Solve the following quadratic equation for all values of x in simplest form. 4(3x - 5)^2+5 = 13 (will give brainly)

Answers

Answer 1

Answer:

Step-by-step explanation:

4(3x-5)^2+5=13

4(3x-5)^2+5-13=0

As  (a-b)^2=a^2-2ab+b^2

4((3x)^2-2(3x)(5)+(5)^2)-8=0

4(9x^2-30x+25)-8=0

36x^2-120x+100-8=0

36x^2-120x+92=0

using the Quadratic Formula where

a = 36, b = -120, and c = 92

x=(−bc± sqrt(b^2-4ac))/2a

x=(-(-120)±sqrt((−120)^2−4(36)(92))/2(36)

=120±sqrt(14400−13248−)/72

=120±sqrt(1152)/72

The discriminant b2−4ac>0

so, there are two real roots.

x=(120±24sqrt(2))/72

x=(120/72)±24sqrt(2)/72

implify fractions and/or signs:

x=5/3±sqrt(2)/3

hich becomes

x=2.13807

x=1.19526


Related Questions

please help im stuck on this​

Answers

Answer:

[tex]x = 0 \: y = - 2 \: \: \: \: x = 1 \: y = \frac{ - 13}{9} [/tex]

Answer:

X= ( 18/5 , 0)

Y= (0,-2)

Step-by-step explanation:

substitute 0 for y and solve for x

-5x+9(0) = -18

-5X + 0 = -18

-5X= - 18 - 0

-5X = -18

X = - 18/-5

X = 18/5

solve for Y

-5(0) +9y = -18

= 9y = -18

y= -2

Suppose one serving of vegetables is 3/4 cup. How many servings there in 3 1/2 cups?

Explain your reasoning​

Answers

Answer:

14/3 or 4.6

Step-by-step explanation:

you would do 3.5 divided by .75 (=^w^=)

Check this out mate! Good luck

PLEASE HELP ASAP
Find the greatest common factor of these two expressions:
30x^8 w^4 v^3 and 12w^7 v^5

Answers

Answer:

[tex]Factor = 6w^4 v^3[/tex]

Step-by-step explanation:

Given

[tex]30x^8 w^4 v^3[/tex] and [tex]12w^7 v^5[/tex]

Required

Determine the common factor.

To do this, we simply factorize each. SO, we have:

[tex](1)\ 30x^8 w^4 v^3=: 2 * 3 * 5 * x^8 * w^4 * v^3[/tex]

[tex](2)\ 12w^7 v^5:=\ 2 * 2 * 3 * w^4*w^3 * v^3 * v^2[/tex]

Check for similar factors.

[tex]Factor = 2 *3 * w^4 * v^3[/tex]

[tex]Factor = 6w^4 v^3[/tex]

The above represents the similar factor

Find the measure of the exterior angle

Answers

Answer:

Step-by-step explanation:

The sum of two interior angles in a triangle is equal to the exterior angle that is supplementary to the third interior angle

for first triangle

90 + 53 = u

143 = u

for the other triangle

102 + x = 4x + 6

102 = 4x + 6 - x

102 = 3x + 6 subtract 6 from both sides

96 = 3x divide both sides by 3

32 = x

John took all his money from his savings account. He spent $108 on a radio and 5/9 of what was left on presents for his friends. Of the money remaining, John put 5/6 into a checking account and the last remaining $80 was left to charity. How much money did John originally have in his savings account? ​

Answers

Answer:

I believe its 313$

Step-by-step explanation:

John originally have $1,118 in his savings​ account.

Here,

We have to find the original savings account of John.

What is Number system?

A system of writing to express numbers is called Number system.

Now,

Let us assume amount of money John originally have in his savings​ account = $x

Money spent on a radio = $108

Remaining money = x - 108

Money spent on presents for his friends = Two third of remaining money                                  = 5/9 (x - 108).

(Because 1 - 5/9  = 1/1 - 5/9  = 4/9)

Remaining money = 4/9 (x - 108).

Five sixth of his remaining money into a checking account = 5/6 * 4/9(x - 108)

( because 1 - 5/6 = 1/1 -5/6 = 1/6)

Remaining money = 1/6 *4/9 (x - 108).

Final remaining money =  1/6 *4/9 (x - 108)

And that is equal to the money donated to charity.

We can setup an equation now.

