Mathematics College

## Answers

**Answer 1**

**Answer:**

**The expression is given below as**

[tex]\frac{4}{\sqrt{x-2}-\sqrt{x}}[/tex]

**Concept:**

To rationalize the denominator, we will multiply by the conjugate given below

The conjugate is given below as

[tex]\frac{\sqrt{x-2}+\sqrt{x}}{\sqrt{x-2}+\sqrt{x}}[/tex]

**Step 1:**

Multiply the expression in the question by the conjugate, we will have

[tex]\frac{4}{\sqrt{x-2}-\sqrt{x}}\times\frac{\sqrt{x-2}+\sqrt{x}}{\sqrt{x-2}+\sqrt{x}}[/tex]

By expanding the brackets, we will have

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

**Step 2:**

Factor our the common number and divide

[tex]\begin{gathered} =\frac{4(\sqrt{x-2}+\sqrt{x})}{-2} \\ =-2(\sqrt{x}+\sqrt{x-2)} \end{gathered}[/tex]

**Hence,**

**The final answer is**

[tex]\Rightarrow-2(\sqrt{x}+\sqrt{x-2)}[/tex]

**OPTION A is the right answer**

## Related Questions

Algebra help. I'm a little confused on how to do these. I get they should be easy but I'm not aware how to do it.

### Answers

we have the equation

-6x+5=2x-11

solve for x

step 1

adds 6x both sides

-6x+5+6x=2x-11+6x

5=8x-11

step 2

adds 11 both sides

5+11=8x-11+11

16=8x

step 3

Divide by 8 on both sides

16/8=8x/8

2=x

x=2

what is the y- intercept of the quadratic function below ?

### Answers

Okay, here we have this:

Remember that the y -intercept of a graph is the point where the graph crosses the y -axis.

Considering this we can see in the graph that **the point where the graph crosses the y -axis is (0,-1). This mean that the correct answer is the fourth option.**

A marine biologist is studying the growth of a particular species of fish. She writes the following equation to show the length of the fish, f(m), in cm, after m months:f(m) = 4(1.08)mPart A: When the marine biologist concluded her study, the length of the fish was approximately 6.86 cm. What is a reasonable domain to plot the growth function? Part B: What does the y-intercept of the graph of the function f(m) represent? Part C: What is the average rate of change of the function f(m) from m = 3 to m = 7, and what does it represent?

### Answers

The given equation is:

[tex]f(m)=4(1.08)^m[/tex]

Where m is the number of months and f(m) is the length of the fish in cm.

a. When the study ended the function had a value f(m)=6.86 cm.

To find the domain for the growth function, we need to equal the equation to 6.86 and solve for m, as follows:

[tex]\begin{gathered} 4(1.08)^m=6.86 \\ 1.08^m=\frac{6.86}{4} \\ 1.08^m=1.715 \\ \text{Apply log on both sides} \\ \log (1.08)^m=\log (1.715) \\ \text{Apply the power of logs} \\ m\cdot\log (1.08)=\log (1.715) \\ m=\frac{\log 1.715}{\log 1.08} \\ m=\frac{0.234}{0.033} \\ m=7months \end{gathered}[/tex]

Thus, a reasonable domain to plot the growth function is (0,7).

b. The y-intercept of the graph of the function f(m) represents the length of the fish when the study started.

c. The average rate of change of an exponential function is given by the following formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Where (x1, y1) and (x2,y2) are the coordinates of the points at m=3 and m=7.

First, let's solve the function at m=3:

[tex]\begin{gathered} f(3)=4(1.08)^3 \\ f(3)=4\cdot1.26 \\ f(3)=5.04 \end{gathered}[/tex]

When m=7:

[tex]\begin{gathered} f(7)=4(1.08)^7 \\ f(7)=4\cdot1.71 \\ f(7)=6.86 \end{gathered}[/tex]

Thus the coordinates are (3,5.04) and (7,6.86), by replacing these values in the formula we obtain:

[tex]m=\frac{6.86-5.04}{7-3}=\frac{1.82}{4}=0.45[/tex]

The average rate of change is 0.45 in the interval (3,7). It represents the growth rate in cm per month.

**Step-by-step explanation:**

Where m is the number of months and f(m) is the length of the fish in cm.

a. When the study ended the function had a value f(m)=6.86 cm.

To find the domain for the growth function, we need to equal the equation to 6.86 and solve for m, as follows:

Thus, a reasonable domain to plot the growth function is (0,7).

b. The y-intercept of the graph of the function f(m) represents the length of the fish when the study started.

c. The average rate of change of an exponential function is given by the following formula:

Where (x1, y1) and (x2,y2) are the coordinates of the points at m=3 and m=7.

First, let's solve the function at m=3:

When m=7:

Thus the coordinates are (3,5.04) and (7,6.86), by replacing these values in the formula we obtain:

The average rate of change is 0.45 in the interval (3,7). It represents the growth rate in cm per month

Rewrite the functionf(x)=3(x-3)^2 + 5 in the form f (x) = ax²+bx+c.

### Answers

Answer:

Explanation:

Given the below function;

[tex]f(x)=3(x-3)^2+5[/tex]

To rewrite the above function in the form f(x) = ax²+bx+c, we have to clear the parentheses as shown below;

[tex]\begin{gathered} f(x)=3(x^2-6x+9)+5 \\ f(x)=3x^2-18x+27+5 \\ f(x)=3x^2-18x+32 \end{gathered}[/tex]

I need to write 3 questions that you would ask to answer the problem.A steel beam can be cut to different lengths for a project. Assuming the weight of a steel beam is proportional to its length, what information would you need to know to write an equation that represents this relationship?

### Answers

Two quantities x and y are proportional if they are related by:

[tex]y=a\cdot x[/tex]

Where a is known as the proportionality factor. In this case the quantities related are the length and the weight of a steal beam so the first two question would be:

**- What's the length of the beam?**

**- What's its weight?**

Then it is also important to know the proportionality factor so knowing that the length and the weight are proportionally related I would ask:

**- What's the proportionality factor?**

needing help with homework kinda rusty on this.

### Answers

Solve

[tex]\begin{gathered} \frac{5}{4}\times\frac{12}{5} \\ =\frac{5\times12}{4\times5} \\ \text{The 5 at the top cancels out the one at the bottom of the fraction.} \\ \text{Also, 12 divides 4 and gives us 3. Hence;} \\ \frac{5\times12}{4\times5}=\frac{5\times12}{5\times4} \\ =3 \end{gathered}[/tex]

The solution to the multiplications is 3

A medical researcher administers an experimental medical treatment to 300 patients. The patients in the study are categorized by blood types A, B, AB, and O. The researcher observed that the treatment had a favorable outcome for 63 of the 90 patients with blood type A, 31 of the 124 patients with blood type B, 6 of the 6 patients with blood type AB, and none of the 80 patients with blood type O. Use this information to complete parts (a) through (d).a) Determine the empirical probability of a favorable outcome for those patients with blood type A.P(favorable A)= nothing (Type an integer or decimal rounded to the nearest hundredth as needed.)b) Determine the empirical probability of a favorable outcome for those patients with blood type B.P(favorable B)= nothing (Type an integer or decimal rounded to the nearest hundredth as needed.)c) Determine the empirical probability of a favorable outcome for those patients with blood type AB.P(favorable AB)= nothing (Type an integer or decimal rounded to the nearest hundredth as needed.)d) Determine the empirical probability of a favorable outcome for those patients with blood type O.P(favorable O)= nothing (Type an integer or decimal rounded to the nearest hundredth as needed.)

### Answers

We have to determine the empirical (frequentist) probability of each of the blood types.

We have a treatment with a total of 300 patients.

The outcome we get out of the experiment is:

- Blood type A: 63 positives out of 90.

- Blood type B: 31 positives out of 124.

- Blood type AB: 6 positives out of 6.

- Blood type O: 0 positives out of 80.

The probability for each group can be estimated as the ratio between the positive outcomes and the total of each blood type.

Blood type A:

[tex]P_A(\text{favorable})=\frac{63}{90}=0.70[/tex]

Blood type B:

[tex]P_B(\text{favorable})=\frac{31}{124}=0.25[/tex]

Blood type AB:

[tex]P_{AB}(\text{favorable})=\frac{6}{6}=1[/tex]

Blood type O:

[tex]P_O(\text{favorable})=\frac{0}{80}=0[/tex]

**Answer:**

**a) 0.70**

**b) 0.25**

**c) 1**

**d) 0**

six more than five times a numbers that increased by eighteen. use the given conditions to write the equation, solve the equation and find the number

### Answers

Using the variable x to represent the number, we have:

Five times a number: 5x

Six more than five times a number: 5x + 6

the number increased by eighteen: x + 18

So, equating the expressions 5x + 6 and x + 18, we have our equation:

[tex]5x+6=x+18[/tex]

Now, solving the equation for x, we have:

[tex]\begin{gathered} 5x-x=18-6 \\ 4x=12 \\ x=\frac{12}{4} \\ x=3 \end{gathered}[/tex]

So the number we want is **x = 3.**

Consider the following quadratic function. Y=x^2-7x+12Find the real zeros, if any, of this function. Reduce all fractions to lowest terms.

### Answers

[tex]\mleft(3,0\mright)and(4,0)[/tex]

**Explanation**

The zeros of a polynomial are the values of x which satisfy the equation y = f(x). Here f(x) is a function of x, and the zeros of the polynomial is the values of x for which the y value is equal to zero

so

**Step 1**

when the graph crosses the x-axis

let y=0

so

[tex]\begin{gathered} y=x^2-7x+12 \\ \end{gathered}[/tex]

The middle number is -7 and the last number is 12.

Factoring means we want something like

[tex]\begin{gathered} \mleft(x+_{}\mright)\mleft(x+_{}\mright) \\ \end{gathered}[/tex]

We need two numbers that...

Add together to get -7

Multiply together to get 12

so, the number are

[tex]\begin{gathered} -3\text{ and -4} \\ so \end{gathered}[/tex]

[tex]\begin{gathered} y=(x-3_{})(x-4_{}) \\ 0=(x-3_{})(x-4_{}) \end{gathered}[/tex]

so, the solutions are

x=3

and

x=4

(3,0) and (4,0)

I hope this helps you

Solve the system by graphing and determine the number of solutions it has. (Hint: to graph find the y-intercept and slope of the line.)

### Answers

To graph a line, find two points that belong to that line, plot them into the coordinate plane and draw a line through them.

For instance, we can use *x=0* to determine the corresponding value of *y* and then use *y=0* to find the corresponding value of *x*, to plot the points.

For the first equation:

[tex]\begin{gathered} y=2x-1 \\ x=0\Rightarrow y=-1 \\ y=0\Rightarrow2x=1\Rightarrow x=\frac{1}{2} \end{gathered}[/tex]

Then, the following points belong to the first line:

[tex]\begin{gathered} (0,-1) \\ (\frac{1}{2},0) \end{gathered}[/tex]

Plot both boints on the coordinate plane and draw a line through them:

Use the same method to find two points over the second line.

[tex]\begin{gathered} -6x+3y=-3 \\ x=0\Rightarrow3y=-3\Rightarrow y=-1 \\ y=0\Rightarrow-6x=-3\Rightarrow x=\frac{1}{2} \end{gathered}[/tex]

Then, the following points belong to the line:

[tex]\begin{gathered} (0,-1) \\ (\frac{1}{2},0) \end{gathered}[/tex]

They turn out to be the same two points. Then, both lines overlap. Therefore, the system has **infinite solutions**.

I just need the answers to my math homework. Last problem

### Answers

The maximum value of a graph is the point on the graph where the y-coordinate has the lasgest values. In other words, its the highest point on the graph. Then, t**he maximum value of the graph of the function is 225 feet, which corresponds to 3.75 seconds approximately:**

More than 60 million plastic water bottles end up in landfills and incinerators everyday. Each bottle is about 8 inches tall. If you lined up all 60 million bottles, how manymiles long would they stretch end to end? (5280 ft = 1 mile; 12 in = 1 ft]

### Answers

The amount of plastic water bottles that is wasted to either landfills and/or incinerators is given as follows:

[tex]n\text{ = 60,000,000 bottles}[/tex]

Each bottle has a height ( on average ) of:

[tex]h\text{ = 8 in}[/tex]

If we were to line up all the bottles ( n ) along their height ( h ) in a straight line. We will have the following length of the string of bottles in ( inches ):

[tex]\begin{gathered} \text{Total length = n}\cdot h \\ \text{Total length = 60,000,000 }\cdot\text{ 8 in} \\ \text{\textcolor{#FF7968}{Total length = }}\textcolor{#FF7968}{480,000,000}\text{\textcolor{#FF7968}{ in}} \end{gathered}[/tex]

To convert the length of all the bottles lined up from **inches to feet** we will use the following scale:

[tex]\begin{gathered} 1\text{ ft = 12 in , then:} \\ x\text{ ft = 480,000,000 in} \\ ============= \\ x\text{ = }\frac{480,000,000}{12} \\ \textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ = 40,000,000 ft}} \end{gathered}[/tex]

