Answers
we have the functions
[tex]\begin{gathered} g(x)=-2x^2+13x+7 \\ h(x)=-x^2+4x+21 \end{gathered}[/tex]Part A
Equate both equations
[tex]-2x^2+13x+7=-x^2+4x+21[/tex]Solve for x
[tex]\begin{gathered} -2x^2+13x+7+x^2-4x-21=0 \\ -x^2+9x-14=0 \end{gathered}[/tex]Solve the quadratic equation
using the formula
a=-1
b=9
c=-14
substitute
[tex]x=\frac{-9\pm\sqrt{9^2-4(-1)(-14)}}{2(-1)}[/tex][tex]x=\frac{-9\pm5}{-2}[/tex]The values of are
x=2 and x=7
The answer Part A
The distances are x=2 units and x=7 units
Part B
f(x)=g(x)/h(x)
so
[tex]f(x)=\frac{-2x^2+13x+7}{-x^2+4x+21}[/tex]Rewrite in factored form
[tex]\begin{gathered} f(x)=\frac{-2(x+\frac{1}{2})(x-7)}{-(x+3)(x-7)} \\ \\ f(x)=\frac{(2x+1)}{(x+3)} \end{gathered}[/tex]The given function has a discontinuity at x=7 (hole), a vertical asymptote at x=-3
and horizontal asymptote at y=2
Related Questions
Which is greater, 2 or 8 ?
Answers
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
the cost of a ticket to the circus is 21.00 for children and 36.00 for adults on a certain day attendance at the circus was 19,000 and the total gate revenue was 56,400 how many children and how many adults bought tickets?the number of children was______The number of adults was____
Answers
We know that
• The ticket for children costs $21.
,• The ticket for adults costs $36.
,• There were 19 people.
,• The total gate revenue is $56,400.
To solve this we have to form a system of linear equations. The first equation would be
[tex]x+y=1,900[/tex]Where x is children and y is adults, there were 19 in total.
The second equation would be
[tex]21x+36y=56,400[/tex]This equation represents the total earnings.
Let's isolate y in the first equation.
[tex]y=1,900-x[/tex]Now, we replace this expression in the second equation.
[tex]\begin{gathered} 21x+36(1,900-x)=56,400 \\ 21x+68,400-36x=56,400 \\ -15x=56,400-68,400 \\ -15x=-12,000 \\ x=\frac{-12,000}{-15} \\ x=800 \end{gathered}[/tex]There were 800 children.Then, we use this value to find y.
[tex]\begin{gathered} y=1,900-x \\ y=1,900-800 \\ y=1,100 \end{gathered}[/tex]There were 1,100 adults.Therefore, the number of children was 800, and the number of adults was 1,100.In the coordinate plane, the point X (4, -2) is translated to the point X'(-1, 3). Under the same translation, the points Y (1, -4) and Z (2, 0) aretranslated to Y' and Z', respectively. What are the coordinates of Y' and Z'?
Answers
As given by the question
There are given that the point X (4, -2) is translated to the point X' (-1, 3).
Now,
A given point A (X, Y) when translated by the rule (h, k) maps to A' (x+h, y+k).
Then,
[tex]undefined[/tex]Find the average rate of change of the following function on the given interval. y=5^x on [0,2]
Answers
To find the rate of change within this interval, we have
[tex]\begin{gathered} \text{ Rate of change =}\frac{f(2)-f(0)}{2-0} \\ =\frac{25-0}{2-0} \\ =\frac{25}{2} \\ =12.5 \end{gathered}[/tex]Hence, the average rate of change of the function within the interval
[0,2] is 12.5
please help me please help me
Answers
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:
what are the x and y-intercepts of the line described by the equation? 3x - 9y = 10.8A) x-intercept = 1.2 y-intercept = 3.6B) x-intercept = -3.6 y-intercept = 1.2C) x-intercept = 1.2y-intercept -3.6D) x-intercept = 3.6 y-intercept = -1.2
Answers
we have the equation
3x - 9y = 10.8
Remember that
x-intercept ----> value of x when the value of y is zero
so
For y=0
substitute
3x-9(0)=10.8
3x=10.8
x=3.6
y-intercept -----> is the value of y when the value of x is zero
For x=0
3(0)-9y=10.8
-9y=10.8
y=-1.2
therefore
the answer is option DStella rewrites -2 1/2 plus 3.7 using commutative Property of addition. Which expression did she write?
Answers
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]Choose the equation that satisfies the data in the table. in pic
Answers
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
Perform the indicated operation by removing the parentheses and combining like terms.(-2x2 + 5) + (6x2 + 7)
Answers
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:
Find the value of 5y - 6 given that -4y - 7= 9. Simplify your answer as much as possible.
Answers
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]using the formula above, find the surface area of a cube whise sides are all two thirds inches
Answers
Given:
The sides of the cube is, s=2/3 inches.
The objective is to find the surface area of cube.
The surface area can be calculated as,
[tex]\begin{gathered} SA=6s^2 \\ =6(\frac{2}{3})^2 \\ =6(\frac{4}{9}) \\ =2.667in^2 \end{gathered}[/tex]Hence, the surface area of the cube is 2.667 square inches.
Kumar has twice as many $1 bills as $5 bills. If the total value of all of Kumar's $1 and $5 bills together is $35, how many $1 bills does Kumar have?
Answers
Let the number of $1 bills that Kumar has = x
Let the number of $5 bills that Kumar has = y
Given that Kumar has twice as many $1 bills as $5 bills
mathematically,
[tex]x=2y\ldots\ldots\ldots\text{.}(1)[/tex]Given also that the total value of all of Kumar's $1 and $5 bills together is $35
mathematically,
[tex]\begin{gathered} x\times\text{ \$1 + }y\times\text{ \$5= \$35} \\ x+5y=35\ldots\ldots\ldots\text{.}(2) \end{gathered}[/tex]Solve equations (1) and (2) simultaneously using substitution method
[tex]\begin{gathered} x=2y\ldots\ldots\ldots\text{.}(1) \\ x+5y=35\ldots\ldots\ldots\text{.}(2) \\ \text{substitute }2y\text{ for }x\text{ in equation (2)} \\ 2y+5y=35 \\ 7y=35 \\ y=\frac{35}{7}=5 \\ To\text{ find x,} \\ \text{substitute 5 for y in equation (1)} \\ x=2(5)=10 \end{gathered}[/tex]Therefore, the number of $1 bills that Kumar has is 10
In a lab, a substance was heated by 6 each hour for 36 hours. What was the total change in temperature?
Answers
The definition of temperature is a measurement of how warm or cold an object or substance is in relation to a reference value.
Explain about the temperature?
An assessment of a material's or, more broadly, of any physical system's capacity to transport heat energy to another physical system. The average kinetic energy of a substance's molecules and its temperature are strongly connected.
The average kinetic energy of one atom or molecule is only revealed by the measurement of temperature. As a result, when we use the terms hot or cold to describe something, we are usually referring to something else.
Fahrenheit, Celsius, and Kelvin are the three scales that are most frequently used to measure temperature (K). Utilizing materials that expand or contract when heated or cooled, thermometers monitor temperature.
Since 6x36 is 216, the temperature climbed by 216 degrees.
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Find the values of x and y. (90 - 4y)° (50 - 2x)° (х +5y)° (2x+3y)°
Answers
1) According to the Vertical angle Theorem
We can state that
50-2x =90-4y
-2x +4y=90
2x -4y = -90
In addition to that, since those three angles make up a straight angle:
2x +3y + x +5y +50 -2x = 180º Combine like terms
x+6y =180º
2) Now, we can set this linear system:
x +6y = 180 x-2 To eliminate x
2x -4y = -90
-2x -12y =-360
2x -4y = -90
----------------
-16y = -450
16y= 450
y = 28.12
y ≅ 28
x + 6(28)=180
x+168=180
x=12
What’s the answer to this problem please help me
Answers
[tex]f(g(2))=f(2)=3 \\ \\ g(f(1))=g(2)=2 \\ \\ f(f(4))=f(2)=3[/tex]
The Associative Property applies to which operations? Check all that apply. A. divideb -c.xD+
Answers
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)+
Determine the restriction of x using inequality. Show your work.
Answers
The sides of a triangle rule states that the sum of the lenghts of the sides of a triangle has to be greater than the lenght of a third side.
4x+2 +8 >18
x>2
4x+2+18>8
x>-3 (reject)
Answer: x>2
Estimate a 15% tip on a dinner bill of $32.47 by first rounding the bill amount to the nearest ten dollars.
Estimated tip: $
Answers
Answer:
$4.50
Step-by-step explanation:
First round to the nearest $10, as instructed. This will give us a bill amount of $30 once rounded. We do not round up as $32.47 is closer to $30 than 40$.
To get 15% of $30 we can simply multiply $30 by 0.15, which is the decimal equivalent of 15%.
This leaves us with an answer of $4.50.
If you roll a standard six-sided die, what is the probability that you get a 1 or 5? Give your answer as a simplified fraction.
Answers
Step 1: Theorem
[tex]\text{Probability of an event = }\frac{N\text{umber of required outcome}}{N\text{umber of sample space}}[/tex]Step 2: Given data
Sample space = { 1, 2, 3, 4, 5, 6}
Number of sample space = 6
Event space = {1, 5}
Number of event space = 2
Step 3: Substitute to find the probability that you get 1 or 5
[tex]\begin{gathered} \text{Probability that you get 1 or 5 = }\frac{2}{6} \\ =\text{ }\frac{1}{3} \end{gathered}[/tex]Answer: 1/3
There are 6 sides. Both of those numbers are two numbers, so it would be 2/6. To simplify it, divide the top and the bottom by the same number. I divided both the numerator and the denominator by 2.
then, your answer would be 1/3
One evening, Hazel and her brother each needed to use the family computer for part of their homework. They worked on their homework for 3 hours, and agreed to share the computer equally for that time.
How long did each person use the computer?
Write your answer as a proper fraction or mixed number.
Answers
Each person used the computer for [tex]\frac{3}{2}[/tex] hours.
Define fraction.A fraction is a number that is a component of a whole. By breaking a whole into a number of parts, it is evaluated. For instance, the symbol for half of a complete number or item is 12. The components of a whole or group of items are represented by fractions. A fraction consists of two components. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection. The denominator is the figure that appears below the line. A fractional equation is one in which one or more of its terms have the unknown as their denominator.
Given Data
They worked on their homework for 3 hours, and agreed to share the computer equally for that time.
They share computer equally, so
[tex]\frac{time}{2}[/tex]
Fraction - [tex]\frac{3}{2}[/tex]
Each person used the computer for [tex]\frac{3}{2}[/tex] hours.
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2. BANKING Brayden deposited $2700 into a savings account that has an annual
simple interest rate of 0.3%. Find the amount in the savings account after each
number of years.
se notes
a. 2 year
b. 3 years
s
c. 6 years
Answers
Answer:
a) $2716.20
b) $2724.30
c) $2748.60
Step-by-step explanation:
You want the account balance after 2, 3, and 6 years if $2700 is deposited into an account earning 0.3% simple interest.
BalanceThe value of an investment P earning simple interest at rate r for t years is given by ...
A = P(1 +rt)
For the given savings deposit, the balance will be ...
A = 2700(1 +0.003t) . . . . . for t = 2, 3, 6
Another way to write this is ...
A = 2700 + 8.10t
The balances are ...
2 years: $2716.203 years: $2724.306 years: $2748.60<95141404393>
Function f is represented by f(x) = 3(x + 4). Find the value of x such that
f(x) = 39
Answers
Answer:
x = 9
Step-by-step explanation:
[tex]3(x + 4) = 39[/tex]
[tex]x + 4 = 13[/tex]
[tex]x = 9[/tex]
Write the standard form of the quadratic function whose graph is a parabola with the given vertex and that passes through the given point. (Let x be the independent variable and y be the dependent variable.)
Vertex:
(3, 18);
point:
(5, 21)
Answers
The standard form of the quadratic function is- 3y = x² - 6x + 27
Here, we are given-
Vertex coordinate = (3, 18)
Point on the graph = (5, 21)
The vertex form of a quadratic equation is given as-
y = a(x - h)² + k
Where h, k are the coordinates of the vertex.
a is the letter in general form of quadratic equation which is-
y = ax² + bx + c
Thus, here, h = 3, k = 18, x = 5 and y = 21
Substituting these values in the vertex form we get-
21 = a(0 - (3))² + 18
⇒ 21 - 18 = 9a
9a = 3
a = 3/9
a = 1/3
Thus, the standard form of the quadratic equation can be calculated as-
y = 1/3(x - (3))² + 18
3y = x² - 6x + 9 + 18
3y = x² - 6x + 27
Thus, the standard form of the quadratic function is- 3y = x² - 6x + 27
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21. The table below describes a sample of 15 players in Major League Baseball, chosen from the starting lineups of teams in 2019. The table shows the team, age, position, height, and salary for each player, as well as several statistics from that season. These include the number of games they played (G), their batting average (AVE) (the proportion of their at-bats for which they got a hit), and their home runs (HR).NameTeamAgeHeightGAVEHRSalaryCedric MullinsOrioles25173 cm22.0940$557,500Tim AndersonWhite Sox26185 cm123.33518$1,400,000Christin StewartTigers25183 cm104.23310$556,400Alex GordonRoyals35185 cm150.26613$20,000,000Jonathan SchoopTwins27185 cm121.25623$7,500,000Marcus SemienAthletics29183 cm162.28533$5,900,000Yandy DiazRays28188 cm79.26714$558,400Randal GrichukBlue Jays28188 cm151.23231$5,000,000Josh DonaldsonBraves33185 cm155.25937$23,000,000Joey VottoReds36188 cm142.26115$25,000,000Cody BellingerDodgers24193 cm156.30547$605,000Ryan BraunBrewers35188 cm144.28522$19,000,000Maikel FrancoPhillies27185 cm123.23417$5,200,000Ian KinslerPadres37183 cm87.2179$3,750,000Marcell OzunaCardinals28185 cm130.24129$12,250,000Calculate the Five Number Summary for the number of games played by the players.Min: Q1 : Median: Q3 : Max:
Answers
Given:
The number of games played by 15 players are,
22, 123, 104, 150, 121, 162, 79, 151, 155, 142, 156, 144, 123, 87, 130.
The objective is to find five number summary for the number of games.
Explanation:
The five number summary are minimum value, quartile 1, median, quartile 2 and maximum value.
Increasing order:
The increasing order of the given data is,
22, 79, 87, 104, 121, 123, 123, 130, 142, 144, 150, 151, 155, 156, 162.
Minimum and Maximum value:
By considering the increasing order of the data, the minimum value is 22 and the maximum value is 162.
To find median:
The median can be calculated as the middle term of total number of data.
Since, the total number of data is 15, which is odd, then the median can be calculated as,
[tex]\begin{gathered} \text{Median}=\frac{15+1}{2} \\ =\frac{16}{2} \\ =8th\text{ term} \end{gathered}[/tex]Thus, the 8th term of increased order is 130.
To find Q1:
The quartile 1 can be defined as the middle term of the left side of the median.
Since, the left side of the median contains 7 terms, which is odd, then the quartile 1 can be calculated as,
[tex]\begin{gathered} Q1=\frac{7+1}{2} \\ =\frac{8}{2} \\ =4th\text{ term (left)} \end{gathered}[/tex]Thus, the 4th term on left side of median is 104.
To find Q3:
The quartile 3 can be defined as the middle term of the right side of the median.
Since, the right side of the median contains 7 terms, which is odd, then the quartile 3 can be calculated as,
[tex]\begin{gathered} Q3=\frac{7+1}{2} \\ =\frac{8}{2} \\ =4th\text{ term (right)} \end{gathered}[/tex]Thus, the 4th term on right side of median is 151.
Hence, the five number summary are,
Min: 22
Q1: 104
Median: 130
Q3: 151
Max: 162.
Members of a band estimated that 200
people were at their show last night. Their manager told them that 227
people had actually been at the show. What was the band's percent error?
Answers
Answer:
13.5%
Step-by-step explanation:
Using the percent error formula,
[tex]\frac{227-200}{200}=13.5\%[/tex]
Select all of the stories that can be represented by the equation.If none of the stories can be represented, select "None of the above".(a) 40x-20= 620
Answers
The correct answers are the first and fourth options
Here, we want to select all stories that goes in line with the equation
a) This can be represented
By multiplying x which is the cost of one training hour by the number of hours which is 40;and subtracting the one-time discount, we can get the or equate to the total paid
b) This cannot be represented
In this case, 20 multiplied by x would give the total amount to be paid after which we can deduct the discount
c) This cannot be represented
It multiplies the charge x by the 20 training hours would give 20x; less the discount of $40 would give 620
d) This can be represented
This narrative is similar to what we have at the first option since the total cost would be 40x and less the discount of $20 would give the after discount payment amount
Consider the system of equations.
7j-h=9
3j+h=21
What is the value of j?
Answers
After considering the system of equations the value of j is 3.
What is a system of equations?
Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.
Types of systems of linear equations
Dependent: There are innumerable solutions for the system. The same lines are shown on the equation graphs.
Independent: There is just one solution for the system. The equations' graphs come together at a single point.
Inconsistent: There is no solution for the system. The equations' graphs are parallel lines.
Here. we have
The given system of equations is:
7j-h=9
3j+h=21
we simplify the given system of equations and get
h = 7j - 9
now, put the value of h in 3j+h=21 and get
3j + (7j-9) = 21
10j = 30
j = 3
h = 12
Hence, after considering the system of equations the value of j is 3.
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In Exercises 1 and 2, graph ACDE and its image after a reflection in the given line.1. C(3, 4), D(2, -1), E(0, -5); y-axis 2. C(1,6), D(12, 2), E(7,-8); x = 8
Answers
graph CDE and its image reflection in the given line
C (3,4)
D (2,-1)
E (0,-5)
reflection line: y-axis
If we locate these three points on a graph, we will obtain the following:
now, the reflection points in the y-axis are calculated by multiplying x * -1 ,
for example: the new location for point C is C' = (3*-1 , 4) , therefore, C ' = (-3,4), following the same logic,
D(2,-1) -> D' (-2,-1)
E(0,-5) -> E' (0,-5)
notice that E does not change its location, since it is located on the y-axis, so it doesn't have a relfection.
Now, the graph with the points reflected is the following:
lassify the number as natural, whole, integer, rational, and/or irrational.
Select all terms that are correct.
Natural Whole Integer Rational Irrational
7√
1. Natural – square root of 7
2. Whole – square root of 7
3. Integer – square root of 7
4. Rational – square root of 7
5. Irrational – square root of 7
wich ones are the right ones
Answers
Square root of 7 is classified as an irrational number
What are irrational numbers?Proceeding from definition of rational numbers we say that rational numbers are real numbers that can be expressed as a fraction.
hence such numbers can have areal number in the numerator and a real number in the denominator.
Irrational numbers are the opposite of rational numbers such that when numbers cannot be expressed as fraction such number is said to irrational number.
The number asked in the question √7 is an example of irrational number. Numbers like this there decimal is usually continuous
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g(x)=4f(x)=×^2-5find (g+f)(n)
Answers
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
