alex is running in a clockwise direction around a circular track with radius 60 yards. he runs for 20 minutes at a speed of 4 yards per second. find the shortest distance between their starting point and their ending point measured along the track

Answer:

  (b)  x +2y = 8

Step-by-step explanation:

There are at least a couple of ways to come to the conclusion.

  1) use the given information to write the equation of the desired line

  2) check to see which of the answer choices satisfies the requirement

__

The given line has two specified points on it. These can be used to find its slope. (Or, you can count grid square to see it has a rise of -1 for a run of +2.)

The slope formula is ...

  m = (y2 -y1)/(x2 -x1)

  m = (-4 -0)/(4 -(-4)) = -4/8 = -1/2

Comparing this to our grid square count, we see they are the same:

  m = rise/run = -1/2

Now, we have a slope (-1/2) and a point (2, 3), so we can use these to write the point-slope equation of the desired line:

  y -k = m(x -h) . . . . . . . line with slope m through point (h, k)

  y -3 = -1/2(x -2) . . . . . point-slope equation of the desired line

  y -3 = -1/2x +1 . . . . . . eliminate parentheses

  1/2x +y = 4 . . . . . . . . add 1/2x +3 to both sides

  x +2y = 8 . . . . . . . . . multiply by 2

__

Perhaps easier in this case is to try the given equations to see which is satisfied at the given point. There are two different left-side expressions to evaluate at the point (x, y) = (2, 3):

  x +2y = (2 +2(3)) = 2+6 = 8

  2x +y = 2(2) +3 = 4 +3 = 7

Only the equation ...

  x +2y = 8

is satisfied at the given point.

_____

Additional comments

While I encourage you to learn to solve questions like this "from scratch", modern math curriculum is often "multiple choice."

When faced with multiple choices for answers, it is often easiest to ...

  (a) eliminate the ones that are not self-consistent or that are false on their face;

  (b) eliminate the ones that have an obviously fatal flaw (wrong sign of slope, too large or too small, for example);

  (c) choose from the remaining ones the one that properly answers the question (satisfies all requirements).

__

When you solve a standard-form equation for y, you get ...

  ax +by = c

  by = -ax +c

  y = -a/bx +c/b

That is, the slope of the line is -a/b.

For the two left-side expressions in the answer choices, the slopes are ...

  x +2y   ⇒   slope = -1/2

  2x +y   ⇒   slope = -2/1 = -2

The scales on the graph are the same in the x- and y-directions, so the shallow negative slope of the given line is clearly less than 1. That eliminates the last two answer choices already.

Answer:

a) 2x+4

b)x=8

Step-by-step explanation:

a) x+x+4 =2x +4

b) 2x+4= 20

2x = 16

x=8

Jay bought 8 packets of Chips

c) Jay: 8 x 60

=£4,80

Lauren : 12 × 60

= £7,2

Answer:

2d+20

Step-by-step explanation:

since he is 20 pounds greater than denny you would just add 2d and 20 im pretty sure

or ig you want to write out the whole thing it would be y=2d+20

Hope This Helps!!

Answer:

[tex]2d + 20[/tex]

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

The expression 40 is equivalent to 20 × 2=40

Step-by-step explanation:

20 ×2=40

Answer:

7(9 + 14)

Step-by-step explanation:

The Greatest Common Factor of 35 and 63 is 7; both 35 and 63 are evenly divided by 7.  Thus, 35 + 63 can be rewritten as 7(5) + 7(9), or 7(14)

So 35 + 63 = 7(9 + 14)

Answer:

= 98

Step-by-step explanation:

Step-by-step explanation:

the line was translated. in other words : it was shifted. it only changed its position. no other attribute changed.

so, the length is still 4.

Answer: 28/9 as a mixed number is 3 1/9

Step-by-step explanation:

Answer:

3 1/9

Step-by-step explanation:

3 times 9 is 27

27 plus 1 is 28

Answer:

75m

Step-by-step explanation:

They are similar triangles: they have two corresponding angles: in a triangle with an angle of 90°, the other two will be of 45°.

Now that we know they are similar, we can calculate the ratio of the sides, by doing 10/2=5

We want to know the side AT, so we can do that by multiplying DC for 5:

DC = 15 × 5 = 75m

You can also check this by applying Pythagoras' Theorem:

DB =

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

Which equals 15.1 m

The hypotenuse of the other triangle is 15.1 × 5 = 75.5 m

Finally, we can apply for the last time the Pythagoras' Theorem to find AT:

[tex] \sqrt{75.5^{2} - 10 {}^{2} } [/tex]

Which equals 74.8 = 75 m

Answer:

8

Step-by-step explanation:

2^1 = 2×1 = 2

2^2= 2×2= 4

2^3= 2×2×2= 8

Answer:

−7y+8

Step-by-step explanation:

1. Simplify each term.

−4y+8−3y

2. Subtract 3y from −4y.

−7y+8

Hope this helps :D

Answer:

the answer should be 2

Step-by-step explanation:

8×13=104

208÷104=2

Answer:

w = 2

Step-by-step explanation:

V_rectangular prism = l * w * h

208 = 13 * w * 8

208 = 104 * w

w = 208/104

w = 2

-Chetan K

The equation that represents they function f(x) = (1.6)^x after it has been translated 5 units up and 9 units to the right is;

g(x) = [(1.6)^(x - 9)] + 5

We are given the function;

f(x) = (1.6)^x

Now,when we translate a function 9 units to the right, it means that we will subtract 9 from the x unit to give;

g(x) = (1.6)^(x - 9)

Now, when we translate it 5 units upwards, it means we are adding 5 to f(x). Therefore, we now have;

g(x) = [(1.6)^(x - 9)] + 5

Read more on translation of graphs at; https://brainly.com/question/11468584

Answer:

Answer: 375 adult tickets were sold and 125 children tickets were sold.

Answer:

Its 96 bro :) 96 students

Step-by-step explanation:

Basically yeah, 800 is 100% of the population yeah. So just multiply 800 times 12%. 800 x 12% is 96.

96 = 12% of 800, I hope this helps!

Answer: Factoring is essentially the reverse of the distributive property. You are basically trying to simplify the polynomial by taking out common factors. You also may try reducing the power (or the highest exponent) of the polynomial with factoring. I would say that factoring is the breaking down of a bigger polynomial into a product of two expressions that are usually multiplied by each other. One specific use of factoring we see a lot is the quadratic formula.

1. Quadratic Factoring --> [tex]x^2+2x-15[/tex] --> we have an [tex]x^2[/tex] but we want there to only be "[tex]x[/tex]"s. Here we need to constant numbers (integers), that multiply together to get [tex]-15[/tex], and add up to [tex]+2[/tex]. (5 and -3)

    - [tex]x^2+2x-15[/tex] ==> [tex]x^2+5x-3x-15[/tex] ==> [tex]x(x+5)-3(x+5)[/tex] ==> [tex](x-3)(x+5)[/tex]

Above: We can see that we factor out [tex]x[/tex] from [tex]x^2+5x[/tex] (This shows that we are aiming to break it down to make it easier to evaluate).

Remember: Factoring does not always mean that the polynomial is in a simpler form. There are many situations where factoring is totally unnecessary and complicates the polynomial even more.

--------------------------------------------------------------------------------------------------------------On a separate note: Distributive Property, if you are unsure or not fully sure on what that means, is when you multiply two expressions together to create one expression. Multiple expressions are combining into one.

Answer:

y=3/2x-7

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(5-(-1))/(8-4)

m=(5+1)/4

m=6/4

simplify

m=3/2

y-y1=m(x-x1)

y-(-1)=3/2(x-4)

y+1=3/2(x-4)

y=3/2x-12/2-1

y=3/2x-6-1

y=3/2x-7

Answer: The solution is k = -171.92.

Answer:

k = - 171.92

Step-by-step explanation:

[tex]\frac{k}{5.6}[/tex] + 41.5 = 10.8 ( subtract 41.5 from both sides )

[tex]\frac{k}{5.6}[/tex] = - 30.7 ( multiply both sides by 5.6 to clear the fraction )

k = - 171.92

Answer:

5x^5

Step-by-step explanation:

5x^2*4x^3/4

Divide

5x^2*1x^3

Multiply and Calculate

5x^5

answer: [tex]25x^{3}[/tex]

steps to solve:

→ let's write this out as an equation instead of in word form. 5x to the power of 2 times 4x to the power of 3 divided by 4 is [tex]\frac{5^{2} * 4x^{3}}{4}[/tex].

→ first, calculate the power of [tex]5x^{2}[/tex]. [tex]5x^{2} = 25[/tex], so now we have [tex]\frac{25^{2} * 4x^{3}}{4}[/tex]

→ now, multiply the monomials. [tex]25 * 4x^{3} = 100x^{3}[/tex].

→ [tex]\frac{100x^{3}}{4}[/tex]. we need to cross out the common factor, which is 4. 100 divided by 4 is 25. we're now left with [tex]25x^{3}[/tex].

so, [tex]25x^{3}[/tex] is the answer

i dont understand

what do we need to do?

Answer:

The personal hygiene part of the store (I think)

Step-by-step explanation:

This is an ultimately weird question, so I don't really know. But my answer is what I think, (I don't even know if it exists though).

Find total ounces mixed for each flower:

Daisies = 2+5 = 7 ounces

Tulips = 3 +6 = 9 ounces

Now find the ratio of purple to white for each one:

Daisies = 5/7 = 0.714

Tulips = 6/9 = 0.666

Daisies have more purple so would be the darker ones.

Answer:

Daisies

Step-by-step explanation:

IXL told me it was right

if u can get a better picture I can help you

Answer:

383.5

Step-by-step explanation:

We want to round 383.52 to the nearest tenth.

The tenth would be the 5.

To round we look at the number after the one we want to round ( so 2 )

If the number is greater than 4 so ( 5, 6, 7, 8 or 9 ) then we raise the number that we want to round but if its less than 5 ( 4, 3, 2, 1 , 0 ) we keep the number as it is.

2 is less than 5 so we keep 5 as it is to get 383.5

Happy Holidays!

We can use the following equation to calculate uniform acceleration:

[tex]\large\boxed{a = \frac{\Delta v}{\Delta t} = \frac{v_f - v_i}{\Delta t}}}[/tex]

Plug in the given values to solve:

[tex]\frac{85 - 65}{16}}} = \frac{20}{16} = \boxed{1.25 m/s^2}}[/tex]

Answer:

Hope it will help you...

Answer:

each student gets 2 bars and a quarter of one (2.25 or 2 1/4)

Step-by-step explanation:

In attachment I have answered this problem.

Answer:

the correct answer is ( ZYXW ) because the given polygon is a rectangle and its properties is that the opposite sides are equal means the lenght and breath of the unknown side for the big rectangle is 6 , 3 and for small rectangle the the unknown sides are 1 , 2 only so now you've got all the side of both polygons so now you take the ratio of each side and then you can easily find the sides

Step-by-step explanation:

Hope it helps

Have Nice Day : )

The inequality that best describes the possible values of x is; Choice A: 2 < x < 10

In a polygon such as that given in the question;

Two scenarios may occur regarding angle; (3x -6)

They are as follows:

This is so because angle 3x - 6 must be between 0° and 24° since 36 > 34

By evaluation;

x < 10

Also,

x > 2.

Therefore, the inequality that best describes the possible values of x is; Choice A: 2 < x < 10

Read more on inequalities:

https://brainly.com/question/22137960

The inequality that describes the possible values of x is 2 < x < 10.

The given parameters:

From the given polygon, the angle facing the shorter length (34) will have the following possible values;

The range of of values of x is calculated as follows;

3x - 6 < 24

3x < 24 + 6

3x < 30

[tex]x < \frac{30}{3} \\\\x< 10[/tex]

or

3x - 6 > 0

3x > 6

[tex]x >\frac{6}{3} \\\\x >2[/tex]

Thus, the inequality that describes the possible values of x is 2 < x < 10.

Learn more about inequality here: https://brainly.com/question/14361489