Mia’s average driving speed is 6 kilometers per hour faster than Kirk’s. In the same length of time it takes Mia to drive 558 kilometers, Kirk drives only 522 kilometers. What is Mia’s average speed?

Answers

Answer 1

Answer:

93km/hr

Step-by-step explanation:

Using the formula Speed = Distance/Time. From the formula we can substitute for time as shown;

Time = Distance/Speed

Let the distance and speed  travelled by Mia be Dm ans Ds respectively

Distance travelled by Kirk be Km and and Ks respective.

Time taken be Mia to travel Tm = Dm/Sm

Time taken be Kirk to travel Tk = Dk/Sk

Since it takes the same length of time for both of them to travel, then Tm = Tk. Hence Dm/Sm = Dk/Sk

Given parameters

Dm = 558 kilometers

Dk = 522 kilometres

If Mia’s average driving speed is 6 kilometers per hour faster than Kirk’s, then Mia's driving speed Sm = 6 + Sk

Required

Mia’s average speed (Sm)

Since Dm/Sm = Dk/Sk

Substituting the given values to get Sk first we have;

558/6+Sk = 522/Sk

Cross multiply

558Sk = 522(6+Sk)

open the parenthesis

558Sk = 3132 + 522SK

558Sk-522Sk = 3312

36Sk =3132

Sk = 3132/36

Sk =87km/hr

SInce Sm = 6+Sk

Sm = 6+87

Sm = 93km/hr

Hence Mia's average speed is 93km/hr


Related Questions

A pair of opposite vertices of a square is (1, 2) and (3,4). Find the coordinates of the remaining
vertices of the square.​

Answers

Answer:

(3, 2) and (1, 4)

Step-by-step explanation:

Plot the two points on a graph.

The other two points are (3, 2) and (1, 4).

To do this with algebra, it takes a few steps.

The diagonals of a square are perpendicular and bisect each other. You are given opposite vertices, so first, find the midpoint of that diagonal.

((1 + 3)/2, (2 + 4)/2) = (2, 3)

The midpoint of the diagonal is (2, 3).

This diagonal has slope 1 and y-intercept 1, so its equation is

y = x + 1

The perpendicular bisector has equation

y = -x + 5

The two vertices we are looking for, lie in a circle whose center is the midpoint of the diagonals, (2, 3), and whose radius is half of the diagonal.

Use Pythagoras to find the diagonal's length.

2^2 + 2^2 = c^2

c^2 = 8

c = sqrt(8) = 2sqrt(2)

Half of the diagonal is sqrt(2). This is the radius if the circle.

The equation of the circle is

(x - 2)^2 + (y - 3)^2 = (sqrt(2))^2

(x - 2)^2 + (y - 3)^2 = 2

The points of intersection of this circle and the second diagonal are the two vertices you are looking for.

System of equations:

(x - 2)^2 + (y - 3)^2 = 2

y = -x + 5

Use substitution and substitute y with -x + 5 in the equation of the circle.

(x - 2)^2 + (-x + 5 - 3)^2 = 2

(x - 2)^2 + (-x + 2)^2 - 2 = 0

x^2 - 4x + 4 + x^2 - 4x + 4 - 2= 0

2x^2 - 8x + 6 = 0

x^2 - 4x + 3 = 0

(x - 3)(x - 1) = 0

x - 3 = 0   or x - 1 = 0

x = 3 or x = 1

Now we find corresponding y values.

y = -x + 5

x = 3

y = -3 + 5 = 2

This gives us (3, 2).

y = -x + 5

x = 1

y = -1 + 5 = 4

This gives us (1, 4).

Answer: (1, 4) and (3, 2)

PLEASE ANSWER!!! Select the correct answer from each drop-down menu. Consider the function f(x) = 3x + 1 and the graph of the function g(x) shown below.

Answers

Function transformation involves changing the position of a function.

The graph of g(x) is the graph of f(x) translated 2 units right, and [tex]\mathbf{g(x) = 3(x -2) + 1}[/tex]

The function is given as:

[tex]\mathbf{f(x)=3x + 1}[/tex]

The graph of g(x) passes through (2,1) and (0,-5).

Start by calculating the slope (m)

[tex]\mathbf{m = \frac{y_2 - y_1}{x_2 - x_1}}[/tex]

So, we have:

[tex]\mathbf{m = \frac{-5-1}{0-2}}[/tex]

[tex]\mathbf{m = \frac{-6}{-2}}[/tex]

[tex]\mathbf{m = 3}[/tex]

The equation is then calculated as:

[tex]\mathbf{g(x) = m(x -x_1) + y_1}[/tex]

So, we have:

[tex]\mathbf{g(x) = 3(x -2) + 1}[/tex]

By comparing [tex]\mathbf{f(x)=3x + 1}[/tex] and [tex]\mathbf{g(x) = 3(x -2) + 1}[/tex]

The graph of f(x) is shifted 2 units to the right

Read more about function transformation at:

https://brainly.com/question/13810353

The house Trevor's family lives in has 6 people (including Trevor) and 3 bathrooms. In the past month, each person showered for an average of 480 minutes and used an average 72 liters of shower water (over the entire month). Water costs 0.20 dollars per liter.

Answers

Answer:

$86.40

Step-by-step explanation:

The house Trevor's family lives in has 6 people (including Trevor) and 3 bathrooms. In the past month, each person showered for an average of 480 minutes and used an average 72 liters of shower water (over the

entire month). Water costs 0.20 dollars per liter.

How much did Trevor's family pay per minute on shower water

Average person=72 liters of water

6 people=72*6= 432 liters

Each person = 480 minutes

6 people=480*6= 2,880 minutes

Water=$0.20 per liter

Total cost of water= 432 * 0.20

= $86.40

Answer:

o.o3

Step-by-step explanation:

Which geometric figure has 120 rotational symmetry?

Answers

Answer:

Triangle

Step-by-step explanation:

Has 120° degrees of rotation and measure of the central angle and has 3-fold rotational symmetry

Solve for x. This is for my math class, and I’ve been stuck on this for a while. Please help!

Answers

Answer:

Hey there!

Angles in a triangle add to 180 degrees.

24+134+2x=180

158+2x=180

2x=22

x=11

Let me know if this helps :)

Tell me the answer
69:?::89:36​

Answers

?????????????????????????????????????

how many seconds are there in a month of 30 days express it in scientific notation​

Answers

Answer: 2.592 x 10^6 seconds

Explanation:

There are 3600s in 1 hr

And 24hrs in 1 day which mean

There are 3600 x 24 = 86400s in 1 day

And one month = 30 days

86400 x 30 = 2, 592, 000s in 1 month

Write in scientific notation:

2, 592, 000 = 2.592 x 10^6

Recall the equation that modeled the average number of non-defective refrigerators produced per hour in terms of x, the number of hours of production per day: Now, open the graphing tool and graph the equation. Use the pointer to determine how many hours of production there are in a day if the average number of non-defective refrigerators produced per hour is 15.

Answers

Answer:

The graph representing the above equation is attached below.

Step-by-step explanation:

The equation that modeled the average number of non-defective refrigerators produced per hour in terms of x, the number of hours of production per day is:

[tex]y=\frac{196-3x}{x}[/tex]

Simplify the expression as follows:

[tex]y=\frac{196-3x}{x}[/tex]

[tex]y=\frac{196}{x}-3[/tex]

The graph representing the above equation is attached below.

On moving the pointer to y = 15, it was determined that the value of x was 10.89.

The point is also plotted on the graph

Answer:

There would be 11 hours of production in a day.

Step-by-step explanation:

X+2/x-2 - x+3/x-1 solve ​

Answers

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[tex]x+\frac{2}{x} -2-x+\frac{3}{x} -1[/tex]

[tex]= \frac{-3x + 5}{x}[/tex]

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Hope this helped you.

Could you maybe give brainliest..?

❀*May*❀

multiple choice
a. 126 pie cm^3
b. 84 pie cm^3
c. 504 pie cm*3

Answers

Answer:

a. 126 pie cm^3

Step-by-step explanation:

Area of a circle = pi*r²

Volume = area*height

(pi*r²)*14

Since your answers are with Pi omit the Pi and times 3² * 14 = 126 pie cm³

Answer:

A. 126pi cm^3

Step-by-step explanation:

The volume of a cylinder can be found using the following formula.

[tex]v=\pi r^2 h[/tex]

First, we must find the radius. The radius is half of the diameter.

[tex]r=\frac{d}{2}[/tex]

The diameter of the cylinder is 6 cm.

[tex]r=\frac{6cm}{2}[/tex]

[tex]r= 3cm[/tex]

The radius is 3 cm.

Now, we can substitute values into the formula.

[tex]v=\pi r^2 h[/tex]

[tex]r= 3cm\\h=14 cm[/tex]

[tex]v=\pi (3cm)^2*14 cm[/tex]

Evaluate the exponent.

[tex](3cm)^2=3cm*3cm=9cm^2[/tex]

[tex]v=\pi*9cm^2*14cm[/tex]

Multiply 9 cm^2 and 14 cm

[tex]9 cm^2*14cm=126cm^3[/tex]

[tex]v=\pi*126cm^3[/tex]

The answer choices are in terms of pi, so we can simply rearrange our answer:

[tex]v=126\pi cm^3[/tex]

The volume of the cylinder is 126pi cubic centimeters and A is the correct answer.

What is the value of x?
7
7 square root 2
14
14 square root 2

Answers

Answer:

14

Step-by-step explanation:

Using the sine ratio in the right triangle and the exact value

sin45° = [tex]\frac{1}{\sqrt{2} }[/tex] , thus

sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{7\sqrt{2} }{x}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )

x = 7[tex]\sqrt{2}[/tex] × [tex]\sqrt{2}[/tex] = 7 × 2 = 14

Answer:

x = 14i hope it helps :)

Step-by-step explanation:

[tex]Hypotenuse = x \\Opposite = 7\sqrt{2} \\\alpha = 45\\\\\Using \: SOHCAHTOA\\Sin \alpha = \frac{Opposite}{Hypotenuse}\\ \\Sin 45 = \frac{7\sqrt{2} }{x} \\\\\frac{\sqrt{2} }{2} = \frac{7\sqrt{2} }{x} \\\\\sqrt{2x} = 14\sqrt{2} \\\\\frac{\sqrt{2x} }{2} = \frac{14\sqrt{2} }{2} \\x = 14[/tex]

I need help ASAP!!

Can someone explain this? And answer it? I am so confused!!

Answers

Answer:

Step-by-step explanation: hope this helps

Convert to slope-intercept from: y-4=9(x-7)

Answers

Answer:

y = 9x - 59

Step-by-step explanation:

y - 4= 9(x-7)

y - 4 = 9x - 63

y - 4 + 4 = 9x - 63 + 4

y = 9x - 59

Answer:

Below

Step-by-step explanation:

● y-4 = 9(x-7)

Multiply 9 by (x-7)

● y-4 = 9x - 63

Add 4 to both sides

● y-4+4 = 9x-63 +4

● y = 9x - 59

there are 400 pages-to be read from a book.yesterday you read 1/4 of the pages. today you read 2/3 of the remains pages from the book.how many pages are left in the book

Answers

Answer:

100 pages

Step-by-step explanation:

Yesterday, there were 400 pages left unread so you read 1/4 * 400 = 100 pages yesterday. Today, there are 400 - 100 = 300 pages left unread so today, you read 2/3 * 300 = 200 pages. This means that there are 300 - 200 =   100 pages left in the book.

