Mimi and Rita both plan to run for a spot on the school
board in their city. They must each collect a certain
number of signatures to get their name on the ballot. So
far, Mimi has 30 signatures, but Rita just started and
doesn't have any yet. Mimi is collecting signatures at an
average rate of 8 per hour, while Rita can get 14
signatures every hour. Assuming that their rate of
collection stays the same, eventually the two will have
collected the same number of signatures. How many
signatures will they both have?
Create two tables showing hours and signatures. Write,
graph, and solve a system of equations for this situation.
Explain what your solution means for the situation.
Answers
Answer:
The equal number of signatures Mimi and Rita eventually collects are 70 signatures
Step-by-step explanation:
1) The initial number of signatures Mimi has = 30 Signatures
The average rate at which Mimi can collect signatures = 8 signatures per hour
The average rate at which Rita can collect signatures = 14 signatures per hour
The table of values showing the number of signatures Mimi and Rita can have at a given hour is presented as follows;
For Mimi, we have;
Hour [tex]{}[/tex] Number of Signatures
0 [tex]{}[/tex] 30
1 [tex]{}[/tex] 38
2 [tex]{}[/tex] 46
3 [tex]{}[/tex] 54
4 [tex]{}[/tex] 62
5 [tex]{}[/tex] 70
For Rita, we have;
Hour [tex]{}[/tex] Number of Signatures
0 [tex]{}[/tex] 0
1 [tex]{}[/tex] 14
2 [tex]{}[/tex] 28
3 [tex]{}[/tex] 42
4 [tex]{}[/tex] 56
5 [tex]{}[/tex] 70
2) The equation representing the number of signatures Mimi has at a given time, t, is given as follows;
The number of signatures Mimi has = 30 + 8 × t
The equation representing the number of signatures Rita has at a given time, t, is given as follows;
The number of signatures Rita has = 14 × t
3) Please find attached the required graph of the number of signatures Mimi and Rita has
4) The solution if the system of equations is given as follows;
30 + 8 × t = 14 × t
From which we have;
30 = 14 × t - 8 × t = 6 × t
t = 30/6 = 5 Hours
By substituting t = 5 hours in the above equations, the equal number of signature of signatures Mimi and Rita can have is therefore;
30 + 8 × 5 = 70 signatures = (14 × 5) signatures
The equal number of signatures Mimi and Rita eventually collects are 70 signatures
5) The meaning of the solution is that is Mimi and Rita continue collecting signatures at their respective constant rate of 8 and 14 signatures per hour, given that Mimi already has 30 signatures, they will have the same number of 70 signatures after 5 hours
Related Questions
Michael and Ming-Wei are selling fruit for a school fundraiser. Customers can buy small boxes of
oranges and large boxes of oranges. Michael sold 3 small boxes and 14 large boxes for a total of $203.
Ming-Wei sold 11 small boxes and 11 large boxes for a total of $220. Find the cost of each size box.
Answers
3s + 14l = 203
11s + 11l =220
You can eliminate a variable, I'm going to eliminate s but from the 2 equation since it's easier to do the math. I'm going to multiply the equation by -3. I'm going to multiply the first one by a positive 11.
-33s-33L=-660
33s + 154L= 2233
121L=1573
1573÷121 =13
So one large box equals 13, now find the price of a small by plugging it into an equation.
3s + 14 (13)=203
3s+ 182 =203
203-182=21÷3=7
Now a small equals 7, check if both are correct by putting it into another equation.
11 (7)+11 (13)=220
77+143 =220
220=220
A small equals $7, while a large equals $13.
0.04 divided by 3.3284
Answers
Answer:
The answer is 0.01201778632
Step-by-step explanation:
Which graph represents the solution to the inequality?1/3(9x+27)>x+33
Answers
Answer:
its c
Step-by-step explanation:
Graph D represents the inequality of the given Equation.
What is inequality?An inequality shows whether one value is less than, greater than, or simply not equal to another value by comparing them.
When two quantities are equal, we use the symbol "=," and when they are not equal, we use the symbol "≠". The first value can either be greater than (>) or less than (<).
Given equation 1/3(9x+27) > x+33
simplify the Equation
multiply both sides by 3 we get,
[1/3(9x+27)] 3 > (x+33)3
9x + 27 > 3x + 99
9x > 3x + 99 -27
9x - 3x > 72
6x > 72
x > 12
the Equation of inequality is x > 12
the line will be more than 12 and in which 12 is not included,
option D follows the required conditions, the empty circle in 12 shows 12 is not included and the line moves towards the positive side.
Hence option D is the correct representation of the given inequality.
Learn more about inequality;
https://brainly.com/question/28823603
#SPJ2
M (18, 24) is the midpoint of segment JL with J (- 4, - 2). What are the coordinates for L?
Answers
Answer:
mid point (x,y) = M (18, 24)
let J (- 4, - 2) be ( x1, y1)
L(a,b) be (x2,y2)
using midpoint formula
(x,y) = [(x1+x2)/2, (y1 + y2)/2]
or, (18, 24) = [(-4+a)/2, (-2+b)/2]
comparing corresponding element we get
18 = (-4+a)/2 24 =(-2+b)/2
or 36 = -4+ a or 48 = -2 +b
or a = 40 or b= 50
L(40,50)
B. What is (64) ? What is (19) ?
Answers
PLEASE GIVE BRAINLIST
1. 6,4x10^1
2. 1,9x10^1
^ = exponent
HOPE THIS HELPED
102 + 7y = 16
15x + 8y 29
Is this consistent or inconsistent
Answers
Answer:
Step-by-step explanation:
18y
F(x)=(x-2)^2
Evaluate for f(5)
Need Answers ASAP
Answers
Answer:
f(5) = 9
Step-by-step explanation:
To evaluate f(5) substitute x = 5 into f(x), that is
f(5) = (5 - 2)² = 3² = 9
Answer:
f(5) = 9Step-by-step explanation:
f(x) = ( x - 2)²
To find f(5) substitute the value of x that's 5 into f(x). That's for every x in f (x) replace it with 5
That's
f(5) = ( 5 - 2)²
= 3²
We have the final answer as
f(5) = 9Hope this helps you
So, what is the pattern? For positive integers a and b: (x^a)^b
Answers
Answer: (x^b)^a
Step-by-step explanation:
the inverse of a monomial with an exponent raised to another power will give the same product if you flip the exponents.
Here we have a general rule for exponents.
We will find that:
[tex](x^a)^b = x^{a*b}[/tex]
To get this, we can first check it with some values for the exponents.
a = 2
b = 3
[tex](x^2)^3 = (x^2)*(x^2)*(x^2) = (x*x)*(x*x)*(x*x) = x^6 = x^{2*3}[/tex]
Similarly, we can prove it for two general values of a and b:
[tex](x^a)^b = (x^a)*(x^a)*...*(x^a)\\b\ times[/tex]
Now each one of these parentheses has a multiplying by itself a times.
So when we write all the x's, we will see that there are a total of b*a x's
Thus we will have:
[tex](x^a)^b = (x^a)*(x^a)*...*(x^a) = x^{a*b}[/tex]
If you want to learn more, you can read:
https://brainly.com/question/5497425
Just need answer, that fills in the blanks, i dont need work shown ty
will give brainly!!
Answers
Evaluate 6 + 4/a +
b/3
when a = 4 and b = 3.
Answers
The answer to your problem would be 8.
In 2008, Scott Dixon won the Indianapolis 500, completing 500 laps in approximately 3.5 hours. Approximately how long did it take for him to complete 1 lap?
Answers
Answer:
0.007 hour or 25.2 seconds
Step-by-step explanation:
From the question, we are told that for Scott Dixon,he completed
500 laps in approximately = 3.5 hours. 1 lap approximately =
Cross Multiply
= 1 lap × 3.5 hours = 500 laps × a hours
a hours = 1 lap × 3.5 hours/500 laps
a hours = 0.007hours
We can convert 0.007 hours to seconds
60 seconds = 1 minute
60 minutes = 1 hour
1 hour = 60 × 60
= 3600 seconds
1 hour = 3600 seconds
0.007 hour =
0.007 hour × 3600 seconds
= 25.2 seconds
Therefore, it took Dixon approximately 0.007 hour or 25.2 seconds did it take for him to complete 1 lap
I’m only solving for x, it’s triangle mid-segment.
Answers
Step-by-step explanation:
Hey there!!
I hope you remember that mid-segment theorem, in which it is stated that, line which passes through the midpoint of one side triangle bisects base, are parallel to another side of triangle and that line is half of parallel side. (i.e CB = 1/2 of RT) .
Now, Let's simply solve it.
[tex]cb = \frac{1}{2} \times rt[/tex]
Put their values as given in question.
[tex]x + 19 = \frac{1}{2} \times (x + 29)[/tex]
Simplify them.
2x + 38 = x +29
2x - x = 29 - 38
x = -9.
Hope it helps...
im learning about absolute value with positive and negative, any tips?
Answers
Given the functions, f(x) = 3x - 6 and g(x) = x2 + 5x + 7, perform the indicated operation. When applicable, state the domain restriction.
Answers
Answer:
D
Step-by-step explanation:
it is D i did this quiz before.
1) Freddy was unhappy that his bank account was in _____, and he knew he had to get a job in order to pay his rent. *
Answers
Answer:
the answer is debt
Step-by-step explanation:
compare 0.8 and 7/10
Answers
Answer:
O.8 is greater than 7/10
Step-by-step explanation:
0.8 is in the tenths Place So you know that equals 80 ones Out of one hundred. So you have 80/100 if you divide 80 and 100 by ten it reduces to 8/10. You know that 8/10 is greater than 7/10. Hope this helped .
When an exponent is a negative number, we can think of it as taking the...?
Answers
Answer:
We can think of it as the zeros after the decimal point.
Step-by-step explanation:
Negative exponents always move the number to the right putting the decimal in front of it.
Bai bought balloons for each of her 15 friends.
If she spent $3.25 per balloon, how much did she spend?
Answers
Answer:
48.75
Step-by-step explanation:
All you haft to do really is 3.25 x 15 and you get 48.75, Because she spent 3.25 on each balloon and she has 15 friends. So 15 friends multiplied by 3.25 gets you 48.75 she spent total.
Answer:
$48.75
Step-by-step explanation:
3.25 x 15 = 48.75
I hope this helps :)
9(18) using disributive property.
Answers
Answer:
162
Step-by-step explanation:
9 * 18 = 162
Answer:
162
Step-by-step explanation:
During the winter, the amount of water that flows down a river remains at a low constant. In the spring, when the snow melts, the amount of water increases drastically, until it decreases to a steady rate in the summer. The flow then slowly decreases through the fall into the winter. Consider the graphs shown. Which graph best represents the given situation?
Answers
Answer:
Its Graph B
Step-by-step explanation:
I got the quiz correct
Half the sum of 42 and 16 What is The Expression
Answers
Answer:
i dont understand the question
Step-by-step explanation:
Answer:
(42+16)/2 = 29
Step-by-step explanation:
an expression contains operations and values
half the sum of 42 and 16
(42+16)/2 = x
(42+16)/2 = 29
Jasmine bought two dozen roses for $31 .20.How much did she pay per rose?
Answers
Answer:
Step-by-step explanation:
$31.20/24
24 roses = 2 dozen roses
Each rose cost $1.30
HELP ME PLESE ,3 I NEED THIS
Answers
Answer:
270°
Step-by-step explanation:
[tex]m\widehat{BC} = 360\degree - (146\degree + 90\degree) \\
m\widehat{BC} = 360\degree -236\degree \\
m\widehat{BC} = 124\degree \\\\
m\widehat{ABC} =m\widehat {AB} + m\widehat {BC} \\
m\widehat{ABC} =146\degree + 124\degree \\
\huge \red {\boxed {m\widehat{ABC} =270\degree}} \\
[/tex]
(sqrt(6))/(8+\sqrt(10))
Answers
Answer:
[tex]\frac{4\sqrt{6}-\sqrt{15}}{27}[/tex]
Step-by-step explanation:
[tex]\frac{\sqrt{6} }{8+\sqrt{10} } \\\\\mathrm{Multiply\:by\:the\:conjugate}\:\frac{8-\sqrt{10}}{8-\sqrt{10}}\\=\frac{\sqrt{6}\left(8-\sqrt{10}\right)}{\left(8+\sqrt{10}\right)\left(8-\sqrt{10}\right)}\\\\\sqrt{6}\left(8-\sqrt{10}\right)=8\sqrt{6}-2\sqrt{15}\\\left(8+\sqrt{10}\right)\left(8-\sqrt{10}\right)=54\\\\=\frac{8\sqrt{6}-2\sqrt{15}}{54}\\\\\mathrm{Factor}\:8\sqrt{6}-2\sqrt{15}:\quad 2\left(4\sqrt{6}-\sqrt{15}\right)\\\\=\frac{2\left(4\sqrt{6}-\sqrt{15}\right)}{54}\\[/tex]
[tex]\mathrm{Cancel\:the\:common\:factor:}\:2\\\\=\frac{4\sqrt{6}-\sqrt{15}}{27}[/tex]
Triangle ABC contains the point A(5,2). Find the coordinates of A' after a reflection over the x-axis
Answers
Answer:
Step-by-step explanation:
Should be 5,-2 OR NOT
which angles are complementary?
Answers
Answer:
<LKM and <MKN
<PKO and <LKM
Step-by-step explanation:
<LKM and <MKN = 90°
<PKO and <LKM = 90°
A bag contains 7 red marbles 4 blue marbles and 5 green marbles. If three marbles are drawn out the bag what is the probability to the nearest 1000th that all three marbles drawn will be green
Answers
Answer:
0.063
Step-by-step explanation:
A. 5x = 3x B. 5 = 3 How can we get equation b from equation a? A. Add/subtract the same quantity to/from both sides B. Add/subtract a quantity to/from only one side C. Multiply/divide both sides by the same non-zero constant D. Multiply/divide both sides by the same variable expression
Answers
Answer: D- multiply divide both sides by the same variable expression. B- no
Step-by-step explanation:
Multiply/divide both sides by the same variable expression. The correct option is D.
What is an expression?
Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
The given expression will be solved as below:-
5x = 3x
Multiply both sides of the expression by (1/x ).
( 1/x ) 5x = ( 1/x )3x
5 = 3
Divide both sides by x.
5x = 3x
5x / x = 3x / x
5 = 3
Therefore, multiply/divide both sides by the same variable expression. The correct option is D.
To know more about expression follow
https://brainly.com/question/723406
#SPJ2
Find the distance between (-5, 2) and (-7, 6).
Answers
2/3 of the difference of a number t and 8
Answers
Answer:
Step-by-step explanation:
Begin at the end. By this I mean to start at the end of that expression and work your way backwards to the beginning. "The difference of t and 8" looks like this: t - 8. "2/3 of" means we are multiplying (the word "of" means to multiply): 2/3(t - 8) is your algebraic translation of that expression.
The required mathematical expression of a statement is 2 / 3 (t - 8 ).
Given that,
To transform the statement into the mathematical form,
2/3 of the difference between a number t and 8
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here,
given statement,
2/3 of the difference between a number t and 8
implies,
The difference between t and 8 is,
= t - 8
Now the difference is 2/3, now the statement become,
= 2 / 3 (t - 8 )
above equation is the required mathematical expression.
Thus, the required mathematical expression of a statement is 2 / 3 (t - 8 ).
Learn more about arithmetic here:
brainly.com/question/14753192
#SPJ2