The lengths of two sides of a triangle are shown.
Side 1: 3x² - 4x-1
Side 2: 4x-x² + 5
The perimeter of the triangle is 5x³ - 2x² + 3x - 8.
Part A: What is the total length of the two sides, 1 and 2, of the triangle? Show your work. (4 points)
Part B: What is the length of the third side of the triangle? Show your work. (4 points)
Part C: Do the answers for Part A and Part B show that the polynomials are closed under addition and subtraction? Justify your answer. (2 points)

Answer:

C

Step-by-step explanation:

trust me c is the correct answer

let's recall that whenever omitted, the base is assumed to be 10.

[tex]\begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} ~\hspace{4em} \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\log_{10}(2)=m\implies \log(2)=m\hspace{5em}\log_{10}(3)=n\implies \log(3)=n \\\\[-0.35em] ~\dotfill\\\\ \log_{10}(24)\implies \log(24)\implies \log(8\cdot 3)\implies \log(2^3\cdot 3) \\\\\\ \log(2^3)+\log(3)\implies 3\log(2)+\log(3)\implies 3m+n[/tex]

The scale of the dilation is 7/15.

The scale of dilation between two similar figures is the ratio of their corresponding side lengths. In this case, since triangle A'B'C is a dilation of triangle ABC, we can find the scale of dilation by comparing the corresponding side lengths.

Let's say that the scale of dilation is k. Then we can write:

AB' = k × AB

AC' = k × AC

BC' = k × BC

To find k, we can choose any two corresponding sides and set their ratio equal to k. For example, we can choose AB' and AB, and write:

AB' / AB = k

So, AC' / AC = 7/15

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a) Note that the concentration after 8 hours is 24mg/l

b) the concentration increases over 0 to 3 hours

c) the concentration decreases over 3 to 20 hours

d) after the drug reaches it's maximum concentration, it takes 8 hours for it to decrease to 16m/L

e) the graph predicts that after 1 week, or 1 month, the drug would have been completely removed from the blood stream.

f) Over the first 20 hours, the drugs concentration increases rapidly over a space of 2 hours, then gradually declines finally reaching about 2m/L over the speace of 18 hours.

In discrete mathematics, and more particularly in graph theory, a graph is a structure consisting of a set of objects, some of which are "related" in some way.

The items correspond to mathematical abstractions known as vertices, and each pair of connected vertices is known as an edge.

Note that all the above observations are arrived at by studying the graph.

One must understand that the time (t) is on the x-axis and the concentration (mg/l) is depicted by the y-axis.

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6. Each ordered pair on the line represent the weight on Earth (pounds) and weight on Moon (pounds).

7. An equation to represent the relationship shown in the graph is [tex]y=\frac{1}{6} x[/tex].

8. Yes, this a proportional relationship.

9. In this problem situation, it is not all the points on the graph that make sense.

10. a. The weight of a person on Earth given a weight of 12 lb on the Moon is 72 lb.

b. The weight of a person on Earth given a weight of 21 lb on the Moon is 126 lb.

c. The weight of a person on Earth given a weight of 36 lb on the Moon is 216 lb.

In Mathematics, a proportional relationship produces equivalent ratios and it can be modeled or represented by the following mathematical equation:

y = kx

Where:

Part 7.

Next, we would determine the constant of proportionality (k) based on the data points provided as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 10/60 = 20/120 = 30/180 = 40/240

Constant of proportionality, k = 1/6.

Therefore, the required equation is given by;

y = kx

y = x/6

Part 8.

Since the data points have a constant of proportionality, yes, it is a proportional relationship.

Part 9.

By critically observing the graph, it is not all the data points on the graph that make sense

Part 10.

a. When y = 12 lb, the weight of a person on Earth is given by;

x = 6y

x = 6(12)

x = 72 lb.

b. When y = 21 lb, the weight of a person on Earth is given by;

x = 6y

x = 6(21)

x = 126 lb.

c. When y = 36 lb, the weight of a person on Earth is given by;

x = 6y

x = 6(36)

x = 216 lb.

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Answer:

the answer was 7.71

Step-by-step explanation:

hope this helps

A fraction is usually split into two parts: the first part is the number on top, called the numerator; and the second part is the number on the bottom, called the denominator. These are both separated by a line called the “divisor line”. We can use the division method help to solve this question: to get a decimal, simply divide the numerator 54 by the denominator 7 (which you can enter in any calculator):

54 (numerator) ÷ 7 (denominator) = 7.71

And finally, you get 7.71 as your answer when you convert 7 5/7 (or 54/7) to a decimal.

Answer:

7.71

Step-by-step explanation:

We will use Sine Law to find the third side and then according to measurements we will draw the triangle.