PLZ HELP! please answer both if you can!!
1. What is the area of the following triangle in square meters? Do not round your answer. A = a0 m 2

2.What is the average of the two bases in the following trapezoid in feet? 18 ft 11 ft 14.75 ft 22 ft

Answers

Answer:

0.324m^2 ; 18 ft

Step-by-step explanation:

Given the triangle :

Base (b) of triangle = 54cm

Height (h) of triangle = 1.2m

Area(A) of a triangle is given by:

0.5 * base * height

Base = 54cm = 54/100 = 0.54 m

Therefore,

A = 0.5 * 0.54m * 1.2m

A = 0.324m^2

2.) Average of the two bases in the trapezoid :

From the trapezium Given :

Base 1 = 15 feets

Base 2 = 7 yards

1 yard = 3 Feets

Therefore, base 2 in Feets = 7 * 3 = 21 Feets

Average of the two bases :

(21 Feets + 15 Feets) / 2

= 36 Feets / 2

= 18 Feets

Which of the following describes a change in a shape's position or size?
A. reflection symmetry
B. image
O C. transformation
D. rotational symmetry

Answers

Answer:

The correct option is;

C. Transformation

Step-by-step explanation:

In mathematics, transformation refers to the relocation of an object called the pre-image from initial position to another new location at which point the object will be known as the image whereby there is a one to one mapping from each point on the pre-image to the image

The types of transformation includes reflection, rotation, and translation which involve changes in position and dilation, which involves changes in the size of the pre-image.

Please answer these 3 questions for 70 points 1 thanks 5 stars and brainiest

Answers

Answer:

Step-by-step explanation:

Problem 14: Mean 5.5, Range: 5.8

Problem 15: question #1 4, mode: 63

Probelm 16: Median 63, Range:  8.3

Answer:

14: Mean is 5.5 Hours

Range is 7.9 Hours

15: 4 Numbers

Mode is 6.3

16: Median is 6.3

Range is 8.3

Step-by-step explanation:

(I'll edit in the explanations momentarily)

Event A: Flipping heads on a coin #1. Event B: Flipping heads on a coin #2. What is P(A and B)?

Answers

Answer:

coin 1

Step-by-step explanation: i think this is it

Answer:

Heads is a 50, 50 situation. so 1/2 plus 1/2 is 1/4

please help!!!! Use the graph to complete the statement. O is the origin. Ry−axis ο Ry=x: (-1,2)
A. (1, -2) B. (-1, -2) C. (2, -1) D. (-2, -1)

Answers

Answer:  D. (-2, -1)

Step-by-step explanation:

Here we do two reflections to the point (-1, 2).

First, we do a reflection over the line x = y.  Remember that a reflection over a line keeps constant the distance between our point and the given line, so we have that for a pint (x, y), the reflection over the line y = x is:

Ry=x (x, y) = (y, x)

so for our point, we have:

Ry=x (-1, 2) = (2, -1)

Now we do a reflection over the y-axis, again, a reflection over a line keeps constant the distance between our point and the given line, so if we have a point (x,y) and we do a reflection over the y-axis, our new point will be:

Ry-axis (x,y) = (-x, y)

Then in our case:

Ry-axis (2, -1) = (-2, -1)

The correct option is D.

Fill in the blank with a constant, so that the resulting expression can be factored as the product of two linear expressions: 2ab-6a+5b+___

Answers

Answer:

-15

Step-by-step explanation:

In this question, we want to fill in the blank so that we can have the resulting expression expressed as the product of two different linear expressions.

Now, what to do here is that, when we factor the first two expressions, we need the same kind of expression to be present in the second bracket.

Thus, we have;

2a(b-3) + 5b + _

Now, putting -15 will give us the same expression in the first bracket and this gives us the following;

2a(b-3) + 5b-15

2a(b-3) + 5(b-3)

So we can have ; (2a+5)(b-3)

Hence the constant used is -15

How do you solve
n= (2s-1)+(s-1)

Answers

Answer:

n=3s-2

Step-by-step explanation:

Step 1: Remove unnecessary parentheses (2s-1)

Step 2: Collect "Like Terms" (2s+s= 3s)

Last Step: Put them all together (n=3s - 2)

The radius of the circle is increasing at a rate of 1 meter per day and the sides of the square are increasing at a rate of 3 meters per day. When the radius is 3 meters, and the sides are 20 meters, then how fast is the AREA outside the circle but inside the square changing

Answers

Answer:

The area inside the square and outside the circle is changing at a rate of 101.150 square meters per day.

