james is shopping for hiking boots for a trip he will take in 3months. He has $150 saved and is saving$20/week. The boots he wants are normally $240 but are on sale this weekend for 20% off. should james A. Use his savings to buy the shoes now on a credit card
B. wait until he has enough saved and buy the shoes later at full price with his savings.
explain please

Answers

Answer 1

As $80 >  $42, He will have more than enough money to the credit on next month, thus James should purchase the shoes immediately with his funds and charge the remaining amount to a credit card.

What is sales discount?

A sales discount is a lower price that a company offers on a good or service. Find out how to add discounts to invoices. A sales discount, usually referred to simply as a "discount," offers clients of a business a lower price on a few of the goods or services being provided.

Given data:

Saved money by James = $150savings per week = $20Time = 3 monthsTotal price of shoes = $240Discount = 20% = 0.20

James should buy with his money and charge the remaining price on his credit card due to the sale's discount. James will have the opportunity to save thanks to the discount;

Now,

Discounted price = (0.2 × $240)

Discounted price = $48

Sales price = $240 - $48

= $192

Money he need to pay on credit next month = $192 - $150

= $42

He saves $20 a week, so in month that is 4 weeks he will save:

4 × $20

= $80

As $80 >  $42, He will have more than enough money to the credit on next month,

When his savings are sufficient to cover the cost in full, this discount will prove to be a great deal and will no longer be available.

James can, however, put the remaining sum on his credit card as well as sort this credit balance later because he has a repayment channel (the $20/week saving).

Thus, James should purchase the shoes immediately with his funds and charge the remaining amount to a credit card.

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Related Questions

pla shop mathematics ​

pla shop mathematics

Answers

The number of trees more than 10m tall but not more than 20m tall is 18 trees.

How many of the trees are more than 10m tall but not more than 20m tall?

0 < h ≤ 5 = 5

height greater than 0m less than or equal to 5m

5 < h ≤ 10 = 9

height greater than 5m less than or equal to 10m

10 < h ≤ 15 = 13

height greater than 10m less than or equal to 15m

15 < h ≤ 20 = 5

height greater than 15m less than or equal to 20m

20 < h ≤ 25 = 1

height greater than 20m less than or equal to 25m

The number of trees that are more than 10m tall but not more than 20m tall are;

10 < h ≤ 15 = 13

15 < h ≤ 20 = 5

So,

13 + 5 = 18 trees

Therefore, the total number of trees which are 10m tall but not more than 20m tall is 18 trees.

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4(8g+5)+6
I thought the answer was 32g+26 but its not on there

Answers

Answer:

32g + 6

(you got it right, not quite sure why it isn't there though!)

Step-by-step explanation:

remember PEMDAS

parentheses first

(8g+5) but we can't add them up since they not like terms

now we go from left to right (since we have Multiplication first and then Addition)

distribute the 4 to the (8g+5)

which makes it 32g +20

now we go back to the equation,

32g +20 + 6

are there any like terms we can combine?

yes, the 20 and the 6

20+6=26

leaving us with

32g + 26

A train traveled 252 miles in 4 hours at a constant speed through Norway. How far did the train travel per hour?

Answers

Answer:

63

Step-by-step explanation:

252/4 is 63

Answer: The train traveled 63 miles per hour

Step-by-step explanation:

252/4=63

f(x)=2x^3+ax^2-24x+1 has a local maximum at x=-4. find a

Answers

Step-by-step explanation:

ax2+2x3−24x+1=y

Step 2: Add -2x^3 to both sides.

ax2+2x3−24x+1+−2x3=y+−2x3

ax2−24x+1=−2x3+y

Step 3: Add 24x to both sides.

ax2−24x+1+24x=−2x3+y+24x

ax2+1=−2x3+24x+y

Step 4: Add -1 to both sides.

ax2+1+−1=−2x3+24x+y+−1

ax2=−2x3+24x+y−1

Step 5: Divide both sides by x^2.

ax2

x2

=

−2x3+24x+y−1

x2

a=

−2x3+24x+y−1

x2

Answer:

a=

−2x3+24x+y−1

x2

Which equation represents a line which is parallel to the line
x + 3y = 21?

1. y=-3x+1
2. y=x-3
3. y = 3x - 5
4. y=-x-7

Which equation represents a line which is parallel to the line x + 3y = 21?1. y=-3x+12. y=x-33. y = 3x

Answers

Answer:

4 or y=-1/3x-7

1 is the answer love

Q2 - Divide in a given ratio 1
Ruth and Mary divide £42 in the ratio 1:5.
Ruth 1
Mary 5
Use the bar model to find the amount they each receive.
Ruth receives £_
Mary receives £_​

Answers

The amount received by each person is given as follows:

Rush: £7.Mary:  £35.

How to obtain the amount received?

The amount received by each person is obtained applying the proportions in the context of this problem.

Ruth and Mary divide £42 in the ratio 1:5, hence the fraction that each received is given as follows:

Ruth: 1/(1 + 5) = 1/6.Mary: 5/(1 + 5) = 5/6.

Then the amount received by Ruth is given as follows:

1/6 x 42 = 7 euros.

The amount received by Mary is given as follows:

5/6 x 42 = 35 euros.

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g a group of people were asked if they had run a red light in the last year. responded yes, and responded no. find the probability that if a person is chosen at random, they have run a red light in the last year.

Answers

The probability that a person chosen at random has run a red light in the last year can be calculated by taking the number of people who said “yes” to running a red light and dividing it by the total number of people in the group.

For example, if 10 people said “yes” and 20 said “no”, the probability of a person chosen at random running a red light in the last year is 10/30, or 1/3.

The probability of an event happening is calculated using the formula:

Probability = Number of Favorable Outcomes / Total Number of Outcomes

In this case, the favorable outcome is running a red light in the last year, and the total number of outcomes is the total number of people asked.

To calculate the probability, we take the number of people who said “yes” to running a red light in the last year and divide it by the total number of people in the group. In our example, 10/30 = 1/3, so the probability that a person chosen at random has run a red light in the last year is 1/3.

In conclusion, the probability of a person chosen at random having run a red light in the last year is calculated by taking the number of people who responded “yes” and dividing it by the total number of people in the group.

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I'm not 100% sure on how to figure out this equation, can can anyone help out?

I'm not 100% sure on how to figure out this equation, can can anyone help out?

Answers

Answer:

Aonnalin, great name  :)  answer as below

Step-by-step explanation:

They tell us to use slope-intercept form.   This is something you will just have to remember  y = mx+b    

It is confusing b/c there is the other one, the point-slope formula too.  but just remember both and know that the point-slope one is to get to the slope-intercept one.    y-y1 = m(x-x1)  

m= slope

m = (y2-y1) / (x2-x1)

P1= (0,7)  in the form (x1,y1)

P2 =(8,-2) in the form (x2,y2)

m = -2-7 / 8-0

m = -9 / 8

now that we have the slope, just use either point with the point-slope

y-7 = (-9/8)(x-0)

y-7 = -9x/8

y = -9x/8 + 7

y = \(\frac{-9}{8}\) X + 7

slope-intercept form  :)

14129 Marks

***

Hamid has 20 T-shirts.

The information shows the colours of his T-shirts.

7 black

4 dark blue

4 red

1 light blue

2 white

2 grey

Hamid is going to take one of his T-shirts at random.

a) What is the probability that the T-shirt will be grey?

b) What is the probability that the T-shirt will not be red?

c) He takes one of his blue T-shirts at random.

What is the probability that the T-shirt is light blue?

Answers

Hamid is going to take one of his T-shirts at random.

