At 10:00 AM a truck started traveling from point A with a speed of 40mph. 3 hours and 10 minutes later a car started to drive from point A in the same direction with an average speed of 60mph. At what time will the car catch up with the truck?

Answer:

f(x) = [tex]3x^3 - 3x^2 - 6x[/tex]

Step-by-step explanation:

Which polynomial function has x intercepts -1,0, and 2 and passes through the point (1,-6)?

There are 3 distinct and real roots given in the question, which means that the  function must be a third degree polynomial. The roots are -1, 0, and 2. This means that f(x) = 0 at these points. The general form of the cubic equation is given by:

f(x) = ax^3 + bx^2 + cx + d; where a, b, c, and d are arbitrary constants.

From the given data:

f(-1)=0 implies a*(-1)^3 + b*(-1)^2 + c(-1) + d = -a + b - c + d = 0. (Equation 1).

f(0)=0 implies a*(0)^3 + b*(0)^2 + c(0) + d = 0a + 0b + 0c + d = 0. (Equation 2).

f(2)=0 implies a*(2)^3 + b*(2)^2 + c(2) + d = 8a + 4b + 2c + d = 0. (Equation 3).

f(1)=0 implies a*(1)^3 + b*(1)^2 + c(1) + d = a + b + c + d = -6. (Equation 4).

Equation 2 shows that d = 0. So rest of the equations become:

-a + b - c = 0;

8a + 4b + 2c = 0;  (Divide 2 on both sides of the equation to simplify).

a + b + c = -6

This system of equation can be solved using the Gaussian Elimination Method. Converting the system into the augmented matrix form:

• 1 1 1 | -6  

• -1 1 -1 | 0

• 4 2 1 | 0

Adding row 1 into row 3:

• 1 1 1 | -6  

• 0 2 0 | -6

• 4 2 1 | 0

Dividing row 2 with 2 and multiplying row 1 with -4 and add it into row 3:

• 1 1        1 | -6

• 0 1       0 | -3

• 0 -2 -3 | 24

Multiplying row 2 with 2 and add it into row 3:

• 1 1       1 | -6

• 0 1       0 | -3

• 0 0 -3 | 18

It can be seen that when this updated augmented matrix is converted into a system, it comes out to be:

• a + b + c = -6

• b  = -3

• -3c = 18 (This implies that c = -6.)

Put c = -6 and b = -3 in equation 1:

• a + (-3) + (-6) = -6

• a = -6 + 3 + 6

• a = 3.

So f(x) = [tex]3x^3 - 3x^2 - 6x[/tex] (All conditions are being satisfied)!!!

Answer:

x=3

Step-by-step explanation:

First we will distribute the 4 into the (x+7) and 9 into (x-1).

You should then got

4x+28=9x-9+22

Afterwards we combine like-terms

4x+28=9x+13

Then, we put all the alike values on the same side together.

4x+28=9x+13

-4x           -4x

___________

28=5x+13

-13        -13

____________

15=5x

You then divide both sides by 5 to isolate x

15/5= 3

x=3

The Louvre Museum's glass pyramid could hold approximately 908,448 cubic feet of water if converted into an aquarium.

The Louvre museum's glass pyramid with sides measuring 114 feet and a height of 71 feet can hold water if converted into an aquarium. To calculate the volume to hold water, we use the formula for the volume of a rectangular pyramid: 1/3 * base area * height. Substituting the values, the pyramid could hold approximately 908,448 cubic feet of water.

Answer:

3 * pi

B

Step-by-step explanation:

The diameter is 3 inches.

radius = diameter / 2

radius = 3 / 2 = 1.5 inches.

The circumference of a circle = 2*pi*r where r is the radius, and pi = 3.14

C = 2 * pi * 1.5

C = 3 * pi

B

Answer: {MMM ,MCC ,CMC, CCM ,CMM ,MCM ,MMC ,CCC }

Step-by-step explanation:

Let C denotes the event when dog catches the throw and M denotes the event when dog misses the throw.

Given: Caleb throws a ball three times for his dog leo.

Then the sample space for the situation is given by :-

{MMM ,MCC ,CMC, CCM ,CMM ,MCM ,MMC ,CCC }

Using the provided radioactive decay formula and the half-life information for Silicon-32, we can predict there will be approximately 21.978 grams of Silicon-32 remaining after a 300 year period.

The question refers to the concept of half-life in physics, particularly in relation to radioactive substances. In this case, we're dealing with silicon-32, which has a half-life of 710 years. This means in 710 years, half of the silicon-32 will have decayed.

Given that the half-life of silicon-32 is 710 years, and we're examining a span of 300 years, let's use the decay formula A(t)=A0e^(ln(0.5)/T)t . Here, A0 is the initial quantity of the substance (30 grams in this case), T is the half-life (710 years), and t is the time elapsed (300 years).

Plugging these values into the formula gives us:

A(300) = 30e^(ln(0.5)/710)*300

Calculating this, we find that the amount of Silicon-32 remaining after 300 years would be approximately 21.978 grams, rounded to three decimal places.

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Answer:

Your answer would be 76.4.

____________________________________________________

Step-by-step explanation:

First, lets take out some key information in the question:

------------------------

Key information:

388 milliliters

19.7%

------------------------

With the information above, it will make it easier to find the answer for your question.

To find the answer to your question, we would need to find how much is 19.7% of 388 millimeters

Therefore, we would need to multiply 388 and 19.7% to get our answer.

In order for this to work, we would need to move the decimal places to times to the left from 19.7; 19.7 will turn to .197. After you move the decimal place, we can now multiply.

[tex]388 * .197=76.436[/tex]

In the question, it asks that we need to round to the nearest tenth, so that's the place right after the decimal place.

The 3 is not a big enoug hnumber to change the number before it, so we would keep the tenth place the same.

It would be rounded up as 76.4

76.4 would be your FINAL answer. There are 76.4 milliliters of acid

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Answer:

22

Step-by-step explanation:

To calculate the amount of steel needed to construct the oil tank, we need to find the surface area of the cylinder. A cylinder's surface area is composed of two parts: the area of its circular top and bottom (which are identical), and the area of its side.
Let's start by calculating the area of the two circular ends of the cylinder.
1. The area of one circle (either the top or the bottom) is given by the formula:
 \[ A_{\text{circle}} = \pi r^2 \]
  where \( r \) is the radius of the circle.
  Since the diameter is twice the radius, we have:
  \[ d = 12 \ \text{ft} \]
  \[ r = \frac{d}{2} = \frac{12 \ \text{ft}}{2} = 6 \ \text{ft} \]
  Now, we calculate the area of one circle:
  \[ A_{\text{circle}} = \pi (6 \ \text{ft})^2 = \pi \times 36 \ \text{ft}^2 \]
  \[ A_{\text{circle}} = 36\pi \ \text{ft}^2 \]
  Since there are two circles (top and bottom), we double this area:
  \[ A_{\text{circles}} = 2 \times 36\pi \ \text{ft}^2 \]
  \[ A_{\text{circles}} = 72\pi \ \text{ft}^2 \]
2. Next, we calculate the area of the side of the cylinder. The side is essentially a rectangle that is wrapped around the circular ends. The width of this rectangle is the height of the cylinder, and the length is the circumference of the circle.
 The circumference of the base circle is given by:
     \[ C = 2\pi r \]
  Using the radius we found before:
  \[ C = 2\pi \times 6 \ \text{ft} = 12\pi \ \text{ft} \]
 The area of the side is then:
  \[ A_{\text{side}} = C \times \text{height} \]
  \[ A_{\text{side}} = 12\pi \ \text{ft} \times 18 \ \text{ft} \]
  \[ A_{\text{side}} = 216\pi \ \text{ft}^2 \]
3. The total surface area of the steel needed to make the tank is the sum of the areas of the circular ends and the side:
  \[ A_{\text{total}} = A_{\text{circles}} + A_{\text{side}} \]
  Substitute the values found above:
  \[ A_{\text{total}} = 72\pi \ \text{ft}^2 + 216\pi \ \text{ft}^2 \]
  \[ A_{\text{total}} = 288\pi \ \text{ft}^2 \]
  To find a numerical value, we use the approximation \( \pi \approx 3.14159 \) (you can use a more precise value based on your requirements):
  \[ A_{\text{total}} \approx 288 \times 3.14159 \ \text{ft}^2 \]
  \[ A_{\text{total}} \approx 904.77792 \ \text{ft}^2 \]
  So approximately 904.78 square feet of steel are needed to make the tank.

Answer:

C. infinite

Step-by-step explanation:

We want to solve the system:

First equation: [tex]y=2x+3[/tex]

Second equation: [tex]2y=4x+6[/tex]

Multiply the first equation by 2.

This gives us:

Third equation: [tex]2y=4x+6[/tex]

Subtract the third equation to obtain;

[tex]2y-2y=4x-4x+6-6[/tex]

[tex]0=0[/tex]

This implies that, the solution is all real numbers.

This means that the two lines coincide with each other. Therefore there are infinitely many solutions.

(36x^3-36x-1)/6x+6 or 6x^2-6x+(-1/6x+6)

For this case we must find the product of the following expression:

[tex]6 (x ^ 2-1) * \frac {6 (x-1)} {6 (x + 1)}[/tex]

We can rewrite [tex]x ^ 2-1[/tex] as:

[tex](x + 1) (x-1)[/tex], then:

[tex]6 (x + 1) (x-1) * \frac {6 (x-1)} {6 (x + 1)} =[/tex]

Canceling similar terms of the numerator and denominator:

[tex](x-1) * 6 (x-1) =\\6 (x-1) ^ 2[/tex]

ANswer:

[tex]6 (x-1) ^ 2[/tex]

Well convert all of them into fourths. 3 1/2 = 3 2/4. Add all the whole numbers 2 + 4 + 3 = 9 and then add the fractions 1/4 + 3/4 + 2/4 = 6/4 = 1 2/4.  Finally add the whole number and fraction together, 10 2/4 or 10 1/2.

10 1/2 cases of popcorn.

The total number of cases of popcorn sold by Emily, Brenda, and Shannon is 10 1/2 cases. We arrived at this number by converting their sales to improper fractions, finding a common denominator, and then adding the fractions together.

The question asks us to calculate the total number of cases of popcorn sold by three girls: Emily, Brenda, and Shannon. Emily sold 2 3/4 cases, Brenda sold 4 1/4 cases, and Shannon sold 3 1/2 cases. To find the total, we need to add these amounts together.

To perform the addition, convert any mixed numbers to improper fractions:

Emily: 2 3/4 = 11/4 cases

Brenda: 4 1/4 = 17/4 cases

Shannon: 3 1/2 = 7/2 cases

Now, add these improper fractions together:

(11/4) + (17/4) + (7/2)

To add these fractions, we need a common denominator, which is 4 in this case. So, we need to multiply the numerator and denominator of Shannon's sales by 2 to get 14/4.

Now we have:

(11/4) + (17/4) + (14/4) = 42/4

After adding the fractions, we get 42/4, simplifying to 10 1/2 cases. Therefore, the girls sold a total of 10 1/2 cases of popcorn in all.

For the first question there is no mode because none of the numbers are the same. Mode means the popular number.

Answer: There is no mode.

For the second question , the answer is 3. Median means the middle number.

Answer:

5. ○ There is no mode.

6. ○ 3

Step-by-step explanation:

6. Median means the "midst" term [greatest to least (or vice versa)]:

5, 3,5, 3, 2,3, 2,2

5. Mode means "Most Often". We do not see any replicas in the data chart, therefore there is no mode.

I am joyous to assist you anytime.

Hi,

The volume of the cylinder is :

V = π × r^2 × h

V = 3,142 × (2)^2 × 5

V = 62, 8319 cm^3

π : Pi => 3,142

r : radius of the cylinder (2 units).

h : height of the cylinder (5 units).

The base of the cylinder is a circle , so to calculate the area we have to use the formula : area = π × r^2. And to find the volume , we have to multiply the area by the height.

•It was nice to help you, Bellalocc!

The population growth of the ants represents a non-linear function or exponential growth. After one year, the ant farm will contain 384 ants.

Exponential growth is evident in this situation as the number of ants in the farm doubles every three months. This doubling is characteristics of exponential functions, therefore, this population growth is a non-linear function, not a linear function. In terms of how many ants will be in the farm after a year, there will be four 3-month periods in a year. So, the ants double four times. Using the formula of exponential growth 2n (where 'n' is the number of cycles), we can precisely calculate the final number of ants. Therefore, the total number of ants after one year, or four 3-month cycles, would be 24 ants * 24 = 24 ants * 16 = 384 ants.

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Answer:

People left for last raft is 3

Step-by-step explanation:

Total Number of person on a raft = 4

Number of adults would like to raft = 29

Number of children would like to raft = 22

Total Number of would like to raft = 29 + 22 = 51

Number of people left for last raft = remainder of division of 51 and 4

When 51 divided by 4,

we get

Quotient = 12

Remainder = 3

Therefore, People left for last raft is 3

Answer:

x>14

Step-by-step explanation:

If Hayden get's $1.5 per pizza, and he wants to earn at least $20, then the equation is:

$1.5*x> $20

x>20/1.5 = 13.3333

Like Hayden cannot deliver 13.333 pizzas, just an integer number, we round it to 14.

Then x>14

If he delivers 14 pizzas, he would be earning: $21, so he needs to deliver at least 14 pizzas to earn at least $20

The answer is (4)(x)(x) because it’s 4 times 2 x’s

Answer:

(4)(x)(x)

Step-by-step explanation:

The square ONLY effects the x

Answer:

88cm^2

Step-by-step explanation:

Answer: 0.4 repeading

Step-by-step explanation: this is extremely easy all you have to do is divide 4 / 9 which gives you 0.4 repeating or it might look like this

The cost per square foot of tiles

The given expression is the total cost of tiling and fencing the patio , Option D is the correct answer.

A square is a two-dimensional figure , and a polygon with four sides , All the sides and angles of square is equal .

It is given that

Lucia is building a square patio with a side length of n feet.

She will cover the floor of the patio with tiles and put a fence around the

perimeter of the patio.

The tiles cost $5 per square foot

The fencing costs $3 per foot

She will also buy additional supplies for $25.

Let n represent the edge length, in feet, of the patio.

the expression 5n² + 12n + 25 represent = ?

Area of the patio in square shape will be given by

side * side = n * n =n²

Title cost total = $5 * n²

Title cost total = 5 n²

Perimeter of the patio is given by 4 * side

Perimeter of the patio = 4n

The fencing cost = 3 * 4n = 12n

and the additional cost is $25

The total cost = 5 n² + 12n + 25

Therefore the given expression is the total cost of tiling and fencing the patio , Option D is the correct answer.

To know more about Square

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Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identity

tanx = [tex]\frac{1}{cotx}[/tex], then

tanx = [tex]\frac{1}{\sqrt{3} }[/tex]

x = [tex]tan^{-1}[/tex]( [tex]\frac{1}{\sqrt{3} }[/tex]) = [tex]\frac{\pi }{6}[/tex]

Hence x = [tex]\frac{\pi }{6}[/tex] + kπ ( k ∈ Z )

Answer:

Option B

Step-by-step explanation:

Given are three tables in x and y and we have to find which table shows a linear relation.

We know in  a linear relation between x and y the graph would be a straight line and also the slope would be constant

i.e. change of y/change of x for any pair in the table would be a constant.

Out of three tables given, only second table satisfies this.

Hence B is the answer

Answer:

22.5

Step-by-step explanation:

the formula is A=a+b

2h

Answer:

I think the answer will be B or C

Step-by-step explanation:

It might be wrong but do the best you can

Answer:

The answer is 5x^2+32x-21

Step-by-step explanation:

To find the area of a rectangle, you have to multiply the length by the width. Then, you will get the equation of (5x-3)(x+7). Then, multiply these two together, therefore getting 5x^2+32x-21.

Arlo rented a car, and after accounting for the base price of the rental, it is determined he drove 175 miles

Arlo's total cost for car rental is the base price plus the cost per mile driven. To find out how many miles Arlo drove, we use the equation total cost = base price + (cost per mile  imes number of miles). Arlo paid $75.49, which includes the base price of $29.99 and $0.26 per mile.

We first subtract the base price from the total cost to find out how much was spent on the mileage:
$75.49 - $29.99 = $45.50 spent on mileage

Now, we divide the amount spent on mileage by the cost per mile to get the number of miles driven:
$45.50 / $0.26 per mile = 175 miles driven

Arlo drove 175 miles with his rented car.

The student asked how many miles Arlo drove when he rented a car, given that the total cost was $75.49, with an initial fee of $29.99 and an additional charge of $0.26 per mile. To calculate the number of miles driven, we first subtract the initial fee from the total cost:

Total cost - Initial fee = Cost for miles
$75.49 - $29.99 = $45.50

Next, we divide the remaining cost for the miles by the per-mile charge to find the distance driven:

Cost for miles / Charge per mile = Number of miles
$45.50 / $0.26 = 175 miles

Therefore, Arlo drove 175 miles with the car he rented.

Answer:

(-2,-3/2)

Step-by-step explanation:

Midpoint formula=(x1+x2/2, y1+y2/2)

So...

(3+-7/2, -5+2/2) =

(-2, -3/2)

Answer:

[tex](-2, -1.5)[/tex]

x-coordinate:-2

y-coordinate:-1.5

Step-by-step explanation:

You need to use this formula to find the coordinates of the midpoint:

[tex]M=(\frac{x_A+x_B}{2},\frac{y_A+y_B}{2})[/tex]

In this case, given the points  (3, -5) and (-7, 2), you can identify that:

[tex]x_A=3\\x_B=-7\\y_A=-5\\y_B=2[/tex]

Therefore, you need to substitute these values into the formula  [tex]M=(\frac{x_A+x_B}{2},\frac{y_A+y_B}{2})[/tex]. Then you get that the coordinates of this midpoint are:

[tex]M=(\frac{3+(-7)}{2},\frac{-5+2}{2})[/tex]

[tex]M=(\frac{3-7}{2},\frac{-5+2}{2})[/tex]

[tex]M=(-2, -1.5)[/tex]

Answer:

-2 1/4z +1/4

Step-by-step explanation:

3/4 - 4z +5/4 z- 1/2 + 1/2 z

Put like terms near each other

3/4- 1/2  - 4z +5/4 z+ 1/2 z

We need to get common denominators to combine

First the constant terms

3/4 - 1/2*2/2  

3/4 - 2/4 = 1/4

Then the variable terms

-4z *4/4 +5/4z + 1/2z *2/2

-16z/4 + 5/4z +2/4z

-9/4z

Changing from an improper fraction to a mixed number

-2 1/4 z

-2 1/4z +1/4

Answer:

A. $14.5 B. $23.5

Step-by-step explanation:

You are adding .75 cents to your bank account each day so you can do .75 *18 days plus one dollar from day one to get $14.5 dollars on may 19. If you do 30 * .75 you get 22.5 plus a dollar from what you start with to get $23.5 at the end of may in your account. Hope this helped you!!

Answer:

a) 47 people (count each leaf)

b) 66 - 1 = 65 (max - min)

c) 4 (occurs the most)