Mathematics High School

Patrick drives from P to Q at an average speed of 40 mph . His drive back from Q to P is at an average speed of 45 mph and takes two minutes less.

How far, in miles, is it from P to Q?

Answers

Answer 1

Answer:

Distance=12 miles

Step-by-step explanation:

d=distance

t=time going

d/t=40 mph going

t-2/60=time returning      (2 minutes/60 minutes per hour)

d/(t-2/60)=45 mph returning

set up equations:

d=40t

d=45(t-2/60)

substitute:

40t=45(t-2/60)

40t=45t-90/60

40t=45t-3/2

0=5t-3/2

5t=3/2

t=0.3 hours or 18 minutes

(time returning=16 minutes)

substitute:

d=40t=40(0.3)

d=12 miles

Answer 2

P and Q are 12 miles far from each other.

Given that

Patrick drives from P to Q at an average speed of 40 mph

Also he drives from Q to P at an average speed of 45  mph

Let "s" be the distance between P and Q in miles.

Let "t" be  the time in minutes

There are 60 minutes in 1 hours

[tex]\rm So \;in \; "t" \; minutes \; there\; will\; be = \dfrac{t}{60} \ hours[/tex]

By the definition pf average speed we can write that

[tex]\rm Average \; Speed = \dfrac{Total \; distance }{Total \; time}\\[/tex]

The speed is given in two situations in miles per hour

Case 1  When average speed = 40 mph

[tex]\rm 40 = \dfrac{s}{t/60} \\\\\rm {40 = \dfrac{60s}{t} .....(1) }[/tex]

Case 2 When  average speed = 45 mph  

Given that Patrick takes two minutes less  

[tex]\rm 45 = \dfrac{s}{(t-2)/60} \\\\45 = \dfrac{60s}{t-2 } ....(2)[/tex]

Solving for "s" from equations (1) and (2) gives us

[tex]\rm \bold {s = 12}}[/tex]

So we can conclude that P and Q are 12 miles far from each other.

For more information please refer to the link given below

https://brainly.com/question/21470320

Related Questions

Calculate the perimeter of this shape.
12 cm
18 cm

Answers

Answer:

Step-by-step explanation:

P = 2l + 2w

= 2(12) + 2(18)

= 24 + 36 = 60

Enter a formula using k to connect the two variables.
F is proportional to a.


Please help​

Answers

Answer:

Weres The Formula?

Step-by-step explanation:

Answer:

f=ka

Step-by-step explanation:

Type the missing number in this sequence:

47, 51, 55, 59, ,




PLEASE HELP

Answers

the answer would be 62
the answer would be 62

WILL GIVE BRAINLIEST

A line has a slope of 2 and a y-intercept of 9, what is the equation of the line

Answers

Answer:

y=2x+9

Step-by-step explanation:

Slope intercept form is y=mx+b

m is the slope  (2)

b is the y-intercept  (9)

Plug the slope and intercept you were given in and you get the equation of the line in slope intercept form

y=2x+9

Compared to last year the population of city had decreased by 15% the population is now 6800 what was the population last year?

Answers

Answer:

6800 x ( 100%-15% ) =5780 population

Step-by-step explanation:

evaluate 11.5x + 10.7y when x = 3 and y = 4

Answers

Answer: 77.3

Step-by-step explanation:

11.5(3)+10.7(4)

11.5 times 3 equals 34.5

and 10.7 times 4 equals 42.8

34.5 plus 42.8 equals 77.3

Answer:

77.3 (see below)

Step-by-step explanation:

To solve, plug in the values given into the expression given and simplify:

11.5x + 10.7y

11.5 (3) + 10.7 (4)

34.5 + 42.8

77.3

Question 7(Multiple Choice Worth 1 points)
(05.02 MC)

A standard American Eskimo dog has a mean weight of 30 pounds with a standard deviation of 2 pounds. Assuming the weights of standard Eskimo dogs are normally distributed, what range of weights would 99.7% of the dogs have?

Approximately 26–34 pounds
Approximately 24–36 pounds
Approximately 28–32 pounds
Approximately 29–31 pounds

Answers

Answer:  C

Step-by-step explanation: I took the test and got it right


HELP PLS PLSSSSS


ASAP

Answers

Answer:

9(9d+4)

Step-by-step explanation:

Hope I helped!

plz help me
(a²-b²)²+a²b²
factorise
plzz​

Answers

Answer:

a^4+b^4−a^2b^2

Step-by-step explanation:

you have to subtract first

Some teenagers collected trash for a beach cleanup. The data for the number of pounds of trash collected by each teenager are shown below. 26, 26, 21, 22, 20, 25, 35 What is the standard deviation of the data? 0 pounds 4.66 pounds 5.03 pounds 25.33 pounds

Answers

Answer:

4.66

Step-by-step explanation:

We are given the following data

26, 26, 21, 22, 20, 25, 35

Step 1

We find the Mean

Mean = 26+ 26+ 21+ 22+20+25+ 35/7

= 175/7

= 25

Step 2

We find the Standard Deviation

The formula for Standard deviation that we would use is the Population Standard deviation, this is because the data given above is the data of the number of pounds of trash collected by each teenager

= √(x - Mean)²/n

= √(26 - 25)²+( 26 - 25)²+ (21 - 25)²+ (22 - 25)² +(20 - 25)²+(25 - 25)²+ (35 - 25)²/7

= √152/7

= √21.7142857

= 4.65985898

Approximately = 4.66

Answer:

5.03 Pounds (C)

ED2021

The person above me is right, but you gotta solve for sample data; not population.

!This is for standard deviation!

a triangle has two sides of length 5 and 4 what is the smallest possible whole-number length for the third side​

Answers

Answer:

1

Step-by-step explanation:

HI WHAT IS 7/6 OF 456327=
PLEEEEAAASE HEEEELLLP ME!!!!!!!!

Answers

Answer:

532381.5

Step-by-step explanation:

456327 divided by 6 to get 1/6 = 76054.5

76054.5 x 7 to get 7/6 = 532381.5

or 456327 (6/6) + 76054.5 (1/6) =532381.5

3 of 8
The area of a circle is 16.71cm2.
Find the length of the radius rounded to 2 DP.

Answers

Answer:

Radius = 2.31 cm

Step-by-step explanation:

Area of circle = 16.71 square centimeters

[tex]\pi r^2 = 16.71 \\3.14r^2=16.71\\r^2=\frac{16.71}{3.14}\\r^2=5.32\\\sqrt{r^2}=\sqrt{5.32}\\r=2.306[/tex]

Radius of circle = 2.31 centimeter

y = 3x - 1
y = x - 7
Solve with Substitution

Answers

Y = 3x -1. Y = 3x - 1
(-3) Y = x - 7. -3y = -3x + 21

-2y = 20
-2. = -2
Y = - 10

Y = 3x - 1
-10 = 3x - 1
+ 1. + 1
-9. = 3x
3. 3

-3 = x

(-3,-10)
Solution : {y,x } = { -10 , -3 }
Solve the equation [2] for the variable of y
2 . Y = x-7
Plug this in for variable y in the equation [1]
1 (x -7 ) -3x = -1
1 -2x = 6
Solve the equation [1] for the variable x
1 2x =-6
1 x= -3
By now we know this much
Y = x-7
X =-3
Use the x value to solve for y
Y= ( -3 ) -7 = -10

PLEASE HELP ME ON THIS THE ANSWERS ARE 1/3 cm/s, 1/2 cm/s, 2/3 cm/s, and 3/2 cm/s

Answers

Answer:  3/2 cm per second

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

Explanation:

We could compute the slope of this line to get the answer, or we could simply compute y/x. This shortcut only works because the line goes through the origin. If the line didn't go through the origin, then we would have to use the slope formula.

The unit rate is y/x = 9/6 = 3/2 cm per second. I used the point (9,6) to compute the unit rate.

We can think of the fraction 3/2 as 1.5, so the unit rate is equivalent to 1.5 cm/sec.

