Answer: 12
Step-by-step explanation:
1 2
5 ⟌ 6 0
- 5
1 0
- 1 0
0
The population of a town has been decreasing since 1991. The population of the town was 26,700 people in the year 1995. In the year 2003, the population of the town had decreased to 20,300 people.
i. Find the linear function P=m- t+b that models the town's population P as a function of the number of years, t, since 1991
ii. Find a reasonable domain for the function P
Domain:
iii. Find a reasonable range for the function P
Range:
iv. Interpret the slope of the function P
The population is Select an answer at a rate of
v. In what year will the population of the town be 14,700?
Year:
Answer:
i. P = -800t + 29900
ii. as an inequality: 0≤t≤37.375; interval notation: [0,37.375]
iii. as an inequality: 0≥P≥29900; interval notation: [0,29900]
iv. the population decreases at a rate of 1600 people every 3 years
v. 2010
Step-by-step explanation:
i. a) use the points *(4,26700) and **(12,20300) to find the slope (m)
*: the year 1995(4 years after 1991) and the population that year
**: the year 2003(12 years after 1991) and the population that year
m = (20300-26700)/(12-4) = -6400/8 = -800
b) use one of the points and m in (a) to find b
26700 = -800(4) + b
26700 = -3200 + b
29900 = b
ii. starting value for domain will be 0 since 1991 is year 0. Find the ending domain value by using P=0 and solving the equation for t:
0 = -800t + 29900
800t = 29900
t = 37.375
iii. population starts at a high of 29900 people and can't go lower than 0 people.
iv. the slope is given in (population change) / (number of years)
v. make P=14700 and solve the equation for t
14700 = -800t + 29900
800t = 15200
t = 19 (19 years after 1991)
Given h(x)=-x+1, find h(2)
Please Help me!!!!
just replace x with 2
h(x) = - x+ 1
find h(2):
h(2) = -2 + 1
h(2) = -1
n x 4/5 = 3/4 what is n
A. n = 1/2
B. n = 15/16
C. n = 1 2/3
Brody and Qasim are both driving along the same highway in two different cars to a stadium in a distant city. At noon, Brody is 272 miles away from the stadium and Qasim is 320 miles away from the stadium. Brody is driving along the highway at a speed of 43 miles per hour and Qasim is driving at speed of 59 miles per hour. Let BB represent Brody's distance, in miles, away from the stadium tt hours after noon. Let QQ represent Qasim's distance, in miles, away from the stadium tt hours after noon. Write an equation for each situation, in terms of t,t, and determine the number hours after noon, t,t, when Brody and Qasim are the same distance from the stadium.
B= -43t +272 and Q=-59t+320 equations for each situation, in terms of t, and at 3 hours Brody and Qasim are the same distance from the stadium.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
At noon, Brody is 272 miles away from the stadium
B represent Brody's distance, in miles, away from the stadium tt hours after noon.
Brody is driving along the highway at a speed of 43 miles per hour
Qasim is 320 miles away from the stadium
Qasim is driving at speed of 59 miles per hour.
Q represent Qasim's distance, in miles, away from the stadium t hours after noon
B= -43t +272
Q=-59t+320
-43t+272=-59t+320
-43t+59t=320-272
16t=48
t=3
Hence, B= -43t +272 and Q=-59t+320 equations for each situation, in terms of t, and at 3 hours Brody and Qasim are the same distance from the stadium.
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How can the logarithmic expression be written?
Select True or False for each statement.
Answer:
False, True, False-------------------------------------------
Simplify the left side and compare if the answer matches the right side.
[tex]log_3\ v-4log_3\ w=log_3\ v-log_3\ w^4 \implies False[/tex][tex]log_4\ (n\sqrt{m})= log_4\ (nm^{1/2})=log_4\ n+log_4\ m^{1/2}=log_4 n+\frac{1}{2} \ log_4 \ m\implies True[/tex][tex]log_2\ (\cfrac{cd^3}{e^4} )=log_2\ c+log_2\ d^3-log_2\ e^4=log_2\ c+3log_2\ d-4log_2\ e\implies False[/tex]PLEASE ANSWER
Carter and his children went into a movie theater and he bought $33 worth of drinks and candies. Each drink costs $4.50 and each candy costs $3. He bought 3 times as many drinks as candies. Determine the number of drinks and the number of candies that Carter bought.
