Suppose f(x)=6x-2 and g(x)= 2x+4
a.
(f+g) (x) = 6x - 2 + 2x + 4
(f+g) (x) = 8x + 2
b.
(f-g) (x) = 6x - 2 -( 2x + 4)
(f-g) (x) = 6x - 2 - 2x - 4
(f-g) (x) = 4x - 6
Final answer:
The combined function (f+g)(x) is 8x + 2, and the function (f-g)(x) is 4x - 6.
Explanation:
To find the combined functions (f+g)(x) and (f-g)(x) for the given functions f(x)=6x-2 and g(x)=2x+4, we carry out the operations as follows:
Function (f+g)(x)
(f+g)(x) = f(x) + g(x) = (6x - 2) + (2x + 4).
Combine like terms:
(f+g)(x) = 6x + 2x - 2 + 4.
(f+g)(x) = 8x + 2.
Function (f-g)(x)
(f-g)(x) = f(x) - g(x) = (6x - 2) - (2x + 4).
Combine like terms and distribute the negative sign:
(f-g)(x) = 6x - 2x - 2 - 4.
(f-g)(x) = 4x - 6.
If 120 men used the gym how many more women were there
need more info in order to kinda see how many women there were
Which statement best describes the constant in this expression?
Answer:
A. It is the total cost for entertainment and cleaning.
Step-by-step explanation:
If we look at the information it says:
Facility rental is dependent upon number of hours we are renting the facility for.
Linen, food, and decoration also depends upon the number of attendees. Also, the table decorations depend upon the number of attendee.
The things that are independent of the number of attendees are entertainment and cleaning fee. These are fixed charges.
So, the total cost for entertainment and cleaning are the constants in the expression. This is the amount that will remain constant regardless of the number of attendees.
Which of the following is graphed below?
Answer:
[tex]f(x)=\left \{ {{x^2+4}\ \ \ \ \ x<2 \atop {-x+4}\ \ \ x\geq 2}\right[/tex]
C is correct
Step-by-step explanation:
In the given graph function break at point x=2.
Left side about point x=2 is parabolic and right side straight line.
So, it would be piece wise function.
For parabola:
vertex: (0,4) and passing point (2,8)
[tex]y=a(x-h)^2+k[/tex]
[tex]y=ax^2+4[/tex]
[tex]a=1[/tex]
[tex]y=x^2+4[/tex] For x<2
For straight line:
Twp points (4,0) and (2,2)
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-2=\dfrac{0-2}{4-2}(x-2)[/tex]
[tex]y-2=-1(x-2)[/tex]
[tex]y=-x+4[/tex] For x≥2
Hence, The piece wise function will be
[tex]f(x)=\left \{ {{x^2+4}\ \ \ \ \ x<2 \atop {-x+4}\ \ \ x\geq 2}\right[/tex]
Write four decimals with the digit 4 in a different place in each ones, thenths,hundredths, and thousandths.Then write a statement that compares the value of the digit 4 in the different decimals.
The number 87.65487.65487, point, 654 can be placed on a place value chart as follows:
Tens Ones . Tenths Hundredths Thousandths
888 777 ..point 666 555 444
Decimal place value
The first digit after the decimal represents the tenths place. The next digit after the decimal represents the hundredths place. The remaining digits continue to fill in the place values until there are no digits left.
Example: 0.810.810, point, 81
The number 0.\blueD8\greenD10.810, point, start color blueD, 8, end color blueD, start color greenD, 1, end color greenD is made up of \blueD88start color blueD, 8, end color blueD tenths and \greenD11start color greenD, 1, end color greenD hundredth.
We can also write this as:
0.\blueD8\greenD1=\blueD{0.8}+\greenD{0.01}0.81=0.8+0.010, point, start color blueD, 8, end color blueD, start color greenD, 1, end color greenD, equals, start color blueD, 0, point, 8, end color blueD, plus, start color greenD, 0, point, 01, end color greenD
or
0.\blueD8\greenD1=\blueD{\dfrac8{10}}+\greenD{\dfrac1{100}}0.81=
10
8
+
100
1
0, point, start color blueD, 8, end color blueD, start color greenD, 1, end color greenD, equals, start color blueD, start fraction, 8, divided by, 10, end fraction, end color blueD, plus, start color greenD, start fraction, 1, divided by, 100, end fraction, end color greenD
Or we can use a place value chart:
Ones . Tenths Hundredths
000 ..point \blueD88start color blueD, 8, end color blueD \greenD11start color greenD, 1, end color greenD
Want to learn more about decimal place value? Check out this video.
Want to review whole number place value? Check out this article.
Practice
There are 12 people in maggies book club if 18 muffing are divided evenly among each person, how much muffin would each person get?
x-5≥ 9 need answer plsss
Add 5 to both sides.
x−5+5≥9+5
Answer: x≥14
Let C ( t ) be the number of US cell phone subscribers in millions in t years since 1995. A linear model for the data is F ( t ) = 18.997 t + 17.711 .
Use the model to predict the year in which the number of subscribers will 324 million
ANSWER
In 16 years time.
EXPLANATION.
If the number of subscribers is 324 million, then it means
[tex]f(t)=324[/tex]
But we were given that,
[tex]f(t)=18.997t+16.711[/tex]
This implies that,
[tex]324=18.997t+16.711[/tex]
We now solve for t,
[tex]324-16.711=18.997t[/tex]
[tex]307.289=18.997t[/tex]
[tex]\frac{307.289}{18.997}=t[/tex]
[tex]16.17566=t[/tex]
That will be approximately in the 16th year.
In order to calculate the year where the number of US cell phone subscribers matches a certain number using the given linear model equation, you solve for the time variable. With the specified 324 million subscribers, the corresponding year would be approximately 2011.
Explanation:To use the provided linear model F(t) = 18.997t + 17.711 to predict the year where the number of subscribers will be 324 million, we need to solve the equation for t with C(t) set to 324:
324 = 18.997t + 17.711
To do so, subtract 17.711 from both sides to isolate the term with t:
324 - 17.711 = 18.997t
Then, divide both sides by 18.997 to solve for t:
(324 - 17.711) / 18.997 = t
After calculating, you will get approximately t = 16.123. Remember, t is the number of years after 1995, so you would add 16 (rounded from 16.123) to 1995. Thus, the model predicts that the number of US cell phone subscribers will reach 324 million in 2011.
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Jan has a 10-ounce smoothie.Four ounces in the smoothie are vanilla yogurt,and the rest is orange juice.What are two equivalent fraction that represents the fraction of the smoothie that is vanilla yogurt?
PLEASE HELP!!! 28 Points!!!
I need to have this for a discussion!
Create an equation taking 2 or more steps to solve. Explain how the algebraic properties are applied in the steps to solving equations and use them to solve your equation.
Lily's car has a fuel efficiency of 888 liters per 100 kilometers.
What is the fuel efficiency of Lily's car in kilometers per liter?
Answer:
12.5
Step-by-step explanation:
if you get the answer to all of them ill mark you brainliest even if its wrong
Identify the slope and y intercept for each question
1. (-5,4), slope = - 7/5
2. M= 1, (-1,5)
3. y = 5/4x-8
4. y+1=1/4(x-4)
5. y+12=5(x+2)
6.y+5=-2/5(x-5)
7. (-2.19) and (-1,14
8. (3,0) and (4,2)
9. y=-5/4 (x+4)
10. (5,0), slope =-4/5
I'm so sorry if these are wrong...
1. y=-7/5x-3
2. y=1x+6
3. y=5/4x-8
4. y=1/4x-2
5.y=-5x-2
6. y=-2/5x-3
7. y=5x+19
8. y=2x-6
9. y=-4/5x-5
10. y=-4/5x+4
Tatum wants to use partial products to find 14x39 how do I do this?
Answer: 546
Step-by-step explanation:
14 ⇒ 10 + 4
x 39 ⇒ 30 + 9
36 | ← 9 x 4
90 | ← 9 x 10
120 | ← 30 x 4
300 | ← 30 x 10
546
Please help asap 25 pts
[tex]8x > -32\qquad|\text{divide both sides by 8}\\\\x > -4\\-----------------------------------\\\\6x\leq-48\qquad|\text{divide both sides by 6}\\\\x\leq-8\\\\Answer:\ c)\ x > -4\ or\ x\leq-8[/tex]
Carrie has 140 coins. She has ten times as much coins as she did last month. How many coins did carrie have last month
Last month, Carrie had 14 coins.
How long will it take you to drive 120 miles at a speed of 15 per hours
All we have to do is divide 120 by 15
120 ÷ 15 = 8
Therefore, it will take 8 hours to drive 120 miles at a speed of 15 mph
Hope this helps
-AaronWiseIsBae
15miles = 60minutes
divide 15 by 120 which equals 8
8 times 60 equals 480
your answer should be 8 hours
Struggling with an assignment that requires finding the probability of compound events. Can anyone please explain how to find it? Thank you!
Answer:
4/9 probability
Step-by-step explanation:
Imagine winning something, there's 3 possible prizes that you get to choose from and get to keep let's say 4 days? These all written on the paper that you must pull from a box.
Your three prizes are
D1 D2 D3 D4
1. a car
2. a bike
3. skateboard.
Now if you can imagine a grid and you mark 1 dot in each day we'll end up with 12 slots total.
Let's say you don't want a skateboard you rather have a car or a bike. We need to figure out of the 12 possibility (assuming all are equal) What's the possibility of you pulling out anything BUT a skateboard?
You want at least 3 days in either or. So we must find P = (Days without skateboard)
We know it's all equal outcomes, you're going to get 1 day of that 1 item.. soo..
p (DWS) = _____
12 outcomes
Now you want how many days MORE THAN 3, can you use anything but the skateboard?
You have 3 & 4 days with a car...
You have 3 or 4 days with a bike.. Which gives us 4 of the days we do want!
Giving your final problem the looking like this .. P(DWS) = 4/9
In respects/C to KhanAcademy.
Answer:
4/9 probrabitaty
Step-by-step explanation:
Solve 24>−3r≥−9. please help
[tex]24 > -3r\geq-9\ \ \ \ |\text{change the signs}\\\\-24 < 3r\leq9\ \ \ \ |\text{divide both sides by 3}\\\\\boxed{-8 < r\leq3}[/tex]
Inequalities are used to represent unequal expressions.
The solution to [tex]24>-3r \ge -9[/tex] is [tex]-8<r \le 3[/tex]
Given
[tex]24>-3r \ge -9[/tex]
Divide through by -3
[tex]\frac{24}{-3}>\frac{-3r}{-2} \ge \frac{-9}{-3}[/tex]
Negative division changes the inequality sign
So, we have:
[tex]-8<r \le 3[/tex]
Hence, the solution to [tex]24>-3r \ge -9[/tex] is [tex]-8<r \le 3[/tex]
See attachment for the graph of [tex]-8<r \le 3[/tex]
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Marc has 45 CD in his collection and Corona has 61 if Marc buys 4 new CD each month and corina buys 2 new CD each month after how many months will marc and corina have the same number of cds
Marc and Corlina will have the same amount of CD's after 8 months.
45 + 4(8) = 77
61 + 2(8) = 77
What is the length of the hypotenuse of the right triangle defined by the points (–3, –1), (1, –1), and (1, 2)?
First we have to see which is the right angle. This triangle has its legs oriented parallel to the axes. (-3,-1) and (1,-1) form the horizontal leg, (1,-1) and (1,2) the vertical leg.
So the right angle vertex is (1,-1) and the hypotenuse endpoints are (-3,-1) and (1,2)
The length is given by
[tex]d = \sqrt{ (1 - -3)^2 + (2 - -1)^2} = \sqrt{4^2+3^2}=\sqrt{25} = 5[/tex]
This is a 3/4/5 right triangle.
Answer: 5
Paula bought a 5-pound bag of granola. She plans to use equal amounts of granola to make 10 bags of trail mix and add the remaining amount to her bird feeder. She created the given function to model the amount of granola, in ounces, that she can add to her bird feeder if she puts x ounces in each bag.
