The given function f is increasing over the interval 0 < x < 2 and
decreasing over the interval 2 < x < 5.
What is a function?
A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. Let A & B be any two non-empty sets; mapping from A to B will be a function only when every element in set A has one end, only one image in set B.
An example of a simple function is f(x) = x^2. In this function, the function f(x) takes the value of “x” and then squares it. For instance, if x = 3, then f(3) = 9. A few more examples of functions are: f(x) = sin x, f(x) = x^2 + 3, f(x) = 1/x, f(x) = 2x + 3, etc.
Now,
As the given function f is increasing till x<2 and increasing after x>2
Hence,
f is increasing over the interval 0 < x < 2 and
decreasing over the interval 2 < x < 5.
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a. Write the function if Cecily releases the ball 40 feet above the ground at a velocity of 64 feet per second
The function that describes the height of the ball as a function of time t (in seconds) can be represented as:
h(t) = -16t^2 + 64t + 40
Where h(t) is the height of the ball in feet above the ground, t is the time in seconds, and the -16t^2 represents the acceleration due to gravity. The 64t represents the initial velocity of the ball, and 40 is the initial height of the ball above the ground.
Check the picture below.
what is 5 less than 4 times 7
Answer:
-31
Step-by-step explanation:
Let's put this into an equation:
[tex]4-5 *7[/tex]
Note that 5 less than 4 means I take 5 AWAY from 4, not 5-4.
Most people would go about this straight across, doing 4-5, -1, and then times 7 which would be -7.
BUT if there are no parentheses around 4-5, we do 5 times 7 first.
Why? In PEMDAS or order of operations, you multiply before subtracting.
That means I do 5 times 7 first. That is 35.
Now I subtract 4-35. That is -31.
please someone help me with this escape room question! i’ve been stuck on this problem for so long now
Answer:
all of them are 17
Step-by-step explanation:
7+9=16
16+1+0=17
9+7=16
16+1+0=17
1+0+9=10
10+7=17
7+1=8
8+9+0=17
hope this helped!
Find two consecutive whole numbers that square root of 32 lies between
Answer:
5 and 6
Step-by-step explanation:
sqrt of 32= 4sqrt2 = 5.656
you download a digital soccer game for . you can add new players for each to upgrade your team. the total cost is a function of the number of new players that you add. which of the following statements about the domain and the graph of the function is correct?
The domain is discrete and the range is continuous, which can be an accurate statement regarding the two terms.
What are domain and range?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.
So, the parameters are as follows, taken from the query:
Downloaded Amount = $2.50
Added amount to each player = $1.50
Use x to indicate how many players there are.
The following representations are what we have.
Total amount = Amount to download + Amount to add each player * Number of players
Now, we obtain:
y = 2.50 + 1.50 * x
y = 2.50 + 1.5x
The number of players serves as the input to the aforementioned linear function.
The domain is discrete as a result.
The amount, though, can have decimal points
The range is continuous as a result.
Therefore, the domain is discrete and the range is continuous, which can be an accurate statement regarding the two terms.
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If the function h(x) goes
through the point (−5, 7),
then the function −h(x)
must go through what
point?
Answer: (-5, -7)
Multiply the y coordinate by -1. Keep the x coordinate the same. The point (-5,7) reflects over the x axis to land on (-5,-7)
The reason why we multiply by -1 is because [tex]\text{y} = \text{h}(\text{x})[/tex], so [tex]-\text{y} = -\text{h}(\text{x})[/tex]
Answer:
(-5,-7)
................
Is (1 5/2) a solution ?
Answer:
No!
Step-by-step explanation:
(1 5/2)
is a mixed fraction so you will change it to proper fraction.
the solution is
=7/2 or 3.5
You will multiple two by one and add by five given 7/2.
3
10 points
(5x - 4)(x + 5)
O 5x²+21x-20
O4x²-17x+4
O 10x²+20x+10
O 10x²-10
Answer:
First choice: 5x²+21x-20
Step-by-step explanation:
This is easy to answer if you realize that there is only one way an x² term can appear in the result and that is by the multiplication of 5x and x which results in 5x².
