I drove to my summer home at 75 mph. The next day I drove back, it took me a hour longer because of traffic, and I drove at 50 mph. How long was the drive on the first day?

Answer:

33.  AB = √45.  CD = √40.  Not congruent.  AB is greater.

34.  EF = 5.  GH = √41.  Not congruent.  GH is greater.

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]

Given endpoints:

Substitute the given endpoints into the formula and solve:

[tex]\begin{aligned}\overline{AB}&=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\&=\sqrt{(-3-0)^2+(8-2)^2}\\&=\sqrt{(-3)^2+(6)^2}\\&=\sqrt{9+36}\\&=\sqrt{45}\\& \approx 6.7\; \sf (1 \; d.p.)\end{aligned}[/tex]

Given endpoints:

Substitute the given endpoints into the formula and solve:

[tex]\begin{aligned}\overline{CD}&=\sqrt{(x_D-x_C)^2+(y_D-y_C)^2}\\&=\sqrt{(0-(-2))^2+(-4-2)^2}\\&=\sqrt{(2)^2+(-6)^2}\\&=\sqrt{4+36}\\&=\sqrt{40}\\& \approx 6.3\; \sf (1 \; d.p.)\end{aligned}[/tex]

Therefore, the segments at not congruent.

[tex]\textsf{As\; $\sqrt{45} > \sqrt{40}$ \; then \; $\overline{AB} > \overline{CD}$}.[/tex]

Therefore, the length of segment AB is greater.

Given endpoints:

Substitute the given endpoints into the formula and solve:

[tex]\begin{aligned}\overline{EF}&=\sqrt{(x_F-x_E)^2+(y_F-y_E)^2}\\&=\sqrt{(5-1)^2+(1-4)^2}\\&=\sqrt{(4)^2+(-3)^2}\\&=\sqrt{16+9}\\&=\sqrt{25}\\&=5\end{aligned}[/tex]

Given endpoints:

Substitute the given endpoints into the formula and solve:

[tex]\begin{aligned}\overline{GH}&=\sqrt{(x_H-x_G)^2+(y_H-y_G)^2}\\&=\sqrt{(1-(-3))^2+(6-1)^2}\\&=\sqrt{(4)^2+(5)^2}\\&=\sqrt{16+25}\\&=\sqrt{41}\\& \approx 6.4\; \sf (1 \; d.p.)\end{aligned}[/tex]

Therefore, the segments at not congruent.

[tex]\textsf{As\; $\sqrt{41} > 5$ \; then \; $\overline{GH} > \overline{EF}$}.[/tex]

Therefore, the length of segment GH is greater.

Answer:

-2w-20

Step-by-step explanation:

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

Explanation:

A thing that jumps out at me right away is the presence of x/3 on both sides. When subtracting x/3 from both sides, these terms cancel out and we're left with this equation

5 = 6 + (x/9)

Let's say w = x/9. We now have this equation 5 = 6 + w. Subtract 6 from both sides to isolate w and you should get w = -1

Then plug in w = x/9 and solve for x.

w = -1

x/9 = -1

x = 9*(-1)

x = -9

We get exactly one solution and it is x = -9

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

Check:

5 + x/3 = x/3 + 6 + x/9

5 + (-9)/3 = (-9)/3 + 6 + (-9)/9

5 - 3 = -3 + 6 - 1

2 = 3 - 1

2 = 2

We get the same thing on both sides, which leads to a true statement. This causes a domino effect to lead the first equation to be true when x = -9. Therefore, the solution is confirmed.

Answer:

9

Step-by-step explanation:

guess

The rule that describes ( -1, 1), (1, 2), (3, 3), (5, 4) is c. Output = (0.5)(Input) + 1.5

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, On a coordinate plane, points are at ( -1, 1), (1, 2), (3, 3), (5, 4).

By observing the given options we conclude that it is Output = (0.5)(Input) + 1.5 to confirm let's put the values.

Given when input is - 1 output is 1.

∴ 1 = 0.5(-1) + 1.5.

1 = - 0.5 + 1.5.

1 = 1  ( satisfied).

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Answer:

12x^5+18x^2+10x^3+15

Step-by-step explanation:

first you apply the distribution property (FOIL) and you get

12x^5+18x^2+10x^3+15

Answer:

A ≈ 6538.35 cm²

Step-by-step explanation:

Calculating the area (A) using Heron's formula

A = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]

where s is the semi perimeter and a, b, c the 3 sides

here

s = 380 ÷ 2 = 190

given perimeter = 380 and unequal side is 150 , then

equal sides = (380 - 150) ÷ 2 = 230 ÷ 2 = 115 cm

then a = 150, b = 115 , c = 115

A = [tex]\sqrt{190(190-150)(190-115)(190-115)}[/tex]

   = [tex]\sqrt{190(40)(75)(75)}[/tex]

   = [tex]\sqrt{42750000}[/tex]

   ≈ 6538.35 cm² ( to 2 dec. places )

Answer:

D

Step-by-step explanation:

D) 1755 yards is the closest amount to 1760 yards, which is how much is in a mile

Answer: 163$

Step-by-step explanation:

Measures which examine the spread of different values around the measures of central tendency is measures of variability.

A central tendency in statistics is a typical or characteristic value for a probability distribution. Measures of central tendency are commonly referred to as averages in everyday speech. In the late 1920s, the phrase "central tendency" first appeared. The arithmetic mean, the median, and the mode are the three most popular ways to measure central tendency. The number used to represent the center or middle of a set of data values is known as the central tendency measure.

Given,

Measures which examine the spread of different values around the measures of central tendency:

B. Measures of variability

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The measure of angle 2 is 75°

From the question, we have

∠1= 105°

∠2= 180°- 105° (Linear pair)

∠2=75°

Subtraction:

Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.

The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.

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The total number of toys is 45 Samuel if Samuel has a collection of toy cars. His favorites are the 27 red ones.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

It is given that:

Samuel has a collection of toy cars. His favorites are the 27 red ones.

Let Samuel has x number of toys:

From the equation:

60% of x = 27

(60/100)x = 27

0.6x = 27

x = 27/0.6

x = 45

Thus, the total number of toys is 45 Samuel if Samuel has a collection of toy cars. His favorites are the 27 red ones.

The complete question is:

Samuel has a collection of toy cars. His favorites are the 27 red ones which make up 60% of his collection. How many toy cars does Samuel have?

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If the actual length of the pool table is 6 feet , then the length of the pool table in the drawing is 12 inches   .

In the question,

it is given that ,
Barbara drew an scale drawing of the game room.

the scale that she used is 1 feet in the actual length is represented by 2 inches in the drawing ,

which means ,

1 feet = 2 inches

to find the length of 6 feet in the drawing ,

6 feet = 6 × 2 inches

= 12 inches

Therefore , If the actual length of the pool table is 6 feet , then the length of the pool table in the drawing is 12 inches   .

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By solving a system of equations we can see that each goat costs $30 and each sheep costs $25.

Let's define the variables:

x = cost of a goat

y = cost of a sheep.

We can write the system of equations with the given info:

6*x + 5*y = 305

2*x + 9*y = 285

If we subtract 3 times the second equation from the first one, we get:

(6*x + 5*y) - 3*(2*x + 9*y) = 305 - 3*285

-22*y = -550

y = -550/-22 = 25

Now that we know the value of y we can try to find the value of x:

2*x +9*25 = 285

2*x = 285 - 9*25 = 60

x = 60/2 = 30

These are the costs of each animal.

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Answer:

Arithmetic

Step-by-step explanation:

The difference between consecutive terms is 5. Thus, this is an arithmetic sequence with a common difference of 5.

The number that will be next in the series will  be  63 .

In the question ,

a recurrence relation is given that is  0, 3, 8, 15, 24, 35, 48, ? .

we have to find the number that will come in place of question mark .

