the length of a rectangle is 3 more than 3 times it’s width. the perimeter of the rectangle is 174 inches. what is the length of the rectangle?

"Find all real solutions of" basically means solve for x. You're looking for the real numbers x such that the given equation is satisfied. "Zeros" is synonymous with "solutions".

It looks like the first equation is

3x³ + x² - 38x + 24 = 0

It's not immediately obvious whether this can be factorized, so we first carry out the rational zero test to see if there are any rational solutions. *If* this equation has any rational solutions, then they must take the form of (divisor of 24)/(divisor of 3). That is, take any divisor of the constant coefficient and divide it by any divisor of the leading term's coefficient.

We have

• divisors of 24 : ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24

• divisors of 3 : ±1, ±3

Sadly, there are 64 possible roots to test, but we only need one to make the rest of the problem easier.

• Let x = +1 / +1 = 1. Then plugging x = 1 into the equation gives

3•1³ + 1² - 38•1 + 24 = -10 ≠ 0

so x = 1 is *not* a solution

• Let x = +2 / +1 = 2. If x = 2, then

3•2³ + 2² - 38•2 + 24 = -24 ≠ 0

so x = 2 is *not* a solution.

• Let x = +3 / +1 = 3. If x = 3, then

3•3³ + 3² - 38•3 + 24 = 0

so x = 3 is a solution.

By the remainder theorem, this means that x - 3 divides 3x³ + x² - 38x + 24. Using long or synthetic division,

(3x³ + x² - 38x + 24) / (x - 3) = 3x² + 10x - 8

so that

3x³ + x² - 38x + 24 = 0

is the same as

(x - 3) (3x² + 10x - 8) = 0

We factorize the remaining quadratic to get

3x² + 10x - 8 = (3x - 2) (x + 4)

and so the original equation is equivalent to

(x - 3) (3x - 2) (x + 4) = 0

Solve for x :

x - 3 = 0   or   3x - 2 = 0   or   x + 4 = 0

x = 3   or   x = 2/3   or   x = -4

The other equations can be solved similarly, though some of the others you included are much simpler.

For the second problem (note that you left out an exponent), we solve the equation

x³ - 2x² - 23x + 60 = 0

Again, not immediately obvious how to factorize this. But using the rational root test, we have

• divisors of 60 : ±1, ±2, ±3, ±4, ±5, ±6, ±10, ±12, ±15, ±20, ±30, ±60

• divisors of 1 : ±1

If you follow the same steps as before, you'll find the first rational solution with x = 3. So x - 3 divides x³ - 2x² - 23x + 60, and long division gives

(x³ - 2x² - 23x + 60) / (x - 3) = x² + x - 20

and the resulting quadratic is easily factored,

x² + x - 20 = (x - 4) (x + 5)

So, we have

x³ - 2x² - 23x + 60 = (x - 3) (x - 4) (x + 5) = 0

which means

x - 3 = 0   or   x - 4 = 0   or   x + 5 = 0

x = 3   or   x = 4   or   x = -5

For the third problem, we can factor by grouping.

x³ - 4x² - x + 4 = 0

x² (x - 4) - (x - 4) = 0

(x² - 1) (x - 4) = 0

(x - 1) (x + 1) (x - 4) = 0

Then

x - 1 = 0   or   x + 1 = 0   or   x - 4 = 0

x = 1   or   x = -1   or   x = 4

For the fourth problem, we use the rational root test again, but twice this time.

x⁴ - 6x³ + 7x² + 6x - 8 = 0

• divisors of -8 : ±1, ±2, ±4, ±8

• divisors of 1 : ±1

We find that x = 1 and x = 2 are both rational roots, so both x - 1 and x - 2 divide x⁴ - 6x³ + 7x² + 6x - 8. By long division,

(x⁴ - 6x³ + 7x² + 6x - 8) / ((x - 1) (x - 2)) = x² - 3x - 4

and factoring this gives

x² - 3x - 4 = (x + 1) (x - 4)

So, we have

x⁴ - 6x³ + 7x² + 6x - 8 = (x - 1) (x - 2) (x + 1) (x - 4) = 0

which means

x - 1 = 0   or   x - 2 = 0   or   x + 1 = 0   or   x - 4 = 0

x = 1   or   x = 2   or   x = -1   or   x = 4

For the last problem,

x⁴ + 4x³ + 7x² + 16x + 12 = 0

we use the rational root test again.

• divisors of 12 : ±1, ±2, ±3, ±4, ±6, ±12

• divisors of 1 : ±1

We find that both x = -1 and x = -3 are rational solutions, and dividing gives

(x⁴ + 4x³ + 7x² + 16x + 12) / ((x + 1) (x + 3)) = x² + 4

which we cannot factorize further over the real numbers. So we end up with

x⁴ + 4x³ + 7x² + 16x + 12 = (x + 1) (x + 3) (x² + 4) = 0

so that

x + 1 = 0   or   x + 3 = 0   or   x² + 4 = 0

x = -1   or   x = -3

(We omit the third equation here because it has no real solution since x² + 4 ≥ 4 for all real x.)

Answer:

8×1=8+64=72

Step-by-step explanation:

there is your answer are you happy now

Answer:

-1

sorry if this is wrong I really am

Answer:

m= -1

Step-by-step explanation:

Have a nice day

Answer:

A and B

Step-by-step explanation:

They both have the same numbers and at least one of the given numbers is negative.

Hope this helps :)

Answer:

5/36

Step-by-step explanation:

Answer:

the probability of getting a total greater than 8 is  10/36=5/18

Step-by-step explanation:

Of the 36 different possible results of rolling a die twice, 10 of them have a total greater than 8.

Therefore, the probability of getting a total greater than 8 is  10/36 which equals 5/18

Answer: Spencer is 24.75 inches tall

Step-by-step explanation: Just subtract 6 from 30.75 to find the answer

Answer:

The percentage increase in Spencer's height is 125%

Step-by-step explanation:

Solution:

Initial height of spencer = 28 inches  

Increased height of spencer = 5 feet 3 inches  

= 5 feet + 3 inches  

(5 feet = 5 ×12=60 inches)

= 60  + 3

Answer:

36

Step-by-step explanation:

You would multiply 6x8+6x(-2), and that would equal 48+(-12) which is basically 48-12 = 36.

Answer:

3.1

Step-by-step explanation:

lemme know if you want the explanation

Answer:

5a. $1.50R + $7

5b. 14 rides

Step-by-step explanation:

5b. $28 - $7= $21/1.50= 14

He can go on 14 rides

If rides be x

The equation is

#B

Put y=28

Total 14 rides

Answer:

28 is 10% of 280

Steps to solve "28 is 10 percent of what number?"

We have, 10% × x = 28

or,  

10

100

× x = 28

Multiplying both sides by 100 and dividing both sides by 10,

we have x = 28 ×  

100

10

x = 280

If you are using a calculator, simply enter 28×100÷10, which will give you the answer.

Answer:

Ok the answer is 200 feet

Answer:

(2,11)

Step-by-step explanation:

what i did was actually substitution

It's like ..what I do when I've forgotten how to solve a particular equation in math or even physics

But I'd recommend you find the real solution cuz there's a formula

Amanda family cannot travel more than 244 miles without needing to refill the gas tank.

Inequality is the non equal comparison of numbers or variables.

Let x represent the number of miles that they can travel before filling their gas tank.

Their car can travel no more than 352 miles without filling their tank. Also, they have traveled 108 miles since they last filled the gas tank. Hence:

x + 108 < 352

x < 244

This means that Amanda family cannot travel more than 244 miles without needing to refill the gas tank.

Find out more at: https://brainly.com/question/25285332

Answer:

Maybe

Step-by-step explanation:

maybe

Answer:

yes because it can be written as a fraction 225/1000

Answer:

20 m

Step-by-step explanation:

1/50 = 40/x

Cross multiply.

1 × x = 50 × 40

x = 2000

2000 cm × (1 m)/(100 cm) = 20 m

Answer: 20 m

Answer:

D,no if you graph both inequalitiesvon thevsame geaph ,you will get b =16

Answer:

$12

Step-by-step explanation:

Answer:the answer is true

Step-by-step explanation:

Because the two triangle are congruent ASA

Answer:

A: 9.5s+19.95 is less than or equal to 55

Step-by-step explanation:

She has no more than 55 dollars to spend so it cant be greater than but it can be equal to 55 so the answer is the first option

Hey there!

70 minutes

= 1 hour 10 minutes

2 hours

= 60 minutes * 2 minutes

= 60 minutes + 60 minutes

= 120 minutes

70/120

= 70 ÷ 10 / 120 ÷ 10

= 7 / 12

Therefore, your answer is: 7:12 OR 7/12

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

3/4x - 5 = x

= -3/10 -> -0.15

2 Decimal places = 0.150

Answer:

32.5

Step-by-step explanation:

order the numbers) 30, 31, 32, 32, 33, 34, 36, 37

cancel the numbers from each side to the middle) 32 and 33

add the values together and divide by two) [32+33] divide by 2=65/2=32.5

Answer:

7/8

Step-by-step explanation:

7/16×2=7/16×2/1

          =14/16

          =7/8

This can be simplified to 2x-y = 2

Solving for y leads to y = 2x-2

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

Explanation:

Anything perpendicular to Ax+By = C is of the form Bx-Ay = D

The given equation 2x+4y = 14 tells us that A = 2, B = 4, C = 14.

So Bx-Ay = D updates to 4x-2y = D.

We'll plug in the coordinates of the given point (x,y) = (4,6) to solve for D.

4x-2y = D

D = 4x-2y

D = 4(4)-2(6)

D = 16-12

D = 4

So 4x-2y = D updates to 4x-2y = 4

Optionally, we can divide each term by 2 to go from 4x-2y = 4 to 2x-y = 2

If we wanted to solve for y, then we'd get y = 2x-2

Answer:

x = 24°

Step-by-step explanation:

Using 180-degree formula, we can find x.

=> 84 + 4x = 180°

=> 4x = 180 - 84

=> 4x = 96

=> 24°

Therefore, x = 24°

Hoped this helped.

Answer:

[tex] {\boxed {\sf{x = 24 \degree}}}[/tex]

Step-by-step explanation:

In the given figure we have two consecutive interior angles.

We know that each pair of consecutive interior angles is supplementary.

So,

Therefore, x = 24°

x = 16

7 times 2 = 14

8 times 2 = 16

Hope that helped:)

Answer:

493/40

i tried my best on it

Answer:

493 /40

Step-by-step explanation:

(12.325 × 100) /  (1 × 1000)  =  

=12325/ 1000