A car-carrier trailer weighs 35,000 pounds when empty. The driver loads 7 cars on the trailer. The cars are identical except for color. The weight of the loaded trailer is 50,855 pounds. The maximum vehicle weight allowed on U.S. highways is 80,000 pounds. What number best describes the weight of one car?

Answer:

[tex]f(x)=-\frac{1}{12}(x-3)^2(x+2)^2(x-4)[/tex]

Step-by-step explanation:

The standard form for a polynomial equation in its factored form is:

[tex]f(x)=a(x-p)(x-q)...[/tex]

Where p and q are the zeros and a is the leading coefficient.

We know that the degree of the polynomial is 5.

We are also given roots at x=3 and x=-2. Hence, our factors are (x-3) and (x+2).

These have a multiplicity of two, so we will square them.

We also know that there is a root at x=4. Hence, the factor is (x-4). This has a multiplicity of 1.

Therefore, our polynomial is now:

[tex]f(x)=a(x-3)^2(x+2)^2(x-4)[/tex]

We know that the y-intercept is 12. Therefore, if we substitute in 0 for x, we should get 12 for y. Here, we are solving for our a. Therefore:

[tex]12=a(0-3)^2(0+2)^2(0-4)[/tex]

Evaluate:

[tex]12=a(9)(4)(-4)[/tex]

Evaluate:

[tex]-144a=12[/tex]

Divide both sides by -144:

[tex]a=-1/12[/tex]

Hence, our entire polynomial is:

[tex]f(x)=-\frac{1}{12}(x-3)^2(x+2)^2(x-4)[/tex]

Answer:

y = -3x + 1

Step-by-step explanation:

Perpendicular lines have opposite reciprocal slopes, so the slope will be -3.

Plug in the slope and given point into y = mx + b

y = mx + b

-5 = -3(2) + b

-5 = -6 + b

1 = b

Then, plug in the slope and y intercept into y = mx + b again:

y = -3x + 1 will be the equation of the line

Answer:

given, y≥2x+1 and

y>

2

1

x−1

first, draw the graph for equations y=2x+1 and y=

2

1

x−1

for y=2x+1

substitute y=0 we get, 2x+1=0⟹x=−0.5

substitute x=0 we get, y=1

therefore, y=2x+1 line passes through (0.5,0) and (0,1) as shown in fig.

Hence, y≥2x+1 includes the region above the line.

for y=

2

1

x−1

substitute y=0 we get,

2

1

x−1=0⟹x=2

substitute x=0 we get, y=−1

therefore, y=2x+1 line passes through (2,0) and (0,-1) as shown in fig.

Hence, y>

2

1

x−1 includes the region above the line.

the intersection region is the shaded region as shown in above figure which includes I, II and III quadrants.

Therefore, quadrant IV has no solution please make as brainlelist

Answer:

Step-by-step explanation:

6.7578 *x = 13 divide both sides by 6.7578

[tex]\frac{6.7578}{6.7578} *x = \frac{13}{6.7578}[/tex]

x= 1.923

Answer:

A

Step-by-step explanation:

remember y=Mx+b where M is slope mad B is y intercept

Answer:

[tex]x^{2} -6x+xy-6y[/tex]

Step-by-step explanation:

Answer:

The values of coefficients a, b and c are

a=1

b=6

c=6

Step-by-step explanation:

We need to give the values of coefficients [a],[b] and [c]  regarding the product in the form of [tex]ax^2-bx + xy - cy[/tex]

The term given is: [tex](x+y)(x-6)[/tex]

First we will multiply the terms

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

Now comparing the product [tex]x^2-6x+yx-6y[/tex]  with the given form [tex]ax^2-bx + xy - cy[/tex]

The values of coefficients a, b and c are

a=1

b=6

c=6

Answer:

180-112=68

Step-by-step explanation:

Answer:

to get a green and pink it would be 24

i cant find find the special edit sorry

Step-by-step explanation:

Answer:

Fraction of composite numbers = 6/10

Fraction of prime numbers = 4/10

Step-by-step explanation:

A composite number can be defined as a positive integer that will be formed when we multiply two smaller positive integers. It can also be said to be a positive integer that has at least one divisor of which 1 and itself are not included.

Thus, it means that the set of numbers given to us which is;

(11, 12, 13, 14, 15, 16, 17, 18, 19, 20), the composite numbers are;

12, 14, 15, 16, 18, 20

This is because each of them have at least one divisor that is neither itself or 1.

Thus, we have 6 out of the 10 numbers as composite.

Fraction of composite numbers = 6/10

Now, a prime number is a number that are only divisible by itself and 1.

Thus,from the given set, the prime numbers are; 11, 13, 17 & 19

We have 4 out of 10 numbers as prime numbers.

Thus, fraction of prime numbers = 4/10

Answer:

125 boys, 90 girls and 20 adults

Step-by-step explanation:

Let the number of boys be x

Let the number of girls be y

Let the number of adults be z

If there are 235 people at the summer camp, then;

x + y+ z = 235 ..... 1

If there are 35 more boys than girls, then;

x = y + 35 .... 2

If there are 70 fewer adults than girls then;

y = z - 70

z = y - 70....3

Substitute 2 and 3 into 1;

x + y+ z = 235 ..

(y+35)+y+(y-70) =235

3y -35 = 235

3y = 270

3y/3 = 270/3

y = 90

Since x = y + 35

x = 90 + 35

x = 125

Also z = y - 70

z = 90+70

z = 20

There are 125 boys, 90 girls and 20 adults

Answer:

There are 90 girls, 125 boys, and 20 adults.

Step-by-step explanation:

Let x be the number of girls. How many boys were there?

x + 35

How many adults were there?

x - 70

We know that 235 people are at RSM summer camp. Use this to make an equation.

x + (x + 35) + (x - 70) = 235

x + x + 35 + x - 70 = 235

3x - 35 = 235

3x - 35 + 35 = 235 + 35

3x = 270

3x ÷ 3 = 270 ÷ 3

x = 90

x, x + 35, x - 70

90, 125, 20

Answer:

I didn't know the answer and sorry I am here taking freepoint because I needed them in a hurry so that I can ask my questions from someone else that's why I really sorry and thank you for free points

Answer:

Answer: A. 5:4 Step-by-step explanation: Since the question mentions twelfths of a pie, it is easier to say each pie has 12 pieces or 36 total pieces ordered from the 3 pies. Ty ate 5 and Rob ate 15 which is 3 times more than Ty. A total of 20 pieces have been eaten from the 36 you started with. Eaten = 16. So the ratio is 20:16 which is simplified to = 20 and Remaining 5:4.

Answer:

x=1

You solve for x by cross multyplying

9514 1404 393

Answer:

  101 feet

Step-by-step explanation:

Multiply the number of boards by the length of the boards, and add the products.

  2(12 3/4) +4(13 5/8) +2(10 1/2) = 25 1/2 +54 1/2 +21 = 101

The total length of the boards is 101 feet.

Answer:

yea

Step-by-step explanation:

Yes.

16 could also be written as 16.0, or 16.00 or even 16.00000.

16.4 could also be written as 16.40, or 16.400.

And of course, you know 4 is greater than 0.

This is why 16.4 is greater.

When you add a decimal to a number, it always makes it larger. its like saying 16 and 4 tenths.

Answer:

25 miles

pls tell if I'm wrong

Answer:

12 hours

Step-by-step explanation:

Answer:

12 hours

Step-by-step explanation:

Answer:

$16

Step-by-step explanation:

To find the cost per square foot we have to solve the given equation for x:

6.4x - 3.7x = 43.2

2.7x = 43.2

Divide both sides of the equation by 2.7 to isolate the x:

2.7x/2.7 = 43.2/2.7

x = 16

The sheet metal costs $16 per square foot.

