A boat has a speed of 18 km/hr in still water. In a particular river, it takes 2 hours more to go 32 km upstream than to return to the same spot. What is the speed at which the water is flowing in the river?

Answer:

-x^3 + x^2 - 2x - 4

Step-by-step explanation:

You have to subtract

Let o = the polynomial

So you know 2x^3 - x^2 + 4x + 5 - o = x^3 + 2x - 9

Now you do 2x^3 - x^3 = x^3

then you -x^2 + answer = 0

you need to cancel it out

to cancel, you found out that it is x^2

Now you need to make from 4x to 2x.

To do that, you do 4x - 2x and you get 2x

Lastly you need to change -5 to 9. To do that you add -4.

Now since it is subtraction you have to distribute

2x^3 - x^2 + 4x - 5 -(x^3 - x^2 + 2x + 4)

= 2x^3 - x^2 + 4x + 5 - x^3 + x^2 -2x -4

= x^3 -2x + 9

Answer:

C is the answer.

0.75 = 3/4

1 = 4/4, 1-0.25 = 0.75

4/4 -1/4 = 3/4

Step-by-step explanation:

Answer:

14x + 7y= -2

Step-by-step explanation:

y + 2x = -2/7

↓

7y + 14x = -2

↓

14x + 7y = -2

Answer:

18.75

Step-by-step explanation:

[tex]\\ \rm\Rrightarrow 18\dfrac{3}{4}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{75}{4}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{75(25)}{100}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{1875}{100}[/tex]

[tex]\\ \rm\Rrightarrow 18.75[/tex]

Answer:

x is 10 and y is 20

Step-by-step explanation:

A city starts with a population of 500,000 people in 2007. Its population declines according to the equation

P(t) = 500,000e -0.099t

where P is the population in t years later. Approximately when will the population be half the initial amount?

Answer:

2014

Step-by-step explanation:

Given the exponential growth function :

P(t) = 500,000e^-0.099t

Where P is population in t years later

When the population will 1/2 the initial amount

1/2 the initial amount = 1/2 * 500,000 = 250,000

P(t) = 250,000

250,000 = 500000e^-0.099t

250,000/500000 = e^-0.099t

In(0.5) = - 0.099t

t = −0.69314 / - 0.099

t = 7.0014

t = 7

Year which population = 500,000 = 2007

Hence, half the population will be attained on (2007 + 7) = 2014

After 7 years population of the city will be half of the initial amount.

Population function:

[tex]P(t) = 500000 e^{-0.099t}[/tex]

Initial population means population at t=0

P(0) = 500000

Half of initial population = 250000

So, we need to calculate the time t when the population will be half of the initial amount.

[tex]250000= 500000 e^{-0.099t}\\\\e^{-0.099t} = \frac{1}{2}[/tex]

Taking log both sides

-0.099t (log e)= log (1/2)

The logarithm of e is 1 when considering the base of the log as e.

So, -0.099 t= -0.693

t=7

Therefore, After 7 years population of the city will be half of the initial amount.

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Answer: 17 pages

Step-by-step explanation:

One eighth of 136:

136 divided by 8 = 17

Answer:

17 pages

Step-by-step explanation:

1/8 x 136 = 17

Answer:

the answer of the question is 2.5

Answer:

C: -1 and 1/3

Step-by-step explanation:

Answer:

a number line or something like this

Answer:

B is the answer in the first quadrant x is positive

The number closest to 0 is the number whose absolute difference from 0 is the smallest

0.5 is the closest number to 0

The numbers are given as:

–4, 3, 0. 5, 1

Calculate their absolute difference with 0

|-4 - 0| = 4

|3 - 0| = 3

|0.5 - 0| = 0.5

|1 - 0| = 1

The smallest absolute difference is 0.5

Hence, 0.5 is the closest number to 0

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Answer:

A and C for sure. I'm not sure about D and E because I can't see the picture. If you tell me the other coordinates I can figure it out.

Answer:

5

Step-by-step explanation:

it is 5 because 5 + 6 + 7 + 8 =26

and 5 is the least

Answer:

Step-by-step explanation:

The polynomial that is prime is given by Option C: [tex]10x^2 - 4x +3x +6[/tex]

Those polynomials with integer coefficients that cannot be factored further, with factors of lower degree and integer coefficients are called prime polynomial.

(it is necessary that no factors exists having their coefficients are still integers and they're of lower degree)

Checking all the listed polynomials for them being prime or not:

Rewriting it as:

[tex]x^3+3x^2+2x+6 = x^2(x+3) + 2(x+3) = (x^2 + 2)(x+3)[/tex]

shows that this polynomial has factors. Thus, it isn't prime polynomial

Rewriting it as:

[tex]x^3 + 3x^2 -2x -6 = x^2(x+3) -2(x+3) = (x^2-2)(x+3)[/tex]

shows that this polynomial has factors. Thus, it isn't prime polynomial

We can rewrite it as:

[tex]10x^2 -4x + 3x -6 = 10x^2 -x -6 = f(x) \: \rm (say)[/tex]

This polynomial is prime polynomial as it is irreducible in terms of polynomials having their coefficients as integers.

Case 4: [tex]10x^2 -10x + 6x - 6[/tex]

It can be factored as:

[tex]10x(x-1) + 6(x-1) = (x-1)(10x-6)[/tex]

This is not a prime polynomial.

Thus, the polynomial that is prime is given by Option C: [tex]10x^2 - 4x +3x +6[/tex]

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Answer:

The polynomial that is prime is given by Option C:

What are prime polynomials?

Those polynomials with integer coefficients that cannot be factored further, with factors of lower degree and integer coefficients are called prime polynomial.

(it is necessary that no factors exists having their coefficients are still integers and they're of lower degree)

Checking all the listed polynomials for them being prime or not:

Case 1:

Rewriting it as:

shows that this polynomial has factors. Thus, it isn't prime polynomial

Case 2:

Rewriting it as:

shows that this polynomial has factors. Thus, it isn't prime polynomial

Case 3:

We can rewrite it as:

This polynomial is prime polynomial as it is irreducible in terms of polynomials having their coefficients as integers.

Case 4:

It can be factored as:

This is not a prime polynomial.

Thus, the polynomial that is prime is given by Option C:

Learn more about prime polynomials here:

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Step-by-step explanation:

Answer:

A Trinomial expression has 3 terms.

If it has degree 2, then the exponent of the leading term will be 2.

If the leading coefficient is -5, then the leading term will be [tex]-5x^2[/tex]

Written in standard form:  [tex]y=-5x^2+bx+c[/tex]

We are not given any information about the coefficients of the remaining two terms, so we can substitute any values for these:

Therefore, [tex]y=-5x^2+3x+2[/tex]

Note the standard form

Here we have

So

the expression is

Answer:

Step-by-step explanation:

They all give 8r so that is not the distinguishing characteristic.

The first one in column A gives

12r + t - 4r + 6t

12r - 4r + t + 6t

8r + 7t  

This is the third one in column B

2nd one in Column A

12r + 2t - (4r + 10t)               Remove the brackets

12r + 2t - 4r - 10t                  Pay close attention to 10t becoming -10t. The minus sign effects both terms inside the brackets.

12t - 4t + 2t - 10t                  Combine

8r - 8t                                   Now take out the common factor (8)

8(r - t)                                    That's the top one in column B

3rd one in column A

12(r + t) - 6(r +t) + 4(r + t) - 2(r+t)    They all have r+t so r + t is a common factor)

(r+t) [12 - 6 + 4 - 2]                          Combine

(r + t ) [ 8 ]

This is the second one in  column B

The trick here is to look out for common factors. Don't remove the brackets. But it takes a bit of practice before you know that

Answer:

<3 ~= <5 - Alternate Interior Angles Theorem

<3 ~= <7 - Corresponding Angles Theorem

<5 ~= <7 - Vertical Angles Theorem

line I || line m - Transitive Property

Answer:

C

Step-by-step explanation:

You divide first than you get ur fraction

Answer:

I think the answer may be option C

2 km east and 10 km north

Step-by-step explanation:

I did the activity and got the right answer.

Answer: 12km west and 2km south

Step-by-step explanation:

Just did it

Base on the similarity principle of triangles, the distance d across the lake as shown is 90 ft.

Two triangles are similar if they are only difference in size but have the same shape.

In similar triangles, corresponding sides are always in the same ratio.

Therefore, let's create a proportion from the triangles since they are similar.

40 / d = 20 / 45

cross multiply

45 × 40 = 20d

1800 = 20d

divide both sides by 20

1800 / 20 = 20d / 20

d = 90 ft

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Answer:

a + b = 30

Step-by-step explanation:

If we convert the percentages to decimals (120% = 1.2 & 80% = 0.8), we can use this equation to find B:  1.2A = 0.8b

Since we know a, we then have 1.2 * 12 = 0.8b

Solving for B gives us b = 18

12 + 18 = 30

Answer: c-it’s the same price

Step-by-step explanation: 20% off 200 is 160 and 200-160=40 so it’s the same