12. A cyclist travels 40 km at a speed of x km/h. Find the time
taken in terms of x. Find the time taken when his speed is
reduced by 2 km/h. If the difference between the times is
1 hour, find the original speed x.

[tex]3x+12=2(8+4x)[/tex] distribute

[tex]3x+12=16+8x\\[/tex] collect like-terms

[tex]3x-8x=16-12\\-5x=4\\x=-\frac{4}{5}=-0.8[/tex]

x = - 4/5

3x + 12 = 2(8 + 4x)

3x + 12 = 16 + 8x

12 - 16 = 8x - 3x

- 4 = 5x

x = - 4/5

Answer:

The area of the lake is actually 182 square miles 1 inch represents one side 3 miles long the other side is also 3 miles. 3×3=9 square miles. 1 Square Inch on the map represents 9 Square Miles.Step-by-step explanation:

The actual area of the lake is 162 square miles if the map that was created using a scale of 1 inch : 3 miles.

The ratio among comparable dimensions of an object and a model with that object, is known as an exponent in algebra. The replica will be larger if the scale factor is a whole number. The duplicate will be lowered if the step size is a fraction.

We have:

A map that was created using a scale of 1 inch : 3 miles

1 inch = 3 miles

1 square inch = 9 square miles

The area of the lake = 18 square inches

The actual area of the lake = 18×9 = 162 square miles

Thus, the actual area of the lake is 162 square miles if the map that was created uses a scale of 1 inch : 3 miles.

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Answer:

7/12

Step-by-step explanation:

well first you have subtract 2/3 from 1/12 how you do that is that you have to change the denominator into twelve by multiplying 3 times 4 and 2 times for which you get 8/12 them subtract 8/12 from 1/12 which is 7/12

If Jan's tank is 1/12 full and after addition it becomes 2/3 full then she added 7/12 gas as a fraction of tank.

Fraction is a combination of two numbers one in numerator and the other one in denominator. The number which is above the division sign is known as numerator and the number which is below the division sign is known as  denominator. It is expressed as v/u where v is numerator and u is denominator.

Initial quantity of gas is 1/12 of the tank.

Quantity of gas after filling is 2/3 of the tank.

So the initial fraction is 1/12 and final fraction is 2/3.

let the fraction of gas added be x.

So,

1/12+x=2/3

x=2/3-1/12

x=(8-1)/12

x=7/12

Hence the gas which is added by Jan is 7/12 fraction of the tank.

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Answer:

Answer: 48cm^2

Step-by-step explanation:

The formula for area of rectangle is length × width

So u do 12 × 4 = 48cm^2

Step-by-step explanation:

Answer:

48 cm^2

Step-by-step explanation:

Multiply the length and width of this rectangle to obtain its area:

(12 cm)(4 cm) = 48 cm^2

*Since each card is worth -50 points, you need to remember that a positive times a negative integer gives you a negative integer.*

Part A) Theresa has 5 cards so: 5 x -50 = -250

Theresa has -250 points.

Part B) Mark has 8 cards so: 8 x -50 = -400

Mark has -400 points.

Part C) Theresa has more points because -250 is closer to 0 on a number line.

Answer:

Negative x Positive = Negative

A) -50 x 5 = -250

B) -50 x 8 = - 400

C) Theresa

-250 > -400

Answer:$360

Step-by-step explanation:

I=PRT

I=12/100×2000×1.5

I=24×1.5

I=$360

Answer:

The Angle of C = 46

X = 180 - 46

X = 134

Step-by-step explanation:

Hey There!!

Simplify the following:

2 (-20)+3 (5/4 (-20))+5×2/5×50+4×50

5/4 (-20) = (5 (-20))/4:

2 (-20)+3×(5 (-20))/4+5×2/5×50+4×50

2/5×50 = (2×50)/5:

2 (-20)+3×(5 (-20))/4+5×(2×50)/5+4×50

3×(5 (-20))/4 = (5 (-20) 3)/4:

2 (-20)+(5 (-20) 3)/4+5×(2×50)/5+4×50

5×(2×50)/5 = (2×50×5)/5:

2 (-20)+(5 (-20) 3)/4+(2×50×5)/5+4×50

(-20)/4 = (4 (-5))/4 = -5:

2 (-20)+5×-5×3+(2×50×5)/5+4×50

(2×50×5)/5 = 5/5×2×50 = 2×50:

2 (-20)+5 (-5) 3+2×50+4×50

2 (-20)  =  -40:

-40+5 (-5) 3+2×50+4×50

5 (-5)  =  -25:

-40+-25×3+2×50+4×50

-25×3  =  -75:

-40+-75+2×50+4×50

2×50  =  100:

-40-75+100+4×50

4×50  =  200:

-40-75+100+200

-40-75+100+200 = (100+200)-(40+75):

(100+200)-(40+75)

300-(40+75)

300-115

Answer: |  185

Hope It Helps!

