Scott trained for the marathon.
On day 1, he took 70 min to run 10 km.
On day 10, he took 2 h 40 min to run 20 km.
On day 20, he took 4 h 15 min to run 30 km.
a) What was Scott's running rate, in minutes per kilometre,
for each day?
i) Day 1 ii) Day 10 iii) Day 20
b) What do you think Scott's running rate, in minutes per
kilometre, might be for the 44 km of the marathon?
How long do you think it will take him? Explain.

Answer:

[tex]\mathrm{Distance\:between\:}\left(1,\:0\right)\mathrm{\:and\:}\left(9,\:15\right)=\:17[/tex]

Step-by-step explanation:

Given the points

[tex]\mathrm{Compute\:the\:distance\:between\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]

[tex]\mathrm{The\:distance\:between\:}\left(1,\:0\right)\mathrm{\:and\:}\left(9,\:15\right)\mathrm{\:is\:}[/tex]

[tex]=\sqrt{\left(9-1\right)^2+\left(15-0\right)^2}[/tex]

[tex]=\sqrt{8^2+\left(15-0\right)^2}[/tex]

[tex]=\sqrt{8^2+15^2}[/tex]

[tex]=\sqrt{64+225}[/tex]

[tex]=\sqrt{289}[/tex]

[tex]=\sqrt{17^2}[/tex]

[tex]=17[/tex]                   ∵  [tex]\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{a^n}=a[/tex]

Therefore,

[tex]\mathrm{Distance\:between\:}\left(1,\:0\right)\mathrm{\:and\:}\left(9,\:15\right)=\:17[/tex]

Answer:

[tex]m=\frac{1}{4}[/tex]

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

Point (-8, -1)

Point (-12, -2)

Step 2: Find slope m

Answer:

The area of the square is 2.25cm

Step-by-step explanation:

Here's what we know:

-Each letter represent a side

-A square is made up of 4 congruent sides

-To find the area of a square you need 2 sides

-We have 2 sides (A and B)

Now we can solve:

If 3cm is the length of A and B together, then we can determine that separately The sides are 1.5cm. We can then multiply 1.5 by itself to get 2.25cm.

Hope this helps :)

Answer:

sorry if its incorrect

Step-by-step explanation:

I think its 18:54

Answer:

Part A: 24

Part b: 384

Part c: larger over the interval

Step-by-step explanation:

Answer:

x - 6

Step-by-step explanation:

Answer:

14 and 15

Step-by-step explanation:

Answer:

20°

Step-by-step explanation:

the sum of the angles gives 180°

20+2x+6x=180

20+8x=180°

8x=180-20

x=160°÷8°

x=20°

thank you!

Answer:

c) 20

Step-by-step explanation:

on edge 2021 || pls mark brainliest

Answer:

Solve the equation so it is in the y=mx+b form.

Step 1. 6x+9y = 216

Step 2. 9y = -6x+216

Step 3. y = -6/9x+24

Step 4. Simplify/Reduce to get y = -2/3x+24

Since it is Parallel then the slope is the same so the slope is -2/3x.

The slope of line parallel to line with equation → 6x + 9y = 216 is

m = -2/3.

Parallel lines are those lines that are equidistant from each other and never meet, no matter how much they may be extended in either directions.

Given is a line which is parallel to a line whose equation is 6x + 9y = 216.

We know that the general equation of straight line is -

y = mx + c             ... Eq [ 1 ]

where 'm' represents the slope of the line.

The equation of line given -

6x + 9y = 216.

Rearranging it -

9y = - 6x + 216

y = (-6/9)x + (216/9)

y = (-2/3)x + 24              ... Eq [ 2 ]

Comparing Eq[2] with Eq[1], we get -

m = -2/3

Therefore, the slope of the line with equation → 6x + 9y = 216 is -2/3.

Two parallel lines have same slope. Hence, the slope of line parallel to

line with equation → 6x + 9y = 216 is -2/3

Therefore, the slope of line parallel to line with equation →

6x + 9y = 216 is -2/3.

To solve more questions on Straight lines, visit the link below-

https://brainly.com/question/17986304

#SPJ2

Answer:

45 candidates are expected to be rejected

Step-by-step explanation:

Here, we want to calculate the number of candidates to be rejected

The number of candidates to be rejected can be calculated from;

100% - (28% + 12%) = 60%

So 60% of the 75 interviewed are to be rejected

Thus, we have

60/100 * 75

= 45

The number of candidate expected to be rejected is 45 if the 12% of candidates can be selected and 28% of Canada can be put on hold for the next hiring date.

It is defined as the ratio of two numbers expressed in the fraction of 100 parts. It is the measure to compare two data, the % sign is used to express the percentage.

We have:

A walk in interview 12% of Candidates can be selected and 28% of Canada can be put on hold for the next hiring date if 75 candidates are interviewed.

Let's suppose total candidate is 100%

So,

= 100 - (12+28)

= 60%

Number of candidate expected to be rejected:

= 60% of 75

= (60×75)/100

= 45

Thus, the number of candidate expected to be rejected is 45 if the 12% of candidates can be selected and 28% of Canada can be put on hold for the next hiring date.

Learn more about the percentage here:

brainly.com/question/8011401

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Answer:

(B). 15.75

Step-by-step explanation:

If Kristens dog weighs 2.5 pounds less, then you just have to subrtact 2.5 from 18.25

The answer is B. 15.75 pounds. Kristen's dog weighs 2.5 pounds less than Milo's dog which is 18.25. So, all you have to do is subtract 2.5 from 18.25. 18.25 - 2.5 = 15.75.

Answer:

[tex]\frac{24}{5}[/tex]

Step-by-step explanation:

Answer:

y = - 24/5

Step-by-step explanation:

Answer:

107

Step-by-step explanation:

(x - 79)° + (x - 45)° = 90°

2x - 124 = 90

2x = 214

x = 107

Answer:

Cherries cost $2.50 per pound

Yes, it is constant.

Weight would go on the x-axis and the cost would go on the y-axis.

The two points are (2, 5) and (3, 7.5)

5 pounds of cherries would cost $12.50. To solve the problem I multiplied the 5 pounds by 2.5, the cost per pound to find the cost.

Step-by-step explanation:

$5 for 2 pounds and $7.50 for 3 pounds can be turned into the points (2, 5) and (3, 7.5).

To find the cost per pound, input the two points into the slope formula: [tex]\frac{y2-y1}{x2-x1}[/tex]

[tex]\frac{7.5-5}{3-2}[/tex]

Solve:

7.5 - 5 = 2.5

3 - 2 = 1

[tex]\frac{2.5}{1}[/tex] = 2.5

The cost of cherries per pound is $2.50. This is our slope.

The equation that represents the cost of cherries for x amount of pounds is:

y = 2.5x

To find how much 5 pounds of cherries would cost, replace x with 5 in the equation:

y = 2.5(5)

y = 12.5

5 pounds of cherries would cost $12.50.

I hope this helps :)

Answer:

[tex]6c-8[/tex]

Step-by-step explanation:

We have:

[tex]-(2c+8)+8c=[/tex]

[tex]-2c-8+8c=\\[/tex]

[tex]6c - 8[/tex]

Answer:

169

Step-by-step explanation:

3(4)+1

=12+1

=13

f(g(4))

f(x)=x^2 ---- (13)^2

=13x13

=169

Answer:

hmm, let me think some more

Step-by-step explanation:

Answer:

164

Step-by-step explanation:

65+65=130

17+17=34

130+34=164

Answer:

You will need 164 feet of fencing.

Step-by-step explanation:

Add up 17+17+65+65 or follow along to the perimeter formula to get your answer of 164 feet.

Answer:

False

True

True

False

Step-by-step explanation:

Answer:true true true false

Step-by-step explanation: did it in class

Answer: D, F, G / 4, 6, 7

Step-by-step explanation:

We have the following equations:

5 + 3x - 2 and x + 2(x+1) + 1

Before checking the statements. Let's solve the syste of equations:

5 + 3x - 2 = x + 2(x+1) + 1

5 + 3x - 2 = x + 2x+2 + 1

3x + 3 = 3x + 3

Both equations are equivalent. Now, let's judge the statements:

1. The expressions are only equivalent when evaluated with odd values.

Given that the both expression are the same, the expressions are equivalent for ALL values.

Therefore, the statement IS FALSE ❌

2. The expressions are only equivalent for x=3 and x=7.

Given that the both expression are the same, the expressions are equivalent for ALL values, not only x=3 and x=7.

Therefore, the statement IS FALSE ❌

3. The expressions should have been evaluated with one odd value and one even value.

If two expressions are equivalent, they should be equivalent for ALL values. Sometimes, evaluating just one odd and one even value isn't enough. That's why the best approach is to solve the system of equations.

Therefore, the statement IS FALSE ❌

4. The expressions have equivalent values when x=6.

Given that the both expression are the same, the expressions are equivalent for x=6 (And all the real values too).

Therefore, the statement IS TRUE ✅

5. When x=0, the first expression has a value of 3 and the second expression has a value of 4.

Given that BOTH expressions are equvalent, they have the same value when x=0, which is 3.

Therefore, the statement IS FALSE ❌

6. The expressions have equivalent values for any value of x.

Given that the both expression are the same, the expressions are equivalent for ALL values of x.

Therefore, the statement IS TRUE ✅

7. When x=10, both expressions have a value of 33

Given that the both expression are the same, the expressions are equivalent for ALL values of x. That's why when x=0, both expressions have a value of 33.

Therefore, the statement IS TRUE ✅

Answer:

Y = -3/2x + 5

Step-by-step explanation:

Slope (rise/run) is -3/2 and the y - intercept is 5.

Hope this helps. Pls give brainliest.

Answer:

I think so it is false

Hope it helps you

Usual speed is given by :

[tex]s = \dfrac{45\times 60}{35} \ mph\\\\s=77.14 \ mph[/tex]

Now, we want to reach job exactly at 10 : 00 .

So, time taken is , t = 10:00 - 09:30

t = 30 minutes = 0.5 hours .

New speed is :

[tex]s'= \dfrac{45}{0.5} = 90 \ mph[/tex]

Therefore, increase in speed is ( 90 - 77.14 ) = 12.86 mph.

Hence, this is the required solution.

Answer:

0.88, 8.08, 8.80

2.4, 2.49, 3.71, 3.87, 4.92

Step-by-step explanation:

By logic.

Or mathematically speaking, if x is greater than y, means that x-y > 0.

Answer:

Of course it doesn't work, 3 x 24 = 72, not 32 (3 tens and 2 ones)

Step-by-step explanation:

This method is similar to decomposition, but it doesn't work. The problem is that she is mixing multiplication, division and addition all together without any sense at all. The way decomposition works is as follows.

Examples of decomposition:

first you can multiply 3 x 4 = 12

then 3 x 20 = 60

add them and you get 72

for example: 6 x 122

6 x 2 = 12

6 x 20 = 120

6 x 100 = 600

add them together = 732

another example: 9 x 356

9 x 6 = 54

9 x 50 = 450

9 x 300 = 2700

add them to get 3,204

Answer:

c = [tex]\frac{5}{2}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula and equate to [tex]\frac{1}{2}[/tex]

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

with (x₁, y₁ ) = (5, 4) and (x₂, y₂ ) = (2, c)

m = [tex]\frac{c-4}{2-5}[/tex] = [tex]\frac{c-4}{-3}[/tex] , then

[tex]\frac{c-4}{-3}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

2(c - 4) = - 3

2c - 8 = - 3 ( add 8 to both sides )

2c = 5 ( divide both sides by 2 )

c = [tex]\frac{5}{2}[/tex]

Answer:

C (-6,-8)

good luck buddie

Answer:

(-6, -8)

Step-by-step explanation:

Answer: