What is the first step for finding the quotient of 3x^3 z^5/5y * x^2 z^6/20y^3

Answers

Answer 1

The initial expression is:

[tex]\frac{3x^3z^5}{5y}\text{ / }\frac{x^2z^6}{20y^3}[/tex]

So the first step is to multiply the numerator of the second fraction with the denominator of the first franction and the denominator of the second fraction by the numerator of the first fraction so:

[tex]\frac{3x^3z^6}{5y}(\frac{20y^3}{x^2z^6})[/tex]

So is option C)


Related Questions

1. flight 1007 will hold 300 passengers the airline has booked 84% of the plane already. How many seats are open for the last-minute Travelers?2.Carly interviewed students to ask their favorite kind of television programs. 12 students claimed that they preferred comedies, 18 like drama 13 enjoy documentaries, and 7 voted for news programs what percentage of the students selected comedies?

Answers

The total passengers in the flight is P=300.

Determine the passenger who booked the seat in the flight.

[tex]\begin{gathered} Q=\frac{84}{100}\cdot300 \\ =252 \end{gathered}[/tex]

The number of seats booked by passenger is 252.

Determine the seats available for last-minutes travelers.

[tex]\begin{gathered} S=300-252 \\ =48 \end{gathered}[/tex]

So 48 seats available for the last minute travelers.

According to projections through the year 2030, the population y of the given state in year x is approximated byState A: - 5x + y = 11,700State B: - 144x + y = 9,000where x = 0 corresponds to the year 2000 and y is in thousands. In what year do the two states have the same population?The two states will have the same population in the year

Answers

The x variable represents the year in question. The year 2000 is represented by x = 0, 2001 would be repreented by x = 1, and so on.

The year in which both states would have the same population can be determined by the value of x which satisfies both equations.

We would now solve these system of equations as follows;

[tex]\begin{gathered} -5x+y=11700---(1) \\ -144x+y=9000---(2) \\ \text{Subtract equation (2) from equation (1);} \\ -5x-\lbrack-144x\rbrack=11700-9000 \\ -5x+144x=2700 \\ 139x=2700 \\ \text{Divide both sides by 139} \\ x=19.4244 \\ x\approx19\text{ (rounded to the nearest whole number)} \end{gathered}[/tex]

Note that x = 19 represents the year 2019

ANSWER:

The two states will have the same population in the year 2019

The width of a rectangle measures (5v-w)(5v−w) centimeters, and its length measures (6v+8w)(6v+8w) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?

Answers

The most appropriate choice for perimeter of rectangle will be given by -

Perimeter of rectangle = (22v + 14w) cm

What is perimeter of rectangle?

At first it is important to know about rectangle.

Rectangle is a parallelogram in which every angle of the parallelogram is 90°.

Perimeter of rectangle is the length of the boundary of the rectangle.

If l is the length of the rectangle and b is the breadth of the rectangle, then perimeter of the rectangle is given by

Perimeter of rectangle = [tex]2(l + b)[/tex]

Length of rectangle = (5v - w) cm

Breadth of rectangle = (6v + 8w) cm

Perimeter of rectangle = 2[(5v - w) + (6v + 8w)]

                                      = 2(11v + 7w)

                                      = (22v + 14w) cm

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Complete Question

The width of a rectangle measures (5v−w) centimeters, and its length measures(6v+8w) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?

The half-life of radium is 1690 years. If 70 grams are present now, how much will be present in 570 years?

Answers

Solution

Given that

Half life is 1690 years.

Let A(t) = amount remaining in t years

[tex]\begin{gathered} A(t)=A_0e^{kt} \\ \\ \text{ where }A_{0\text{ }}\text{ is the initial amount} \\ \\ k\text{ is a constant to be determined.} \\ \end{gathered}[/tex]

SInce A(1690) = (1/2)A0 and A0 = 70

[tex]\begin{gathered} \Rightarrow35=70e^{1690k} \\ \\ \Rightarrow\frac{1}{2}=e^{1690k} \\ \\ \Rightarrow\ln(\frac{1}{2})=1690k \\ \\ \Rightarrow k=\frac{\ln(\frac{1}{2})}{1690} \\ \\ \Rightarrow k=-0.0004 \end{gathered}[/tex]

So,

[tex]A(t)=70e^{-0.0004t}[/tex][tex]\Rightarrow A(570)=70e^{-0.0004(570)}\approx55.407\text{ g}[/tex]

Therefore, the answer is 55.407 g

Use the distance formula to find the distance between the points given.(-9,3), (7, -6)

Answers

Given the points:

[tex](-9,3),(7,-6)[/tex]

You need to use the formula for calculating the distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1^})^2[/tex]

Where the points are:

[tex]\begin{gathered} (x_1,y_1) \\ (x_2,y_2) \end{gathered}[/tex]

In this case, you can set up that:

[tex]\begin{gathered} x_2=7 \\ x_1=-9 \\ y_2=-6 \\ y_1=3 \end{gathered}[/tex]

Then, you can substitute values into the formula and evaluate:

[tex]d=\sqrt{(7-(-9))^2+(-6-3)^2}[/tex][tex]d=\sqrt{(7+9)^2+(-9)^2}[/tex][tex]d=\sqrt{(16)^2+(-9)^2}[/tex][tex]d=\sqrt{256+81}[/tex][tex]d=\sqrt{337}[/tex][tex]d\approx18.36[/tex]

Hence, the answer is:

[tex]d\approx18.36[/tex]

factoring out: 25m + 10

Answers

Answer:

5(5m + 2)

Explanation:

To factor out the expression, we first need to find the greatest common factor between 25m and 10, so the factors if these terms are:

25m: 1, 5, m, 5m, 25m

10: 1, 2, 5, 10

Then, the common factors are 1 and 5. So, the greatest common factor is 5.

Now, we need to divide each term by the greatest common factor 5 as:

25m/5 = 5m

10/5 = 2

So, the factorization of the expression is:

25m + 10 = 5(5m + 2)

If the given is -3x+20=8 What should the subtraction property of equality be?

Answers

Given the equation

[tex]-3x+20=8[/tex]

To apply the subtraction property of equality, we subtract 20 from both sides.

[tex]-3x+20-20=8-20[/tex]

triangle HXI can be mapped onto troangle PSL by a reflection If m angle H = 157 find m angle S

Answers

From the information provided, the triangle HXI can be mapped onto triangle PSL. This means the vertices of the reflected image would now have the following as same measure angles;

[tex]\begin{gathered} \angle H\cong\angle P \\ \angle X\cong\angle S \\ \angle I\cong\angle L \end{gathered}[/tex]

Measure of angle S cannot be determined from the information provided because there is insufficient information given to determine the measure of angle X, hence the angle congruent to it (angle S) likewise cannot be determined.

2. Luis hizo una excursión de 20 km 75 hm 75 dam 250 m en tres etapas. En la primera recorrió 5 km 5 hm, y en la segunda 1 km 50 dam más que en la anterior. ¿Cuánto recorrió en la tercera etapa? Expresa el resultado de forma compleja

Answers

[tex]\begin{gathered} 5\text{ km 5 hm - first stage} \\ 6\text{ km 5 hm 50 dam - second stage} \\ \text{Subtract that from the total} \\ 14\text{ km 70 hm 25 dam 250 m - this would be third stage} \end{gathered}[/tex]

12 + 24 =__(__+__)
Find the GCF. The first distributing number should be your GCF

Answers

A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common. For instance, the numbers 12, 20, and 24 share the components 2 and 4.

Therefore, 12 and 24 have the most things in common. Figure 2: LCM = 24 and GCF = 12 for two numbers.

Find the other number if one is 12, then. What does 12 and 24's GCF stand for?

Example of an image for 12 + 24 = ( + ) Locate the GCF. You should distribute your GCF as the first number.

12 is the GCF of 12 and 24. We must factor each number individually in order to determine the highest common factor of 12 and 24 (factors of 12 = 1, 2, 3, 4, 6, 12; factors of 24 = 1, 2, 3,.

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4) What is perimeter of this shape? * 4 cm 2 cm

Answers

the perimeter is the sum of the outside sides. So in this case is 4+4+2+2+2+2=16

so the answer is 16cm

Identify the vertex of the function below.f(x) - 4= (x + 1)2-onSelect one:O a. (-4,1)O b.(1,-4)O c. (-1,-4)O d.(-1,4)

Answers

The standard equation of a vertex is given by:

[tex]f(x)=a(x-h)^2+k[/tex]

where (h,k) is the vertex.

Comparing with the given equation after re-arranging:

[tex]f(x)=(x+1)^2+4[/tex]

The vertex of the function is (-1, 4)

Help me please Circle describe and correct each error -2=-3+x/4-2(4)-3+x/4•48=-3+x+3X=11

Answers

Answer

The error in the solution is circled (red) in the picture below.

