The correct matching of the functions is as follows:
(A) The price of a movie ticket is currently $10 but increases at a rate of 2.5% per year: (1) f(x) = 10(1.025)(B) There are currently 15 students with laptops, and the number increases at a rate of 25% per year: (6) f(x) = 15(1.25)(C) An animal shelter has 50 dogs, and the number of dogs increases by 7% per year: (3) f(x) = 50(1.07)What are functions?In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable). A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. Four broad categories can be used to classify different types of functions. One-to-one function, many-to-one function, onto function, one-to-one, and into function—all based on the element.So, matching each function with a correct scenario:
(A) The price of a movie ticket is currently $10 but increases at a rate of 2.5% per year: (1) f(x) = 10(1.025)(B) There are currently 15 students with laptops, and the number increases at a rate of 25% per year: (6) f(x) = 15(1.25)(C) An animal shelter has 50 dogs, and the number of dogs increases by 7% per year: (3) f(x) = 50(1.07)Therefore, the correct matching of the functions is as follows:
(A) The price of a movie ticket is currently $10 but increases at a rate of 2.5% per year: (1) f(x) = 10(1.025)(B) There are currently 15 students with laptops, and the number increases at a rate of 25% per year: (6) f(x) = 15(1.25)(C) An animal shelter has 50 dogs, and the number of dogs increases by 7% per year: (3) f(x) = 50(1.07)Know more about functions here:
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The correct question is given below:
Drag each tile to the correct box. Not all tiles will be used.
Match each function to the correct scenario.
f(x) = 10(1.025)*f(x) = 7(1.50)*f(x) = 50(1.07)*f(x) = 25(1.10)*f(x) = 15(0.25)*f(x) = 15(1.25)*(A) The price of a movie ticket is currently $10 but increases at a rate of 2.5% per
year.
(B) There are currently 15 students with laptops, and the number increases at a
rate of 25% per year.
(C) An animal shelter has 50 dogs, and the number of dogs increases by 7% per
year.
Submit
000
Which is greater, 2 or 8 ?
Answer:
8
Step-by-step explanation:
Counting up from 1 to 10 you go:
1 2 3 4 5 6 7 8 9 10
As you can see the eight is further to the right meaning it has more value.
(I did this for the points)
8. My proof is the number line (I'm also doing this for points pff) 2<8
An amusement park is creating signs to indicate the velocity of a roller coaster car on certain hills of the most popular ride. A roller coaster gains kinetic energy as itgoes down a hill. The velocity of an object in kilometers per hour kph) can be determined by Vwherekes the kinetic energy of the object in joulesand is the mass of the object in kilogramskeA roller coaster car has a mass of 350 kg and the car has a kinetic energy of 437.500 on the first hill. What velocity does the car obtain on the first hill?
Answer
v = 180 kph
Velocity of the car on the first hill = 180 kph
Explanation
The kinetic energy of a body is given as
K.E = ½ mv²
For this question,
K.E = Kinetic Energy = 437,500 J
m = mass = 350 kg
v = velocity = ?
K.E = ½ mv²
Making v the subject of formula,
v = (2K/m)^(½)
K.E = ½ mv²
437,500 = ½ (350) v²
437,500 = 175v²
We can rewrite this as
175v² = 437,500
Divide both sides by 175
(175v²/175) = (437,500/175)
v² = 2500
We can then take the square root of both sides
√(v²) = √(2500)
v = 50 m/s
To convert this to kilometer/hour or kph, we need to note that
1,000 meters = 1 km
3600 s = 1 hour
[tex]\begin{gathered} v=\frac{50m}{s} \\ v=50\frac{m}{s}\times\frac{1\operatorname{km}}{1000m}\times\frac{3600s}{1hr} \\ v=180\text{kph} \end{gathered}[/tex]Hope this Helps!!!
6. An apartment building contains 12 units consisting
of one- and two-bedroom apartments that rent for
$360 and $450 per month, respectively. When all
units are rented, the total monthly rental is $4,950.