Hope this helps :)

Answer: y = -1x + 3

Step-by-step explanation:

it's going through the y intercept ( 3 )

and down ( negative by 1 )

you can also write the answer as y = -x + 3

either one, its the same.

Answer:

I'll try my best in explaining the steps.

Considering both signs are greater than and less than sign, its an open circle.

For the first equation, you would have an open circle, basically one that isn't colored in, on 8 on the number line. The arrow would be pointing to the left because the equation is telling us numbers that are less than 8.

For the second equation, you would have an open circle, basically one that isn't colored in, on -1 on the number line. The arrow would be pointing to the right because the equation is telling us numbers that are greater than -1.

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

The answer is 60 because the equation u = 26 tells us u is 26

So we can plug in 26 into u + 34

It should look like this 26 + 34 and it equals 60

pls mark brainliest

Answer:

I would believe that it would be close 7 whatever is closest to seven bro

Answer:

12

Step-by-step explanation:

20%=2/5

2/5 is equivalent to 12/30

therefore 12 uniforms are medium

Answer:

its 2x+3y>100

Step-by-step explanation:

BTW the greater than sign is greater than or equal to I just cant input that sign so make sure the sign is > with a line underneath it.

Answer:

2 bonus stars

Step-by-step explanation:

0.04 million= 40,000

40000/1701= 23.5

23.5(3)= 70.5

70.5/33= 2 stars

Answer:

8.4 hours

Step-by-step explanation:

Given that:

Speed of asteroid = 55000 miles/hr

Distance traveled by asteroid = 4.62 [tex]\times[/tex] [tex]10^5[/tex] miles

We are required to find here how many hours the asteroid will take to travel the given distance with the given speed.

Formula for speed can be given as following:

[tex]Speed = \dfrac{Distance}{Time}[/tex]

OR, the formula for time in terms of speed and distance can be given as following:

[tex]Time= \dfrac{Distance}{Speed}[/tex]

Putting the given values in the formula to find the Time:

[tex]Time= \dfrac{4.62\times 10^5}{55000}\\\Rightarrow \bold{Time = 8.4\ hours}[/tex]

Answer:

B

Step-by-step explanation:

First, let's rearrange the given equation into something more recognizable. If we add 13 to both sides, we now have the polynomial [tex]x^{2}-10x+13[/tex]. We can now use the quadratic formula to solve.

Remember that the quadratic formula is

[tex]\frac{-b+/-\sqrt{b^{2}-4ac } }{2a}[/tex]

Substitute the numbers from the equation into the formula.

[tex]\frac{-(-10)+/-\sqrt{(-10)^{2}-4(1)(13) } }{2(1)}[/tex]

Simplify:

[tex]\frac{10+/-\sqrt{100-52} }{2}[/tex]

[tex]\frac{10+/-\sqrt{48} }{2}[/tex]

Here, I'm going to assume that there was a mistype in option B because if we divide out the 2 we end up with [tex]5+/-\sqrt{48}[/tex].

Hope this helps!

Answer:

b

Step-by-step explanation:

80% +15% +5%=100

15/100= 0.15

5/100= 0.05

therfore

0.15 + 0.05 = number of flaws

=0.20

Based on the flaws that the manufacturer notices, we can infer that the expected number of flaws will be 0.25 which is e. none of the above.

The expected number of flaws is a weighted average of the percentages that have flaws:

=∑ (Percentage of flaws x Number of flaws)

The expected number of flaws is therefore:

= (80% x 0) + (15% x 1) + (5% x 2)

= 15% + 10%

= 0.25

In conclusion, you would expected the number of flaws to be 0.25.

Find out more at https://brainly.com/question/13412627.

Answer:

(b) -6

Step-by-step explanation:

=3x-x+2

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

=-12+4+2

=-12+6

=-6

Answer:

The length would be l=3.46

Step-by-step explanation: