Find the slope, unit rate, and equation of y. Thanks.

Susie plans to run 2 miles per day the first week and then increase the daily distance by a half a mile each of the following we

AlekseyPX

Due to length restrictions, we kindly invite to see the explanation below to know the answer with respect to each component of the question concerning linear equations.

<h3>How to determine a linear equation describing the daily distance of a runner</h3>

In this question we need to derive an expression of the daily distance as a function of time. Now we proceed to complete the components:

Linear equations have an independent variable (t - time) and a dependent variable (x - daily distance).
We notice that the daily distance increases linearly in time, then then we have the following pattern:

t 1 2 3 4 5 6
x 2 2.5 3 3.5 4 4.5
The equation that represents the n-th term of the sequence is x(n) = 2 + 0.5 · (n - 1).
The week when Susie will run 10 miles per day is:

10 = 2 + 0.5 · (n - 1)
8 = 0.5 · (n - 1)
n - 1 = 16
n = 17

Susie will run 10 miles per day in the 17th week.
It is not reasonable to think that pattern will continue indefinitely as it is witnessed in the difficulties experimented by fastest runners in the world to increase their peak speeds.
A marathon has a distance of 26 miles, then we must solve the following equation:

26 = 2 + 0.5 · (n - 1)
24 = 0.5 · (n - 1)
48 = n - 1
n = 49

Susie should start her training 49 weeks before the marathon.

To learn more on linear equation: brainly.com/question/11897796

#SPJ1

7 0

2 years ago

On blueprint of a house, 48 millimeters represents 9 meters. The actual length of the living room is 6 meters. What is its lengt

Temka [501]

The blueprint length (b) will be
.. (6 m)/(9 m) = b/(48 mm)
.. b = (48 mm)*2/3
.. b = 32 mm

8 0

4 years ago

What is the GCF of 40 and 21

trasher [3.6K]

40 and 21 do not have common factors, except for one. So the answer is 1.

5 0

3 years ago

Read 2 more answers

In ANOP, NP is extended through point P to point Q,

kompoz [17]

Answer:

x = 10

Step-by-step explanation:

Form the information given, we can deduce that:

m<OPQ is an exterior angle of ∆NOP = (6x - 15)°

m<PNO = (2x + 18)° and m<NOP = (2x - 13)° are both interior angles that are opposite to the exterior angle.

Therefore, based on the exterior angle theorem:

m<OPQ = m<PNO + m<NOP

(6x - 15)° = (2x + 18)° + (2x - 13)°

Solve for x

6x - 15 = 2x + 18 + 2x - 13

6x - 15 = 4x + 5

6x - 15 - 4x = 4x + 5 - 4x (Subtraction property of equality)

2x - 15 = 5

2x - 15 + 15 = 5 + 15 (addition property of equality)

2x = 20

2x/2 = 20/2 (division property of equality)

x = 10

8 0

3 years ago

Find the surface area of the composite solid.

Kaylis [27]

Hey there!

To find the surface area of this solid, we will want to find the surface area of the two 3d shapes we are given and then add them.

SQUARE PRISM

For the square prism, we want to find the area of the front, back, two sides, top, and bottom.

FRONT AND BACK

As we can see, one side length for the front and back is 5. The one that goes upward is 4. If we multiply the two, we get twenty. Therefore, the front and back are each twenty square feet.

20+20= 40

SIDES

Now, we want to find the two sides. These have the same dimensions as the front and back: a 5 and a four. This is two twenties once again.

20+20=40

TOP AND BOTTOM

Now, we want to find the top and bottom. Our two lengths on the bottom are 5 and 5, so this area will be 25 on the bottom and 25 on the top. However, in our final solid, you cannot see the top part of the cube because it is covered up by the square pyramid, therefore, we will just use one of our 25s.

25

Now, let's add up these areas to see the surface area of the square prism.

25+40+40= 105 square feet.

SQUARE PYRAMID

To find the surface area of our square pyramid, we want to find the area of the four triangles and then add them up. We will not count the actual base because it's not part of the surface of the solid, so it is not part of the surface area.

TRIANGLE FACES

The formula for a triangle is 1/2 multiplied by the base times the height. We have four congruent triangles so we can multiply this result by four.

Our base is 5, our height is six, we multiply both by 1/2 and four, and we will then get our answer.

4*1/2*5*6= 60

Therefore, the surface area of our square pyramid is 60 square inches.

COMPOSITE SOLID

Now, we simply add up the two surface areas we gathered.

Square Prism: 105 square feet

Square Pyramid: 60 feet

105+60=165

Therefore, the surface area is 165 square feet.

I hope that this helps! Have a wonderful day!

6 0

3 years ago