What is the number of two-bedroom apartments?
a) 3
b) 4
c) 5
d) 6
e) 7
* also comment your name and grade ( so I can be impressed- it doesn't have to be your real name)
Using a system of equations, the number of two-bedroom apartments is e) 7.
What is an equation?An equation is a mathematical statement that shows that two expressions are equal.
Equations are written with the equation symbol (=) to show that they enjoy equivalent relationships.
The total number of units in the apartment building = 12
Let one-bedroom apartments = x
Let two-bedroom apartments = y
x + y = 12 ...equation 1
x = 12 - y ... equation 2
The cost of one-bedroom apartments = $360 per unit
The cost of two-bedroom apartments = $450 per unit
The total monthly rental = $4,950
Let 4,950 = 360x + 450y ... equation 3
Substitute x = 12 - y in equation 2 in equation 3:
360 (12 - y) + 450y = 4,950
4,320 - 360y + 450y = 4,950
4,320 + 90y = 4,950
90y = 4950 - 4,320
90y = 630
y = 7
In equation 2, x = 12 - y
x = 12 - 7
x = 5
Check Total Monthly Rental:360x + 450y = 4,950
360(5) + 450(7) = 4,950
1,800 + 3,150 = 4,950
4,950 = 4,950
Thus, based on equivalent values, the number of two-bedroom apartments is 7, while the number of one-bedroom apartments is 5, giving a total of 12.
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Nancy has 120,000 in a bank savings account. The bank pays 4% simple interest a year. How much will his money earn after two years? How much money will he have after two years?
Given:
Principal (P) = $120,000
Interest Rate (r) = 4% annually or 0.04 annually
Time in years (t) = 2
Find: interest and the accumulated value after 2 years
Solution:
Since this is simple interest, the formula for getting the simple interest of a principal amount is:
[tex]Interest=Principal\times Rate\times Time[/tex]Since we already identified the principal, rate, and time in the given information, let's plug them into the formula.
[tex]Interest=120,000\times0.04\times2[/tex]Then, multiply the three of them.
[tex]Interest=9,600[/tex]The interest is $9, 600.
Therefore, after 2 years, Nancy will earn $9, 600 in his bank account.
Since Nancy already has $120,000 and he earned $9, 600, then Nancy will have a total of $129, 600 in his bank account after 2 years.
[tex]\begin{gathered} A=Principal+Interest \\ A=120,000+9,600 \\ A=129,600 \end{gathered}[/tex]I need help with this question. The graph below is option a. I have options to choose from
In this type of exercise ≥ values mean values that are inside the 'area' that the function is determining.
So the correct answer can only be now A or C because B and D are 'outside' areas.
In the letter A we can choose a point to validate the function. Let's choose the point (6,-4):
[tex]y\ge x^2-7x+10[/tex][tex]-4\ge6^2-7\times6+10[/tex][tex]-4\ge36-42+10[/tex][tex]-4\ge4\text{ !!!}[/tex]Look that this result is impossible. -4 is not greater than 4. This invalidate letter A! Therefore the correct answer will be the letter C.
D Suppose you are asked to write an equation of the form y = mx + b to
represent a linear function. What is your strategy for each situation?
1. You are given a description of the function in words.
2. You are given two or more (x, y) values or a table of (x, y) values.
3. You are given a graph showing points with coordinates.
HELP PLS this is my homework for tomorrow
What are the different strategies used to write an equation of the slope-intercept form y = mx + b to represent a linear function?
1. When given a description of the function in words.
The y intercept can be represented by b The slope can be represented by m The point through which the line passes is given by (x, y).So, the equation in the slope-intercept form of a linear function is given by y = mx + b.2. When given two or more (x, y) values or a table of (x, y) values.
The two or more (x, y) values are the coordinates which should be used to find slope m using the formula [tex]m =\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex].Substituting the values of m and (x, y) in the equation y =mx+ b , find y intercept b.Substitute the values of m and y intercept b in the equation.So, the equation in the slope-intercept form of a linear function is given by y = mx + b.3. When given a graph showing points with coordinates.
In a graph with coordinates (x, y) given ,find slope m using the formula [tex]m =\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]. Substitute the values of slope m and coordinates (x, y) in the linear equation y =mx+ b so as to find y intercept b. Substitute the values of m and y intercept b in the equation .So, the equation in the slope-intercept form of a linear function is given by y = mx + b.To learn more about slope-intercept form, refer:
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What additional piece of information is needed to show that ABC ≅ XYZ by AAS?
There are two triangles, triangle ABC and triangle XYZ. Side BC is congruent to side YZ and angle ABC is congruent to angle XYZ.
There are several congruence criteria between triangles. The case of your figure, the congruence must be given by the equality of the sides BC and ZY.
If we have an equal side on both sides, we need 2 angles at the end of that segment to be equal to each other. Your exercise shows that angle B and angle Y are equal.
So for them to be congruent, the angle C and the Z need to be equal.
Then the answer would be the letter C.
The first thing we have to do is identify all the angles, as shown in the figure. Triangles also show lines in yellow (single and double) in both triangles and this notation means that those sides are the same length. In other words, both triangles are isoceles.
What information can we get:
- By opposite vertices we know that R1 = R2=R
- The angles of the isosceles triangles are equal at their ends, that is: P=Q and S=R2=R
We also know that the internal sum of the angles of the triangles gives 180º. This gives us 2 more equations
[tex]\begin{gathered} S+R+44º=180º \\ Q+R+P=180º \end{gathered}[/tex]We replace the equalities taken from the isosceles triangles
[tex]\begin{gathered} S+S+44º=180º \\ 2S=180º-44º \\ S=\frac{136º}{2} \\ S=68º=R \\ P+S+P=180º \\ 2P+68º=180º \\ P=\frac{112º}{2} \\ P=56º=Q \end{gathered}[/tex]A civil air patrol unit of fifteen members includes three officers. In how many ways can three members be selected for a search and rescue mission such that at least one officer is included
The three members be can selected in 455 ways.
What in mathematics is a combination?
Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up.
The officers can be selected in 15C3 ways.
15c3
=15!/(15-3)! . 3!
After calculating get that,
= 5 x 7 x 13
=455
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Two piecewise functions are shown below. What is the value of 6f * (- 2) + 3g * (1) ?
To find the value of f(-2), we replace x = -2 into the second piece of the function. Then, we operate.
[tex]\begin{gathered} f(-2)=\frac{1}{3}(-2)^3 \\ f(-2)=\frac{1}{3}(-8) \\ f(-2)=-\frac{8}{3} \end{gathered}[/tex]Second partTo find the value of g(1), we replace x = 1 into the first piece of the function. Then, we operate.
[tex]\begin{gathered} g(1)=2|1-1|+3 \\ g(1)=2|0|+3 \\ g(1)=2\cdot0+3 \\ g(1)=0+3 \\ g(1)=3 \end{gathered}[/tex]Finally, we find the value of the given expression:
[tex]\begin{gathered} 6f(-2)+3g(1)=6\cdot-\frac{8}{3}+3\cdot3 \\ 6f(-2)+3g(1)=-\frac{6\cdot8}{3}+9 \\ 6f(-2)+3g(1)=-\frac{48}{3}+9 \\ 6f(-2)+3g(1)=-16+9 \\ 6f(-2)+3g(1)=-7 \end{gathered}[/tex]One simple method to predict adult height is to average the parents’ heights in inches and then add 2.5 inches if the child is a boy or subtract 2.5 inches if the child is a girl. This method can be fairly accurate, but can also be as much as 5 inches above or below the child’s eventual height.Use the variable D, which means height of dad and M, which means height of mom1. Write the formula for a boy’s adult height.(5 points) 2. Write the formula for a girl’s adult height.(5 points)
We are given that a boy's height is predicted by adding 2.5 inches to the average of the height of the parents. If "D" is the height of the father and "M" is the height of the mother then the average is determined by adding the two heights together and dividing by 2, like this:
[tex]\frac{D+M}{2}[/tex]Since the height of the boy is determined by adding 2.5 inches to this average, this means that the height of the boy "B" is:
[tex]B=\frac{D+M}{2}+2.5[/tex]The height of a girl "G" is determined by subtracting 2.5 to the average, therefore we have:
[tex]G=\frac{D+M}{2}-2.5[/tex]what is the relation ships for 1 2 3 4 5 and n please help
To find the relationship you:
1. The relation can be the difference between every term in the sequence:
In the first sequence you have between every term a diferencen of:
Where n is the term
Youn can notice that the relationship is the way you get that term and is equal to the previous term plus an odd number (3,5,7,9), as the sequences do not have a constant difference the sequence is a non-regular succession. But as the set of differences (1,3,5,7,9) Follows a regular succesion of (2n-1) you have quadratic sequences that have the next formula:
1. First sequence:
[tex]n^2+10[/tex]2. Second sequence:
[tex]n^2-4[/tex]The Associative Property applies to which operations? Check all that apply. A. divideb -c.xD+
C) x
D)+
Explanation
The assoaciative property states that when three or more are added (or multiplied), the sum (or the ) is the same regardless of the grouping of the multiplicands
[tex]\begin{gathered} a\cdot(b\cdot c)=(a\cdot b)\cdot c \\ a+(b+c)=(a+b)+c=(a+c)+b \end{gathered}[/tex]Associative property can only be used with addition and multiplication and not with subtraction or division
so, the answer is
C) x
D)+
g(x)=4f(x)=×^2-5find (g+f)(n)
g(x)=4
f(x)=×^2-5
(g+f)(n)
Add both equations and replace x by n
(g+f) (n) = n^2-5+4 = n^2-1
please help me please help me
Answer:
Only did for Problem 1:
Square is: 4x^2-20x+25
Side is: 2x-5
A^2=4
2AB=-20
B^2=25
Step-by-step explanation:
Evaluate each expression for the given value of the variable. #8
8.
You evaluate the expression given the value of n.
The expression is:
[tex]4(n-1)^2[/tex]We want the value of this expression, GIVEN that n is 6.
So, let's substitute 6 into n and find out the answer. Shown below:
[tex]\begin{gathered} 4(n-1)^2 \\ =4(6-1)^2 \\ =4(5)^2 \\ =4\times25 \\ =100 \end{gathered}[/tex]Stella rewrites -2 1/2 plus 3.7 using commutative Property of addition. Which expression did she write?
The rule for the commutative property of addition is:
a + b = b + a
Stella writes:
[tex]-2\frac{1}{2}\text{ plus 3.7}[/tex]This can be expressed mathematically as:
[tex]-2\frac{1}{2}+3.7[/tex]Which according to the property of commutativity can also be written as:
[tex]\begin{gathered} 3.7\text{ + (-2}\frac{1}{2}) \\ 3.7\text{ - 2}\frac{1}{2} \end{gathered}[/tex]The expression Stella wrote based on the commutative property of addition is therefore:
[tex]\begin{gathered} -2\frac{1}{2}+\text{ 3.7 or} \\ 3.7\text{ - 2.5 (Note that 2}\frac{1}{2}=2.5) \end{gathered}[/tex]Write the algebraic expression representing the perimeter of marlene’s house in simples form.
The perimeter of Marlene's house is the total distance around the edge of her house.
The perimeter can be calculated thus:
[tex]\begin{gathered} (2x-10)+(x-2)+(\frac{1}{2}x-4)+(x-2)+(x-2)+(x)+(2x+2)+ \\ (\frac{1}{2}x-4)+(x-2)+(x-2)+(x) \end{gathered}[/tex]Collect like terms
[tex]\begin{gathered} (2x+x+\frac{1}{2}x+x+x+x+2x+\frac{1}{2}x+x+x+x)\text{ +} \\ (-10-2-4-2-2+2-4-2-2) \\ =12x-26 \end{gathered}[/tex]Therefore, the algebraic expression representing the perimeter of Marlene's house is
[tex]12x-26[/tex]kaitlin, john and carlos sent a total of 109 text messages during the weekend. kaitlin sent 7 more messages than carlos. John 4 times as many messages as carlos How many messages did they each send?number of text messages kaitlin sent=number of text messages john sent =number of text messages carlos sent =
let k be Kaitlin, j be John and c be Carlos. We get that
[tex]\begin{gathered} k+j+c=109 \\ k=c+7 \\ j=4c \end{gathered}[/tex]so we get that
[tex]\begin{gathered} c+7+4c+c=109 \\ 6c=109-7=102 \\ c=\frac{102}{6}=17 \end{gathered}[/tex]so carlos sent 17 messages. Kaitlin sent 24 and John 68
Find the value of 5y - 6 given that -4y - 7= 9. Simplify your answer as much as possible.
Given that:
[tex]-4y-7=9[/tex]We are told to find 5y - 6
Solving for y
[tex]-4y-7=9[/tex]Add 7 to both sides
[tex]\begin{gathered} -4y-7+7=9+7 \\ -4y+0=16 \\ -4y=16 \end{gathered}[/tex]Divide both sides by -4
[tex]\begin{gathered} \frac{-4y}{-4}=\frac{16}{-4} \\ y=-4 \end{gathered}[/tex]Let us now solve for 5y - 6 by substituting y = -4
[tex]\begin{gathered} 5y-6 \\ 5(-4)-6 \\ -20-6=-26 \\ \therefore5y-6=-26 \end{gathered}[/tex]Hence,
[tex]5y-6=-26[/tex]The frequency F of a fire truck siren heard by a stationary observer is given below, where ± v represents the velocity of the accelerating fire truck in meters per second (see figure). (Round your answers to 3 decimal places).
In order to calculate the rate of change, we can use the following derivatives:
[tex]\begin{gathered} u=\frac{1}{a+x} \\ \frac{du}{dx}=-\frac{1}{(a+x)^2} \\ \\ u=\frac{1}{a-x} \\ \frac{du}{dx}=\frac{1}{(a-x)^2} \end{gathered}[/tex]So, calculating the rate of change in each case, we have:
a)
[tex]\begin{gathered} F=\frac{130600}{321-x} \\ \frac{dF}{dx}=\frac{130600}{(321-x)^2}=\frac{130600}{(321-25)^2}=\frac{130600}{296^2}=\frac{130600}{87616}=1.491 \end{gathered}[/tex]b)
[tex]\begin{gathered} F=\frac{130600}{321+x} \\ \frac{dF}{dx}=-\frac{130600}{(321+x)^2}=-\frac{130600}{(321+25)^2}=-\frac{130600}{346^2}=-\frac{130600}{119716}=-1.091 \end{gathered}[/tex]An organism is losing half of its weight each day. The function y=(0.5)^x represents the percent (in decimal form) of the original weight of the organism. where x is the number of days since the organism began to lose weight A. Describe the domain and range of the function. Then graph the function.B. Find and interpret the y interceptC. What percent (in decimal form) of the original weight does the organism weigh on the 5th day?
the domain of this function is:
[tex]x\in\lbrack0,\infty)[/tex]because we count the days.
The range is
[tex]y\in(0,1_{}\rbrack[/tex]because the maximum value of the percentage of wait is 100% = 1
the y- intercept in this case is when the organism has not lose any weight. So the percentage of weight is 100% (1 in decimal form)
after 5 days we get
[tex]0.5^5=0.03125[/tex]Perform the indicated operation by removing the parentheses and combining like terms.(-2x2 + 5) + (6x2 + 7)
Given the expression:
[tex]\mleft(-2x^2+5\mright)+(6x^2+7)[/tex]Removing the parentheses and combining like terms.
