A truck has a bed 6 ft long, 5 ft wide, and
3 ft deep. If it was filled /4 of the way with
dirt. What is the volume of dirt in the bed
of the truck?

Answer:

The first term is, x2 its coefficient is 1 .

The middle term is, -17x its coefficient is -17 .

The last term, "the constant", is +60

Step-1 : Multiply the coefficient of the first term by the constant 1 • 60 = 60

Step-2 : Find two factors of 60 whose sum equals the coefficient of the middle term, which is -17 .

-60 + -1 = -61

-30 + -2 = -32

-20 + -3 = -23

-15 + -4 = -19

-12 + -5 = -17 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -12 and -5

x2 - 12x - 5x - 60

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (x-12)

Add up the last 2 terms, pulling out common factors :

5 • (x-12)

Step-5 : Add up the four terms of step 4 :

(x-5) • (x-12)

Which is the desired factorization

Equation at the end of step

1

:

(x - 5) • (x - 12) = 0

STEP

2

:

Theory - Roots of a product

2.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

2.2 Solve : x-5 = 0

Add 5 to both sides of the equation :

x = 5

Solving a Single Variable Equation:

2.3 Solve : x-12 = 0

Add 12 to both sides of the equation :

x = 12

Supplement : Solving Quadratic Equation Directly

Solving x2-17x+60 = 0 directly

Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

Parabola, Finding the Vertex:

3.1 Find the Vertex of y = x2-17x+60

For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 8.5000

Plugging into the parabola formula 8.5000 for x we can calculate the y -coordinate :

y = 1.0 * 8.50 * 8.50 - 17.0 * 8.50 + 60.0

or y = -12.250

Parabola, Graphing Vertex and X-Intercepts :

Root plot for : y = x2-17x+60

Axis of Symmetry (dashed) {x}={ 8.50}

Vertex at {x,y} = { 8.50,-12.25}

x -Intercepts (Roots) :

Root 1 at {x,y} = { 5.00, 0.00}

Root 2 at {x,y} = {12.00, 0.00}

Solve Quadratic Equation by Completing The Square

3.2 Solving x2-17x+60 = 0 by Completing The Square .

Subtract 60 from both side of the equation :

x2-17x = -60

Now the clever bit: Take the coefficient of x , which is 17 , divide by two, giving 17/2 , and finally square it giving 289/4

Add 289/4 to both sides of the equation :

On the right hand side we have :

-60 + 289/4 or, (-60/1)+(289/4)

The common denominator of the two fractions is 4 Adding (-240/4)+(289/4) gives 49/4

So adding to both sides we finally get :

x2-17x+(289/4) = 49/4

Adding 289/4 has completed the left hand side into a perfect square :

x2-17x+(289/4) =

(x-(17/2)) • (x-(17/2)) =

(x-(17/2))2

Things which are equal to the same thing are also equal to one another. Since

x2-17x+(289/4) = 49/4 and

x2-17x+(289/4) = (x-(17/2))2

then, according to the law of transitivity,

(x-(17/2))2 = 49/4

We'll refer to this Equation as Eq. #3.2.1

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

(x-(17/2))2 is

(x-(17/2))2/2 =

(x-(17/2))1 =

x-(17/2)

Now, applying the Square Root Principle to Eq. #3.2.1 we get:

x-(17/2) = √ 49/4

Add 17/2 to both sides to obtain:

x = 17/2 + √ 49/4

Since a square root has two values, one positive and the other negative

x2 - 17x + 60 = 0

has two solutions:

x = 17/2 + √ 49/4

or

x = 17/2 - √ 49/4

Note that √ 49/4 can be written as

√ 49 / √ 4 which is 7 / 2

Solve Quadratic Equation using the Quadratic Formula

3.3 Solving x2-17x+60 = 0 by the Quadratic Formula .

According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :

- B ± √ B2-4AC

x = ————————

2A

In our case, A = 1

B = -17

C = 60

Accordingly, B2 - 4AC =

289 - 240 =

49

Applying the quadratic formula :

17 ± √ 49

x = —————

2

Can √ 49 be simplified ?

Yes! The prime factorization of 49 is

7•7

To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).

√ 49 = √ 7•7 =

± 7 • √ 1 =

± 7

So now we are looking at:

x = ( 17 ± 7) / 2

Two real solutions:

x =(17+√49)/2=(17+7)/2= 12.000

or:

x =(17-√49)/2=(17-7)/2= 5.000

Two solutions were found :

x = 12

x = 5

Step-by-step explanation:

please mark my answer in brainlist

Answer:

Answer:

C

Step-by-step explanation:

Remember when using the inequality sign < or > the line will be dotted so we can immediately eliminate answer choices b and d

Now let us solve for y

6x-2y>-11

step 1 subtract each side by 6x

now we have

-2y>-11-6x

step 2 divide each side by -2

-11-/2=11/2

-6/-2=3

IMPORTANT -when you divide inequalities by a negative number you flip the inequality sign

So now we have

See image below for reference

When the inequality is facing x the solutions are going to be on top of the line

hope this helps!