On carefully examining the series , we can see that

3 - 0 = 3

8 - 3 = 5

15 - 8 = 7

24 - 15 = 9

35 - 24 = 11

48 - 35 = 13

we can se that increments 3,5,7,9,11,13,... form an Arithmetic Progression

with first term as 3 and common difference as 2 ,

So ,the next increment will be 13+2 = 15

let the next term be "x" .

x - 48 = 15

x = 15 + 48 = 63

the number in place of ? is 63 .

Therefore , The number that will be next in the series will  be  63 .

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Answer:

Step-by-step explanation:

We have to the graph from x = -4 to x = 2

2y + x + 3 = 0

Rearrange the equation to make y the subject

2y = -x - 3

y = (-1/2)x -3/2

-3/2 is the y intercept

the gradients is -1/2

since the value is negative, the graph will be sloping downwards

Point your pen at y = -3/2 on the y axis (-3/2 is -1.5)

go 1 point down and 2 points to the right, make a point and connect these 2 dots and make a line across the graph.

Do the same with the other equation:

3y - x + 1 = 0

3y = x - 1

y = (1/3)x -1/3

y intercept is -1/3

gradient is 1/3

point your pen at -1/3 on the y axis, go 1 point up and 3 points to the right

and mark this point and connect these 2 points and make a line across the graph.    

Answer:

which of the following ratios are connected to 5/20?

multiple choice

a 1/5

c 20/100

d 25/100

d is the option 25/100 and

b 1/4

Answer:

B

Step-by-step explanation:

given 1 pound = 16 ounces , then

5 pounds = 5 × 16 = 80 ounces

The graph of the image of the triangle in the question following the dilation by a scale factor of (5/3) with vertices (10, 15), (10, 10), (15, 10) created with MS Excel is attached.

In a dilation transformation, the dimensions of the original figure is changed by multiplying the lengths by a scale factor.

The coordinates of the vertices of the triangle in the are (6, 9), (6, 6), and (9, 6)

The coordinate of a point (x, y) following a dilation by a scale factor of k, centered at the origin is the point (k·x, k·y)

The coordinates of the vertices of the image of the triangle in the question following a dilation of 5/3 centered at the origin, are therefore;

(6, 9)      [tex]\overset{R_{5/3}}\longrightarrow[/tex]  ((5/3)×6, (5/3)×9) = (10, 15)

(6, 6)      [tex]\overset{R_{5/3}}\longrightarrow[/tex]  ((5/3)×6, (5/3)×6) = (10, 10)

6(9, 6)      [tex]\overset{R_{5/3}}\longrightarrow[/tex]  ((5/3)×9, (5/3)×6) = (15, 10)

The graph of the image of the triangle following a dilation by a scale factor of 5/3) can therefore be plotted using points (10, 15), (10, 10), and (15, 10) and the plot function on MS Excel

Please find attached the graph of the image of the triangle following a dilation by a scale factor of (5/3) about the origin.

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a. Creating a system of equations, the length of each plan A's workout is 3/4 hour, while the length of each plan B's workout is 3/4 hour.

b. x = -8, y = 2.

Write equations of a system that represents the information given and solve accordingly.

Let the length of plan A = x

Length of plan B = y

Equation for Monday would be:

9x + 7y = 12 --> eqn. 1

Equation for Tuesday:

3x + 5y = 6 --> eqn. 2

Multiply eqn. 1 by 3 and eqn. 2 by 9

27x + 21y = 36 --> eqn. 3

27x + 45y = 54 --> eqn. 4

Subtract the equations:

-24y = -18

y = -18/-24

y = 3/4

Plan B's length of workout is: 3/4 hour.

Substitute y = 3/4 into equation 2:

3x + 5(3/4) = 6

3x + 15/4 = 6

3x = 6 - 15/4

3x = 9/4

12x = 9

x = 9/12

x = 3/4

Length of plan A's workout is: 3/4 hour.

b. 2x + 4y = -8 --> eqn. 1

-2x + 3y = 22 --> eqn. 2

Add both equations together:

7y = 14

y = 2

Substitute y = 2 into equation 1:

2x + 4(2) = -8

2x + 8 = -8

2x = -8 - 8

2x = -16

x = -16/2

x = -8

The solution is: x = -8, y = 2.