To convert the length of all the bottles lined up from feet to miles we will use the following scale:

[tex]\begin{gathered} 1\text{ mile = 5280 ft} \\ x\text{ miles = 40,000,000} \\ ============= \\ x\text{ = }\frac{40,000,000}{5280} \\ \textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ = 7,575.758 miles}} \end{gathered}[/tex]

Hence, the total length of ( 60,000,000 ) bottles lined up together would result in:

[tex]\textcolor{#FF7968}{7,575.758}\text{\textcolor{#FF7968}{ miles}}[/tex]

4030ت کا اس2015.10YX0-5w-10Which two points on the model combine to make a zero pair?A Points Z and XB. Points Y and XC. Points W and XD. Points W and Z

### Answers

From the diagram given, we can observe that W = -10, X = 0, Y=5 and Z=10

So we can see that

THE PAIR THAT CAN COMBINE TO GIVE ZERO IS W and Z

I.e W + Z = -10 + 10 = 0

Answer is option D

Translate to a system of equations and solve:Whitney has a collection of nickels and dimes, with a total value of $5.40. The number of nickels is two less than four times the number of dimes. How many nickels and how many dimes does she have?

### Answers

Let n and d be the number of nickels and dimes, respectively. Since the total values is $5.40, we can write

[tex]0.05n+0.10d=5.40[/tex]

On the other hand, since the number of nickels is two less than four times the number of dimes, we have

[tex]n=4d-2[/tex]

Then, we have the following system of equations:

[tex]\begin{gathered} 0.05n+0.10d=5.40\ldots(a) \\ n=4d-2\ldots(b) \end{gathered}[/tex]

Solving by substitution method.

By substituting equation (b) into (a), we have

[tex]0.05(4d-2)+0.10d=5.40[/tex]

By distributing 0.05 into the parenthesis, we have

[tex]0.2d-0.1+0.10d=5.40[/tex]

and by combining similar terms, we have

[tex]0.3d-0.1=5.40[/tex]

then, we have

[tex]\begin{gathered} 0.3d=5.40-0.1 \\ 0.3d=5.30 \end{gathered}[/tex]

By dividing both sides by 0.3, we get

[tex]\begin{gathered} d=\frac{5.30}{0.3} \\ d=17.666 \end{gathered}[/tex]

Question 15 of 21Which of the following represents the factorization of the polynomial below?2x2 +11x+5A. (2x + 2)(x+5)B. (2x+5)(x+2)C. (2x + 1)(x+5)D. (2x+5)(x+1)SUBMITPREVIOUS

### Answers

Given:

[tex]2x^2+11x+5[/tex][tex]2x^2+11x+5=2x^2+10x+x+5[/tex][tex]2x^2+11x+5=2x(x+5)+1(x+5)[/tex][tex]2x^2+11x+5=(2x+1)(x+5)[/tex]

Therefore, Option C is the correct answer.

Solve your equation and enter your answers below as a list of numbers, separated with a comma where necessary.

### Answers

Solution

Given

[tex]\begin{gathered} (x+7)^2=16 \\ \\ \text{ Taking the square root of both sides} \\ \Rightarrow(x+7)=\pm\sqrt{16} \\ \\ \Rightarrow(x+7)=\pm4 \\ \\ \Rightarrow x=-7\pm4 \\ \\ \Rightarrow x=-7-4,-7+4 \\ \\ \Rightarrow x=-11,-3 \end{gathered}[/tex]

**Answer(s): -11, -3**

For a certain kind of plaster work, 1.9 cu yd of sand are needed for every 100 sq yd of surface. How much sand will beneeded for 290 sq yd of surface?...cu yd of san will be needed for 290 sq yd of surface.(Type a whole number or a decimal.)

### Answers

**INFORMATION:**

We know that:

- 1.9 cu yd of sand are needed for every 100 sq yd of surface

And we must find how much sand will be needed for 290 sq yd of surface

**STEP BY STEP EXPLANATION:**

To find it, we can write that 1.9 cu yd of sand are needed for every 100 sq yd of surface in the form of a fraction

[tex]\frac{1.9yd^3}{100yd^2}[/tex]

Then, to find how much sand will be needed for 290 sq yd of surface, we must multiply it by the fraction

[tex]290yd^2\times\frac{1.9yd^3}{100yd^2}[/tex]

Finally, simplifying

[tex]5.51yd^3[/tex]

So, **5.51 cu yd of sand will be needed for 290 sq yd of surface.**

**ANSWER:**

**5.51**** cu yd of sand will be needed for 290 sq yd of surface.**

Which equation is a radical equation?O4p = -3 + pO x3 + x = 3/2x07/11 - W= -34O 5-3/8 = 16

### Answers

Radical equations are equations in which the unknown value appears under the radical sign. As we can note, the equation which fulfill this requirement is

[tex]x\sqrt[]{3}+x=\sqrt[3]{2x}[/tex]

which **corresponds to option 2**

Quadrilateral WXYZ is a parallelogram. Which equation CANNOT be used to prove that WXYZ is also a rectangle?

### Answers

There are two ways to prove that WXYZ is a rectangle.

1. Opposite sides must be parallel or have the same slope.

2. Adjacent sides must be perpendicular or the slope of the sides are negative reciprocal of each other.

Find the point on the curve y=2x+5 closest to the point (0,8).

### Answers

step 1

we have the curve

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

Find out the derivative

[tex]y^{\prime}=2\text{ ----slope of the curve}[/tex]

step 2

Find out the equation of the line perpendicular to the given curve that passes through the point (0,8)

Remember that

If two lines are perpendicular, then their slopes are negative reciprocal

so

The slope of the perpendicular line is m=-1/2

The equation of the line is given by

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

where

m=-1/2

point (0,8) ----> y-intercept

substitute

[tex]y=-\frac{1}{2}x+8[/tex]

step 3

Find out the intersection of both lines

[tex]\begin{gathered} y=2x+5 \\ y=-\frac{1}{2}x+8 \end{gathered}[/tex]

Equate both equations

[tex]\begin{gathered} 2x+5=-\frac{1}{2}x+8 \\ 2x+\frac{1}{2}x=8-5 \\ \\ \frac{5}{2}x=3 \\ \\ x=\frac{6}{5} \end{gathered}[/tex]

Find out the y-coordinate of the point

[tex]\begin{gathered} y=2(\frac{6}{5})+5 \\ \\ y=\frac{12}{5}+5 \\ \\ y=\frac{37}{5} \end{gathered}[/tex]The coordinates of the point are[tex](x,y)=(\frac{6}{5},\frac{37}{5})[/tex]

how do I find the indicated term in this geometric sequence?

### Answers

A geometric sequence has a common ratio, in this case r = 0.1. The formula for the n term is aₙ = arⁿ⁻¹. where aₙ is the term of the sequence, a first term of the seuqence and r the commun ratio. So, aₙ = arⁿ⁻¹

a⁸ = (1,000,000) (0.1) ⁸⁻¹

a⁸ = (1,000,000) (0.1)⁷

a⁸ = 0.1

The road that leads to the beach is 3 miles long. What is the length in kilometers?

### Answers

1) Let's convert it to kilometers, using for that a Rule of three

1 mile ---------- 1.600 km

3 -----------------x

2) Multiplying it crossed

3*1.600=1x

4800=x

x = 48

If Samuel sold a watch for $102 and lost $55 on the sale, he bought the watch for $132.

### Answers

The selling price of watch = $102

Loss on the watch = $55

Since, the expression for the Lost, Cost Price and selling price is :

**Cost Price -Selling Price = Loss**

*Here we have, Selling Price =102, Loss =55*

*Substitute the value and solve for Cost Price*

*Cost Price -Selling Price = Loss*

*Cost Price -102=55*

*Cost Price =102+55*

*Cost Price =157*

*So, the cost price of the watch is 157*

*But it in the given statement they show that the cost price is 132*

*so, the statement is False.*

**Answer :**

**False**

using law of sines state an equation that will solve x .

### Answers

Given the triangle ABC, you need to remember that the Law of Sines states that:

Tom has a certain number of cookies he wants to give to his three friends so that his three friends will each get three cookies. How many cookies does Tom have?x=9x=10x=6x=405

### Answers

**Given:**

Tom has a certain number of cookies he wants to give to his three friends so that his three friends will each get three cookies.

**Required:**

How many cookies does Tom have?

**Explanation:**

Let no. of cookies is x.

[tex]\begin{gathered} \text{ He has three friends and he wants each to get three cookies.} \\ 3\times3=9 \\ \text{ Total number of cookies equal 9.} \end{gathered}[/tex]

**Answer:**

The number of cookies x = 9.

Will make brainlistPlease help me with this homework question I do not understand how do I get the answer what steps do I have to take? Please explain fully?

### Answers

The vertex format = a(x - h)^2 + k

where (h,k) is the vertex of quadratics

so, from the graph (h,k) = (-2, 8)

so,

y = a(x - h)^2 + k = a(x - (-2))^2 + 8

y = a ( x + 2)^2 + 8

as shown the graph pass through (0 , 0)

substitute with (0,0) to find a

so,

0 = 4a + 8

4a = -8

a = -2

y = -2 ( x + 2)^2 + 8

check by another point (-4 , 0)

if x = -4

y = -2 ( -4 + 2)^2 + 8 = -2 * 4 + 8 = -8 + 8 = 0

So, the answer is true

what is 1/2 into a decimals

### Answers

**0.5**

1) To find out that, let's divide 1 by 2

1 ÷ 2 = 0.5

2) So 1/2 is 0.5 in decimal form.

In number 6, determine the value of x in the diagram and what the three angular relationships required to determine x are.

### Answers

To answer this question we will use the following diagram as reference:

Notice that the angles that measures 80 degrees and a degrees are** vertical angles**, therefore:

[tex]a^{\circ}=80^{\circ}.[/tex]

Also, notice that the angles that measures b degrees and (6x+30) degrees are **supplementary angles**, therefore:

[tex]b^{\circ}+(6x+30)^{\circ}=180^{\circ}\text{.}[/tex]

Solving the above equation for b degrees we get:

[tex]\begin{gathered} b^{\circ}+(6x+30)^{\circ}-(6x+30)^{\circ}=180^{\circ}-(6x+30)^{\circ}, \\ b^{\circ}=180^{\circ}-(6x+30)^{\circ}\text{.} \end{gathered}[/tex]

Now, recall that the **interior angles of a triangle add up to 180 degrees**, therefore:

[tex]50^{\circ}+a^{\circ}+b^{\circ}=180^{\circ}\text{.}[/tex]

Substituting a degrees and b degrees we get:

[tex]50^{\circ}+80^{\circ}+180^{\circ}-(6x+30)^{\circ}=180^{\circ}\text{.}[/tex]

Adding like terms we get:

[tex]310^{\circ}-(6x+30)^{\circ}=180^{\circ}.[/tex]

Subtracting 180 degrees we get:

[tex]\begin{gathered} 310^{\circ}-(6x+30)^{\circ}-180^{\circ}=180^{\circ}-180^{\circ}, \\ 130^{\circ}-(6x+30)^{\circ}=0^{\circ}. \end{gathered}[/tex]

Therefore:

[tex]130-(6x+30)=0.[/tex]

Applying the distributive property we get:

[tex]130-6x-30=0.[/tex]

Adding 6x to the above equation we get:

[tex]\begin{gathered} 130-6x-30+6x=0+6x, \\ 100=6x\text{.} \end{gathered}[/tex]

Dividing the above equation by 6 we get:

[tex]\begin{gathered} \frac{100}{6}=\frac{6x}{6}, \\ x=\frac{50}{3}\text{.} \end{gathered}[/tex]

**Answer:**

(a)

[tex]x=\frac{50}{3}\text{.}[/tex]

(b)

1) Vertical angles.

2) Supplementary angles.

3) The interior angles of a triangle add up to 180 degrees.

Suppose it takes 5 years for $20000 investment using continuous interest to doble

### Answers

Given a continuous compound interest :

r is the interest rate per period and t is the number of periods = 5yrs

(1) A = amount, P = pricipal

[tex]A=Pe^{rt}[/tex][tex]\begin{gathered} \frac{A}{P}=e^{rt} \\ 2=e^{rt} \\ \ln 2=\ln e^{rt} \\ \ln e^{rt}=\ln 2 \\ rt=\ln 2 \\ r=\frac{\ln 2}{5} \end{gathered}[/tex]

(2) A(t) = Amount of money in the account after t years

[tex]\begin{gathered} A(t)=20000 \\ A(t)=e^{rt} \\ 20000=e^{rt} \end{gathered}[/tex]

Hey everyone! Anybody think they can help me out with this problem? Read the instructions carefully because they might be confusing. I don't need a huge explanation but something brief leading to the answer but also explaining it.

### Answers

First, notice that the line has negative slope, since it is decreasing, then, we have that the relationship is inverse.

Now, we have that the line passes through the points (3,-2) and (-3,2), then, we can calculate the slope using the general formula:

[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \Rightarrow m=\frac{2-(-2)}{-3-3}=\frac{4}{-6}=-\frac{2}{3} \end{gathered}[/tex]

**therefore, the equation is y = -2/3**