Simplify. (In the problems where you combine fractions with unlike denominators leave the denominators in factored form.)

Answer: 432 sq ft.

Step-by-step explanation: I decomposed the figure above into halves where the dotted line is drawn. I multiplied 25 x 10 to find the area of the rectangle on the right, pretending for now that it is a complete rectangle, which equals 250. Then, I subtracted 15 from 25, which equals 10, to find the length of the right triangle that’s missing to make the right half of the decomposed figure a rectangle. Then I multiplied 10 x 10, or 10 to the second power divided by 2 because 10 x 10 would be the formula to find a rectangle, and a right triangle is half of a rectangle so you would divide by 2. 10 x 10 divided by 2 because equals 50. 250 - 50 = 200. Next, you do the same thing for the other half of the irregular figure. I subtracted 4 from 25 to get 21. Then, I multiplied 21 x 16 divided by 2 which equals 168. Now, you multiply 25 x 16 which equals 400. 400 - 168 = 232. 200, the answer for the area of the other half of the decomposed figure, must be added to 232 to find your answer for the total area.

Answer:

Given:

< or > = open circle

≤ or ≥ = closed circle

So we are looking for:

Therefore, the attached is the correct answer.

Answer: 5/3

Step-by-step explanation:

1. 3/x = 5/y

2. Cross multiply

3y = 5x

3. Dividing the sides by 3

y = 5x/3

4. Dividing the sides by x

y/x = 5/3

Answer:

[tex]Hi, ~I'm ~beinggreat78,~ and~ am~ here~ to~ help~ you.[/tex]

The answer is D. Tanɵ. But why? Let's break it down. Tan pi + theta in the base equation should look like this...

[tex]\frac{tan\pi+ tanTheta}{1 - tan\pi * tanTheta}[/tex]

We now have to simplify this expression. Let's do that.

[tex]tan(\pi) = \frac{sin\pi }{cos\pi } = \frac{0}{-1} = 0[/tex]

Now that we have broken this problem into simpler fragments, we have to put it all together, The final equation should look like the one below!

[tex]tan(\pi + Theta) = \frac{0 + tanTheta}{1 - 0} = tanTheta[/tex]

With that information, we have solved the problem, your final answer is tanɵ

What have we learned?

Answer: 96

Step-by-step explanation: formula for volume is lwh. 2 times 8 times 12 equals 192. divide that by 2 because there is only half left.

Answer:

Rational:2.1,2.2

Irrational:[tex]\sqrt{5},\sqrt{6}[/tex]

Step-by-step explanation:

Trial and error

It's a geometric sequence

Formula:&

[tex]\\ \sf\longrightarrow a(n)[/tex]

[tex]\\ \sf\longrightarrow ar^{n-1}[/tex]

[tex]\\ \sf\longrightarrow 1.3125(4)^{n-1}[/tex]

Answer:

Step-by-step explanation:

(i)

PQRS is a parallelogram (given)

      ∴ QT = TS (Diagonals of a parallelogram bisects each other)

also,   QT = RM (given)

      ∴TS = RM

PQRS is a parallelogram,

     ∴RT = PT (Diagonals of a parallelogram bisects each other)

also, SM = PT (given)

    ∴RT = SM

TS = RM

RT = SM

∴ RTSM is a parallelogram (both pairs of opposite sides are equal in length)

(ii)

QP // RS (Opposite sides of a parallelogram are parallel)

∴ ∡RQP = ∡NRS (Corresponding ∡s)

RTSM is a parallelogram(Proved above)

∴MS // RT (Opposite sides of a parallelogram are parallel)

∴NS//RP

∴∡RNS = ∡ QRP (Corresponding ∡s)

in ΔPQR and Δ NSR,

QP = RS (Opposite sides of a parallelogram are equal)

∡RQP = ∡NRS (Proved above)

∡RNS = ∡ QRP(Proved above)

∴ ΔPQR≡ΔSRN (AAS)

Corresponding sides of ≡ Δs are equal, ∴QR = RN

Answer:

The fully factored form of the function f(x) is : (x+5)(x-1)(x-3)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Look at the photo.

Step-by-step explanation:

The formula is y=mx+b. So, for the first one you start at the coordinate (0, 2) and then move down 2 and right one.

For the second one you start at the coordinate (0, -2) and then move down two and move right one.

Answer:

1/2

Step-by-step explanation:

It appears to be 1/2 because the areas labeled "parrots" and "sparrows" takes up half of the pie chart. hope this helped!

Answer: the answer is 1 over 2 as a fraction

Step-by-step explanation:

Using it's concept, it is found that there is a 0.625 = 62.5% probability that an individual owns a stock.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, out of 200 graduates, 35 + 90 = 125 of them own stocks, hence:

p = 125/200 = 0.625.

There is a 0.625 = 62.5% probability that an individual owns a stock.

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The equation solved for w is:

w = A/l

The correct option is A.

A pair of algebraic equations with the equal symbol (=) in the center and the same value are referred to as an equation.

Starting with the equation:

A/l = lw/l

We can simplify it by multiplying both sides by l:

A = lw

To solve for w, we need to isolate it on one side of the equation.

We can do this by dividing both sides by l:

A/l = w

Therefore, the required equation is A/l = w.

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Answer:

slope = 3x

Step-by-step explanation:

Equation is y = 3x - 6
3x is slope

Answer:

we need more information

Answer:

triangle D and F

Step-by-step explanation:

triangle D and F are the same as A, just angled differently.

God bless! hope i helped someone, somehow.