The probability of selecting a light blue T-shirt is \(\frac{1}{4}\) or \(0.25\).

a) To find the probability that the T-shirt will be grey, we need to determine the ratio of grey T-shirts to the total number of T-shirts.

From the given information, we know that Hamid has 2 grey T-shirts out of a total of 20 T-shirts.

Therefore, the probability of selecting a grey T-shirt at random is \(\frac{2}{20}\), which simplifies to \(\frac{1}{10}\) or \(0.1\).

b) To find the probability that the T-shirt will not be red, we need to determine the ratio of non-red T-shirts to the total number of T-shirts.

Hamid has 4 red T-shirts, so the number of non-red T-shirts is

\(20 - 4 = 16\).

Therefore, the probability of selecting a T-shirt that is not red is \(\frac{16}{20}\), which simplifies to \(\frac{4}{5}\) or \(0.8\).

c) If Hamid takes one of his blue T-shirts at random, we need to consider the ratio of blue T-shirts to the total number of T-shirts.

From the information provided, we know that Hamid has a total of 4 blue T-shirts.

Therefore, the probability of selecting a blue T-shirt at random is \(\frac{4}{20}\), which simplifies to \(\frac{1}{5}\) or \(0.2\).

d) If Hamid takes one of his blue T-shirts at random, the probability that the T-shirt is light blue depends on the ratio of light blue T-shirts to the total number of blue T-shirts.

From the information provided, there is only 1 light blue T-shirt and a total of 4 blue T-shirts.

Hence, the probability of selecting a light blue T-shirt is \(\frac{1}{4}\) or \(0.25\).

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The following image was reflected across the x-axis. What are the coordinates for C'?

The following image was reflected across the x-axis. What are the coordinates for C'?

Answers

Answer:  C ' (-2, 3)

=========================================================

Explanation:

Point C is located at (-2, -3).

When we apply an x axis reflection, the x coordinate stays the same and the y coordinate flips from negative to positive.

The x axis reflection rule is \((x,y) \to (x,-y)\)

So that's how we go from (-2,-3) to (-2,3)

Answer:

-2,3

Step-by-step explanation:

Reflection in the x -axis:

A reflection of a point over the x -axis is shown. The rule for a reflection over the x -axis is. (x,y)→(x,−y) .

8 times something is 100

Answers

Answer:

that would be 12.5

Step-by-step explanation:

Select the correct answer from each drop down menu. In the figure, AB=__inches and AC=___
10" inches

Select the correct answer from each drop down menu. In the figure, AB=__inches and AC=___10" inches

Answers

Answer: In the figure AB is about 8.4 inches and AC is about 13.05 inches.

Step-by-step explanation: We can use cosine to find the hypotenuse. \(cos(40)=\frac{10}{x} \\cos(40) (x)=\frac{10}{x}(x)\\cos(40) (x) =10\\\frac{cos(40) (x)}{cos (40)} =\frac{10}{cos (40)} \\x=\frac{10}{cos(40)}\)

Using a calculator x is about 13.05

Using tangent we can find the length opposite of <C

\(tan(40)=\frac{x}{10} \\tan(40) (10)=\frac{x}{10}(10)\\tan(40) (10) = x\)

Using a calculator x would be about 8.4

Answer:

Step-by-step explanation:

Select the correct answer from each drop down menu. In the figure, AB=__inches and AC=___10" inches

Do the equations x + y = -2 and 3x + 3y = −6 define the same line? Explain.

Answers

Answer:

Yes, they do.

Step-by-step explanation:

They both pass through the same points of -2 on the x and y axis.

with one method of a procedure called acceptance sampling a sample of items is randomly selected without replacement and the entire batch is accepted if every item is in the sample is okay a company is just manufactured 1,938 CDs and 316 are defective A) if there are 316 defective CDs then that means there were ___ good CDs produced B) what is the probability that all 4 CDs are good if you are selecting without replacement C) now in certain circumstances we can use the 5% guideline for cumbersome calculations to treat events that are really dependent as independent instead so that calculations are easier and this problem here can we implement the 5% guideline? A. No, because 4 CDs chosen out of 1938 is not less than 5% B. yes, because 4 CDs chosen out of 1938 is more than 5%C. yes, because four CDs chosen out of 1938 is less than 5%D. no, because 316 defective CDs out of 1938 is not less than 5%E. no, because 1,622 good CDs out of 1938 is not less than 5%D) assuming that you can treat this situation as independent disregarding your answer to part C to utilize that 5% guideline what is the probability that all 4 CDs are good? E) assuming that you can treat the situation as independent regardless of your answer for part C which of the answers above part D or part B is the best to use? A. answer choice D is best because sampling with the replacement is the most effective way to conduct acceptance samplingB. answer choice DS best to use because the 5% guideline is very accurateC. answer choice B is the best because part D was calculated with the 5% guideline meaning it is just an estimateD. is your choice B is best because it utilizes the 5% guideline

Answers

Since we have that 316 CDs are defective from 1938, then:

\(1938─316=1622\)

A) we have that 1622 good CDs were produced.

B) If A is the probability that all 4 cds are good if you are selecting without replacement is:

\(\begin{gathered} P(A)=(\frac{1622}{1938})(\frac{1621}{1937})(\frac{1622}{1936})(\frac{1619}{1935})=0.490372393 \\ P(A)=0.4904 \end{gathered}\)

C)In this case, we can use the 5% guideline, since the sample size is 4 and it's less than the 5% of 1938 (option C).

D) We can check this by calculating the probability assuming each selection is with replacement:

\(\begin{gathered} P(A)=(\frac{1622}{1938})^4=0.490668648 \\ P(A)=0.4907 \end{gathered}\)

Then, the probability that all 4 CDs are good assuming this situation is independent is 0.4907

E)We have seen that both probabilities are almost the same, but in most cases, it's best to use the 5% guideline. Therefore, the answer D is the best choise because the 5% guideline is very accurate in this case (otpion B)

All of the following are measures of central tendency except the ________.
Select one:
A. None of the answers are correct
B. mode
C. range
D. mean
E. median

Answers

All of the following are measures of central tendency except the range.

The range is a measure of dispersion, representing the difference between the largest and smallest values in a dataset. It provides information about the spread or variability of the data but does not provide information about the central tendency.

On the other hand, measures of central tendency are statistical measures that aim to summarize the center or typical value of a dataset. They include the mode, median, and mean.

The mode represents the most frequently occurring value(s) in the dataset.

The median is the middle value when the data is arranged in ascending or descending order. It divides the dataset into two equal halves.

The mean is the arithmetic average of all the values in the dataset. It is calculated by summing all the values and dividing by the total number of values.

Therefore, option C, range, is not a measure of central tendency as it focuses on the spread or dispersion of the data rather than summarizing the central or typical value.

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Maria’s hard drive holds 1.0 ×10^6 megabytes of data. Larry has two hard drives, one that holds 5.1 × 10^5 megabytes of data and one that holds 7.7 × 10^5 Which statement is true? A) Maria can store more data than Larry because 10^6 > 10^5 B) Larry can store more data than Maria because 5.1 + 7.7 = 12.8 and 12.8 > 1.0 C) Larry can store more data than Maria because the sum of his hard drive space is 1.28 ×10^5 D) Larry can store more data than Maria because the sum of his hard drive space is 1.28 ×10^6

Answers

Answer:

D

Step-by-step explanation:

when you add 5.1 and 7.7 together it would be 12.8 but you have to move the decimal to the left again since it has more than one number to the left then the ^5 would turn into ^6 and 1.28x10^6 is 1,280,000 and the other is only 1,000,000

Answer:

D

Step-by-step explanation:

Express each of these statment using quantifires :
a) every student in this classes has taken exactly two mathematics classes at this school.
b) someone has visited every country in the world except Libya

Answers

Using quantifiers; a) ∀ student ∈ this class, ∃ exactly 2 mathematics classes ∈ this school that the student has taken and b) ∃ person, ∀ country ∈ the world (country ≠ Libya), the person has visited that country.

a) "Every student in this class has taken exactly two mathematics classes at this school."

