Mathematics College

## Answers

**Answer 1**

Note:

For two or more triangles to be similar, they must be equiangular, that is , they must have equal angles

For question a, all we are intersested in proving is that triangles ABC, ACD and CBD have equal angles

In triangles ABC, In triangles ABC and ACD, they both have common angle A which are equal

Since two angles of triangles ABC and ACD are equal, then their third angle too must be equal ( i.e < B = < C)

In triangles ABC and CBD, they both have coomon angle B,

Therefore, their third angles are equal

hence, since we have established that the 3 triangles are equiangular, therefore they are similaar triangles

Part B

In triangles CAB, line FG joins the midpoint of AC and CB, therefore line FG is parallel to line AB (the line joining the midpoints of two side of a triangle is parallel to the third side)

therefore,

in triangle CFG, in triangle CFG, in triangle CGFSince we have established that triangle CFG and triangle CAB have equal angles, they are similar triangles

## Related Questions

I understand how to put it in point-slope form and how to solve it! I don’t understand how to get the points that are used in the equation. If that makes sense.

### Answers

It is given that,

At an altitude of 1000 ft, water boils at 210 degree farenheit.

At an altitude of 3000 ft, water boils at 206 degree farenheit.

Let x be the boiling point and y be altitude.

To find the point-slope form:

Let find the slope first,

Using the two points are, (210,1000) and (206,3000)

So, the slope is

[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{3000-1000}{206-210} \\ =\frac{2000}{-4} \\ =-500 \end{gathered}[/tex]

Hence, m=-500.

Take any one point and the slope, (210,1000) , m=-500

The point slope form is,

[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-1000=-500(x-210) \end{gathered}[/tex]

When, the altitude is 6000 ft, then substitute y=6000 in the above equation we get,

[tex]\begin{gathered} 6000-1000=-500(x-210) \\ 5000=-500(x-210) \\ (x-210)=\frac{5000}{-500} \\ (x-210)=-10 \\ x=210-10 \\ x=200 \end{gathered}[/tex]

**Hence, if an altitude is of 6000 ft, then the boiling point is 200 degree farenheit.**

Use the standard normal distribution or the t-distribution to construct a 90% confidenceinterval for the population mean. Justify your decision. If neither distribution can be used,explain why. Interpret the results.In a random sample of 50 people, the mean body mass index (BMI) was 26.9 and thestandard deviation was 6.06.O B. Neither distribution can be used to construct the confidence interval.Interpret the results. Choose the correct answer below.O A. If a large sample of people are taken approximately 90% of them will have aBMI between the bounds of the confidence interval.OB. It can be said that 90% of people have a mi between the bounds of theconfidence intervalO C. With 90% confidence, it can be said that the population mean BMI is betweenthe bounds of the confidence interval.OD. Neither distribution can be used to construct the confidence interval.PS

### Answers

**SOLUTION **

A confidence interval, in statistics, refers to the probability that a population parameter will fall between a set of values for a certain proportion of times.

Strictly speaking a 90% confidence interval means that if we were to take 100 different samples and compute a 90% confidence interval for each sample, then approximately 90 of the 100 confidence intervals will contain the true mean value (μ).

Comparing these statements to the options, we can say that

**The correct answer is option C. Because it reflects the definition of Confidence interval **

Twenty-one goats were shown in the county fair. This was seven less than four times the number of horses shown.What is an equation that could be used to solve the problem?A) 4x - 7 = 21B) 4x - 21 = 7C) 7X -4 = 21D) 4x = 21

### Answers

**ANSWER**

A) 4x - 7 = 21

**EXPLANATION**

We have that 21 goats were shown in the county fair.

The number of goats is 7 less than 4 times the number of horses.

Let the number of horses be h.

