The solution to the following functions are 1) 6x5-3x4, 3x4+1, 6x5-3x4, 3x4 / (2x-1), 2)(x-1)/x3, (x-1)/x2 - 1/x, (x-1)/x3, x-1
What are functions?The relationship between two sets of numbers is described mathematically by a function. It is a mathematical equation that assigns a unique output value to each input value inside a specific domain. Functions are frequently expressed by a letter, such as F(x) = 3x+ 4 or g(x), where the letter indicates the function and the input value is represented by the variable x.
Functions can be either linear or nonlinear, and they can have a single or numerous outputs for each value of the input. They are frequently employed to simulate real-world situations and generate predictions based on available information. Functions can be graphed on a coordinate plane to visualise their behavior, and they can be combined or transformed using various mathematical operations.
How to solve?
1)a. (fg)(x) = (3x4)(2x-1) = 6x5-3x4
b. (f-g)(x) = (3x4) - (2x-1) = 3x4+1
c. (f *g )(x) = (3x4) * (2x-1) = 6x5-3x4
d. (f/g) (x) = (3x4) / (2x-1) = 3x4 / (2x-1)
2)a. (fg)(x) = (x-1/x2) * (1/x) = (x-1)/x3
b. (f-g)(x) = (x-1/x2) - (1/x) = (x-1)/x2 - 1/x
c. (f *g )(x) = (x-1/x2) * (1/x) = (x-1)/x3
d. (f/g) (x) = (x-1/x2) / (1/x) = (x-1)/x2 / (1/x) = (x-1)/x2 * x = x-1
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After a nowball fight, Nathan wanted to warm up with a cup of hot chocolate. He decided to make enough to hare with hi friend. Firt, he heated 6 cup of milk and 1 pint of cream in a large pot. Then, he tirred in 4 cup of melted chocolate. How many cup of hot chocolate did Nathan make?
The number of cups of hot chocolate drink Nathan made is 12 cups.
According to the given information
Nathan made how many glasses of hot chocolate?number of milk cups 6 cups cooked by Nathan
4 cups of melted chocolate equals the number of cups.
Total number of creams = 1 PINT
Pint to cup conversion: 1 pint = 2 cups
Total number of cups of hot chocolate that were made by nathan
= Cups of milk heated + cups melted + number of cream
As a result, Nathan prepared 12 cups of hot chocolate.
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Question 7 - 5 Points
Dec 18, 7:12:35 PM
Santiago finds some dimes and quarters under the couch cushions. How much money
(in dollars) does he have if he has 4 dimes and 7 quarters? How much money (in
dollars) does he have if he has a dimes and y quarters?
Answer:
Step-by-step explanation:
4x+7y=2.15
a dime is worth 10 cents each and because there are 4 dimes then there are 40 dimes. a quarter is worth 25 cents 4 quarters is a dollar, there are 7 quarters, minus 4, your left with 3 quarters so you have $1.75 of quarters but then you add .40 so now you have 2.15. So Santiago has $2.15 dollars.
x+y=2.15
For the 2nd question I think that it is asking a question and I think that this might be the answer but i'm not sure...if wrong I'm sorry.
There are 35 questions total that will be posted in mathematics as this is Algebra I!
Whoever answers correctly and with an explanation will receive Brainliest when the option shows up on my end!
PLEASE ANSWER ASAP!!
Answer: x=5
Step-by-step explanation:
Answer:
(x - 1)² = 16
Step-by-step explanation:
x² - 2x - 15 = 0
x² - 2x + 1 = 15 + 1
(x - 1)² = 16
4. The Johnsons' bill at a restaurant is $124.00. How much money should the Johnsons leave if they plan to tip their waiter 15%?
Answer:
142.6
Step-by-step explanation:
100% + 15% = 115%
115÷100 = 1.15
1.15 x 124 = 142.6
Hope that helped
Prove that tan(A+B)
cot(A−B)
=
2−2
2−2�
Triagonometric function tan(A+B)/cot(A−B) is tan²A-tan²B/1-tan²Atan²B
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Given,
tan(A+B)/cot(A-B)
tan(A+B)/1/tan(A-B)
(tanA+tanB/1-tanAtanB)/1/(tanA-tanB/1+tanAtanB)
tanA+tanB/1-tanAtanB)×tanA-tanB/1+tanAtanB
We know algebraic identity
(a+b)(a-b)=a²-b²
(tanA+tanB/1-tanAtanB)×(tanA-tanB/1+tanAtanB)
tan²A-tan²B/1-tan²Atan²B
Hence, triagonometric function tan(A+B)/cot(A−B) is tan²A-tan²B/1-tan²Atan²B
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Problem Situation: Ike has $126 in his bank account. He gets $20 for his birthday. He also has a part-time job that pays $8 per hour. How many hours will he need to work to have $250 in his bank account?
Choose the equation that correctly models the situation. The letter h represents the hours Ike will need to work.
(250−126)h=20+8
126+20+8+250=h
126+20+8h=250
250+126+20=8h
Answer:
126+20+8h=250
Step-by-step explanation:
A lighthouse is 160 feet tall. A scale model of the lighthouse has a scale of 1 in: 8 ft. How tall is the model of the lighthouse in inches?
Answer:
The Answer is 20 inches tall
Andrew invet $200 into an account with a 2. 9% interet rate that i compounded emiannually. How much money will he have in thi account if he keep it for 5 year? Round your anwer to the nearet dollar
Andrew will have $251.91 in his account after 5 years, assuming he does not add or withdraw any money from the account and that interest is compounded semiannually at a rate of 2.9%.
What Does an Interest Rate Mean?The fee that a lender assesses on a borrower is known as the interest rate, which is expressed as a percentage of the principal, or the loaned amount. Usually, the annual percentage rate (APR), which is how loans' interest rates are expressed, is indicated (APR).
What is the process of an interest rate?Once your loan is fully repaid, interest will have an impact on the overall cost you pay. For instance, if the interest rate on a $100 loan is 5%, you will have to pay the lender $105 in order to repay the money. $5 will be profit for the lender.
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would somebody be nice enough to help me with this? i’m confused
The triangles ΔPQR ~ ΔPXY are similar by using the AA test for the similarity of triangles.
What is the Angle-Angle similarity theorem of triangles?
The AA Similarity Theorem states: If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
In the given figure,
In ΔPQR and ΔPXY
∠P ≅ ∠P ----- Common Angle
∠PQR ≅ ∠PXY ----Corresponding angles.
So, ΔPQR ~ ΔPXY -----(AA test)
Hence, the triangles ΔPQR ~ ΔPXY are similar by using the AA test for the similarity of triangles.
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Annabelle kicks a football. Its height in feet is given by h = -16t² + 96t
where t represents the time in seconds after kick. What is the football's greatest height?
The kicked football is an example of a projectile. The football's greatest height is 144 m.
What is the projectile?A projectile is any object that is launched into space and moves under the influence of gravity and air resistance. A kicked football is a good example of a projectile. Given the height of the kicked football to be:h = -16t² + 96tThus, the height of the kicked football is a function of time taken. So that differentiating the equation of the height with respect to time, we have;0 = -32t + 9632t = 96t = [tex]\frac{96}{32}[/tex] = 3
Thus the greatest height of the kicked football is attained when the time is 3 seconds.
Thus,h = -16t² + 96t = -16 (3)² + 96 (3) = -144 + 288h = 144
Therefore the football's greatest height is 144 m.
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149 cars are waiting to take a ferry across the channel. Each ferry can only hold 18 cars. How many trips will it take to get all the cars across?
5
8
6
9
Answer: the answer is 8
Step-by-step explanation:
The Answer is: 8
Simply divide 149 by the numbers you see,
The choices below are data sets. In the choices, w is a constant. Each choice has the same mean.
Which choice has the greatest standard deviation?
A.)
w-2, w-1, w, w + 1, w+ 2
B.)
w-2, w-2, w, w + 2,w+2
C.)
w-3, w-1, w, w + 1, w+3
D.)
w-3, w, w, w, w +3
Answer:
C)w-3, w-1, w, w + 1, w+3
Step-by-step explanation:
I'm not great with standard deviation, but I know that the greater the standard deviation, the more spread out the data is.
C) is the correct answer, the data points do not repeat and are spread out more than A.
You can check this by calculated each standard deviation (but only if you are crazy ;] )
Hope this helps,
:]
Diego is also training for the tournament. The graph shows the relationship between the time in the distant he rows how many meters does Diego Roper minute
Diego rows 300 meters per minute
How to determine the the number of rows per minuteInformation given in the question include
The graph shows the relationship between the time in the distant, Diego rows
The data is plotted as a linear function
A linear function consists of functions where the variables has exponents of 1. The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
The slope is represented as m, The slope by definition is the change of the output values to the input values
the slope, m calculating using the points on the graph (1, 300) and (2, 600)
m = (y₀ - y₁) / (x₀ - x₁)
m = (600 - 300) / (2 - 1)
m = 300 / (1)
m = 300
The number of meters Diego rows per minute is solved to be 300
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A company manufactures water bottles. The list below describes the number of water bottles manufactured in three months.
• February: 4, 100 water bottles
• March: 7% more water bottles in February
• April: 500 more water bottles in March
What is the percent change, to the nearest percent, in the number water bottles the company manufactured from February to April. show your work
Answer:
19%
Step-by-step explanation:
You want the change from February to April if 4100 bottles were manufactured in February, 7% more were manufactured in March, and 500 more were manufactured in April.
ChangeThe change from February to March is given as 7%.
The change from March to April is 500 bottles. In terms of the February quantity, this is ...
500/4100 × 100% ≈ 12.2%
Then the total of changes from February to April is ...
change = 7% +12.2% = 19.2% ≈ 19%.
The number of bottles manufactured increased by about 19% from February to April.
__
Additional comment
When working with percentages, one must always be aware of the base amount—what it is that represents 100%. Here, we know the 7% number for March uses the February value as its base.
Since we want a percent change from the February base, we can use that same base to find the percent difference from March to April. Then the total difference from February is the difference to March plus the difference from March to April.
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1) Is the pattern linear? If yes, state the initial value and constant rate
2) Is the pattern discrete or continuous? How can you tell
1. It can be piecewise linear; from x = 1 to x = 4, the y-value increases by the same amount each time. From x = 0 to x = 1, the y-value stays the same.
However, if it is supposed to be a single function, it would be non-linear because it changes slope.
2. It is discrete because there is no data between the points.
what is y-3=5(x-1) in slope intercept form?
Answer:
The answer is y = 5x - 2
Step-by-step explanation:
Distribute 5 through the parentheses:
y - 3 = 5x - 5
Move the constant to the right-hand side and change its sign:
y = 5x - 5 + 3
Calculate the sum:
y = 5x - 2
A type of green paint is made by mixing 2 cups of yellow with 3.5 cups of blue.
A. Find a mixture that will make the same shade of green but a smaller amount.
B. Find a mixture that will make the same shade of green but a bigger amount.
C. Find a mixture that will make the different shade of green that is bluer.
D. Find a mixture that will make the different shade of green more yellow.
(Please provide a detailed expiation/step-by-step).
To determine a mixture that will make the same shade of green but a smaller amount, we can divide both the yellow and blue amounts by the same number.
How to find a mixture that will make the same shade of green but a smaller amount?To solve this problem, we can use the principle of proportionality, which states that if two ratios are equal, then the quantities they represent are proportional.
A. To find a mixture that will make the same shade of green but a smaller amount, we can divide both the yellow and blue amounts by the same number. For example, if we divide both amounts by 2, we get 1 cup of yellow and 1.75 cups of blue. This will create a smaller amount of the same shade of green.
B. To find a mixture that will make the same shade of green but a bigger amount, we can multiply both the yellow and blue amounts by the same number. For example, if we multiply both amounts by 2, we get 4 cups of yellow and 7 cups of blue. This will create a larger amount of the same shade of green.
C. To find a mixture that will make a different shade of green that is bluer, we can increase the amount of blue relative to the amount of yellow. For example, we could use 2 cups of yellow and 4 cups of blue, which would create a green that is bluer than the original shade.
D. To find a mixture that will make a different shade of green that is more yellow, we can increase the amount of yellow relative to the amount of blue. For example, we could use 3 cups of yellow and 2 cups of blue, which would create a green that is more yellow than the original shade.
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0=x2+18x+45
I need help with this place
The factorise quadratic equation x² + 18x + 45 = 0 is (x + 3)(x + 15)
How to factorise quadratic equation?A quadratic equation is a polynomial equation that contains the second degree, but no higher degree, of the variable.
Therefore, quadratic equation can be represented as follows:
ax² + bx + c
where
a, b and c are constantHence, let's factorise x² + 18x + 45 = 0
x² + 18x + 45 = 0
Let's find the two numbers to add to get 18 and multiply to get 45
Therefore, the numbers are 3 and 15
x² + 18x + 45 = 0
x² + 3x + 15x + 45 = 0
x(x + 3) + 15(x + 3) = 0
(x + 3)(x + 15) = 0
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A school sold 461 tickets for the school play. Student tickets cost $3 and adult tickets cost $4. Ticket sales totaled $1624.
Part A. Write and solve a system of equations to model this situation.
Part B. Then explain the meaning of your solution.
Total 241 adult ticket and 220 student ticket are sold.
What is system of equation ?system of equations, orsimultaneous equations, In algebra, two or more equations to be solved together (i.e., the solution must satisfy all the equations in the system). For a system to have a unique solution, the number of equations must equal the number of unknowns.
a + s = 461 or s = 461 -a
Value of student tickets sold = s × 3 = 3 × (461-a)
Value of adult ticket sold = 4 a
Summed they total 1624
System of equations :
s = 461-a3 (461-a) + 4a
= 16241383 -3a +4a
= 1624a
= 241
then s = 461 -a = 220 ticket
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i need help fast pleaseeeeeeeeeee :) (:()
Answer:
translation down 2 and reflection across x axis
Find the product of 7/30? multiplied by 5/14 simplify your answer
Answer:
Should be 1/12
Step-by-step explanation:
7/30x5/14
Simply multiply the numerators and denominators separately:
5/14× 7/30 = 5 × 7/14 × 30 = 35/420
After reducing the fraction, the answer is
1/12
do upperclassmen (seniors and juniors) spend more money on alcoholic beverages then underclassmen (freshman and sophomores)? what type of inference is this?
The type of interference is this :
Comparing proportions from 2 independent samples
Given,
In the question:
Complete question is this:
Do upperclassmen (Seniors and Juniors) spend more money on alcoholic beverages then underclassmen (Freshman and Sophomores)? What type of inference is this?
a. Comparing proportions from 2 independent samples
b. One proportion
c. Comparing means from dependent samples
d. Comparing means from 2 independent samples
e. Comparing proportions from dependent samples
f. One mean
Now, According to the question:
Hence, The type of interference is this :
a. Comparing proportions from 2 independent samples
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The formula K=1/2mv² is used to find the kinetic energy of an object in
motion using its mass, m, and its velocity (speed), v. Solve the equation
for the mass, m.
What is the Equation?
Is it: m = K/2v²
Answer:
m = 2k/v²
Step-by-step explanation:
K = ½mv²
multiply both sides by 2
2 × k = ² × ½mv²
2k = mv²
divide both sides by (v²)
m = 2k/v²
i hope this helped
Which triangle is the original image and which triangle was the dilation? Explain how you know?
Answer:
ABC is the original
Step-by-step explanation:
The scale factor is 1/2 which means that the triangle would get 2 times smaller. Therefore, triangle ABC is the original because it is the bigger one.
Rick bought 5 yogurt bars at a snack shop. Each yogurt bar cost $1.80. Complete the table to show the price of 2, 3, 4, and 5 yogurt bars.
By using multiplication, it can be calculated that
The complete table is
Number of yogurt bars Cost of yogurt bars ($)
1 1.80
2 3.60
3 5.40
4 7.20
5 9.00
What is multiplication?
Repeated addition is called multiplication. Multiplication is used to find the product of two or more integers.
This is a word problem on multiplication
Cost of 2 yogurt bars = $1.80 [tex]\times[/tex] 2 = $3.60
Cost of 3 yogurt bars = $1.80 [tex]\times[/tex] 3 = $5.40
Cost of 4 yogurt bars = $1.80 [tex]\times[/tex] 4 = $7.20
Cost of 5 yogurt bars = $1.80 [tex]\times[/tex] 4 = $9.00
So the table is
Number of yogurt bars Cost of yogurt bars ($)
1 1.80
2 3.60
3 5.40
4 7.20
5 9.00
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PLEASE HELP!!!!!! It’s algebra
When the cost of a gallon of milk increases from $2.81 to $3.48 over a period of 10 years the annual inflation rate is 2.15 percent.
What is a annual inflation rate?
A percentage is used to represent the inflation rate. For instance, a yearly inflation rate of 2% indicates that the cost of products and services as a whole has increased by 2%. As an illustration, a product that cost $10 last year will cost $10.20 this year.
Here, we have
Given
The cost of the gallon of milk earlier was $2.81
The cost of a gallon of milk now is $3.48.
The total time period is 10 years.
r = (F/P)ⁿ⁻¹ - 1
r = {(3.48/2.81)^(1/10) - 1}×100
r = {(1.238)^(1/10) - 1}×100
r = 0.0215 ×100
r = 2.15
Hence, when the cost of a gallon of milk increases from $2.81 to $3.48 over a period of 10 years the annual inflation rate is 2.15 percent.
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The typing rate per minute of a person who can type 225 words in 7.5 minutes.
Answer: 30 wpm.
Step-by-step explanation:
Do 225 divided by 7.5 and you get 30.
30 words in one minute.
1) Triangle ABC has vertices A(6,2), B(3,4), and C (2,8). If the triangle is rotated
counterclockwise, what are the coordinates of the image A'B'C'?
90°
2) Which transformation(s) preserve congruence?
3) Which transformation(s) produce similar figures that are not congruent?
1) image of the coodinate A(6,2) be A'(-2,6)
image of the coodinate B(3,4) be B'(-4,3)
image of the coodinate C(2,8) be C'(-8,2)
2) A transformation that preserves congruence is called an isometry
3) A dilation would produce a similar figure.
What do you mean by transformation?
Transformation is a collective term for four specific ways of manipulating the shape and position of points, lines, or geometric figures. The original shape of the object is called the master, and the final shape and position of the object is the image under transformation. There are four types of transformations in mathematics
1) When rotating a point 90 degrees counterclockwise about the origin our point A(x,y) becomes A'(-y,x).
Therefore, image of the coodinate A(6,2) be A'(-2,6)
image of the coodinate B(3,4) be B'(-4,3)
image of the coodinate C(2,8) be C'(-8,2)
2) A transformation that preserves congruence is called an isometry. In other words, a transformation in which the Image and Pre-Image have the same side lengths and angle measurements. Translations, reflections, and rotations are isometries.
3) A dilation would produce a similar figure.
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Karima made 9 pairs of earrings in 9 hours. At this rate: How long will it take Karima to make 12 pairs of earrings?
Answer:
12 hours
Step-by-step explanation:
1 pair per hour ?
explain the process of the square root of 80n3
The square root of 80 is 4√5 ≅ 8.92.
What is a square root of a number?
In mathematics, the square root of a number is a value that gives the original number on multiplication by itself. The positive number, when multiplied by itself, represents the square of the number. Thus, the square root of the square of a positive number gives the original number.
Using Prime Factorization:
The first step in this method is to find the prime factors of 80.
80 = 2 × 2 × 2 × 2 × 5
To find the root from here, we can simplify this to
√80 = √(2 × 2 × 2 × 2 × 5)
√80 = 4√5
We can either leave it at this or find the root of 5 which is 2.23 and simplify further.
Hence, Square Root of 80 = 4√5 ≅ 8.92.
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