1/6 *4/9 (x - 108) = 80

4(x - 108) = 80 * 9 *6

x - 108 = 20 * 54

x = 1080 + 108

x = 1,188

Therefore, John originally have $1,118 in his savings​ account.

Learn more about the number system visit:

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Write a number of grams between 10 and 20, and then write an equivalent amount in milligrams.

Answers

Answer:

15 grams and 15000 milligrams

Step-by-step explanation:

PLEASE HELP IMMEDIATELY!!

Answers

Answer:

}

Step-by-step e.xplanati:kljkjk

a chemist is researching different sustainable fuel sources

Answers

Answer:

Wind

Hydroelectric Power

Solar

Geothermal

NEED ANSWER ASAP WILL GIVE BRAINLIEST FOR CORRECT ANSWER

Answers

Answer:

a person jumping on a trampoline

A person jumping on a trampoline.
This is because they would be going up and down and the graph wouldn’t stay the same as they are constantly moving.

Find the missing angle. Find x

Answers

Answer: 20

Reason: They're opposite meaning they are the same when compared to the side

Find the length of the chord made by 3x2 - y2 = 3 and y + x – 5 = 0.

Answers

Answer:

The correct answer is "9√2 units".

Step-by-step explanation:

The given equations are:

⇒ [tex]3x^2-y^2=3[/tex]...(equation 1)

⇒ [tex]y+x-5=0[/tex]...(equation 2)

According to the 2nd equation, we get

⇒ [tex]y+x-5=0[/tex]

⇒              [tex]y=5-x[/tex]

On substituting the value of "y" in the 1st equation, we get

⇒  [tex]3x^2-y^2=3[/tex]

     [tex]3x^2-(5-x)^2=3[/tex]

     [tex]3x^2-(25+x^2-10x)=3[/tex]

     [tex]2x^2+10x-28=0[/tex]

On taking common, we get

     [tex]x^2+5x-14=0[/tex]

On applying factorization, we get

     [tex]x^2+7x-2x-14=0[/tex]

   [tex]x(x+7)-2(x+7)=0[/tex]

           [tex](x+7)(x-2)=0[/tex]

                        [tex]x+7=0[/tex]

                              [tex]x=-7[/tex]

or,

                         [tex]x-2=0[/tex]

                                [tex]x=2[/tex]

Now,

The points are:

(-7, 12) = (x₁, y₁)

(2, 3) = (x₂, y₂)

By using the distance formula, the length of chord will be:

= [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

On substituting the values in the above formula, we get

= [tex]\sqrt{(2-(-7))^2+(3-12)^2}[/tex]

= [tex]\sqrt{(9)^2+(-9)^2}[/tex]

= [tex]\sqrt{81+81}[/tex]

= [tex]9 \sqrt{2}[/tex] units

Draw a circle whose radius is 3cm?​

Answers

Answer:

In this problem, first we need to draw a circle of radius 3 cm having a center at point O. Now, take a point P at a distance of 5.5 cm from the center of the circle. Draw a line joining the point O and P. Now draw a perpendicular bisector of the line OP that cuts OP at M.

Interpreting Algebraic Expressions
11+9k=6n
The expressions has 2 terms.
True or false?

Answers

The statement is false as the number of terms in the equation is not two

How to determine the number of terms?

The equation is given as

11 + 9k = 6n

Consider an equation represented as

a + b = c

The variables a, b and c are the terms of the equation

This means that the equation 11 + 9k = 6n has the following terms

11, 9k and 6n

The number of these terms is 3

So, the equation has three terms

Hence, it is false that the equation has two terms

Read more about expressions at

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What is the slope of the line represented by the equation y = x-3?
0 -3
5
O
3

Answers

Answer:

slope (m) = 4/5

Step-by-step explanation:

Equation of straight line: y = mx + b

∴ 4/5 is the slope

Determine the value of x and name the type of triangle.
8x + 2
70°
60°
The value of x
Type of triangle

Answers

8x+2+70°+80° = 180°

8x+132° = 180°

8x = 180°- 132°

x = 48°/8

Hence, x = 6

Solve
k -4 > 3.2

A) k< -12.8
B) K< -0.8
C) k> -12.8
D) k= -12.8

Answers

Please look through my recent questions

The differnce in price in colerd pencils and mechanical pencils is $0.20. If I purchased 18 colord pencils and 22 mechanical pencils for $27.60, what is the cost of the mechical pencil

Answers

Answer: Mechanical Pencils are $0.60

Colored Pencils are $0.80

Step-by-step explanation:

18c+22m=27.60

c-m=.20

+m    +m

so c= .20+m

Susitituete 18(.20+m)+22m=27.60

                  3.6+18m  +22m=27.60

                                    40m=27.60

                                      40m=24

                                         m=.60

c=.20+(.60)

c=.80

PLEASE HELP !! ILL GIVE BRAINLIEST !!

Answers

Answer:

∠VWT and ∠UTW

∠STW and ∠XWT

Step-by-step explanation:

help please need asap

Answers

Answer:

A. Obtuse B. Right C. Acute D. Acute Hope this helps :)

Find the area of the semicircle. Round to the nearest hundredth if necessary.

Answers

9514 1404 393

Answer:

  8π m² ≈ 25.13 m²

Step-by-step explanation:

The formula for the area of a circle is ...

  A = πr²

The area of a semicircle is half that. Also, the radius (r) is half the diameter. So. the area of this semicircle is ...

  A = (1/2)π(4 m)² = 8π m² ≈ 25.13 m²

__

Comment on pi

If you use the 3-digit value 3.14 for pi to compute this 4-digit result, you will get 25.12.

Jose car rental company charges $2.75 for a pick up plus $1.25 for each mile driven. How much would you pay to travel 25 miles ? How far could you travel for $100 ? Please no link. I can't view them

Answers

Answer:

it would be 28.44 sorry if it does not help

A political pollster wants to know what proportion of voters are planning to vote for the incumbent candidate in
an upcoming election. A poll of 150 randomly selected voters is taken from the more than 2,000 voters in the
population, and 78 of those selected plan to vote for the incumbent candidate.
Based on this sample, which of the following is a 90% confidence interval for the proportion of all voters who
plan to vote for the incumbent candidate?

Answers

Answer:

90% confidence interval -> {0.4529, 0.5871}

Step-by-step explanation:

Check conditions for a 1-proportion z-interval:

np>10 -> 150(0.52)>10 -> 78>10 √

n(1-p)>10 -> 150(1-0.52)>10 -> 72>10 √

Random sample √

n>30 √

For a 90% confidence interval, the critical value is z=1.645

The formula for a confidence interval is:

CI = p ± z√[p(1-p)/n]

Given:

p = 78/150 = 0.52

n = 150

z = 1.645

Therefore, the 90% confidence interval is:

CI = 0.52 ± 1.645√[0.52(1-0.52)/150] = {0.4529, 0.5871}

Context: We are 90% confident that the true proportion of all voters who

plan to vote for the incumbent candidate is contained within the interval

A party rental company has chairs and tables for rent. The total cost to rent 5 chairs and
3 tables is 31$. The total cost to rent 2 chairs and 6 tables is 52$. What is the cost to rent each chair and each table?

Answers

Answer:

1 Chair= $1.25     1 table= $8.25

Step-by-step explanation:

5c+3t=31

2c+6t= 52

-2(5c+3t=31)

-10c-6t=-62

+

2c+6t=52

= -8c=-10

/-8      /-8

c= 1.25 or 1 1/4

2c+6t=52

2(1.25)+6t=52

2.5+6t=52

-2.5        -2.5

6t= 49.5

/6      /6

t= 8 1/4

How do I solve 8/x-0.16=0.64

Answers

Answer:

yo my bad

x=10 the other person solved it

Answer:

x=10

Step-by-step explanation:

8/x=0.8

8=0.8x

x=10

Solve: 7.2h = 57.6 A. h= 0.8 B. h = 8 C. h = 50.4 D. h = 80

Answers

Answer:

B. h=8

Step-by-step explanation:

The answer is B. h=8. I know because I solved to get h by itself. First, I set up the problem.

7.2h=57.6

Then, I divided each side by 7.2, so I could get h by itself.

h=8

You can check to make sure this is correct by plugging in the value we got for h into the equation.

7.2(8)=57.6

In conclusion, the answer is B. h=8

What is a cubic polynomial function with zeros -20, -15, and -6?
What is a quartic polynomial function with zeros -20, -16, -11, and -9?
What are the zeros of x^3 + 16x^2 + 60x? What are their multiplicities?

Answers

Answer:(x + 1)(x - 1)(x + 5)(x - 3) is the fully factored form of the polynomial.

The zeros are (-1, 0), (1, 0), (-5, 0), and (3, 0).

x^4 + 2x^3 - 16x^2 - 2x + 15

We can use the rational roots theorem to find some of the possible roots, and after finding just one root, we can simplify this polynomial.

List factors of 15:

1, 3, 5, 15.

List factors of 1:

1.

Our possible rational factors are:

+/- 1, +/- 3, +/- 5, +/- 15.

To find factors, we can use the remainder theorem.

Replace all x values with 1.

1^4 + 2(1)^3 - 16(1)^2 - 2(1) + 15 = 0

Because the answer is zero, it means that 1 is a root.

We can divide this polynomial by x - 1 to find a simplified form.

After dividing, our quotient is: x^3 + 3x^2 - 13x - 15

We can continue finding factors by using the rational roots theorem. Once we have only three terms, we can try to factor using the AC method.

Our next possible root is -1.

(-1)^3 + 3(-1)^2 - 13(-1) - 15 = 0

We know that -1 is also a root, and so we can divide the polynomial by x + 1.

After diving we're left with x^2 + 2x - 15.

Now, we can try to factor using the AC method.

List factors of -15.

1 * -15

-1 * 15

3 * -5

-3 * 5 (these digits satisfy the criteria.)

Split the middle term.

x^2 - 3x + 5x - 15

Factor binomials.

x(x - 3) + 5(x - 3)

Rearrange binomials.

(x + 5)(x - 3)

Add in the two factors we already factored out.

(x - 1)(x + 1)(x + 5)(x - 3)

Step-by-step explanation:

Given an equilateral triangle with sides of length 9, find the length of the altitude.

Answers

If the sides are 9 the height will be 7.8

A city councilwoman is concerned that the new contractor she hired is taking too long to replace defective streetlights. She would like to perform a hypothesis test to determine if the replacement time for streetlights under the new contractor is in fact longer than the replacement time under the previous contractor, which was 3.2 days on average. She selects a random sample of 12 streetlight service calls and obtains the following times to replacement (in days). Use a significance level of 0.05

6.2 7.15.4 5.57.52.6 4.3 2.9 3.7 0.7 5.6 1.7

Required:
a. Define μ in the context of the problem and state the appropriate hypotheses.
b. State and check the conditions for a hypothesis test of the mean. Since the sample size is smaller than 30, you will need to calculate a normal probability plot to determine if the data come from a normal distribution.

Answers

Answer:

There is significant evidence to conclude that the replacement time for streetlights under the new contractor is longer than the replacement time under the previous contractor.

Step-by-step explanation:

Given the data :

6.2 7.1 5.4 5.5 7.5 2.6 4.3 2.9 3.7 0.7 5.6 1.7

The hypothesis:

H0: μ = 3.2

H1 : μ > 3.2

n = sample size = 12

The sample mean, xbar = ΣX / n

xbar = 53.2 / 12

xbar = 4.43

Using calculator;

Sample standard deviation, s = 2.147

The test statistic :

(xbar - μ) ÷ (s/sqrt(n))

(4.43 - 3.2) ÷ (2.147/sqrt(12)

1.23 / 0.6197855

Test statistic = 1.985

The Pvalue using the Pvalue from Tscore calculator :

Tscore = 1.985 ; df = 12 - 1 = 11

Pvalue = 0.036

Since Pvalue < α ; We reject the Null

Hence, we conclude that the replacement time for streetlights under the new contractor is longer than the replacement time under the previous contractor.


What is the volume, in cubic feet of the tent.

Answers

Answer:

96ft³

Step-by-step explanation:

Okay, so the formula for finding the volume of a triangular prism is base x height, so we first have to find the base:

6 x 4 ÷ 2 = 12

So then we plug our numbers into the formula:

12 x 8 = 96

So, the volume of the tent is 96ft³

hope this helps:)

Cquation
Question 2 of 5
How many solutions does 6 -3x = 12 - 6x have?
A. Infinitely many solutions
B. Two solutions
C. One solution
D. No solutions

Answers

One solution because it only has one answer that can come out if those properties. If you add the -3 to -6 it will make it 6=12 -3x. Subtract the 12 it will be -6=-3x divide by -3 and x=2
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