Joseph traveled from Boston to Framingham at 50 mph and then back to Boston
at 40 mph. What was Joseph's average speed on the round trip?

Answer:

The magnitude of the vector is 9.165 and it's direction is 40.6°

Step-by-step explanation:

A vector quantity is a quantity that has both size (magnitude) and direction. Examples of vector quantities are force, velocity and impulse.

Magnitude of vector v is given by

|v| = √6²+7²

= √36+49

= √84

= 9.165

Direction of vector v is obtained by:

\( \tan( \theta) = \frac{x}{y} \)

\(\theta = {tan}^{ - 1} ( \frac{6}{7}) \)

\(\theta = {40.6°}\)

Learn more about vector quantities from: https://brainly.in/question/3437975

#SPJ1

Answer:

Question 15: x = 17

Question 16: area = 5610 units

Step-by-step explanation:

Question 15:

The perimeter is the sum of all sides of a triangle.

It is given that the perimeter is 374 units.

\(p = 8x - 4 + 9x + 4 + 4x + 17\)

\(374 = 8x - 4 + 9x + 4 + 4x + 17\)

Add all the like terms.

\(374 = 21x + 17\)

Subtract 17 from both sides.

\(357 = 21x\)

Divide by 21 from both sides.

\(17 = x\)

Question 16:

The area of a triangle can be found by using the following formula:

\(a = \frac{1}{2} bh\)

(where a is the area, b is the base, and h is the height)

Using the value of x you just found previously (17), you can calculate the base and height by substituting 17 with x in their respective equations.

\(h = 8x - 4\)

\(h = 8(17) - 4\)

\(h = 134\)

\(b = 4x + 17\)

\(b = 4(17) + 17\)

\(b = 85\)

Now that you found the base and height, substitute the values, 134 and 75, into the area of a triangle formula.

\(a = \frac{1}{2} bh\)

\(a = \frac{1}{2} (85)(132)\)

\(a = 5610\)

Answer:

2a²+8a+7

Step-by-step explanation:

Based on the intersecting secants theorem:

a. CG*CE = CH*CD

b. length of DH = 10 in.

When an exterior point is formed by two secant segments to a circle, the product of the length of one secant segment and its external segment will always be equal to the product of the length of the other secant segment and its external segment, according to the intersecting secants theorem.

a. Based on the intersecting secants theorem, the relationship that describes the lengths of the segments formed by the two secants is:

CG*CE = CH*CD

b. Given the following lengths:

CG = 3 in, CH = 2 in, and GE = 5 in

CE = CG + GE = 3 + 5 = 8 in.

CD = CH + DH = 2 + DH

Substitute into CG*CE = CH*CD:

3*8 = 2*(2 + DH)

24 = 4 + 2DH

24 - 4 = 2DH

20 = 2DH

20/2 = DH

DH = 10 in.

Learn more about intersecting secants theorem on:

https://brainly.com/question/1626547

#SPJ1

Answer:

15

Step-by-step explanation:

30/2= 15 feet per second

Answer:

I believe it is 48

Step-by-step explanation:

because 4 is two less than 6, and 4 doubled would be 8

Answer:

6. 9^2+4x-1

7. 7x - 3 cm

8. -6x^2+3x-4

9. 4x+10y+4z

10 13x^2 - 2x

11. -5x^2 - 8x - 16

Step-by-step explanation:

6. (13x^2+x-3)-(4x2-3x-2) = 9x2+4x-1

7. x +4+2x+1+4x-8

= 7x-3 cm

8. (-8x^2 + 8x + 1) + (14x^2-11x+3)

10. (8x^2+x)-(-5x^2+3x)

11. (-x^2-6x+5) - (4x^2+2x+11)

Answer:

it should be 21 if I did this right.

Step-by-step explanation:

you multiply the width times the length (6 × 7) =42 then 882 divided by 42 to get 21

A random sample of n = 25 observations will be used to test the hypotheses H0: Î14 = 75 and Ha: Î14 75.the test statistic is lower than -1.96, we can reject the null hypothesis and conclude that the mean drying time is less than 75.

H0: μ = 75

Ha: μ < 75

Test Statistic: z = (x - μ) / (σ / √n)

critical Value: z crit = -1.96

Conclusion: Reject H0 if the test statistic is less than -1.96.

