Cait can bike 32 miles in the same amount of time that Carl can bike 24 miles. If Cait bikes 2 mph faster than Carl, how fast does Cait bike?

Answers

Answer 1

Let t = time in hrs for both to go 32 mi

Let s = Carl's speed in mi/hr

s + 2 = Caits speed in mi/hr

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

Carl's equation:

(1) 24 = s · t

Cait's equation:

(2) 32 = (s+2) · t

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

(2) 32 = s · t + 2t

and

(1) s = 24/t

Plug (1) into (2)

(2) 32 = (24/t) · t + 2t

(2) 32 = 24 + 2t

(2) 2t = 8

(2) t = 4

and

(1) s = 24/4

(1) s = 6

Answer 2

The speed of Cait is 8 mph

What is Algebra?

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them. Variables are the name given to these symbols because they lack set values. We frequently observe constant change in specific variables in our day-to-day situations. But the need to depict these shifting values is ongoing. These values are frequently represented in algebra by symbols such as x, y, z, p, or q, and these symbols are known as variables. In order to determine the values, these symbols are also subjected to different addition, subtraction, multiplication, and division arithmetic operations.

Let x be the time in hours for both to go 32 miles

Let y be Carl's speed

Then Caits speed  is = y+ 2

So, Carl's equation:

x y= 24

and, Cait's equation:

32 = (y+2) · x

32 = xy + 2x...............(1)

and, y = 24/x

Put the above value in equation (1)

(24/x) x + 2x = 32

2x+ 24 = 32

2x= 8

x=4

Also, y= 24/x= 24/4 = 6

Hence, speed of Cait is 8 mph

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Related Questions

I really need help someone?

Answers

Answer:

$11.80

Step-by-step explanation:

5x.90=4.5

63.5-4.5=59

59/5=11.8

cscy-siny=cosy(coty)

Answers

Step-by-step explanation:

[tex]\csc y - \sin y = \dfrac{1}{\sin y} - \sin y[/tex]

[tex]\:\:\:\:\:\:\:\:=\dfrac{1 - \sin^2y}{\sin y}[/tex]

[tex]\:\:\:\:\:\:\:\:= \dfrac{\cos^2y}{\sin y}[/tex]

[tex]\:\:\:\:\:\:\:\:=\cos y \left(\dfrac{\cos y}{\sin y}\right)[/tex]

[tex]\:\:\:\:\:\:\:\:= \cos y \cot y[/tex]

Work out an expression for the nth term of this sequence. 3, 11, 19, 27, …

Answers

Answer:

8n-5

Step-by-step explanation:

Find the difference between the numbers, +8 so 8n then subtract the diffference from the first number so 3 - 8= -5

The expression will be 8n - 5

Help plz. I will give brainilest!

Answers

Answer:

4.35

Step-by-step explanation:

Make the numerator improper, by doing 8x4+3 which equals 35. And then drag that whole number to the front and slap a decimal between the whole number (4) and your new numerator (35)! Which would be: 4.35

Lori is solving the equation 4x2 + 5x - 6 = 0 using the quadratic formula. Which
expression shows the correct numbers substituted into the quadratic formula to
solve?

Answers

Answer:

[tex] \frac{ - 5 + \sqrt{( {5})^{2} } - 4(4)( - 6) }{ 2(4)} [/tex]

please help and give easy to understand explanation.​

Answers

Answer:

ok send the work now I am ready

Answer:

I’m not trying to mooch off points, just want to know where the flipping question is

Step-by-step explanation:

Would help if could

50 pounds of pet food for
$37.99
Unit rate

Answers

Answer:

$0.76

Step-by-step explanation:

$37.99 divided by 50 pounds = $0.7598 per pound

Round 0.7598 and you will end up with 0.76.

first distribute, then combine like terms 5(2x+7)+4x

Answers

Answer:

14x+35

Step-by-step explanation:

10x+4x=14x

5*7=35

Answer:6x+12

Step-by-step explanation: combine like terms.

