a bus traveled 60 km of north of its terminal. From this point, it traveled km east. How far is the bus from the terminal?

Given:

The equations are

[tex]5y=2x-5[/tex]

[tex]5y=4+3x[/tex]

[tex]5y-3x=-1[/tex]

To find:

The two parallel lines.

Solution:

Slope intercept form of a line is

[tex]y=mx+b[/tex]

where, m is slope and b is y-intercept.

Isolate variable y in each of the given equations, to get the slope intercept form of the lines.

The slope intercept forms of given lines are

[tex]y=\dfrac{2}{5}x-1[/tex]

[tex]y=\dfrac{4}{5}+\dfrac{3}{5}x[/tex]

[tex]y=-\dfrac{1}{5}+\dfrac{3}{5}x[/tex]

On comparing these equations with slope intercept form, we get

Slope of I line = [tex]\dfrac{2}{5}[/tex]

Slope of II line = [tex]\dfrac{3}{5}[/tex]

Slope of III line = [tex]\dfrac{3}{5}[/tex]

Slope of parallel lines are equal. So, lines II and III are parallel because their slopes are equal.

Therefore, the correct option is C.

Answer:

762 days

Step-by-step explanation:

Given

[tex]Rate = 200 + 10t + 13t^2[/tex]

Let the rate be R.

So the rate change with time is represented as:

[tex]\frac{dR}{dt} = 200 +10t + 13t^2[/tex]

So:

[tex]dR = (200 + 10t + 13t^2)\ dt[/tex]

To get the number of insects between day 0 and day 3, we need to integrate dR and set the bounds to 0 and 3

i.e.

[tex]dR = (200 + 10t + 13t^2)\ dt[/tex] becomes

[tex]\int\limits^3_0 {dR} \, =\int\limits^3_0 (200 + 10t + 13t^2)\ dt[/tex]

[tex]R =\int\limits^3_0 (200 + 10t + 13t^2)\ dt[/tex]

Integrate

[tex]R = 200t + \frac{10t^2}{2} + \frac{13t^3}{3} [3,0][/tex]

Solve for R by substituting 0 and 3 for t

[tex]R = (200*3 + \frac{10*3^2}{2} + \frac{13*3^3}{3}) - ( 200*0 + \frac{10*0^2}{2} + \frac{13*0^3}{3})[/tex]

[tex]R = (200*3 + \frac{10*9}{2} + \frac{13*27}{3}) - (0 + \frac{10}{2} + \frac{0}{3})[/tex]

[tex]R = (200*3 + 5*9 + 13*9) - (0)[/tex]

[tex]R = 600 + 45 + 117 - 0[/tex]

[tex]R =762[/tex]

The population of insect between the required interval is 762

The required change in the population of insects between day 0 and day 3 is 762.

Given that,

A population of insects increases at the rate of 200++ 10t + 13t2.

We have to determine,

What is the change in the population of insects between day 0 and day 3.

According to the question,

The rate change with time is represented as:

[tex]\frac{dr}{dt} = 200+10t+13t^{2}[/tex]

To determine the change in the population of insects between day 0 and day 3,

Integrating the given function with respect to time with limit 0 days to 3 days.

[tex]\int\limits^3_0 dr = \int\limits^3_0 (200+10t+13t^{2} ). dt\\\\\int\limits^3_0dr =\int\limits^3_0 \, 200dt + \int\limits^3_0 10tdt +\int\limits^3_0{13t^{2} dt\\\\\\\\R = [200t]^3_0 + [5t^{2} ]^3_0 + [\frac{13t^{3} }{3} ]^3_0\\\\R = 200[(3) - (0)] + 5 (3^{2} - 0^{2} ) + \frac{13}{3} [ 3^{3} - 0^{3} ]\\\\R = 200(3) + 5 (9) + \frac{13}{3}(27)\\\\R = 600+45+117\\\\R = 762[/tex]

Hence, The required change in the population of insects between day 0 and day 3 is 762.

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Answer:

x < 5

x > -3

Step-by-step explanation:

I didn't see the graph you mentioned, but this is the graph I did.

|x - 1| < 4

x-1 < 4    ,  -(x-1) < 4

x < 5

x > -3

Answer:

C

Step-by-step explanation:

The simplified expression of the given expression -5[tex]w^2y^{-2[/tex] / -15[tex]w^{-6}y^2[/tex] is [tex]w^{16[/tex].

The expression -5[tex]w^2y^{-2[/tex] / -15[tex]w^{-6}y^2[/tex]  can be simplified as follows:

= -5 * [tex]w^{2 - (-6)[/tex] * [tex]y^{-2 - 2[/tex] / -15 * [tex]w^{-6 - 2[/tex] * [tex]y^{2 - (-2)[/tex]

= -5 * [tex]w^8[/tex] * [tex]y^{-4[/tex] / -15 * [tex]w^{-8[/tex] * [tex]y^4[/tex]

= (-5 / -15) * ([tex]w^8[/tex] / [tex]w^{-8[/tex]) * ([tex]y^{-4[/tex] / [tex]y^4[/tex])

= 1 * [tex]w^{16[/tex] * [tex]y^0[/tex]

= [tex]w^{16[/tex]

Therefore, the simplified expression is w^16.

Here is a breakdown of the steps involved in the simplification:

The powers of w and y are combined using the distributive property of exponents.

The negative exponents are changed to positive exponents by dividing by the same base raised to the power of the negative exponent.

The factors of 5 and 15 are simplified.

The common factors of w and y are simplified.

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Answer:

The percentage decrease = 0.9%

Step-by-step explanation:

Using the formula

Percentage Decrease = [ (Initial Value - Final Value) / |Initial Value| ] × 100

                                    = [(9.80 - 9.71 ) / (9.80)] × 100

                                    = [0.09 / 9.80] × 100

                                    = 0.009 × 100  

                                    = 0.9%

Therefore, the percentage decrease = 0.9%

Answer:

the answer to that is 5 laps per day

Step-by-step explanation:

15 laps ÷ 3

3 days ÷3

5 laps

=

1 day

5 laps=days

Answer:

Umm !! it's 260

Step-by-step explanation:

Hope I'm right ?!!!!?!??

Answer:

x ≠ 5

Step-by-step explanation:

x ≠ 5

The reason for this is because if we use the input 5, this will be the result:

f(x) = 3/(5) - 5

f(x) = 3/0 = Undefined

Answer:

6

Step-by-step explanation:

s=9, t=12

2s-t = 2*9 -12 = 18 -12 = 6

Answer:

the answer is 6

Step-by-step explanation:

Because you do 2 times 9 = 18 then 18 - 12 = 6

Answer:

∠A = 45°

Step-by-step explanation:

It is given that,

sin A = sin B

∠C is a right angle.

If sin A = sin B, it means

sin 45 = sin 45 = [tex]\dfrac{1}{\sqrt2}[/tex]

It means that angle A and angle B is 45 degrees.

Answer:

a) 2002 different groups of 5 problems can be chosen from the 14 problems.

b) P=0.04995%

c) 21 different groups of 5.

P=1.04895%

Step-by-step explanation:

a)

In order to solve this problem we must ask ourselves: Does the order matter? We can see that in this case the order in which the problems are chosen doesn't really matter, so we are talking about a combination:

[tex]_{n}C_{r}=\frac{n!}{r!(n-r)!}[/tex]

in this case, n=14 while r=5, so our combination will be:

[tex]_{14}C_{5}=\frac{14!}{5!(14-5)!}[/tex]

which yields:

[tex]_{14}C_{5}=2002[/tex] which will be the answer for part a.

b)

In order to find the probability we can use the probability formula:

[tex]Probability=\frac{desired \hspace{5}outcome}{number\hspace{5} of \hspace{5} possible \hspace{5} outcomes}[/tex]

so in this case there is only 1 desired outcome out of the 2002 possible outcomes so our probability is:

[tex]P=\frac{1}{2002}[/tex]

which is the same as:

P=0.04995%

c) The same applies to part c. In order to find the number of groups Silvia did, we can make us of the combination formula:

[tex]_{7}C_{5}=\frac{7!}{5!(7-5)!}[/tex]

which yields:

[tex]_{14}C_{5}=21[/tex]

so there are 21 different groups of 5 she did by solving 7 problems.

So we can use the same formula to find the probability that one of the groups she completed comprised the group selected to be graded so we get:

[tex]P=\frac{21}{2002}=\frac{3}{286}[/tex]

which is the same as:

P=1.04895%

(remember that in order to turn a decimal number into a percentage you need to multiply the decimal number by 100)

Answer:

28

Step-by-step explanation:

-3 * (x-11) = -51

x-11 = 17

x = 28

Answer:

9x^6 over 4y^8

Step-by-step explanation:

Answer:

E. 9x^6 / 4y^8

Step-by-step explanation:

Use exponent rule: a^-b = 1/a^b

Answer:

4

Step-by-step explanation:

7+7+7+7 or 28/7 =4

Answer:

28.26 cm^2

Step-by-step explanation:

A = (pi)r^2

A = 3.14 * (3 cm)^2

A = 3.14 * 9 cm^2

A = 28.26 cm^2

Answer:

thanswer to this is...................

Step-by-step explanation:

unknown

or 148 degrees

Answer:

148 degrees... if it's so easy then why u couldn't u answer it

Answer:

C. y=4x+13

Step-by-step explanation:

To solve this equation first find the slope. Do this by using the slope formula, m=[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex], so plug in the points[tex]\frac{1+3}{-3+4}[/tex] which equals 4/1 or 4. Since now we know the slope is 4 we can put the equation into slope-point form, I will be using (-4,-3) for this equation. y+3=4(x+4), then solve for y. After solving you get y=4x+13.

Answer:

x = 15

Step-by-step explanation:

137+28=165

All angles in a triangle add up to 180

So 180-165 = 15

15 = x

Answer:

I think c is the answer....

Answer:

The calculated mean price is a sample mean and it is denoted by x.

Step-by-step explanation:

Given that

Mean price of paintings = $3550

Number of paintings = 20

In order to decide whether it is a population mean or a sample mean we have to understand the terms first.

Population:

Population is the overall collection from which a sample or observations are taken.

Sample:

The small or less number of observations that we take from a large population to perform data analysis is called sample.

In the given scenario, all the paintings at the art fair are population while the number of paintings that the art collector bought is a sample.

Hence,

The calculated mean price is a sample mean and it is denoted by x.

Answer: Yes

Step-by-step explanation:

Answer:

yesh it does :>

Step-by-step explanation:

Answer:

1. is Line C

2. is line A

(slope, y-intercept)

4. (1, 4)

6. (-5/7, -2)

8. (6, 2)

9. (1/2, -7)

10.

a) you've already done this

b)-4200

c)21000

d) 5

11.

draw a line between the intercepts and add arrows to each end to graph the line easily

y- intercept is -6 ( at 0, -6)

x intercept is 2 ( at 2, 0)

Answer:

Two angles are called complementary when their measures add to 90 degrees. Two angles are called supplementary when their measures add up to 180 degrees.

Answer:

the oldest sister spent 2.70$ (given)

the middle sister spent 10.80$

and the youngest sister spent 7.12$

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

[tex]M = (9,3)[/tex]

Step-by-step explanation:

Given

[tex](x_1,y_1) = (4,8)[/tex]

[tex](x_2,y_2) = (14,-2)[/tex]

Required

Find the midpoint (M)

The midpoint is calculated as follows:

[tex]M = (\frac{1}{2}(x_1+x_2),\frac{1}{2}(y_1+y_2))[/tex]

Substitute values for x's and y's

[tex]M = (\frac{1}{2}(4+14),\frac{1}{2}(8-2))[/tex]

[tex]M = (\frac{1}{2}(18),\frac{1}{2}(6))[/tex]

[tex]M = (\frac{1}{2}*18,\frac{1}{2}*6)[/tex]

[tex]M = (9,3)[/tex]

Hence, the midpoint is (9,3)