Select the equation of a straight line that is parallel to the line 4y = 3x + 5

Answer:

Step-by-step explanation:

From the information given:

Tank's Capacity = 600 gal

Original content of water = 200 gal

Salt solution = 100 lb

In the tank:

Suppose x(t) = amount of salt at time (t); &

V(t) = volume of water

Then,

V(t) = 200 + t

and [tex]x'(t) = 3 - \dfrac{2x(t)}{200+t}[/tex]

From the above linear equation, the integrating factor can be computed as:

[tex]x(t) = \Bigg(e^{\int \dfrac{2}{200+t}} \Bigg)^{dt}[/tex]

[tex]= e^{2 \ log (200+t)}[/tex]

= (200 + t)²

The general solution can now be expressed as:

[tex]x(t) = \dfrac{1}{(200+t)^2}\Bigg( \int 3(200+t)^2 \ dt +C\Bigg)[/tex]

We know that C = integrating factor, thus taking the integral:

[tex]x(t) = \dfrac{(200+t)^3 +C}{(200+t)^2}[/tex]

At the initial condition, x(0) = 100

∴

[tex]100= \dfrac{(200)^3 +C}{(200)^2}[/tex]

C = ((200)²×100) - 200³

C = -4 × 10⁶

Hence, at any time t, the amount of salt is:

[tex]x(t) = \dfrac{(200+t^2) - 4\times 10^6}{(200+t)^2}[/tex]

Answer: A. 30 students in the lunchroom.

Step-by-step explanation:

A representative sample simply refers to the sample that has same characteristics just like the population.

A random-based selection is regarded as a representative of the population. In this case, the random sample that represents a representative sample of the number of students who enjoy science class is "30 students in the lunchroom".

When the students in the lunchroom are chosen, then it's a representation of the entire students in the school. This is the best option when compared to other options as they don't represent the students entirely.

Answer:

30 students in the lunchroom

Step-by-step explanation:

Got it right on the test.

Answer:

∠ Y ≈ 32.7°

Step-by-step explanation:

Using the law of Cosines

cosY = [tex]\frac{x^2+z^2-y^2}{2xz}[/tex]

with x = 90, y = 55, z = 50

cosY = [tex]\frac{90^2+50^2-55^2}{2(90)(50)}[/tex] = [tex]\frac{8100+2500-3025}{9000}[/tex] = [tex]\frac{7575}{9000}[/tex] , then

∠ Y = [tex]cos^{-1}[/tex] ([tex]\frac{7575}{9000}[/tex] ) ≈ 32.7° ( to the nearest tenth )

Answer:

(x, y) = (-5, 5)

Answer:

Step-by-step explanation:

5x+2y=-15

Step 1: Add -2y to both sides.

5x+2y+−2y=−15+−2y

5x=−2y−15

Step 2: Divide both sides by 5

[tex]\frac{5x}{5}[/tex]=[tex]\frac{-2y-15}{5}[/tex]

x=[tex]\frac{-2-15}{5}[/tex]

x+2y=5

Step 1: Add -x to both sides.

x+2y+−x=5+−x

2y=−x+5

Step 2: Divide both sides by 2.

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

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

(gx2)-2

Hope this helps! :)

______________

Answer:

[tex]area = \frac{1}{2} \times base \times height \\ = \frac{1}{2} \times 2.9 \times 2.6 \\ = 3.77 \: ft {}^{2} [/tex]

Answer:

3.77 ft²

Step-by-step explanation:

Area of a triangle is half base length multiplied by the height.

0.5(2.9 × 2.6) = 3.77 ft²

Answer:

Option B. 489.8 ft²

Step-by-step explanation:

From the question given above, the following data were obtained:

Height (h) = 13 ft

Radius (r) = 6 ft

Pi (π) = 3.14

Lateral surface area (Aₗ) =?

The lateral surface area of the cylinder can be obtained as follow:

Aₗ = 2πrh

Aₗ = 2 × 3.14 × 6 × 13

Aₗ = 489.8 ft²

Therefore, the lateral surface area of the cylinder is 489.8 ft²

Answer:

9:42

Step-by-step explanation:

First, convert his second run into minutes so its easier to simplify

than divide both the timings by 5

to get the answer as 9:42 as the simplest ratio form

The given triangle is not a right-angle triangle as the sides don't form a Pythagorean triplet.

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the le right triangle is equal to the square on the hypotenuse (the Pythagoras the right angle)—or, in familiar algebraic notation, a² + b² = c².

Given her:  Three squares whose sides form one Pythagoreans of a triangle .

Now a²=58

b²=10

b=√10

c²=64

c=8

Clearly √10<√58<8

Thus c must be the hypotenuse of the triangle.

Using Pythagoras' theorem we get

√10²+√58²=68≠64

Hence, The given triangle is not a right angle triangle as the sides don't form a Pythagorean triplet.

Learn more about the Pythagoras theorem here:

https://brainly.com/question/343682

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Answer:

I agree with Elena. See explanation below.

Step-by-step explanation:

A right angle is equal to 90 degrees.

A straight line is equal to 180 degrees.

Elena: w + 148 = 180

Elena's equation is correct because 148 degrees is represented by variable k. When adding variable k and w together, they form a straight line which is equiavlent to 180 degrees. By using this equation, Elena can solve for w after isolating the variable:

w + 148 = 180

w + 148 - 148 = 180 - 148

w = 32 degrees

Diego: x + 90 = 148

Diego is incorrect. He added 90 degrees because of the right angle, but he failed to realize that x is within 90 degrees, meaning he would either have to subtract x from 90 degrees or add both x and w to get to 90 degrees. He cannot solve for x or w by using this equation.

To solve for x, add both w and x to get 90 degrees. Since Elena showed us w equals 32 degrees, we can set up an equation:

w + x = 90

32 + x = 90

32 - 32 + x = 90 - 32

x = 58 degrees

Answer:

(x , y ) = (39/22 , -2/11 )

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

Answer:

-2,3 3,-7

Step-by-step explanation:

took test :)

Answer:

-2i - 3

I can't see a simpler way to explain it. You just have to work your way through each step.

Step-by-step explanation:

The question is what is i^303?

Remember that when the power is divisible by 4 the expression changes to 1

i^1 = i

i^2 = i * i = sqrt(-1)*sqrt(-1) = - 1

i^3 = i^2 * i = - i

i^4 = i^2 * i^2 = -1 * - 1 = 1

So what does i^303 =

i^300 * i^3

But 300 is evenly divisible by 4. (300 / 4 = 75) so i^300 = 1^75

i^3 = -i

So now you are ready to do the question

(2 - 3i) * -i

2*-i - 3i(-i)

-2i - 3(i^2 * - 1)

-2i - 3(-1 * - 1)

-2i - 3(1)

-2i - 3

Answer:

See below.

Step-by-step explanation:

Alternate Interior Angles - 1

Alternate Exterior Angles - 2

Corresponding Angles - 4

Same-side Exterior Angles - 5

Same-side Interior Angles - 3

Answer:38292

A

Step-by-step explanation:w

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Step-by-step explanation:

With reference to the regular hexagon, from the image above we can see that it is formed by six triangles whose sides are two circle's radii and the hexagon's side. The angle of each of these triangles' vertex that is in the circle center is equal to 360∘6=60∘ and so must be the two other angles formed with the triangle's base to each one of the radii: so these triangles are equilateral.

The apothem divides equally each one of the equilateral triangles in two right triangles whose sides are circle's radius, apothem and half of the hexagon's side. Since the apothem forms a right angle with the hexagon's side and since the hexagon's side forms 60∘ with a circle's radius with an endpoint in common with the hexagon's side, we can determine the side in this fashion:

tan60∘=opposed cathetusadjacent cathetus => √3=Apothemside2 => side=(2√3)Apothem

As already mentioned the area of the regular hexagon is formed by the area of 6 equilateral triangles (for each of these triangle's the base is a hexagon's side and the apothem functions as height) or:

Shexagon=6⋅S△=6(base)(height)2=3(2√3)Apothem⋅Apothem=(6√3)(Apothem)2

=> Shexagon=6×62√3=216

Answer:

5.5 hours

Step-by-step explanation:

Since every house has an initial charge of $50, we can begin with that

($50)

Then, let's define h as the number of hours. We know every hour is $70, although the hours is yet unknown so that can be

($70 * h) or simply ($70h)

Now, we know the total should end up to be $435, so after PEMDAS the equation will be

($70h + $50 = $435).

We subtract 50 from both sides so now we have $70h = $385.

