Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

A pair of kids and a pair of adults decided to compete in a three-legged race. The kids got to start 15 yards ahead of the adults, since they had shorter legs. When they were told to start, the kids hobbled forward at a rate of 1 yard per second, and the adults hobbled after them at a rate of 4 yards per second. Soon they were side-by-side. How long did that take? How far did the adults go?


It took seconds for the adults to go yards and catch up to the kids?

Answer:

[tex](A) - \sqrt2[/tex]

Step-by-step explanation:

Let's find the velocity and acceleration first:

[tex]v(t) = \dot x(t) = cos\ t -( -sin \ t) = cos \ t + sin \ t\\a(t) = \ddot x(t) = -sin\ t + cos\ t = cos\ t - sin t[/tex]

(you can also rewrite the position as [tex]\sqrt 2 sin(t-\frac\pi4)[/tex] and determine velocity and acceleration from there, but I do prefer handling it as a sum for the sake of the derivatives)

At this point, the first time when the velocity is 0 is given by

[tex]cos\ t + sin\ t = 0 \rightarrow cos\ t = - sin t \rightarrow tan\ t = -1 \\t = \frac34 \pi = 2.36s[/tex]

At this point the acceleration is (let's use the first value of t for the sake of our sanity!)

[tex]cos (\frac34 \pi) - sin \frac 34 pi = -\frac1{\sqrt2} -\frac1{\sqrt2} = \sqrt 2 = -1.41[/tex]

Answer:

62

Step-by-step explanation:

Just do 5/8 = 40/x, and cross-multiply to get:

320 = 5x,

And x will be equal to 62

Answer:4$

Step-by-step explanation

The cost of one token is 7.2 dollars.

A linear equation is an algebraic equation of highest degree 1 the number of variable is 1 also.

According to the given question Jane & Jim spent the same amount of money today.

Jim spent 5.25 dollars on food and rode the train 3 times, and Jane spent 12.45 dollars on food and rode the roller coaster twice.

Assuming cost of a token to be T.

∴ 5.25 + 3T = 12.45 + 2T.

3T - 2T = 12.45 - 5.25

T = 7.2.

learn more about linear equation here :

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Answer:

  No; no sign change of g(x) in that interval

Step-by-step explanation:

The intermediate value theorem tells you there will be at least one zero between any two points where the function changes sign. The table shows sign changes in the intervals [-2, -1], [0, 1], and [1, 2]. So, the three zeros of the cubic lie in those intervals.

There are no additional zeros to be found, and there are no sign changes of g(x) between x=2 and x=3, so there is no zero in the interval [2, 3].

_____

Additional comments

We can only answer this with certainty because we have already found the locations of the three real zeros this cubic has. If there were two that were unaccounted for, then the possibility might exist for the graph to make an excursion across the x-axis and back in the interval [2, 3].

__

First differences of the table values are ...

  -5, +1, +2, -3, 0

Second differences are ...

  6, 1, -5, 3

Third differences are ...

  -5, -6, +8

This table cannot represent a real cubic function. For evenly-spaced x-values, a cubic polynomial must have constant 3rd differences. If the last two values in the table were -1 and -12, the function would be ...

  g(x) = -5/6x^3 +1/2x^2 +7/3x -1

You may want to discuss this question with your teacher.

If the price of the meal is less than $71, then the $25 gift card would be better than the 35% off coupon.

Let y represent the price of the meal.

For a $25 gift card to be applied, the final price is:

Final price = y - 25

For a 35% off coupon, the final price is:

Final price = y - 0.35y = 0.65y

y - 25 < 0.65y

0.35y < 25

y < 71.42

If the price of the meal is less than $71, then the $25 gift card would be better than the 35% off coupon.

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Answer:

2y-3

Step-by-step explanation:

the product of y and 2 is just multiplying

then 3 less means subt. 3

Answer:

-7 4/5 or -7.8

Step-by-step explanation:

Product means multiplication

( - 13/8 )( 24/5)

= (-13 · 24)/(8 · 5)    negative · positive = negative

= - 312/40

=  -7  32/ 40 = -7 4/5 or 7.8

Answer:

b

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

3 is being distributed into x and 3 inside the parenthesis. So it is distributive property.

Garnetta will have 3,200 shares worth $ 34,125 each.

Given that Garnetta owned 2400 shares of Metropolitan Corporation at a price of $ 45.50, and the stock split 4-for-3, to determine how Garnetta was financially affected by the split the following calculation must be performed:

Therefore, Garnetta will have 3,200 shares worth $ 34,125 each.

