Solve the equations.
[tex]3(x+4)^{2} =10x+32\\(x+4)^{2} =3x+40\\\frac{x^{2} -1}{2} -11x=11[/tex]

Answers

Answer 1

Answer:

  a) x = {-2 2/3, -2}

  b) x = {-8, 3}

  c) x = {-1, 23}

Step-by-step explanation:

If all you want are solutions, a graphing calculator can give them to you easily. The attachment shows the solutions as x-intercepts when the equation is rearranged to the form f(x) = 0.

__

In general, it can be convenient to write the equation in standard form with integer coefficients. Common factors among the coefficients should be removed.

a)

  3(x+4)^2 = 10x +32 . . . . . given

  3(x^2 +8x +16) -10x -32 = 0

  3x^2 +14x +16 = 0

To factor this, we're looking for factors of 3·16 that total 14.

  48 = 1·48 = 2·24 = 3·16 = 4·12 = 6·8

The last pair of factors has a total of 14, so we can rewrite the equation as ...

  (3x +6)(3x +8)/3 = 0

  (x +2)(3x +8) = 0

The solutions are the values of x that make the factors zero:

  x = -2, x = -8/3

__

b)

  (x +4)^2 = 3x +40 . . . . . . . . given

  x^2 +8x +16 -3x -40 = 0 . . . . subtract the right side

  x^2 +5x -24 = 0 . . . . . . . . simplify

  (x +8)(x -3) = 0 . . . . . . factor

The solutions are the values of x that make the factors zero:

  x = -8, x = 3

__

c)

  (x^2 -1)/2 -11x = 11 . . . . . given

  x^2 -1 -22x -22 = 0 . . . . . . multiply by 2, subtract the right side

  x^2 -22x -23 = 0 . . . . . . simplify

  (x -23)(x +1) = 0 . . . . . . factor

  x = 23, x = -1

_____

Additional comment

Factoring often gets to the solution with the least fuss when the solutions are rational. There are several ways factoring can be done when the leading coefficient is not 1. One of them is illustrated in (a) above. We will show two other methods that give the same result.

factoring by pairs

We have identified the factors of 3·16 = 48 that have a total of 14. We can use those factors to rewrite the 14x term in the equation.

  3x^2 +6x +8x +16 = 0

Now, we can group the terms in pairs, and factor each pair. It does not matter which of the factors (6 or 8) you write first. You will end with the same result.

  (3x^2 +6x) +(8x +16) = 0

  3x(x +2) +8(x +2) = 0

  (3x +8)(x +2) = 0   ⇒   x = -8/3, x = -2

__

factoring using the X method

This method is usually shown using a large graphic X. In the top quadrant is written the product of the leading coefficient and the constant: 3·16 = 48.

In the bottom quadrant is written the coefficient of the x-term: 14.

If one or the other, or both, of these top/bottom values is negative, be sure to keep the sign.

The side quadrants are then filled with values that have a product equal to the top number, and a sum equal to the bottom number. (Pay attention to the signs.) Further, in each of those quadrants, the number written is divided by the leading coefficient, and the fraction reduced to lowest terms.

Here, we would have 6/3 = 2 on one side, and 8/3 on the other side. Now the factors are written as (bx+a), where the reduced fraction on either side is a/b. In our example, the factors are (x+2) and (3x+8)

__

alternate X method

This starts off in the same way the X method does, as described above. However, the factors on either side of the X are not divided by the leading coefficient (a). If those side values are 'p' and 'q', the quadratic is written in factored form as ...

  (ax +p)(ax +q)/a = 0

You will notice we used this form above: (3x +6)(3x +8)/3 = 0.

Now, the divisor 'a' can be used to reduce either or both of the numerator factors. Here, the entire factor of 3 can be removed from (3x+6) to make the factorization be ...

  (x +2)(3x +8) = 0

__

Sometimes, one factor of the divisor will be removed from one term, and the other factor of it will be removed from the other term. An example of this might be ...

  [tex]\dfrac{(6x+3)(6x+2)}{6}=\dfrac{6x+3}{3}\cdot\dfrac{6x+2}{2}=(2x+1)(3x+1)[/tex]

Solve The Equations.[tex]3(x+4)^{2} =10x+32\\(x+4)^{2} =3x+40\\\frac{x^{2} -1}{2} -11x=11[/tex]

Related Questions

A cone has a volume of 94.2 cubic feet and a height of 10 feet. What is its radius?

Answers

Answer:

  3 ft

Step-by-step explanation:

The formula for the volume of a cone is ...

  V = 1/3πr²h

Solving for r, we find ...

  r = √(3V/(πh))

  r = √((3×94.2)/(π×10)) ≈ √9 = 3 . . . . ft

The radius of the cone is 3 ft.

If 2 caterpillars eat 6 leaves each day, how many leaves do 12 caterpillars need each day?

Answers

Hey there. I like to lay out this sort of question in this way…

2 caterpillars = 6 leaves

We’ve been told to work out how many leaves 12 caterpillars eat each day.

So we can fill in our extra information…

2 caterpillars = 6 leaves
12 caterpillars = x leaves

From 2 to 12, we have multiplied by 6. What we do to one side, we must do to the other. Therefore, 6 x 6 = 36 leaves.

So for 12 caterpillars, they eat 36 leaves each day.


Answer:

72 Leafs

Step-by-step explanation:

Find the slope of the line containing the points (3,2) and (6,9).

Answers

Answer:

7/3

Step-by-step explanation:

Please help (Math)......

Answers

[tex]|x|^2 -2|x|-3=0\\\\\implies |x|^2 - 3|x| + |x| - 3 =0\\\\\implies |x|(|x| -3) + (|x| -3) = 0\\\\\implies (|x| - 3)(|x| +1) =0\\\\\implies |x| -3 = 0~~ \text{Or} ~~ |x| +1 =0\\\\\implies |x| = 3 ~~ \text{Or}~~ |x| = -1;\\\\\text{For}~ |x|= -1 ,~\text{ there are no solution for } x \in \mathbb{R}\\\\\text{So,}\\\\|x| = 3 \implies x = \pm 3[/tex]

For homework Tina is asked to write down the opposite value for each number listed which comparison did Tina write incorrectly

Answers

In writing down the opposite value of each number, the comparison Tina wrote incorrectly is: Comparison X

Recall:

Opposite values of a number are numbers that are of the same distance from point zero on a number line.For example, if a is a number, the opposite of a is -a. Or if -3 is a number, the opposite of -3 is 3 because -3 and 3 are both 3 units away from point zero on a number line.

Thus, Tina's comparison is given in the diagram attached below.

The comparison labelled X is incorrect because -(-9) = 9. Opposite of 9 is -9.

Therefore, in writing down the opposite value of each number, the comparison Tina wrote incorrectly is: Comparison X

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Find the x and y-intercepts of y= 2/5x-12​

Answers

y intercept is -12
then find points when going 2 up on the y and 5 over right on the x axis

Need help fast hs geometry

Answers

Measure of angle C = 100°Measure of angle A = 40°We know, sum of all angles of a triangle is 180°.Therefore, the measure of angle B

= [180 - (100 + 40)]° = 40°

When two angles of a triangle are equal, then the triangle is isosceles.Here, the measure of angle A and B are equal, i.e., 40°So, ∆ABC is an isosceles triangle.

Answers:

40°Yes

Hope you could get an idea from here.

Doubt clarification - use comment section.

Which equation could have been used to create this table? need answer fast


y = x + 6


y = x + 5


y = 6x

y = 7x

Answers

Answer:

y=6x

Step-by-step explanation:

Each value for y is can be divided by 6 for the value of x

Answer:

y=6x

Step-by-step explanation:

question 5. Write an equation of the line that passes through the points (-2, -6) and (4, 6).
Answer in slope-intercept form

Answers

Answer:

y=2x-2

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(6-(-6))/(4-(-2))

m=(6+6)/(4+2)

m=12/6

m=2

y-y1=m(x-x1)

y-(-6)=2(x-(-2))

y+6=2(x+2)

y=2x+4-6

y=2x-2

Note that the slope-intercept form is y=mx+b where m=slope and b=y-intercept.

(5a^3-2)(5a^3+2) expand and combine like terms

Answers

Step-by-step explanation:

(5a³-2)(5a³+2)

5a³×5a³+ 5a³×2 - 2× 5a³+ 5a³×2 5a³+10a³- 10a³ + 10a³5a³+10a³ + 10a³-10a³15a³ Answer

Find the slope of the line that passes through the points given in the first column and match them with the appropriate result.
Number: (10,7) and (1,2)
Drags And Drops:5/9, -7/8, 2/7, 6/7, 5/7

Answers

Answer:

5/9.

Step-by-step explanation:

The slope is the difference in y-values  divided by corresponding difference in x-values.

So here:

Slope = (7-2)/(10-1)

= 5/9.

Mathew grew a sunflower that was 1 7/8 meters tall. She cut 3/4meters off the height. How much of the steam is left?

Answers

First find a common denominator so how can you change 4 and 8 to be the same, multiply 4 by 2 and what you do to the bottom you have to do to the top. You should get 6/8. So, usually you would change the mixed number to an improper fraction but for this problem you don’t need to. Now you would subtract 1 7/8 -6/8 and that would be 1 1/8. Sometimes you need to simply you final answer but right now it’s already at the lowest it can go. Answer : 1 1/8 Hope this helped :)

Determine whether the lines 3x+2y=6 and 4y=-6x-12 are parallel, intersect, or coincide

Answers

Answer:

parallel

Step-by-step explanation:

3x + 2y = 6 can be written as y = -3/2x +3

4y = -6x -12 can be written as y= -3/2x-3

same slope different y intercept so parallel

What are the vertices of PQR?

Answers

Answer:

D

Step-by-step explanation:

i may be wrong. if i am, sorry. but a vertice is basically just a point.

The vertices of the given triangle PQR are P, Q and R. Therefore, the correct answer is option D.

A vertex (plural vertices) in geometry is the intersection of two straight lines. Three line segments come together to form a triangle. The ends of a triangle's three sides meet at three separate points in a plane to form the triangle, which has three sides with two endpoints each. The vertices of a triangle are the three distinct intersecting points or corners.

Vertices of the triangle are represented by letters.

In triangle PQR, vertices are P, Q and R.

Therefore, the correct answer is option D.

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What is the end behavior of the function shown in the graph above?
A
As x approaches 0, y approaches 15.
As x approaches 25, y approaches 0.

B
As x approaches∞, y approaches 0.
As x approaches −∞, y approaches ∞.

C
As x approaches 0, y approaches ∞.
As x approaches ∞, y approaches −∞.

D
As x approaches ∞, y approaches 0.
As x approaches ∞, y approaches ∞.

Answers

Answer:

B

Step-by-step explanation:

Write 56xy^3 as a prime factorization.
Show all your work.

Answers

Answer:53

Step-by-step explanation:56-3 =53

Last week, you finished Level 2 of a video game in 32 minutes. Today, you finish Level 2in 28 minutes. What is your percent of change

Answers

Answer:

12.5% decrease

Step-by-step explanation:

[(V2 - V1)  /  V1] x 100 = Percent Change

313 people were surveyed in total. 183 of the people surveyed are from East Harlem and 130 people are from the Upper East Side. What percent of people surveyed are from each neighborhood?

Answers

1. The percentage of people surveyed in East Harlem is 58.5%

2. The percentage of people surveyed in Upper East Side is 41.5%

From the question given above, the following data were obtained:

People surveyed in East Harlem = 183People surveyed in Upper East Side = 130Total people surveyed = 313

1. Determination of the percentage of people surveyed in East Harlem.

People surveyed in East Harlem = 183Total people surveyed = 313Percentage of East Harlem =?

Percentage of East Harlem = (people surveyed in East Harlem / Total) × 100

Percentage of East Harlem = (183/313) × 100

Percentage of East Harlem = 58.5%

2. Determination of the percentage of people surveyed in Upper East Side.

Percentage of East Harlem = 58.5%Total percentage = 100%Percentage of Upper East Side =?

Percentage of Upper East Side = (Total percentage) – (Percentage of East Harlem)

Percentage of Upper East Side = 100 – 58.5

Percentage of Upper East Side = 41.5%

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The first step for deriving the quadratic formula from the quadratic equation, 0 = ax^2 + bx + c, is shown.

Step 1: –c = ax^2 + bx

Which best explains or justifies Step 1?

subtraction property of equality
completing the square
factoring out the constant
zero property of multiplication

Answers

Answer:

Subtraction property of equality

Step-by-step explanation:

You subtracted c from both sides of the equation to preserve equality

The step 1 is explained by subtraction property of equality.

The correct option is A.

The standard form of Quadratic Equation is

ax² + bx + c = 0

Also, we must remove c from the right side and move it to the left side in order to derive the quadratic formula from the quadratic equation.

And to do that, we must subtract c from both sides, which is

-c = ax² + bx

Then, we have used subtraction property here.

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4.5% of it is 23% of 45

Answers

Answer:

230

Step-by-step explanation:

23% of 45 = 10.35

10.35 / 4.5 = 2.3

2.3 x 100 = 230

Step-by-step explanation:

it will be equal 230 as in the shown photo

100 points!! ASAP do all problems with steps to your answer

Answers

Answer:

11. 10

12. -9v + 7

13. 1-10b

14. 5n+10

15. 12v

16. 0

17. 0

18. -4n+10

19. 9b - 9

20. 5v-8

Hope it help.

Answer: 13: 1-10b

14: 5n +10

15: 12v

16: nothing

17 0

18: 10 -4n

19: 11 + 5b

20: 5x + -8

Step-by-step explanation:

13: 6b + 4b = 10b

1-0=1

1-10b

14: n+4n = 5n

5n+10

15: 10v + 2v = 12v

16: 6v - 6v = 0

17: -2 +2 =0

18: 9 + 1 = 10

5n + n = 4n

10 - 4n

19: 10 + 1 = 11

7b-2b = 5b

11 + 5b

20: 1 -9 = -8

5x + -8

please help me, please and thank youuu! :D

Answers

Answer:

f = - [tex]\frac{19}{7}[/tex]

Step-by-step explanation:

Given f varies directly with m then the equation relating them is

f = km ← k is the constant of variation

To find k use the condition f = - 19 when m = 14

- 19 = 14k ( divide both sides by 14 )

- [tex]\frac{19}{14}[/tex] = k

f = - [tex]\frac{19}{14}[/tex] m ← equation of variation

When m = 2 , then

f = - [tex]\frac{19}{14}[/tex] × 2 = - [tex]\frac{19}{7}[/tex]

what is the slop of the line 2x - 5y=9

Answers

The slope is 2The slope is 2The slope is 2The slope is 2The slope is 2The slope is 2

Answer:

(5,2)

Step-by-step explanation:


In AABC, mzA = 39°,
mzB = (3x+7)°, and
mzC = (5x-2)°. Find x. PLEASE HELP

Answers

Answer:

The sum of measures of angles in a triangle is 180. So if you take the three angles, add them, and set it to 180, you will get the answer. (39 + 3x + 7 + 5x - 2 = 180)

Step-by-step explanation:

Answer:

[tex]x = 17[/tex]

Step-by-step explanation:

[tex]m < a + m < b + m < c = 180 \\ \\ 39 + (3x + 7) + (5x - 2) = 180 \\ 39 + 8x + 5 = 180 \\ 44 + 8x = 180 \\ 8x = 180 - 44 \\ 8x = 136 \\ x = \frac{136}{8} \\ \\ x = 17[/tex]

I NEED SOME HELP PLS

Answers

Answer: I might have done some of the math wrong but I think this is the answer.

Step-by-step explanation:

Jose would be able to save $16,400 including the $2,000 and he will need $166,000 in financial aid.

what is the meaning of the word treacherous mean in the sentence below

QUICK plzzzz
i-ready lvl F

Answers

Answer: Guilty of or involving betrayal or deception.

Step-by-step explanation:

Mattie Evans drove 350 miles in the same amount of time that it took a turbopropeller plane to travel 1350 miles. The speed of the plane Has 200 mph faster than
the speed of the car. Find the speed of the plane.

(Simplify )

Answers

let

d1 = 250 mi the distance that Mattie Evans drove

v1 = the speed of Mattie Evans

d2 = 1300 mi the distance the plane traveled

v2 = the speed of the plane

The speed of the plane was 190 mph faster than the speed of the car:

v2 = v1 + 190

since time = distance/speed and they both traveled the same time we have

d1/v1 = d2/v2

250/v1 = 1300/v2 cross multiply

250v2 = 1300v1 divid eboth sides by 50

5v2 = 26v1

by solving the system of equations:

v2 = v1 + 190

5v2 = 26v1

we find

v1 = 45.24 mph

v2 = 235.24 mph

really confused helppppppppp

Answers

Answer:

slope=100

$100 per deposit

Step-by-step explanation:


Based on the graph below, f(x) and g(x) where g(x) =f(x)+h are shown

Answers

Answer:

The value of h is 5

Step-by-step explanation:

Remember the if two lines are parallel and one is taller than the other and is asking for what that is the difference it is the y-intercept or what you call in this problem "h" since h is 5 digits above the answer is 5

I will give these ponts for free if u answer 100+100x100. (help me get brnliest)

Answers

In the beginning operations are performed with multiplication,,,so
100x100=10.000+100=
10.100result…

Answer:

10,100

Step-by-step explanation:

100*100=10000+100=10,000

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