Two cyclists start at the same point and travel in opposite directions. One cyclist travels 4 mile per hour slower than the other. If the two cyclists are 56 miles apart after 2 hours, what is the rate of each cyclist.?

Answers

Answer 1

Answer:

12 mph and 16 mph

Step-by-step explanation:

distance = speed * time

56 = s * 2 + (s - 4) * 2

56 = 2s + 2s - 8

56 = 4s - 8

64 = 4s

16 = s

s = 16

s - 4 = 12

Answer 2

Let the speed of the faster bike = X

The slower bike would be x - 4 ( 4 mph slower)

Multiply each speed by time and add to equal total distance:

2x + 2(x-4) = 56

Simplify:

2x + 2x -8 = 56

4x -8 = 56

Add 8 to each side:

4x = 64

Divide both sides by 4:

x = 64/4

x = 16

The faster bike rode at 16 miles per hour

The slower bike traveled at 16-4 = 12 miles per hour


Related Questions

Consider f(x) = 2x2 + 1 and g(x) = 3x − 6. Which statement about f + g is true?
A. It is a linear function.
B. It is a quadratic function.
C. The domain is x ≥ −3.
D. The range is all real numbers.

Answers

Given:

The two functions are:

[tex]f(x)=2x^2+1[/tex]

[tex]g(x)=3x-6[/tex]

To find:

The correct statement about the function [tex]f+g[/tex].

Solution:

We have,

[tex]f(x)=2x^2+1[/tex]

[tex]g(x)=3x-6[/tex]

Adding both functions, we get

[tex]f+g=f(x)+g(x)[/tex]

[tex]f+g=2x^2+1+3x-6[/tex]

[tex]f+g=2x^2+3x-5[/tex]

It is a quadratic function. So, option A is incorrect and option B is correct.

The domain of [tex]f+g[/tex] is all real numbers because it is defined for all real values of x. So, option C is incorrect.

The range of [tex]f+g[/tex] cannot be the all real numbers because it has a minimum value of y as the leading coefficient is positive. So, option D is incorrect.

Therefore, the correct option is B.

how do i solve for x? thank you!

Answers

Answer:

[tex]x = \frac{7}{2}[/tex]

Step-by-step explanation:

[tex]6^{x-1} = 36 \sqrt6\\\\6^{x-1} = 6^2 \times 6^{\frac{1}{2}}\\\\6^{x-1} = 6^{2 + \frac{1}{2} }[/tex]                        [tex][ \ a^x \times a^ y = a^{x+ y} \ ][/tex]

[tex]x - 1 = 2 + \frac{1}{2}[/tex]                          [tex][ \ b^x = b^y => x = y \ ][/tex]

[tex]x = 2 + \frac{1}{2} + 1\\\\x = 3 + \frac{1}{2} \\\\x = \frac{6+ 1}{2} \\\\x = \frac{7}{2}[/tex]

Answer:

x = 3.5

Step-by-step explanation

       

Using the rules of exponents

[tex]a^{m}[/tex] × [tex]a^{n}[/tex] ⇔ [tex]a^{(m+n)}[/tex] and [tex]\sqrt{a}[/tex] = [tex]a^{\frac{1}{2} }[/tex]

Then

36[tex]\sqrt{6}[/tex] = 6² × [tex]6^{\frac{1}{2} }[/tex] = [tex]6^{(2+0.5)}[/tex] = [tex]6^{2.5}[/tex]

Thus

[tex]6^{x-1}[/tex] = [tex]6^{2.5}[/tex]

Since the bases on both sides are equal, both 6, equate the exponents

x - 1 = 2.5 ( add 1 to both sides )

x = 3.5


Consider the graph. Which inequality best represents the graph?

Answers

Answer:

y >= x/2 - 1

Step-by-step explanation:

the slope (rise/run) is 1/2 and the y-intercept is -1 so in point-slope form

y = x/2 - 1 but everything above the line (unshaded part) is valid so y is equal to or greater than.

A group of people were asked if they had run a red light in the last year where 140 responded "yes," and 208 responded "no." If a person is randomly chosen, find the probability that he/she has run a red light in the last year. Give your answer as a fraction or decimal.

Answers

Answer:

35/87

Step-by-step explanation:

To find the probability, we must find (total number of favorable outcomes)/ (total number of outcomes). We thus need to find the total number of outcomes. As people have only answered "yes" or "no", the total number of outcomes is 208+140 = 348.

The total number of favorable outcomes, or what we're looking for, is 140 (140 people responded that they had run a red light). Thus, our fraction is 140/348, or 35/87

What are biofertilisiers​

Answers

Bio fertilizer :- Biofertilisers are organisms that enrich the nutrient quality of the soil. The main source f biofertilizers are bacteria, fungi and cyanobacteria.

HOPE IT HELPS ❣️

The graph of y - 3x + 2 is:

Answers

The answer should be D!

The coordinates of point C are . The slope of is . The possible coordinates of point D are and .

Answers

Answer:

The answer is below

Step-by-step explanation:

The endpoints of AB are A(2, 3) and B(8, 1). The perpendicular bisector of AB is CD, and point C lies on AB. The length of CD is (root of 10) units.

The coordinates of point C are (-6, 2) (5, 2) (6, -2) (10, 4) . The slope of is -3 -1/3 1/3 3 . The possible coordinates of point D are (4, 5) (5, 5) (6, 5) (8, 3) and (2, 1) (4, -1) (5, -1) (6, -1) .

Solution:

Since CD is the perpendicular bisector of AC, hence line CD is perpendicular to AB and divides line AB into two equal parts.

Point C(x, y) is the midpoint of AB.

hence:

x = (2 + 8) / 2 = 5

y = (3 + 1)/2 = 2

The coordinates of point C = (5, 2)

The slope of line AB is:

slope of AB = (1 - 3) / (8 - 2) = -1/3

Since CD is perpendicular to AB, hence the product of the slope of AB and the slope of CD is -1

slope of AB * slope of CD = -1

slope of CD * -1/3 = -1

slope of CD = 3

Line CD has slope of 3 and pass through C(5, 2). The equation of line CD is:

y - 2 = 3(x - 5)

y = 3x - 13

The possible coordinates of point D are (6, 5) and (4, -1), because this point lie on line CD.

A 68-year old retiree has a pension savings of $51,000, a 401k of $58,000, and an IRA account of $68,000. Before 2008, he had 2% more cash in the pension, 12% more in the IRA, and −1% in the 401k. He wants to take out 2% from each account before he turns 72, which will cost him a penalty of an extra 1% from the pension, 2% from the 401k, and 6% from the IRA. What is the relevant information for the amount that the retiree will have in his pension if he doesn't take money out now?

A: The retiree had 2% more cash in the pension in 2008
B: The retiree has a pension savings of $51,000
C: The retiree has a 401k of $58,000
D: The retiree has an IRA account of $68,000

Answers

Answer:

B: The retiree has a pension savings of $51,000

Step-by-step explanation:

solve for " x "

[tex]x = 42 - 9[/tex]

Answers

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {x\:=\:33}}}}}}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex]x = 42 - 9[/tex]

➼[tex]\:x = 33[/tex]

Therefore, the value of [tex]x[/tex] is 33.

[tex]\sf\pink{Thank\:you. \:ヅ}[/tex]

Answer:

x =33

Step-by-step explanation:

x = 42-9

We are solving for x, which is already isolated

42-9 = 33

x = 33

Check 33+9 = 42

The tile along the edge of a triangular community pool needs to be replaced. A right triangles, where the hypotenuse is labeled 8 x squared, the height is labeled 4 x squared + 15, and the base is labeled 8 x + 10. Which expression represents the total perimeter of the pool edge? 12x2 + 15 20x2 + 25 12x2 + 8x + 25 24x2 + 16x + 50

Answers

Answer:

C. 12x² + 8x + 25

Step-by-step explanation:

A. 12x² + 15

B. 20x² + 25

C. 12x² + 8x + 25

D. 24x² + 16x + 50

Hypotenuse = 8x²

Height = 4x² + 15

Base = 8x + 10

Perimeter of the triangle = hypotenuse + height + base

= 8x² + (4x² + 15) + (8x + 10)

= 8x² + 4x² + 15 + 8x + 10

Perimeter of the triangle = 12x² + 8x + 25

C. 12x² + 8x + 25

Answer:The answer is C

If f(x)=2x2+3x−6, determine the value of f(2)

Answers

Answer: 4

2x2+3(2)−6

lets make sure we do OOO (order of operations correctly)

2x2+3(2)−6

4+3(2)−6

4+6−6

10−6

4

Step-by-step explanation:

The theater sells two types of tickets: adult tickets for $18 and
child tickets for $9.
Last night, the theater sold a total of 221 tickets for a total of
$2466. How many adult tickets did the theater sell last night?

Answers

The answer to your question is 137

help please on all of these

Answers

the answer is on the picture

Simplify (4x - 6) - (3x + 6).
Ox- 12
O -X- 12
Ox+ 12
0-x + 12

Answers

Answer:

Ox-12

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

(4x - 6) - (3x + 6)              Remove the brackets

4x - 6 - 3x - 6                   Collect like terms

4x - 3x - 6 -6

x - 12

The answer   is A

Montserrat is training for her first race. In her first training week she runs 3 km, and in the second training week she runs 3.5 km. Every week she runs 0.5 km more than the previous one.
a Find how many kilometres Montserrat runs in her 10th training week.
b Calculate the total number of kilometres that Montserrat will have run by her 15th training week.​

Answers

Answer:8

Step-by-step explanation:

0.5*10=5

3+5=8

a. Montserrat runs 7.5 kilometers in her 10th training week.

b. by her 15th training week, Montserrat will have run a total of 78.75 kilometers.

To find how many kilometers Montserrat runs in her 10th training week, we can use the arithmetic sequence formula to find the nth term:

[tex]a_n = a_1 + (n - 1) * d[/tex]

where:

[tex]a_n[/tex] is the nth term (the number of kilometers in the nth week),

[tex]a_1[/tex] is the first term (the number of kilometers in the first week, which is 3 km),

n is the number of weeks (in this case, 10), and

d is the common difference (the amount by which the distance increases each week, which is 0.5 km).

[tex]a_{10} = 3 + (10 - 1) * 0.5\\a_{10} = 3 + 9 * 0.5\\a_{10} = 3 + 4.5\\a_{10 }= 7.5 km[/tex]

So, Montserrat runs 7.5 kilometers in her 10th training week.

b. Next, to calculate the total number of kilometers Montserrat will have run by her 15th training week, we use the sum of the first n terms formula:

[tex]S_n = (n / 2) * (a_1 + a_n)[/tex]

where:

[tex]S_n[/tex] is the sum of the first n terms (the total number of kilometers run by the nth week),

[tex]a_1[/tex] is the first term (3 km),

[tex]a_n[/tex] is the nth term (which we found to be 7.5 km in her 10th week),

n is the number of weeks (15 in this case).

[tex]S_{15} = (15 / 2) * (3 + 7.5)\\S_{15} = 7.5 * 10.5\\S_{15} = 78.75 km[/tex]

So, by her 15th training week, Montserrat will have run a total of 78.75 kilometers.

To know more about training:

https://brainly.com/question/28942187

#SPJ3

i need help asap Please ​

Answers

Answer: F. is a linear relation.

Step-by-step explanation:

Answer:

G

Step-by-step explanation:

Equation of the eventual line:

(y-4)/(5-4) = x

y-4 = x

y = x + 4

this equation can’t be used to determine the last three values. In fact, for examples:

7 = 2 + 4

7 = 6 (false)

So the relation is non linear

Solve for x.
3x + 7
2x + 3)

Answers

Answer: x = 34

Step-by-step explanation:

2x+3+3x+7=180

5x+10=180

5x=170

x = 34

x=34 your welcome !!!

A piece of ribbon is x inches long. Find the total length of 7 equal pieces of ribbon. Express the answer in terms of x.

Answers

Answer:

7x

or 7*x

Step-by-step explanation:

What is the relationship between the diameter d and circumference c of a circle

Answers

Answer:

π × d

Step-by-step explanation:

The relationship between the diameter and circumference is that the circumference is equal to π multiplied by the diameter. This means that our answer is π × d, or the third option

A duck can fly 2400 m in 10 minutes with the wind. Against the wind, it can fly only 2/3 of this distance in 10 minutes. What is the rate of the wind?