The equation can be solved correctly as follows

[tex]\begin{gathered} -2=\frac{-3+x}{4} \\ \\ Multiply\text{ }both\text{ }sides\text{ }by\text{ }4 \\ \\ -2(4)=\frac{-3+x}{4}\cdot4 \\ \\ -8=-3+x \\ \\ Add\text{ }3\text{ }to\text{ }both\text{ }sides \\ \\ -8+3=-3+x+3 \\ \\ x=-5 \end{gathered}[/tex]

f(x) = x2 + 4 and g(x) = -x + 2Step 2 of 4: Find g(d) - f(d). Simplify your answer.Answer8(d) - f(d) =

Answers

Answer:

[tex]\begin{equation*} g(d)-f(d)=-d^2-d-2 \end{equation*}[/tex]

Explanation:

Given:

[tex]\begin{gathered} f(x)=x^2+4 \\ g(x)=-x+2 \end{gathered}[/tex]

To find:

[tex]g(d)-f(d)[/tex]

We can find g(d) by substituting x in g(x) with d, so we'll have;

[tex]g(d)=-d+2[/tex]

We can find f(d) by substituting x in f(x) with d, so we'll have;

[tex]f(d)=d^2+4[/tex]

We can now go ahead and subtract f(d) from g(d) and simplify as seen below;

[tex]\begin{gathered} g(d)-f(d)=(-d+2)-(d^2+4)=-d+2-d^2-4=-d^2-d+2-4 \\ =-d^2-d-2 \\ \therefore g(d)-f(d)=-d^2-d-2 \end{gathered}[/tex]

Therefore, g(d) - f(d) = -d^2 - d -2

what is 12 + 0.2 + 0.006 as a decimal and word form

Answers

[tex]12+0.2+0.006=12.206[/tex]

twelve and two hundred six thousandths

The beginning mean weekly wage in a certain industry is $789.35. If the mean weekly wage grows by 5.125%, what is the new mean annual wage? (1 point)O $829.80O $1,659.60O $41,046.20$43,149.82

Answers

Given:

The initial mean weekly wage is $ 789.35.

The growth rate is 5.125 %.

Aim:

We need to find a new annual wage.

Explanation:

Consider the equation

[tex]A=PT(1+R)[/tex]

Let A be the new annual wage.

Here R is the growth rate and P is the initial mean weekly wage and T is the number of weeks in a year.

The number of weeks in a year = 52 weeks.

Substitute P=789.35 , R =5.125 % =0.05125 and T =52 in the equation.

[tex]A=789.35\times52(1+0.05125)[/tex]

[tex]A=43149.817[/tex]

[tex]A=43149.82[/tex]

The new mean annual wage is $ 43,149.82.

Final answer:

The new mean annual wage is $ 43,149.82.

A chemist has 30% and 60% solutions of acid available. How many liters of each solution should be mixed to obtain 570 liters of 31% acid solution? Work area number of liters | acid strength | Amount of acid 30% acid solution 60% acid solution 31% acid solution liters of 30% acid liters of 60% acid

Answers

Let the amount of 30% acid solution be a

Let the amount of 60% acid solution be b

Given, "a" and "b" mixed together gives 570 liters of 31% acid. We can write:

[tex]0.3a+0.6b=0.31(570)[/tex]

Also, we know 30% acid and 60% acid amounts to 570 liters, thus:

[tex]a+b=570[/tex]

The first equation becomes:

[tex]0.3a+0.6b=176.7[/tex]

We can solve the second equation for a:

[tex]\begin{gathered} a+b=570 \\ a=570-b \end{gathered}[/tex]

Putting this into the first equation, we can solve for b. The steps are shown below:

[tex]\begin{gathered} 0.3a+0.6b=176.7 \\ 0.3(570-b)+0.6b=176.7 \\ 171-0.3b+0.6b=176.7 \\ 0.3b=176.7-171 \\ 0.3b=5.7 \\ b=\frac{5.7}{0.3} \\ b=19 \end{gathered}[/tex]

So, a will be:

a = 570 - b

a = 570 - 19

a = 551

Thus,

551 Liters of 30% acid solution and 19 Liters of 60% acid solution need to be mixed.

What is the solution set of x over 4 less than or equal to 9 over x?

Answers

we have

[tex]\frac{x}{4}\leq\text{ }\frac{9}{x}[/tex]

Multiply in cross

[tex]x^2\leq36[/tex]

square root both sides

[tex](\pm)x\leq6[/tex]

see the attached figure to better understand the problem

the solution is the interval {-6,6}

the solution in the number line is the shaded area at right of x=-6 (close circle) and the shaded area at left of x=6 (close circle)

If b is a positive real number and m and n are positive integers, then.A.TrueB.False

Answers

we have that

[tex](\sqrt[n]{b})^m=(b^{\frac{1}{n}})^m=b^{\frac{m}{n}}[/tex]

therefore

If b is a positive real number

then

The answer is true

Add the rational expression as indicated be sure to express your answer in simplest form. By inspection, the least common denominator of the given factor is

Answers

Notice that the least common denominator is 9*2=18, therefore:

[tex]\begin{gathered} \frac{x-3}{9}+\frac{x+7}{2}=\frac{2(x-3)}{9\cdot2}+\frac{9(x+7)}{9\cdot2}, \\ \frac{x-3}{9}+\frac{x+7}{2}=\frac{2x-6}{18}+\frac{9x+63}{18}, \\ \frac{x-3}{9}+\frac{x+7}{2}=\frac{2x-6+9x+63}{18}, \\ \frac{x-3}{9}+\frac{x+7}{2}=\frac{11x+57}{18}\text{.} \end{gathered}[/tex]

Answer:

[tex]\frac{x-3}{9}+\frac{x+7}{2}=\frac{11x+57}{18}\text{.}[/tex]

Percents build on one another in strange ways. It would seem that if you increased a number by 5% and thenincreased its result by 5% more, the overall increase would be 10%.7. Let's do exactly this with the easiest number to handle in percents.(a) Increase 100 by 5%(b) Increase your result form (a) by 5%.(C) What was the overall percent increase of the number 100? Why is it not 10%?

Answers

Answer:

a) 105

b) 110.25

c) Increase of 10.25%. It is not 100% because the second increase of 5% is over the first increased value, not over the initial value.

Step-by-step explanation:

Increase and multipliers:

Suppose we have a value of a, and want a increse of x%. The multiplier of a increase of x% is given by 1 + (x/100). So the increased value is (1 + (x/100))a.

(a) Increase 100 by 5%

The multiplier is 1 + (5/100) = 1 + 0.05 = 1.05

1.05*100 = 105

(b) Increase your result form (a) by 5%.

1.05*105 = 110.25

(C) What was the overall percent increase of the number 100? Why is it not 10%?

110.25/100 = 1.1025

1.1025 - 1 = 0.1025

Increase of 10.25%. It is not 100% because the second increase of 5% is over the first increased value, not over the initial value.


Find the domain of the function f(x)=√100x²

Answers

The domain of the function √(100x²) will be (-∞,∞) as the definition of domain states that the set of inputs that a function will accept is known as the domain of the function in mathematics

What is domain?

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the set of values it can take as input.

What is function?

A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

Here,

The function is √(100x²).

The domain would be (-∞,∞).

The set of inputs that a function will accept is known as the domain of the function in mathematics, and the domain of the function √(100x²) will be (-∞,∞), according to the definition of domain.

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I'm attempting to solve and linear equation out of ordered pairs in slopes attached

Answers

Line equationInitial explanation

We know that the equation of a line is given by

y = mx + b,

where m and b are numbers: m is its slope (shows its inclination) and b is its y-intercept.

In order to find the equation we must find m and b.

In all cases, m is given, so we must find b.

We use the equation to find b:

y = mx + b,

↓ taking mx to the left side

y - mx = b

We use this equation to find b.

1

We have that the line passes through

(x, y) = (-10, 8)

and m = -1/2

Using this information we replace in the equation we found:

y - mx = b

↓ replacing x = -10, y = 8 and m = -1/2

[tex]\begin{gathered} 8-(-\frac{1}{2})\mleft(-10\mright)=b \\ \downarrow(-\frac{1}{2})(-10)=5 \\ 8-5=b \\ 3=b \end{gathered}[/tex]