Therefore, **7 less than 4 times the number of horses ****is:**

4 * x - 7

= 4x - 7

We have this is equal to the number of goats. Therefore, **the equation that can be used to solve the problem is**:

**4x - 7 = 21**

Square root of X + 3 times square root of X -3

### Answers

We will have the following:

[tex]\begin{gathered} \sqrt{x+3}\ast\sqrt{x-3}=\sqrt{(x+3)(x-3)} \\ \\ =\sqrt{x^2-9} \end{gathered}[/tex]

will 4.5 , 6 and 7.5 make a right triangle

### Answers

It's important to know that the three given sides must be congruent with the Pythagorean's Theorem in order to form a right triangle.

The theorem is

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

Where *c* is the longer side. Let's replace each side.

[tex](7.5)^2=6^2+(4.5)^2[/tex]

Let's solve each side of the equation.

[tex]\begin{gathered} 56.25=36+20.25 \\ 56.25=56.25 \end{gathered}[/tex]

**Since the three given sides satisfy the Pythagorean's Theorem, we can deduct that they form a right triangle.**

Find the length of DC please

### Answers

18

as u can see the height it's the same for b to c so therefore d to c is 18

18

**Step-by-step explanation:**

the length of DC is the same as the length of BC, therefore the length is 18.

4. Determine the slope of the line represented by the equation16x + 4y = 8.

### Answers

SOLUTION:

Step 1:

In this question, we are given the following:

Determine the slope of the line represented by the equation

16x + 4y = 8.

Step 2:

In determining the slope of the equation:

[tex]\begin{gathered} 16\text{ x + 4y = 8} \\ \text{Comparing with y = mx + c, we have that:} \\ 4y\text{ = - 16 x + 8} \\ \text{Divide both sides by 4, we have that:} \\ \frac{4y}{4}\text{ =}\frac{-16x}{4}\text{ +}\frac{8}{4} \\ y\text{ = - 4 x + 2} \end{gathered}[/tex]

**CONCLUSION: **

** Hence , the slope of the line, m = - 4**

Identify the percent, amount, and base in this problem:What is 20% of 50?a) Percent = unknown, Amount =20, Base=50b) Percent = 20% , Amount = unknown, Base = 50c) Percent =20% , Amount =50 , Base = unknownd) Percent =50% , Amount = unknown, Base = 20

### Answers

We are told athat we want to know what is 20% of 50. This means that we are going to take 50 as our **base** as it is the reference to which we want to know the 20%. This means that the percent is **20%**, and since we don't know yet what the 20% of 50 is, then the **amount is unknown**. This three options correspond to option B

Can you hurry please and thank you yo have to graph it

### Answers

**Answer:**

There is nothing here

**Step-by-step explanation:**

You have posted jack diddly squat for anyone to solve for you

Can you please explain how this was solved i am having a head time understanding.

### Answers

It is required to calculate the annual interest rate earned by a T-bill, whose maturity value is $1000 and sells for $966.16 over 33 days.

Here, the amount the bill is sold for is the **principal (initial amount)**, the **time elapsed** is **33 days**, the** amount** at the end of 33 days is the maturity value.

Since it is an annual interest, convert the time to years. Divide 33 by the number of days in a year (365):

[tex]33\text{ days}\equiv\frac{33}{365}\text{years}[/tex]

Recall the formula for **amount earned (A)**:

[tex]A=P(1+rt)[/tex]

Substitute **A=1000, P=966.16, **and **t=33/365**:

[tex]1000=966.16(1+r(\frac{33}{365}))[/tex]

Solve the equation for **r**:

[tex]undefined[/tex]

5. Find the area of the trapezoid. *D5 cmс4 cmA12 cmB68 cm squared34 cm squared120 cm squared48 cm squared

### Answers

The formula for the are of a trapezoid is as follows:

[tex]A=\frac{(b_1+b_2)h}{2}[/tex]

where the b₁ and b₂ are the lengths of the bases and the h is the height of the trapezoid.

Substitute the given values into the equation.

[tex]A=\frac{(5+12)(4)}{2}[/tex]

Simplify the expression inside the parentheses. Add.

[tex]A=\frac{17(4)}{2}[/tex]

Divide 4 by 2.

[tex]A=17(2)[/tex]

Multiply 17 by 2.

[tex]A=34[/tex]

Therefore, the area is 34 cm squared.

Which characteristic is correct for the function f(x)=−6x5+4x3? neither even nor oddoddevenboth even and odd

### Answers

The given function is:

[tex]f(x)=-6x^5+4x^3[/tex]

Even functions are unchanged when reflected over the y-axis, so:

[tex]f(-x)=f(x)[/tex]

Odd functions are unchanged when rotated 180° about the origin, so:

[tex]f(-x)=-f(x)[/tex]

Now, replace -x as the argument of the function and let's observe the result:

[tex]\begin{gathered} f(-x)=-6(-x)^5+4(-x)^3 \\ f(-x)=-6*-x^5+4*-x^3 \\ f(-x)=6x^5-4x^3 \end{gathered}[/tex]

As can be observed, f(-x) is not equal to f(x), then this is not an even function.

Now, let's evaluate -f(x):

[tex]\begin{gathered} -f(x)=-(-6x^5+4x^3) \\ -f(x)=-(-6x^5)-(4x^3) \\ -f(x)=6x^5-4x^3 \\ THEN \\ f(-x)=-f(x) \end{gathered}[/tex]

**This function is odd.**

I’m trying to understand this practice (What is the correct way to name the circle)BHd Bcd E

### Answers

The correct way in naming a circle is by its center.

From the figure, The circle is centered at B

So the answer is **Option A. Circle B**

Jess drew point A on the number line. What fraction does point A represent? 1/8 What does the number line represent? What does each part of the number line represent?

### Answers

For point A on the number line

Since 8 parts represent a unit

point A is just one part out of the 8 parts

so A = 1/8

The number line represents values in the range of 0 to 1

and each part represents one-eight or 0.125 unit

Which statement about the slopes of the functions is true? A. The slopes of the functions are the same in both the graph and the table. B.There is not enough information given to determine the slopes of the functions. C.The slope of the function shown in the graph is greater than the slope of the function shown in the table.. D The slope of the function shown in the table is greater than the slope of the function shown in the graph.

### Answers

In order to compare the slopes for the lines we need to find the slope of the function given in the table using the formula:

[tex]m=\frac{y_2-y_1}{x_2-x_{1_{\square}}}[/tex][tex]\begin{gathered} m=\frac{-6-(-3)}{-4-0} \\ m=-\frac{3}{-4} \\ m=\frac{3}{4} \end{gathered}[/tex]

then selecting two points for the function graphed we apply the formula and find the slope

points: (0,1) & (3,2)

[tex]\begin{gathered} m=\frac{2-1}{3-0} \\ m=\frac{1}{3} \end{gathered}[/tex]

then we know that

[tex]\frac{1}{3}<\frac{3}{4}[/tex]

for that reason the slope for the function shown in the table is greater than the slope in the graph.

Amy Rented 3 movies and 2 video games for a total of $21 the next month she rented 8 movies and 4 video games for a total of $49. Find the cost for each movie in each video game

### Answers

Amy Rented 3 movies and 2 video games for a total of $21 the next month.

**Let x represent movies be x ,**

**Let y represent video games be y,**

**3 x + 2 y = 21 -----------------equ 1**

She rented 8 movies and 4 video games for a total of $49.

** 8 x + 4 y = 49 -------------- equ 2**

Find the cost for each movie in each video game

**Solving equ 1 and equ 2 , we have:**

**3 x + 2 y = 21 -----------------equ 1 x 2 = 6x + 4 y = 42 ------------------- equ 3**

**8 x + 4 y = 49 -------------- equ 2 x 1 = 8x + 4y = 49 -------------------equ 4 **

** equ 4 minus equ 3 , we have **

Factor the quadratic expressionx^2 + 7x + 6

### Answers

**Given:**

[tex]x^2+7x+6[/tex]

**Find-:**

Factor the quadratic expression

**Explanation-:**

Factor is:

[tex]\begin{gathered} =x^2+7x+6 \\ \\ =x^2+6x+x+6 \\ \\ =x(x+6)+1(x+6) \\ \\ =(x+6)(x+1) \end{gathered}[/tex]

So, factor of quadratic function is:

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

Chen has a part-time job at a bakery. The table below shows his daily earnings.Which stem-and-leaf plot correctly represents the data in the table?