Answers

Answer:

The rate (or speed) of the wind is 40 meters per minute.

Step-by-step explanation:

Let's define:

S = speed (or rate) of the duck alone

S' = speed (or rate) of the wind.

When the duck travels with the wind, its speed is:

(S + S')

While when the duck travels against the wind, its speed is:

(S - S')

Also, remember the relation:

Distance = Speed*Time

ok, we know that the duck can travel a distance of 2400 m in 10 minutes with the wind, then:

2400m = (S + S')*10 min

And against the wind, it can travel 2/3 of that distance, then we can write:

(2/3)*2400m = (S - S')*10 min

Then we have a system of 2 equations:

2400m = (S + S')*10 min

(2/3)*2400m = (S - S')*10 min

We want to find the speed of the wind, then we want to find the value of S'.

To solve this, we first need to isolate S in one of the equations.

Let's isolate S in the first one:

2400m = (S + S')*10 min

2400m/10min = (S + S')

240 m/min = S + S'

240 m/min - S' = S

Now we can replace this in the other equation:

(2/3)*2400m = (S - S')*10 min

(2/3)*2400m = ( 240 m/min - S' - S')*10 min

Now let's solve this for S'

(2/3)*2400m/10min = 240 m/min - 2*S'

(2/3)*240 m/min = 240 m/min - 2*S'

2*S' = 240 m/min - (2/3)*240 m/min

2*S' = (1/3)*240 m/min

2*S' = 80 m/min

S' = (80 m/min)/2

S' = 40 m/min

The rate (or speed) of the wind is 40 meters per minute.

How many kilograms equals 984.2 grams?

Answers

0.9842 kilograms equal to 984.2 grams

what should I do if I accidentally break my pet rock that has googly eyes on him? i need to fix Rocky Ronny McRonkster

Answers

Answer:

Try to glue it back together

Step-by-step explanation:

I heard gorilla glue works, but be careful and don't get the glue on your body. If that happens it can cause irritation and call posion control immediately.

translate the sentence into an inequality


the sum of 2 and y is greater than 16

Answers

Answer:

2 + y > 16

Step-by-step explanation:

the sum of 2 and y is greater than 16

                   2 + y           >                   16

2 + y > 16

2+y > 16 (sum means addition)

If f(x) = 4x1/2 , find f(4)

Answers

Answer:

f (4) = 8

Step-by-step explanation:

f (x) =2

2 x 4 = 8

Application: Sandy wants to cover a wooden cylinder with a diameter of 1 ft and a height of 4 ft with carpet to build a scratching post for her cats. What are the steps she needs to take to complete this task?

Answers

Step-by-step explanation:

Finding the (maximum) respective prime powers would yield the answer. Also we need not ... Is perfectly divisible by 720^n? ... So we can say that for any positive value of n it not divisible.

Question is in photo.
Thanks

Answers

Answer:

what do you mean for this question. What do you need help on?

PLS HELP GIVING BRAINLIEST

Answers

Answer:

1. reflection- a figure is flipped over

2. translation- a figure is slide

3. rotation- a figure is turned

1. Reflection —> a figure is flipped over
2. translation—> a figure is slid
3. Rotation—> a figure is turned

Hope this helps!

Find the length of the missing side

Answers

Answer:

25 in and 9 cm

Step-by-step explanation:

Using Pythagoras' identity

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

let x be the missing side

A

x² = 7² + 24² = 49 + 576 = 625 ( take square root of both sides )

x = [tex]\sqrt{625}[/tex] = 25

B

x² + 12² = 15²

x² + 144 = 225 ( subtract 144 from both sides )

x² = 81 ( take square root of both sides )

x = [tex]\sqrt{81}[/tex] = 9

Answer:

A) [tex]\sqrt{7^{2} +24^{2} }[/tex] = 25

B) [tex]15^{2} -12^{2} = B^{2}[/tex]

   [tex]B^{2} =81\\[/tex]

B = 9

Step-by-step explanation:

Solve for x. Round to the nearest tenth, if necessary.
K
L
99
х
15°
M

Answers

Answer:

x≈95,6

Step-by-step explanation:

x= cos 15⁰ x 99 ≈95,6

What combination of bracelets does dimitri have?

Answers

7 simple and 3 deluxe bracelet
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