A water taxi travels around an island in a path that can be modeled by the equation y =0.5(x - 16). A water skier is skiing along a path that begins at the point
(6,6) and ends at the point (8. - 4).
a. Write a system of equations to model the problem.
b. Is it possible that the water skier could collide with the taxi? Explain

Answer:

1. ac = 36

2. b = 13

3. 4 and 9

Step-by-step explanation:

Given

6x² + 13x + 6

Required

Fill in the gaps

Solving (1): The value of AC

The general form of an equation is:

ax² + bx + c

By comparison:

a = 6

b = 13

c = 6

So,

ac = a * c

ac = 6 * 6

ac = 36

Solving (2): The value of b

In (1) above, we showed that

b = 13

Solving (3): Two numbers that satisfy product ac and sum b

We have that.

ac = 36

If one of the numbers is 4, then the other number is

Other number = 36/4

Other number = 9

Alternatively, we have that.

b = 13

If one of the numbers is 4, then the other number would be:

Other number = 13 - 4

Other number = 9

Answer:

ac = 36

b = 13

The two numbers that have a product of ac and a sum of b are 4 and 9

Step-by-step explanation:

Answer:

-24

Step-by-step explanation:

Answer: -24

Step-by-step explanation:

3xy

3(4)(-2)

12(-2)

-24

Answer:

-3x-6

Step-by-step explanation:

distribute the -3

Answer:

-3x-6

Step-by-step explanation:

Answer:

[tex]x = \frac{5 + \sqrt{53}}{2}[/tex]  or  [tex]x = \frac{5 - \sqrt{53}}{2}[/tex]

Step-by-step explanation:

Given

[tex]x^2 - 5x - 7 = 0[/tex]

Required

Solve for x using:

[tex]x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}[/tex]

First, we need to identify a, b and c

The general form of a quadratic equation is:

[tex]ax^2 + bx + c = 0[/tex]

So, by comparison with [tex]x^2 - 5x - 7 = 0[/tex]

[tex]a = 1[/tex]     [tex]b = -5[/tex]      [tex]c = -7[/tex]

Substitute these values of a, b and c in

[tex]x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}[/tex]

[tex]x = \frac{-(-5) \± \sqrt{(-5)^2 - 4 * 1 * -7}}{2 * 1}[/tex]

[tex]x = \frac{5 \± \sqrt{25 +28}}{2}[/tex]

[tex]x = \frac{5 \± \sqrt{53}}{2}[/tex]

Split the expression to two

[tex]x = \frac{5 + \sqrt{53}}{2}[/tex]  or  [tex]x = \frac{5 - \sqrt{53}}{2}[/tex]

To solve further in decimal form, we have

[tex]x = \frac{5 + 7.28}{2}[/tex]  or  [tex]x = \frac{5 - 7.28}{2}[/tex]

[tex]x = \frac{12.28}{2}[/tex]  or  [tex]x = \frac{-2.28}{2}[/tex]

[tex]x = 6.14[/tex] or [tex]x = -1.14[/tex]

Answer:

A. $99,195.055

B. $72,000

C. $27,195.055

Step-by-step explanation:

A. Calculation for How much will you have in the account in 30 years

Using future annuity formula

Future value=[Deposit amount* (1+Interest rate^n-1)/Interest rate]

Let plug in the formula

Where,

Deposit amount=$200

Number of days=30*12=360

Interest rate=0.02/12=0.0017

Let plug in the formula

Future value=[$200*(1+0.0017^360-1)/0.0/17]

Future value=[$200*(1+0.0017^360-1)/0.0/17]

Future value=[$200*(1.0017^360-1)/0.0/17]

Future value=$99,195.055

Therefore the amount you will have in the account in 30 years will be $99,195.055

B. Calculation for How much total money will you put into the account

Using this formula

Total money=Deposit amount*Number of days

Let plug in the formula

Total money=$200*360 days

Total money=$72,000

Therefore the total money you will put into the account is $72,000

C. Calculation for How much total interest will you earn

Total Interest=$99,195.055-$72,000

Total Interest=$27,195.055

Therefore the total Interest you will earn is $27,195.055

Answer:

a. True

b. True

c. True

d. False

e. False

I hope this helped! Thank You!

Answer:

a. False

b. True

c. True

d. False

e. False

The y-intercept of the line is 1

Using the slope - intercept relation :

Substituting the values into the relation :

7 = 3(2) + c

7 = 6 + c

c = 7 - 6

c = 1

Therefore, the y-intercept of the line is 1.

Learn more on Intercept:https://brainly.com/question/25987747

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Answer:

It should be B- an=3n+1 because it seems to be adding one every time

Step-by-step explanation:

Answer:

We will count number of squares

first term is 4

so,

second term is 7

so,

third term is 10

so,

We can see that this sequence is in arithematic sequence

we can use nth term formula

where

an is nth terms

a1 is first term

d is common difference

n is total number of terms

now, we can plug values

and we get

b 3n+1

Step-by-step explanation:

Answer:

y = -2x + 5

Step-by-step explanation:

A(4, -3) ;      B(2, 1)

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

          [tex]= \frac{1-[-3]}{2-4}\\\\= \frac{1+3}{2-4}\\\\= \frac{4}{-2}\\\\= -2[/tex]

m = -2 ;  A(4,-3)

[tex]y - y_{1}=m(x-x_{1})\\\\y -[-3] = (-2)(x - 4)\\\\y + 3 = -2*x -4 *(-2)\\\\y + 3 = -2x + 8\\\\ y = -2x + 8 - 3 \\\\ y = -2x + 5[/tex]

Final Answer: [tex]r = 2[/tex]

Steps/Reasons/Explanation:

Question: [tex]8 = r^{3}[/tex]. [tex]r[/tex] = ?

