Help 4567778776655555
In order to calculate the function (f/g)(x), we need to divide f(x) by g(x).
First, let's find the zeros of the function f(x), so we can write it in the factored form:
[tex]\begin{gathered} f(x)=-10x^2+30x+40\\ \\ a=-10,b=30,c=40\\ \\ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\ \\ x=\frac{-30\pm\sqrt{900+1600}}{-20}\\ \\ x_1=\frac{-30+50}{-20}=-1\\ \\ x_2=\frac{-30-50}{-20}=4 \end{gathered}[/tex]So the factored form is:
[tex]\begin{gathered} f(x)=a(x-x_1)(x-x_2)\\ \\ f(x)=-10(x+1)(x-4) \end{gathered}[/tex]Now, calculating the composite function, we have:
[tex]\frac{f(x)}{g(x)}=\frac{-10(x+1)(x-4)}{-5x-5}=\frac{-10(x+1)(x-4)}{-5(x+1)}=2(x-4)=2x-8[/tex]write x<19 in interval notation
The inequality x<19 is the unbounded interval
answer:____
The resulting inequality equation in interval form is (-∞, 19).
Interval form of an inequalityThe range of values that might result in an inequality being true can be represented using interval notation.
There are two kinds of intervals, called open and closed (explained below), and each has a unique manner to notate it so we can distinguish between the two.
Given the inequality expression x < 19. This means that the interval must contain values that are less than 19 (19 excluded.)
The inequality x<19 as an unbounded interval is given as (-∞, 19).
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what is the domain of the relation shown below?
a student computes -8-2(-3) by writing -10(-3)=30 how would you help this student?
Answer:
-2
Step-by-step explanation:
You want to help a student evaluate -8-2(-3).
Order of operationsThe given expression consists of a sum of a number and a product. The first operation to be performed is to find the product:
-8-2(-3) = -8 +6
Then the sum can be performed:
-8 +6 = -2
The student should be reminded to identify the parts of the expression and use the order of operations to evaluate them.
9(x)=1/4x+1
What is g(-16)?
G(-16)=
Answer:
1; 4/35
2; -16g
sorry if wrong
Are the lines created using the given points perpendicular?L1: (1,2), ( 3,1) and L2: (0,-1), (2,0)
Answer:
[tex]No,\text{ they are not}[/tex]Explanation:
To check for this, we have to get the slope of the two lines
The slope of a line can be calculated using the formula:
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex]where (x1,y1) are the coordinates of the first point and (x2,y2) are the coordinates of the second
Mathematically, we have the slope of the first as follows:
[tex]m\text{ = }\frac{1-2}{3-1}\text{ = -}\frac{1}{2}[/tex]For the second line, we have it that:
[tex]m\text{ = }\frac{0+1}{2-0}\text{ = }\frac{1}{2}[/tex]When two lines are perpendicular, the product of their slopes is equal to -1
We have it that:
[tex]\frac{1}{2}\times(-\frac{1}{2})\text{ = -}\frac{1}{4}[/tex]This shows that the two lines are not perpendicular
If a skier travels 4700 feet up a ski lift whose angle of inclination is 30°, how high above his starting level is the skier?
If a skier travels 4700 feet up a ski lift whose angle of inclination is 30°, how high above his starting level is the skier is 2350 feet.
HeightGiven data:
Distance = 4700 feet
Angle of inclination = 30°
Now let determine the height by formulating an equation which will help us to find the height
4700 × sin 30°
Where:
Sin 30° = 0.5 or 1/2
Hence,
Height :
Height = 4700 feet × 0.5
Height = 2350 feet
So,
Height = 2350 feet above the starting level
Therefore we can conclude that the skier is 2350 feet above the starting level.
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I need Help!!!!!!!!!
Answer: The photo below will show you how to do the problem. (i used 2 as an example)
Step-by-step explanation:
: Find the x- and y- intercepts. ...
Step 2: Find at least one more point. ...
Step 3: Plot the intercepts and point(s) found in steps 1 and 2. ...
Step 4: Draw the graph. ...
Step 1: Find the x- and y- intercepts.
Step 2: Find at least one more point. ...
Step 3: Plot the intercepts and point(s) found in steps 1 and 2.
An election ballot asks voters to select five city commissioners from a group of eighteen candidates. In how many ways can this be done?
Number of ways to select five city commissioners from a group of eighteen candidates is equal to 8568.
As given in the question,
Total number of candidates = 18
An election ballot asks voters to select five city commissioners from 18 candidates
Number of ways to select 5 city commissioners from a group of 18 candidates
= ¹⁸C₅
= ( 18!) ) / (5!)(18 - 5)!
= (18!) / (5!)(13!)
= ( 18 ×17×16×15×14×13! ) / ( 5×4×3×2×1 )( 13! )
= 8568
Therefore, number of ways to select five city commissioners from a group of eighteen candidates is equal to 8568.
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Part I
Find the domain and the range of the following function.
f(x)=
x+3, for x≤ -3
1, for -3
1/2x, for x ≥4
The domain of the function is
(Type your answer in interval notation)
Range and Domain. The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
What Separates a Function's Domain from its Range?
A function's domain and range are its constituent parts. In contrast to a function's range, which is the set of all potential outputs, a function's domain is the set of all possible inputs.
All real numbers fall under the expression's domain, with the exception of cases where it is undefined. No real number exists in this situation, rendering the statement undefinable.
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Carlo and Anita make mailboxes and toys in their craft shop near Lincoln. Each mailbox requires 4 hours of work from
Carlo and 4 hours from Anita. Each toy requires 2 hours of work from Carlo and 4 hours from Anita. Carlo cannot work
more than 20 hours per week and Anita cannot work more than 28 hours per week. If each mailbox sells for $15 and
each toy sells for $24, then how many of each should they make to maximize their revenue? What is their maximum
revenue?
Answer:
7 toys and 0 mail boxes
Step-by-step explanation:
Answer:
Given that:!
Carlo mailbox = 1
Anita mailbox = 3
Carlo toy = 1
Anita toy = 4
Carlo work = 7 hours per week
Anita work= 24 hours per week
mailbox sells = $8
toy sells $14 =
solution
we consider here number of mailboxes is m
and m≥0
and
number of toys is t
and t≥0
so we can say equation will be
1m + 1t ≤7
3m+ 4t≤ 2
solve these equation 1,2,3 and 4 in graph and we will get graph that is attach here
we get here are 4 corner that is
The corner points are: (0, 0), (7, 0), (4, 3), (0, 6)
so objective revenue function is
F(m, t) 8m + 14t =
put here all value of corner
F(0, 0) = $0
F(7, 0) = 7×8 = $56
F(4, 3) = 4×8+ 3×14= $74
F(0, 6) = 6×14 = $84
so here maximize the revenue they should make 6 toys
The maximum revenue is $84Please help I’ll mark you as brainliest if correct!
Answer: a = 30
d = 4
c = 18
b = 6
Step-by-step explanation:
(2y-1)+3y+5
please help
Answer:
5y + 4; y = -4/5
Step-by-step explanation:
combine like terms
add 2y+3y together, and -1+5
5y+4=0
-4 -4
5y= -4
/5 /5
y= -4/5
Solve the equation.
−3=z−8
Answer:
add -8 to -3 so thats 5 and your answer is 5=z
Step-by-step explanation:
Which pair of similar triangles can be mapped from one to the other by dilation with scale 3 and center of dilation (0,0) followed by the translation (x,y) (x -6, y -6)
Triangles P is equal to triangle v and triangles A is equal to triangle J.
Consider the unit of the scale on the X-axis is 1 unit. and
Consider the unit at Y-axis is 1 unit.
Take a triangle p and measure each unit.
1/2 + 1/2 + 1/2 + 1 + 1 + 1 = 9/2
=4.2
Take a triangle V and measure each unit.
1/2 + 1/2 + 1/2 + 1 + 1 + 1 = 9/2
=4.2
∴ The calculation is too same.
Here, ΔP=ΔV
Take a triangle I and measure each unit.
unit of I is 1.
Take a triangle J and measure each unit.
unit of J is 1.
∴ ΔI=ΔJ
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I inserted a picture of a question please state whether the answer is a b c or d
Given:
[tex]\begin{gathered} y=x^2 \\ y=\mleft(\frac{1}{3}x\mright)^2 \end{gathered}[/tex]The graph of g(x) is the graph of f(x) horizontally stretched by a factor of 3.
ption D is the final answer.
This season, the probability that the
Yankees will win a game is 0.6 and the
probability that the Yankees will score 5 or
more runs in a game is 0.61. The
probability that the Yankees win and score
5 or
more runs is 0.51. What is the
probability that the Yankees would score
fewer than
5 runs when they lose the
game? Round your answer to the nearest
thousandth.
Answer:
0.156
Step-by-step explanation:
P(A & B) = P(A) * P(B)
P(Yankess score less than 5 and lose) = P(score less than 5) * P(lose)
0.39 * 0.4 = 0.156
Let f(x)=x − 3 and g(x)=x2−x. Find and simplify the expression. (f+g)(−6)
Answer: 33
Step-by-step explanation:
(f+g)(−6)=
f(-6)+g(-6)=
-6-3 + (-6)^2-(-6)=
-(6+3) + 36+6=
-9+42=
42-9=33
A container has a capacity of 2/3 gallons. How many gallons are there in six of these containers in each container is filled to capacity.
The number of gallons in 6 containers is 4
How to determine the number of gallons?The statement is given as
A container has a capacity of 2/3 gallons
This means that
1 container = 2/3 gallons
Multiply both sides of the equation by 3/2
So, we have
3/2 * 1 container = 2/3 gallons * 3/2
Evaluate the products
So, we have
3/2 containers = 1 gallon
Multiply both sides by 4
So, we have
4 * 3/2 containers = 4 gallons
This gives
4 gallons = 6 containers
Hence, the number of gallons is 4
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Dion has a pizza with a diameter of 10 1/3 in. Is the square box song big enough to fit the pizza inside?
justify your answer
yes, the square box song big enough to fit the pizza inside.
what is square?
A square is a regular quadrilateral , which means that it has four equal sides and four equal angles.
we have that,
the diameter of the pizza is
D = 10 1/3in
the wide of the square box is
b=10.38in
we know that
for the pizza to fit inside the box ,it must be fulfilled that
D ≤ b
convert 10.38 in to fraction number
10.38 (100/100)= 1.038/100=519/50
convert 101/3 in to an improper fraction
10 1/3 = 10+3+1/3=31/3
multiply the diameter of the pizza by 50 both numerator and denominator =31+50/50+3= 1.550/150 in
multiply the wide of the box by 3 both numerator and denominator 1.550/150in ≤ 1.557 /150 in
therefore
the pizza fit inside the box .
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18. Convert the following base-ten number to a number in the indicated base.
130 to base six
130=_____six
Please show work.
The result of converting the number 130 base 10 to the base six is [tex]334_{6}[/tex]
Given the number 130 base 10
Here we have use base conversion 130 base 10 to the number base six
.Here we have to follow 2 steps
In first step : Converting 130 to base 10
1 × [tex]10^{2}[/tex] = 100
3 × [tex]10^{1}[/tex] = 30
0 × [tex]10^{0}[/tex] = 0
Add of the result together
100 + 30 + 0 = [tex]130_{10}[/tex]
In second step : Converting [tex]130_{10}[/tex] to base 6
We can solve it by using the method
6 | 130
6 | 21 | 4
6 | 3 | 3
6 | 3 | 3
Then the result will be [tex]334_{6}[/tex]
Hence, the result of converting the number 130 base 10 to the base six is [tex]334_{6}[/tex]
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Plot the image of point P under a translation by 4 units to the left and 3 units down.