Step-by-step explanation:

According to the statement of the problem, the circle is inside the square and the area inside the square but outside the circle, measured in square meters, is represented by the following formula. It is worth to notice that radius ([tex]r[/tex]) is less than side ([tex]l[/tex]), both measured in meters:

[tex]A_{T} = A_{\square} -A_{\circ}[/tex]

[tex]A_{T} = l^{2}-\pi\cdot r^{2}[/tex]

Now, the rate of change of the total area is calculated after deriving previous expression in time:

[tex]\frac{dA_{T}}{dt} = 2\cdot l\cdot \frac{dl}{dt} -2\pi\cdot r\cdot \frac{dr}{dt}[/tex]

Where [tex]\frac{dl}{dt}[/tex] and [tex]\frac{dr}{dt}[/tex] are the rates of change of side and radius, measured in meters per day.

Given that [tex]l = 20\,m[/tex], [tex]r = 3\,m[/tex], [tex]\frac{dl}{dt} = 3\,\frac{m}{day}[/tex] and [tex]\frac{dr}{dt} = 1\,\frac{m}{day}[/tex], the rate of change of the total area is:

[tex]\frac{dA_{T}}{dt} = 2\cdot (20\,m)\cdot \left(3\,\frac{m}{day} \right)-2\pi\cdot (3\,m)\cdot \left(1\,\frac{m}{day} \right)[/tex]

[tex]\frac{dA_{T}}{dt} \approx 101.150\,\frac{m^{2}}{day}[/tex]

The area inside the square and outside the circle is changing at a rate of 101.150 square meters per day.

Compare the slopes of the linear functions f(x) and g(x) and choose the answer that best describes them.

A. The slope of f(x) is greater than the slope of g(x).

B. The slope of f(x) is less than the slope of g(x).

C. The slope of f(x) is equal to the slope of g(x).

D. The slope of g(x) is undefined ​

Answers

Answer:

The slope of f(x) is equal to the slope of g(x).

Step-by-step explanation:

The question is incomplete. Here is the complete question.

Compare the slopes of the linear functions f(x) and g(x) and choose the answer that best describes them.

a graph of a line labeled f of x passing through 0, negative 1 and 3, 1

x g(x)

0 2

3 4

6 6

Slope is defined as the change of the y axis to the z axis of a plane.

Slope = ∆y/∆x

Slope = y2-y1/x2-x1

For f(x) with coordinates (0, -1) and (3,1)

x1 = 0, y1 = -1, x2 = 3 and y2 = 1

Slope of f(x) = 1-(-1)/3-0

Slope = 1+1/3

Slope = 2/3

For g(x), we will choose any two of the coordinates from the table. Using the coordinates (3,4) and (6,6)

x1 = 3, y1 = 4, x2 = 6 and y2 = 6

Slope of g(x) = 6-4/6-3

Slope of g(x) = 2/3

It can be seen that the value of both slopes are equal. Hence, the slope of f(x) is equal to the slope of g(x) is the correct option.

Answer:

The answer is C. The slope of f(x) is equal to the slope of g(x).

Step-by-step explanation:

Did the test.

please help me

Expand ( p + 6 )( p - 3 )​

Answers

Answer:

(p^2) + 3p - 18

Step-by-step explanation:

Have a nice day!