[tex]ItsNobody^{[/tex][tex]ItsNobody[/tex]

Answer:

.466.7 miles

Step-by-step explanation:

[tex]total \: cost - rental \: cost = \: the \: total \: cost \: for \: travel \: in \: miles[/tex]

[tex]200 - 59.99 = 140.01 [/tex]

[tex]\ 140.01 \div 0.30 = 466.7 \: miles[/tex]

Answer:

Yes

Step-by-step explanation:

-7.5 is a rational number because it can be made by dividing two integers(-75/10)

The answer is 0.5 and 2 in.

Answer:

The coordinates of the trasformed image is W(-4,11) X(-1,11) Y(1,6) Z(-6,6)

WZ and YZ are not parallel

Step-by-step explanation:

Answer:

C. The function shown on the graph has a greater rate of change, but a lower starting point.

Step-by-step explanation

5x-6=y (equation on the graph)

4x+2=y

5 is a greater rate of change (slope) compare to 4, however the y-intercept on the graph is lower (starting point) compare to the equation (2)

Greetings from Brasil...

Let's apply the given formula:

A = (1/2)·B·H

The base of this polygon (in this case, the triangle) is B

B = X² - 2X + 6

The height of this polygon is H and is H

H = X + 4

Applying these values (B and H) in the given formula.....

A = (1/2)·B·H

A = (1/2)·(X² - 2X + 6)·(X + 4)

A = (1/2)·(X³ + 2X² - 2X + 24)

A = (X³/2) + X² - X + 12

OR

A = (X³ + 2X² - 2X + 24)/2

Answer:

First find hypotenuses

Step-by-step explanation:

First you must find h by using formula

A^2+b^2=c^2 when you find this you already given base and put the c you find is h and b is given in the formula you will get area

Answer:

50

Step-by-step explanation:

Answer:

Nine and eight hundred six thousandths

Step-by-step explanation:

You probably already know nine. The digits to the right of the decimal point are 8, 0, and 6. Their places are tenths, hundredths, and thousandths. When referring to a group of numbers in a sentence like in this situation, refer to them as the place value of the smallest number, in this case thousandths, making the answer nine and eight hundred six thousandths.

The correct answer would be options (A), (D), and (E)

x + y = 28

28 - y = x

28 - x = y

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

The first column, yards of red fabric, x, has the entries 1, 2, 3, 4.

The second column, yards of blue fabric, y, has entries 27, 26, 25, and 24.

Sophie is buying fabric to make items for a craft fair.

when substitute x = 1 and y = 27

⇒ x + y = 1 + 27 = 28

So the equations model the total yards of fabric Sophie will buy as

⇒ x + y = 28

⇒ 28 - y = x

⇒ 28 - x = y

Hence, the correct answer would be options (A), (D), and (E)

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Answer: B

Step-by-step explanation:

Answer:

the area represents 40.5 square miles

Step-by-step explanation:

Since 1 inch represents 3 miles, then 1 inch x 1 inch = 1 square inch represents 3 mi x 3 mi = 9 square miles

Therefore, 4.5 square inches would represent 4.5 x 9 square miles = 40.5 square miles

Answer:

Step-by-step explanation:

distance = rate times time, so

           distance

time = --------------

               rate

Here the distance is 40 km and the rate is x.  Then

              40 km

time = --------------  =  (40/x) hr

             x km/hr

If the speed is reduced by 2 km/hr, we get:

              40 km                                            40 km                  40

time = -------------------------------  or time = ----------------------- = --------- hr

             (x km/hr - 2 km/hr)                      (x - 2) (km/hr)       x - 2

The difference between the times is:

 40          40

-------- - --------- = 1 hr          Solve this for the original speed, x

x - 2         x

40x - 40x + 80                                80

-----------------------  =  1 hr     or     ------------ = 1     or 80 = x^2 - 2x

     x(x - 2)                                     x(x - 2)

Rewriting this in standard quadratic form:  x^2 - 2x - 80 = 0

Here a = 1, b = -2 and c = -80, and so the discriminant b^2 - 4ac is:

(-2)^2 - 4(1)(-80) = 324

The solutions are:

      -(-2) ± √324       2 ± 18

x = -------------------- = ------------ = 1 ± 9, or 10 (discard the other root)

              2                      2

The original speed was 10 km/hr

the answer is 10 km/hr.

Answer:

k = -1

Step-by-step explanation:

-3(k-8)-(k+5)=23

Distribute

-3k +24 -k-5 = 23

Combine like terms

-4k +19 = 23

Subtract 19 from each side

-4k +19-19 = 23-19

-4k = 4

Divide by -4

-4k/-4 = 4/-4

k = -1

Answer:

  k = -1

Step-by-step explanation:

Use the distributive property to eliminate parentheses. That property tells you that the outside factor multiplies each term inside parentheses:

  -3(k -8) -(k +5) = 23

  -3k -3(-8) -k -(+5) = 23

  -3k +24 -k -5 = 23 . . . . simplify

  -4k +19 = 23 . . . . . . . . . collect terms

  -4k = 4 . . . . . . . . . . . . . subtract 19 from both sides

  k = -1 . . . . . . . . . . . . . . . divide both sides by -4

_____

The rule for manipulating equations is, "any operation performed on one side of the equation must also be performed on the other side." Operations include addition, subtraction, multiplication, division, application of a function. Using the distributive property and collecting terms are ways to simplify equations that don't affect the truth of the equal sign (if those are done correctly).

In general, you make use of inverse operations to undo the operations you don't want. The goal is to get the variable by itself on one side of the equal sign.

Answer:

y = 6x

Step-by-step explanation:

Choose two points on the graph of this line for the purpose of calculating the slope (rise/run).  One such point is (0, 0), which is a good choice because both x and y are exactly zero there.  Another point would be (16, 96), as the line goes through this point exactly.

Then the slope is m = rise / run = 96/16 = 6.

We'll use y = mx + b, with x = 0 and y = 0, learning immediately that b must be 0.  

Thus, the equation of this graph is y = mx + b =>  y = 6x, which is a proportional relationship.

Hi Dear Brainly User!

Answer: y = 6x

y  and  x:

12  -  2

24  -  4

36  -  6

.......

If we want to find m, we divide y by x. (m: the slope)

m = y/x = 12/2 = 24/4 = 36/6 = ... = 6

We use for find the y:

y = ax + b

Then, we write y = 0 and x = 0 on the formula.

And we find the b is 0.

If we multiply the slope by x, we get y.

y = 6*x = 6x

Sorry for my bad English.

-You should smile, everytime :)

Answer:

It takes the Dolphin 2 hours for swimming 40 miles. The penguin takes 8 hours and the swordfish will take 2/3 of an hour, which is 40 minutes to travel 40 miles.

Step-by-step explanation:

Given :

The bottlenose dolphin travels 40 miles in 2 hours. Or it takes 20 miles in 1 hour.

Now, dividing the distance by unit rate given in the question:

40/20=2 hours

40/5=8 hours

40÷60= 2/3 hour

Therefore,

- the dolphin takes 2 hours for swimming 40 miles.

- the penguin takes 8 hours

- the swordfish takes 2/3 rd of an hour

Answer:

2-x

Step-by-step explanation:

Answer: 3 has a different value because its in a different place value. It says 3 but it's value isn't 3. It's 0.003.

Answer:

Because they're in different places the 3 in the ones place couldn't equal as much as the three in the thousands place those places make them have different values

Hope this helps \_(OwO)_/ can i get marked brainliest o.O

Answer:

Add 5, and then multiply by 2

Step-by-step explanation:

Answer: [tex]-6[/tex]

Subtract

[tex]-4(3-1+2)=-4(2)+2[/tex]

Multiply

[tex](-4)(2)+2=-8+2[/tex]

Add

[tex]-8+2=-6[/tex]

Answer:

-6

Step-by-step explanation:

Follow the PEMDAS order of operations

Calculate within parentheses: 3 - 1 = 2

Multiply and divide (left to right): - 4 * 2 = -8

Add and subtract (left to right): -8 + 2 = -6

*see attachment showing the box plot

Answer:

8 schools

Step-by-step explanation:

In a typical box plot, data set are usually represented and denoted by quartiles in almost equal proportion. That is, 25% of the data set falls between the min and the Q1 value. From Q1 to median value, we have about 25%. From median to Q3, we have 25%, and from Q3 to the max, we have about 25%.

In the box plot given, we have:

Schools that have participated for at least 3 - 7 years fall within Q1 (3) and Q3 (7). Therefore, we have about 50% of the total number of schools that have spent 3 to 7 years.

No of schools that have spent at least 3 - 7 years = [tex] \frac{50}{100}*16 = 8 schools [/tex]

Answer:

8 schools

Step-by-step explanation:

I took the test and got it right.