Now we divide both sides by 70, giving us h = 5.5. Hope it helped!

The number of hours that the plumber work on the house calls should be 5.5.

Given that,

Based on the above information, the equation is as follows:

70h + 50 = 435

70h = 385

h = 5.5 hours

Therefore we can conclude that the number of hours that the plumber work on the house calls should be 5.5.

Learn more: brainly.com/question/3530056

Answer:

Hope you find it helpful

9514 1404 393

Answer:

  (A) -2, 3/7, 1/2, 1.2

Step-by-step explanation:

The numbers are in increasing order when they are listed left-to-right as they appear on the number line.

The only numbers that may give you trouble are 3/7 = 6/14 and 1/2 = 7/14.

The negative number is less than any positive number. 1.2 is greater than any fraction that is less than 1.

The correct ordering is found in choice A.

Answer:

try 492.43, this should be correct if I did this right

Answer:

12000 rad/min

Step-by-step explanation:

One formula we can use here is that the linear speed is the same, and the linear speed is equal to the angular speed multiplied by the radius.

Therefore, 2400π rad/min* 35 cm = 7 cm* x, with x representing the angular speed of the smaller wheel in radians per minutes. Dividing both sides by 7 cm, we get

2400π rad/min * 35 cm / 7 cm = x

2400 π rad/min * 5 = 12000 rad/min = x as our answer

Answer:

(x+1) (x+2)

Step-by-step explanation:

I this is it? If you meant x to the second power than I think this is the answer

Answer:

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

Step-by-step explanation:

To get the equation in the slope-intercept form first, put the equation in slope-point form using the information given. The slope-point form is [tex]y-(-2)=-3(x-2)[/tex]. Then solve for y.

Distribute -3 to [tex](x-2)[/tex],

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

Then, add -2 to both sides,

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

This is your final answer; the slope is -3 and the y-intercept is 4. There are also a few other ways to solve but I find this the easiest.

A)they have 20 dollar's in total

b)she is left with -12 dollar's

Explanation

total money = 5 + 7 + 8

                    = 20

Money Dalila had = 7 dollars

Money she spent = 12 dollars

money she is left with = 7 - 12 dollars

                                     = -5 dollars

Answer:

0.36

Step-by-step explanation:

Given, There Are 10000 Registered Voters in a City & Two Candidates Brown & Felix .

The Day Before Election , A Telephonic Poll Of 200 Randomly Registered Voters Was Conducted .

72 said they would vote for Brown , 118 Said they would vote for felix & 10 Were Undicided .

Now, The sample statistic is the number who would vote for Brown divided by the total number in the sample, or 72/200 = 0.36    

& To Find How Many of 10000 voters to vote Brown Just Multiply 0.36 With 10000 ⇔ 0.36×10000=3600

Answer:

27°

Step-by-step explanation:

angle A + angle B + angle C=180 degree (sum of interior angles of a triangle )

angle A +90 + 63 =180

angle A +153 = 180

angle A =180 - 153

angle A =27 degree

Answer:

<A=27°

Step-by-step explanation:

D=63°

B= 90°

Angles in a triangle adds up to 180°

Therefore A= 180- (63+90)

=180 - 153

=27

Answer:

-22 and -23

hope this helped :D

Answer:

- 23 & - 22

Step-by-step explanation:

Let one integer be x, so the other integer is x + 1

x + x + 1 = - 45

2x + 1 = - 45

2x = - 46

x = - 23

The integers are - 23 and - 22.

Answer:

9

Step-by-step explanation:

3 - ( -6 ) = 9

Hope this helps! Brainliest?

Answer:

9

Step-by-step explanation:

the other answer is right.

to add a little bit of explanation :

you need to calculate the difference between -6 and +3.

and we are looking on the number line only for a distance and not for a direction, as the distance (or simple difference) between -6 and +3 is the same as between +3 and -6.

so, whatever we get as difference, we need to treat that result as positive number.

so, we get the difference between two numbers by subtracting one from the other.

either 3 - (-6), or -6 - 3

you do know that subtracting a negative number is the same as adding the same positive number ?

e.g. 3 - (-6) = 3 + 6 = 9

as for the other direction -6 - 3 = -9

but again, we have to take this in this context as a positive number.

in math we call this the absolute value of a number.

so, the answer is always 9.