Comparing Two Linear Functions (Context - Graphically)
Answers
start identifying the slope and y-intercept for each high school.
The slope represents the growth for each year, in this case for high school A is 25 and for high school B is 50.
The y-intercept is the number of students that are enrolled currently, in this case for A is 400 and for B is 250.
The complete equations in the slope-intercept form are
[tex]\begin{gathered} A=25x+400 \\ B=50x+250 \end{gathered}[/tex]Continue to graph the equations
High school B is projected to have more students in 8 years.
Related Questions
Identify the key features of the graph, including the x - intercepts. Y-intercept, axis of symmetry, and vertex. (3)
Answers
The graph of the given finction is:
Here, the x-intercept is at -1 and -6
The y-intercept is at 6
The axis of symmetry is x=-3.5
The vertex is (-3.5,-6.2)
Write a recursive formula for the following sequence. You are welcome to submit an image of handwritten work. If you choose to type then use the following notation to indicate terms; a_n and a_(n-1). To earn full credit be sure to share all work/calculations and thinking.a_n = { \frac{3}{5}, \frac{1}{10}, \frac{1}{60}, \frac{1}{360} }
Answers
Answer:
[tex]a_n=a_{n-1}\left(\frac{1}{6}\right)[/tex][tex]a_n=\frac{3}{5}\left(\frac{1}{6}\right){}^{n-1}[/tex]
Explanation:
we can see for the fractions with 1 as the numerator that the denominator is multiplied by 6 and the numerator remains the same, that corresponds to multiply the previous fraction by 1/6 and when verifying with the first fraction we observe that applies for all the terms.
g(n) = n2 − 4
h(n) = n − 5
Find g(n) · h(n)
g(x) = 4x + 4
f(x) = x3 − 1
Find (g ◦ f)(x)
Answers
The value of
g(n) · h(n) = n³ - 5n² - 4n + 20 (g ◦ f)(x) = 4x³What is function?The core concept of mathematics' calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
g(n) = n² − 4, h(n) = n − 5
g(n).h(n)
= (n² − 4).(n-5)
= n³ - 5n² - 4n + 20
and, g(x) = 4x + 4, f(x) = x³ − 1
(gof)(x)
=g(f(x))
=g(x³-1)
= 4(x³-1) + 4
= 4x³ - 4 + 4
= 4x³
Learn more about function here:
https://brainly.com/question/12431044
#SPJ1
how many hours did the plumber work to fix the plumbing
Answers
The total cost of the fix is C = $375.
The plumber charges a fixed rate per call of F = $50 and charges a variable rate of v = $25 per hour, if h is the number of hours he worked, we can write:
[tex]\begin{gathered} C=F+v\cdot h \\ 375=50+25\cdot h \end{gathered}[/tex]This equation shows that the total cost is equal to the fixed cost plus the variable cost. The variable cost is equal to the hourly rate times the number of hours of work.
Then, we can calculate h as:
[tex]\begin{gathered} 375=50+25h \\ 375-50=25h \\ 325=25h \\ h=\frac{325}{25} \\ h=13 \end{gathered}[/tex]Answer: he worked 13 hours.
NOTE:
Table of values:
If we need to use a table of values to solve this, we will have two columns: one for the number of hours and the other for the total cost.
We can make the table have more detail and separate the cost column in 3: one for the fixed cost, one for the variable cost and the last one for the total cost.
Then, we would write in each column:
1) Hours: the number of hours, from 0 to the amount we consider.
2) Fixed cost: this column will have the value $50 for all the rows, as it is independent of the number of hours.
3) Variable cost: this column will have values proportional to the hours. This values will be 25 times the number of hours.
4) Total cost: this column will add both the fixed cost and variable cost.
Then, we will obtain the following table.
We can now look for the value $375 in the Total cost column.
We find that this cost correspond to 13 hours:
Graph:
We can now use the data from the table to graph the total cost in function of the number of hours.
3
y + yz + z + y use y = -2, and z = 6
Answers
Step by step
3y + yz + z + y
Use y= -2 and z = 6
Substitute values for y and z
3(-2) + (-2*6) + 6 + (-2)
Multiply first per PEMDAS rule
-6 + (-12) + 6 + (-2)
Add and subtract
= -14
Hi, i tried to solve this problem, but I can't manage to do it, can you help me ?