GIVING BRAINLIST!!!
The point (5, -6) is reflected over the x-axis. The coordinates of reflected point are (_______).
Group of answer choices

(5, 6)

(-5, 6)

(-5, -6)

(5, -6)

Answers

The correct answer is (5,-7) Hope that helps!

Answer:

it would be (-5,6)

Step-by-step explanation:

since it is just reflected and not moving anywhere it would just be the same coordinates but flipped values. if its positive then when its reflected it would be negative.

The sum of the digits of a certain two-digit number is 7. Reversing its digits increases the number by 9. What is the number?

Answers

Answer:

34

Step-by-step explanation:

how is the following written with only one exponent?
a^3 . a^5​

Answers

Answer:

The expression 103 is called the exponential expression. ... The exponent applies only to the number that it is next to. ... If −3 is to be the base, it must be written as (−3)4, which means −3 • −3 • −3 ... From row 1 to row 2, the exponential form goes from 105 to 104. ... Following the pattern, you see that 100 is equal to 1.

Step-by-step explanation:

25,002,000 in scientific notation

Answers

Answer:

2.5002 × 10^3 i think, dont quote me on that

Step-by-step explanation:

What is the slope of this line

Answers

Answer:

K=2

Step-by-step explanation:

I es Smrt

A and B are two mutually exclusive events.
P(A) = 0.3 and P(A or B) = 0.7
Work out the value of P(B).

Answers

If the events are mutually exclusive, then P(B)=P(A or B)-P(A). This is 0.7-0.3, which is 0.4.

Please help it’s a test and I only have 50 minutes left

Find x. Round to the nearest hundredth if necessary.

Answers

Answer:

60

Step-by-step explanation:

X is equal to 60 degrees

simplify
5p - 4p - 4p

Answers

Answer:

-3p

Step-by-step explanation:

Answer:

-3p

Step-by-step explanation:

5p - 4p = 1p - 4p = -3p

Which is a true statement?
A. 7/4 is a rational number but not a whole number
B. 7/4 is a whole number but not a rational number
C. 7/4 is a whole number and a rational number
D. 7/4 is not a rational number, and is not a whole number​

Answers

A. 7/4 is a rational number but not a whole number.

5x + 4x - 4x plz help me

Answers

the answer is 5x
hipe that helps
5x is the answer because 4x-4x=0 and 5x+0=5x.

If QRS is dilated by a scale factor of 6 through the origin, which of the following points represent the coordinates of R?
OA. (-12,-24)
OB. (-24,-12)
OC. (12.24)
OD. (24,12)

Answers

Answer:

OD. (24,12) This is the right answer ok

Answer:

oopp

Step-by-step explanation:

can someone help me with this?

-5k = 12

thanks!

Answers

Answer:

Not sure what you wanted but here Divide each term by

−

5

-

5

and simplify.

Exact Form:

k

=

−

12

5

k

=

-

12

5

Decimal Form:

k

=

−

2.4

k

=

-

2.4

Mixed Number Form:

k

=

−

2

2

5

Step-by-step explanation:

Answer:

k= -2.4

Step-by-step explanation:

Work out the area of a rectangle with base, b = 20mm and perimeter, P = 42mm.

Answers

Answer:

20mm

Step-by-step explanation:

base=20mm

base x 2 because there are two long lines

20 x 2 = 40

42-40=2

amount needed on either side to balance

height=1mm

20 x 1 = 20mm

area = 20mm

Answer:

Let the length of the rectangle be 'l'

We have,

Perimeter of rectangle, P = 42mm.

[tex]or, 2(l+b) = 42\\or, l +b = \frac{42}{2} = 21\\or, l + 20 = 21\\or, l = 1mm\\[/tex]

Area of rectangle = [tex]lb = 1(20) = 20mm^{2}[/tex]

Find the area of the figure.

Answers

Answer:

area = 164

Step-by-step explanation:

Divide the square into 2 pictures.

; Square 1 = 5×2 = 10

Square 2 = 14×11 (11 from 16-5 )

so, square 2 = 154

all of area = 154+10 = 164

hope it helps ☺️

Find the 10th term in the
following sequence:
-21, -27, -33, -39,

Answers

-75 is the answer for the tenth term
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