### Answers

In the steam and leaf plot, the steam represents the tens and the units, and the leaf represents the tenths of each daily earning.

Then, to represent $37.30 we have to write 37 on the steam column and 3 on the leaf column, that is, **the key is 37 | 3 = $37.30**

Applying this rule to the values of the table, we get:

Steam | Leaf

37 | 3

38 | 1 1 3

39 | 0 8

40 |

41 | 7 8

42 | 5 5

What is the surface area of the cylinder with height 8 yd and radius 8 yd? Round youranswer to the nearest thousandth.

### Answers

Given: a cyliner with height 8 yd and radius 8yd.

Find: the surface area of the cylinder

Explanation:we know that the surfafe area of cylinder is

[tex]2\pi r(h+r)[/tex]

here we have

[tex]r=8,h=8[/tex]

on putting we get,

[tex]\begin{gathered} 2\text{ }\pi(8)(8+8) \\ =2\pi8\times16 \\ =2\times3.14\times8\times16 \\ =803.84yd^2 \end{gathered}[/tex]

**Final answer**: the required surface area of cylinder is 803.84 square yd

Frations is what i need help with8 x 1/4 = ?

### Answers

Given the expression :

[tex]8\times\frac{1}{4}[/tex]

so, the answer will be as following :

[tex]8\times\frac{1}{4}=\frac{8}{4}=2[/tex]

so, the answe is 2

What is the z-score if u = 89, 0 = 11.5, and x = 82?O 1.370 -0.610.790 -1.21

### Answers

The standard normal distribution (Z) is defined as the difference between the value of the variable, X, and the population mean, μ, and the result divided by the population standard deviation, σ.

[tex]Z=\frac{X-\mu}{\sigma}\approx N(0,1)[/tex]

For a determined population with normal distribution, the mean is μ=89, the standard deviation is σ=11.5 and the value of the variable is X=82, you can calculate the Z-value as follows:

[tex]\begin{gathered} Z=\frac{82-89}{11.5} \\ Z=\frac{-7}{11.5} \\ Z=-0.608\approx-0.61 \end{gathered}[/tex]

**The Z-value is -0.61**

If fyou vertically stretch the exponential function f(x) = 2^x by a factor of 5, whatis the equation of the new function?O A. f(x) = 7^xB. f(x) = 5(2^x)C. f(x) = 2(5x)O D. f(x) = 10^x

### Answers

[tex]\begin{gathered} B)f(x)=5(2^x) \\ \end{gathered}[/tex]

**Explanation**

a stretch or compression occurs when we multiply the parent function for a constant, if the constant si greater than 1, it is a stretch

so

**Step 1**

to find the new function, multiply the original function by the constant

Let

constant= 5

function

[tex]f(x)=2^x[/tex]

so

[tex]\begin{gathered} \text{new function} \\ f(x)=5(2^x) \end{gathered}[/tex]

so, the answer is B

Ms. Gartland bought x number of shirts forthe new members of her chorus. The cost forx number of shirts, including $3.99 shipping, was$77.49. Each shirt cost $12.25. There was nosales tax on this purchase. Which equation couldbe used to find x?A. 3.99(x + 12.25) = 77.49B. 3.99x + 12.25 = 77.49C. 12.25(x + 3.99) = 77.49D. 12.25x + 3.99 = 77.49

### Answers

**Answer:**

[tex]\text{ D. 12.25x+3.99=77.49}[/tex]

**Step-by-step explanation:**

This situation can be represented as a linear equation since it has an initial fee (shipping) and a constant rate of change since each shirt costs $12.25.

Linear equations are given as:

[tex]\begin{gathered} y=mx+b \\ \text{where,} \\ m=\text{slope or constant rate of change} \\ b=\text{initial amount} \end{gathered}[/tex]

Therefore, the equation that could be used to find x is:

[tex]77.49=12.25x+3.99[/tex]

A manufacture has been selling 1700 television sets a week at $390 each. A market survey indicates that for each $20 rebate offered to a buyer, the number of sets sold will increase by 200 per week. a) How large rebate should the company offer to a buyer, in order to maximize its revenue? b) If the weekly cost function is 110500+130x, how should it set the size of the rebate to maximize its profit?

### Answers

Assume the demand Q(P) is a linear function.

Q(390) = 1700

The slope = -200 /20 (The slope - demand line is always negative)

=-10

The point slope form of the equation is

Q - 1700 = -10 (P - 390)

Open the parenthesis

Q - 1700 = -10p + 3900

Q = -10p + 3900 + 1700

Q = -10p + 5600

Now solve for P

Q + 10P = 5600

10P = -Q + 5600

Divide through by 10

P = -1/10 Q + 560

Substitute Q = x

[tex]P(X)=-\frac{1}{10}x\text{ + 560}[/tex]

The above is the demand function (price p as a function of units sold x).

a) The revenue function is defined as ;

R(P) = P * Q(P)

= p ( -10p + 5600)

= -10p² + 5600P

To maximaize the revenue,

Differentiate the above

R'(P) = -20P + 5600

Set R'(P)=0

-20P + 5600 =0

20P = 5600

Divide both-side by 20

P = 280

Hence, to maximize they should offer $280 to the buyers.

C)

C(x) is the cost to produce x television sets

C(Q(p)) is the cost to produce the demanded quantity

The distance of Josh throwing a javelin are normally distributed. What is thepercentage of these distances that are within 2 standard deviation of themean?

### Answers

Josh's throwing follows a normal distribution curve according to the question. Therefore, we can say that the probability of his throws reaching certain distances is represented by the normal distribution.

The normal distribution is sketched below:

From the distribution curve shown above, his mean throw distance is at the center and has the largest percentage of occurrence because his throws are usually around that distance.

When we examine the curve even further, we shall see that after the first standard deviation

(σ), the range of values his throws can take increases. This time his throws can be around any value greater than: MEAN + σ.

But the question asks us for the percentage of his throw distances that are within 2 standard deviations. Thus, they are asking for the area of the whole curve EXCEPT the two shaded regions at the tails of the curve shown above.

The normal distribution percentages for each standard deviation is given below:

From the distribution above, we can see that his throws can either be lower than his mean or

greater than his mean.

Therefore, we can add the percentages together:

13.5% + 34% + 34% + 13.5% = 95%

**Therefore the final answer is 95%**

In a recent year, 26.4% of all registered doctors were female. If there were 59,600 female registered doctors that year, what was the total number of registerdoctors?Round your answer to the nearest whole number.

### Answers

The given information is:

26.4% of all registered doctors were female

There were 59,600 female registered doctors (this is 26.4% of the total registered doctors).

Then to know what was the total number of registered doctors:

[tex]59600\times\frac{100\text{ \%}}{26.4\text{ \%}}=225758[/tex]

**Answer: **There were 225,758 total registered doctors that year.

Which compound inequality is equivalent to lax-bl > C for all real numbers a, b, and c, where c_>o?-Cc-c> ax-b>cax-b>-c or ax->Cax-b<-c or ax-b>c

### Answers

In general,

[tex]\begin{gathered} |a|>b,b\geq0 \\ then, \\ a<-b \\ or \\ a>b \end{gathered}[/tex]

Applying this rule to our inequality, we have:

[tex]\begin{gathered} |ax-b|>c \\ \text{then,} \\ ax-b<-c------\text{Inequality}1 \\ or \\ ax-b>c-------\text{Inequality}2 \end{gathered}[/tex]

From the answer choices, the **last answer choice** is correct!

