7·x + 7

The equation representing the translation of the line f(x) = 7·x + 3 down 4 units is f(x) = 7·x + 7

-4(x-5 ) - 25 = -5 x =?*

Answers

Answer:

x=0

Step-by-step explanation:

First distribute -4 to x and -5 and get -4x+20-25=-5

Then you combine like terms and get -4x-5=-5

Then add 5 to both sides and get -4x=0

Then divide both sides by -4 and get x=0

Let f(x) = 4x + 8 and g(x) = 2x - 12. Perform the function operation, (f - g)
(x), and then find the domain of the result.

Answers

Answer:

See below.

Step-by-step explanation:

So we know that:

[tex]f(x)=4x+8\text{ and } g(x)=2x-12[/tex]

First, know that:

[tex](f-g)(x)[/tex]

Is the same as:

[tex]=f(x)-g(x)[/tex]

Substitute:

[tex]=(4x+8)-(2x-12)[/tex]

Distribute:

[tex]=4x+8-2x+12[/tex]

Combine like terms;

[tex]=2x+20[/tex]

Thus:

[tex]f(g(x))=2x+20[/tex]

This is simply a linear equation.

Thus, the domain is all real numbers.

In interval notation, this is:

[tex](-\infty, \infty)[/tex]

Point M is the segment bisector. what is the value of x?

Answers

Answer: x = 5

============================================

Explanation:

"Bisect" means to cut in half

M is the midpoint as it cuts segment ST in half

SM and MT are the same length

SM = MT

2x+3 = 4x-7

2x-4x = -7-3

-2x = -10

x = -10/(-2)

x = 5

----------

If x = 5, then

SM = 2x+3 = 2(5)+3 = 10+3 = 13

MT = 4x-7 = 4(5)-7 = 20-7 = 13

Both SM and MT are the same length (13 units). This confirms the answer.

The test for goodness of fit​ a. ​is always an upper tail test. b. ​is always a two-tailed test. c. ​can be a lower or an upper tail test. d. ​is always a lower tail test.

Answers

Answer: a. ​is always an upper tail test.

Step-by-step explanation:

The chi-square goodness-of-fit test is a test to check whether the sample comes from the population with the expected distribution or not.

If the observed frequency is close to the expected frequency, then the square of the deviations will be small. The square of the deviation is divided by the expected frequency to get the weighted frequencies.

If the sum of these weighted squared deviations is large is then it creates a doubt for the distribution claimed other wise not. Therefore, the chi-square goodness-of-fit test is always a right tail test.

Hence correct option is "a. ​is always an upper tail test. "

3.3 x 10^11 in standard notation

Answers

Answer:

330,000,000,000

Step-by-step explanation:

Move the decimal to the right eleven times!

Answer:

3.3*10¹¹ = 330000000000

Step-by-step explanation:

3.3*10¹¹ = 330000000000

What will be the location of U’ in the image trapezoid S’T’U’V’?

Answers

Answer:

(14,1)

Step-by-step explanation:

You can see with the LKMJ rectangle, it moves over 7 and up 3.

We can do this for STUV and U is originally (7,-2) but moves up and right to the point (14,1)

a body of mass 2kg travelling with a velocity of 10 m/s what is the momentum this body colloids with another body of equal mass travelling in the same direction with a velocity of 5m/s what is the total momentum of the 2 objects before and after coliision

Answers

Your question has been heard loud and clear.

M1 = 2kg , M2=2kg , V1=10m/s V2=5m/s

Total momentum before collision = M1V1+M2V2 = 2*10 + 2*5 = 30kgm/s  

Now , by law of conservation of momentum ,

Total momentum before collision = total momentum after collision

Therefore , total momentum of objects before and after collision = 30kgm/s

Thank you

For the residual plot below, explain whether the plot shows a linear or non-linear model and why.

Answers

Answer:

It is a linear model

Step-by-step explanation:

The answer choices imply that you can model the relationship between the variables with a line or curve.

find the relevant data points on the scatter plot and draw a line of best fit to visualize this relationship. The line of best fit should be drawn through appropriate points. The only far away point can be ignored. The line of best fit need not pass through the majority of the points.

According to the scatter plot and the line of best fit, it will be seen that as X - variables increases, Y - variable decreases, leading to a strong negative correlation.

The Majority of the data points are fairly close to the line of best fit, which means the correlation is strong.

the sum of n and 7 is equal to 50

Answers

Answer:

43

Step-by-step explanation:

Sum means total

n+7=50

n=50-7

n=43

write the equation of the line that passes through (3, 4) and (2,-1) in point slope form

Answers

Step-by-step explanation:

Using Point Slope formula :

[tex](y - y_1) = \frac{(y_2 - y_1)}{(x_2 - x_1)} (x - x_1)[/tex]

[tex](y - 4) = 5(x - 3)[/tex]

[tex]y = 5x - 11[/tex]

Answer:

The point slope formula is : y-y₁ =m(x-x₁), so first u need to find the value of slope.

Step-by-step explanation:

finding the value of slope:

slope(m)= y₂-y₁ ÷ x₂-x₁

              = -1-4 ÷ 2-3

               = 5

now finding equation;

y-y₁=m(x-x₁)

y-4 = 5(x-3)

11=5x - y

0= 5x - y -11

therefore equation of line in point slope is : 5x-y-11=0

Y = (x+2) (-X-1)
Answer the question using null law

Answers

Answer:

x = - 2, x = - 1

Step-by-step explanation:

Given

y = (x + 2)(- x - 1)

To solve for x let y = 0, that is

(x + 2)(- x - 1) = 0

Equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

- x - 1 = 0 ⇒ - x = 1 ⇒ x = - 1

Step-by-step explanation:

y=(x+2) (-x-1)

(45) - (+14)

y= (x+2) (-x-1)

y=-2

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