The only choice which has 5x² as a term is the first: 5x²+21x-20
However, it is important to know the FOIL method to multiply two terms together
FOIL stands for First Outer Inner Last and is a technique for multiplying two terms of the form (a+b) and (c+d)
In (a + b) (c + d),
First terms are a and c so their product is ac
Outer terms are a and d so their product is ad
Inner terms are b and c with product bc
Last terms are b and d with product bd
The result is the sum of all these terms
Let's take (5x - 4)(x + 5)
F: 5x·x = 5x²
O: 5x · 5 = 25x
I: -4 ·x = -4x
L: -4·5 = -20
Adding up these individual terms we get
5x² +25x - 4x - 20 = 5x²+21x-20
So first choice is the correct answer
use traces to sketch the surface. (if an answer does not exist, enter dne. select update graph to see your response plotted on the screen. select the submit button to grade your response.) 9x2 y2 9z2
In order to accurately represent the surface, we would need to be able to plot the equation in 3-dimensions using 3-dimensional coordinates. Since this is not possible, the answer is dne.
In order to accurately represent the surface, we would need to be able to plot the equation in 3-dimensions using 3-dimensional coordinates. Since this is not possible, the answer is dne.
dne
Since 9x2 y2 9z2 is a 3-dimensional equation, it cannot be sketched on a 2-dimensional plane. Therefore, the answer is dne.
The equation 9x2 y2 9z2 is a 3-dimensional equation and cannot be represented on a 2-dimensional plane. Therefore, it is not possible to sketch the surface using this equation. As a result, the answer is dne. The equation contains three variables, x, y and z, and cannot be represented on a graph without the use of three axes. In order to accurately represent the surface, we would need to be able to plot the equation in 3-dimensions using 3-dimensional coordinates. Since this is not possible, the answer is dne.
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Determine the range of the following graph:
Answer:
-1 ≤ y ≤ 6
[-1, 6]
Step-by-step explanation:
The y coordinates of all points on the graph are from -1 to 6, so the range is:
-1 ≤ y ≤ 6
[-1, 6]
write about how to solve 8 divided by 5
Answer: 1⅗
Step-by-step explanation: We can write 8 divided by 5 as 8/5.
As 8/5 is an improper fraction, when we divide 8 by 5, we get 1 as quotient and 3 as remainder.
To convert an improper fraction into a mixed fraction, we take quotient 1 as a whole part and in the fractional part remainder 1 as the numerator, and divisor 5 as the denominator.
The GCF of 5 and 1 is 1. So, divide both the numerator and denominator by the GCF to simplify and convert it to a mixed fraction.
Thus, 8 divided by 5 as a fraction in simplest form is 1⅗.
Finding a cubic function in exercises 61 and 62, find a,b,c, and d such that the cubic f(x) - ax^3 + bz^2 + cz + dsatisfies the given conditions. 61. relative maximum: (2,4) Relative minimum: (4,2) Inflection point: (3,3)
-12a is a cubic function in exercises when Relative minimum (4,2).
What in mathematics is a relative maximum?
A point (x,y) on the graph of the function whose y-coordinate is larger than all other y-coordinates on the graph at locations "near to" is known as a relative maximum point (x,y). ( x , y ) .
f'(x) = 3ax² + 2bx + c
(3,3) and (5,1 ) are print of relative maximum
so, f'(3) = f'(5) = 0
3a(3)² + 2b(3) + c = 0
or 27a + 6b + c = 0
and 3a(5)² + 2b(5) + c = 0
75a + 10b + c = 0 ...................... 2
the Inflection point occurs at point where f''(x) = 0
d/dx ( 3ax² + 2bx + c ) ∫x = 4 = 0
because (4,2) is point of Inflection .
6a(4) + 2b = 0
24a + 2b = 0
b = -12a
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can you help me solve this? it says I have to prove, using statements and reasons, (ASA traingle congruence)
Richard is incorrect, As if two angles are same then the 3rd angle must be same too using angle sum property and therefore ΔJFH ≅ ΔJGH with AAA congruency.
What is the congruent triangle?Two triangles are congruent if they have the same shape and size. Congruent triangles have all corresponding angles and sides congruent, meaning they are equal in measure.
A triangle can be shown to be congruent to another triangle by using one or more of the following criteria:
SSS (Side-Side-Side) Congruence: If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.
SAS (Side-Angle-Side) Congruence: If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
ASA (Angle-Side-Angle) Congruence: If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
HL (Hypotenuse-Leg) Congruence: If the hypotenuse and one leg of one right triangle are congruent to the hypotenuse and one leg of another right triangle, then the two triangles are congruent.
Richard is incorrect, As if two angles are same then the 3rd angle must be same too using angle sum of property and therefore ΔJFH ≅ ΔJGH
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20 POINTS! WRITE A LINEAR EQUATION PERPENDICUALR TO -2Y = 5X + 8 PASSING THROUGH POINT (10,-1)
The equation of the line perpendicular to -2y = 5x + 8 and passes through (10, -1) is y = 2 / 5 x - 5.
How to represent linear equation?Linear equation can be represented in slope intercept form as follows:
y = mx + b
where
m = slope of the lineb = y-interceptTherefore, the equation is perpendicular to -2y = 5x + 8 and passes through (10, -1).
Perpendicular lines have slopes that are negative reciprocals of one another.
Therefore,
-2y = 5x + 8
y = - 5 / 2 x - 4
Therefore,
slope = 2 / 5
Let's find the y-intercept using (10, -1)
-1 = 2 / 5(10) + b
-1 = 20 / 5 + b
b = -1 - 4
b = -5
Therefore, the equation of the line is y = 2 / 5 x - 5
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tell me what spending and saving habits you have learned from your parents, guardians, family and friends. what will you do the same in your adult life and what will you change?
I learned to save for the future and spend responsibly. In my adult life I will continue to save and be mindful of my spending habits. I will change my attitude towards money and become more frugal.
How can I save money for the future?Saving money for the future requires discipline and dedication. One of the easiest ways to start saving is to create a budget and stick to it. Make sure to include a line item for savings in your budget and allocate a specific amount each month to save.
Additionally, set up automatic transfers from your checking account to your savings account to ensure money is put into savings each month. It's also important to find ways to minimize expenses. Cutting back on eating out, reducing your cell phone bill, and shopping for discounts are all great ways to save money.
Finally, look into investing your money in stocks, bonds, and other investments to help your savings grow. Saving money for the future takes time, but it is possible with the right strategies.
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A fair dice is rolled 3 times in a row. The outcomes are shown below.
Calculate the probability of all three events occurring.
Roll Outcome
1st even
2nd prime
3rd multiple of 5
Answer: 1/24
Step-by-step explanation:
1st even = 3/6 (2,4,6)
2nd Prime = 3/6 (2,3,5)
3rd multiple of 5 = 1/6 (5)
3/6 x 3/6 x 1/6 = 9/216
9/216 = 1/24
one positive point charge q1 is located at (x, y) coordinate (-2.22, -6.56) and a second positive point charge q2
Electric potential energy is the energy that is needed to move a charge against an electric field.
What is electrical potential energy?The power required to move a charge in opposition to an electric field is known as electric potential energy. A charge must be moved through a stronger electric field with more energy, but it also must be moved through a weaker electric field with more energy.The energy that is held in a charge as a result of its placement in an electric field is known as electric potential energy (Ep). Moving two like charges in close proximity, for instance, stores potential energy because the charges repel one another. Since the charges are attracted to one another, separating opposite charges also stores potential energy.The configuration of a particular set of point charges within a given system is connected with the potential energy known as electric potential energy, which is a product of conservative Coulomb forces.Completed question :
A point charge q1 , is held stationary at the origin. A second charge q2 is placed at a point a, and the electric potential energy of the pair of charges is -6.4 x [tex]10^{-8}[/tex] J. When the second charge is moved to point b, the electric force on the charge does 4.2 x [tex]10^{-8}[/tex] J of work. What is the electric potential energy of the pair of charges when the second charge is at point b?