What is the range of the function?
A. all whole numbers between and including 0 and 8
B. all whole numbers between and including 0 and 80
C. all real numbers between and including 0 and 80
D. all real numbers between and including 0 and 8
Given function: P(x) = -10x + 80.
Where function represents the amount of granola, in ounces and x represents the number of ounces Paula puts in each bag.
Range of the function is the values of the function we would get.
That is the amount of granola in ounces for different x values.
For x=0 the number of ounces would be -10(0)+80 = 80.
And for x=8, it would be -10(8) + 80 = 0.
But even we could take decimal values too.
Like x=0.5 ounces, x=0.55 ounces etc.
And that 0.55 would give a decimal value.
Therefore, we can take any real number for x between 0 and 8.
But we need to find the range.
So, the range would be between 0 and 80 and it could be any real number.
Therefore, correct option is :
C. all real numbers between and including 0 and 80.
it is A. for all plato users
Which graph represents the inequality y > 3 − x ?
To solve this problem you must think in this way.
First we see that function y is greater than 3-x, conclusion is the following
shaded area must be above function. That condition is satisfied by the graph 3 and 4.
Then we write inequality in the slope form y> -x+3.
We see that the coefficient of direction is -1 (negative) which mean that the graph is decreasing. That condition is satisfied by the graph No 4.
The correct answer is graph number 4 ( or D.)
Good luck!!!
A 4-digit pin number is to be created using the digits 0 through 9. The first digit must be a 5 or an 8, and the last digit cannot be 0. How many pin numbers can be created?
A.
5,040
B.
6,561
C.
1,458
D.
1,800
A family's lunch bill is $10.19 before tax and tip. Using the percents shown for sales tax and gratuity, how much money should the family pay if the gratuity is calculated after tax?
Answer:
12.36
Step-by-step explanation:
Answer:
Its: 12.36
Step-by-step explanation:
What is the results of converting 1500 yards into miles ?Remember that 1mile =1760yards
Answer:
0.85 mile(rounded to nearest hundredth)
Step-by-step explanation:
We have to convert 1500 yards into miles.
To convert 1500 yards into miles, we first need to know the relation between yards and miles.
So we have,
[tex]1 \:\text{mile}=1760\:\text{yards}[/tex]
Now, to convert 1500 yards into miles, we need to know how many miles are there in 1 yard.
So, we have
[tex]1\:\text{yard}=\frac{1}{1760} \:\text{miles}[/tex]
[tex]\implies1500 \:\text{yards}=\frac{1500}{1760} \:\text{mile}[/tex]
[tex]\implies1500 \:\text{yards}=\frac{150}{176} \:\text{mile}[/tex]
[tex]\implies1500 \:\text{yards}= \frac{75}{88}\:\text{mile}[/tex]
[tex]\implies1500 \:\text{yards}= 0.85\:\text{mile}[/tex]
Hence, 1500 yards is 0.85 mile, rounded to nearest hundredth.
A large group can weigh 1/3 ton.How much does a large grouper weigh to the nearest pound. I don’t understand this question it’s my homework but i really don’t understand it
667 pounds is the answer. There are 2000 pounds in a ton. 1/3 of a ton is 666.666667 pounds. I think this question is a conversion from tons to pounds?
Given: △DMN, DM=10 3 m∠M=75°, m∠N=45° Find: Perimeter of △DMN
Answer:
The perimeter of [tex]\triangle DMN[/tex] will be 62.1939...
Step-by-step explanation:
In [tex]\triangle DMN[/tex], the length of side [tex]DM = 10\sqrt{3}[/tex] and the measures of [tex]\angle M[/tex] and [tex]\angle N[/tex] are 75° and 45° respectively.
As the sum of all angles in a triangle is always 180°, so the measure of [tex]\angle D[/tex] will be: 180°- (75°+45°) = 180°- 120° = 60°
Now using Sine rule, we will get......
[tex]\frac{MN}{Sin(D)}=\frac{DN}{Sin(M)}=\frac{DM}{Sin(N)}\\ \\ \frac{MN}{Sin(60)}=\frac{DN}{Sin(75)}=\frac{10\sqrt{3}}{Sin(45)}\\ \\ MN= \frac{10\sqrt{3}}{Sin(45)}*Sin(60)=21.2132...\\ \\ DN=\frac{10\sqrt{3}}{Sin(45)}*Sin(75)=23.6602...[/tex]
So, the perimeter of [tex]\triangle DMN[/tex] will be: [tex]DM+MN+DN = 10\sqrt{3}+21.2132...+23.6602... =62.1939...[/tex]
Let f(x) = 5x2 – 4x and g(x) = 5x + 1.
Answer:
5x^2+x+1
Step-by-step explanation:
the expression for f(x) - g(x) is 5x² - 9x - 1.
To find f(x) - g(x), we simply subtract the expression for function g(x) from the expression for f(x):
f(x) - g(x) = (5x² - 4x) - (5x + 1)
Now, let's simplify the expression by combining like terms:
f(x) - g(x) = 5x² - 4x - 5x - 1
Next, combine the x terms:
f(x) - g(x) = 5x² - (4x + 5x) - 1
Now, combine the x terms inside the parentheses:
f(x) - g(x) = 5x² - 9x - 1
So, the expression for f(x) - g(x) is 5x² - 9x - 1.
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17 bundles of 10 straws how how many straws did she bundle in all
Using mathematical operations we know that 170 straws were used in all.
What are mathematical operations?In mathematics, an operation is a function that converts zero or more input values into a discrete output value. The number of operands in the operation determines how difficult it is. The order of operations refers to the rules that outline the sequence in which certain operations should be carried out in order to solve an expression. The following is the order of operations: parentheses, exponents, multiplication, division (from left to right), addition, and subtraction. PEMDAS (from left to right) (from left to right).So, the total straws used:
Bundles are 17 and the straw used in each bundle us 10.Then, calculate as follows:
17 × 10170Therefore, using mathematical operations we know that 170 straws were used in all.
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A rectangle has an area of 228 ft and a length that measures 12ft find the perimeter
The area of a rectangle is the width times the length:
[tex] A = w\cdot l \iff 228 = w\cdot 12 \iff w = \dfrac{228}{12} = 19 [/tex]
The perimeter is twice the sum of the dimensions:
[tex] 2p = 2(12+19) = 2\cdot 31 = 62 [/tex]
The perimeter of the rectangle with dimensions 19 ft*12 ft comes to be 62 square feet.
Suppose the breadth of the rectangle is x.
What is the perimeter of a rectangle?The perimeter of a rectangle is the sum of all its sides i.e. the sum of two lengths and two breadths.
If length and breadth are a and b respectively then perimeter =2(l+b).
According to the question
Length =12 ft
Area=228 square ft
So, length * breadth = 228
[tex]12x =228[/tex]
[tex]x=\frac{228}{12}[/tex]
x=19
So, breadth of the rectangle =19 ft
So, perimeter = 2(12+19) = 62 square feet.
Hence, the perimeter of the rectangle with dimensions 19 ft*12 ft comes to be 62 square feet.
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98 POINTS
Alice, Deepak, and Ivan each measure the length of a 6.5-inch pencil five times. They record their measurements as shown below. Who took the most ACCURATE measurements? Who took the most PRECISE measurements?
Alice: 6.25 in., 6.83 in., 6.11 in., 6.94 in., 6.19 in.
Deepak: 7 in., 7 in., 6 in., 7 in., 6 in.
Ivan: 6.5 in., 6.4 in., 6.5 in., 6.5 in., 6.4 in.
precise and accurate are two different things in measurements:
most precise means the most detailed. here Alice has 2 decimals so her measurements are the most precise.
but her measurements are very different so they are not accurate.
most accurate measurements are Ivan's as they are very close to each other.
Answer:
✔ Ivan
took the most accurate measurements.
✔ Alice
took the most precise measurements.
Step-by-step explanation:
got it right:)