The given relation is a function
Step-by-step explanation:
When a relation is given in the form of ordered pairs, for each ordered pair, the first element of ordered pair represents elements of domain and the second element represents elements of set of range.
In order for a relation to be a function, there should be no repetition in domain i.e. every element should be unique.
Given relation is:
{(2, 2), (3, 2), (4, 3), (5,4)}
As we can see that the domain of given relation is:
{2,3,4,5} i.e. every element is unique
So,
The given relation is a function
Keywords: Relations, functions
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The provided set of ordered pairs {(2, 2), (3, 2), (4, 3), (5,4)} represents both a relation and a function. This holds because each input maps to exactly one output, with no repeating input values.
Explanation:In mathematics, a set of ordered pairs is a relation if input values (also known as the domain or x-values) may have any number of corresponding output values (the range or y-values). A set of ordered pairs is a function if each input value maps to exactly one output value.
Considering the set of ordered pairs: {(2, 2), (3, 2), (4, 3), (5,4)}, we can see that each input (x-value) matches with one corresponding output (y-value) and none of the input values is repeating. Hence, according to the definition, this set of ordered pairs represents both a relation and a function.
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Two-thirds of a number added to itself is 20. What is the number?
Answer:
12
Step-by-step explanation:
2/3 x + x = 20
2/3 x + 3/3x = 20
5/3 x = 20 ... times 3/5 both sides
x = 12
check: 2/3 x 12 + 12 = 8 + 12 = 20
Janet charges an upfront fee of $20 plus $7.50 an hour for babysitting. Lisa does not charge an upfront fee, but charges $8.75 an hour. After how many hours will their charge be equal?
After 16 hours, the charges will be same.
Step-by-step explanation:
Given,
Janet's upfront fee = $20
Charges per hour = $7.50
Let,
x be the number of hours.
J(x) = 7.50x+20
Lisa has no upfront fee.
Charges per hour = $8.75
L(x) = 8.75x
For the charges to be equal;
J(x) = L(x)
[tex]7.50x+20=8.75x\\20=8.75x-7.50x\\20=1.25x\\1.25x=20[/tex]
Dividing both sides by 1.25
[tex]\frac{1.25x}{1.25}=\frac{20}{1.25}\\x=16[/tex]
After 16 hours, the charges will be same.
Keywords: function, division
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A little towns population is growing at an annual rate of 7.5%, annually. What is it’s growth rate per 3 years? Per 5 years? Round to the nearest tenth of a percent.
Answer:
A) The increase population of town after 3 years is 1.2 times initial population
B) The increase population of town after 5 years is 1.4 times initial population .
Step-by-step explanation:
Given as :
The rate of growth of population of a town = r = 7.5%
Let The initial population of town = p
A ) Let The increase population of town after 3 years = P
The time period = n = 3 years
Now, According to question
The increase population of town after n years = initial population of town × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]
Or, The increase population of town after n years = initial population of town × [tex](1+\dfrac{\textrm r}{100})^{\textrm n}[/tex]
Or, The increase population of town after 3 years = p × [tex](1+\dfrac{\textrm 7.5}{100})^{\textrm 3}[/tex]
Or, P = p × [tex](1.075)^{3}[/tex]
Or, P = p × 1.242
So, The increase population of town after 3 years = P = 1.2 times initial population
Hence,The increase population of town after 3 years is 1.2 times initial population . Answer
B ) Let The increase population of town after 5 years = P'
The time period = n = 5 years
Now, According to question
The increase population of town after n years = initial population of town × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]
Or, The increase population of town after n years = initial population of town × [tex](1+\dfrac{\textrm r}{100})^{\textrm n}[/tex]
Or, The increase population of town after 5 years = p × [tex](1+\dfrac{\textrm 7.5}{100})^{\textrm 5}[/tex]
Or, P' = p × [tex](1.075)^{5}[/tex]
Or, P' = p × 1.4356
So, The increase population of town after 5 years = P' = 1.4 times initial population
Hence,The increase population of town after 5 years is 1.4 times initial population . Answer
A candy store sells caramels and milk chocolate by the pound the table below shows the total cost in dollars for a pound of each type of candy the store sells
Caramels: $10.28
Milk Chocolate: $13.85
How much more is the cost for 1 3/4 pounds of milk chocolate than the cost for 1 3/4 pounds of caramels?
The cost of [tex]1\frac{3}{4}[/tex] pounds chocolate milk is $6.25 more than the cost of [tex]1\frac{3}{4}[/tex] pounds of Caramel.
Step-by-step explanation:
Given,
Cost of one pound of Caramels = $10.28
Cost of [tex]1\frac{3}{4}[/tex] pounds of Caramel = [tex]10.28*1\frac{3}{4}[/tex]
Cost of [tex]1\frac{3}{4}[/tex] pounds = [tex]10.28*\frac{7}{4}=\frac{71.96}{4}= \$17.99[/tex]
Cost of one pound of chocolate milk = $13.85
Cost of [tex]1\frac{3}{4}[/tex] pounds = [tex]13.85*1\frac{3}{4}=13.85*\frac{7}{4}[/tex]
Cost of [tex]1\frac{3}{4}[/tex] pounds = [tex]\frac{96.95}{4}=\$24.24[/tex]
Difference = 24.24 - 17.99 = $6.25
The cost of [tex]1\frac{3}{4}[/tex] pounds chocolate milk is $6.25 more than the cost of [tex]1\frac{3}{4}[/tex] pounds of Caramel.
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Final answer:
The cost for 1 3/4 pounds of milk chocolate is $6.25 more than the cost for 1 3/4 pounds of caramels, after calculating the total cost of each based on their per pound price.
Explanation:
To find out how much more the cost for 1 3/4 pounds of milk chocolate is than the cost for 1 3/4 pounds of caramels, we first need to calculate the cost of 1 3/4 pounds of each type of candy. Since the cost per pound of caramels is $10.28 and the cost per pound of milk chocolate is $13.85, we can set up our calculations as follows:
Total cost of caramels = 1.75 (pounds) * $10.28 (per pound) = $17.99
Total cost of milk chocolate = 1.75 (pounds) * $13.85 (per pound) = $24.24
Now, we subtract the total cost of caramels from the total cost of milk chocolate to find the difference:
Cost difference = $24.24 - $17.99 = $6.25
So, the cost for 1 3/4 pounds of milk chocolate is $6.25 more than the cost for 1 3/4 pounds of caramels.
5/6 ÷2/7 divide the fraction
Answer:
35/ 12
Step-by-step explanation:
5/6 divided by 2/7
= 5/6 x 7/2
= 35/ 12
Absolute value of 225
225
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Answer: 3x-x+2=4
Step-by-step explanation:
absolute value of 225 = | 225 | = 225
please help me I need it.
Deon needs 50g of shugger to make 15 biscuits.
she also needs three times as much flour as sugar
two times as much butter as sugar
Deon is going to make 60 biscuits
work out the amount of flour she needs.
Answer:
200g of sugar, 600g of flour, 400g of butter
Step-by-step explanation:
50g sugar = 15 biscuits
3 x 50g = flour --) 150g = flour
2 x 50g = butter --) 100g = butter
60/15 = 4; 4 times as much
4 x 50g = 200g of sugar
4 x 150g = 600g of flour
4 x 100g = 400g of butter
The amount of flour she needed is 600g.
Given that,
Deon needs 50g of shugger to make 15 biscuits. she also needs three times as much flour as sugar two times as much butter as sugar. Deon is going to make 60 biscuits.Based on the above information, the calculation is as follows:
50g sugar = 15 biscuits
[tex]= 3 \times 50g\\\\ = 150g\ flour[/tex]
And.
[tex]= 2 \times 50g \\\\= 100g \ butter[/tex]
Now
[tex]= 60\div15[/tex]
= 4 times
Therefore, the amount of floor should be
[tex]= 150 \times 4[/tex]
= 600 grams.
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Please help! A chemist has 100ml of 25% acid solution. How much of the solution does she need to drain and replace with 70% acid solution to obtain 100ml of 60% acid solution?
Answer:
77.78
Step-by-step explanation:
Answer:
77.78
Step-by-step explanation:
i had this ? on rsm student portal.
here is an inequality 2x + 5 > 50 explain the steps you would use to solve the equation for x what would the graph look like
Answer:
[tex]x>22.5[/tex]
Step-by-step explanation:
Given linear inequality:
[tex]2x+5>50[/tex]
Solving for [tex]x[/tex]
Subtracting both sides by 5.
[tex]2x+5-5>50-5[/tex]
[tex]2x>45[/tex]
Dividing both sides by 2.
[tex]\frac{2x}{2}>\frac{45}{2}[/tex]
∴ [tex]x>22.5[/tex]
The graph of the inequality is shown below.
The line is represented by dotted line because the inequality sign is only greater than which means 22.5 is not included in the solution.
Emily has $3.15 worth of dimes and quarters. She has twice as many dimes as quarters. Determine the number of dimes and the number of quarters that Emily has.
Answer:
The number of dimes is 14 and the number of quarters is 7.
Step-by-step explanation:
Given:
Emily has $3.15 worth of dimes and quarters.
She has twice as many dimes as quarters.
Now, to determine the number of dimes and the number of quarters.
Let the number of quarters be [tex]x.[/tex]
And the number of dimes be [tex]2x.[/tex]
So, the total worth of dimes and quarters = $3.15.
Now, to get the number of dimes and quarters:
According to question:
[tex]0.10(2x)+0.25x=3.15[/tex]
[tex]0.20x+0.25x=3.15[/tex]
[tex]0.45x=3.15[/tex]
Dividing both sides by 0.45 we get:
[tex]x=7.[/tex]
Thus, the number of quarters = 7.
So, the number of dimes = [tex]2x=2\times 7=14.[/tex]
Therefore, the number of dimes is 14 and the number of quarters is 7.
a 20.00 pair of jeans is discounted 20%. What is the final price of the jeans?
Answer:
16.00
Step-by-step explanation:
When you divide twenty percent(0.20) to 20.00 you will get sixteen or 4.00 dollars off
What is the y-intercept of the function f(x) = -3x
Ο
Ο
on who wire on
Ο
Ο
Answer:
see the explanation
Step-by-step explanation:
we know that
The y-intercept is the value of the function when the value of x is equal to zero. Also is called the initial value of the function
I will analyze two cases
Part 1) we have
[tex]f(x)=-3x[/tex]
so
For x=0
substitute
[tex]f(0)=-3(0)=0[/tex]
therefore
The y-intercept is the point (0,0)
Part 2) we have
[tex]f(x)=-3^x[/tex]
so
For x=0
substitute
[tex]f(0)=-3^0=-1[/tex]
therefore
The y-intercept is the point (0,-1)
help a girl out
(2a^3−5a)−(7a+3a^2)
For this case we must simplify the following expression:
[tex](2a ^ 3-5a) - (7a+ 3a ^ 2) =[/tex]
By definition of the law of multiplication signs we have to:
[tex]- * + = -[/tex]
Rewriting the expression we have:
[tex]2a ^ 3-5a-7a-3a ^ 2 =[/tex]
We add similar terms taking into account that:
Equal signs are added and the same sign is placed.
[tex]2a ^ 3-3a ^ 2-12a[/tex]
ANswer:
[tex]2a ^ 3-3a ^ 2-12a[/tex]
which formula can be used to find an ?
Answer:
Step-by-step explanation:
an = 6n - 13
If n = 10 , a10 = 6*10 - 13 = 60-13 = 47
If n = 11 , a11 = 6*11 - 13 = 66-13 = 53
If n = 12 , a12 = 6*12 - 13 = 72-13 = 59
The formula to find the nth term of the sequence an, is a(n) = -13 + 6n
How to determine the formula to find an ?From the question, we have the following parameters that can be used in our computation:
a(10) = 47
a(11) = 53
a(12) = 59
a(13) = 65
The nth term of an arithmetic sequence can be represented as
a(n) = a(1) + (n - 1) * d
Where,
common difference,
d = 6
So, we have
a(n) = a(1) + (n - 1) * 6
Using the 12th term, we have
a(1) + (12 - 1) * 6 = 59
a(1) = 59 - 66
a(1) = -7
So,, we have
a(n) = -7 + (n - 1) * 6
Expand
a(n) = -13 + 6n
Hence, the formula to find an is a(n) = -13 + 6n
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There were 9 beluga whales, 3 bowhead whsles, and 2 narwhales. Each whale travels 6 miles. How many miles did the whale trvael?
84 miles I would think
Explanation:
14 whales in all, each travelled 6 miles.
14x6=84
Hope I helped :)
What’s equivalent to 25x + 35y
Answer:5x+7y
Step-by-step explanation:
Your welcome
The scatterplot represents the total fee
for miles traveled on a toll road.
The line of best fit for the data is
y = 0.043x + 0.324.
Use the line of best fit to predict the toll
when 100 miles are driven.
Answer:
[tex]4.624[/tex]
Step-by-step explanation:
[tex]y=0.043x+0.324\\given \ miles \ x=100\\y= 0.043\times100+0.324\\=4.3+0.324\\=4.624[/tex]
Worst Buy, a local electronics store, advertises a sale price of 25% off all televisions 42" or bigger. Model the sale price (original price minus discount) of those televisions, y, as a function of the regular price of the TV, x.
25% off means it would be selling for 75% of the original price ( 100% - 25% = 75%).
To find the sale price you would multiply the regular price by 75%:
The equation would be y = 0.75x
What is the domain for the piece of the function represented by f(x) = x + 1? x < –1 –1 ≤ x ≤ 1 1 ≤ x < 2 x > 1
Note: As you missed to mention the graph for f(x) = x + 1 from where we had to check which option defines the accurate graph. But, after a little research, I was able to get the graph of this question, and hence attaching the graph. So, I am answering based on that graph which, anyways, would clear your concept about determining the domain of the function that shows in a graph.
Answer:
x > 1 is the domain of the f(x) = x + 1.
Step-by-step explanation:
A domain is the set of all x values that a function passes through. It means a domain is set of all input values where the function is defined, meaning whatever you input the x value, for every x-value there is only one y-value that corresponds to it.
So, now lets talk about the given function f(x) = x + 1 and its graph as shown in attached figure. Carefully observe the top right part of the graph of f(x) = x + 1. It is validating the condition of x > 1.
For example,
Just input some x values, greater than 1 i.e. x > 1, in f(x) = x + 1 to determine the output values.
For example, for x > 1
For x = 2, f(x) = 3. So, the graph must pass through of P(2, 3)For x = 3, f(x) = 4. So, the graph must pass through of P(3, 4)For x = 4, f(x) = 5. So, the graph must pass through of P(4, 5)and so on.
So, the top right part of the graph of f(x) = x + 1 is validating the condition of x > 1 as it is passing through P(2, 3), P(3, 4) and P(4, 5) etc. and so on.
So, x > 1 is the domain of the f(x) = x + 1.
Keywords: domain, function
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Answer:
"D" X > 1
Step-by-step explanation:
HOPE THIS HELPS!!!
What is the point (5, -3) after a rotation of 90 degrees counterclockwise
Answer:
It would be (3,5)
Step-by-step explanation:
On a coordinate plane it would be changed in which the 2nd number becomes first & the + or - changes. Same for the first number.
please help I need to get this done today
Answer:
18) If ∠1 = 124° , then ∠4 = 56°.
19) if ∠2 = 48°, then ∠3 = 132°.
20) if ∠4 = 55°, then ∠2 = 55°.
21) if ∠6 = 120° , then ∠8= 120°.
22) if ∠7 = 50.5 , then ∠6= 50.5°.
23) if ∠3 = 118.7°, then ∠2= 61.3°
Step-by-step explanation:
Given two parallel lines a and b.
And other line, which is called transversal line cuts these two parallel lines to make 8 angles.
Now,
18) Given, ∠1 = 124°
Now, sum of consecutive interior angles made by transversal line with parallel lines = 180° .
⇒∠1 + ∠4 = 180°
⇒∠a = 180° - 124° = 56°.
19) ∠2 = 48°.
as sum of consecutive interior angles made by transversal line with parallel lines = 180° .
∠2 + ∠3 = 180°.
⇒ ∠3 = 180° - 48° = 132°.
20) ∠4 = 55°
Alternate angles made by transversal line with parallel lines are equal .
⇒∠2 = ∠4 = 55°.
21) ∠6 = 120°
As corresponding angles made by transversal line with parallel lines are equal. ∠6 = ∠3 = 120°.
now, also opposite angles are equal
⇒ ∠3 = ∠8 = 120°.
22) ∠7 = 50.5
As corresponding angles made by transversal line with parallel lines are equal. ∠7 = ∠2 = 50.5°.
now, also opposite angles are equal
⇒ ∠2 = ∠6 = 50.5°.
23) ∠3 = 118.7°
as sum of consecutive interior angles made by transversal line with parallel lines = 180° .
∠3 + ∠2 = 180°.
⇒ ∠2 = 180° - 118.7° = 61.3°
Is x-4 equivalent to x3•x-7
Answer:
No.
Step-by-step explanation: Assuming you mean x^3*x-7, these two equations do not produce the same line.
Answer:
YESStep-by-step explanation:
[tex]x^3\cdot x^{-7}=x^{3+(-7)}=x^{-4}\\\\\text{used}\ a^n\cdot a^m=a^{n+m}\\\\\text{Other way}\\\\a^{-n}=\dfrac{1}{a^n}\\\\x^3\cdot x^{-7}=x^3\cdot\dfrac{1}{x^7}=\dfrac{x^3}{x^7}=\dfrac{x\!\!\!\!\diagup^1\cdot x\!\!\!\!\diagup^1\cdot x\!\!\!\!\diagup^1}{x\!\!\!\!\diagup_1\cdot x\!\!\!\!\diagup_1 \cdot x\!\!\!\!\diagup_1 \cdot x\cdot x\cdot x\cdot x}=\dfrac{1}{x^4}=x^{-4}[/tex]
Which fraction is the reciprocal of 2 5/7 ASAP!!!
7/19
bc 2 5/7 = 19/7. the reciprocal is a fraction reversed. or upside down that is. So, your answer is 7/19
Answer:
7/19
Step-by-step explanation:
2 5/7=19/7
What is a rational number equivalent to ——
3.12
Answer:
[tex]\frac{78}{25}[/tex]
Step-by-step explanation:
A rational number has the form
[tex]\frac{a}{b}[/tex] ← where a and b are integers
3.12 = [tex]\frac{312}{100}[/tex] ← divide numerator/denominator by 4, thus
3.12 = [tex]\frac{78}{25}[/tex] ← in simplest form
Six more than five times a number is the same as nine less than twice the number. Find the number.
Answer:
x = -5
Step-by-step explanation:
let the number be x
"five times a number" : 5x
"Six more than five times a number" : 5x + 6
"twice the number" = 2x
"Six more than five times a number = 2x - 9
"Six more than five times a number" = "Six more than five times a number
5x + 6 = 2x - 9
5x - 2x = -9 -6
3x = -15
x = -15 / 3
x = -5
A rectangular prism with a volume of 555 cubic units is filled with cubes with side lengths of \dfrac13
3
1
start fraction, 1, divided by, 3, end fraction unit.
How many \dfrac13
3
1
start fraction, 1, divided by, 3, end fraction unit cubes does it take to fill the prism?
135 cubes are required to fill the prism
Solution:
Given that a rectangular prism with volume of 5 cubic units is filled with cubes with side lengths of [tex]\frac{1}{3}[/tex] units
Then the number of cubes required to fill the prism will be given by:
[tex]\text { number of cubes }=\frac{\text {volume of rectangular prism}}{\text {volume of cube}}[/tex]
Volume of rectangular prism = 5 cubic units
[tex]\text{ Volume of cube}=(\text { side })^{3}$[/tex]
[tex]\text { Volume of cube }=\left(\frac{1}{3}\right)^{3}=\frac{1}{27}[/tex]
Therefore number of cubes required to fill the prism are:
[tex]\text { number of cubes }=\frac{5}{\frac{1}{27}}=5 \times 27=135[/tex]
Therefore 135 cubes are required to fill the prism
Answer:
135
Step-by-step explanation:
Someone please help!
Answer:
See explanation
Step-by-step explanation:
1. Lines l and k are parallel. These lines are cut be transversal n. Angles 2 and 7 are corresponding angles when parallel lines l and k are cut by transversal n. By Corresponding Angles Ttheorem, angles 2 and 7 are congruent.
2. Lines m and n are parallel. These lines are cut be transversal k. Angles 2 and 10 are alternate interior angles when parallel lines m and n are cut by transversal k. By Alternate Interior Angles Theorem, angles 2 and 10 are congruent.
3. Angles 2 and 7 are congruent (see 1)
Angles 2 and 10 are congruent (see 2)
Hence, angles 7 and 10 are congruent by transitive property.
3x + 4x − 2x = − 76 + 96
Answer:
4
Step-by-step explanation:
first add up the xs that gives you 5x because first 3x+4x gives you 7 then minus that with 2x that gives you five,
now add the numbers -76+96 that gives you 20 now the equation becomes
5x=20
now divide 20 by 5 that gives you 4
3.3(x – 8) - x = 1.2
Answer:
3.3 x - (3.3*8) - x = 1.2
2.3 x - (3.3*8) = 1.2
2.3 x - 26.4 = 1.2
2.3 x - 26.4 + 26.4 = 1.2 + 26.4
2.3 x = 27.6
2.3 x / 2.3 = 27.6 / 2.3
x = 12
Determine the y-intercept of x 12 + y 3 = 2
The y-intercept of [tex]\(12x + y^3 = 2\) is at \((0, \sqrt[3]{2})\).[/tex]
To find the y-intercept of the equation [tex]\(12x + y^3 = 2\)[/tex], we first need to understand what the y-intercept represents. The y-intercept is the point where the graph intersects the y-axis, which means the x-coordinate of this point is 0.
To find the y-intercept, we set [tex]\(x = 0\)[/tex] in the equation and solve for y:
[tex]\[12(0) + y^3 = 2\][/tex]
[tex]\[y^3 = 2\][/tex]
To solve for y, we take the cube root of both sides:
[tex]\[y = \sqrt[3]{2}\][/tex]
So, the y-intercept of the equation is [tex]\((0, \sqrt[3]{2})\).[/tex]