Solve the equations below. Give exact solutions only. Show your work.

a) 5x^2 - 7 = 72
b) x(x + 2) = 5
c) 3x^2 + 2x - 4 = 0

Please help!

Answers

Answer 1

Step-by-step explanation:

remember, the general formula to solve a quadratic equation ax² + bx + c = 0 is

x = (-b ± sqrt(b² - 4ac))/(2a)

a)

I think there is a typo, and this should be

5x² - 7x = 72

5x² -7x - 72 = 0

x = (7 ± sqrt(49 - -1440))/10 = (7 ± sqrt(1489))/10

x1 = (7 + sqrt(1489))/10

x2 = (7 - sqrt(1489))/10

b)

x(x + 2) = 5

x² + 2x - 5 = 0

x = (-2 ± sqrt(4 - -20))/2 = (-2 ± sqrt(24))/2 =

= (-2 ± sqrt(4×6))/2 = (-2 ± 2×sqrt(6))/2 =

= -1 ± sqrt(6)

x1 = -1 + sqrt(6)

x2 = -1 - sqrt(6)

c)

3x² + 2x - 4 = 0

x = (-2 ± sqrt(4 - -48))/6 = (-2 ± sqrt(52))/6 =

= (-2 ± sqrt(4×13))/6 = (-2 ± 2×sqrt(13))/6 =

= (-1 ± sqrt(13))/3

x1 = (-1 + sqrt(13))/3

x2 = (-1 - sqrt(13))/3


Related Questions

Pleaseeee help meee with this!!!!!!!!!!!!

Answers

Answer:

x=19

Step-by-step explanation:

The 2 angles are same side interior angles, so together they add to 180 degrees. So you can make this equation:

6x + 4 + 4x - 14 = 180

10x - 10 = 180 (Combine like terms)

10x = 190 (add 10 to each side)

x = 19 (divide both sides by 10)

These two angles add up to 180°

So just add them together and make them equal to 180°

6x + 4 + 4x - 14 = 180

Add like terms

10x - 10 = 180

10x = 190

x = 19

Write the following in simplified radical form.

Answers

Step-by-step explanation:

I think the answer is like this

yesterday 5% of the 120 sixth graders at school were late. How many sixth graders were late?

Answers

Answer:

6

Step-by-step explanation:

5% of 120 were late

= [tex]\frac{5}{100}[/tex] × 120

= 0.05 × 120

= 6

A car is traveling at a steady speed. It travels 2 1/2 miles in 3 1/3 minutes. How far will it travel in ​21 minute? In ​1 hour?

Answers

15 3/4 miles in 21 minutes
45 miles in an hour
hope this is helpful!

9) the formula for the volume
I of a cone is v= 1/3 TT r ² h
Solve the formula for the
height h

Please show your work!!!

Answers

Answer:

V=TTr²h

Step-by-step explanation:

Why?

Because you will v=TT r² h/3

so the answer is

v=TT h/3,r É R,h É R

That's my hardwork lick it brainliest and liked my hardwork please

Select the postulate that is illustrated for the real numbers. 3x + 3 = 3(x + 1) The commutative postulate for multiplication Multiplication by one The distributive postulate The multiplication inverse The addition of zero postulate Commutative postulate for addition The addition inverse postulate

Answers

distributive postulate.

The expression 3x + 3 = 3(x + 1) is an example of a distributive postulate. It says that multiplying a number by a group of numbers added together is the same as doing each multiplication separately.

3 equivalent ratio to 9/2

Answers

Answer:

10/12 i took the test

Step-by-step explanation:

Answer:

18/4  ,  27/6   ,   36/8

Step-by-step explanation:

9 to 2 x 2 = 18 to 4

9 to 2 x 3 = 27 to 6

9 to 2 x 4 = 36 to 8

im stumped on this question. please help:)​

Answers

Answer:

(-2,6)

Step-by-step explanation:

the actual solution to the system of equations is (-(64/27),(56/9)).

however, we can estimate by looking at the graph. the solution is where both lines intersect, and that looks to be around (-2,6) as an approximation. hope this helps!

(-2 , 6 )

Sorry for the late answer!

Consider the rectangle shown.
3x + 5
2x-1
If the perimeter of the rectangle is 52, what is the value of x?

Answers

Step-by-step explanation:

Perimeter of rectangle = 2(a+b) or 2a +2b

a=perimeter of the first side of the rectangle

b=perimeter of the second side of the rectangle

Perimeter = 2(3x+5 + 2x-1)=52

Open the bracket by multiplying the number outside by the number inside

=6x+10+4x-2=52

C.L.T ( Collect like terms), that means put the terms that have co-efficients together (those with variables "X") and those that don't have in the other side of the equation. While collecting like terms, if a number is taken to the other side, the sign changes

6x+4x=52-10+2

10x=44

D.B.S by 10, to make variable X subject

x=4.4

If the perimeter of the rectangle is 52. Then the value of the variable 'x' will be 4.4.

What is the perimeter of the rectangle?

Let W be the rectangle's width and L its length.

The perimeter of the rectangle will be defined as the total length of all of its sides. So the rectangle's perimeter will be

Perimeter of the rectangle = 2(L + W) units

The dimension of the rectangle is (3x + 5) and (2x - 1).

If the perimeter of the rectangle is 52. Then the value of the variable 'x' will be given as,

2[(3x + 5) + (2x - 1)] = 52

Simplify the equation, then we have

2[(3x + 5) + (2x - 1)] = 52

3x + 5 + 2x - 1 = 26

5x + 4 = 26

5x = 22

x = 22 / 5

x = 4.4

If the perimeter of the rectangle is 52. Then the value of the variable 'x' will be 4.4.

More about the perimeter of the rectangle link is given below.

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Simplify (x^3 + 2x^2 - x) + (4x^3 + x^2 + x)

Answers

Answer: 5x^3 + 3x^2

Step-by-step explanation:

Answer:

Step-by-step explanation:

           6x2 - 8x - 2

Simplify   ————————————

              x - 1    

STEP

3

:

Pulling out like terms

3.1     Pull out like factors :

  6x2 - 8x - 2  =   2 • (3x2 - 4x - 1)

Trying to factor by splitting the middle term

3.2     Factoring  3x2 - 4x - 1

The first term is,  3x2  its coefficient is  3 .

The middle term is,  -4x  its coefficient is  -4 .

The last term, "the constant", is  -1

Step-1 : Multiply the coefficient of the first term by the constant   3 • -1 = -3

Step-2 : Find two factors of  -3  whose sum equals the coefficient of the middle term, which is   -4 .

     -3    +    1    =    -2

     -1    +    3    =    2

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Polynomial Long Division :

3.3    Polynomial Long Division

Dividing :  3x2-4x-1

                             ("Dividend")

By         :    x-1    ("Divisor")

dividend     3x2  -  4x  -  1

- divisor  * 3x1     3x2  -  3x    

remainder      -  x  -  1

- divisor  * -x0      -  x  +  1

remainder          -  2

Quotient :  3x-1

Remainder :  -2

Final result :

 2 • (3x2 - 4x - 1)

 ——————————————————

       x - 1      

See results of polynomial long division:

1. In step #03.03

Dante’s chocolate bar is 36% cocoa. If the weight of the chocolate bar is 73 grams, how many grams of cocoa does it contain round your answer to the nearest tenth?

Answers

Answer:

26.3 grams

Step-by-step explanation:

36% = 36/100 = 0.36

73 * 0.36 = 26.28 grams ≈ 26.3 grams

Answer:

i think 26.3 grams

Step-by-step explanation:

0.36×73 = 26.28

When rounded to the nearest tenth, 26.28 should be equal to 26.3

So Dante's the chocolate bar contains 26.3 grams of cocoa.