We are given the following point:
[tex]P=(-2,-4)[/tex]The given transformation is the following:
[tex](x^{\prime},y^{\prime})=(x-4,y-3)[/tex]Replacing the values:
[tex]\begin{gathered} P^{\prime}=(-2-4,-4-3) \\ P^{\prime}=(-6,-7) \end{gathered}[/tex]Therefore, the image is (-6,-7)
-2(x-1)+4x=10
What is the answer to this question
Answer:
4
Step-by-step explanation:
to solve this equation you should add the values on the left side then divide 10 by whatever value you get
-2(x-1)+4x=10
-2x+2+4x=10
2x+2=10
2x=10-2
2x=8
x=4
Bernie is making wooden stools for a local charity. He has 12 1/2 feet of wood. The instructions call for 2 1/2 feet of wood to make two stools. Which of the following correctly shows the total number of complete stools that Bernie can make?
The most appropriate choice for fraction will be given by -
Bernie can make 10 stools
What is a fraction?
Suppose there is a collection of objects and a part of collection has been taken. The part which is taken is called fraction. In other words, part of a whole is called fraction.
The upper part of fraction is called numerator and the lower part of fraction is called denominator.
[tex]2\frac{1}{2}[/tex] feet = [tex]\frac{5}{2}[/tex] feet of wood can be used to make 2 stools
1 feet of wood can be used to make [tex]2 \div \frac{5}{2}[/tex] stools
[tex]2 \times \frac{2}{5}[/tex] stools
[tex]\frac{4}{5}[/tex] stools
[tex]12\frac{1}{2} = \frac{25}{2}[/tex] feet of wood can be used to make [tex]\frac{4}{5} \times \frac{25}{2}[/tex] stools
= 10 stools
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A merchant bought several pieces of silk for $70. He sold all but two of them at a profit of $4 per piece. His total profit was $18. How many pieces did he originally purchase?
A merchant bought several pieces of silk for $70. He sold all but two of them at a profit of $4 per piece. His total profit was $18. How many pieces did he originally purchase?
Let n be the number of pieces. He sold n - 2 pieces
Let p be the original price. His selling price = p + 4
Then n · p = 70.00
And (n - 2) · (p + 4) = 70.00+18.00 ---> np + 4n - 2p - 8 = 88.00
---> np + 4n - 2p = 96.00
---> 70.00 + 4n - 2p = 96.00
4n - 2p = 26.00
2n - p = 13.00
Trying some possibilities (7 & 1), (8 & 3), (9 & 5), and (10 & 7), finally gets us to the answer: n = 10 and p = 7.00.
therefore
the number of pieces was 10Step-by-Step Example: Sketch a graph for a situation.
A carnival game booth begins the evening with 40 prizes.
In the first 30 minutes that the booth is open, no one wins
a prize. In the next hour, 8 prizes are won. In the next 45
minutes, 10 prizes are won. During the next 45 minutes,
the booth owner brings in 16 additional prizes. In the next
2 hours, 12 prizes are won. An hour later, 4 prizes are
won, and the carnival closes for the evening.
Sketch a graph that shows the number of prizes the booth
had over the time it was open.
By using the method subtraction, Total prizes are left over are 52- 34= 18
What is subtraction?To subtract in mathematics is to take something away from a group or a number of objects. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction issue are the minuend, subtrahend, and difference. An arithmetic operation called subtraction simulates the process of deleting items from a collection. The action of subtracting a matrix, vector, or other quantity from another according to predetermined rules in order to find the difference.
Given that,
A carnival game booth begins the evening with 40 prizes.
In the first 30 minutes that the booth is open, no one wins
a prize.
In the next hour, 8 prizes are won. In the next 45
minutes, 10 prizes are won.
During the next 45 minutes, the booth owner brings in 16 additional prizes.
In the next 2 hours, 12 prizes are won.
An hour later, 4 prizes are won, and the carnival closes for the evening.
Total prizes are 52 prizes.
Total prizes given are 34 prizes
Total prizes are left over are 52- 34= 18
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Chris bought 18.4 gallons of gasoline. There are approximately 3.8 liters in 1 gallon. Which measurement is closest to the number of liters of gasoline Chris bought? Question 1 options: 6.21 L 14.6 L 4.84 L 69.92 L
The measurement that is closest to the 18.4 gallons of gasoline that Chris bought is 69.92 liters , the correct option is (d) 69.92 L .
In the question ,
it is given that ,
number of gallons that Chris bought = 18.4 gallons
also given that 1 gallon = 3.8 liter
Using the conversion , 1 gallon = 3.8 liter ,
we get ,
18.4 gallons = 3.8 × 18.4
= 69.92
hence, 18.4 gallons = 69.92 liters
Therefore , the measurement that is closest to the 18.4 gallons of gasoline that Chris bought is 69.92 Liters, the correct option is (d) 69.92 L .
The given question is incomplete , the complete question is
Chris bought 18.4 gallons of gasoline. There are approximately 3.8 liters in 1 gallon. Which measurement is closest to the number of liters of gasoline Chris bought?
(a) 6.21 L
(b) 14.6 L
(c) 4.84 L
(d) 69.92 L
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Use 3.1 < sqrt 10 <3.2 to find the possible values of each expression. 2-sqrt 10
Thanks for the response.
i did the same for 2-square root 10, for 2 - 3.1 < 2 - sqrt 10 < 2 - 3.2 and thought 2 -3.1 < 2 -sqrt 10 < 2 -3.2,
-1.1<< 2 - sqrt 10 < -1.2 will be the answer but doesn't look like its right. Appreciate your help for this. thanks
Think of -1.1 as -11
Think of -1.2 as -12
I moved the decimal points to the right for each value
Then on a vertical number line, notice how -12 is below -11, so -12 < -11
If we divide both sides by 10, then we go from -12 < -11 to -1.2 < -1.1
In short, the final expression you have -1.1 < middleStuff < -1.2 is in the wrong order.
It should be -1.2 < 2 - sqrt(10) < -1.1
I swapped the places of -1.1 and -1.2
If you were to use a calculator, then 2-sqrt(10) = -1.162 approximately which fits the description of being between -1.2 and -1.1; this helps confirm we have the correct upper lower and upper bounds.
------------------------------------
Here's another way to look at it
3.1 < sqrt(10) < 3.2
-1*3.1 > -1*sqrt(10) > -1*3.2 ............ see note1 below
-3.1 > -sqrt(10) > -3.2
-3.1+2 > -sqrt(10)+2 > -3.2+2 ....... see note2
2-3.1 > 2-sqrt(10) > 2-3.2
-1.1 > 2 - sqrt(10) > -1.2
-1.2 < 2 - sqrt(10) < -1.1 ........... see note3
Footnotes
note1: For this step I multiplied all three sides by -1. Multiplying by a negative will flip the inequality signsnote2: I added 2 to all three sides. This does not flip any of the inequality signs.note3: We go from the form a > b > c to c < b < a. The outer sides 'a' and 'c' swap places while b in the middle stays where it is. The inequality signs flip. It might help to think of something like 3 > 2 > 1 flipping to 1 < 2 < 3.F(x)=1/2x4x domain:(0,1,2,)
area of composite figures worksheet #1 (don’t mind the pen it’s a mistake)
Answer:
Given that,
Rectangular room is of the dimension 12 feet by 18 feet
To find the number of square feet of carpet needed.
Explanation:
Area of the rectangle is,
[tex]\text{ length}\times\text{ breadth}[/tex]Area of the rectangular room is,
[tex]12\times18[/tex][tex]=270\text{ ft}^2[/tex]Area of the rectangular room is 270 square feet.
Therefore, 270 square feet of carpet are needed to cover the room.
we know that,
[tex]1\text{ yard }=3\text{ feet}[/tex]Using this conversion we get,
[tex]270\text{ ft}^2=270(\frac{1}{3}\text{ yd})^2[/tex]