Answer:

D,F

Step-by-step explanation:

Answer:

6x³ - 15x² - 1

3x divided by 3x is 1

So, here we are to simplify the polynomial :

[tex] \\ \longrightarrow \sf \qquad6x^3 - 15x^2 - \frac{3x}{ 3x}\\ \\[/tex]

We can simplify it as,

[tex]\\ \longrightarrow \sf \qquad6x^3 - 15x^2 - 1 \\ \\[/tex]

Some points to know :

Answer:

156,000

Step-by-step explanation:

291 divided by 97 is 3. 52,000 x 3 = 156,000.

Population will be 6 times of present population in 291 years.

The number of people in the city at a particular time is called population of the city.

Present population of the city = 52000

According to the problem, Population doubles in size in every 97 years.

After 97 years, the population = Double of present population

                                                  = 2 × 52000 = 104000

Population in 97 years = 104000

Population in 1 year = [tex]\frac{104000}{97}[/tex]

So, population in 291 years =  [tex]\frac{104000}{97}[/tex]× 291 = 104000×3 = 312000

Population in 291 years from now = [tex]\frac{312000}{52000}[/tex] = 6 times

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Answer:

Step-by-step explanation:

Find the width as below

Substitute the values and solve for w

Now find the volume

Answer:

width = 3ft

volume = 144 ft³

Step-by-step explanation:

Pythagoras Theorem

[tex]\sf a^2+b^2=c^2[/tex]

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

The diagonal of the base of the aquarium, its height, and the length from the top corner to the opposite bottom corner forms a right triangle.  As we know two of the lengths, we can use Pythagoras Theorem to calculate the unknown length (diagonal of base).

Given:

[tex]\implies \sf 12^2+b^2=13^2[/tex]

[tex]\implies \sf b=\sqrt{13^2-12^2}[/tex]

[tex]\implies \sf b=5[/tex]

Now we know the length of the diagonal of the base, we can again use Pythagoras Theorem to find the width of the aquarium.

Given:

[tex]\sf \implies 4^2+b^2=5^2[/tex]

[tex]\sf \implies b=\sqrt{5^2-4^2}[/tex]

[tex]\sf \implies b=3[/tex]

Therefore, the width of the aquarium is 3 ft.

As the aquarium is modeled as a rectangular prism:

[tex]\begin{aligned}\textsf{Volume of a rectangular prism} & = \sf width \times length \times height\\ \implies \textsf{Volume of aquarium} & = \sf 3\:ft \times 4\:ft \times 12\:ft\\& = \sf 144 \:\:ft^3\end{aligned}[/tex]

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Let's use section formula ~

[tex]\qquad \sf  \dashrightarrow \:x = \dfrac{mx_2 + nx_1}{m + n} [/tex]

[tex]\qquad \sf  \dashrightarrow \:y = \dfrac{my_2 + ny_1}{m + n} [/tex]

And since mid point divides a line segment Into two equal parts, m : n = 1 : 1

so, take m = n = 1

[tex]\qquad \sf  \dashrightarrow \:x = \dfrac{(1 \times - 1)+(1 \times - 2)}{ 1+ 1} [/tex]

[tex]\qquad \sf  \dashrightarrow \:x = \dfrac{- 1- 2}{ 2} [/tex]

[tex]\qquad \sf  \dashrightarrow \:x = \dfrac{ - 3}{ 2} [/tex]

Now, let's find y - coordinate ~

[tex]\qquad \sf  \dashrightarrow \:y = \dfrac{(1 \times - 5) + (1 \times - 4)}{1 + 1} [/tex]

[tex]\qquad \sf  \dashrightarrow \:y = \dfrac{ - 5 - 4}{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \:y = \dfrac{ - 9}{2} [/tex]

So, coordinates of midpoint is ~

[tex]\qquad \sf  \dashrightarrow \:( - \dfrac{3}{2} ,- \dfrac{9}{2} )[/tex]

Answer: 100 grams

Step-by-step explanation:

Mass remains constant. So 100 grams of water will be 100 grams of water vapor

Answer:

Length = 8+7 = 15

Width = 8

Step-by-step explanation:

                       New

Length = x+7 , x+4

Width = x ,x+2

(x+7) x = (x+4)( x+2)

expand and simplify x =8

The length of the shorter side length of original rectangle is 8 inches and of original rectangle longer side length is 15 inches.

Let l is the length and b is the breadth of the rectangle.

then the area of the rectangle is ab.

Given One side of a rectangle is 7 inches longer than another side.

then shorter side length is x and the large side length is 7+x.

then the area of the original rectangle is x(x+7)

Now calculate the sides of the new rectangle.

longer side of this rectangle decreases by 3 then new side is 7+x -3= 4+x

The shorter side increases by 2 inches then x+2.

So new rectangle area is (x+4)(x+2)

Both rectangle area is equal then

(x+4)(x+2) = x(x+7)

x² +2x+4x+8 = x²+7x

x²+6x+8 = x²+7x

x²-x²+7x-6x = 8

x = 8

Since a shorter side length is 8 inches and a longer side length is 8+7 =15 inches.

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Answer:

When dissolved, bases release hydroxide ions, OH-(aq) into solution.

Step-by-step explanation:

Water is the product of an acid and base reacting. Chemists say that the acid and base cancel or neutralise each other, hence the reaction is known as "neutralisation"

Answer: It increases the concentration of OH- in solution.

Step-by-step explanation:

The possible number of cupcakes is less than or equal to 23

let

The inequality:

2k ≤ 46

divide both sides by 2

k ≤ 46 / 2

k ≤ 23

Therefore, the possible number of cupcakes is less than or equal to 23

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103-7 = 96 then 96/2 = 48 so we can say that Sydney is 48 and devaughn is 48+7 = 55 years old.

Therefore, Sydney is 48 years of age.

Answer:x=4 (0,0)

Step-by-step explanation:

Determine the zeros of function,factor the functions. Set the factored function equal to 0 and solve. Then find the y-y-intercept of the given function by setting x equal to 00and Solving for y.