Step 1: Take the cube root of both sides.

[tex]\sqrt[3]{8} = r[/tex]

Step 2: Calculate using a calculator.

[tex]2 = r[/tex]

Step 3: Switch sides.

[tex]r = 2[/tex]

~I hope I helped you :)~

Answer:

7   1/3

Step-by-step explanation:

Lets do this in steps ok? K!

Important!!!: Look what operation is first in order of operation no parentheses or exponents so division and multiplication is first!

Step 1-- 4 x 7=28

Step 2-- 62 divided by 3 = 20      2/3

Step 3-- 28- 20   2/3

Step 4-- 27   3/3 - 20    2/3= 7    1/3

Hope this helps ∞<3

Answer:

[tex]-11.3333333333[/tex] [tex]or[/tex] [tex]-\frac{34}{3}[/tex] [tex]or[/tex] [tex]7\ \frac{1}{3}[/tex]

Step-by-step explanation:

[tex]--------------------------------------------[/tex]

[tex]\frac{4\cdot7-62}{3}[/tex] = [tex]?[/tex]

[tex]4\cdot7[/tex] = [tex]28[/tex]

[tex]\frac{28-62}{3}[/tex] = [tex]?[/tex]

[tex]28-62[/tex] = [tex]-34[/tex]

[tex]\frac{-34}{3}[/tex] = [tex]?[/tex]

[tex]\frac{-34}{3}[/tex] = [tex]-11.3333333333[/tex] = [tex]7\ \frac{1}{3}[/tex]

[tex]--------------------------------------------[/tex]

Hope this helps! <3

[tex]--------------------------------------------[/tex]

Answer:

ok

Step-by-step explanation:

Answer:

G

Step-by-step explanation:

(x)0 months: (y)15 toys, 1:17, 2:19, 3:21, 4:23, 5:25, 6:27, 7:29, 8:31, etc.

The equation that represents best shows this relationship between the number of toys Rudolfo has will be y = 2x + 15. Then the correct option is G.

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

Rudolfo has 15 toys in his toy box, and he adds 2 new toys every month.

Let x be the number of months and y be the total number of toys. Then the equation is given as,

y = 2x + 15

The equation that represents best shows this relationship between the number of toys Rudolfo has will be y = 2x + 15. Then the correct option is G.

More about the linear equation link is given below.

https://brainly.com/question/11897796

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It's 6 srry that guy above just stole free points

9514 1404 393

Answer:

  8, 9. Correct

  10. 6.1×t

Step-by-step explanation:

8, 9. The answers shown are correct.

__

10. The only product in the given expression is 6.1t, which can be written as ...

  6.1×t

when a symbol is used to represent multiplication.

The parts of the product are the multiplicand and the multiplier. Those parts are also called factors.

Answer:

$200

Step-by-step explanation:

First Change the percent to a decimal

In this case the percent was %8, change it into a decimal; 8%=.08

Next multiply 2,500 x .08  which gives you 200

The answer is $200! Hope this helps!.

Answer:

Step-by-step explanation: the answer is c

Answer:

angle t is 55 degrees

Step-by-step explanation:

Here's my work:

Isoscelese means two of the same length sides. A triangle is 180 degrees. 180-70=110

110/2=55 (two because those are the two angles associated with the equal sides)

Answer:

=5x2+5x

Step-by-step explanation:

Let's simplify step-by-step.

3x+3x2+2x2+2x

Answer:

-11

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Answer:

ratio number 1-  14:12

ratio number 2- 21:18

ratio number 3- 28:24

Answer:Example 1:

Find the sum of the first 8 terms of the geometric series if a1=1 and r=2.

S8=1(1−28)1−2=255

Example 2:

Find S10 of the geometric sequence 24,12,6,⋯.

First, find r.  

r=r2r1=1224=12

Now, find the sum:

S10=24(1−(12)10)1−12=306964

Example 3:

Evaluate.

∑n=1103(−2)n−1

(You are finding S10 for the series 3−6+12−24+⋯, whose common ratio is −2.)

Sn=a1(1−rn)1−rS10=3[1−(−2)10]1−(−2)=3(1−1024)3=−1023  

In order for an infinite geometric series to have a sum, the common ratio r must be between −1 and 1.  Then as n increases, rn gets closer and closer to 0.  To find the sum of an infinite geometric series having ratios with an absolute value less than one, use the formula, S=a11−r, where a1 is the first term and r is the common ratio.

Example 4:

Find the sum of the infinite geometric sequence

27,18,12,8,⋯.

First find r:  

r=a2a1=1827=23

Then find the sum:

S=a11−r

S=271−23=81

Example 5:

Find the sum of the infinite geometric sequence

8,12,18,27,⋯ if it exists.

First find r:  

r=a2a1=128=32

Since r=32 is not less than one the series has no sum.

Step-by-step explanation: