Answers
Answer:
a. The relation is a function because every input has an output.
Step-by-step explanation:
a relation in which for every input there is exactly one output (for every x there is just one y)
quizlet
Answer:
A. The relation is a function because every input has an input
Step-by-step explanation:
A relation is a function as long as there are not multiple outputs for one input. It's okay if there are multiple inputs for one output, like we can see here with points (-6, 1) and (2, 1).
Another way to test if a graphed relation is a function is the vertical line test. Draw vertical lines at multiple spots on the graph and if any of the vertical lines touches 2 points, the graphed relation is not a function.
:)
Related Questions
Solve the system of two linear inequalities graphically.Graph the solution set of the second linear inequality?
Answers
According to the second inequality, y is greater than or equal to -2, which means that the graph will have a solid line, the first step is to pick solid choice.
The boundary line is y=2, we know this by replacing the inequality sign by an equal sign. Two points one this line are (-1,2) and (2,2). We know it because it is an horizontal line that represents a constant function, it means that all the values of y will be 2 (boundary line).
As the equal sign is greater than or equal to, the region that must be shaded is the one above the boundary line.
Question 11 > Alvin can go upstream at a rate of 25 miles per hour and downstream at a rate of 35 miles per hour. One day while Alvin was on the river, he received a call telling him he needs to turn around and come home. So he turned around and went back to his starting point. If his entire trip took 12 hours, how far did he travel on the river? Alvin traveled miles. (Roundtrip) Question Help: Message instructor Submit Question
Answers
Given Data:
The upstream speed is, 25 miles/hr.
The downstream speed is, 35 miles/hr.
The total time is, 12 hr.
Let d be the distance traveled. He can travel 25 miles/ hr in upstream, so the time taken will be,
[tex]t=\frac{d}{25}[/tex]He can travel 35 miles/ hr in upstream, so the time taken will be,
[tex]t^{\prime}=\frac{d}{35}[/tex]Total time is, 12 hr. So we have,
[tex]\begin{gathered} 12=\frac{d}{25}+\frac{d}{35} \\ 12=\frac{d}{5\times5}+\frac{d}{7\times5} \\ 12=\frac{1}{5}(\frac{d}{7}+\frac{d}{5}) \\ 12\times5=\frac{d}{7}+\frac{d}{5} \\ 60\times35=5d+7d \\ 2100=12d \\ d=\frac{2100}{12}=175 \end{gathered}[/tex]Therefore the total distance is, 350 mile
On a recent survey, students were asked if they ice skate, snowboard, or ski. The Venn diagram below shows the results of the survey
Answers
The number of students who took the survey was 47 (option B).
How to identify the number of students who took the survey?To identify the number of students who took the survey, we must look at the number of students in each of the Venn diagram spaces. In this case, the number of students who practice each sport are:
Ice Skate: 7 students.Snowboarding: 10 students.Ski: 13 students.Ice Skate and Snowboard: 4 students.Ski and Snowboard: 8 students.Ice Skate and Ski: 2 students.Ice Skate, Snowboard and Ski: 3 students.To know the number of students who took the survey, we must add the number of students in each space as shown below:
7 + 10 + 13 + 4 + 8 + 2 + 3 = 47According to the above, the correct answer is option B, since 47 students took the survey.
Note: This question is incomplete because there is some information missing. Here is the complete information:
Question:
How many students took the survey?
Options
A.32
b.47
c.53
D.56
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Tori is writing an essay for her English class. She already has 235 words, andon average writes 175 words every hour. The essay needs to be at least 1,600words. How many more hours should she plan to work on it? Write and solvean inequality for the situation.
Answers
Let be "h" the number of hours Tori should plan to work on it.
You know that she writes an average of 175 per hour. This can be represented with this expresion:
[tex]175h[/tex]You also know that there must be at least 1,600 words in the essay for her English class. Since she has 235 words written, you can set up the following inequality:
[tex]235+175h\ge1,600[/tex]The symbol used in the inequality means "Greater than or equal to".
In order to solve it, you can follow these steps:
1. Subtract 235 from both sides of the inequality:
[tex]\begin{gathered} 235+175h-(235)\ge1,600-(235) \\ 175h\ge1,365 \end{gathered}[/tex]2. Divide both sides of the inequality by 175:
[tex]\begin{gathered} \frac{175h}{175}\ge\frac{1,365}{175} \\ \\ h\ge7.8 \end{gathered}[/tex]The answer is:
[tex]7.8\text{ }hours[/tex]The average adult heart pumps about 84. mL/s of blood at 72 beats per minute. Suppose you need to calculate how long it would take the average heart tocirculate 6300. mL of blood.Set the math up. But don't do any of it. Just leave your answer as a math expressionAlso, be sure your answer includes all the correct unit symbols.
Answers
There are two ways to interpret the problem.
1) One is that a heart circulates 84ml of blood per second, although this makes the information of the beats per minute unnecessary.
In that case, an average heart would circulate 6300 ml of blood as shown in the next expression:
[tex]\begin{gathered} 6300=84t \\ \Rightarrow t=\frac{6300}{84} \end{gathered}[/tex]Where t is the time expressed in seconds
2) A second approach, and the one that makes better sense, is that each beat of the heart pumps 84ml per beat. Then, the expression that gives us the time needed to reach 6300ml of blood is:
[tex]\begin{gathered} \frac{84ml}{\text{beat}},\frac{72beats}{\min } \\ \Rightarrow84\cdot\frac{72ml}{\min}=\frac{6048ml}{\min } \end{gathered}[/tex]In that case, the equation that expresses the time needed by the heart to bump 6300ml of blood is:
[tex]\begin{gathered} 6300=6048\cdot t \\ \Rightarrow t=\frac{6300}{6048} \end{gathered}[/tex]With t being the time given in minutes
The distance to your grandparent's house is 259 miles, and the distance to Atlanta is 555 miles. If it took 7 hours to drive to your grandparent's house, how long would you estimate the drive to Atlanta to take?
Answers
Answer:
15 Hours
Step-by-step explanation:
259miles = 7 hours
555miles = x
Cross Multiply
259x = 555×7
259x = 3885
Divide Both sides by 259
x = 3885 ÷ 259
x = 15 hours
It would take the driver 15 hours to get to Atlanta
solve for x. z=5x-9y
Answers
ANSWER:
[tex]x=\frac{z+9y}{5}[/tex]STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]z=5x-9y[/tex]We solve for x as follows:
[tex]\begin{gathered} z+9y=5x \\ 5x=z+9y \\ x=\frac{z+9y}{5} \end{gathered}[/tex]Hello,May I please request for help on the word problem number 37, please?
Answers
As the last stand-up comic of the evening is granted. The combination of schedules is made with the other 5 performers.
To find how many ways you can order 5 performers you multiply 5x4x3x2x1 (or factorial 5: 5!)
[tex]5!=5\times4\times3\times2\times1=120[/tex]Then, there are 120 different ways to schedule the appearances4. (A.20) Natasha and her friends go out for ice cream. They decide to create their own ice cream, which costs $1.60 plus 8 cents per topping. If x represents the number of toppings on the ice cream, then which'equation describes y, the total cost for the ice cream?A. y = 0.08 + 1.60)x B. y = .08 + 1.60x C. y = 1.60 +.08x D. y = 8x + 1.60
Answers
Answer:
C. y = 1.60 +.08x
Explanation:
The cost of the ice cream will be equal to the fixed cost of $1.60 plus the cost that depends on the number of toppings. So, if Natasha chooses x number of topping, the total cost of the toppings will be 8 cents times x or $0.08x
So, the total cost for the ice cream is represented by the equation:
y = 1.60 +.08x
Consider the two polynomials p(x), q(x) in Z[x] by p(x) = 1+2x+3x2, q(x) = 4+5x+7x3. Then p(x) + q(x) is
Answers
The solution for polynomials p(x) + q(x) is 7x³ + 3x² + 7x + 5
Given,
The polynomials
p(x) = 1 + 2x + 3x²
q(x) = 4 + 5x + 7x³
We have to find the solution for p(x) + q(x)
Then,
p(x) + q(x) = (1 + 2x + 3x²) + ( 4 + 5x + 7x³)
p(x) + q(x) = 7x³ + 3x² + 2x + 5x + 1 + 5
p(x) + q(x) = 7x³ + 3x² + 7x + 5
That is,
The solution for polynomials p(x) + q(x) is 7x³ + 3x² + 7x + 5
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Solve.Draw a rectangular fraction model to explain yourthinking.Then, write a number sentence.1/3of3/7=
Answers
We are asked to find 1/3 of 3/7 using a rectangular fraction model.
Let us draw a rectangular fraction model.
1/3 means make 3 rows
3/7 means make 7 columns
[tex]\frac{1}{3}\times\frac{3}{7}=\frac{3}{21}[/tex]Three 3 filled boxes represent the numerator and the total 21 boxes represent the denominator.
Therefore, the result is 3/21
need help with math
Answers
Simplify (v2 + 10v + 11)(v2 + 3v – 4) using the distributive property of multiplication ove addition(DPMA)
Answers
Given:
[tex](v^2+10v+11)(v^2+3v-4)[/tex]To find- the simplification.
Explanation-
We know that the distribution property of multiplication over addition says
[tex]a(b+c)=ab+ac[/tex]Use this property to simplify, and we get
[tex]\begin{gathered} =(v^2+10v+11)(v^2+3v-4) \\ =v^2(v^2+3v-4)+10v(v^2+3v-4)+11(v^2+3v-4) \end{gathered}[/tex]Multiply by opening the bracket, and we get
[tex]=(v^4+3v^3-4v^2)+(10v^3+30v^2-40v)+(11v^2+33v-44)[/tex]Now, open the bracket and combine the like terms.
[tex]\begin{gathered} =v^4+3v^3-4v^2+10v^3+30v^2-40v+11v^2+33v-44 \\ =v^4+(3v^3+10v^3)+(11v^2-4v^2+30v^2)-40v+33v-44 \end{gathered}[/tex]On further solving, we get
[tex]=v^4+13v^3+37v^2-7v-44[/tex]Thus, from the distributive property of multiplication over addition, we get v⁴+13v³+37v²-7v-44.
The answer is v⁴ + 13v³ + 37v² - 7v - 44.
Aaquib can buy 25 liters of regular gasoline for $58.98 or 25 liters of permimum gasoline for 69.73. How much greater is the cost for 1 liter of premimum gasolinz? Round your quotient to nearest hundredth. show your work :)
Answers
The cost for 1 liter of premium gasoline is $0.43 greater than the regular gasoline.
What is Cost?This is referred to as the total amount of money and resources which are used by companies in other to produce a good or service.
In this scenario, we were given 25 liters of regular gasoline for $58.98 or 25 liters of premium gasoline for $69.73.
Cost per litre of premium gasoline is = $69.73 / 25 = $2.79.
Cost per litre of regular gasoline is = $58.98/ 25 = $2.36.
The difference is however $2.79 - $2.36 = $0.43.
Therefore the cost for 1 liter of premimum gasoline is $0.43 greater than the regular gasoline.
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Jordan wants to use the Starz princess hall, the Dynamic DJ's as his music And Roscoe's for his equipment. If Jordan has a total of $800 and wants the music to play for 4 hours, how many people can Jordan party?
Answers
The number of people that can attend Jordan's party would be; 50 people.
What is equation?The equation that represents the total amount that would be spent at the party would be a linear equation. A linear equation increases at a constant rate.
The form of the linear equation will be;
The Total amount = rental fee + (charge per hour of the Dynamic DJ x number of hours he plays) + (cost per person of Roscoe's rentals x number of people)
Now substitute;
$800 = $400 + ($50 x 4) + ($4 x p)
$800 = $400 + $200 + 4p
$800 = $600 + 4p
$800 - $600 = 4p
$200 = 4p
p = $200 / $4
p = 50 people
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in a class the ratio of the boy to the girls is 7:8 what part of the whole class are girls
Answers
Is x = -2 the linear equation that matches this table of ordered pairs?Explain why or why not.Xy-2 7-2 1-2 -5(x, y)(-2,7)(-2, 1)(-2,-5)
Answers
Answer:
All the points given (-2,7) (-2,1) (-2,-5) have the x-coordinate of -2, then those points lie in the x=-2, so it matches the table.
The population of a town is decreasing at a rate of 1% per year. In 2000there were 1300 people. Create a function to find the populationin 2008.
Answers
Given that;
The population of a town is decreasing at a rate of 1% per year.
[tex]\text{Rate r = 1\% = 0.01}[/tex]In 2000 there were 1300 people.
[tex]P_o=1300[/tex]To find the population in 2008;
[tex]P_8[/tex]The time taken is;
[tex]\begin{gathered} t=2008-2000 \\ t=8\text{ years} \end{gathered}[/tex]We can calculate the population of the town in 2008 by applying the formula;
[tex]P_8=P_o(1-r)^t[/tex]Substituting, the given values;
[tex]\begin{gathered} P_t=1300(1-0.01)^t \\ P_t=1300(0.99)^t \end{gathered}[/tex]Above is a functon for calculating the population of the town at time t years after 2000.
The population of the town in the year 2008 is;
[tex]\begin{gathered} P_8=1300(0.99)^8 \\ P_8=1,199.568 \\ P_8\approx1,200 \end{gathered}[/tex]Therefore, the population of the town in 2008 is approximately 1,200 people.
We can also write the equation as;
[tex]y=1300(0.99)^8[/tex]Where y is the population of the town in year 2008.
Why might you use a different power of 10 instead of leaving bothnumbers in scientific notation?
Answers
Why might you use a different power of 10 instead of leaving both
numbers in scientific notation?
Because scintific notation is a simplification for large or small numbers, so a big number with a lot of zeros can be writen by a power of 10 multiplied by a number. But we cannot make substractions using this, because the powers ten represents very different values, for instance
[tex]\begin{gathered} 1\times10^1=10 \\ 1\times10^2=100 \end{gathered}[/tex][tex]1\times10^2-1\times10^1=100-10=90,[/tex]But if they have the same power, we can use the distibutive law to make the substraction
[tex]1\times10^2-1\times10^1=10\times10^1-1\times10^1=(10-1)\times10^1=9\times10^1^{}[/tex]which is the same thing. No matter the power of 10, if the power is the same you can use the same argument I've made before.
if(f) (x)= x/2 - 2 and (g) (x) = 2x^2 + x - 3 find (f+g) (x)|| how do i add functions when the number is a fraction? ||
Answers
Solution
Given
[tex]\begin{gathered} f(x)=\frac{x}{2}-2 \\ \\ g(x)=2x^2+x-3 \\ \\ (f+g)(x)=f(x)+g(x)=\frac{x}{2}-2+2x^2+x-3=2x^2+\frac{3x}{2}-5 \end{gathered}[/tex]The country of Scotstats requires the people in their country to have license tags on their car such that the first 3 characters are English letters but no letter may repeat. The last 3 characters must each be a number 0-9 and again no numbers can be repeated. How many license tags are possible?
Answers
Answer
11,232,000 possible license tags.
Explanation
The licenses have space for 6 characters.
We need to note that there are 26 alphabets and 10 numbers to pick from.
So, for the first character, any of the 26 alphabets can take this spot.
For the second character, 25 alphabets are now available for that space. (Since repetition is not allowed)
For the third character, 24 alphabets are available for that.
For the fourth character, any of the 10 numbers can take up that spot.
For the fifth character, only 9 numbers can take this spot now. (No repetition rule too)
For the sixth character, 8 numbers can take that spot.
So, mathematically, the number of license tags possible will be
26 × 25 × 24 × 10 × 9 × 8 = 11,232,000 possible license tags
Hope this Helps!!!
umm i need help on my math reducing fractions Im new to them and i dont understand it at all, Btw im in 5th grade not middle school it wont let me change it
Answers
since the smallest number is 2, and 2 can go into itself and 2 also can go into 10, that is the largest common number
[tex]\frac{2}{10}\div\text{ }\frac{2}{2}[/tex][tex]\begin{gathered} 2\text{ divided by 2 = 1} \\ 10\text{ divided by 2 =5} \end{gathered}[/tex]We can not make the number go any smaller since any number divied by one will equal itself
so that means
[tex]\frac{2}{10}\text{ reduced is }\frac{1}{5}[/tex]Write the following linear equation in function notation. Y = 2x + 5a.) f(y) = 2x+ 5b.) f = 2x + 5c.)f(x) = 2x + 5d.)It is already written in function notation
Answers
Answer
Option C is correct.
The function notation
Explanation
sarah spent a total of 10 on oranges and apples at the supet market. if she spent 3 dollars less for oranges than she did on apples how much did sarah spend on oranges
Answers
Let's write 2 equations from the two statements given.
Sarah spent 10 dollars on both oranges and apples
Let the price of oranges be "x" and price of apples be "y", thus we can write:
[tex]x+y=10[/tex]Oranges cost 3 less than apples, thus we can say:
[tex]y-3=x[/tex]We can substitute this into the first equation and solve for y:
[tex]\begin{gathered} x+y=10 \\ y-3+y=10 \\ 2y=10+3 \\ 2y=13 \\ y=\frac{13}{2} \\ y=6.5 \end{gathered}[/tex]Thus, let's solve for x now,
[tex]\begin{gathered} x=y-3 \\ x=6.5-3 \\ x=3.5 \end{gathered}[/tex]We want the price of oranges (x), thus,
Price of Oranges = $3.50
For a standard normal distribution,Find P(-1.21 < Z< 2.26)
Answers
Answer:
The range of z-score is given below as
[tex]P(-1.21Using a graphing calculator, we will have the image be[tex]\begin{gathered} P(z<-1.21)=0.11314 \\ P(z<2.26)=0.9881 \\ P(-1.21Hence,The final answer is
[tex]P(-1.21\lt z\lt2.26)=0.8750[/tex]Find an equation for the line that passes through the points (2,2) and (-6,4)
Answers
Answer:
y=-1x/4+5/2
Step-by-step explanation:
use the slope formula
the difference of four times a number and seven is 13
Answers
ExplanatIon
Step 1
let x represents the number
hence,
four times a number =4*x=4x
the difference of four times a number and seven=4x-7
is can be written as equal or "="",so
the difference of four times a number and seven is 13
[tex]4x-7=13[/tex]Step 2
solve for x
[tex]\begin{gathered} 4x-7=13 \\ \text{add 7 in both sides} \\ 4x-7+7=13+7 \\ 4x=20 \\ \text{divide both sides by 4} \\ \frac{4x}{4}=\frac{20}{4} \\ x=5 \end{gathered}[/tex]so, the number is 5.
I hope this helps you
Solve the problem.
3) During the last four months of a recent year, Annie's Natural Food Store reported the following sale: 3)
September
$3087
October
$2891
$2377
November
December
$4224
How much more were the sales in December than the sales in November?
A) $1847
B) $6501
C) $6601
D) $1747
What’s the answer?
Answers
Answer:
The answer will be A) 1847
Find all solutions to the equationin the interval [O, 27). Enter thesolutions in increasing order.cos 2x = cos X[?]Tx = 0,2Remember: cos 20 = cos20 – sin20
Answers
SOLUTION
From
[tex]\begin{gathered} \cos 2x=\cos x \\ \cos ^2x-\sin ^2x=\cos x \\ \cos ^2x-(1-\cos ^2x)=\cos x \\ 2\cos ^2x-1=\cos x \\ 2\cos ^2x-\cos x-1=0 \\ \text{From the quadratic formula} \\ \cos x=\frac{1\pm\sqrt[]{1-(-8)}}{4} \\ \\ \cos x=\frac{1\pm3}{4} \\ \cos x=\text{ 1 or -}\frac{1}{2} \\ \text{Taking the cos}^{-1}of\text{ 1 and -}\frac{1}{2} \\ We\text{ have }\theta\text{ = 0, }\frac{2\pi}{3},\frac{4\pi}{3},\frac{8\pi}{3}\ldots\ldots\ldots2\pi \end{gathered}[/tex]So your answer is
[tex]0,\text{ }\frac{2\pi}{3},\text{ }\frac{4\pi}{3}[/tex]Jan draws a card from the set below, replaces it and then draws another card. Which of the following tree diagrams correctly shows the sample space?
Answers
Given the word problem, we can deduce the following information:
1. Jan draws a card from the set below, replaces it and then draws another card.
Based on the given information, there is a replacement happening. It means that Jan put a card back in the set before selecting another card. So the tree diagram that shows all the possible outcomes is Diagram A.
Therefore, the answer is A.