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Answer:

480 lbs

Step-by-step explanation:

First, find the ratio of weight on the moon to weight on the earth. I will put the two known values in a fraction like this:

[tex]\frac{25}{150}[/tex]

Now, I can create a proportion, making sure to keep the same types of measurements in the numerator and denominator. I will use w for the unknown weight on earth.

[tex]\frac{25}{150}=\frac{80}{m}[/tex]

Now, I will simplify the fractions as much as I can.
[tex]\frac{1}{6}=\frac{80}{m}[/tex]

Now, I can see a correlation. 1 times 80 is 80, so 6 times 80 is m. Simplified, here is the answer!

[tex]6*80=m\\480=m\\m=480[/tex]

Answer:

480 pounds

Step-by-step explanation:

we times for objects on earth and divide for objects on the moon by the same number

150

[tex]150 \div x = 25[/tex]

150/-25=-x

-6/-1= -x/-1

6=x

[tex]150 \div 6 = 25[/tex]

so when in object is on earth you multiple by x Wich 6

[tex]80 \times 6 = 480[/tex]

you can also cross multiply

Answer:

Step-by-step explanation:

The average annual rainfall for a town is 43.2 inches.

This is converted to average monthly as:

The difference is:

Answer:

Yeah, they exceeded by 0.4 inches.

Step-by-step explanation:

It is given that,

→ the average monthly rainfall for the previous 9 months was 4 inches.

The monthly rainfall in 12 months,

→ 43.2 inches ÷ 12 months

→ 43.2/12

→ 3.6 inches

Then the difference will be,

→ 4 inches - 3.6 inches

→ 4 - 3.6

→ 0.4 inches

Hence, the difference is 0.4 inches.

The distance on the map, in cm, given the real distances, and the scale of the map are:

A scale of 1 : 200, 000 means that every 1 cm on the map is 200, 000 cm on the ground.

To find the distance on the map of 10 km, first convert it to cm:
= 10 km x 100, 000 cm per km

= 1, 000, 000 cm

The distance on the map is therefore:

= 1, 000, 000 / 200, 000 cm scale

= 5 cm on map

The distance of 15 km on the map is:

= (15 km x 100, 000) / 200, 000

= 7.5 cm

The distance of 4 km is:

= (4 x 100, 000) / 200, 000

= 2 cm

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The net value of the items purchased is ₹ 900.

Raman purchased books and stationery items and paid the total amount of rupees 963.

Paid tax = 7%

Let the net value of the items purchased be `x.

VAT = 7%

Selling price = ₹x + (7% of x)

                    = ₹x+ ₹ ( 7/100 * x)  

                    =₹( x +7 x /100)

                    = ₹ 107 x /100

But Raman purchased books and stationery items for ₹963.

107x/100 = ₹963

               x =  963 x 100/107

               x = 900

Hence the answer is the net value of the items purchased is ₹ 900.

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You got to set it up to boys to girls

Answer:

0,1

Step-by-step explanation:

simplest form

Answer: 2>=n

Step-by-step explanation:

3n-6 +2 >= 5n-8

3n-4 >= 5n-8

-4>= 2n -8

4>=2

2>=n

Hope this helped!!

The coordinates of each base is listed below

preimage     image

1 (3, 3)         1. (3, -3)

2 (13, 3)       2' (3, -13)

3 (3, 13)       3' (13, -3)

Rotation is one of  the numerous types of transformation. it involves circular movement about an axis

The transformation rule for 270° counterclockwise rotation

(x, y) → (y, -x)

The preimage coordinates of the base field and the image coordinates

Applying the transformation rule  rule gives

preimage      image

1 (3, 3)    →      1. (3, -3)

2 (13, 3)  →      2' (3, -13)

3 (3, 13)  →      3' (13, -3)

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Answer:

2.8 pounds per hour

Step-by-step explanation:

[tex] \frac{3.5}{1.25} = \frac{350}{125} = \frac{14}{5} = 2.8[/tex]