In this statement, we have two main quantifiers:

Universal quantifier (∀): This quantifier denotes that we are making a statement about every individual student in the class. It indicates that the following condition applies to each and every student.

Existential quantifier (∃): This quantifier indicates the existence of something. In this case, it asserts that there exists exactly two mathematics classes at this school that each student has taken.

So, when we combine these quantifiers and their respective conditions, we get the statement: "For every student in this class, there exists exactly two mathematics classes at this school that the student has taken."

b) "Someone has visited every country in the world except Libya."

In this statement, we also have two main quantifiers:

Existential quantifier (∃): This quantifier signifies the existence of a person who satisfies a particular condition. It asserts that there is at least one person.

Universal quantifier (∀): This quantifier denotes that we are making a statement about every individual country in the world (excluding Libya). It indicates that the following condition applies to each and every country.

So, when we combine these quantifiers and their respective conditions, we get the statement: "There exists at least one person who has visited every country in the world (excluding Libya)."

In summary, quantifiers are used to express the scope of a statement and to indicate whether it applies to every element or if there is at least one element that satisfies the given condition.

Therefore, Using quantifiers; a) ∀ student ∈ this class, ∃ exactly 2 mathematics classes ∈ this school that the student has taken and b) ∃ person, ∀ country ∈ the world (country ≠ Libya), the person has visited that country.

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Identify the expression equivalent to 16x + 24y

1. 2 (8x + 24y)
2. 8 (8x + 3y)
3. 8 (2x + 3y)
4. 4 (2x + 6y)

Answers

Correct answer is 3: 8 (2x + 3y)
3. 8(2x + 3y)

I hope it helps you out

find the area of the trapezoid below by decomposing it into fimilar shape?​

find the area of the trapezoid below by decomposing it into fimilar shape?

Answers

Answer:

168 feet

Step-by-step explanation:

area of trapezoid = length (a)+ breadth(b) / 2 height

find the area of the trapezoid below by decomposing it into fimilar shape?

What is the average rate of change for the function g(x) for the interval [3, 7]? Show all work. g(x)=8x^2-7x+2

Answers

Answer:

73

Step-by-step explanation:

g(x)=8x^2-7x+2

g(3)=8(3)^2-7(3)+2 = 53

g(7)=8(7)^2-7(7)+2 = 345

The average rate of change for the function g(x) for the interval [3, 7] is

= [g(7) - g(3)] / (7 - 3)

= (345 - 53) / 4

= 73

Let's see

g(7)

\(\\ \rm\rightarrowtail 8(7)^2-7(7)+2=8(49)-49+2=392-47=345\)

g(3):-

\(\\ \rm\rightarrowtail 8(3)^2-7(3)+2=8(9)-21+2=72-19=53\)

Now rate of change:-

\(\\ \rm\rightarrowtail \dfrac{345-53}{7-3}==\dfrac{292}{4}=73\)

Write a function rule that represents the sentence.8.7 more than the quotient of h and 2 is w.

Answers

8.7 more:

8.7 +

the quotient of h and 2:

\(\frac{h}{2}+8.7\)

is w:

\(\frac{h}{2}+8.7=w\)

I really need help I don’t understand how to do this

I really need help I dont understand how to do this

Answers

Answer:

Step-by-step explanation:

Remark

The way this is worded, it sounds like it is a horizontal distance. However by the marking it looks like they want the hypotenuse. Life can be very confusing sometimes.

The angle of the triangle that you need to know is the one on the right. The line of sight line is parallel to the base of the triangle. So the angle on the right is 8 degrees by the Z theorem.

Solution

Sin(8) = 1817 / x           Multiply both sides by x

x*sin(8) = 1817             Divide by sin(8)

x = 1817/sin(8)

sin(8) = 0.1392

x = 1817/0.1392

x = 13055.7

Note

Watch how you do this. I would put it into your calculator as

1817

÷

sin(8)

=

If you use the rounded answer I gave for sin(8), you might get it wrong. This is a big distance and you should just use the exact number you get for sin(8).

Find the area of PQRS. (Hint: Use the Pythagorean Theorem to find the height .)

Find the area of PQRS. (Hint: Use the Pythagorean Theorem to find the height .)

Answers

Height = sqrt(5^2 - 4^2) = sqrt(9) = 3

Area = length x height
Area = 8 x 3 = 24m^2

how do you find the perimeter of an isosceles trapezoid

Answers

the formula for the perimeter (P) of an isosceles trapezoid is:

P = 2 * (base1 + base2) + leg1 + leg2

To find the perimeter of an isosceles trapezoid, follow these steps:

1. Identify the given measurements: In an isosceles trapezoid, know the lengths of the two parallel sides (the bases) and the two non-parallel sides (the legs).

2. Add the lengths of the bases: Add the lengths of the two parallel sides (bases) of the trapezoid.

3. Multiply the sum by 2: Multiply the sum from step 2 by 2 to account for both sides of the trapezoid.

4. Add the lengths of the legs: Add the lengths of the two non-parallel sides (legs) of the trapezoid.

5. Add the results: Add the results from steps 3 and 4 to find the perimeter of the isosceles trapezoid.

Mathematically, the formula for the perimeter (P) of an isosceles trapezoid is:

P = 2 * (base1 + base2) + leg1 + leg2

Alternatively, know the lengths of all four sides of the trapezoid, simply add them together to find the perimeter.

Keep in mind that the measurements used in the formula should be in the same unit (e.g., centimetres, inches) for accurate results.

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Answer:

P = a + b + 2c

Step-by-step explanation:

P = a + b + 2c

where a is the top, b is the bottom, and c is a leg of the trapezoid. The perimeter is the sum of the outer edge of the shape, so you just need to add the lengths of the sides.

A 90% confidence interval for the mean of a population is computed to be 135 to 160. Which one of the following claims would the interval tend to refute?A. The population mean is more than 110.B. The population mean is less than 150.C. The population mean is between 140 and 150.D. The population mean is more than 140.E. The population mean is less than than 125.

Answers

Therefore, the only claim that the interval would tend to refute is option E: The population mean is less than 125.

Based on the 90% confidence interval of 135 to 160, we can conclude that the population mean is likely to be within this interval with a 90% degree of confidence.

A. The claim that the population mean is more than 110 is not refuted by the confidence interval since the lower limit of the interval is above 110.

B. The claim that the population mean is less than 150 is not refuted by the confidence interval since the upper limit of the interval is above 150.

C. The claim that the population mean is between 140 and 150 is not refuted by the confidence interval since both values are within the interval.

D. The claim that the population mean is more than 140 is not refuted by the confidence interval since the lower limit of the interval is above 140.

E. The claim that the population mean is less than 125 is refuted by the confidence interval since the lower limit of the interval is above 125.

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Which values have 2 significant figures?A. 0.0056B. 0.356C. 1200.1D. 4500

Answers

Answer:

The values that have 2 significant figures are;

A. 0.0056

D. 4500

Both A and D are correct

Explanation:

We want to find which of the values have 2 significant figures.

From the opthoins;

0.0056 -----------2 significant figure

0.356 ------------3 significant figure

1200.1 -------------5 significant figure

4500 --------------2 significant figure

Therefore, the values that have 2 significant figures are;

A. 0.0056

D. 4500

Both A and D are correct

A cattle farmer wants to save for his daughter's college tuition. He will have to pay P50,000 at the end of every year for the next four years that his daughter attends college. He has 8 years until his daughter starts college to save up for her tuition. Using a 7\% interest rate compounded annually, what is the amount the farmer would have to save every year for the 8 years?

Answers

Calculating this expression will give us the amount the farmer needs to save annually over the 8-year period.

Given:

Payment required at the end of each year: P50,000

Number of years until the daughter starts college: 8

Interest rate: 7% (compounded annually)

We can calculate the annual savings using the formula for the present value of an ordinary annuity:

P = \dfrac{PMT \times (1 - (1 + r)^{-n}{r}

Where:

P = Present value (amount to be saved annually)

PMT = Payment amount (P50,000)

r = Interest rate per period (7% or 0.07)

n = Number of periods (8)

Let's substitute the given values into the formula:

\[ P = \dfrac{50,000 \times (1 - (1 + 0.07)^{-8}{0.07} \]

Calculating this expression will give us the amount the farmer needs to save annually over the 8-year period.

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PLEASE HELP LIKE ASAP:
Find the length of r
A.53.9
B.94.9
C.101.4
D.105.6

PLEASE HELP LIKE ASAP:Find the length of rA.53.9B.94.9C.101.4D.105.6

Answers

Answer:

B = 94.9

Step-by-step explanation:

If we know 2 of the 3 angles of the triangle, we can estimate the base of the triangle as 90ft, after calculation, if the base was 90ft, side r would be 71.97584 which rounds to 94.9.

Result

Obtuse Scalene Triangle

Side r = 71.97584

Side 53* = 50.39643

Side 34* = 90

C=93°B=34°A=53°b=50.396a=71.976c=90

Which is all rational?

Which is all rational?

Answers

Answer:

B

Step-by-step explanation:

the other answers have irrational numbers

B is the only with rational numbers only

Decide whether the numbers can represent the side lengths of a triangle. If they can, classify the triangle as right, acute, or obtuse.

(pls help me im desperate for an answer for 5, 6, 7, and 8)

Decide whether the numbers can represent the side lengths of a triangle. If they can, classify the triangle

Answers

Answer:

4) i) The numbers can represent the side lengths of a triangle

ii) Right triangle

5) i) The numbers can represent the side lengths of a triangle

ii) Isosceles triangle

6) i) The numbers can represent the lengths of the sides of a triangle

ii) Pythagoras theorem

7) The numbers do not represent the lengths of sides of a triangle

8) i) The numbers can represent the side lengths of a triangle

ii) Scalene triangle

Step-by-step explanation:

In a triangle, the sum of the lengths of the two shorter sides is longer than the length of the longest side

The given numbers are;

4) i) 15, 20, 25

Given that 15 + 20 < 25, the numbers can represent the side lengths of a triangle

ii) 15² + 20² = 25²

Therefore, the sides lengths are in line with the side length of a right triangle as their relation is given by Pythagoras theorem

The triangle is a right triangle

5) i) The given numbers are;

2, 6, 6

Given that 2 + 6 > 6, the numbers can represent the side lengths of a triangle

ii) Given that the lengths of two sides are equal (6 each), the triangle formed by the numbers is an isosceles triangle

6) i) 0.27, 0.36, 0.45

0.27 + 0.36 = 0.63 > 0.45, therefore, the numbers can represent the lengths of the sides of a triangle

ii) Given that 0.27² + 0.36² = 0.45², according to Pythagoras theorem, the type of triangle formed is a right triangle

7) 2.5, 1.5, 4

Given that 2.5 + 1.5 = 4, the numbers do not meet the criteria for forming triangles and therefore they cannot represent the side lengths of a triangle

8) i) 12,  16, 25

12 + 16 = 28 > 25, the numbers can represent the side lengths of a triangle

ii) 12² + 16² = 400 < 25² = 625, therefore, the triangle formed by the numbers is not a right triangle but a scalene triangle.

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