We can test the hypotheses H0: μ = 75 versus Ha: μ < 75 by using the test statistic z = (x - μ) / (σ / √n). The critical value for this test is z crit = -1.96. The decision rule for this test is to reject H0 if the test statistic is less than -1.96. This means that if the test statistic is lower than -1.96, we can reject the null hypothesis and conclude that the mean drying time is less than 75.

Learn more about null hypothesis here

https://brainly.com/question/28920252

#SPJ4

Answer:

d.

Step-by-step explanation:

They are the same shape just turned different ways

Answer:

$5,665

Step-by-step explanation:

First, you multiply 5,500 times 3 to get 16,500, and then divide by 100 to get 165. That is how much she earned over the past three years, but it is NOT her new account balance, because you have to add 5,500 and 165, which you would get a final sum of $5,665. I hope this helps :)

When only 4 players remain, the fewest number of matches that can be played is 37.

Given information:

When only four players remain, the smallest number of matches that can be played is calculated as follows:

Now, divide both sides by 3 as follows:

Therefore, when only 4 players remain, the fewest number of matches that can be played is 37.

Know more about algebra here:

https://brainly.com/question/11927971

#SPJ9

1) Matrices that have determinants are square matrices

2) Due to the inverse matrix's calculation utilizing a matrix's determinant, the determinant and the inverse matrix are connected.

3) The determinant affects whether a matrix has an inverse.

A matrix is a collection of numbers that have been sorted into rows and columns to create a rectangular array. The elements, or entries, of the matrix are the integers.

If and only if the determinant of a square matrix A is nonzero, the matrix has an inverse. The matrix A is referred to as singular and devoid of an inverse if its determinant is zero.

Learn more about matrix:https://brainly.com/question/29132693

#SPJ1

The volume of the cube with side length 8 inches is 512 inches cube.

The cube with side length s has volume s³. Matt has a cube-shaped wooden box that he uses to store his marble collection. It has 8-inch sides.

The volume of the cube can be calculated as follows:

A cube has all side length equal to each other.

Therefore,

volume of the cube = s³

where

Therefore,

s = 8 inches

Hence,

volume of the cube = 8³

volume of the cube = 8 × 8 × 8

volume of the cube = 512 inches cube

learn more on cube here: https://brainly.com/question/29684985

#SPJ1

Answer:

18 inches

Step-by-step explanation:

54*1/3=18(inches)

Answer:y=2.50x+5

Step-by-step explanation:

y=2.50x+5

that's all i can do with the information provided

Answer:

Can you give me some more context?

Answer:

-54 is a integer and rational number

Step-by-step explanation:

Irene has 49 Books, and Alejandro has 24 books.

Let's assume that Irene has x books, and Alejandro has y books. According to the given information, we can form the following equations:

1. Irene has twice as many books as Alejandro plus 1:

  x = 2y + 1

2. The total number of books between Irene and Alejandro is 73:

  x + y = 73

We can now solve this system of equations to find the values of x and y.

Substituting the value of x from equation (1) into equation (2), we have:

(2y + 1) + y = 73

3y + 1 = 73

3y = 72

y = 24

Now, we can substitute the value of y into equation (1) to find x:

x = 2(24) + 1

x = 49

Therefore, Irene has 49 books, and Alejandro has 24 books.

To verify our solution, we can check if the sum of their books equals 73:

49 + 24 = 7

So, our solution is correct.

In conclusion, Irene has 49 books, and Alejandro has 24 books.

For more questions on Books.

https://brainly.com/question/30630608

#SPJ8

The number of people that like sausage or mushrooms as shown in the Vann diagram is 30.

Venn diagrams are diagrams used to visually depict sets, relationships between sets, and operations on sets

To determine the number of people that like sausage or mushrooms from the Vann diagram, we use the Formula below.

Formula:

n (S ∪ M) = n (S) + n (M) − n (S ∩ M) ................. Equation 1

Where:

From the diagram,

Given:

Substitute these values into equation 1

Hence, the people who like sausage or mushrooms is 30

Learn more about Vann diagram here: https://brainly.com/question/24713052

#SPJ1

Answer: S wanted points I

Step-by-step explanation:

The areas, diameters, and radii can be grouped as follows:

1. Area: 221.5584 square units

Diameter: 16. 8 units

Radius: 8.4 units

2. Area: 78.5 square units

Diameter: 10 units

Radius: 5 units

3. Area: 452.16 square units

Diameter: 24 units

Radius: 12 units

4. Area: 36.2984 square units

Diameter: 6.8 units

Radius: 3.4 units

5. Area: 314 square units

Diameter: 20 units

Radius: 10 units

6. Area: 886.2336 square units

Diameter: 33.6 units

Radius: 16.8 units

First, we are given the area of the circles. Next, we need to note the formula of the area of a circle and this is: πr²

To get the radius, we can use the formula: √(A/π)

For the first case, we have:

Area = 221.5584 square units

Thus, radius = √(221.5584/3.14)

= 8.4

Since diameter is = 2r, then diameter in this case

= 16.8 units.

Learn more about the area of a circle here:

https://brainly.com/question/14068861

#SPJ1

Answer:

Yes, It is equivalent to 5p.

Step-by-step explanation:

Answer:

It is.

Step-by-step explanation:

It is.

I had this same problem when I was younger so I'm going to explain it to you how I would've liked it to be explained to me.

2p+4p=6p. Why? Because if two things are multiplied by the same thing (for example, 49 * 5 + 51*5), you can do 100 * 5 instead of doing it out. So any time you see a variable without a co-efficient which is the number before the variable, think of it as 1p instead of p, so it would be 1p+4p which does equal 5p. Since multiplying anything by 1 is just the identity property, it doesn't change the value of p but it becomes a little easier to visualize. As you practice this more, it'll get more familiar and you won't have to remember it like this anymore.

Hope this helped, tell me if you have any questions.

Answer:

  19 mL

Step-by-step explanation:

You want the volume of a rock with density 45 g/mL and mass of 855 g.

The units of density are mass per volume, so we can find the volume by dividing the mass by the density. The units basically tell you how to work the problem.

  \(\dfrac{855\text{ g}}{45\text{ g/mL}}=\dfrac{855}{45}\,\dfrac{\text{g$\cdot$mL}}{\text{g}}=\boxed{19\text{ mL}}\)

__

Additional comment

Sometimes we like the volumes of things that aren't liquid to be expressed in cubic units. 1 mL = 1 cm³, so the volume could be described as 19 cm³.

\(0.685\)

the expanded notation form.

\(0\)

\( + 0.6\)

\( + 0.08\)

\( + 0.005\)

it can be written as a sentence also,

0 + 0.6 + 0.08 + 0.005

The largest absolute value is |29,400|, and the smallest absolute value is |667|.

The given expression |3 × 10^4 - 6 × 10^2| equals |30000 - 600|, which simplifies to |29,400|. This represents the largest possible absolute value using the digits 1 to 9. It is the largest because it maximizes the value by using the highest digits (9 and 8) in the tens of thousands and hundreds places, respectively.

To find the smallest possible answer, we need to arrange the remaining digits (1, 2, 3, 4, 5, 6, and 7) to minimize the value. Since we want to subtract the largest possible number from the smallest, we arrange the digits in ascending order, resulting in |1,234 - 567|.

Calculating this expression gives us |667|, which represents the smallest possible absolute value using the remaining digits. It is the smallest because it minimizes the value by using the lowest digits (1, 2, 3, 4, 5, 6, and 7) in their respective places.

Know more about ascending order here:

https://brainly.com/question/320500

#SPJ8

The travelled distance of the traveller is equal to 195 kilometers.

According to the statement of the problem, a traveller already walked a third part of his trail and if he travels the half of his trail, then the half of his trail shall be covered. Mathematically, the travelled distance shall be described by following expression:

x = d / 3

x + 65 = d / 2

Where:

Now we proceed to determine the travelled distance:

d / 3 + 65 = d / 2

d / 2 - d / 3 = 65

3 · d - d = 390

2 · d = 390

d = 195

To learn more on travelled distances: https://brainly.com/question/29055485

#SPJ1

The equation 8(x+2) can be expressed using the distributive property as 8x + 16.

The distributive property can be described as the as the multiplication system of solving a particular expressions easily through the process of distributing another number  within the given  brackets.

The expression that was given as  8(x+2) , if it so be solved using the distributive property the we will have 8x + 16 because this result means that it has been shared in to part,  because the multiplication operation has been performed on the given expression.

Read more about distributive property at:

https://brainly.com/question/2807928

#SPJ1