Then, the equation of this line is:

y = mx + b,

y = -1/2x + 3

Equation 1: y = -1/2x + 3

2

Similarly as before, we have that the line passes through

(x, y) = (-1, -10)

and m = 0

we replace in the equation for b,

y - mx = b

↓ replacing x = -1, y = -10 and m = 0

-10 - 0 · (-1) = b

↓ 0 · (-1) = 0

-10 - 0 = b

-10 = b

Then, the equation of this line is:

y = mx + b,

y = 0x - 10

y = -10

Equation 2: y = -10

3

Similarly as before, we have that the line passes through

(x, y) = (-6, -9)

and m = 7/6

we replace in the equation for b,

y - mx = b

↓ replacing x = -6, y = -9 and m = 7/6

[tex]\begin{gathered} -9-\frac{7}{6}(-6)=b \\ \downarrow\frac{7}{6}(-6)=-7 \\ -9-(-7)=b \\ -9+7=b \\ -2=b \end{gathered}[/tex]

Then, the equation of this line is:

y = mx + b,

y = 7/6x - 2

Equation 3: y = 7/6x - 2

4

The line passes through

(x, y) = (6, -4)

and m = does not exist

When m does not exist it means that the line is vertical, and the equation looks like:

x = c

In this case

(x, y) = (6, -4)

then x = 6

Then

Equation 4: x = 6

5

The line passes through

(x, y) = (6, -6)

and m = 1/6

we replace in the equation for b,

y - mx = b

↓ replacing x = 6, y = -6 and m = 1/6

[tex]\begin{gathered} -6-\frac{1}{6}(6)=b \\ \downarrow\frac{1}{6}(6)=1 \\ -6-(1)=b \\ -7=b \end{gathered}[/tex]

Then, the equation of this line is:

y = mx + b,

y = 1/6x - 7

Equation 5: y = 1/6x - 7

1 4/5 + (2 3/20 + 3/5) use mental math and properties to solve write your answer in simpleist form

Answers

Given data:

The given expression is 1 4/5 + (2 3/20 + 3/5).

The given expression can be written as,

[tex]\begin{gathered} 1\frac{4}{5}+(2\frac{3}{20}+\frac{3}{5}_{})=\frac{9}{5}+(\frac{43}{20}+\frac{3}{5}) \\ =\frac{9}{5}+\frac{43+12}{20} \\ =\frac{9}{5}+\frac{55}{20} \\ =\frac{36+55}{20} \\ =\frac{91}{20} \end{gathered}[/tex]

Thus, the value of the given expression is 91/20.

solve for x. then find the missing piece(s) of the parallelogram for #7

Answers

[tex]\begin{gathered} 2x+30+2x-10=180 \\ 2x+2x+30-10=180 \\ 4x+20=180 \\ 4x=160 \\ x=\frac{160}{4} \\ x=40^0 \end{gathered}[/tex]

Let us find the angles of the parallelogram below

[tex]\begin{gathered} 2x+30 \\ x=40 \\ 2(40)+30 \\ 80+30 \\ 110^0 \end{gathered}[/tex][tex]\begin{gathered} 2x-10 \\ 2(40)-10 \\ 80-10 \\ 70^0 \end{gathered}[/tex]

Theorem+: opposite angles of a parallelogram are the same

Hence the angles of the parallelogram are 110, 70, 110, and 70

А ВC D0 2 4 68 10 12Which point best represents V15?-0,1)A)point AB)point Bpoint CD)point D

Answers

We have to select a point that is the best representative of the square root of 15.

We can calculate the square root of 15 with a calculator, but we can aproximate with the following reasoning.

We know that 15 is the product of 3 and 5. If we average them, we have 4.

If we multiply 4 by 4, we get 16, that is a little higher than 15.

If we go to the previous number (3) and calculate 3 by 3 we get 9, that is far from 15 than 16.

So we can conclude that the square root of 15 is a number a little less than 4.

In the graph, the point B is the one that satisfy our conclusion, as it is a point in the scale that is between 3 and 4, and closer to 4.

The answer is Point B

Question 34: Find the polar coordinates that do NOT describe the point on the graph. (Lesson 9.1)

Answers

Notice that the polar coordinates of the point on the simplest form are (2,30). Then, the only option that does not match a proper transformation of coordinates is the point (-2,30)

Which function has the greatest average rate of change on the interval [1,5]

Answers

Answer:

Explanation:

Given: interval [1,5]

Based on the given functions, we start by computing the function values at each endpoint of the interval.

For:

[tex]\begin{gathered} y=4x^2 \\ f(1)=4(1)^2 \\ =4 \\ f(5)=4(5)^2 \\ =100 \\ \end{gathered}[/tex]

Now we compute the average rate of change.