Answer:

2p+3

Step-by-step explanation:

(p+6)(p-3)

you have to open the brackets i.e

p+p+6-3

add p+p and you get 2p then you  subtract positive 6 from 3 and you get 3

so your answer will be 2p+3

Find b.
Round to the nearest tenth:

Answers

Answer:

always b is equal to 9 is rhdx forum post in is ek of

Answer:

6.7 cm

Step-by-step explanation:

A+B+C=180°

55°+B+82°=180°

B=43°

Using the formulae

(Sin A)/a = (Sin B)/b

(Sin 55)/8 = (Sin 43)/b

b = [8(Sin 43)]/(Sin 55)

b= 6.7 cm

Factorise : x^2-9x-70 Step by Step​

Answers

Answer:

Step-by-step explanation:

x^2 - 9x - 70

we need to find two numbers whose sum is -9 and product id -17

The numbers are -14 and 5

By splitting the middle term,

x^2 - 14x + 5x - 70

= x ( x - 14 ) + 5 ( x - 14 )

( x + 5 ) ( x - 14 )

Hope this helps

Plz mark as brainliest!!!!!

Answer:

Step-by-step explanation:

Sum = -9

Product = -70

Factors = -14 , 5

x² - 9x - 70 = x² + 5x - 14x + (-14) * 5

                  =x(x + 5) - 14(x + 5)

                  = (x + 5)(x - 14)

Suppose that there are two types of tickets to a show: advance and same-day. The combined cost of one advance ticket and one same-day ticket is $65 . For one performance, 25 advance tickets and 35 same-day tickets were sold. The total amount paid for the tickets was 1875 . What was the price of each kind of ticket?

Answers

Answer:

same day = 25

advanced = 40

Step-by-step explanation:

Let a = advanced tickets

s = same day tickets

s+a = 65

25a+35s = 1875

Multiply the first equation by -25

-25s -25a = -1625

Add this to the second equation

25a+35s = 1875

-25a -25s= -1625

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

     10s = 250

Divide each side by 10

10s/10 = 250/10

s =25

Now find a

s+a = 65

25+a = 65

a = 40

Answer: same day = 25

advanced = 40

If a number is divided by 3 or 5, the remainder is 1. If it is divided by 7, there is no remainder. What number between 1 and 100 satisfies the above conditions?

Answers

Answer:

91

Step-by-step explanation:

Look at multiples of 7 and you’ll find 91.

91 dived by 3 is 30 with a remainder of 1.

91 divided by 5 is 18 with a remainder of 1.

91 divid by 7 is 13 with no remainder.

91 is the number between 1 and 100 satisfies the above conditions

What is Number system?

A number system is defined as a system of writing to express numbers.

Given that a number is divided by 3 or 5, the remainder is 1.

If it is divided by 7, there is no remainder

We need to find the number between 1 and 100 which satisfies the given conditions.

Let us consider 91.

When 91 is divided by 3 we get 30 and 1 as remainder.

91 divided by 5 is 18 with a remainder of 1.

91 divided by 7 is 13 it does not have any remainder or remainder is zero.

Hence, 91 is the number between 1 and 100 satisfies the above conditions

To learn more on Number system click:

https://brainly.com/question/22046046

#SPJ2

Simplify 2√28 - 3√63. I will give BRAINLIEST!

Answers

[tex]2\sqrt{28}-3\sqrt{63}=2\sqrt{4\cdot7}-3\sqrt{9\cdot7}=4\sqrt7-9\sqrt7=-5\sqrt7[/tex]

if "f" varies directly with "m," and f = -19 when m = 14, what is "f" when m = 2

Answers

Answer:

f = - [tex]\frac{19}{7}[/tex]

Step-by-step explanation:

Given f varies directly with m then the equation relating them is

f = km ← k is the constant of variation

To find k use the condition f = - 19 when m = 14, thus

- 19 = 14k ( divide both sides by 14 )

- [tex]\frac{19}{14}[/tex] = k

f = - [tex]\frac{19}{14}[/tex] m ← equation of variation

When m = 2, then

f = - [tex]\frac{19}{14}[/tex] × 2 = - [tex]\frac{19}{7}[/tex]

Other Questions
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