Which sentence illustrates the commutative property for addition? (1) (a+b)+c=a+(b+c)
(2) a(b+c)=ab+ac
(3) a+0=a
(4) a+b=b+a

Answers

Answer:

the answer is 2a(b+c)=ab+ac

Answer:

The 4th option is correct. a+b = b+a

Step-by-step explanation:

guys pls answer my question i am very confused

Answers

Given 2y = 5(3 + y):

You’ll have to solve for y:

Start by distributing 5 into (3 + y):

2y = 5(3 + y)
2y = 15 + 5y

Subtract 15 from both sides:
2y - 15 = 15 - 15 + 5y

2y - 15 = 5y

Then, subtract 2y from both sides:
2y - 2y - 15 = 5y -2y

-15 = 3y

Then , divide both sides by 3 to solve for y:

-15/3 = 3y/3

-5 = y

Therefore, y = -5
Answer : Y = -5

You’re solving for Y

pls answer the question important

Answers

Step-by-step explanation:

no they are not parallel

Answer:

not equal

Step-by-step explanation:

its not parallel because sum of angles of alternate angle are not equal.

solve pls brainliest

Answers

Step-by-step explanation:

(a) 46-(-6)= 52

(b) -6+11= 5

Mrs. Taylor earns $3,462 a month.
If she spends $1,958 a month and saves the rest,
how much will she save in 9 months?

Answers

Answer:

1m she saves 3.462-1.958=1.504

9m she saves 1.504*9=13.536

Step-by-step explanation:

Mason goes to a store an buys an item that costs xx dollars. He has a coupon for 30% off, and then a 7% tax is added to the discounted price. Write an expression in terms of x that represents the total amount that Mason paid at the register.

Answers

THE TOTAL AMOUNT THAT MASON PAID IS 549

Work out the percentage change to 2 decimal places when a price of £15 is decreased to £14.

Answers

Answer:

The total change is £21.02 from the original amount of £78.98. Therefore, the percentage change is directly related to the original amount.

so the answer in a percentage is 15.22%.

Step-by-step explanation:

Answer:

the answer is $ 15 is decreased to $ 14 = 6.67 percent.

Step-by-step explanation:

A pigeon was sitting 15 feet from the base of a telephone pole and flew 25 feet to reach the top of the pole. How tall is the telephone pole?

Answers

I don’t know which one of us is right, but I got 20ft

Write an
equation of the line that passes through each pair of points.
(-3,9), (-3,-5)

Answers

Answer:

since slope(m) = y2 -y1/x2- x1

-5 - 9/ -3 - (-3)= -14/0

m = -14/0 (undefined)

using the formula

y-y1 = m(x -x1)

y - 9 = -14/0(x - (-3)

y-9 = -14/0(x + 3)

0 = -14( x+3). (cross multiplication)

0 = -14x - 42

14x = -42

x = -3( equation of the line)


Find the slope of the line that passes through (7,5) and (4, 9)

Answers

Answer:

-4/3

Step-by-step explanation:

(9-5)/(4-7)

4/-3

-4/3

18634 to the nearest hundred​

Answers

Answer:

18600

lf you like my answer than please mark me brainliest thanks


What is the constant of proportionality in miles per hour?
a.) 0.85 miles per hour
.85
b. 55 miles per hour
IS112.15
c. 60 miles per hour 4
120
d. 51 miles per hour
15
75
8

Answers

9514 1404 393

Answer:

  (d)  51 miles per hour

Step-by-step explanation:

The constant of proportionality can be found by dividing the distance by the time. It is convenient to choose a time that makes this division simple. We choose 30 min = 1/2 hour.

  (25.5 mi)/(1/2 h) = 2(25.5) mi/h = 51 mi/h

The constant of proportionality is 51 miles per hour.

Aaron's car used 3- gallons of gas when
he drove it 60 miles. How many miles
does his car get per gallon?

Answers

We want to find miles per gallon. Another way of saying miles per gallon is miles/gallon. So we will plug the numbers into this equation:

60 miles/3 gallons = 20 miles/gallon

This is because 60/3=20.

I hope this makes sense.

Answer:

His car gets 20 miles per gallon.

Step-by-step explanation:

1. 60 = 3x (divide by 3)

2. 20 = x

Therefore, the car uses 20 miles per gallon.

solve pls brainliest

Answers

Answer:

a) -10

b) +150

Answer: (a.) -50/5=-1          (b.) 5*30=+150

Step-by-step explanation:

(a.) each stock went down by -10x5=-50

(b.) 5x10=50.  50x3=150

half way I was doing this it got deleted


Find the distance Between points (3,7) and (-3,4).

Answers

Answer:

the distance is 3√5 !

Step-by-step explanation:

Answer:

Since the points form a triangle, you can use Pythagorean theorem to solve this.

Side A is 3 Units, and side B is 6. The letters do not matter when corresponding them to the sides.

So Pyth Theorem = a^2 + b^2 = c^2

And c^2 is the distance we must find

So a^2 = 9

b^2 = 36

So 36 + 9 = 45

To find C, you must root c^2

So sqrt of 45 is 6.7

The distance between points (3,7) and (-3,4) is 6.7 units.

Seven plus seven equal to

Answers

Answer:

the answer is 14

Step-by-step explanation:

7+7=14

I hope this help

Answer:

14

Step-by-step explanation:

Solve This

[tex]6 {}^{2} \times 6 {}^{3} [/tex]

[tex]( \sqrt{103} [/tex]

Answers

Hey there!

Question #1

6^2 × 6^3

6^2

= 6 × 6

= 36

6^3

= 6 × 6 × 6

= 36 × 6

= 216

36 × 216

= 7,776

6^2 × 6^3

= 6^5

• Question #1 answer: 7,776 or 6^5 either answer should work because both answers are equivalent

Question #2

√103

= 10.148892

• Question #2 answer: 10.148892

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

[tex] \small \sf \: 6 {}^{5} [/tex]

Alternate form: - 7776.

Step-by-step explanation:

1). 6² × 6 ³.

6² = 6 × 6 = 366³ = 6 × 6 × 6 = 216

6² × 6³ = 36 × 216 = 7776.

Or,

6² × 6³

= [tex] \sf \small \: 6 {}^{2 + 3} [/tex]= [tex] \small \sf \: 6 {}^{5} [/tex]

3 2/3 +2.3 (theres a bar on top of the 3 in 2.3 ) =

A. 5
B. 5 2/3
C. 6
D. 6 1/3

Answers

The answer is C.6…..

Dan has 2 photo albums. Each photo album 8 pages. Dan can fit 4 pictures on each page. How many pictures can Dan fit in the albums?​

Answers

Answer:

64

Step-by-step explanation:

8 x 4 = 32

32 x 2 = 64

The number of pictures can Dan fit in the albums are 64.

What is multiplication?

Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.

Given that, Dan has 2 photo albums. Each photo album 8 pages. Dan can fit 4 pictures on each page.

Here, the number of pictures

= 2×8×4

= 64

Therefore, the number of pictures can Dan fit in the albums are 64.

Learn more about the multiplication here:

https://brainly.com/question/1562995.

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Please help. To see the image larger please hover over image and press the magnifying glass.

Answers

Answer:

See Below

Step-by-step explanation:

The negation of a statement is almost like the opposite, but it needs to cover all cases that the statement does not.

1) x is not equal to 300.

This statement is true for all x except 300 while our original statement is true for all x except 100. These two have overlaps between what values of x could be, meaning that it is not the negation.

2) x is equal to 100.

This statement is true only for the case x equals 100 while our original statement is true for all the cases where x is not 100. These two do not overlap and cover all numbers. This means that it is the negation.

3) It is not the case that x is equal to 400.

This statement is true for all x except 400 while our original statement is true for all x except 100. These two have overlaps between what values of x could be, meaning that it is not the negation.

4) x is equal to 300.

This statement is true only for the case x equals 300 while our original statement is true for all the cases where x is not 100. This two cases have overlaps(300), meaning it is not the negation.

Please please answer super easy

Answers

Answer:

Step-by-step explanation:

You need y by itself on one side of the equal sign and x and the y intercept on the other side.

4x + 2y = - 12                  Subtract 4x from both sides

2y = -4x - 12                    Divide by 2

2y/2 = -4x/2 - 12/2              

y = -2x - 6                        

Note: y also must be plus. x can be either plus or minus

m = - 2

b = - 6

PLZ HELP ME ON THIS QUESTION GUYS THANK YOU IF U HELP ME 30 POINTS

Answers

The answer to this question is -1.75

Answer:

The value of the expression is 0.5.

Step-by-step explanation:

To evaluate, we need to do order of operations.

To solve, we start with the parenthesis because they come first in the order of operations.

-1+3[(10-12)³/(-16)]

-1+3[-2³/-16]

Now we do the second thing in the order of operations, which is to simplify the exponents.

-1+3[-8/-16]

Now we do the third thing left to do, which is to do division and multiplication from left to right.

-1+3[0.5]

-1+1.5

Now we do the last thing left to do, which is to do addition and subtraction from left to right.

0.5

So the value of this expression is 0.5.

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