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Answer:

p(0)= -7

Step-by-step explanation:

Answer:

yes, yes they do

Step-by-step explanation:

i dont know what you're asking

we have f (x)= -3x + 10

so f(-5)= (-3)(-5) +10 = 15 + 10 = 25

we have g (x) = x^2 - 7x

so g(2)= 2^2 - 7.2 = 4 - 14 = -10

we have f (x)= -3x + 10

so f(4m)= -3(4m)+10 = -12m + 10

ok done. Thank to me :>

Answer:

The answer is 31

Explanation:

25 - (-6) = 31

we have 25 - (-6) = 25 + 6 = 31

so the answer is D

ok done. thank to me :>

Answer:

x=4

Step-by-step explanation:

11x - 2(x + 3) = 30

distribute: 11x-2x-6=30

add like terms: 9x-6=30

add 6: 9x=36

divide by 9: x=4

Answer:

x = 4

Step-by-step explanation:

11x - 2(x +3) = 30

11x -2x - 6 = 30

11x - 2x = 30 + 6

9x = 36

9x/9 = 36/9

x = 4

Answer:

y = - x + 3

Step-by-step explanation:

Assuming you require the equation of the line

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - 1 , then

y = - x + c ← is the partial equation

To find c substitute (5, - 2 ) into the partial equation

- 2 = - 5 + c ⇒ c = - 2 + 5 = 3

y = - x + 3 ← equation of line

Answer:

(3,7)

Step-by-step explanation:

n will be located in x positive , y positive

Answer:

12

Step-by-step explanation:

divid half of line

Answer:

Perimeter = 60

Step-by-step explanation:

In order to find the perimeter of the given triangle, we must first determine the value of the missing side. We can use the Pythagorean Theorem to find the missing side of the given right triangle.

According to the Pythagorean Theorem: c² = a² + b², where c is the hypotenuse (the side that is opposite of the right angle, 90°), and a and b represent the legs of the triangle. Use the formula to solve for the missing side. Rearrang the formula to isolate the variable, a:

a² + b²  =  c²

Subtract b² from both sides:

a² + b² - b² =  c² - b²

a² =  c² - b²

Next, substitute the given values into the formula:

c (hypotenuse) = 26

b (leg) = 24

a² =  c² - b²

a² =  (26)² - (24)²

a² = 676 - 576

a² = 100

[tex]\sqrt{(a)^{2}} = \sqrt{100}[/tex]

a = 10

The value of the missing side is 10.

Now, we can solve for the perimeter of the triangle:

P = a + b + c

P = 10 + 24 + 26

P = 60

Therefore, the perimeter of the given right triangle is 60.

Answer:

Step-by-step explanation:

HSB will equal BCH

The four internal angles of a parallelogram sum to 360°

Opposite internal angles are equal.

2(3x - 3.86) + 2(2x + 6.58) = 360

6x - 7.72 + 4x + 13.16 = 360

10x = 354.56

x = 35.456

HSB = (3(35.456) - 3.86) = 102.508°

Answer:  F distribution. chi-square distribution. t distribution. normal distribution.

Step-by-step explanation:

Answer:

When you explain the problem, it makes it easier to understand how you solved it.​

I hope this helped at all.

Answer:

W4 is our new scaled side

Step-by-step explanation:

Look at scale factor like this and it helps everytime so if it doesn’t help you there different methods.

3/2 has a larger number as a numerator so that means that the shape being scaled will get larger and if the number is smaller than denominator then the scaled figure will get smaller :3

In our case it gets bigger

do 16 divided by 2 which gives us 8 then times that by 3 to get 24

now thats how I solved this problem but if that not how you did it then you can do it your way :3

HOOE THIS HEEELPPED :DDD

Answer: 84%

Step-by-step explanation:

Answer:

a) A. Arithmetic Sequence

b) A. Arithmetic Sequence

c) A. Arithmetic Sequence

d) A. Arithmetic Sequence

e) B. Not an arithmetic Sequence

Step-by-step explanation:

if there is a common difference it is arithmetic, if there not then it is not arithmetic.

a) d= 3

b)d=3

c)d=2

d)d=-4

e)not arithmetic

Answer:

[tex](x-4)(x^2+6)[/tex]

Step-by-step explanation:

x³-4x²+6x-24 is our equation

Once we factor it we get

[tex](x-4)(x^2+6)[/tex]

Answer:

$63.75

Step-by-step explanation:

10% = 7.5

5% = 3.75

15% = 11.25

75.00

-11.25

63.75

[tex]\frac{x}{5} +3=2\\\frac{x}{5} =-1\\x=-5[/tex]

Let me know if you need any clarification, I just don't have much to say on a simple question like this

Answer: the daughters got 216 stickers each

Step-by-step explanation:

27 times 24 is 648

648 devided by 3 is 216

so therefore your answer would be 216

hope this helps

Answer:

There are two solutions.

Step-by-step explanation:

x = -3

x = -11