The number of drinks and the number of candies that Carter bought are 6 and 2 respectively.
How to determine the number of drinks and candies?In order to determine the number of drinks and the number of candies that Carter bought, we would have to write a system of linear equation and assign variables to the number of drinks and number of candies respectively, and then translate the word problem into algebraic equation as follows:
Let the x indicate the number of drinks.Let the y indicate the number of candies.Since each drink costs $4.50 and each candy costs $3 and Carter bought 3 times as many drinks as candies;
x = 3y .......equation 1.
4.50x + 3y = 33 .......equation 2.
Substituting equation 1 into equation 2, we have:
4.50(3y) + 3y = 33
13.50y + 3y = 33
16.50y = 33
y = 33/16.50
y = 2 candies.
For the value of x, we have:
x = 3(2)
x = 6 drinks.
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resolve 75 = 15r. how do i resolve this
The value of r in the given expression is 5.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
We are given that the expression as;
75 = 15r
Now we need to find the value of r.
Therefore, we wil divide the 15 both side;
r = 75/ 15
r = 5
Hence, the value of r in the given expression is 5.
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Can someone explain how to find the answer
Let f = {(x, y) | x, y ∈ ℕ and y = 2x} be a relation on ℕ. Find the domain, co-domain and range. Is this relation a function? (2pts. )
Find the greatest common factor of 10b³ and 4b.
Solution:
2b would be the greatest common factor (GCF) between both 10b^3 and 4b.
Hope this helps!
kara divided 560.9 by 1000 and got a quotient of 0.5609. Kevin thinks the quotient of 0.5609. Who is correct
Answer:
both are correct
Step-by-step explanation:
theyre the same answer I think the questions wrong
If CB is the diamater...Find x:
Assuming [tex]\overline{BC}[/tex] is a diameter, minor arc [tex]AB[/tex] has a measure of [tex]180^{\circ}-108^{\circ}=72^{\circ}[/tex].
Using the inscribed angle theorem, [tex]36=x+3 \implies x=\boxed{33}[/tex].
A roofer creates a price quote to repair a
roof using shingles. Which is least likely to
affect the value of the price quote?
the estimated cost of the shingles
chosen for the roof
the estimated time to lay the
shingles and underlayment
the square footage of the front yard
and backyard
the square footage of the house and
garage
Answer:
Step-by-step explanation:
the estimated time to lay the shingles and underlayment
The Estimation cost of the shingles chosen for the roof.
What is Estimation cost?Estimation cost is the process of predicting how much a project or task will cost. It is used to help make decisions about the feasibility of the project and to plan for its budget. Estimation cost is based on past experiences, the current market and expected future conditions. The accuracy of an estimate can be improved by gathering detailed information about the project and its components. This information can include the cost of materials, labor and time needed to complete the project. Estimation cost is an important part of project management and is used in combination with other project management tools and methods such as scheduling, budgeting and risk management.
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6. A chemist needs to create 100mL of 38% acid solution. On hand she has a 20% acid solution and
a 50% acid solution. How many mL of each solution should she use?
Answer:
Step-by-step explanation:
:On hand she has a 20% acid solution and a 50% acid solution. How many ml of each solution should sheStep-by-step explanation:this is the answer
A chemist needs 40mL of 20% acidic solution and 60mL of 50% acidic solution.
What is percentage?The percentage is the ratio of number expressed as a fraction of 100.
Assume chemist needs x mL of 20% of acidic solution and y mL of 50% acidic solution.
A total of 100mL solution is to be created.
x+y=100
x=100-y
The concentration of 20% acidic solution will be 0.2x, concentration of 50% acidic solution will be 0.5x and the sum of their concentrations should be 0.38(100).
0.2x+0.5y=0.38(100)
0.2x+0.5y=38
Substitute x=100-y into the obtained equation.
0.2(100-y)+0.5y=38
20-0.2y+0.5y=38
20+0.3y=38
0.3y=18
y=18/0.3
y=60
Substitute y=60 into x=100-y.
x=100-60
=40
So, the chemist needs 40mL of 20% acidic solution and 60mL of 50% acidic solution.
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The number of total employees if there
are 150 employees that drive to work.
Answer:
150.
Step-by-step explanation:
If 150 total drive to work, then 150 work there....
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 4 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
Linear Algebra question.
Answer:
ax + y = (21, -16, 29)
Step-by-step explanation:
ax + y = [(-6a + 3), (3a - 7), (-8a + 5)]
now,
-8a + 5 = 29
a = (29 - 5)/-8
a = -3
ax + y = [(-6)(-3)+3, 3(-3)-7, 29]
ax + y = (21, -16, 29)
Consider a weighted voting system with three players. If n one has veto power, and no one is a dummy., find the Banzhof power distribution.
Player 1 ____
Player 2 ____
Player 3 ____
Give each value as a fraction or decimal.
The Banzhaf power distribution value in the fraction is,
Player 1: = 0.6
Player 2: = 0.2
Player 3: = 0.2.
What is the distribution?
The mathematical expression known as a distribution function expresses the likelihood that a system would adopt a certain value or range of values. The traditional examples include games of chance.
List of winning coalitions:
1. P1, P2, P3
2. P1, P2
3. P1, P3
No. of times P1 is critical = 3 (P1 is critical all 3 times as it has veto power)
No. of times P2 is critical = 1 (in the second coalition)
No. of times P3 is critical = 1 (in the third coalition)
Total no. of critical times = 3 + 1 + 1 = 5
Banzhof Power Distribution:
Player 1: No. of times P1 is critical/Total no. of critical times
= 3/5 = 0.6
Player 2: No. of times P2 is critical/Total no. of critical times
= 1/5 = 0.2
Player 3: No. of times P3 is critical/Total no. of critical times
= 1/5 = 0.2
Hence, the Banzhaf power distribution value in the fraction is,
Player 1: = 0.6
Player 2: = 0.2
Player 3: = 0.2
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If V is the incenter of APQR, QT = 5, VO = 7, and PV = 29, find each measure.
Answer:
each measure 120
Step-by-step explanation:
Find the value of x.
The 7x side is half the length of the 28 side.
7x = 14
x = 2
15(2 x+3)+100=110-5x
30 x+45+100=110-5x
30 x+145=110-5x
35 x+145=110
35 x=-35
x=-1
Step-by-step explanation:
Reasons for each step
1. Distribute: 15(2x + 3) = 30x + 45
2. Combine Like Terms: 45+100 = 145
3. Addition Property of Equality: 30x+5x+145 = 110-5x+5x => 35x+145 = 110
4. Subtraction Property of Equality: 35x+145-145 = 110-145 => 35x = -35
5. Division Property of Equality: 35x/35 = -35/35 => x = -1
Given f(x) = -3x + 3, solve for x when f(x) = 9.
Answer:
Step-by-step explanation: x=-2. -3•-2=6+3=9
pla help.me with this question
Answer:
7. A
8. B
Step-by-step explanation:
7.
1 3
4 ------- - 2 -------
2 4
9 11
------- - -------
2 4
9(2) 11
------- - -------
2(2) 4
18 11 7 3
------- - ------- = ------- = 1 -------
4 4 4 4
----------------------------------------------------------------------------------------------------------
8.
3 3
13 ------- + 16 -------
8 4
107 67
------- + -------
8 4
107 67(2)
------- + -------
8 4(2)
107 134 241 1
------- + ------- = -------- = 30 -------
8 8 8 8
I hope this helps!
Simplify the expression: -3(2x+4)-8x
Answer:
- 14x - 12
Step-by-step explanation:
- 3(2x + 4) - 8x ← distribute terms in parenthesis by - 3
= - 6x - 12 - 8x ← collect like terms
= - 14x - 12
Answer:
-14x-12
Step-by-step explanation:
1) Expand by distributing terms.
-(6x+12)-8x
2) Remove parentheses.
-6x-12-8x
3) Collect like terms.
(-6x-8x)-12
4 Simplify.
−14x−12
The diagram shows the graphs of y=x²-3x - 2 and
y = x + 3.
Use the diagram to solve the equation x² – 3x − 2 = x + 3
=
graphically.
Y
11+
10
9
8-
7-
6543
6-
5-
4-
2-
1
-8-7-6-5-4-3-2-1, 1-2-3/4-5_6_7_8
23456
-2-
-3-
-4-
-5-
-6-
-7-
-8-
-9-
--10-
-11+
x
The solution of the expression is,
⇒ x = - 1 and x = 5
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Solve the expression,
x² – 3x − 2 = x + 3
Now, We can simplify as;
x² – 3x − 2 = x + 3
x² – 3x − 2 - x - 3 = 0
x² - 4x - 5 = 0
x² - 5x + x - 5 = 0
x (x - 5) + 1(x - 5) = 0
(x + 1) (x - 5) = 0
x = - 1
x = 5
Thus, The solution of the expression is,
⇒ x = - 1 and x = 5
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PLS HURRY DUE TOMMOROW!!!
1) Farmer John has cows and chickens on his farm. His farm animals have 120 legs and 48 heads total. How many cows and how many chickens are on the farm?
a. Setup a system, of two equations, to help you solve this riddle.
b. Solve this system using either Elimination or Substitution, show your work, and state your answer as a complete sentence.
The number of cows is 12 and number of chickens are 36.
What is a system of linear equation?A "system" of equations is a set or collection of equations that you deal with all together at once.
Given that, Farmer John has cows and chickens on his farm. His farm animals have 120 legs and 48 heads total.
Let the number of chickens be x and that of cows be y,
A cow has 4 legs and that of chickens have 2,
Setting the equations, we get,
2x+4y = 120
x+2y = 60
x+y = 48
Solving the equation by elimination, we get,
2y - y = 60 - 48
y = 12
Therefore, x = 36
Hence, The number of cows is 12 and number of chickens are 36.
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13/7 + 3 2/3 solve the expression
this answer was wrong that i looked up on here please help
Answer: try quizlet
Step-by-step explanation:
Prove that () = + 5 and () = √ − 5 are inverse functions without finding the inverse of either function.
if two functions are inverse of each other, that means that their composite will result in "x" alone.
meaning, that if f(x) and g(x) are inverse of each other, then f( g(x) ) = x and the other way around will be the same, hmmm let's see if that's true
[tex]f(x)=x^3 + 5\hspace{5em}g(x)=\sqrt[3]{x-5} \\\\[-0.35em] ~\dotfill\\\\ f( ~~ g(x) ~~ )=[g(x)]^3 + 5\implies f( ~~ g(x) ~~ )=[\sqrt[3]{x-5}]^3 + 5 \\\\\\ f( ~~ g(x) ~~ )=(x-5) + 5\implies f( ~~ g(x) ~~ )=x ~~ \textit{\LARGE \checkmark} \\\\[-0.35em] ~\dotfill\\\\ g( ~~ f(x) ~~ )=\sqrt[3]{[f(x)]-5}\implies g( ~~ f(x) ~~ )=\sqrt[3]{[x^3 + 5]-5} \\\\\\ g( ~~ f(x) ~~ )=\sqrt[3]{x^3}\implies g( ~~ f(x) ~~ )=x ~~ \textit{\LARGE \checkmark}[/tex]
Please help heres a pic
The fourth arrow is used to represent inequality x>3.2
What is Number system?A number system is defined as a system of writing to express numbers.
Number line is a picture of a graduated straight line that serves as visual representation of the real numbers.
All the positive numbers are represented on the right side of the origin and all the negative numbers are represented on the left side of the origin, with a definite scale.
Here x>3.2 which means that values of x are greater than 3.2 so we use Open circle with right arrow.
Hence, the fourth arrow is used to represent inequality x>3.2
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The line x - y = 5 passes through
O (0,5)
O (-5, 0)
O (0,-5)
Answer:
(0,-5)
Step-by-step explanation:
solve & check the linear equation
3(x-4) + 14=2(x+3)
Answer:
x = 4
Step-by-step explanation:
3(x - 4) + 14 = 2(x + 3)
3x - 12 + 14 = 2x + 6
3x + 2 = 2x + 6
-2x -2x
-----------------------
x + 2 = 6
-2 -2
---------------
x = 4
I hope this helps!