Given that a triangle has two sides of length 5 cm and 7 cm with an angle of 35°, [check the figure attached]

Using the Sine Law,

Sin A / BC = Sin C / AB

Sin 35° / 7 = Sin C / 5

Sin C = Sin 35° / 7 × 5

Sin C = 0.4096

C ≈ 24°

Using the angle sum property of a triangle we get the angle B = 121°.

Again, using the Sine Law,

Sin B / a = Sin C / 5

Sin 121° / a = Sin 24° / 5

a = Sin 121° × 5 / Sin 24°

a = 10.53

Therefore, we get the three sides and the three angles of the triangle so we can draw the triangle using these measurements.

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Answer:the values is y x 2=  the domain is no it does not make sense because it as nothing to do with the shape of the rainbow  

Step-by-step explanation:

Answer:9360 - 9000 - 500 is equal to 860.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Note that the digit 5 in 50321 represents 50000 whereas the digit 5 in 42570 represents 500.

So, the total value is:

[tex]50000+500=50500[/tex]

Answer:

Step-by-step explanation:

The perimeter of the triangle ABC is 146.

Given that a triangle we need to find it perimeter,

We know that the tangents from a common point to the circle are equal,

Therefore,

DB = BE

EC = FC

FA = AD

So,

FA = AC - FC

FA = 52-13 = 39

Therefore,

FA = AD

AD = 39

Now,

9x-56 = 17x - 120

8x = 64

x = 8

DB = BE = 16

AB = 16 + 39 = 55

BC = 16+13 = 29

AC = 52

Perimeter = AC + BC + AB = 55 + 29 + 52 = 146

Hence the perimeter of the triangle ABC is 146.

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Answer:

It is 4 million or Million

because the place it is in is called million.

The solution to the conversions are: (1) 1.60934 km/min, (2) 20.8333 m/s, (3) 49.7097 mi/h, (4) 27.7778 m/s, (5) 118100.64 ft/h

1. 60mi/h to km/min  

First, convert miles to kilometers:

1 mile (mi) = 1.60934 kilometers (km)

60mi/h = 60 x 1.60934 = 96.5604km/h

Next, convert hours to minutes:

1 hour = 60 minutes

96.5604 km/h = 96.5604 km/h x (1 h / 60 min)

                        = 1.60934 km/min.

Therefore, 60 mi/h is equal to approximately 1.60934 km/min.

2. 75km/h to m/s

First, convert kilometers to meters:

1 kilometer = 1000 meters

75 km/h  = 75 km/h x (1000 m / 1 km)

               = 75000 m/h

Next, convert hours to seconds:

1 hour = 3600 seconds

75000 m/h = 75000m/h x (1 h / 3600 s)

                   = 20.8333 m/s.

Therefore, 75 km/h is equal to approximately 20.8333 m/s.

3. 80km/h to mi/h

First, convert kilometers to miles:

1 mile = 1.60934 kilometers

1 kilometers = (1/1.60934) mile

80 km/h = 80km/h x (1 mi / 1.60934 km)

              = 49.7097 mi/h.

Therefore, 80 km/h is equal to approximately 49.7097 mi/h.

4. 100km/h to m/s

First, convert kilometers to meters:

1 kilometer = 1000 meters

100 km/h = 100km/h x (1000 m / 1 km)

                = 100000 m/h.

Next, convert hours to seconds:

100000 m/h = 100000 x (1 h / 3600 s)

                    = 27.7778 m/s.

Therefore, 100 km/h is equal to approximately 27.7778 m/s.

5.  10m/s  to ft/h

First, convert meters to feet:

10 m/s = 10 x (3.28084 ft / 1 m)

           = 32.8084 ft/s.

Next, convert seconds to hours:

32.8084 ft/s = 32.8084 x (3600 s / 1 h)

                    = 118100.64 ft/h.

Therefore, 10 m/s is equal to approximately 118100.64 ft/h.

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To solve this problem, we can use Newton's law of cooling, which states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. We can use the formula:

T(t) = T_s + (T_0 - T_s) * e^(-kt)

where:

T(t) is the temperature of the coffee at time t

T_s is the temperature of the surroundings (68F)

T_0 is the initial temperature of the coffee (200F)

k is a constant that depends on the specific heat transfer properties of the coffee and its container

e is the mathematical constant e, approximately 2.71828

We can use the fact that the temperature is 145F after 10 minutes to find the value of k:

145 = 68 + (200 - 68) * e^(-10k)

e^(-10k) = (145 - 68) / (200 - 68) = 77 / 132

-10k = ln(77/132)

k = -ln(77/132) / 10

Now we can use this value of k to find the temperature of the coffee after 15 minutes:

T(15) = 68 + (200 - 68) * e^(-k*15)

T(15) = 68 + (200 - 68) * e^(-15ln(77/132)/10)

T(15) = 111.72

Therefore, the temperature of the coffee 15 minutes after it was poured would be approximately 111.72F.

Answer:

127 F

Step-by-step explanation:

we will use newton's law of cooling to understand the  process. Since the coffee here is losing heat so the heat loss will be proportional to the temperature difference

The amount of the 150 g sample of the strontium-90 that will remain after 116 years, with the half-life of strontium-90 of 29 years, is about 9.375 grams

The half-life of a (radioactive) substance is the duration it takes or required for half of the substance to decay into

The formula for exponential decay indicates that we get;

Amount remaining = Initial amount × (1/2)^(t/h)

Where;

t = The duration that elapses = 116 years

h = The half-life of the substance = 29 years

The initial amount of the strontium-90 = 150 g

Therefore; Amount remaining = 150 × (1/2)^(116/29) = 9.375

The amount of the strontium-90 that will remain after 116 years is 9.375 grams

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Answer:

B

Step-by-step explanation:

square units (units for all area)

a. The concentration would be 0.5 mg/L at approximately t = 40 hours.

b. The table representing the concentration of the drug in the bloodstream, t hours after administration is shown below.

c. A reasonable domain for this function is t ≥ 0.

d. The patient should receive the next intravenous dose of the drug in order to maintain a concentration above 1 mg/L and below 8 mg/L at t = 1.25 hour.

e. The concentration of the oral drug and the concentration of the intravenous drug would keep increasing over the first 20 hours after it is administered.

In order to determine the time when the concentration would be 0.5 mg/L, we would substitute the value of the concentration and then solve the quadratic function for time (t);

c(t) = 20t/(t² + 4)

0.5 = 20t/(t² + 4)

0.5(t² + 4) = 20t

0.5t² + 2 = 20t

0.5t² + 2 - 20t = 0

t² + 4 - 40t = 0

t² - 40t + 4 = 0

Time, t = 38.8998 ≈ 40 hours.

Part b

In this context, we would complete the table of values at various time (t) as follows;

t        0    2      4     6       8           10        12        14     16        18      20

c(t)    0    5      4      3     2.35      1.92     1.62     1.4    1.23     1.10    1.00

Part c

Since the concentration of the drug at time, t = 0 is equal to 0 mg/L and the concentration actually never becomes zero (0) for any value of time (t), we can reasonably infer and logically deduce that a reasonable domain for this quadratic function is t ≥ 0 or {0, ∞}.

Part d and e

Furthermore, the intravenous drug must be administered to the patient between the time interval 1.25 ≤ t ≤ 20 in order to maintain a concentration above 1 mg/L and below 8 mg/L.

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The weighted average of the points A, B, and C with weights 1, 4, and 1 respectively is (A + 4B + C) / 6.

To find the weighted average of the points A, B, and C with weights 1, 4, and 1 respectively, we first need to multiply each point by its corresponding weight and then add them together.

Finally, we divide the sum by the total weight.

The weighted sum of the points is:

(1 × A) + (4 × B) + (1 × C) = A + 4B + C

The total weight is:

1 + 4 + 1 = 6

Therefore, the weighted average of the points A, B, and C with weights 1, 4, and 1 respectively is:

(A + 4B + C) / 6

Note that the weight of B is four times that of A and C.

Therefore, the weighted average will be closer to B than A or C, reflecting the fact that B has a larger weight.

For example, if A = 3, B = 5, and C = 4, then the weighted average is:

(A + 4B + C) / 6 = (3 + 4 × 5 + 4) / 6 = 26 / 6 = 4.33.

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The surface area of the triangular prism is 313.47 cm².

Given is a triangular prism, we need to find the surface area,

A triangular prism is a 3D shape with two identical faces in the shape of a triangle connected by three rectangular faces. The rectangular faces are referred to as the lateral faces, while the triangular faces are called bases. The bases are also called the top and the bottom (faces) of the prism.

Triangular Prism Meaning: A triangular prism is a 3D polyhedron with three rectangular faces and two triangular faces. The 2 triangular faces are congruent to each other, and the 3 lateral faces which are in the shape of rectangles are also congruent to each other. Thus, a triangular prism has 5 faces, 9 edges, and 6 vertices. Observe the following image of a triangular prism in which l represents the length of the prism, h represents the height of the base triangle, and b represents the bottom edge of the base triangle.

so, the surface area of a triangular prism =

perimeter × length + 2 × base area

So,

SA = (4.5+7.2+9) × 8.1 + 2 × 8.1 × 9

= 167.67 + 145.8

= 313.47

Hence the surface area of the triangular prism is 313.47 cm².

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The solution set for the inequality |x-2|>3 is x < -1 or x > 5, represented by the union of the open intervals (-∞, -1) and (5, ∞) on the number line.

To graph the inequality |x-2| > 3 on a number line, we can start by finding the values of x that satisfy the inequality:

|x-2| > 3

x-2 > 3 or x-2 < -3

x > 5 or x < -1

This means that any value of x that is greater than 5 or less than -1 will satisfy the inequality.

On a number line, we can mark -1 and 5 with open circles to indicate that they are not included in the solution set, and shade the regions to the left of -1 and to the right of 5 to show that any value in those regions satisfies the inequality.

The graph should look like this:

         <=========(================>)=========

         -1       2               5

The open circles at -1 and 5 indicate that those values are not included in the solution set, while the shaded regions to the left of -1 and to the right of 5 indicate that any value in those regions satisfies the inequality.

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Answer:

15

Step-by-step explanation:

The interest rate can drastically change the total amount paid to the lender, in the case of mortgages, up to thousands of dollars.The correct answer is c.

The interest rate of a loan is one of the most important factors to consider when shopping around for loans because it directly affects the cost of borrowing money. The interest rate determines the percentage of the loan amount that the borrower will have to pay back to the lender as interest over the loan's term.

A higher interest rate means that borrowers will have to pay more in interest over the life of the loan, increasing the total cost of borrowing. Conversely, a lower interest rate will result in lower interest payments and a reduced overall cost of the loan.

For example, in the case of a mortgage, which is a long-term loan, even a small difference in the interest rate can have a significant impact on the total amount paid to the lender. Over the course of a 30-year mortgage, a higher interest rate could result in thousands of dollars in additional interest payments.

Therefore, it is important to compare and consider different loan offers to find the best interest rate available. This can help borrowers save money and make more informed decisions about their borrowing options. The correct answer is c.

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The logarithm with the common base in this problem is given as follows;

C. log(22)/log(9).

The logarithmic expression used in this problem is given as follows:

[tex]\log_9{22}[/tex]

Which means that the parameters are given as follows:

The common logarithm is found using a common base, that is, we divide the logarithm of the common base of the number by the logarithm of the common base of the base.

The common base is given as follows:

10.

Hence the expression is:

log(22)/log(9).

Hence the correct option is given by the option C in the context of the problem.

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Burger Quick is able to estimate their wait time more consistently than Fast Chicken because it has a smaller IQR.

Burger Quick is able to estimate their wait time more consistently than Fast Chicken because it has a smaller IQR (interquartile range).

The IQR represents the range of the middle 50% of the data, and a smaller IQR indicates that the data is more tightly clustered around the median.

In this case, the IQR for Burger Quick is 15.5 - 9.5 = 6, while the IQR for Fast Chicken is 14.5 - 10 = 4.5.

This means that the wait times reported by Burger Quick are more consistent and predictable than those reported by Fast Chicken.

The range, on the other hand, represents the difference between the largest and smallest data points and does not provide information about the consistency of the data. Therefore, we cannot use the range to determine which drive-thru estimates their wait time more consistently.

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The perimeter of the hollow space is 14 cm².

We have,

From the figure,

We see that the hollow space is a rectangle.

Now,

We see that,

The length of the hollow space is the side of one square.

The width of the hollow space is also the side of another square.

So,

The rectangles dimensions:

Length = 3 cm

Width = 4 cm

The perimeter of the hollow space.

= 2 (length + width)

= 2 (3 + 4)

= 2 x 7

= 14 cm²

Thus,

The perimeter of the hollow space is 14 cm².

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To calculate how long it would take to pay off a $1000 balance with an interest rate of 14% APR when making minimum payments of $20 each month, we need to consider the monthly interest and the decreasing balance.

First, let's calculate the monthly interest. The annual interest rate is 14%, so the monthly interest rate would be 14% divided by 12 months, which is approximately 1.167%.

Now, let's determine how much of the minimum payment goes towards interest each month. The remaining amount after deducting the interest is used to decrease the balance.

In the first month, the interest on the $1000 balance would be 1.167% of $1000, which is approximately $11.67. So, after making a $20 minimum payment, $11.67 is subtracted from the balance, resulting in a new balance of $988.33.

In the subsequent months, the same process is repeated. The interest is calculated based on the new balance, and the minimum payment is made. This continues until the balance reaches zero.

Given the small minimum payment of $20 and the interest accumulating on the balance, it would take significantly longer than 3 months, 1 year, or 3 years to pay off the $1000 balance. Therefore, the correct option is 6 years.

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