Andy and Donald are both running toward the soccer ball during a game.

Andy's path is represented by the parametric equations x(t)=24+2/3t,y(t)=8+16t, where t is on the interval [0,50] and t is measured in tenths of seconds.

Donald's path is represented by the parametric equations x(t)=12+t,y(t)=5+1/4t, where t is on the interval [0,50] and t is measured in tenths of seconds.

Do the boys collide? If so, when do they collide?

Andy and Donald do not collide.

Andy and Donald collide at 4.8 seconds.

Andy and Donald collide at 2.4 seconds.

Andy and Donald collide at 3.6 seconds.

Answers

Answer 1

Answer:

Correct option: second one -> Andy and Donald do not collide.

Step-by-step explanation:

To find if the boys collide, we need to find if there is a common value of t where the their x position are equal and their y position are equal. To do this, we make x(t) of Andy equal to x(t) of Donald, , then if there is a value for t, we do the same for y(t) and check if the values of t are equal:

24 + 23t = 12 + t

22t = -12

t = -0.5455 seconds

As the time is negative, it will not occur, so the boys will never collide.

Correct option: second one


Related Questions

(3x+4)–(2x+9)=15

Help meeeeeeeeeeeee.

Answers

Answer:

x=30

Step-by-step explanation:

you distribute the negative to 2x and 19

3x+4-2x-19=15

then you combine like terms

x-15=15

you add 15 to both sides

x=30

Answer:

x = 20

Step-by-step explanation:

We are given the equation ( 3x + 4 ) – ( 2x + 9 ) = 15;

( 3x + 4 ) - ( 2x + 9 ) = 15 ⇒ Take ( ) out, through distribution of - 1,

3x + 4 - 2x - 9 = 15 ⇒ Subtract 4 from either side,

3x - 2x - 9 = 11 ⇒ Combine like terms,

x - 9 = 11 ⇒ Add 9 on either side,

Solution; x = 20

Jennifer bought a piece of wire for a crafts project that was 8/9 of a yard long. She used 1/2 of a yard. How long was the wire she had left?

Answers

Answer:

7/18 yard long

Step-by-step explanation:

The wire she had left was 7/18 of a yard long. (7 as the numerator and 18 as the denominator)

Solve x/2 + y/3 = 1 for x .

A. y = -5x + 3

B. y = 5x + 3

C. y = -5x - 3

D. y = 5x - 3

Answers

Answer:

x= −2/3y+2

Step-by-step explanation:

Which statement belongs in Step 4?

Answers

Answer:

Step-by-step explanation:

TQ = QR

Ray t bisects TR. TR is divided into  two equal parts

Write the expression in exponential form.
log 3^9= 2

Answers

Answer: 3^2

Step-by-step explanation:

remember logb a=n <---> a=b^n

so therefor the answer is log3 9=2 ---> 9 = 3^2

Solve the following system of equations.
2x + 5y = 19
x - 2y = - 4​

Answers

Answer:

Step-by-step explanation:

。☆✼★ ━━━━━━━━━━━━━━  ☾  

2x + 5y = 19

x - 2y = -4

Multiply the second equation by 2

2x - 4y = -8

Now we have:

2x + 5y = 19

2x - 4y = -8

Subtract the second eq from the first to get:

9y = 27

/ 9

y = 3

Now substitute this value into one of the first equations

x - 2(3) = -4

x - 6 = -4

x = 2

Thus, your answer would be option B

Have A Nice Day ❤    

Stay Brainly! ヅ    

- Ally ✧    

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I need to find the equation of the line

Answers

Answer:

y= -3x + 7

That is the answer.

What are the zeros of A(x) = x(x-7)?
O A. x = 0 only
O B. X = 7 only
O c. x = 0 and x = -7
O D. x = 0 and x = 7

Answers

Answer:

x=0   x=7

Step-by-step explanation:

A(x) = x(x-7)

Set equal to zero

x(x-7) =0

Using the zero product property

x=0     x-7 =0

x=0   x=7

whats the surface area?

Answers

Answer:

95cm

Step-by-step explanation:

3.5 x 4 = 14

14/2 = 7

5 x 4= 20

5 x 4= 20

Add up all the answers to find the surface area

you get 95cm

Calculate the perimeter of the following figure.

Answers

Answer:

29 inches

Step-by-step explanation:

4 + 7 + 4 + 11 = 29 inches

If the radius of a circle is 16 units, what is its area? (Use pie for it)

Answers

Answer:

[tex]804.25unit^2[/tex]

Step-by-step explanation:

[tex]A=\pi r^2\\=\pi 16^2\\=804.25unit^2[/tex]

So the right answer is 804.57 units^2.

Look at the attached picture

Hope it will help you

Good luck on your assignment

need help plzz helpp will give brainliest!!!

Answers

Answer:

12%

Step-by-step explanation:

1,020/8,500= ?/100

correct me if i am wrong

Answer:

Hello There the Correct answer is D. 12%

All you really need to do is Divide 1,020 8,500 and you will get 12. So the answer is D.

what is the radius of a circle thats 16 units?

Answers

Answer:

2.54648ft.

Step-by-step explanation:

r=8/[tex]\pi[/tex](ft.) therefore, the radius of the circle when its circumference is 16 feet is r≈2.54648ft.

Answer:

r =8

Step-by-step explanation:

Therefore,  C = π d .

We know that the circumference,  C , is  16 π , so we can say that:  

16 π = π d

We can divide both sides by  π  to see that  16 = d .

We now know that the diameter of the circle is  16 .

We also know that the diameter has twice the length of the radius.

In equation form:  2 r = d

 2 r = 16

r = 8

A survey was conducted to determine the average age at which college seniors hope to retire in a simple random sample of 101 seniors, 55 was the
average desired retirement age, with a standard deviation of 3.4 years. A 96% confidence interval for desired retirement age of all college students is:
54.30 to 55.70
54.55 to 55.45
54.58 to 55.42
54 60 to 55.40

Answers

Answer:

96% confidence interval for desired retirement age of all college students is [54.30 , 55.70].

Step-by-step explanation:

We are given that a survey was conducted to determine the average age at which college seniors hope to retire in a simple random sample of 101 seniors, 55 was the  average desired retirement age, with a standard deviation of 3.4 years.

Firstly, the Pivotal quantity for 96% confidence interval for the population mean is given by;

                         P.Q. =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample average desired retirement age = 55 years

            [tex]\sigma[/tex] = sample standard deviation = 3.4 years

            n = sample of seniors = 101

            [tex]\mu[/tex] = true mean retirement age of all college students

Here for constructing 96% confidence interval we have used One-sample t test statistics as we don't know about population standard deviation.

So, 96% confidence interval for the population mean, [tex]\mu[/tex] is ;

P(-2.114 < [tex]t_1_0_0[/tex] < 2.114) = 0.96  {As the critical value of t at 100 degree

                                               of freedom are -2.114 & 2.114 with P = 2%}  

P(-2.114 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.114) = 0.96

P( [tex]-2.114 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]2.114 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.96

P( [tex]\bar X-2.114 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+2.114 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.96

96% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-2.114 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+2.114 \times {\frac{s}{\sqrt{n} } }[/tex] ]

                                           = [ [tex]55-2.114 \times {\frac{3.4}{\sqrt{101} } }[/tex] , [tex]55+2.114 \times {\frac{3.4}{\sqrt{101} } }[/tex] ]

                                           = [54.30 , 55.70]

Therefore, 96% confidence interval for desired retirement age of all college students is [54.30 , 55.70].

What is the value of x? 12x+34=9

A.1612

B.1634

C.1612

D.412

Answers

Answer:

The answer is none of the above. x= -2.08

Step-by-step explanation:

Answer: you cant have a answer because it needs to be (-) or (/) not (+)

Step-by-step explanation:

ZE and ZF are vertical angles with mZE=81 +8 and mZF=2.0 + 38.
What is the value of x?
Enter your answer in the box.
X=

Answers

x=5

Since they are vertical angles, it means that they are congruent. So you have to set it equal to each other.

8x+8=2x+38

Subtract 2x from both sides

6x+8=38

Subtract 8 from both sides

6x=30

Divide 6 on both sides

x=5

PLEASE HELP ASAP 5TH GRADE

Answers

Answer:

C

Step-by-step explanation:

10*(1/7)=10/7.   A and B are false.

A product comes from multiplying.   D is false.

Please mark as Brainiest! :)

Have a nice day.

Juanita typed 78 words in 1 minute. What is a reasonable value for the
amount of words she could type in 3 minutes?
A. 240 words
B. 70 words
C. 80 words
D. 160 words

Answers

Answer: 240

Step-by-step explanation:

if you multiply 78 and the 3 it gets you to 240, so the answer is "A"

What is the range of possible sizes for side x?

Answers

i think it’s 3.9597... i used a^2 + b^2 = c^2

an item is regularly priced at $27. kaitlin bought it on sale for 35% off the regular price. how much did kaitlin pay

Answers

Answer:

Kaitlin paid $17.55

Step-by-step explanation:

1.00 - 0.35 = 0.65

$27 (0.65) = $17.55

Use the substitution method to solve the system of equations. Choose the correct ordered pair. 2x-y=8 y=x-3

Answers

X = 5
explanation in the image below

Answer:(5,2)

Step-by-step explanation:

Which equation below will produce a decay curve?

y = 3^x - 4
y = 2(4)^x
y = 1/2(3)^x
y = 6(1/3)^x

Answers

Answer:

Correct option: fourth one -> y = 6(1/3)^x

Step-by-step explanation:

A decay curve is produced by an exponencial function with a rate lesser than 1 and greater than 0. This way, we have an exponencial function where the values of y decrease when the values of x increase.

The first equation is a linear equation.

The second and third equations are exponencial equations, but with a rate bigger than 1

The fourth equation is an exponencial equation with a rate lesser than 1 and greater than 0, so this equation will produce a decay curve.

What is the method given in this article for adding several polynomials?

Answers

Answer:

No options given. But there are two methods of adding polynomials; The horizontal method, and the vertical method.

Step-by-step explanation:

The options are not stated here. However, there are two methods of adding polynomials; The horizontal method, and the vertical method.

Example: Suppose we want to add the polynomials (3x³ + 5x² + 56) + (16x² + 3x) + (4x³ + 4)

Horizontal method

(3x³ + 5x² + 56) + (16x² + 3x) + (4x³ + 4)

First collect the like terms

3x³ + 4x³ + 5x² + 16x² + 3x + 56 + 4

= 7x³ + 21x² + 3x + 60

Vertical method

3x³ + 5x² +...........56

+ ......16x² + 3x

4x³ +...................... 4

...................................................

7x³ + 21x² + 3x + 60

These two methods both yield the same results.

Which graph represents data points that have no correlation?

Answers

Answer:

Scatterplots

Step-by-step explanation:

If there is no apparent relationship between the two variables, then there is no correlation. Scatterplots can be interpreted by looking at the direction of the line of best fit and how far the data points lie away from the line of best fit

a parabola in the coordinate plane passes through the points (-4,7) (3,0) (8,10). When the quadratic function associated with this parabola is expressed as f(x)=ax^2 + bx +c what is the value of c

0

3

3 9/13

8

Answers

Answer:

c = 0

Step-by-step explanation:

A 3-variable linear system of equations is constructed after replacing known values for x and y:

[tex]16\cdot a - 4 \cdot b + c = 7[/tex]

[tex]9\cdot a + 3\cdot b + c = 0[/tex]

[tex]64\cdot a + 8\cdot b + c = 10[/tex]

After making algebraic manipulation, the following solution is found:

[tex]a = \frac{1}{4}[/tex] and [tex]b = -\frac{3}{4}[/tex] and [tex]c = 0[/tex]

The value of c is 0.

An expression that is equivalent to 12-16x

Answers

Answer: an expression equivalent would be 4(3-4x)

Answer:

4(3-4x)

I hope I helped you! Please mark me brainiest if I am correct. Thanks!

Harry and Taylor are running a concession stand for a concert. Hot dogs at the concession stand cost $1.25 each and sodas cost $0.75 each. During one concert, the concession stand earns $352.50 after selling 380 total hot dogs and sodas. The following system of equations can be used to represent the sales at the concession stand where h represents the number of hot dogs sold and s represents the number of sodas sold. 1.25h + 0.75s = 352.50 h + s = 380​ Which ​of the following correctly describes the solution to the system of equations? Group of answer choices
a-135 hot dogs and 245 sodas were sold.
b- 45 hot dogs and 335 sodas were sold.
c- 33 hot dogs and 347 sodas were sold.
d- 125 hot dogs and 255 sodas were sold.

Answers

Answer:

a-135 hot dogs and 245 sodas were sold.

Step-by-step explanation:

Our equations are:

1.25h + 0.75s = 352.50

h + s = 380

Let's use substitution to solve for this system. In the second equation, let's write h in terms of s:

h + s = 380

h = 380 - s

Now, let's plug in 380 - s for h in the first equation:

1.25h + 0.75s = 352.50

1.25(380 - s) + 0.75s = 352.50

We can now solve for s fairly easily:

1.25(380 - s) + 0.75s = 352.50

475 - 1.25s + 0.75s = 352.50

0.5s = 122.5

s = 245 sodas

We can already see which answer choice will match: A, and that is our answer.

Answer:

a-135 hot dogs and 245 sodas were sold.

Step-by-step explanation:

1.25h + 0.75s = 352.50

h + s = 380

h = 380 - s

1.25(380- s) + 0.75s= 352.50

475 - 1.25s + 0.75s = 352.50

122.5 = 0.5s

s = 245

h = 380 - 245

h = 135

What is the approximate distance from one corner of the soccer field to the opposite corner?

Answers

Answer:

116.62 yards

Step-by-step explanation:

information that we have about the soccer field:

length: [tex]l=100yards[/tex]

width: [tex]w=60yards[/tex]

the line that crosses from one corner to another is the hypotenuse of a right triangle that is formed with the sides [tex]l[/tex] and [tex]w[/tex].

So if we call this distance [tex]h[/tex], by the Pythagorean theorem we will obtain that:

[tex]h^2=l^2+w^2[/tex]

solving for  [tex]h[/tex]:

[tex]h=\sqrt{l^2+w^2}[/tex]

substituting the known values:

[tex]h=\sqrt{100^2+60^2} \\h=\sqrt{10,000+3,600}\\ h=\sqrt{13,600}\\ h=116.62yards[/tex]

the approximate distance from one corner to the opposite corner found by the Pythagorean theorem is: 116.62 yards

Answer:

117

Step-by-step explanation:

Ms. Peterson wrote the expression below on the chalkboard for her class. She asked the students to write an equivalent expression using no more than one set of parentheses.


4(3x+5y+2z)+3(x−z) ​​



• Tom wrote 12x+20y+8z



• Jenna wrote 5(3x+4y+z)



• Chris wrote 15x+20y−5z



Which, if any, of the three students wrote an expression that is equivalent to Ms. Peterson’s expression?



​Answer ​_______ wrote an equivalent expression.

​Show your work to prove which expressions, if any, are equivalent.

Answers

Chris wrote an equivalent expression.

12x+20y+8z+3x-3z
15x+20y-5z

Evaluate
12^-8 over 12^-9=

Answers

Answer:

12

Step-by-step explanation:

We know that a^b / a^c = a^ (b-c)

12 ^ -8  / 12 ^ -9

12 ^ (-8 - -9)

12 ^ (-8+9)

12 ^ 1

12

Answer:

The Answer is 12. (Someone deleted my answer because I didn't show any work.)

Step-by-step explanation:

1. 12^-8/12^-9 -->  12^-8-(-9)

2. 12^-8+9

3. 12^1= 12

4. Therefore the answer is 12.

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