The set 8, 15, 17 is a Pythagorean triple because 8^2 + 15^2 = 17^2. A triangle with sides of 6, 7, and 10 is an obtuse triangle, because 10^2 > 6^2 + 7^2.
Explanation:The set of numbers, 8, 15, 17, represents a Pythagorean triple. A Pythagorean triple consists of three positive integers a, b, and c, such that a^2 + b^2 = c^2. In this case, 8^2 + 15^2 = 64 + 225 = 289, and 17^2 = 289, so the equation is satisfied.
Furthermore, a triangle with sides 6, 7, and 10 would be described as obtuse. In any triangle, if the square of the length of the longest side is greater than the sum of the squares of the other two sides, then the triangle is obtuse. Thus, if 10^2 > 6^2 + 7^2, or 100 > 36 + 49, then the triangle is obtuse. Since this statement holds true, the triangle is indeed obtuse.
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The correct options are: B. 8, 15, 17 and A. obtuse
We can use the Pythagorean theorem to determine which set of numbers is a Pythagorean triple. The theorem states that in a right triangle, the square of the hypotenuse (c) equals the sum of the squares of the other two sides (a and b): a2 + b2 = c2.
Option A: 4, 5, 6: [tex]4^2 + 5^2 = 16 + 25 = 41[/tex], and [tex]6^2=36[/tex], which is not equal to 41.Option B: 8, 15, 17: [tex]8^2 + 15^2 = 64 + 225 = 289[/tex], and [tex]17^2=289[/tex], equal.Option C: 5, 12, 14: [tex]5^2 + 12^2 = 25 + 144 = 169[/tex], and [tex]14^2=196[/tex], which is not equal to 169.Option D: 8, 24, 25: [tex]8^2 + 24^2 = 64 + 576 = 640[/tex], and [tex]25^2=625[/tex], which is not equal to 640.The correct Pythagorean triple is 8, 15, 17.
To determine the type of triangle with side lengths 6, 7, and 10, we use the idea that for a triangle with sides a, b, and c (where c is the longest side):
If [tex]c^2 = a^2 + b^2[/tex], the triangle is right.If [tex]c^2 < a^2+b^2[/tex], the triangle is acute.If [tex]c^2 > a^2+b^2[/tex], the triangle is obtuse.For the triangle with sides 6, 7, and 10:
[tex]6^2+7^2=36+49=85[/tex] and [tex]10^2=100[/tex].
Since 100 > 85, the triangle is obtuse.
A sneaker store salesman had $4,125 in total monthly sales last month. He made $165 in commission from those sales. What is the salesman's commission as a percent of his total monthly sales? Enter your answer in the box. %
Answer:
Salesman's commission 4% of total monthly sales.
Step-by-step explanation:
A sneaker store salesman had $4,125 in total monthly sales last month.
He made $165 in commission from those sales.
Suppose, it is x% of the total sale.
So, x% of $4125 will be,
[tex]=4125\times \dfrac{x}{100}[/tex]
According to the question it is equal to $165, so
[tex]\Rightarrow 4125\times \dfrac{x}{100}=165[/tex]
[tex]\Rightarrow x=\dfrac{165\times 100}{4125}[/tex]
[tex]\Rightarrow x=\dfrac{16500}{4125}[/tex]
[tex]\Rightarrow x=4\%[/tex]
Therefore, salesman's commission 4% of total monthly sales.
Answer: 4%
Step-by-step explanation:
Due to the fact that the salesman had $4,125 in total monthly sales the previous month, the answer would be 4%
A conical tank has height 3 m and radius 2 m at the top. Water flows in at a rate of 0.7m^3/min. How fast is the water level rising when it is 0.8 m?
what is 2/3x5/6x14 can you help me on this problem
Simplify: log base 3 (1/3) ...?
what is the 10th term of this geometric sequence?
1,2,4 ,8...
A)128
B)256
C)512
D)1024
A punch recipe calls for cups of orange juice, cup of pineapple juice, and cups of mango juice. How many total cups of fruit juice does the recipe make?
Answer:I can't answer it without measurements. Sorry
Step-by-step explanation:
Boris bought 22 pounds of rice for $10. How many pounds of rice did he get per dollar?
Linda Frankell pays $50.00 a month for group health insurance. There is a $300 deductible. Her medical bills for the last year were $2,600.00. Linda's insurance company provided payment of 80% of the bills less the deductible.
What was the insurance company's payment? $
What was Linda's total cost (including the monthly premium)? $
If f(x) is an odd function and the graph of f(x) includes points in Quadrant IV, which statement about the graph of f(x) must be true?
It includes points in Quadrant I.
It includes points in Quadrant II.
It does not include points in Quadrant I.
It does not include points in Quadrant II.
Answer:
It includes points in Quadrant II.
It does not include points in Quadrant I.
Step-by-step explanation:
Given : If f(x) is an odd function and the graph of f(x) includes points in Quadrant IV.
To find : which statement about the graph of f(x) must be true.
Solution : We have given that f(x) is an odd function is lies in Quadrant IV.
Definition of an odd function: the y-value of the function at negative x is always opposite sign as the y-value of function at opposite x.
Like (x ,-y) or (x , -y)
In odd function x and y values are in opposite sign that mean odd function always lies in Quadrant II and Quadrant IV.
It does not include points in Quadrant I
Therefore, It includes points in Quadrant II.
It does not include points in Quadrant I.
Answer:
includes quad 2
Step-by-step explanation:
What is the square root of 59,005?
what is an estimation of 492.6 divided by 48
Answer:
10.
Step-by-step explanation:
We are asked to find the estimation of 492.6 divided by 48.
First of all, we will round 492.6 to nearest hundreds and 48 to nearest tens.
Since tens digit of 492.6 is greater than 5, so we will round up to nearest hundred as: [tex]492.6\approx 500[/tex]
Since ones digit of 48 is greater than 5, so we will round up to nearest tens as: [tex]48\approx 50[/tex].
Now, we will find the quotient as:
[tex]\frac{500}{50}=10[/tex]
Therefore, an estimation of 492.6 divided by 48 would be 10.
A bag cost 10.50 but you get 20 percent off how much is the bag now?
Read the numbers and decide what the next number should be 8,4,2,6,3,2,4.
The given sequence involves a two-part pattern. One part is halving the previous number and the other part alternates between 4 and 6. Considering the pattern, the next number should be 0.5.
Explanation:The sequence 8,4,2,6,3,2,4 appears to have a pattern. It seems to be a two-part pattern that alternates. The first part, observed in the numbers 8, 2, and 2, is halving (8 divided by 2 is 4, and 2 divided by 2 is 1, and 1 by 2 is 0.5). Then, the second part, observed in 4,6,4, seems to alternate between 4 and 6. So, if the pattern continues, the next number after 4 should be 0.5 from the first part of the pattern.
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The sequence could actually be representing two series - one series is halving the number (8 to 4 to 2) and the other is multiplying each number by 2 (3 to 2 to 4 to 8). Thus, the next number could either be 1 (if we continue the halving series) or 12 (if we continue the multiplying by 2 series).
Explanation:The number sequence provided seems to be made of two different series interwoven. One series is halving each number (8 to 4 to 2), and the other series is multiplying each number by 2 (2 to 4 to 6 to 12).
Therefore, the next number after 8, 4, 2, 6, 3, 2, 4 should be 1 (half of 2) whereas the next number in the second series after 6, 3, 2, 4 should be 12 (four times 3). So, depending on which pattern the sequence is following, the next number could be either 1 or 12.
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Line AB is tangent to circle C, AB= 4 inches, and AD = 2 inches. Find the radius of the circle.
Explain what the m and b variables represent in the y=mx b equation
If 32% of a number is 64, what is the number?
Express 31% as a fraction in its lowest form
To express 31% as a fraction in its lowest form, divide 31 by 100 and simplify the resulting fraction.
Explanation:To express 31% as a fraction in its lowest form, we need to convert the percent to a decimal first. We do this by writing 31% as a fraction with a denominator of 100 and dividing the numerator by the denominator: 31/100. To reduce the fraction to its lowest form, we find the greatest common divisor (GCD) of the numerator and denominator, which is 1. Dividing both the numerator and denominator by 1, we get the fraction 31/100 in its lowest form.
Learn more about Converting Percent to Fraction#SPJ11A store is having a 10% off sale. It gives an additional 20% off for an item that is above $100 after the first 10% discount.A jacket costs $124.99
if you buy the jacket, how much will you save in total?
*SHOW WORK* ...?
To calculate the total amount saved when buying a jacket at a store with a 10% discount and an additional 20% discount, follow these steps: find the savings from the first discount, calculate the price after the first discount, check if the price is above $100, calculate the additional discount, and add both savings together. In this case, the total amount saved is $34.9972.
Explanation:To calculate the total amount saved, we need to use the following steps:
Find the total savings from the first 10% discount: $124.99 * 0.10 = $12.499Find the price of the jacket after the first discount: $124.99 - $12.499 = $112.491Check if the price is above $100. If it is, calculate the additional 20% discount: $112.491 * 0.20 = $22.4982Add the savings from the additional discount to the previous savings: $12.499 + $22.4982 = $34.9972So, the total amount saved is $34.9972.
Final answer:
To find the total amount saved, apply the discounts and add the amounts together. The total amount saved is $35.00.
Explanation:
To find the total amount saved, you need to calculate the discount for each discount percentage. First, apply the 10% discount to the original price of the jacket:
10% of $124.99 = $12.499.
Next, apply the 20% discount to the price after the first discount:
20% of ($124.99 - $12.499) = 20% of $112.491 = $22.4982.
Finally, add the two discounts together to find the total amount saved:
$12.499 + $22.4982 = $34.9972.
Rounding to the nearest cent, the total amount saved is $35.00.
13 tenths plus 8 tenths plus 32 hundredths <,> =,to 2.42
Solve for x and show work. 2xln(1/x)-x=0
Ruby bought 15 cell phone cases for a total of $145.80. she sells them for $19.50 each, but she is only able to sell 5 of them. what is ruby's net profit or loss?
If you divide 6! by 4! you are evaluating
P(6, 4)
P(4, 6)
P(6, 2)
Taxi ride cost $1 plus 80c more for each quarter mile travel. What was the total cost for 2-mile trip
The Tools Plus Company is planning to produce drills. The company has rented space for its manufacturing operation at $5,000 per month. Each drill requires $61 worth of materials and $36 worth of labor.
Find the total cost if Tools Plus Company makes 460 drills. ...?
Answer:
Step-by-step explanation:
69d+5,000
What is the solution to the system of equations?
y = 1.5x – 4
y = –x
a. (–1.6, 1.6)
b. (–1.5, 1.5)
c. (1.5, –1.5)
d. (1.6, –1.6)
What is the ratio of julios 22 to jonah 8 points?
Which of the following is the statement of the triangle inequality theorem?
A. The sum of the measures of any two angles of a triangle is greater than the measure of the third angle.
B. The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
C. The longest side of a triangle is opposite the largest angle.
D. The largest angle of a triangle is between the two longest sides.
we know that
The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side
so
Let
a,b,c------> the length sides of a triangle
The theorem states that three conditions must be met
case 1)
[tex] a+b > c [/tex]
case 2)
[tex] a+c > b [/tex]
case3)
[tex] c+b > a [/tex]
therefore
the answer is the option
B. The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
The potential energy of an object is jointly related with the mass of the object and the height of the object. A 40-kg object is 2 meters off the ground. The potential energy of the object is 784 joules. A 10-kg object is 3 meters off the ground. What is the potential energy of the 10-kg object?
Answer:
The potential energy of the 10-kg object is 294 joules .
Step-by-step explanation:
As given
The potential energy of an object is jointly related with the mass of the object and the height of the object.
Let the potential energy of an object is denoted by P.E .
Mass of the object = m
Height of the object = h
Than
[tex]P.E \propto mh[/tex]
P.E = mgh
Where g is the accleration due to gravity .
As given
A 40-kg object is 2 meters off the ground. The potential energy of the object is 784 joules.
Put the value in the P.E = mgh
784 = g × 2 × 40
784 = 80g
[tex]g = \frac{784}{80}[/tex]
g = 9.8 joules per kg meter .
As given
A 10-kg object is 3 meters off the ground.
Put the value in P.E = mgh
P.E = 10 × 9.8 × 3
P.E = 294 joules
Therefore the potential energy of the 10-kg object is 294 joules .
what are the translation rules in geometry?
Final answer:
The translation rules in geometry involve moving every point in a figure the same distance and direction. For a horizontal translation, add or subtract the same value from the x-coordinate of each point. For a vertical translation, add or subtract the same value from the y-coordinate of each point.
Explanation:
In geometry, translation is a transformation that moves every point in a figure the same distance and direction. The translation rules involve determining the new coordinates of the translated figure.
The translation rules in geometry can be summarized as:
For a horizontal translation, add or subtract the same value from the x-coordinate of each point.For a vertical translation, add or subtract the same value from the y-coordinate of each point.For example, if you have a point with coordinates (2, 3) and you want to translate it 3 units to the right and 2 units up, you would add 3 to the x-coordinate and 2 to the y-coordinate to get the new coordinates of the translated point: (5, 5).
Which undefined term is used to define a ray?
Answer:
Line
Step-by-step explanation: