Answer:
[tex]y = -\frac{8}{x}[/tex]
Step-by-step explanation:
Given
Inverse Variation:
[tex]Points: \{(-1, 8), (4, -2), (-2, 4)\}[/tex]
Required
Determine the equation of the relation
An inverse relation is represented as:
[tex]y = \frac{k}{x}[/tex]
Where k = constant of variation
Make k the subject:
[tex]k = xy[/tex]
When x = -1, y = 8
So, we have:
[tex]k = -1 * 8[/tex]
[tex]k = -8[/tex]
When x = 4, y = -2
[tex]k = 4 * -2[/tex]
[tex]k = -8[/tex]
When x = -2, y = 4
[tex]k= -2 * 4[/tex]
[tex]k = -8[/tex]
From above calculations, we've established that:
[tex]k = -8[/tex]
Substitute -8 for k in [tex]y = \frac{k}{x}[/tex]
[tex]y = \frac{-8}{x}[/tex]
[tex]y = -\frac{8}{x}[/tex]
Hence, the equation is:
[tex]y = -\frac{8}{x}[/tex]
If I 50% increase is followed by a 33 1\3 % decrease is it greater, less than, or the same as the original
Answer:
Greater than.
Step-by-step explanation:
Let the original value be x.
A 50% increase in x is given by
x + 50%x
=> x + 0.5x
=> 1.5x
Followed by a 33 [tex]\frac{1}{3}[/tex] % decrease in the value gives:
1.5x - 33 [tex]\frac{1}{3}[/tex] %(1.5x)
=> 1.5x - 0.33(1.5x)
=> 1.5x - 0.495x
=> 1.005x
Since 1.005x is greater than the original value, x, then:
A 50% increase followed by a 33 [tex]\frac{1}{3}[/tex] % decrease gives a value that is greater than the original.
Lesley ran 2 3/5 miles in 7/12 of an hour. How many miles can Lesley run in one hour?
A.3 18/35
B.35/156
C. 22 2/7
D. 4 16/35
Answer:
D
Step-by-step explanation:
(3, 5), (y, 2) ; undefined slope
Answer:
x=-3..hope this is right
I literally need help.
Answer:
[tex]4P+2G=96\\3P+1G=60 or 3P+G=60[/tex]
Step-by-step explanation:
Given in the question:
a) A family paid $96 for 4 pool passes and 2 gym memberships.
b) Later that day, an individual bought pool passes for herself and 2 of her friends , and 1 gym membership for her . She paid $60.
Let's write the system of equation for each purchase that happened in the scenario.
Let,
P= Price of each pool passes
G= Price of each gym membership
We get,
a) A family paid $96 for 4 pool passes and 2 gym memberships:
[tex]4P+2G=96[/tex]
b) Later that day, an individual bought pool passes for herself and 2 of her friends , and 1 gym membership for her . She paid $60:
[tex]3P+1G=60[/tex]
Therefore, the equations generated in the scenario were:
[tex]4P+2G=96\\3P+1G=60 or 3P+G=60[/tex]
Where,
P=Price of each pool passes
G=Price of each gym membership
PLEASE MARK ME AS BRAINLIEST
WILL GIVE BRAINLEST
please explain with work if possible
Answer:
a)60°
b)BD=10
c)AB=20
d)100√3
Step-by-step explanation:
B
let's BD be x
according to the question
[tex] \tan( {30}^{o} ) = \frac{x}{10 \sqrt{3} } [/tex]
[tex] \frac{ \sqrt{3} }{3} = \frac{x}{10 \sqrt{3} } [/tex]
[tex]3x = 10 \sqrt{3} \times \sqrt{3} [/tex]
[tex]3x = 30[/tex]
[tex]x = 10[/tex]
thereforeBD=10c)
according to Pythagoras theorem
a²+b²=c²
c=√a²+b²
c=√10²+(10√3)²
c=√100+300
c=√400
c=20
D)
the two triangles are congruent
so AC=2(10√3)
=20√3
as we know
area of a triangle =
½bh
=½×20√3×10
=10√3×10
=100√3
this will guide youWhich line is the graph of y = -2x + 2?
Answer:
Line B → y = ½x + 1
_______________
For question 12, the answer is y = ½x + 1.
None of the lines graphed on question 12 have an equation of y = -2x + 2.
What is the rate of change of g(x)=x^3-9x for x=1 to x=6
Answer:
105
Step-by-step explanation:
[tex]g(x)=x^{3}-9x[/tex]
rate of change of g(x) is
[tex]g^{,}(x)=3x^{2} -9[/tex]
for x=1
[tex]g^{'}(1)=3(1)^{2} -9=-6[/tex]
for x=6
[tex]g^{'}(6)=3(6)^{2} -9=99[/tex]
khan academy help please!!
Answer:
-10
Step-by-step explanation:
rounding decimals to the thousandths place 45.9867
Answer:
45.987
Step-by-step explanation:
Because its the number you get by rounding up
HELP PLZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
Jessica runs between 3 and 7 miles per day. It takes Jessica 12 minutes to run one mile. What is a reasonable amount of time that Jessica spends running every day?
A.
36 minutes
B.
120 minutes
C.
84 minutes
D.
60 minutes
Answer:
36mimutes
Step-by-step explanation:
Simplify this expression 6w+4+8w-1
Answer:
14w + 3
Step-by-step explanation:
6w + 4 + 8w -1 (Given)
14w + 3 (combine like terms)
"The Kid Laroi" - Rapper-Songwriter.
Answer:
14w+3
Step-by-step explanation:
6w+4+8w-1
(6w+8w)+(4-1)
14w+3
A grocery store normally prices milk at $5.00 per gallon. Due to low supply, the grocery store
has marked up the price to $6.00 per gallon,
Answer:
how many gallons
Step-by-step explanation:
I'LL LOVE YOU FOREVER PLZ
btw ik its C but how do i get that answer?
Answer:
Step-by-step explanation:
Alright so just like the other problem we have to use ratios to find if it is parallels or not. In order for AC and DE to be parallels the sides CE and AD and DB and EB have to have the same ration. So in answer c if you do 24/22.5 you would get 1.066666667. So then to find the length of EB we subtract 24 from 40 to get 16 and then we do 16/15 to find out if the ratios are the same. And indeed they are the same both equaling 1.066666667. If you were to divide CE/AD and DB/EB none of the answers would be the same leading to c being the correct answer
A scatter plot is made to model the number of grams of fat in different portions of fried shrimp. The data used for the scatter plot are shown in the table below:
Number of portions 5 3 8 6 1 4
Number of grams of fat 45 27 72 54 9 36
Answer: :the number of grams of fat in each portion of fried shrimp
Step-by-step explanation:
PLEASE SEND HELP I REALLY REALLY NEED IT
Answer:
50 &15
Step-by-step explanation:
Reflect (4,-2) over the y axis then translate the result to the left 2 units
Answer:
(-6,2)
Step-by-step explanation:
for the reflection just go on the opposite side of the y axis and then it would be negative but then going left 2 more would add to 4.
In the given right triangle, find the miss length.
A. 25 m
B. 27 m
C. 26 m
D. 28 m
Answer:
26
Step-by-step explanation:
Answer:
C. 26 m
Step-by-step explanation:
home / math / pythagorean theorem calculator
Pythagorean Theorem Calculator
Please provide any 2 values below to solve the Pythagorean equation: a2 + b2 = c2.
Result
abc
Given a=24 and b=10,
c = 26
∠α = 67.38° = 67°22'48" = 1.17601 rad
∠β = 22.62° = 22°37'12" = 0.39479 rad
area = 120
perimeter = 60
h =
120
13
= 9.2307692307692
+ Show Calculation Steps
a =
24
√
b =
10
√
c =
√
Calculate
Related
Triangle Calculator | Right Triangle Calculator
Pythagorean Theorem
The Pythagorean Theorem, also known as Pythagoras' theorem, is a fundamental relation between the three sides of a right triangle. Given a right triangle, which is a triangle in which one of the angles is 90°, the Pythagorean theorem states that the area of the square formed by the longest side of the right triangle (the hypotenuse) is equal to the sum of the area of the squares formed by the other two sides of the right triangle:
In other words, given that the longest side c = the hypotenuse, and a and b = the other sides of the triangle:
a2 + b2 = c2
This is known as the Pythagorean equation, named after the ancient Greek thinker Pythagoras. This relationship is useful because if two sides of a right triangle are known, the Pythagorean theorem can be used to determine the length of the third side. Referencing the above diagram, if
a = 3 and b = 4
the length of c can be determined as:
c = √a2 + b2 = √32+42 = √25 = 5
It follows that the length of a and b can also be determined if the lengths of the other two sides are known using the following relationships:
a = √c2 - b2
b = √c2 - a2
The law of cosines is a generalization of the Pythagorean theorem that can be used to determine the length of any side of a triangle if the lengths and angles of the other two sides of the triangle are known. If the angle between the other sides is a right angle, the law of cosines reduces to the Pythagorean equation.
There are a multitude of proofs for the Pythagorean theorem, possibly even the greatest number of any mathematical theorem.
Algebraic proof:
In the figure above, there are two orientations of copies of right triangles used to form a smaller and larger square, labeled i and ii, that depict two algebraic proofs of the Pythagorean theorem.
In the first one, i, the four copies of the same triangle are arranged around a square with sides c. This results in the formation of a larger square with sides of length b + a, and area of (b + a)2. The sum of the area of these four triangles and the smaller square must equal the area of the larger square such that:
(b + a)2 = c2 + 4
ab
2
= c2 + 2ab
which yields:
c2 = (b + a)2 - 2ab
= b2 + 2ab + a2 - 2ab
= a2 + b2
which is the Pythagorean equation.
In the second orientation shown in the figure, ii, the four copies of the same triangle are arranged such that they form an enclosed square with sides of length b - a, and area (b - a)2. The four triangles with area ab 2 also form a larger square with sides of length c. The area of the larger square must then equal the sum of the areas of the four triangles and the smaller square such that:
(b - a)2 + 4
ab
2
=
(b - a)2 + 2ab
= b2 - 2ab + a2 + 2ab
= a2 + b2
Since the larger square has sides c and area c2, the above can be rewritten as:
c2 = a2 + b2
which is again, the Pythagorean equation.
There are numerous other proofs ranging from algebraic and geometric proofs to proofs using differentials, but the above are two of the simplest versions.
Help, Will give 100 points.
The following data table represents the total cost of a monthly cell phone bill as a function of the number of minutes that the phone is used each month.
The table shows that as more minutes are used each month, the total monthly cost will increase at the same rate. Assuming that this is true, what is the total monthly cost for the cell phone if it is used for 2,500 minutes?
Answer:
2+6=9 that give u 816
Step-by-step explanation:
Answer:
The total monthly cost would be $214
Step-by-step explanation:
This is rather simple. They gave us 1,250, which is half of 2,500. Simple multiplication:
1,250 = 2,500
107 = x
2 × 1,250 = 2,500
2 × 107 = 214
Therefore, the total monthly cost if the cell phone is used for 2,500 minutes is $214.
Nate wants to predict how long people use the internet each day based on their age. The table below shows the age (in years) and average daily internet usage (in hours) for a sample of people.
Age (years)
3
33
10
1010
16
1616
22
2222
35
3535
55
5555
Internet use (hours per day)
0.0
0.00, point, 0
1.0
1.01, point, 0
2.5
2.52, point, 5
4.0
4.04, point, 0
3.0
3.03, point, 0
0.5
0.50, point, 5
Answer:
A
Step-by-step explanation:
A is correct on Khan academy!
Need answer now. Find m
What is the square root of 10, and 9?
Solve for all values of x by factoring.
x^2 + 4x – 30 = -3x
Answer:
[tex] {x}^{2} + 4x - 30 = - 3x \\{x}^{2} + 7x - 30 = 0 \\ {x}^{2} - 3x + 10x - 30 = 0 \\ x(x - 3) + 10(x - 3) = 0 \\ (x - 3)(x + 10) = 0 \\ \boxed{x = 3} \\ \boxed{x = - 10}[/tex]
x=3 or x=-10 is the right answer.What is the greatest common factor of 30, 48, and 2?
Answer:
The greatest common factor of 30, 48 and 2 is 2Step-by-step explanation:
I HOPE IT HELPS2 is the Greatest common factor
Given numbers:
30 , 48 , 2
Find:
Greatest common factor
Computation:
By taking LCM of given numbers
30 = 2 × 3 × 5
48 = 2 × 2 × 2 × 2 × 3
2 = 2
From the above LCM taking '2' as common factor.
So,
we say that, 2 is the Greatest common factor
Learn more:
https://brainly.com/question/11221202?referrer=searchResults
If a=-6 and b=-10 evaluate the following:
a + 6
Answer:
-6+-10=-16
Step-by-step explanation:
+ - = -
........
Alexis saves up her monthly allowance over a period of eight months to buy a pair of high-resolution headphones. She lends her friend, Janet $26.40 from her savings. If Alexis has $257.60 now, calculate her monthly allowance.
Answer:
26.40+257.60=
284
284÷18
15.7
Factor
k2+7x+10
(k+10)(k+4)
(k+2)(k+5)
(k-2)(k-5)
(k+2)(k-5)
Need it ASAP
Answer:
B. (k+2)(k+5)
Step-by-step explanation:
Answer:
B. (k+2)(k+5)
Step-by-step explanation:
Find the exact length of the third side.
85
13
Answer:
84
Step-by-step explanation:
13^2+84^2=85^2
Mrs. Konings is planning an ice cream social for her students. It is going to cost her $100 to rent the facility plus $3 per person for ice cream and toppings. Which function represents the total cost for Mrs. Konings if x students attend the ice cream social?
f(x)=3x+100
f(x)=103x
f(x)=100x+3
f(x)=3x+100
Each of the 24 students in Mr. Shaw's homeroom sold 10 tickets to a sports event. How many tickets (x) were sold in the homeroom?
Answer:
240
Step-by-step explanation:
24 students sold 10 tickets so 24x10
If f(x)=3.5x, what is f(2)?
PLEASE SOMEONE HELP I DONT UNDERSTAND THIS AT ALL
