Answer:
11 cars
Step-by-step explanation:
There are 20 cars in my building's parking lot, 15 cars are 4-door, then
[tex]20-15=5[/tex] cars are 2-door.
5 cars are 2-door, 4 of them are 2-door and white, then
[tex]5-4=1[/tex] car is 2-door and red.
12 cars are red, 1 car is 2-door and red, then
[tex]12-1=11[/tex] cars are 4-door and red.
(1/3) are red = 30 *1/3 = 10 are red
So...20 are white
50% are 4 door = 15 are 4 door
So....15 are 2 door
8 are 2 door and white.....so 12 are 4 door and white since we have 20 white total
And since 15 are 4 door and 12 of these are white...then 3 must be 4 door and red
ORRRRMake a two-way table as follows:
RED WHITE
2-DOOR 7 8
4-DOOR 3 12
TOTALS 10 20
So, it looks like you have 3 cars that are red and have 4 doors.
The ratio of the side lengths of two squares is 2:5. What is the ratio of the areas of the same two squares?
Answer:
4 : 25
Step-by-step explanation:
Given the ratio of sides = a : b, then
ratio of areas = a² : b²
Thus
ratio of sides = 2 : 5, then
ratio of areas = 2² : 5² = 4 : 25
Pat bounces a basketball 25 times in 30 seconds. At that rate approximately how many times will pat bounce the ball in 150 seconds?
Pat will bounce the ball 125 times in 150 seconds
Solution:
Given that,
Pat bounces a basketball 25 times in 30 seconds
To find: Number of times Pat will bounce the ball in 150 seconds
From given information,
30 seconds = 25 times
Therefore number of times ball bounces in 1 second is:
[tex]\text{1 second } = \frac{25}{30} \text{ times }[/tex]
So to find for 150 seconds, multiply both the sides by 150
[tex]150 \text{ seconds } = \frac{25}{30} \times 150 = 125 \text{ times }[/tex]
Therefore Pat will bounce the ball 125 times in 150 seconds
Answer:
125
Step-by-step explanation:
Mike wants a job as car salesmen. He receives two job offers.
• Hudson cars dealership offers Mike a salary of $2500 per month, plus a commission of
$200 on every car he sells.
• Kennedy used cars dealership offers Mike a salary of $2000 per month, plus a
commission of $250 on every car he sells.
Let T represent the total monthly earning, in dollars, and let n represent the number of cars sold in a
month. For each company, write an equation that represents the relationship between T and n.
Hudson: T = 200n + 2500
Kennedy: T = 250n + 2000
im no math teacher but i do a ton of questions like these, hope this helps
The equation for Mike job which represents the relationship between T and n for Hudson cars is $2500+$200n and for Kennedy used cars is $2000+$250n.
What is linear equation?A linear equation is the equation in which the highest power of the unknown variable is one.
Mike wants a job as car salesmen. He receives two job offers.Let T represent the total monthly earning, in dollars, and let n represent the number of cars sold in a month.
Hudson's cars dealership offers Mike a salary of $2500 per month, plus a commission of $200 on every car he sells. Then the equation for this company is,
[tex]T=2500+200n[/tex]
Kennedy used cars dealership offers Mike a salary of $2000 per month, plus a commission of $250 on every car he sells. Thus, he equation for this company is,
[tex]T=2000+250n[/tex]
Hence, the equation for Mike job which represents the relationship between T and n for Hudson cars is $2500+$200n and for Kennedy used cars is $2000+$250n.
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Help please,
I had a question like this before but got it wrong, can somebody please explain how to get the answer?
Answer:
-4,5
Step-by-step explanation:
Two burgers and one hotdog cost $4.82. At the same price, one burger and two hotdogs cost &3.70. How much does a hotdog cost?
Answer:
Step-by-step explanation:
Price of a hotdog = $0.86
What is an equation?An equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”.
For example, 2x – 5 = 13.
Here,
2x – 5 and 13 are expressions.
The sign that connects these two expressions is “=”.
Given,
2 burgers and 1 hotdog cost = $4.82
1 burger and 2 hotdogs cost = $ 3.70
The price is same
Let the price of burger be x and price of hotdog be y
then,
2x + y = 4.82 ---------(a)
x + 2y = 3.70
Multiplying 2 in above equation
2x + 4y = 7. 40 -----------(b)
Subtracting equation (a) from equation (b)
2x + 4y - (2x+y) = 7.40 - 4.82
2x + 4y -2x -y = 2.58
3y = 2.58
y = 2.58/3
y = 0.86
Price of hotdog = $0.86
Hence, a hotdog costs $0.86.
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Consider the net of a triangular prism where each unit on the coordinate plane represents four feet. If a sheet of plywood measures 4 ft x 8 ft, how many sheets of plywood will a carpenter need to build the prism?
A) 2
B) 3
C) 4
D) 5
Answer:
2 sheets of plywood will be needed.
Step-by-step explanation:
See the attached diagram.
Each three square plywood has area 1 units by 3 units = 4 feet by 12 feet = 48 feet square. {Since each unit on the coordinate plane represents four feet}
Now, the two triangular plywood has area half of a unit square area.
So, two triangular plywood has total area = 1 unit by 1 unit = 4 feet by 4 feet = 16 feet square.
Therefore, the total area of plywood required to make the triangular prism is (48 + 16) = 64 feet square.
Now, if a sheet of plywood measures 4 ft by 8 ft i.e. 32 feet square, then the carpenter will need [tex]\frac{64}{32} = 2[/tex] such sheets of plywood. (Answer)
Answer:A
Step-by-step explanation: HI
How do u add 2 3/4 + 3 3/8
Answer:
change to improper fractions first
6/8 + 6/24
make so there is a common denominator
6/8 × 3/3 = 18/24
now add
18/24 + 6/24 = 24/24 = 1
12. The results of an election for mayor are shown
at the right. Which candidate received the
most votes and which received the least votes?
DATA
Candidate
Leonard Hansen
Margaret O'Connor
Jillian Garcia
Number of Votes
12,409
12,926
12,904
Answer:
Assuming the group of the candidates is ordered the same way as the votes they received, Margaret O'Conner received the MOST votes, at 12,926, while Leonard Hansen received the LEAST votes, at 12,409.
Jackson is working two summer jobs, landscaping and clearing tables. He must work
no less than 14 hours altogether between both jobs in a given week. Write an
inequality that would represent the possible values for the number of hours
landscaping, l, and the number of hours clearing tables, c, that Jackson can work in a
given week.
The inequality l + c ≥ 14 accurately represents the minimum total hours Jackson must work in both his jobs, landscaping and clearing tables, in a week.
Explanation:The subject of this question is Mathematics, more specifically it involves the topic of inequalities. The grade level of this question would be high school as it deals with algebraic concepts.
The inequality that represents the number of hours that Jackson can work in a given week in landscaping (l) and clearing tables (c) would be l + c ≥ 14. This inequality allows for the total number of hours worked to be equal to or more than 14, as stipulated in the conditions.
This represents the total amount of hours Jackson can work in both jobs simultaneously. This inequality is valid as long as he works at least 14 hours, in total, from both jobs.
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Karli and her friend can paint 6/7 of a picture in 3/14 of an hour. How many pictures can they paint in a full hour?
Answer:
4 pictures
Step-by-step explanation:
(6/7)/(3/14)=x/1
cross product
3/14*x=6/7*1
3/14x=6/7
x=(6/7)/(3/14)
x=(6/7)(14/3)
x=(6/1)(2/3)
x=12/3
x=4
The number of pictures which Karli and her friend can paint in a full hour is equal to 4 pictures.
What is algebra ?
Algebra is a branch of mathematics that deals with various symbols and the arithmetic operations such as division , multiplication , etc.
It is given that Karli and her friend can paint 6/7 of a picture in 3/14 of an hour.
Let's assume they can paint x number of pictures in a full hour.
So , the fraction by dividing 6/7 by 3/14 can be written equal to x .
i.e.,
[tex]\frac{6/7}{3/14}[/tex] = x
We need to do the cross product here :
[tex]\frac{3}{14}[/tex] × x = [tex]\frac{6}{7}[/tex]
or
x = ([tex]\frac{6}{7}[/tex]) ÷ ([tex]\frac{3}{14}[/tex])
We know that when dividing two fractions we need to change the division sign to multiplication sign by inverse the fraction value right to the division sign i.e.,
x = ([tex]\frac{6}{7}[/tex]) × ([tex]\frac{14}{3}[/tex])
x = 84 / 21
x = 4
Therefore , the number of pictures which Karli and her friend can paint in a full hour is equal to 4 pictures.
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A fitness club has two options, one for members and one for nonmembers. Members pay a one-time registration fee of $12 plus $8 per gym visit. Nonmembers pay $10 per gym visit.
Upload a graph
Type the system of equations you used to graph the solutions. Use C for the cost of the two payment options and n for number of visits.
After how many gym visits is the payment for the member option more beneficial than the payment for the nonmember option? Explain how you determined your answer.
Answer:
Part 1) The system of equations is
[tex]C=8n+12[/tex] ----> equation 1
[tex]C=10n[/tex] ----> equation 2
Part 2) The graph in the attached figure
Part 3) The number of gym visits must be greater than 6
Step-by-step explanation:
step 1
Find the system of equations that represent the situation
Let
C ----> the total cost in dollars
n ---> the number of gym visits
we know that
The linear equation in slope intercept form is equal to
[tex]C=m(n)+b[/tex]
where
m is the slope or unit rate of the linear equation
b is the C-intercept or initial value of the linear equation
First payment option ---> For Members
we have that
The slope or unit rate is equal to [tex]m=\$8\ per\ gym\ visit[/tex]
The C-intercept or initial value is [tex]b=\$12[/tex] --->one-time registration fee
substitute
[tex]C=8n+12[/tex]
Second payment option ---> For Non-Members
we have that
The slope or unit rate is equal to [tex]m=\$10\ per\ gym\ visit[/tex]
The C-intercept or initial value is [tex]b=\$0[/tex]
substitute
[tex]C=10n[/tex]
we have
[tex]C=8n+12[/tex] ----> equation 1
[tex]C=10n[/tex] ----> equation 2
Part 2) Upload a graph
using a graphing tool
The graph in the attached figure
Part 3) After how many gym visits is the payment for the member option more beneficial than the payment for the nonmember option?
we know that
If the payment for the member option is more beneficial than the payment for the nonmember option, then the cost for the member option is less than the cost for the nonmember option
so
The inequality that represent this situation is
[tex]8n+12 < 10n[/tex]
solve for n
subtract 8n both sides
[tex]12 < 10n-8n[/tex]
[tex]12 < 2n[/tex]
Divide by 2 both sides
[tex]6 < n[/tex]
Rewrite
[tex]n > 6[/tex]
therefore
The number of gym visits must be greater than 6
For the function ƒ(x) = x2 – 4, find the value of ƒ(x) when x = 6.
Answer:8
Step-by-step explanation:They said f(x)=x2–4 and they said find the value of f(x) when x=6
When x=6 you equate the value of x into the question
F(6)=6*2–4=8
Therefore the value of f(x) is 8
Line 1 thru (3,2) and (5,-1)
Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slopw and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (3, 2) and (x₂, y₂ ) = (5, - 1)
m = [tex]\frac{-1-2}{5-3}[/tex] = - [tex]\frac{3}{2}[/tex], thus
y = - [tex]\frac{3}{2}[/tex] x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (3, 2), then
2 = - [tex]\frac{9}{2}[/tex] + c ⇒ c = 2 + [tex]\frac{9}{2}[/tex] = [tex]\frac{13}{2}[/tex]
y = - [tex]\frac{3}{2}[/tex] x + [tex]\frac{13}{2}[/tex] ← equation of line
Answer:
The equation of the line passing through the given points is
[tex]y=-\frac{3}{2}x+\frac{13}{2}[/tex]
Step-by-step explanation:
GIven two points are (3,2) and (5,-1)
To find the equation of the line passing through these two points
Let [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] be the two points (3,2) and (5,-1) respectively
Using the two points formula for finding slope:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m=\frac{-1-2}{5-3}[/tex]
[tex]m=\frac{-3}{2}[/tex]
Therefore [tex]m=-\frac{3}{2}[/tex]
By using formula:
[tex]y=mx+c[/tex]
Here Let (x,y) be (3,2)
[tex]y=mx+c[/tex]
[tex]2=-{\frac{3}{2}}\times 3+c[/tex]
[tex]2=\frac{-9}{2}+c[/tex]
[tex]c=\frac{9}{2}+2[/tex]
[tex]c=\frac{9+4}{2}[/tex]
[tex]c=\frac{13}{2}[/tex]
Therefore substitute values of m and c in
[tex]y=mx+c[/tex]
[tex]y=-\frac{3}{2}x+\frac{13}{2}[/tex]
Therefore the equation of the line passing through the given points is
[tex]y=-\frac{3}{2}x+\frac{13}{2}[/tex]
pls help fast 25 points! 60% of 45 =
Answer:
27
Step-by-step explanation:
Two linear functions are shown below which function has the greater rate of change
Answer:
On this case if we analyze both slopes, we see that function 2 has a greater rate of change because have a slope greater on absolute value than the slope for Function 1 (|-5|>|4|). No matter if the sign is positive or no we are analyzing the rate of change and for this case we need to use the absolute value to find the solution.
Step-by-step explanation:
Assuming the following two functions:
Function 1: y = 4x + 8
Function 2:
x y
2 20
4 10
6 0
We can find the slope for the second function like this:
[tex]m =\frac{10-20}{4-2}=-5[/tex]
And in order to find the intercept we can use any point for example (2,20) and we got:
[tex]20 =-5(2) +b[/tex]
And then [tex] b=30[/tex]
So our function 2 is given by: [tex] y =-5x +30[/tex]
On this case if we analyze both slopes, we see that function 2 has a greater rate of change because have a slope greater on absolute value than the slope for Function 1 (|-5|>|4|). No matter if the sign is positive or no we are analyzing the rate of change and for this case we need to use the absolute value to find the solution.
Jane evaluates x squared minus 3 x + 5 for x = negative 2 below.
Step 1: (negative 2) squared minus 3 (negative 2) + 5
Step 2: Equals negative 4 + 6 + 5
Step 3: Equals 7
What, if any, was Jane’s mistake?
Jane made no mistakes.
Jane incorrectly evaluated (negative 2) squared in step 2.
Jane incorrectly added the terms in step 3.
Jane incorrectly substituted in x = negative 2 in step 1.
Answer:
B On 2020 edge
Step-by-step explanation:
What is the period of the function?
Identify the period of a periodic function from its graph. π 2π 4π 8π
PLEASE HURRY
Answer:
4π
Step-by-step explanation:
Period is whenever a wave repeats itself. I highlighted the period.
The Period of the given function is 0 to 4π.
What is Period of Function?The time interval between two waves is known as a Period whereas a function that repeats its values at regular intervals or periods is known as a Periodic Function.
Here, graph starts from 0 and goes down. After π our graph starts increasing and acheive maximum at 3π and then start coming down to y = 0 at 4π.
It means that from 0 to 4π graph complete its one cycle and in the same trend it start repeating again.
Thus, the Period of the given function is 0 to 4π.
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Which equation in slope-intercept form represents a line that is parallel to y=−4x−5 and passes through the point (0,0)?
y=4x−7
y=4x−9
y=−4x
y=−4x−7
y=−14x−5
Answer:
[tex]\displaystyle y = -4x[/tex]
Step-by-step explanation:
0 = 0 ± b
[tex]\displaystyle 0 = b \\ \\ y = -4x[/tex]
* Parallel Lines have SIMILAR RATE OF CHANGES [SLOPES], so −4 remains the way it is.
I am joyous to assist you anytime.
Heyo! ;D
The equation in slope-intercept form that represents a line that is parallel to y = -4x - 5 and passes through the point (0,0) would be Option C) y = -4x.
Hope this helps! If so, please lmk! Tysm!
A student is solving a system of equations by substitution and comes up with the solution -3=2. Assuming that she solved the problem correctly, which of the following can be said about this system of equations?
A) the system has exactly 1 solution.
B) the system has exactly 2 solutions.
C) the system has infinitely many solutions.
D) the system has no solution.
HELLLP PLZZZZZ
Answer:
D) the system has no solution.
Step-by-step explanation:
A student is solving a system of equations by substitution and comes up with the solution -3=2.
So, the unknown variables are canceled out and there are only numbers in the equation but -3 ≠ 2.
If we assume that she solved the problem correctly, then there will be no solution for that system of equations because there is no variable remaining in the final equation to solve for. (Answer)
1) a, = an-1-9
a, = 25
Answer:
an-1-9
25n-1-9
25n-10=0
25n=0+10
25n=10
divide both sides by 25
25n/25 =10/25
n=2/5
Step-by-step explanation:
Answer:
n=1.4
Step-by-step explanation:
given a=25
a=an-1-9..............(1)
put a=25 in equ (1)
25=25n-1-9
25=25n-10
25n=25+10=35
n=[tex]\frac{35}{25}[/tex]=1.4
n=1.4 answer
I need to know the answers for a, b, and c for 23.
Answer:
Step-by-step explanation:
m∠1 = 50°
m∠2 = 88°
Step-by-step explanation:
Each triangle's angles have to add up to 180°. Use supplementary angles theorem to help solve.
Answer:
m∠1 = 50°
m∠2 = 88°
Step-by-step explanation:
Each triangle's angles have to add up to 180°. Use supplementary angles theorem to help solve.
Writing an equation of the form A/x+B)C to solve a word probl...
Trey has a part-time job and gets pald the same amount each hour. For each hour he works, he puts $2 aside for his mom. Trey works 7 hours a day and the
total amount he keeps each day is $56. How much does he get paid each hour?
(a) Write an equation that could be used to answer the
question above. First, choose the appropriate form. Then,
fill in the blanks with the numbers 2, 7, and 56. Leth
represent the amount (in dollars) Trey gets paid each hour.
(b) Solve the equation in part (a) to find the amount (in
dollars) Trey gets paid each hour.
h =
Answer:
(a) The equation is [tex]7h-2=56[/tex].
(b) Trey gets approximately $8.29 for each hour of work.
Step-by-step explanation:
Given:
Number of hours Trey works = 7
Amount of money he put aside for mom = $2
Total Amount he keeps each day = $56
We need to find the amount he gets for each hour.
Let 'h' represent the amount (in dollars) Trey gets paid each hour.
Solving for part (a).
We need to write the equation to find the amount he gets paid for each hour.
Now we can say that;
Total Amount he keeps each day is equal to Number of hours Trey works multiplied by the amount he gets paid for each hour minus Amount of money he put aside for mom.
framing in equation form we get;
[tex]7h-2=56[/tex]
Hence the equation is [tex]7h-2=56[/tex].
Solving for part (b).
we need to solve the above equation to find the amount he gets paid for each hour.
On solving the equation we get;
Adding both side by 2 we get
[tex]7h-2+2=56+2\\\\7h=58[/tex]
Now Dividing both side by 7 using Division Property we get;
[tex]\frac{7h}{7} = \frac{58}{7}\\\\h \approx \$8.29[/tex]
Hence Trey gets approximately $8.29 for each hour of work.
Mixed number equations that equal 10.
Please hurry.
Answer:
Mixed number equation equals to 10=[tex]9\frac{9}{9}[/tex]
Step-by-step explanation:
Here we have to find mixed number equation that equal 10,
Let, x=10 ------------(equation 1)
Now multiplying both side of equation 1 by 10 we get,
[tex]x\times 10=10\times 10[/tex]
[tex]10x=100[/tex] ------------------(equation 2)
Now by subtracting equation 1 from equation 2 we get,
[tex]10x-x=100-10[/tex]
[tex]9x=90[/tex]
[tex]\therefore\ x=\frac{90}{9}[/tex] ------------------(equation 3)
Equation 3 can be written as,
[tex]x=9\frac{9}{9}[/tex]
Since, [tex]9\frac{9}{9} [/tex]
[tex]= \frac{(9\times 9)+9}{9}[/tex]
[tex]=\frac{81+9}{9}[/tex]
[tex]=\frac{90}{9}[/tex][/tex]
[tex]\therefore 9\frac{9}{9}=\frac{90}{9}[/tex]
Therefore mixed number equation that equals 10=[tex]9\frac{9}{9}[/tex]
Cab companies often charge a flat fee for picking someone up and then charge an additional fee per mile driven. Pick a U.S. city and research the rates of two
different cab companies in that city. Find companies that charge different amounts per mile and have different flat fees. If you have trouble finding this information for two companies, you can make up what you think would be reasonable prices for a cab's flat rate and a cab's rate per mile.
Answer:
1. New York City: The initial charge is $ 2.50 plus $ 0.50 per 1/5 mile when traveling above 12 mph or per 60 seconds in slow traffic or when the vehicle is stopped. There are other surcharges for overnight, rush hour or congestion.
2. Boston: First 1/7 Mile: $2.60 and each 1/7 Mile thereafter: $0.40.
3. Houston: First 1/11 mile $2.80 , each additional 1/11 mile $0.20 . Rate per mile after first mile $2.20 and wait time per minute $0.40.
Step-by-step explanation:
Normally, there's a standard fare for each city, so for answering the question we picked three well-known cities for comparing the fares.
1. New York City: The initial charge is $ 2.50 plus $ 0.50 per 1/5 mile when traveling above 12 mph or per 60 seconds in slow traffic or when the vehicle is stopped. There are other surcharges for overnight, rush hour or congestion.
2. Boston: First 1/7 Mile: $2.60 and each 1/7 Mile thereafter: $0.40.
3. Houston: First 1/11 mile $2.80 , each additional 1/11 mile $0.20 . Rate per mile after first mile $2.20 and wait time per minute $0.40.
A spinner is divided into three equal parts that are colored different. The colors are red white and blue
Mr. Edwards hired a new employee to work in his bakeshop. In one hour, this
employee burned 439 chocolate chip cookies, which represented 25% of all the
cookies the employee burned in that day. How many cookies did the new employee
burn in the course of the day?
To find the total number of cookies burnt in the day, which is the whole, we would use the formula 'whole = part / percentage', or 'whole = 439 / 0.25', which gives us 1756 cookies.
Explanation:The subject of this question is Mathematics, specifically it's a problem on percent. The problem states that 439 cookies represented 25% of all the cookies the employee burnt that day. The question asks us to find the total number of cookies burnt by using this information.
When trying to find the whole from a percent, you can use the formula: whole = part / percentage. In this case, 'part' refers to the 439 cookies, and 'percentage' is 25% expressed as a decimal (0.25).
Using the formula, we find that the total (whole) number of cookies burnt is: whole = 439 / 0.25 = 1756 cookies. So, the new employee burnt 1756 cookies in the course of the day.
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You and your friend are selling magazine subscriptions. You sell 8 fewer magazine subscriptions than your friend. Together you sell 42 magazine subscriptions
The question is incomplete, here is the complete question:
You and your friend are selling magazine subscriptions. You sell 8 fewer magazine subscriptions than your friend. Together you sell 42 magazine subscriptions. Write a system of linear equations that represents this situation.
The system of linear equations that represents this situation is:
x + y = 42
x - y = 8
Step-by-step explanation:
To solve the problem assume that
x represent the number of magazine subscriptions that your friend selly represents the number of magazine subscriptions that you sell∵ Your friend sells x magazine subscriptions
∵ You sell y magazine subscriptions
∵ Together you sell 42 magazine subscriptions
∴ x + y = 42 ⇒ (1)
∵ You sell 8 fewer magazine subscriptions than your friend
∵ Your friend sells x magazine subscriptions
∵ You sell y magazine subscriptions
- That means y = x - 8
∴ y = x - 8
- Add 8 for both sides
∴ 8 + y = x
- Subtract y from both sides
∴ 8 = x - y
- Switch the two sides
∴ x - y = 8 ⇒ (2)
The system of linear equations that represents this situation is:
x + y = 42
x - y = 8
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Round the fraction to the nearest one-half. Start Fraction 14 over 27 End Fraction A. 0 B. one-half C. 1
To round the fraction 14/27 to the nearest one-half, the answer would be 0 (choice A).
Explanation:To round the fraction to the nearest one-half, we need to determine if the fraction is closer to zero, one-half, or one. Start by identifying which two one-half intervals the fraction falls between: 13/27 (closer to zero) and 15/27 (closer to one-half). As 14/27 is closer to 13/27, the answer is A. 0.
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I have been asked this question and I substituted the value of x in f with g(x), and rearranged the equality but is incorrect.
Answer:
if fg(x)=6x+q
then f(gx) =6x+q
3(px+4)+p =6x+q
3px+12+p = 6x+q
3px+p = 6x+q-12
make p the subject
p( 3x+1) = 6x+q-12
p= (6x + q -12 )/ 3x +1
Answer:
p = 2 and q = 14
Step-by-step explanation:
f(g(x)) = 3(px + 4) + p
f(g(x)) = 3px + 12 + p
6x + q = 3px + 12 + p
The trick here is to equate the coefficients.
6 = 3p and q = 12 + p
p = 2 and q = 14
Mr. Harris is packaging items to give to his students. He has 48 pencils and 30 notebooks. He wants each package to contain the same number of pencils and the same number of notebooks.
Answer:
The maximum number of packages that can be made with each package have same number of each item is = 6
Step-by-step explanation:
Given:
Mr. Harris has 48 pencils and 30 notebooks.
To find the number of packages he can make with each package have same number of each item.
Solution:
Number of pencils = 48
Number of notebooks = 30
In order to find the number of packages he can make with each package have same number of each item, we will find the greatest common factor of the given numbers.
To find the G.C.F., we will list down the prime factors of each.
[tex]48=2\times 2\times 2\times 2\times 3[/tex]
[tex]30=2\times 3\times 5[/tex]
We find that the G.C.F. = [tex]2\times 3[/tex] = 6
Thus, the maximum number of packages that can be made with each package have same number of each item is = 6