[tex]\begin{gathered} =-2x^2+5+6x^2+7 \\ =-2x^2+6x^2+5+7 \\ \\ =4x^2+12 \end{gathered}[/tex]so, the answer will be:
[tex]4x^2+12[/tex]Answer 733
Step-by-step explanation:
What is the value of the expression (5)³?
Answer:
125
Step-by-step explanation:
since 5^3=5*5*5then 5^3=125
A cab company charges a $11 boarding fee and a meter rate of $2 per mile. The equation is y = 2x + 11 where x represents the number of miles to your destination. If you traveled 5 miles to your destination, how much would your total cab fee be?
Answer: 2(5) + 11= 21$
Step-by-step explanation:
A football field is 1920 inches wide. What is two thirds of a football field?
Answer:
2/3's of a football field is 1280
Step-by-step explanation:
were going to take 1920 and were going to divide that by 3.
1920/3 = 640
After that your going to multiply 640 by 2
640(2) = 1280
So your answer is 1280
Tickets to the museum cost 7.50 and there is a 15% discount
the cost of the ticket is 7.50
discount is 15 %
so the value of the discount is,
[tex]\begin{gathered} =7.50\times\frac{15}{100} \\ =1.125 \end{gathered}[/tex]so the price of the ticket is 7.50 - 1.125 = 6.375
Actual cost is 6.375
A ball is thrown from an initial height of 3 feet with an initial upward velocity of 29 s. The ball's heighth (in feet) after seconds to given by the following:H=3+29t-16t^2Find all values of for which the ball's height is 15 feetRound your answer(s) to the nearest hundredth(if there is more than one answer, use the "of" button)
The height of the ball at time t is modeled by
[tex]H(t)=3+29t-16t^2[/tex]To find the values of t for which the height is 15 feet, let us solve the equation
[tex]\begin{gathered} H(t)=15 \\ 3+29t-16t^2=15 \\ 16t^2-29t+12=0 \\ x=\frac{29\pm\sqrt[]{73}}{32} \\ =0.64,1.17 \end{gathered}[/tex]So, at t=0.6 sec and =1.173 sec, the height of the ball is 15 feet (Rounding off to the nearest hundredth)
A number is selected at random from the set 2, 4, 6, 8, 10. Which event, by definition, covers the entire sample space of this experiment? A. The number is greater than 2. B. The number is not divisible by 5. C. The number is even and less than 12. D. The number is neither prime nor composite. E. The square root of the number is less than 3.
Answer:
The number is even and less than 12
Step-by-step explanation:
all of these numbers fit into this category
Answer: Numbers that are even or less than 12
Step-by-step explanation:
Choose the equation that satisfies the data in the table. in pic
Question:
Solution:
Note that if we evaluate x = -1, 0, and x=1 in the last equation we get:
y = 3(-1)+ 3 = -3+3 = 0
y = 3(0)+3 = 3
y = 3(1)+3 = 6
So that, we can conclude that the correct solution is
D. y =3x + 3
Is y is proportional to x?What’s the constant of proportionality (k)?K = y/xWhat’s the equation that represents the table?
For two numbers to be proportional, they must verify:
[tex]y=kx[/tex]"y is proportional to x"
In this case, to verify this, we nedd to calculate if each value of y can be founded by multiplying x by a constant k.
If y = kx is true, then:
[tex]k=\frac{y}{x}[/tex]And if k is the same for al pairs (x, y) then the relationship is proportional.
Using the table we do:
[tex]\begin{gathered} k=\frac{2}{12}=\frac{1}{6} \\ k=\frac{3}{18}=\frac{1}{6} \\ k=\frac{4}{24}=\frac{1}{6} \\ k=\frac{5}{30}=\frac{1}{6} \end{gathered}[/tex]Since k is the same for all pair of values, y is proportional to x.
Also we have already calculated k = 1/6
And the equation that represents the table is:
[tex]y=\frac{1}{6}\cdot x[/tex]