Triangle PQR is formed by the three squares A, B, and C:
Which statement best explains the relationship between the sides of triangle PQR?
(PQ)2 + (QR)2 = (PR)2, because 9 + 16 = 25
PQ + QR = PR, because 9 + 16 = 25
(PQ)2 + (QR)2 = (PR)2, because 52 + 32 = 42
PQ + QR = PR, because 52 + 32 = 42
Answers
Answer:
A.[tex]PR^2=PQ^2+QR^2[/tex]
Because [tex]25=9+16[/tex]
Step-by-step explanation:
We are given that
Area of square A=[tex]9[/tex] square units
Are of square B=[tex]16[/tex] square units
Area of square C=[tex]25[/tex] square units
We have to find the relationship between sides of triangle PQR.
Side of square=[tex]\sqrt{Area\;of\;square}[/tex]
Using the formula
Side of square A=[tex]\sqrt{9}[/tex]=3 units
Side of square B=[tex]\sqrt{16}=4[/tex] units
Side of square C=[tex]\sqrt{25}=5[/tex] units
Pythagoras theorem
[tex](hypotenuse)^2=(Base)^2+(Perpendicular\;side)^2[/tex]
Using Pythagoras theorem
[tex]PR^2=PQ^2+QR^2[/tex]
[tex]5^2=3^2+4^2[/tex]
[tex]25=9+16[/tex]
Option A is true
Related Questions
The two lines, A and B, are graphed below: Line A is drawn by joining ordered pairs negative 3,18 and 9, negative 6. Line B is drawn by joining ordered pairs negative 5, negative 2 and 8,17 Determine the solution and the reasoning that justifies the solution to the systems of equations. (−4, 6), because both the equations are true for this point (2, 8), because the graph of the two equations intersects at this point (2, 8), because neither of the two equations are true for this coordinate point (−4, 6), because the graph of the two equations intersects the x-axis at these points
Answers
Enlarging the graph, we find that the intersection of the two lines drawn is at point (2,8). Hence, the solution of the equation is (2,8) because the graphs of the two lines intersect at this point.
The answer is therefore the second choice.
Answer:
B. (2,8) because the graph of the two equations intersects at this point.
Step-by-step explanation:
An arithmetic sequence has a first term of 6.3 and a second term of 8.8 Which term has a value of 78.8?
Answers
Common difference [ d ] = 8.8 - 6.3 = 2.5
Using general term formula,
[tex]t_{n} = a + (n-1)d[/tex]
78.8 = 6.3 + (n-1)*2.5
2.5*(n-1) = 72.5 [ Dividing both sides by 2.5 ]
n-1 = 29
n = 30
Hence, 78.8 is the 30th term in the arithmetic series.
h(x)=|x+2| Find h(-10)
Answers
H(10) = |-10+2|
= |-8|
= 8
The answer is 8.
how would you simplify -2+3i/-3-2i (im doing conjugates in math right now)
Answers
hope this helps
To simplify -2+3i/-3-2i, multiply both the numerator and denominator by the conjugate of the denominator (-3+2i).
Explanation:To simplify -2+3i/-3-2i, we can multiply both the numerator and denominator by the conjugate of the denominator, which is -3+2i. This will help us eliminate the imaginary terms in the denominator.
Multiplying the numerator and denominator, we get:
(-2+3i)(-3+2i) / (-3-2i)(-3+2i)
Expanding and simplifying:
(6i+4i^2-9+6i) / (9+4)
Combining like terms:
(-9+12i+4i^2) / 13
Since i^2 is equal to -1, the expression becomes:
(-9+12i-4) / 13
Combining like terms:
(-13+12i) / 13
Therefore, the simplified form of -2+3i/-3-2i is (-13+12i) / 13.
is 4/2 an integer?
I am stumped, so that is why I want to know
Answers
This means that you can divide 4 by 2 to get 2
2 is a whole number thus 4/2 is an interger.
Hope this helps! :)
Simon used a probability simulator to roll a 12-sided number cube 100 times. His results are shown in the table below:
Number on
the Cube Number of
Times Rolled
1
18
2
5
3
16
4
12
5
10
6
5
7
8
8
14
9
2
10
5
11
2
12
3
Using Simon's simulation, what is the frequency of rolling a 3 on the number cube? (5 points)
100 over 16
100 over 84
16 over 100
84 over 100
Answers
The probability would be 16 over 100.
We can tell this because by the table, the number 3 was rolled 16 total times. You can state the probability by expressing with the number of times rolled over total times rolled. Since it was rolled a total of 100 times, we are left with 16/100.
Answer:
The probability would be 16/100
Step-by-step explanation:
I took the test and got it right!! :)
Find the product of 6, m and 5. Then, identify the coefficient.
Answers
The coefficient is 30, since the coefficient is the number next to the variable.
Solve the equation. 3.1x + 4.6 = 10.8
Answers
3.1x + 4.6 = 10.8
3.1x + 4.6 - 4.6 = 10.8 -4.6
3.1x = 6.2
3.1x/3.1 = 6.2/3.1
x=2
3.1x+4.6(−4.6)=10.8(−4.6)
3.1x=6.2
3.1x/3.1=6.2/3.1
x=2
3.1(2)+4.6=10.8
44 points
The computer store pays its employees $150 per day plus a commission of 15% of their sales. Teagan wants to make at least $450 today. Which equation will help Teagan determine how much he has to sell today?
Answers
he makes 150 plus 15% of what is sold
so 150 + 0.15x has to equal at least 450
so the correct answer is B to find out the total he as to sell
You do Time4Learning to?
find the apporximate side length of a square game board with an area of 151 in2
Answers
To find the approximate side length of a square game board with an area of 151 in², take the square root of 151.
Explanation:To find the approximate side length of a square game board with an area of 151 in2, we can use the formula for the area of a square, which is length x width. Since all sides of a square are equal, we can represent the side length as 's'. So, s x s = 151. To find the side length, we can take the square root of 151, which is approximately 12.29 inches. Therefore, the approximate side length of the square game board is 12.29 inches.
Solve 4w = 2w - 12. Plis help me with that
Answers
4w=2w-12
4w-2w=2w-12-2w
2w/2=-12/2
w=-6
Solve for W and make sure w is isolated
Solve for w;
4w = 2w - 12
First, we need to establish that our primary goal is to get w on one side by itself.
Subtract 2w from both sides.
4w - 2w = 2w
2w - 2w = 0
2w = -12
Divide both sides by 2 to solve for w.
2w / 2 = w
-12 / 2 = -6
w = -6
I hope this helps!
how to find the density of a unknown liquid, the volume is 12.0mL and the mass is 6g.
Answers
To calculate the density of an unknown liquid given its mass of 6g and volume of 12.0mL, divide the mass by the volume, resulting in a density of 0.5 g/mL.
Explanation:To find the density of an unknown liquid with a volume of 12.0mL and a mass of 6g, you need to use the formula for density which is density = mass/volume. Given the mass is 6g and the volume is 12.0mL, you substitute these values into the formula to calculate the density.
Therefore, the calculation would be: density = 6g / 12.0mL = 0.5 g/mL.
This states that the density of the unknown liquid is 0.5 g/mL, which means for every milliliter of this liquid, it weighs 0.5 grams. Understanding the density of a substance can be crucial in identifying it since density is a characteristic property.
Write the decimal number in standard form
Six and five hundred and sixteen ten-thousandths
Answers
The decimal number 'six and five hundred and sixteen ten-thousandths' in standard form is 6.0516, which combines the whole number six with the fractional part written as a decimal. Scientific notation is not necessary here since the number is already reasonably simple.
Explanation:To express the number six and five hundred and sixteen ten-thousandths in standard form, you start by identifying the whole number and the fractional part. The whole number is six, which is straightforward. The fractional part is five hundred and sixteen ten-thousandths, which refers to 516 over 10000. In decimal form, this is written as 0.0516. Combining the whole number with the fractional part gives us the decimal 6.0516. This is the number in standard notation.
Scientific notation simplifies the expression of very large or very small numbers. For example, a large number like 306,000,000 can be written as 3.06 × 108, and a small number like 0.000028 can be expressed as 2.8 × 10-5. However, the number 6.0516 is already concise enough that converting it to scientific notation isn't necessary.
20 pts
Score Number of Students 0 1 1 2 2 5 3 3 4 6 5 7 6 9 Based on the table, what is the mean baseball score?
Answers
The sum of these numbers is 54. 54 divided by 14 is 3.8571428571429.
Answer:
3.8
Step-by-step explanation:
the last one is correct but shorten it to 3.8 so it doesnt look like u used a calculator
solve for y 7y - 6y - 10 = 13
Answers
7y-6y-10=13
7y-6y = y
y-10=13
add 10 to both sides
y = 23
...
please solve x+9.72=21
Answers
which rational number must be added to3\7to get -3\4 ?
Answers
What is the best name for angle Y?
Answers
The weight of a sack of potatoes was more than 11 pounds. Shana wants to write an inequality for the weight of the sack of potatoes. What constant should she use in the inequality?
Answers
Answer: The constant that Shana should use in the inequality is 11.
Step-by-step explanation: Given that the weight of a sack of potatoes was more than 11 pounds and she wants to write an inequality for the weight of the sack of potatoes.
We are to find the constant that she should use in the inequality.
Let x pounds represents the weight of the sack of potatoes.
Then, according to the given information, the inequality can be written as
[tex]x>11.[/tex]
Thus, the required constant that Shana should use in the inequality is 11.
Plz Someone Help Me.
I got to pass this piece of homework to school tomorrow.
Answers
Write two decimal that are equivalent to2.50
Answers
Hope this helped
Given $a \equiv 1 \pmod{7}$, $b \equiv 2 \pmod{7}$, and $c \equiv 6 \pmod{7}$, what is the remainder when $a^{81} b^{91} c^{27}$ is divided by 7?
Answers
[tex]a^{81}\equiv1^{81}\equiv1\pmod7[/tex]
[tex]b^{91}\equiv2^{91}\pmod7[/tex]
[tex]2^{91}\equiv(2^3)^{30}\times2^1\equiv8^{30}\times2\pmod7[/tex]
[tex]8\equiv1\pmod7[/tex]
[tex]2\equiv2\pmod7[/tex]
[tex]\implies2^{91}\equiv1^{30}\times2\equiv2\pmod7[/tex]
[tex]c^{27}\equiv6^{27}\pmod7[/tex]
[tex]6^{27}\equiv(-1)^{27}\equiv-1\equiv6\pmod7[/tex]
[tex]\implies a^{81}b^{91}c^{27}\equiv1\times2\times6\equiv12\equiv5\pmod7[/tex]
Answer:
5 (mod 7)
Step-by-step explanation:
Xavier is two years more than twice as old as Yoko. The sum of their ages is 86. How old is Xavier?
Answers
Xavier is 2+2x of Yoko when you put 28 in x
28 times 2
56 +2
58
58+28
86
Two systems of equations are shown below. The first equation in System B is the original equation in system A. The second equation in System B is the sum of that equation and a multiple of the second equation in System A.
A. 1/2x + 3y = 11 → 1/2x + 3y = 11
5x − y = 17 → 15x − 3y = 51
15 1/2x = 62
B. 1/2x + 3y = 11
151/2x = 62
Answers
A=(3,4)
B=(3,5)
C=(4,3)
D=(5,3)
Answers
Answer: C (4,3)
Step-by-step explanation:
mr. lee had a bag of red beans and a bag of black beans. 20% of the total number of beans were black, and there were 180 ounces more red beans than black beans. he transferred some red beans to the bag containing black beans, so that, the bag now contained 30% of the total number of beans. How many ounces of beans were there in the bag of mixed beans
Answers
b = .2(r+b)
so,
b = 60
r = 240
Total beans = 300 oz
After the transfer, 30% = 90 oz
Final answer:
After finding the total weight of beans based on the given percentages and difference in weight between red and black beans, we determine that there are 90 ounces of beans in the mixed bag.
Explanation:
The question asks us to find out how many ounces of beans are now in the bag of mixed beans, given certain percentages before and after mixing. We know that initially, 20% of the total beans are black, and the rest are red. After Mr. Lee transferred some red beans to the bag containing black beans, the bag contained 30% of the total number of beans.
To solve this, let's denote the total number of beans by T, the number of black beans by B, and the number of red beans by R. According to the information provided:
20% of T is black beans: B = 0.20TThere are R = B + 180 oz of red beans.After transferring, the mixed bag contains 30% of T.First, we use the initial conditions to write an equation for the total number of beans T. Since R is 180 ounces more than B:
T = B + R
T = B + (B + 180)
T = 2B + 180
Given that B is 20% of T, we can also write this as:
T = 2(0.20T) + 180
T = 0.40T + 180
We can now solve for T:
T - 0.40T = 180
0.60T = 180
T = 180 / 0.60
T = 300 ounces
Since we know that the mixed bag contains 30% of the total, we calculate 30% of 300 ounces:
30% of T = 0.30 x 300
30% of T = 90 ounces
Therefore, after transferring, there are 90 ounces of beans in the mixed bag.
Nathan wants to use coordinate geometry to prove that the opposite sides of a rectangle are congruent. He places parallelogram ABCD in the coordinate plane so that A is (0, 0), B is (a, 0), C is (a, b), and D is (0, b).
What formula can he use to determine the distance from point C to point D?
Answers
We take CD as the hypotenuse of the right-angled triangle and the distance between the x-coordinates and y-coordinates as the length of two short sides.
We can write the formula as
CD = [tex] \sqrt{( x_{1}- x_{0}) ^{2}+ ( y_{1}- y_{0}) ^{2} } [/tex]
CD = [tex] \sqrt{(a-0)^{2}+ (b-b)^{2} } [/tex]
Wrong on apex is is a-0+(b-b)2=a2=a
90% of students at a university use a backpack, while the rest do not. Of all the students, 50% carry their laptops with them and 5% carry neither a backpack nor laptop. What percentage of students carry their laptops and use a backpack?
Answers
50% of 90 = 45
5% of 45 = 2.25
The answer is 2.25
The percentage of students who carry their laptops and use a backpack is 45%.
Explanation:To find the percentage of students who carry their laptops and use a backpack, we need to subtract the percentage of students who carry neither a backpack nor laptop from the percentage of students who carry their laptops.
Given that 5% carry neither a backpack nor laptop, we can subtract this from the 50% who carry their laptops to find that 45% of students carry their laptops and use a backpack.
Nina has 5 bills and 10 bills in her wallet. She has a. total of 7 bills with a value of $55. How many of each type of Bill does she have?
Answers
Answer:
4 tens3 fivesStep-by-step explanation:
If all were $5 bills, the total would be $35. It is $20 more than that. Each time a $5 bill is replaced by a $10 bill, the total goes up $5. Since the total is $20 higher, there must be $20/$5 = 4 such replacements.
There are 4 $10 bills and 3 $5 bills.
it takes trevon ten hours to clean an attic. cody can clean the same attoc in seven hours.find how long it would take them if they worked together.
Answers
If Trevon takes 10 hours to clean the attic and Cody takes 7 hours to clean the same attic, it would take them approximately 4.11 hours to clean the attic if they worked together.
Explanation:If Trevon takes 10 hours to clean the attic and Cody takes 7 hours to clean the same attic, we can find the rates at which they clean per hour. Trevon cleans at a rate of 1/10 of the attic per hour, and Cody cleans at a rate of 1/7 of the attic per hour. To find out how long it would take them if they worked together, we add their rates: 1/10 + 1/7 = 17/70. This means that together, they can clean 17/70 of the attic per hour.
To find out how long it would take for them to clean the whole attic, we divide 1 (representing the full attic) by their combined rate: 1 / (17/70) = 70/17 = 4.11 hours (rounded to the nearest hundredth).
Learn more about Time taken to clean attic here:https://brainly.com/question/30967695
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When Emma was born she was 20.5 inches long. At her 6-month checkup, she was 26.25 inches long. what was the approximate percentage change in her length?
Answers
128% - 100% = 28%
Answer:
28% and she increased by 5.75 inches. Hope this helped
Step-by-step explanation: