Thirty years ago Mike McNamara cycled 445.0km in 12 hours – a new British men’s record at that time. In the same time trial Beryl Burton (who died last year) completed 446.2km.

How much faster was Beryl Burton’s average speed than Mike McNamara’s (in metres per hour)?

Answer:

It will weigh 10 pounds per foot

Answer:

[tex]k = 40[/tex]

Step-by-step explanation:

Given

The attached graph

Required

Calculate the constant of proportionality.

Represent the required constant with k.

Such that:

[tex]k = \dfrac{y}{x}[/tex]

Pick any two corresponding values of x and y

[tex](x,y) = (1,40)[/tex]

This means that:

[tex]x = 1\ and\ y = 40[/tex]

[tex]k = \dfrac{y}{x}[/tex] becomes

[tex]k = \frac{40}{1}[/tex]

[tex]k = 40[/tex]

Answer:

3.5

Step-by-step explanation:

Answer:

All parallelograms have 4 equal sides

Answer:

I don't know

Step-by-step explanation:

thanks for the points again.

Answer:

66 and 52?

Step-by-step explanation:

Answer:

Let x be the discounting price of a surfing lessons per person

Let y be the discounted price of a surfing lessons per person

The cost of taking a surfing lesson and go parasailing is $130

x + y = 130--------------(i)

25 people take

Surfing lessons, and 30 people go parasailing and a total of $3,650 is collected

25x + 30y = 3650--------------(ii)

We solve for y using equ (i):

y = 130 - x ------------(iii)

Substitute equ (iii) to equ (ii) and solve for x

25x + 30(130 - x) = 3650

25x + 390 - 30x = 3650

-5x = -250

-x = 50

We solve for y using equ (iii):

y = 130 - x

y = 130 - 50

y = 80

So, the discounted price to take a surfing lesson is $50 and the discounted price to go parasailing is $80

Answer:

D. [tex] x = \frac{5*\sqrt{2}}{2} [/tex]

Step-by-step explanation:

Reference angle = 45°

Length of Opposite side = x

Hypotenuse length = 5

Applying trigonometric ratio, we have:

[tex] sin(45) = \frac{x}{5} [/tex]

Multiply both sides by 5

[tex] 5*sin(45) = \frac{x}{5}*5 [/tex]

[tex] 5*sin(45) = x [/tex]

[tex] 5*\frac{1}{\sqrt{2}} = x [/tex] (sin 45 = 1/√2)

[tex] \frac{5}{\sqrt{2}} = x [/tex]

Rationalize

[tex] \frac{5*\sqrt{2}}{\sqrt{2}*\sqrt{2}} = x [/tex]

[tex] x = \frac{5*\sqrt{2}}{2} [/tex]

Answer:

20

Step-by-step explanation:

Answer:

LM = 20

Step-by-step explanation:

To find LM we have. to subtract MN from LN

So 23 - 3 = 20

Answer:

r = 16.5

Step-by-step explanation:

Move the subtraction over to the over side first

0.1r - 1 = 0.65

It becomes addition on the right side

0.1r = 0.65 + 1

Move the multiplication over to the over side first

0.1r = 1.65

It becomes division on the right side

r = 1.65 / 0.1

r = 16.5

Answer:0.1r-1=0.65  (85% sure this is the answer

Answer:

[tex]z = x + y \\ \huge \boxed{x = z - y}[/tex]

I guess I was wrong

:)

oopsss

Answer:

4 hours.

Step-by-step explanation:

Okay, so they leave the same port. Since they are traveling at the same rate at 24mph, in one hour they will each be 24 miles from the port. Since they are going in opposite directions, they will be 24+24= 48 miles apart. Let another hour pass. They each go 24 more miles from the port so add another 48 to their distance apart. Now their distance is 96 miles apart. Let a third hour pass. Add 48. Now their distance is 144 miles apart. Let the fourth and final hour pass. Now they are 192 miles apart. So, it'll take them  4 hours to be 192 miles apart.

A visual way to interpret this problem is on a number line. We'll have steamer A going to the right of our origin 0 (the port) and steamer B going left. After one hour, steamer A will be at 24 on the number line, and steamer B will be at -24. the distance between these two points is 48. If you continue with the second, third and fourth hours they will each be going 24 points further from the origin, making their distance grow further and further apart by 48 points each hour.

I also completed the table for you :)

Hope this helps.

Answer: 900 times

Step-by-step explanation:

1 kilometer = 1000 meters

1.8 kilometers = 1000 × 1.8

1.8 kilometers = 1800 meters

2 meters = 1 click

1800 meters = 1800 ÷ 2

1800 meters = 900 clicks

The wheel will click 900 times when Ty walks 1.8 kilometers.

Hope this helped!

Answer:

It will click 900 times

Step-by-step explanation:

We know that there are 1000 meter in 1 km.

So 1.8 km is basically

1.8*1000=1800

So 1800 meters

And every 2 meters it clicks once

So 1800/2=900

So 900 times in 1.8 km

Answer:

(5,-1)

x=5

y= -1

Step-by-step explanation:

To solve this we're going to solve for one variable in either equation

so we have

x+y=4

We can subtract y and 4 from both sides to get

x-4= -y

Then divide by -1 so that y will be a positive number

-x+4=y

We can plug this in for y in the other equation

2x -2(-x+4)=12

Distribute the -2 and get

2x+2x-8=12

Combine like terms and add 8 to get

4x=20

divide and get x=5

Plug in x=5 into the first equation to get

5+y=4

subtract 5 to get y= -1

Our answer is (5,-1) or x=5 y= -1

I checked this on desmos and the math is correct

Answer:

The solution to the system of equations will be:

x = 5, y = -1

Step-by-step explanation:

Given the system of equations

x + y = 4

2x - 2y = 12

Isolate x for x + y = 4:    x = 4 - y

substitute x = 4 - y in the equation 2x - 2y = 12

2(4-y) - 2y = 12

8 - 2y - 2y = 12

8 - 4y = 12

4y = 8 - 12

4y = -4

divide both sides by 4

4y/4 = -4/4

y = -1

substitute y = -1 in x + y = 4

x + y = 4

x + (-1) = 4

x - 1 = 4

x = 5

so

(x, y) = (5, -1)

Therefore, the solution to the system of equations will be:

x = 5, y = -1

Answer:

Yes, -125

Step-by-step explanation:

Answer:

-189

Step-by-step explanation:

[tex]\int^9_0 \ |6x-6| \ dx[/tex]

⇒ 6x - 6 = 0

6x = 6

x = 1

[tex]\int^9_0 \ (6x- 6 ) \ dx = \int^9_0 \ -(6x - 6) \ dx[/tex]

[tex]= - \Big[ \dfrac{6x^2}{2}- 6x \Big]^9_0[/tex]

[tex]= - \Big[ \dfrac{6(9)^2}{2}- 6(9) - 0 \Big][/tex]

[tex]= -(243 - 54 - 0 )[/tex]

= -189

Answer:

$125

Step-by-step explanation:

To solve this, we need to find 2.5% of 5,000. To do this, we multiply 5,000 by .025. This gets us 125. That means you earn $125 worth of interest in one year.

Answer:

Monday: 90

Tuesday: 24

Step-by-step explanation:

The baker makes 90 muffins on Monday. The baker makes 24 muffins on Tuesday.

Answer:

Let's go step-by-step ⇒

[tex]\frac{10x + 4}{7} = 8[/tex]

= [tex](\frac{7}{1})\frac{10x+4}{7} = \frac{8}{1}(\frac{7}{1})[/tex]

= [tex]10x+4=56[/tex]

= [tex]10x = 52[/tex]

= [tex]x = 5.2[/tex]

Your answer is x = 5.2

I hope this helps!

- sincerelynini

Answer:

D. 8x³ + 4x⁷ - 3x³ + 3x² - 2x + 9

Step-by-step explanation:

(8x⁸ - 9x³ + 3x² + 9) + (4x⁷ + 6x³ - 2x)

Apply distributive property to eliminate parentheses

8x⁸ - 9x³ + 3x² + 9 + 4x⁷ + 6x³ - 2x

Collect like terms

8x⁸ + 4x⁷ - 9x³ + 6x³ + 3x² - 2x + 9

8x³ + 4x⁷ - 3x³ + 3x² - 2x + 9

Answer:

Step-by-step explanation:

1) slope = 3 ; y-intercept = 1

y = mx + b

y = 3x + 1

0 = 3x + 1 -y

-1 = 3x - y

ANS: 3x - y = -1

2)   Passing through (0,2), slope = -4

y - y₁ = m(x -x₁)

y - 2 = -4(x - 0)

y - 2 = -4x

4x + y - 2 = 0

Ans: 4x + y = 2

3)Passing through (-1,3) and (1,1)

Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

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

m= -1 ; (-1 , 3)

y - y₁ = m(x -x₁)

y - 3 = (-1)(x - [-1] )

y -3 = (-1)(x +1 )

y - 3 = -x - 1

x +  y -3 = -1

x +y = -1 + 3

Ans: x + y = 2

4) Passing through (1,3), slope = 1/2

y - y₁ = m(x -x₁)

[tex]y - 3 = \frac{1}{2}(x - 1)\\\\y - 3 = \frac{1}{2}x - \frac{1}{2}\\\\[/tex]

Multiply the equation by 2

[tex]2*y - 2*3 = 2*\frac{1}{2}x - 2*\frac{1}{2}\\\\2y - 6 = x - 1\\[/tex]

2y - 6 +1 = x

2y - 5 = x

    -5 = x - 2y

Ans: x - 2y = -5

5)  Passing through (1/2,1) and (4,2)

Slope = [tex]\frac{2-1}{4-\frac{1}{2}}[/tex]

         [tex]= \frac{1}{\frac{7}{2}}\\\\= \frac{2}{7}[/tex]

m = 2/7 ; (4 , 2)

y - y₁ = m(x -x₁)

[tex]y - 2 = \frac{2}{7}(x - 4)\\\\7y - 7*2 = 7*\frac{2}{7}(x - 4)\\\\7y - 14 = 2(x -4)\\\\7y - 14 = 2x - 8\\\\[/tex]

7y - 14 + 8 = 2x

7y - 6 = 2x

Ans:  2x - 7y = -6

Answer:

y=1.125×8 or y=1.125×24

Answer:

925.04cm²

Step-by-step explanation:  

Curved surface area of a cylinder = 2πrh

If the sum of the radius of the base and height of the cylinder is 21 cm, then;

r + h = 21

r = 21-h..... 1

The curved surface area is expressed according to the formula

CSA =  2πrh

Substitute the value of CSA given into the formula

616 = 2πrh ....2

Substitute equation 1 into 2;

]616 = 2π(21-h)h

616 = 2π(21h-h²)

Note that π = 3.14

616 = 42(3.14)h - 2(3.14)h²

616 = 131.88h - 6.28h²

98.09 = 21h - h²

h²-21h+98.09 = 0

h = 21±√21²-4(98.09)/2

h = 21±√441-392.36/2

h = 21±√48.64/2

h = 21±6/97/2

h = 21+6.97/2 and 21-6.97/2

h = 27.97/2 and 14.03/2

h = 13.985 and 7.015

Recall that r = 21-h

r = 21 - 13.985

Substitute r = 7.015  into the total surface area of the cylinder

The total surface area = 2πrh + 2πr²

The total surface area = 616 + 2(3.14)7.015²

The total surface area = 616 + 309.04

The total surface area = 925.04

Hence the total surface area of the cylinder is 925.04cm²

Answer:

it would cost £15

Step-by-step explanation:

12 ÷ 4 = 3

3 × 5 = 15

Answer:

y = -x + 7

General Formulas and Concepts:

Pre-Algebra

Equality Properties

Algebra I

Slope-Intercept Form: y = mx + b

Step-by-step explanation:

Step 1: Define

[Standard Form]   5x + 5y = 35

Step 2: Rewrite

Find slope-intercept form.

Answer:

$55.25

1,300×0.0425=$55.25