Answers
Length of y is 25.2.
Given:
The angle is given as 35 degree and a side is 36.
The objective is to find the length of the side y.
In a right angled traingle, the side opposite to the given angle is called oppotise side, the other smaller side is called adjacent side and the longer side is called hypotenuse.
Here, opposite side is y and adjacent side is 36.
Then, the relationship between oppsote and adjacent can be calculated using the trigonometric ratio of tan theta.
[tex]\begin{gathered} \tan \theta=\frac{opposite}{adjacent} \\ \tan 35^0=\frac{y}{36} \\ y=36\cdot\tan 35^0 \\ y=36(0.7) \\ y=25.2 \end{gathered}[/tex]Hence, the length of y is 25.2.
If Allie’s parents are willing to spend $300 for a party, how many people can attend?
Answers
At least 20 people can attend the party
A vase is in the shape of a cone. The height is 12 inches and the diameter is 4.4 inches.
What is the lateral surface area to the nearest tenth of a square inch?
O
O
24.3 square inches
149.1 square inches
168.6 square inches
99.5 square inches
Answers
84.27 square inch is the lateral surface area of cone.
Define lateral surface area.All of an object's sides, excluding its base and top, are considered its lateral surface. The size of the lateral surface is referred to as its area. This must be distinguished from the total surface area, which consists of the base and top areas as well as the lateral surface area. A figure's lateral area consists solely of the non-base faces. The lateral surface area of several forms, such as a cuboid, cube, cylinder, cone, and sphere, is discussed in this article.
Given,
Height = 12 inches
Diameter = 4.4 inches
Radius = 2.2 inches
Lateral surface area:
πr√h² + r²
3.14 × 2.2 √(12)² + (2.2)²
3.14 × 2.2 √144 + 4.84
3.14 × 2.2 √148.84
3.14 × 2.2(12.2)
3.14 × 26.84
84.27
84.27 square inch is the lateral surface area of cone.
To learn more about lateral surface area, visit:
https://brainly.com/question/14001755
#SPJ13
$(20) = 4x^2+ 5x – 3 g(x) = 4x^3 – 3x^2 + 5 Find (f + g)(x)
Answers
The value of (f+g)(x) from the given functions is 4x³+x²+5x+2.
The given functions are f(x)=4x²+ 5x - 3 and g(x)=4x³ - 3x² + 5.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Now, (f+g)(x)=f(x)+g(x)
= 4x²+ 5x - 3+4x³ - 3x² + 5
= 4x³+4x²- 3x²+5x+5-3
= 4x³+x²+5x+2
Therefore, the value of (f+g)(x) from the given functions is 4x³+x²+5x+2.
To learn more about the function visit:
https://brainly.com/question/28303908.
#SPJ1
At the park there is a pool shaped like a circle. A ring-shaped path goes around the pool. Its inner radius is 7 yd and its outer radius is 9 yd.We are going to give a new layer of coating to the path. If one gallon of coating can cover 5v * d ^ 2 how many gallons of coating do we need? Note that coating comes only by the gallon, so the number of gallons must be a whole number. (Use the value 3.14 for pi.)
Answers
Which of the following describes point D?
Answers
Answer:
(0,4)
Step-by-step explanation:
Hi! :)
I am Pretty sure this is what it is, if this is not what you are needing please let me know.
Find the solutions of the following equations in the interval [0, 2π).
Answers
In order to solve this equation, we can first do the following steps to simplify it:
The sum of three consecutive integers is −387. Find the three integers.
Answers
Answer:
-130, -129, -128
Step-by-step explanation:
consecutive integers are when one integer is greater than the previous one and so on... so assuming the smallest integer which we start with is "x", the next integer is "x+1", and the next integer is "x+1+1".
Adding all these together will give us the sum of three consecutive integers:
[tex]x+(x+1)+(x+1+1)[/tex]
Simplifying inside the parenthesis gives us
[tex]x+(x+1)+(x+2)[/tex]
Simplifying the entire expression gives us the following:
[tex]3x+3[/tex]
This is equal to -387 as stated in the problem, so let's set it equal to -387
[tex]3x+3=-387[/tex]
Subtract 3
[tex]3x=-390[/tex]
Divide by 3
[tex]x=-130[/tex]
Since the consecutive integers are just +1, then +2, we can define the three consecutive integers as
-130, -130 + 1, -130 + 2
which simplifies to
-130, -129, -128
What is the domain of the function graphed below?
x<7
x_<7
-2_< X_<3
all real numbers
Answers
The given function is defined everywhere except at x = 7 and a higher value than 7 thus x < 7 will be the domain of the function so option (A) is correct.
What is the range and domain of a function?A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.
The domain is for the independent variable while the range is for the dependent variable.
As per the given graph of the function,
The value of the function at x = -1 is -2.
In another place, the graph is not breaking before x = 7.
So, at x > 7 the function is not defined.
The domain of the function will be (-∞ ,7).
Hence "The given function is defined everywhere except at x = 7 and a higher value than 7 thus x < 7 will be the domain of the function".
For more details about the range and domain of the function,
brainly.com/question/28135761
#SPJ1
The given question is incomplete, the complete question follows with the graph below;
p and q are roots of the equation 5x^2 - 7x +1. find to value of p^2 x q +q^2 x p and (p/q)+(q/p)
Answers
1) Let's find the roots of the equation: 5x² -7x +1
5x² -7x +1
2) Calling x_1 =p and x_2= q
Plugging them into the (p/q)+(q/p) expression, dividing the fractions. And then rationalizing it we'll have finally:
[tex]\frac{\frac{7+\sqrt[]{29}}{10}}{\frac{7-\sqrt[]{29}}{10}}+\frac{\frac{7-\sqrt[]{29}}{10}}{\frac{7+\sqrt[]{29}}{10}}=\frac{7+\sqrt[]{29}}{10}\cdot\frac{10}{7-\sqrt[]{29}}\text{ +}\frac{7-\sqrt[]{29}}{10}\cdot\frac{10}{7+\sqrt[]{29}}\text{ =}\frac{39}{5}[/tex]The 3D object above is sliced parallel to the base. What shape is formed? triangle octagon rectangle hexagon
Answers
When a 3D object is sliced such that the top is parallel to the base, then the top and the base formed same shape.
The shape formed at the base;
It is a six-sided shape. A six-sided polygon is called HEXAGON
What is the solution for the system given below 4x + 8y = 20 and -4x + 2y = -30
Answers
You have the folloiwng system of equations:
4x + 8y = 20
-4x + 2y = -30
In order to solve the previous system, proceed as follow:
Sum the equations and solve for y:
4x + 8y = 20
-4x + 2y = -30
10y = -10
Divide by 10 both sides
y = -10/10
y = -1
Now, replace the previous value of y into the any of the equations of the system, for instance, into the first equation and solve for x:
4x + 8y = 20
4x + 8(-1) = 20
4x - 8 = 20
add 8 boht sides, simlplify and divide by 4 both sides:
4x = 20 + 8
4x = 28
x = 28/4
x = 7
Hence, the solution of the given system of equations is given by:
x = 7
y = -1
Alex has a $100 budget to buy food for his birthday
party. Each pizza costs $10 and each soda bottle
costs $3. Alex will buy 7 pizzas.
What is the greatest number of soda bottles Alex can
buy without going over budget?
Answers
If Alex has a $100 budget to buy food for his birthday, each pizza cost $10 and each soda bottle cost $3, and Alex bought 7 pizzas, then the greatest number of soda bottles Alex can buy without over budget 10 soda bottles
The total budget = $100
The cost of one pizza = $10
Number of pizza he bought = 7
The total cost of pizza = 7×10 = $70
The remaining money = 100-70
= $30
The cost of one soda bottle = $3
Number of soda bottle can he buy using the remaining money = 30/3
= 10 soda bottles
Hence, if Alex has a $100 budget to buy food for his birthday, each pizza cost $10 and each soda bottle cost $3, and Alex bought 7 pizzas, then the greatest number of soda bottles Alex can buy without over budget 10 soda bottles
Learn more about budget here
brainly.com/question/19297741
#SPJ1
Use the cross Products Property to solve the proportions.1. 3/4 = v/142. 5/n = 16/32
Answers
1) 3/4 = v/14
v = (3 x 14) / 4
v = 42/4
v = 10.5
2) 5/n = 16/32
5(32) = n(16)
n = 5(32) / 16
n = 160/16
n = 10
5 Which equations have the same value of x as 6 2 3 -9? Select three options. -9(6) 5x+4=-54 5x+4=-9 5x=-13 5X=-58
Answers
The given equation is-
[tex]\frac{5}{6}x+\frac{2}{3}=-9[/tex]If we multiply the equation by 6, we would have the same value for the variable x since we are multiplying the same number on each side. So, the second choice is an equivalent equation to the given one.
Let's multiply by 6.
[tex]\begin{gathered} 6\cdot\frac{5}{6}x+6\cdot\frac{2}{3}=-9\cdot6 \\ 5x+4=-54 \end{gathered}[/tex]So, the third expression is also an equivalent expression.
Then, let's subtract 4 on each side.
[tex]\begin{gathered} 5x+4-4=-54-4 \\ 5x=-58 \end{gathered}[/tex]The last choice is also an equivalent expression.
Therefore, the right choices are 2, 3, and 6.A figure is made up of three triangles. Each triangle has a baseof 4.5 feet and a height of 4.5 feet. What is the total area of thefigure?
Answers
Area of Compound Figures
A figure is made up of 3 triangles with a base b=4.5 feet and a height h=4.5 feet
The area of a triangle of base b and height h is:
[tex]A=\frac{b\cdot h}{2}[/tex]Substituting the given values:
[tex]A=\frac{4.5ft\cdot4.5ft}{2}=10.125ft^2[/tex]The total area is 3 times the above area, thus:
[tex]A_t=3\cdot10.125ft^2=30.375ft^2[/tex]Answer: a.
A painting is worth $9000 in 2007. The value of the painting increases by 12% eachyear.Estimate the length of time it takes for the value of the painting to double.
Answers
Step 1
State the formula for exponential growth
[tex]P(0)=P(1+r)^t[/tex]where;
[tex]\begin{gathered} P=\text{ worth in 2007=\$9000} \\ r=rate=\frac{12}{100}=0.12 \\ t=\text{ time for growth in years} \\ P(0)=\text{ Required value of growth in t years} \end{gathered}[/tex]Step 2
Find double the value of the painting.
[tex]2P=9000\times2=\text{ \$18000}[/tex]Step 3
Estimate the length of time it takes for the value of the paint to double
[tex]\begin{gathered} 18000=9000(1+0.12)^t \\ \frac{18000}{9000}==\frac{9000(1+0.12)^t}{9000} \\ 2=(1+0.12)^t \end{gathered}[/tex][tex]\begin{gathered} \ln 2=\ln (1.12)^t \\ \ln 2=t\ln (1.12) \\ \frac{t(\ln1.12)}{\ln1.12}=\frac{\ln2}{\ln1.12} \\ t=6.116255374\text{ years} \\ t\approx6.1163years\text{ approxi}mately\text{ to 4 decimal places} \end{gathered}[/tex]Hence, it will take approximately 6.1163 years for the value of the paint to double.
Susanna has played the piano for s years. Patrick has played the piano for 4 more than twice the number of years that susanna has been playing the piano. which expression correctly shows the number of years that Patrick has been playing the piano.2s + 44s + 22 (s + 4)(s - 4) ÷ 3none of the above
Answers
Given data:
The expression for Patrick paly Piano is,
[tex]P=2s+4[/tex]Thus, the first option is correct.
Find the area when length = 5.2
(Equilateral Triangle)
Answers
Answer: 3√3 / 4
Step-by-step explanation:
A = 8^2√3 where s √3
A = ( √3)^2 * √3 / 4
A = 3√3/4
A survey was given asking whether they watch movies at home from Netflix, Redbox, or a video store.Use the results to determine how many people use Redbox.60 only use Netflix64 only use Redbox24 only use a video store 8 use only a video store or Redbox38 use only Netflix or Redbox 35 use only a video store or Netflix5 use all three24 use none of these
Answers
SOLUTION
We will use a Venn Diagram for this problem.
Let N represent those that use Netflix, R represent those that use Redbox and V represent those that use video store. The Venn Diagram is shown below
From the Venn Diagram above, the number in each part of a circle, represents the information
Now, how many people use Redbox?
The number of those that use Redbox is represented by the circle R, so we add all the numbers in this circle, we have
[tex]n(R)=38+64+5+8=115[/tex]Hence the answer is 115
The elevation of a mountain is 6510 feet above sea level.
Write a signed number to represent this elevation.
Answers
A manufacturing company currently uses 15 workers to load and unload trucks. Each worker can move an average of 15 boxes per minute. A robotics firm has built a robot that can load and unload boxes at the rate of 21 boxes per minute. How many robots will it take to do the same job as the 15 humans?
Answers
It will take 11 robots to do the same job as the 15 humans
Explanation:Given:
Workers in use = 15
Each worker can move an average of 15 boxes per minute.
A robot has been built that can move an average of 21 boxes per minute
15 worker would move:
15 * 15 boxes = 225 boxes per minute.
The number of robots it will take to move 225 boxes is:
225/21 = 10.7
It will take 11 robots to do the same job as the 15 humans
Ava graphs the function h(x) = x^2 + 4. Victor graphs the function g(x) = (x + 4)^2. Which statements are true regarding the two graphs? Select three options.Ava’s graph is a vertical translation of f(x) = x^2.Victor’s graph is a vertical translation of f(x) = x^2.Ava’s graph moved 4 units from f(x) = x^2 in a positive direction.Victor’s graph moved 4 units from f(x) = x^2 in a positive direction.Ava’s graph has a y-intercept of 4.
Answers
Given,
Ava graphs the function h(x) = x^2 + 4.
Victor graphs the function g(x) = (x + 4)^2.
Required:
Check the correct statement about graph.
The graph of Ava and vector function is:
Here, victor graph was represented by blue curve and ava graph by green curve.
For first statement,
Ava’s graph is a vertical translated by 4 units.
Hence, statement is true.
For second statement,
The graph of victor is not vertically translated.
Hence, statement is false.
For statement three,
The curve of the Ava graph is moved 4 unit up in the positive direction. It is in y axis. Hence, statement is true.
For statement forth,
The curve of the victor graph is moved to negative direction not positive. Hence, statement is false.
For statement fifth,
The graph of Ava has the y intercept at 4. So, statement is correct.
Hence, option A (Ava’s graph is a vertical translation of f(x) = x^2), option C (Ava’s graph moved 4 units from f(x) = x^2 in a positive direction) and option E (Ava’s graph has a y-intercept of 4.) is true.
Melissa wants to rent a boat and spend at most $38. The boat costs $6 per hour, and Melissa has a discount coupon for $4 off. What are the possible numbers of hours Melissa could rent the boat?Use t for the number of hours.Write your answer as an inequality solved for t.
Answers
ANSWER:
[tex]t\leq7[/tex]EXPLANATION:
Given:
Melissa wants to rent a boat and spend at most $38
Cost of boat per hour = $6
Discount coupon off = $4
Let t represent the number of hours
We can go ahead and set up the below inequality;
[tex]6t-4\leq38[/tex]Let's add 4 to both sides of the inequality;
[tex]\begin{gathered} 6t-4+4\leq38+4 \\ 6t\leq42 \end{gathered}[/tex]Let's divide both sides by 6;
[tex]\begin{gathered} \frac{6t}{6}\leq\frac{42}{6} \\ t\leq6 \end{gathered}[/tex]So Melissa can rent the boat for up to 7 hours
The employees in a firm earn $8.50 an
hour for the first 40 hours per week, and
1.5 times the hourly rate for any hours
worked over 40. How much does an
employee who works 52 hours in one
week eam?
Answers
Using mathematical operations, we know that the salary of a person working for 52 hours a week will be $493.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands. The rules that specify the order in which we should solve an expression involving multiple operations are known as the order of operations. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, and Addition Subtraction (from left to right).So, the amount earned by a person who works 52 hours a week:
Salary if a person works for 40 hours: $8.50 per hourSalary if a person works for more than 40 hours: 1.5 times $8.50 per hour that is, 8.50 × 1.5 = $12.75 per hour.So, if a worker works for 52 hours, his salary will be:
52 - 40 = 12 Hours40 × 8.50 = $34012 × 12.75 = $153Sum: $493Therefore, using mathematical operations, we know that the salary of a person working for 52 hours a week will be $493.
Know more about mathematical operations here:
https://brainly.com/question/28937023
#SPJ13