[tex]\begin{gathered} \text{Average rate of change = }\frac{f(5)-f(1)}{5-1} \\ =\frac{100-4}{5-1} \\ \text{Calculate} \\ =24 \end{gathered}[/tex]

For:

[tex]\begin{gathered} y=4x^3 \\ f(1)=4(1)^3 \\ =4 \\ f(5)=4(5)^3 \\ =500 \end{gathered}[/tex][tex]\begin{gathered} \text{Average rate of change = }\frac{f(5)-f(1)}{5-1} \\ =\frac{500-4}{5-1} \\ =124 \end{gathered}[/tex]

For:

[tex]\begin{gathered} y=4^x \\ f(1)=4^1 \\ =4 \\ f(5)=4^5 \\ =1024 \end{gathered}[/tex][tex]\begin{gathered} \text{Average rate of change = }\frac{f(5)-f(1)}{5-1} \\ =\frac{1024-4}{5-1} \\ =255 \end{gathered}[/tex]

For:

[tex]\begin{gathered} y=4\sqrt[]{x} \\ f(1)=4\sqrt[]{1} \\ =4 \\ f(5)\text{ = 4}\sqrt[]{5} \\ \end{gathered}[/tex][tex]\begin{gathered} \text{Average rate of change = }\frac{f(5)-f(1)}{5-1} \\ =\frac{(4\sqrt[]{5\text{ }})\text{ -4}}{5-1}\text{ } \\ =1.24 \end{gathered}[/tex]

Therefore, the function that has the greatest average rate is

[tex]y=4^x[/tex]

The number of algae in a tub in a labratory increases by 10% each hour. The initial population, i.e. the population at t = 0, is 500 algae.(a) Determine a function f(t), which describes the number of algae at a given time t, t in hours.(b) What is the population at t = 2 hours?(c) What is the population at t = 4 hours?

Answers

a) Let's say initial population is po and p = p(t) is the function that describes that population at time t. If it increases 10% each hour then we can write:

t = 0

p = po

t = 1

p = po + 0.1 . po

p = (1.1)¹ . po

t = 2

p = 1.1 . (1.1 . po)

p = (1.1)² . po

t = 3

p = (1.1)³ . po

and so on

So it has an exponential growth and we can write the function as follows:

p(t) = po . (1.1)^t

p(t) = 500 . (1.1)^t

Answer: p(t) = 500 . (1.1)^t

b)

We want the population for t = 2 hours, then:

p(t) = 500 . (1.1)^t

p(2) = 500 . (1.1)^2

p(2) = 500 . (1.21)

p(2) = 605

Answer: the population at t = 2 hours is 605 algae.

c)

Let's plug t = 4 in our function again:

p(t) = 500 . (1.1)^t

p(4) = 500 . (1.1)^4

p(4) = 500 . (1.1)² . (1.1)²

p(4) = 500 . (1.21) . (1.21)

p(4) = 500 . (1.21)²

p(4) = 732.05

Answer: the population at t = 4 hours is 732 algae.

Select the correct answer from each drop-down menu.
Given: Kite ABDC with diagonals AD and BC intersecting at E
Prove: AD L BC
A
C
E
LU
D
B
Determine the missing reasons in the proof.

Answers

The missing reasons are

ΔCDA ≅ ΔBDA  by SSS [side side side]

ΔCED ≅ ΔBED by SAS [side angle side]

What is Kite?

A kite is a quadrilateral having reflection symmetry across a diagonal in Euclidean geometry. A kite has two equal angles and two pairs of adjacent equal-length sides as a result of its symmetry.

Given,

ABCD is a kite, with the diagonal AD and BC

We have,

               AC = AB

and

               CD = BD                [Property of Kite]

In ΔACD and ΔABD

                AC = AB

and

               CD = BD               [Property of Kite]        

               AD = AD               [Common]

By rule SSS Criteria [Side Side Side ]

              ΔACD ≅ ΔABD

 ∴           ∠CDA = ∠BDA         [CPCT]

Now,

         In ΔCDE and ΔBDA

                 CD = BD

            ∠CDE = ∠BDE

                 DE = DE                [Common]

By rule SAS Criteria [Side Angle Side]  

            ΔCDE ≅ ΔBDA

∴                CE = BE                [CPCT]  

Hence, AD bisects BC into equal parts

The missing reasons are

ΔCDA ≅ ΔBDA  by SSS [side side side]

ΔCED ≅ ΔBED by SAS [side angle side]

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