Step-by-step explanation:

Answer:

you would need three wholes because each whole would represent a loaf of pumpkin bread

Answer:

10

Step-by-step explanation:

13 pieses - 3 pieces = 10 pieces that are eaten

Answer:

10

Step-by-step explanation:

Answer:

y=-x-2

Step-by-step explanation:

The slope is negative 1 and the y intercept is -2

Answer:

11.15 i think

Step-by-step explanation:

Answer:

it is 1 ok have fun babby and enjoy your Christmas ok baby bye bye

Answer:

1) 94, 2) 188, 3) 564

Step-by-step explanation:

This is pretty simple. The first thing you want to do is come up with an algebraic equation to solve this. It will be x + 2x + 6x=846 . The first x represents the smallest part, or the first part. The second part is represented by 2x because it is twice the first, and 6x is 3 times the second part which is 6 times the first part. Combine like terms to get 9x = 846. Now isolate the variable by dividing 9 from both sides. This will give you x = 94. Now just plug in the x to find the second and third part.

Hope this helped :)

Answer:

500 pounds

Step-by-step explanation:

Step-by-step explanation:

To do this divide 2000 by 4.This will give you around 500.

Answer:

i don't know

Step-by-step explanation:

Answer:

Step-by-step explanation:

14/3 = 4⅔

343/32 = 10 ²³/₃₂

26/3 = 8⅔

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:

358 steps

Step-by-step explanation:

Answer:

5 6/7

Step-by-step explanation:

how many times does 7 go onto 41?

7 x 5 = 35

remainder is 6 so;

5 6/7

Hey there!

41/7

= (5 * 7 + 6)/7

= (5 * 7)/7 + 6/7

= 5 6/7

= 5 6/7 ≈ 41/7

Therefore, your answer is: 5 6/7

Good luck on your assignment and enjoy your day’

~Amphitrite1040:)

Answer:

i do not think it is possible to delete a question after you have posted it. if i were you i probably would have just edited it and save myself the emmbarasment

Step-by-step explanation:

Answer:

82.5 miles in 1 1/2 hours

Step-by-step explanation:

Using the information the question gives us we can find the appropriate answer to this question by dividing the miles per hour by two, and then add that number to the additional miles per hour.

55 miles = one hour

2 hours = 110 miles

1 1/2 hours = 55 ÷ 2 = 27.5

55 + 27.5 = 82.5 miles

82.5 miles

Hope this helps

Answer:

No

Step-by-step explanation:

While these values are close, they are not equal, so I know the original fractions cannot be proportional to each other. So my answer is: The fractions are not

Answer:

61.5

Step-by-step explanation:

61.5 + 8.1 + 7.4 = 77

you're welcome

3x + 2 = 2x + 7

Subtract 2 from both sides:

3x = 2x +5

Subtract 2x from both sides:

x = 5

Answer: x = 5

Answer:

250 girls

Step-by-step explanation:

Add the ratio together (2+5=7), then do 350÷7=50

50 is one part of the ratio so to find how many girls, you would do 50x5=250

Step-by-step explanation:

y²+5y+6=0

y²+2y+3y+6=0

y(y+2)+3(y+2)=0

(y+2)(y+3)=0

:. y=2,3

option C.

hope this helps you.

Answer:

Step-by-step explanation:

Y^2+5y+6=0

5^2 - 4*2*6

25-48

23 i

-5 +4.79i =>   -0.21  =>      0.5i

2*2                     4

-5 +4.79i =>   -9.79  =>      2.44i

2*2                     4

[tex]\cos \angle B = \dfrac{2}{7}\\\\\implies \angle B = \cos^{-1} \left( \dfrac{2}{7} \right) = 1.28^{\circ}[/tex]

Answer:

C. 1

Step-by-step explanation:

We have to convert   4/15  into decimal.

Divide 4 by 15

When we divide 4 by 15, we get 0.26666666666.....

As we can see that, the number 6 is repeating

Only one digit is repeating

Hence, the correct answer is one 6

[tex](2x-y)(3x+y)\\\\=2x(3x+y) -y(3x+y)\\\\=6x^2 +2xy - 3xy -y^2\\\\=6x^2 -xy -y^2[/tex]

Answer:

6) 25.57

7) .9

8) don't see a number underlined

Step-by-step explanation:

Answer:

A third is written as ¹/₃

Step-by-step explanation:

The way to understand this is the number on the bottom is the number of pieces being divided into;

So ¹/₃ is 1 whole divided into 3 parts;

So, you need 3 ¹/₃ parts to make a whole

[tex]a \ * \ \frac{b}{c} = \frac{ab}{c} \\\\ 3 \ * \ \frac{1}{3} = \frac{3 \ * \ 1}{3} \\\\ = \frac{3}{3} \\\\ = 1[/tex]

Answer:

The width is 2.5 inches

Step-by-step explanation:

The given ratio is 7 ft to 1 in

Now we will have 17.5 to x in

x * 7 = 17.5 * 1

7x = 17.5

x = 17.5/7

x = 2.5 inches

Answer:

y = 8/5x + (-4) or y = 8/5x -4

Step-by-step explanation:

Slope-intercept form is written like this:

            y = mx + b

The variable m, represents slope and b, represents the y-intercept.

To find slope, you have to find the rise/run or in other words, change of y over change of x.

From the look of the line, the slope has to be positive because the line is going up.

To go from the bottom point to the top, we have to go up 8 points and go to the right 5 points. Thus the slope is 8/5.

Now for the y-intercept. This part is easy. Just ask yourself this...

"Which of the two points is on the y-axis?"

In this case, it is the bottom point which is -4.

So your equation should look like this:

y = 8/5x + (-4)

   or y = 8/5x - 4 because when you have a plus sign and a minus sign, the result is negative.

hope this helps :)