Mandy has $2.25 credit on her mobile phone. It costs $0.10 to send a text message. What is the largest amount of text messages she can possibly send to her friends with $2.25?

Answers

Answer:

22.5

Step-by-step explanation:

since 2.25 divided by 0.10 is 22.5 so she can message 22.5 friends

Reduce the fraction and find the domain:

(c+2)^2 divided by 7c^2+14c

Answers

the answer is c + 2/7c

How many centimeters are there in 1 yard if there are 2.54 centimeters per inch? Show your work and express your answer without rounding.

Answers

Answer: 91.44

Step-by-step explanation:

There are 3 feet in a yard, 12 inches in a foot. 2.54 x 12= 30.48

30.48 x 3= 91.44

I hope this helps!

Find the length of OP.

Answers

Answer:

 OP = 84  

Step-by-step explanation:

The triangle is equilateral meaning all angles equal and all sides are equal.

5y - 6 = 4y + 12

y - 6 = 12

y = 12 + 6

y = 18

Now  

OP = 4y + 12

OP  =  4(18) +12

  OP = 84  

Mattie Evans drove 160 miles in the same amount of time that it took a turbo propeller plane to travel 920 miles. The speed of the plane was 190 mph faster than the speed of the car. Find the speed of the plane.

Answers

Answer:

Step-by-step explanation:

The speed of the plane was 291.13mph.

What is speed?

Speed is distance travelled per unit time. It is scalar quantity

Given

The difference in distances was 600 miles; the difference in speeds was 190mph. That means the time was 600/190 = 3.16 hours.

Since the plane flew 920 miles in that time, its speed was 920/3.16 = 291.13mph.

To know more about speed refer to:

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Is {1, 3, 5} a subset of the set of odd integers?

Answers

Answer: Yes

Step-by-step explanation:

The set of odd integers is all odd numbers with no decimal places after them. This includes 1, 3, 5, 7, 9, 11, 13 (etc.) The numbers 1, 3, and 5 all fall within this set, making the set {1, 3, 5} a subset of the set of all odd integers.

I need help
What does x² equal?

Answers

Answer: we need to know what the equation is

Step-by-step explanation:

Solve the following equation by factoring: x^2+ x– 42 = 0

Answers

Answer:

x=6,x=-7

Step-by-step explanation:

x^2+x-42=0

x^2-6x+7x-42=0

x(x-6)7(x-6)=0

(x-6)(x+7)=0

Given the figure below, which statement correctly completes the following? ABE and HCD are what type of angles

Answers

Angles are classified based on their measures.

Classification of angles

The following are the classification of angles

Acute AnglesRight AnglesObtuse AnglesStraight linesReflex Angles

The smallest angle is 0 degrees and the largest is 360 degrees.

When the measure of an angle is less than 90 degrees, such angle is an acute angle

When the measure of an angle is exactly 90 degrees, such angle is a right angle

Angles greater than 90 degrees, but less than 180 degree are obtuse angles, while angles that measure exactly 180 degrees are straight lines.

The last type of angle is the reflex angle, and it has a measure between 180 degrees and 360 degrees (exclusive)

The question is incomplete, so I gave a general explanation

Read more about angles at:

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Skyler is helping his mother plan a wedding breakfast for his older sister, Jessica. They
are expecting 63 family members to attend, and they are using round tables that seal 8
guests each. How many tables will be needed to seat 63 people?
What do I do with the remainder?

Answers

Answer:

You would count another table for the remainder. Therefore, 8 tables are needed to seat 63 people. It does not matter whether all seats are filled on the 8th table.

A new DVD player has a purchase price of $430. With the extended warranty, the total cost is $512. What percent of the purchase price is the price of the warranty? a. 16% b. 19% c. 24% d. 29% Please select the best answer from the choices provided A B C D.

Answers

The percent of the purchase price that is the price of the warranty is: b. 19%.

Using this formula

Purchase price percent=Total cost-Purchase price/Purchase price

Where:

Total cost=$512

Purchase price=$430

Let plug in the formula

Purchase price percent=$512-$430/$430

Purchase price percent=$82/$430

Purchase price percent=0.19×100

Purchase price percent=19%

Inconclusion the percent of the purchase price that is the price of the warranty is: b. 19%.

Learn more about purchase price here:https://brainly.com/question/6076645

yo can i get some help with this

Answers

Answer:

14

Step-by-step explanation:

Answer:

16 + 2 = 14 + 4

? = 14

Step-by-step explanation:

Find the value of c that makes x^2+ 9x + c a perfect square trinomial. Write the expression as the square of a binomial. The expression is​

Answers

Answer:

[tex]c=\frac{81}{4}[/tex]

I hope this is the right answer and I hope this helps

The value of the variable 'c' to convert the expression as the square of a binomial will be 81 / 4.

What is a perfect square trinomial?

A perfect square trinomial formulation can be created by taking the binomial equation's squared. If and then only if a trinomial satisfying the criterion b² = 4ac has the form ax² + bx + c, it is indeed a perfect square.

The expression is given below.

⇒ x² + 9x + c

The value of the variable 'c' to convert the expression as the square of a binomial will be given as,

c = (9/2)²

c = 81 / 4

The value of the variable 'c' to convert the expression as the square of a binomial will be 81 / 4.

More about the perfect square trinomial link is given below.

https://brainly.com/question/16615974

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help me please brainlist if right​

Answers

Step-by-step explanation:

1B.) Zero power rule

C.) 1

2B.) Product of powers rule

C.) y^(7+11) = y^18

3B.) Quotient of powers rule

C.) b^(18-5) =b^13

4B.) Power of a power rule

C.) 3^(2×2) =3^4= 81

5B.) None

C.) 729

13)The final grade on your math exam was determined by the function f(x) = 100 - 2x. Which statements are correct?
A) 100 is the maximum grade,
B) y equals your final grade..
C) This is an exponential function.
D) 2 is what each question is worth.
E) x is the number of correct problems

Answers

Answer:

A, B, D

Step-by-step explanation:

from this function, we can see that 2x is being subtracted from 100. x is the number of incorrect problems, so this can not be a negative value. therefore, the maximum score you can get is 100. y is equal to your final grade as calculating the right side of the equation results in the grade you receive based on the number of incorrect answers. this is a linear function since its highest power is 1. each question is worth 2 points as 2 is being multiplied by the number of incorrect questions (x).

A and B and D and that’s it

Are these three side lengths a Pythagorean triple? YES
NO

Answers

Answer:

Yes

Step-by-step explanation:

5^2 + 5^2 = c^2

25 + 25 = c^2

50 = c^2

[tex]\sqrt{50}[/tex] = c

[tex]\sqrt{50}[/tex] = 5[tex]\sqrt{2}[/tex]

Answer:

NO

Step-by-step explanation:

no, it is an acute isosceles triangle

(5√2 = 7.01)

Edward deposited ​$5,500 into a savings account 5 years ago. The simple interest rate is 3​%. How much money Need ans

Answers

Answer:$1375 in interest and $6875 total.

Step-by-step explanation:

Paul left his house at 9:45 a.m. and returned home at 6:55 p.m. the same day. How long was Paul away from home?

Answers

Answer:

9 hours and 10 minutes

I FORGOT TO PUT THE ANSWERS SORRY PLEASE HELP​

Answers

Answer:

Step-by-step explanation:

Circumscribed means written around the outside. -scribe means writing and

think of how circumference is the distance around the outside of a circle. It is a little more special and specific...all the segments that make the triangle are tangents to the circle, that is, they only touch the circle at one point.

So the circle is inscribed-- that is, written inside of the triangle (in the same, special specific way).

Circle A is inscribed in triangle RST.

Answer:

Inscribed

Step-by-step explanation:

What is polygon inscribe?

When a polygon is inscribed inside another polygon it is called polygon inscribe.Here Circle A is drawn inside ∆RST so it's inscribed.
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