Answer[tex]\begin{gathered} ax-b<-c \\ or \\ ax-b>c \end{gathered}[/tex]

Tina is saving to buy a notebook computer. She has two options. The first option is to put $300 awayinitially and save $30 every month. The second option is to put $100 away initially and save $50 everymonth. After how many months would Tina save the same amount using either option? How muchwould she save with either option?

### Answers

The first step is to state the equations that describe the given situations.

The first one says that she can put $300 away and save $30 every month. This, written as an expression is:

[tex]30x+300[/tex]

Where x is the number of months.

For the second option she can put $100 away and save $50 every month. This, written as an expression is:

[tex]50x+100[/tex]

Now, to find how many months would Tina save the same amount of money using either options make both expressions equal and solve for x:

[tex]\begin{gathered} 30x+300=50x+100 \\ 30x-50x=100-300 \\ -20x=-200 \\ x=\frac{-200}{-20} \\ x=10 \end{gathered}[/tex]

After 10 months she would have the same amount using either options.

To find how miuch would she save, use one of the expressions, any of them, and replace x for 10, for example, let's use the first expression:

[tex]30(10)+300=600[/tex]

She will save $600 using either option.

one batch of cookies requires 1 3/4 cup of flour. if lena wants to make 2/3 of the recipe how much flour will she needD A. 3.2 B. 2 C. 1.75 D. 1.16

### Answers

To solve the exercise it is easier if you first convert the mixed equation into improper, like this

[tex]1\frac{3}{4}=\frac{4\cdot1+3}{4}=\frac{4+3}{4}=\frac{7}{4}[/tex]

Now, you just have to multiply the amount of flour that is required by the amount of recipe that Lena wants to prepare, like this

[tex]1\frac{3}{4}\cdot\frac{2}{3}=\frac{7}{4}\cdot\frac{2}{3}=\frac{7\cdot2}{4\cdot3}=\frac{14}{12}[/tex]

Simplifying you have

[tex]\frac{14}{12}=\frac{2\cdot7}{2\cdot6}=\frac{7}{6}=1.16[/tex]

Therefore, **the amount of flour Lena will need is 1.16 cups flour, and the correct answer is D. 1.16.**

Jocelyn is pregnant and needs to eat at least 360 more calories a day than usual. When buying groceries one day with a budget of $11.25 for extra food, she buys bananas that have 50 calories each and granola bars that have 90 calories each. The bananas cost $0.75 each and the granola bars cost $2.25 each.Write a system of 2 inequalities to model this situation. Use "x" for the number of bananas and "y" for the number of granola bars.

### Answers

**Answer:**

[tex]\begin{gathered} 50x\text{ + 90y}\ge\text{ 360} \\ 0.75x\text{ + 2.25y}\leq11.25 \end{gathered}[/tex]

**Explanation:**

Here, we want to write a system of inequalities

From the given question:

She needs at least 360 calories

The bananas have 50 calories each and we have x number to be bought

That is a total of 50 * x = 50x calories from bananas

The granola bars have 90 calories each, so for y number of granola, we have a total of y * 90 = 90y calories

She needs at least 360 calories more

Mathematically, that means:

[tex]50x\text{ + 90y }\ge360[/tex]

Now, the bananas cost $0.75 each and the granola cost $2.25 each

for x bananas, we have 0.75 * x = $0.75x cost

For the granola, we have a cost of $2.25 each for them and that is a total of 2.25 * y = $2.25y

The budget values cannot be exceeded, so we have:

[tex]0.75x\text{ + 2.25y }\leq\text{ 11.25}[/tex]

Thus, the system of inequalities would be:

[tex]\begin{gathered} 50x\text{ + 90y}\ge360 \\ 0.75x\text{ + 2.25y}\leq11.25 \end{gathered}[/tex]

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