Answer:
Inverse of a relation
Reasoning:
the inverse of a function is a full function, this is just a set of pairs. A set of pairs, or relation, where x and y values interchange are inverse of the relation. A one to one function is when a function's inverse is also a function (doesn't have more than one y for each x) which can be tested for on the normal function's graph with a HORIZONTAL line test. A normal parabola isn't one to one. An onto function has to do with every value being used (I don't remember much about them, but once again this isn't a function, but rather a specific set of pairs/data)
Example of inverse of a relation:
Relation: {(0,5), (3,2)}
Inverse: {(5,0), (2,3)}
Example of inverse of a function:
f(x)=5x
f-1(x)=x/5
Example of a one to one function:
f(x)=x+1
Answer:
For Plato the inverse of a function
Step-by-step explanation:
Solve the following equations 4x + 3y =17 3x + 2y = 13
Answer:
(5,-1)
Step-by-step explanation:
4x+3y=17
3x+2y=13
So elimination sounds fun but we will have to do manipulation:
Multiply top equation by 2 and bottom equation by 3. This will cause the second term in both by 6y which means we would be setup for elimination.
8x+6y=34
9x+6y=39
--------------------now subtract the equations
-x+0=-5
So x=5
Now plug it into either question (no matter which-pick and choose)
I will go with the second original 3x+2y=13
So if x=5 we have 15+2y=13
Subtract 15 on both sides: 2y=-2
Now divide both sides by 2: y=-1
Answer (5,-1)
Final answer:
To solve the simultaneous linear equations 4x + 3y = 17 and 3x + 2y = 13, the elimination method shows that the solution is x = 5 and y = -1.
Explanation:
To solve the simultaneous linear equations 4x + 3y = 17 and 3x + 2y = 13, one could use either the substitution method, the elimination method, or matrix methods. However, as per the guidance, we will follow the elimination method which is efficient and easily understandable.'
Let's multiply the first equation by 2 and the second equation by 3, which will give us:
8x + 6y = 34 (equation 1 multiplied by 2)
9x + 6y = 39 (equation 2 multiplied by 3)
Now, subtract the first new equation from the second new equation to eliminate y:
9x - 8x + 6y - 6y = 39 - 34
x = 5
Substitute x = 5 into one of the original equations to find y. For example, put x = 5 in 4x + 3y = 17:
4(5) + 3y = 17
20 + 3y = 17
3y = -3
y = -1
Therefore, the solution to the system of equations is x = 5 and y = -1.
a golf ball is dropped onto concrete from 2 meters up. Each time it bounces, it rebounds to 2/3 of its previous height. On the sixth rebound, how much will it rise
Step-by-step explanation:
The ratio is the same each time (2/3), so this can be modeled as a geometric sequence.
an = a₁ (r)^(n-1)
where an is the nth term, a₁ is the first term, and r is the common ratio.
On the first rebound, the ball rises to 2/3 × 2 = 4/3, so a₁ = 4/3.
an = 4/3 (2/3)^(n-1)
On the sixth rebound, the ball rises to:
a₆ = 4/3 (2/3)^(6-1)
a₆ = 4/3 (32/243)
a₆ = 128/729
a₆ ≈ 0.176
Find the missing value 4 = -8 - ?
Answer: -12
Step-by-step explanation:
Answer:
Hi there!
The answer to this question is negative 12.
At the beginning of a class period, half of the students in a class go to the library. Later in the period, half of the remaining students go to the computer lab. If there are eight students remaining in class, how many students were originally in the class?
Answer:
32 students
Step-by-step explanation:
We are given that at the beginning of a class period, half of the students in a class go to the library and half of the remaining to the computer lab.
Given that there are 8 students remaining, we are to find the total number of students in the class initially.
At beginning = [tex]x[/tex] students
After half of them leave = [tex]\frac{x}{2}[/tex] students
After half of the remaining leave = [tex]\frac{x}{4}[/tex] students
So, [tex]\frac{x}{4} = 8[/tex]
[tex]x=8\times 4[/tex]
x = 32
Therefore, there were 32 students in the class originally.
there were 32 students in the class originally.
because in the computer lab before there were 16. 16 times 2 equals 32.
An equilateral triangle has an altitude of 45. Find the length of a side of the triangle.
Answer:
See attachment.
If altitude = 45 then
side = 2 * height (or altitude) / square root of 3
side = 2 * 45 / 1.7320508076
side = 90 / 1.7320508076
side = 51.9615242271
Step-by-step explanation:
Follow below steps;
When dealing with an equilateral triangle, dividing it by an altitude creates two 30-60-90 right triangles. Since we know the length of the altitude (45), which corresponds to the shorter leg in the 30-60-90 triangle, we can find the length of the side of the equilateral triangle (which is the hypotenuse of the 30-60-90 triangle) using the properties of this special right triangle.
To begin, we recognize that the ratios of the sides of a 30-60-90 triangle are 1:\\(extbackslashsqrt{3}\\):2. Thus, if the shorter leg is 45, the hypotenuse will be twice that length, because the ratio of the shorter leg to the hypotenuse is 1:2. Therefore, the length of a side of the equilateral triangle is 45 * 2, which equals 90.
A car rental costs $50 for the first day. Additional days cost $35 per day, unless the car is rented for 7 days or more, in which case there is a 10% discount on the daily rate.
Identify the expression which represents the cost of renting a car if the car has been rented for more than a week.
A) 45 + 35x
B) 45 + 31.5x
Eliminate
C) 50 + 35x
D) 50 + 31.5x
Answer:
D) 50+31.5x
Step-by-step explanation:
10% of 35 is 3.5
35-3.5=31.5
If y is 5 when x is 2.5 and y varies directly with x, find y when x is 10
Answer:
If x varies directly as y, then x=ky. y=5 and x=2.5 are substituted into x=ky to find k.
2.5=5k
k=2.5/5
k=5.
K =5 is substituted in x=ky to find y where x is 10.
x=5y
10=5y
y=10/2
y=2
Answer: The required value of y is 20.
Step-by-step explanation: Given that y is 5 when x is 2.5 and y varies directly with x.
We are to find the value of y when x is 10.
According to the given information, we can write
[tex]y\propto x\\\\\Rightarrow y=kx~~~~~~~~~~[\textup{where k is the constant of proportionality}][/tex]
When y = 5 and x = 2.5, then we have
[tex]5=k\times2.5\\\\\Rightarrow k=\dfrac{5}{2.5}\\\\\Rightarrow k=2.[/tex]
So, we get
[tex]y=2x.[/tex]
Therefore, when x = 10, then the value of y is
[tex]y=2\times10=20.[/tex]
Thus, the required value of y is 20.
The side lengths of different triangles are given. Which triangle is a right triangle? A. 6,7,13 B. 21−−√,99−−√,11 C. 10,60,61 D. 35−−√,14−−√,7
Answer:
D
Step-by-step explanation:
By definition for a right triangle with sides a, b, c, where c is the hypotenuse,
the following must be true:
a² + b² = c²
By using this formula on all the choices, we find that only D satisfies this formula
i.e.
for
a = √35 --------> a² = 35
b = √14 --------->b² = 14
c = 7 ------> c² = 49
a² + b² = 35 + 14 = 49 which is equal to the value of c² above
The correct answer is √35 , √14 , 7
What is Pythagoras theorem?Pythagoras' theorem that the square of a right triangle's hypotenuse is equal to the sum of the squares of the other two sides.
p^2 + b^2 = h^2 ( In a right angled triangle)
p = perpendicular of the triangle
b = base of the triangle
h = hypotenuse of the triangle
According to the Pythagoras theorem:
p^2 + b^2 = h^2 (In a right angled triangle)
In Option D
(√35)^2 + (√14)^2 = 7^2
49 = 49
Pythagoras theorem is followed in this triangle, hence it is a right angled triangle.
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Find the perimeter of the image below
A 32.1 units
B 35.8 units
C 37.6 units
D 39.2 units
Answer:
We need to solve the each side as though it is the hypotenuse:
AB: 6^2 + 5^2 = 61 => 7.81
BC: 8^2 + 5^2 = 89 => 9.43
CD: 4^2 + 3^2 = 25 => 5
DE: 4^2 + 2^2 = 20 => 4.47
EA: 2^2 + 5^2 = 29 => 5.39
Total 32.10 Units
Step-by-step explanation:
Please mark brainliest and have a great day!
A taxi cab charges $1.75 for the flat fee and $0.25 for each time. Write an in equality to determine how many miles Eddie can travel if he has $15 to spend.
Answer:
53 miles
Step-by-step explanation:
I'm going to assume "$0.25 for each time" is "$0.25 per mile."
$1.75 is the flat fee. It costs 25 cents for each mile. We can represent this as:
1.75 + 0.25m
The sum of this equation has to be less than or equal to $15. We can display this as:
1.75 + 0.25m ≤ 15.
To solve, we must first isolate 0.25m. To do this, we subtract 1.75 from each side.
0.25m ≤ 15 - 1.75
0.25m ≤ 13.25.
Now, we must isolate the variable 'm' to determine how many miles Eddie can travel. To do this, we divide 0.25 from each side.
m ≤ 13.25 / 0.25
m ≤ 53.
Therefore, Eddie can travel 53 miles if he has $15 to spend.
Find the solution set
2x^2 -2x -4 =0
please use a comma to separate your answer.
Answer:
2,-1
Step-by-step explanation:
2x^2 -2x -4 =0
Factor out a 2
2(x^2 -x-2) =0
What 2 number multiply to -2 and add to -1
-2*1 = -2
-2 +1 = -1
2(x-2) (x+1) =0
Using the zero product property
x-2 = 0 x+1 = 0
x-2+2=0+2 x+1-1=0-1
x=2 x=-1
If sin pheta < 0 and tan pheta < 0 then:
sin(θ) < 0 is another way to say sin(θ) is negative.
tan(θ) < 0 is another way to say tan(θ) is negative.
let's recall that, on the III Quadrant sine and cosine are both negative, and thus the tangent is positive, recall tan(θ)=sin(θ)/cos(θ).
on the IV Quadrant however, sine is negative and cosine is positive, thus tangent is negative.
how many terms does the polynomial x^2+xy-y^2 have
Answer:
3 TERMS
Step-by-step explanation:
There are total 3 terms in the polynomial [tex]x^{2} + xy - y^{2}[/tex] .
What is the total number of terms of given polynomial ?The given polynomial expression is [tex]x^{2} + xy - y^{2}[/tex] .
The number of terms of any expression is the total number of independent variables present in the given polynomial expression.
We can see that there are total 3 independent variables present in the polynomial expression and therefore the number of terms present is also three.
Thus, there are total 3 terms in the polynomial [tex]x^{2} + xy - y^{2}[/tex] .
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What is the slope of the linear equation 30x-60y=12
Answer:
60y = 30x - 12
y = 1/2x - 1/5
The slope is 1/2
Answer:
1/2
Step-by-step explanation:
30 over 60 is half
What is the y-intercept of the linear equation x-1/2y=-6?
a) –6
b) –3
c) 0
d) 12
Answer:
[tex]\large\boxed{d)\ 12}[/tex]
Step-by-step explanation:
[tex]x-\dfrac{1}{2}y=-6\\\\\text{y-intercept is for x = 0. Substitute:}\\\\0-\dfrac{1}{2}y=-6\\\\-\dfrac{1}{2}y=-6\qquad\text{multiply both sides by (-2)}\\\\\left(-2\!\!\!\!\diagup^1\right)\left(-\dfrac{1}{2\!\!\!\!\diagup_1}y\right)=(-2)(-6)\\\\y=12[/tex]
Solve 3x + 11 = k for x.
3x +11 = K
To solve for X, we need to isolate x on one side.
Subtract 11 from both sides:
3x = K -11
Divide both sides by 3:
x = (k-11)/3
Answer:
3x +11 = K
x = (k-11)/3
Step-by-step explanation:
Two lines that do not intersect are skew. Always Sometimes or Never
Answer:
Never.
Step-by-step explanation:
What is the value of x?
ANSWER
58°
EXPLANATION
The relationship between the measure of the bigger arc and the smaller arc and the angle created by the secant and the tangent is
[tex]51 \degree = \frac{1}{2} (160 - x)[/tex]
Multiply through by 2
This implies that
[tex]2 \times 51 \degree =2 \times \frac{1}{2} (160 - x)[/tex]
We simplify to get:
[tex]102 \degree =160 - x[/tex]
Solve for x.
[tex]102 \degree - 160 \degree =- x[/tex]
[tex] - 58 \degree =- x[/tex]
[tex]58 \degree =x[/tex]
q2 + 3q - 18 = (q + 6)(q - ?)
3x + 4y=17
- 4x – 3y = - 18
Answer:
3
Step-by-step explanation:
Answer:
The correct answer is (3,2)
Combine the following expressions 2√5+ 5√5. A.)35 B.)7√5 C.)7√10
Answer:
B.)7√5
Step-by-step explanation:
2√5+ 5√5 = 7√5
we simply let √5 = x
therefore;
2√5+ 5√5 = 2x + 5x
2x + 5x = 7x
but x = √5
2√5+ 5√5 = 7√5
-6.3x+14 and 1.5x-6
answer in simplified form
Answer:
The simplified form of -6.3x+14 and 1.5x-6 is -4.8x+8
Step-by-step explanation:
We have to simplify the following
-6.3x+14 and 1.5x-6
it can be written as:
=(-6.3x+14) + (1.5x-6)
Adding the like terms
=(-6.3x+1.5x)+(14-6)
= (-4.8x)+(8)
= -4.8x+8
So, the simplified form of -6.3x+14 and 1.5x-6 is -4.8x+8
A sequence is defined recursively using the formula f(n + 1) = –0.5 f(n) . If the first term of the sequence is 120, what is f(5)?
[tex]\bf \begin{array}{rrlll} term&\stackrel{f(n+1)=-0.5f(n)}{~\hfill value~ }\\ \cline{1-2} f(1)&120\\ f(2)&-0.5(120)\\ &-60\\ f(3)&-0.5(-60)\\ &30\\ f(4)&-0.5(30)\\ &-15\\ f(5)&-0.5(-15)\\ &7.5 \end{array}[/tex]
Answer:
f(5) = 7.5
Step-by-step explanation:
The recursive formula allows a term in the sequence to be found from the previous term, thus
f(2) = - 0.5 f(1) = - 0.5 × 120 = - 60
f(3) = - 0.5f(2) = - 0.5 × - 60 = 30
f(4) = - 0.5f(3) = - 0.5 × 30 = - 15
f(5) = - 0.5f(4) = - 0.5 × - 15 = 7.5
What are the solutions of the given equation 2x^2+9x+10=0
Answer:
see explanation
Step-by-step explanation:
Given
2x² + 9x + 10 = 0
To factor the quadratic
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 2 × 10 = 20 and sum = + 9
The factors are + 4 and + 5
Use these factors to split the x- term
2x² + 4x + 5x + 10 = 0 ( factor the first/second and third/fourth terms )
2x(x + 2) + 5(x + 2) = 0 ← factor out (x + 2) from each term
(x + 2)(2x + 5) = 0
Equate each factor to zero and solve for x
x + 2 = 0 ⇒ x = - 2
2x + 5 = 0 ⇒ 2x = - 5 ⇒ x = - [tex]\frac{5}{2}[/tex]
Answer:
1. x = 2
2. x = - 5/2
Step-by-step explanation: First put parenthesis around the equation
( 2x^2 + 4x ) + ( 5x + 10) = 0
2x ( x+ 2) 5 (x + 2),
when you have the same answer inside the parenthesis you know your right.
2x + 5 = 0
x + 2 = 0
Next preform basic algebra
2x = -5
x = -2x = - 5/2The strength of a bar magnet's magnetic field decreases with distance according to what is known as an inverse cube law; multiplying the distance from the magnet by a factor of k divides the magnetic field strength by a factor of k^3. Suppose the magnetic field strength of the magnet is 64 Gauss at a distance of 10 cm away. What is the magnetic field strength of the magnet, 20 cm away?
Answer:
8 Gauss
Step-by-step explanation:
Since your moving the magnet from 10 to 20cm you're essentially multpliying the distance by 2.
K = 2
Therefore k ^ 3 = 2^3
64/2^3
=8
Answer:
8 Guass
Step-by-step explanation:
We multiply the distance by a factor of $2$, and thus divide the magnetic field strength by a factor of $2^3 = 2 \cdot 2 \cdot 2 = 8$. We get a magnetic field strength of 64/8 = 8
Factor k2 - 81.
(k + 9)(K + 9)
(k - 9)(k - 9)
(k - 9)(k + 9)
Answer:
(
k
+
9
)
(
k
−
9
)
(k+9)(k-9)
Step-by-step explanation:
Answer:
It's C
Step-by-step explanation:
Which set of numbers can represent the side lengths, in centimeters, of a right triangle?
0 8, 12, 15
O 10, 24, 26
O 12, 20, 25
15, 18, 20
Mark this and retum
Save and Exit
Next
Answer:
The set {10 , 24 , 26} formed a right triangle
Step-by-step explanation:
* Lets explain how to check the sides lengths which formed a
right triangle
- In triangle ABC
# If AC is the longest side in length
# If (AC)² = (AB)² + (BC)²
∴ AB , BC , AC formed a right angle triangle
∴ m∠B = 90° (The angle opposite to the longest side)
∴ AC is the hypotenuse
* Now lets solve the problem
- In set 8 , 12 , 15
∵ The longest side is 15 cm
∴ (15)² = 225
∵ (8)² + (12)² = 64 + 144 = 208
∵ (15)² ≠ (8)² + (12)²
∴ The set not formed a right triangle
- In set 10 , 24 , 26
∵ The longest side is 26 cm
∴ (26)² = 676
∵ (10)² + (24)² = 100 + 576 = 676
∵ (26)² = (10)² + (24)²
∴ The set formed a right triangle
- In set 12 , 20 , 25
∵ The longest side is 25 cm
∴ (25)² = 625
∵ (12)² + (20)² = 144 + 400 = 544
∵ (25)² ≠ (12)² + (20)²
∴ The set not formed a right triangle
- In set 15 , 18 , 20
∵ The longest side is 20 cm
∴ (20)² = 400
∵ (15)² + (18)² = 225 + 324 = 549
∵ (20)² ≠ (15)² + (18)²
∴ The set not formed a right triangle
* The set {10 , 24 , 26} formed a right triangle
For the equations below which statement is true ? -2x=14 6x=-42
find next number of 32,1312,11131112,31133112
Answer:
The next number is 1321232112
Step-by-step explanation:
32 is read off as "one 3, one 2" = 1312
1312 is read off as "one 1, one 3, one 1, one 2" = 11131112
11131112 is read off as "three 1s, one 3, three 1s, one 2" = 31133112
31133112 is read off as "one 3, two 1s, two 3s, two 1s, one 2" = 1321232112
simplify (4x-6)-(3x+6)
Answer:
[tex]x-12[/tex]
Step-by-step explanation:
First open the brackets
[tex]=(4x-6)-(3x+6)\\\\\\=4x-6-3x-6[/tex]
Then collect the like terms
[tex]4x-3x-6-6[/tex]
Solve the like terms
[tex]4x-3x=x\\\\\\-6-6=-12\\\\\\=x-12[/tex]
The simplified form is
[tex]x-12[/tex]