Answers
Answer:
[tex] \boxed{\sf Length \ of \ leg \ y = 13} [/tex]
Step-by-step explanation:
Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides”.
[tex] \therefore \\ \sf \implies {84}^{2} + {y}^{2} = {85}^{2} \\ \\ \sf {84}^{2} = 7056 : \\ \sf \implies 7056 + {y}^{2} = {85}^{2} \\ \\ \sf {85}^{2} = 7225 : \\ \sf \implies 7056 + {y}^{2} = 7225 \\ \\ \sf Substract \: 7056 \: from \: both \: sides : \\ \sf \implies (7056 - 7056) + {y}^{2} = 7225 - 7056 \\ \\ \sf 7056 - 7056 = 0 : \\ \sf \implies {y}^{2} = 7225 - 7056 \\ \\ \sf 7225 - 7056 = 169 : \\ \sf \implies {y}^{2} = 169 \\ \\ \sf 169 = {13}^{2} : \\ \sf \implies {y}^{2} = {13}^{2} \\ \\ \sf \implies y = \sqrt{ {13}^{2} } \\ \\ \sf \implies y = {13}^{ \cancel{2} \times \frac{1}{ \cancel{2}} } \\ \\ \sf \implies y = 13 [/tex]
So,
Length of leg y of the right triangle = 13
EXPLANATION:
(Using Pythagoras Theorem)
c^2 - a^2 = b^2
85^2 - 84^2 = b^2
7225 - 7056 = b^2
169 = b^2
√169 = b
b= 13
I HOPE THIS HELPED:)
Related Questions
At a central train station, there are 4 different train routes with trains that leave every 6 minutes, 10 minutes, 12 minutes, and 15 minutes. If each train can hold up to 200 passengers, what is the maximum number of passengers who can leave the station on a train in one hour?
Answers
Answer:
5,000 passengers
Step-by-step explanation:
1. Find out how many trains leave each hour.
6 min – 60/6 = 10 x 200 passengers = 2000
10 min – 60/10 = 6 x 200 passengers = 1200
12 min – 60/12 = 5 x 200 passengers = 1000
15 min – 60/15 = 4 x 200 passengers = 800
2. Add it all up.
2000 + 1200 + 1000 + 800 = 5000 passengers
Answer:
5000
Step-by-step explanation:
6 minute train leaves 10 times
10 x 200 = 2000 passengers
10 minute train leaves 6 times
6x200 = 1200
12 minute train leaves 5 times
5x200 =1000
15 minute train leaves 4 times
4x200 =800
2000+1200+1000+800=5000
assuming more than 1 train can be at the station at once
In a scale drawing of a rectangular deck, the
length is 10 inches and the width is 8 inches. In
the drawing, 4 inches represents 3 yards. What
is the length of the actual deck, in yards?
Answers
Answer:
45
Step-by-step explanation:
10/4x3=7.5
8/4x3=6
6x7.5=45yards
Tucker was asked to solve the equation 5x + 3 = 6x + 1. He did not know if his first step should be to add 5 negative x-tiles, or 1 negative unit tile, to both sides. What advice would you give Tucker to help him decide on his first step?
Answers
Answer:
He should use the negative 1 unit tile.
Step-by-step explanation:
He should do this because in this equation you wish to isolate the variable on one side, and it would be better to first take away any constants. Afterwards, the variable would be next.
Answer: It does not matter which he does first. Either way, zero pairs will be created on both sides, which will isolate the variable to determine x. Adding the x-tiles and then the unit tile, or visa versa, will give the same solution.\
Explanation: that's what i put and i got it right
PLZZZZZ MARK ME BRAINIEST
130 students choose to attend one of three after school activities: football, tennis or running. There are 58 boys. 49 students choose football, of which 27 are girls. 27 students choose tennis. 24 girls choose running. A student is selected at random. What is the probability this student chose running? Give your answer in its simplest form.
Answers
Answer: [tex]\dfrac{27}{65}[/tex]
Step-by-step explanation:
There are 130 students.
There are 58 boys --> 72 girls
A) 49 chose football: 27 are girls --> 22 are boys
B) 72 girls: 24 chose running, 27 chose football --> 21 girls chose tennis
C) 27 students chose tennis: 21 are girls --> 6 are boys.
D) 58 boys: 22 chose football, 6 chose tennis --> 30 boys chose running.
[tex]\large\boxed{\begin{array}{l|cc||c}&\underline{Boys}&\underline{Girls}&\underline{Total}\\Football&22&27&49\\Tennis&6&21&27\\\underline{Running}&\underline{\quad 30\quad}&\underline{\quad 24\quad}&\underline{\quad 54\quad}\\Total&58&72&130\end{array}}[/tex]
Total running = 30 boys + 24 girls = 54
Total students = 130
[tex]\dfrac{\text{Total running}}{\text{Total students}}=\dfrac{54}{130}\quad \rightarrow \large\boxed{\dfrac{27}{65}}[/tex]
Consider the functions. F(x)=(x+1)2-4 and g(x)=-4|x+1| which statement compares the range of the functions?
Answers
Answer:
The fourthStep-by-step explanation:
Vertex of f is (-1, -4) so its range is limited to y≥-4
|x+1| is always ≥0 therefore -|x+1| is always ≤0 {4 is insignificant to this - slope doesn't mean in range} so its range is limited to y≤0
Answer:
D
Step-by-step explanation:
i just took the test
List some typical benefits an employee might receive on top of their wage?
Answers
Answer:
paid vacation
paid medical
401k
Solve sin 20 = COS CE-30)
Answers
Answer:
CE = 100°
Step-by-step explanation:
Using the cofunction identity
sin x = cos(90 - x)
Given x = 20°, then 90° - 20° = 70° thus
CE - 30 = 70° ( add 30 to both sides )
CE = 100°
Thus
sin20° = cos(100 - 30)° = cos70°
Answer:
CE = 100
have a nice day!
Step-by-step explanation:
PRST is a trapezium. PQR and PTU are
straight lines. Find the values of x and y.
Answers
Answer:
x = 56 degrees
y = 62 degrees
Step-by-step explanation:
Given TS || PR
x = 56 ................. corresponding angles TS, PR parallel sides of trapezium.
VSK = x ...................... correspoinding angles given TU || SV
y = 118 - VSK .......... given VSR = 118
= 118 - 56
= 62
The base of a regular pyramid is a hexagon.
Answers
Please help
Factorise completely 36ab - 18b+6a-3
Answers
Answer:
[tex]3(6b-1)(2a-1)[/tex]
Step-by-step explanation:
[tex]36ab-18b+6a-3\\18b(2a-1)+3(2a-1)[/tex]
Taking (2a-1) as common
[tex](18b+3)(2a-1)[/tex]
=> [tex]3(6b-1)(2a-1)[/tex]
Answer:
[tex]3(6b+1)(2a-1)[/tex]
Step-by-step explanation:
[tex]36ab - 18b+6a-3[/tex]
Factor the two groups.
[tex]18b(2a-1)+3(2a-1)[/tex]
Take 2a - 1 common.
[tex](18b+3)(2a-1)[/tex]
Factor 18b + 3.
[tex]3(6b+1)(2a-1)[/tex]
In a recent study, volunteers who had 8 hours of sleep were three times more likely to correctly on a math test than were sleep-deprived participants.
1) Identify the sample used in the study.
A) The sample is the math questions in the study.
B) The sample is the responses of the volunteers in the study.
C) The sample is the amount of sleep the volunteers got in the study.
D) The sample is the sleep-deprived participants in the study.
2) What is the sample's population?
A) The population is the collection of all the math questions from the math test.
B) The population is the collection of the responses of all individuals who completed the math test.
C) The population is the collection of all the individuals who completed the math test.
3) Which part of the study represents the descriptive branch of statistics?
Answers
1) Identify the sample used in the study: B) The sample is the responses of the volunteers in the study
2) What is the sample's population: B) The population is collected of the response of all individuals who completed the math test
3) Which part of the study represents the descriptive branch of statistics:
individuals who are not sleep deprived will be more likely to answer math questions correctly than individuals who are sleep deprived.
hope i helpd
-lvr
what is the value of "c" by completing the square. x^2 - 14x +
Answers
Answer:
[tex]\large\boxed{\sf \ \ 49 \ \ }[/tex]
Step-by-step explanation:
Hello,
we need to get the discriminant = 0 meaning
[tex]\Delta = b^2-4ac = 0\\\\<=>14^2-4c=0\\\\<=>c=\dfrac{196}{4}=49[/tex]
And then the square is
[tex]x^2-2\cdot 7\cdot x+7^2=(x-7)^2[/tex]
Hope this helps
in a certain town there are 30000 registered voters, of whom 12000 are Democrats. A survey organization is about to take a simple random sample of 1000 registered voters. a) the expected value for the percentage of Democrats in the sample is
Answers
Answer:
400.
Step-by-step explanation:
The following data were obtained from the question:
Total number of Registered voters = 30000
Total number of Democrats = 12000
Next, we shall determine the percentage of Democrats in the registered voters.
This can be obtained as follow:
Percentage of Democrats = number of Democrats / Total number of registered voters x 100
Percentage of Democrats = 12000/30000 x 100
Percentage of Democrats = 40%
Now, we can obtain the expected value of percentage of Democrats in the 1000 sample as follow:
Percentage of Democrats = 40%
Total number of Sample = 1000
Number of Democrats in the sampl=..?
Percentage of Democrats = number of Democrats in sample / Total number of sample x 100
40% = number of Democrats in sample/1000
Cross multiply
Number of Democrats in sample
= 40% x 1000
= 40/100 x 1000
= 400
Therefore, the expected number of Democrats in the sample is 400.
Which of the following is a key property of the quadratic parent function?
Answers
Answer: B
Step-by-step explanation:
Quadratic parent function is y=x^2 which means the vertex is the origin because if you input 0 into the function you will get an output of zero. (0,0) is the origin which is where the graph intersect.
What the answer question
Answers
its b the answer is b
Answer:
the answer on the B
Step-by-step explanation:
Heyy umm I need help
Answers
Answers
B, D and E are proportional
A, C, and F are not proportional
y = 3+x .... not proportional
y = 1.6x .... proportional
y = 3/(4x) .... not proportional
y = x .... proportional
y = 12x .... proportional
y = 2x+1 ... not proportional
=================================================
Explanations:
Anything in the form y = k*x is a direct proportional equation. As x goes up, so does y. The same happens if x decreases, and we'll have y also decrease. They go up together or down together. This is where the "direct" comes from. Specifically they change the same amount each time (hence the term "proportional").
For something like y = 1.6x, we have k = 1.6
In the equation y = x, we have y = 1x in reality so k = 1 here.
Lastly, y = 12x has k = 12.
----------------------
The other equations are not in the form y = kx. Whenever we have y = mx+b, with b nonzero, then y = mx+b is not proportional. The value of b must be 0 for it to fit y = kx form. This rules out y = 2x+1 and y = 3+x or y = x+3.
The equation y = 3/(4x) is an inversely proportional equation in the form y = k/x. It cannot be written as y = kx. Note how x is in the denominator for y = 3/(4x) while the same can't be said for y = kx. Inversely proportional equations have x increase and y decrease, or vice versa. They go in opposite directions.
Find the indicated functional value for the ceiling function: f(1.5)?
Answers
Answer:
The correct answer is 2Step-by-step explanation:
The ceiling function is a python programming function that rounds a decimal point number to the nearest whole number.
Given the function expression f(1.5), the ceiling function will round 1.5 to the nearest whole number which is 2
griffin ordered a pair of sneakers online. he had 16 credit that he applied toward the purchase, and then he used a credit card to pay for the rest of the cost. if the the shoes cost 80, then how much did griffin charge to his credit card when he bought the sneakers? PLEASE ANSWER I BEG Y'ALL
Answers
Answer: Griffin charge $79.854 to his credit card when he bought the sneakers.
Step-by-step explanation:
Griffin ordered a pair of sneakers online.
Value of each credit point = 1 cent
Then , value of 16 credit points = 16 cents = $0.16 [1$ = 100 cents]
Cost of shoes = Rs $80
Charge to credit card = (Cost of shoes) - (Value of 16 credit points)
= $(80-0.16)
= $79.84
Hence, Griffin charge $79.854 to his credit card when he bought the sneakers.
Multiply. √3 ⋅ √5 ⋅ √7 Enter your answer, in radical form, in the box.
Answers
Answer: square 105
Step-by-step explanation: Confirming answer
A radical expression is an expression containing a square root, mostly a square root.
The value of √3.√5.√7 in radical form is √105.
What is a radical expression?A radical expression is an expression containing a square root, mostly a square root.
We have,
√3.√5.√7
We can multiply the numbers together.
= √(3 x 5 x 7 )
= √(15 x 7)
= √105
Thus the value of √3.√5.√7 in radical form is √105.
Learn more about radical form here:
https://brainly.com/question/27272065
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PLEASE HELP!! ASAP
The two square pyramids are similar. The side length of the smaller pyramid is 3/4 the side length of the larger pyramid. Which fraction represents the ratio of the base area of the smaller pyramid to the base area of the larger pyramid? Answer choices: 9/16 or 16/9
Answers
Which is a qualitative graph? On a coordinate plane, a line with positive slope goes through points (negative 1, 0) and (0, 3). On a coordinate plane, points are at (0, 2), (1, 3), (2, 2.5), (3, 3), (4, 4), and (4.5, 5). A graph has time on the x-axis and height on the y-axis. The graph increases to point A, increases to point B, and then decreases to point C. A graph has time on the x-axis and height on the y-axis. Segment A increases, segment B is increases, and segment C decreases.
Answers
Answer:
(-1,0), (0,3) and (2,2.25)
Step-by-step explanation:
The qualitative graph is as follows:
A(-1,0) ------> B(0,3) ------> C(2,2.25)
Hence, slope = (2.25 - 0)/(2 - (-1)) = 2.25/3
∴ slope = 0.75
Except for the option graph on a coordinate plane, a line with a positive slope goes through points (negative 1, 0) and (0, 3), all the graph is qualitative. Options B, C, and D are correct.
What is a qualitative graph?The kind of graph that shows the quality curve such as decreasing and increasing events, is called a qualitative graph or curve.
Here,
1. On a coordinate plane, a line with a positive slope goes through points (negative 1, 0) and (0, 3), since this graph does not represent any data as well as also constantly increasing between two points so it is not a qualitative graph.
Similarly,
Graphs B, C, and D have an increasing and decreasing order, so all are qualitative graphs.
Thus, except for graph A all the graphs are qualitative graphs.
Learn more about qualitative graphs here:
https://brainly.com/question/21981889
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please help !!!!!!!!
Answers
Answer:
x=3 y=11
Step-by-step explanation:
2x+3=9
2x=6
x=3
y-4=7
y=11
Which best describes the relationship between the lines with equations 5x +y = 4 and 20.0 + 4y = 16?
Answers
Answer:
There is no relationship, except they do intersect at the point (1, -1). Hope this helps :)
Brainliest?
Both given lines are going to intersect at ( 1,-1 ) that's it.
What is a line segment?A line section that can connect two places is referred to as a segment.
The line is here! It extends endlessly in both directions and has no beginning or conclusion.
In other words, a line segment is just part of a big line that is straight and going unlimited in both directions.
Given that
Line 1 ; 5x +y = 4
Line 2 ; 20 + 4y = 16 ⇒ y = -1
At y = -1 the first line is
5x - 1 = 4 ⇒ x = 1
So,
It is clear that line 1 has a point ( 1 .-1 ) and line 2 also passes
through it hence there will an intersection.
For more about line segment
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F(x) = 3x+2 what is f(5)
Answers
Answer:
f(5) = 17Step-by-step explanation:
f(x) = 3x + 2
To find f(5) substitute 5 into f(x)
That's
f(5) = 3(5) + 2
= 15 + 2
= 17
Hope this helps you
Answer:
17
Step-by-step explanation:
You just plug 5 into the equation
f(5)= 3(5)+2
=15+2
=17
Hope this helped! :)
pls answer asap i need this answer quick plus the full explanation #7
Answers
Simplify: 14 - 2+ 8 = 2 *3
helppp meeee
Answers
Answer:
20=6?
Step-by-step explanation:
14-2+8=2*3
14-2+8=6
12+8=6
20=6?
Answer:
These to equations aren't equivalent.
Step-by-step explanation:
14-2+8=2*3
12+8=6
20=6
Hope this helps ;) ❤❤❤
X^4 -33x^2-108 which of the following is equal to the polynomial given above? A. (X+36)(x+v3i)(x-3) B. (X-36)(x+v3i)(x+3)
Answers
Answer:
Answer D I believe :)
Step-by-step explanation:
x^4-33x^2-108
rewrite as a difference
x^4+3x^2-36x^2-108
factor out x^2
x^2(x^2+3)-36x^2-108
factor out -36
x^2(x^2+3)-36(x^2+3)
factor out x^2+3
(x^2+3)(x^2-36)
factor x^2-36
(x^2+3)(x-6)(x+6)
set x^2+3 equal to 0
x^2+3=0
solve for x
x=+/-[tex]\sqrt{3}[/tex]i
set at factors
(x+6)(x-6)(x+[tex]\sqrt{3}[/tex]i)(x-[tex]\sqrt{3}[/tex]i)
I hope this helps.
Simplify each expression.
1) 3(8Z² - 52 - 7)
2) 8d(2d-4)
6) 6(5x - 4)
7) 6q- 4
Answers
Answer:
1) 24Z^2 - 177.
2) 16d^2 - 32d.
6) 30x - 24.
7) 6q - 4.
Step-by-step explanation:
1) 3(8Z^2 - 52 - 7)
= 3(8Z^2 - 59)
= 24Z^2 - 177
2) 8d(2d - 4)
= (8d * 2d) - (8d * 4)
= 16d^2 - 32d
6) 6(5x - 4)
= (6 * 5x) - (6 * 4)
= 30x - 24
7) Already simplified. 6q - 4.
Hope this helps!
∫1/(1+sinx^2 +2cos^2x)
Answers
Answer:
Im not sure, is this correct?
Dan believes he can use the information given in the diagram and the SAS rule to prove the two triangles are congruent. Is he correct? Explain.
Answers
Answer:
Yes. There are two pairs of congruent sides and a pair of congruent angles. This follows the SAS rule.