Given data :
PE1 = -6.4 x [tex]10^{-8}[/tex] J
Work done = 4.2 x [tex]10^{-8}[/tex] J
PE1 = PE2 + Work done
PE2 = PE1 - Work done =
= -6.4 x [tex]10^{-8}[/tex] J - 4.2 x [tex]10^{-8}[/tex] J = -10.6 x [tex]10^{-8}[/tex] J
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Add.
18 9/10 + 8 3/10
In simplest form
Answer:
136/5
Step-by-step explanation:
18 9/10 + 8 3/10
change to improper fraction
=189/10 + 83/10
Adding, you have:
=272/10
2 can further divide both numbers
= 136/5
A group of 12 people on a trek have enough water to last 8 days.
a) If 4 more people join the trek, how long will the water supply last the
whole group?
When the number of people is 16, the water lasts for 6 days, which is found using unitary method.
What is the unitary method?
The unitary method is a strategy for problem-solving that involves first determining the value of a single unit and then multiplying that value to determine the required value.
a) Let the amount of water present = L
Initially, this amount was considered for 12 people for 8 days.
For 12 people,
8 days = L
1 day = L/8
So the water required for one person for one day = (L/8) / 12 = L/96
But now 4 more people joined the trek,
So for 16 people, water used in one day = (L/96)*16 = L/6
Now the water will last for 6 days since,
(L/6 * 6) = L
b) The assumption that is made while solving the question is that the water required by each person is considered the same(L/96) even if the number of persons increases.
Therefore the water lasts for 6 days when the whole group consists of 16 people.
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An accessory shop estimated that to produce one unit of a product the cost for raw materials is RM15. The fixed cost is RM5 000. The product is sold for RM25 per unit.
a. Find the profit function, P(x), where x is the number of units of the product.
b. Find the break-even point.
c. How much was the profit/loss if 350 units were sold.
d. Sketch the graph of the cost function, C(x) and the revenue function, R(x). Indicate the break-even point and shade the profit and loss areas.
please help me to answer a,b,c and d.
a. The profit function P(x) is 10x - 5000.
b. The break even point is at 500 units.
c. If 350 units were sold, the loss was Rs. 1500.
d. The graph of the functions are attached below.
The solutions are obtained using the profit function.
What is profit function?
A profit function is a mathematical relationship that represents the difference produced when the cost function is subtracted from the revenue function. The graph of a profit function shows the optimal combination of revenues and expenses to produce the maximum profit.
a. We are given cost of raw material as Rs. 15 and the fixed cost is Rs. 5000. The product is sold for Rs.25 per unit.
This means that R(x) = 25x
We know that TC= FC + VC(x)
So, TC = 5000 + 15x
Therefore, the profit function will be
⇒Profit = R(x) - TC
⇒Profit = 25x - 5000 - 15x
⇒Profit = 10x - 5000
b. For break even, the profit should be 0.
Therefore,
⇒10x - 5000 = 0
⇒10x = 5000
⇒x = 500
So, the break even will be at 500 units.
c. We are given x=350
Putting this value in profit function, we get
⇒Profit = 10(350) - 5000
⇒Profit = 3500 - 5000
⇒Profit = -1500
So, there is loss of Rs. 1500.
d. The red line represents the cost function and the blue line represents the revenue function.
The break even point is the point where the two lines are meeting.
The area below the break even is the loss area and above it is the profit area.
Hence, the solutions are obtained.
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seven values on the number line above are marked with letters. match the opposites. question 11 options: a) f and h; y and y b) c and l; a and k c) a and k; f and h d) c and l; f and h
The answer to the question is d) c and l; f and h.
The concept of opposite numbers on the number line can be expressed mathematically by the equation -x = y, where x is the original number and y is the opposite number. This equation can be used to calculate the opposite of any number. For example, if the number 5 is located at point a on the number line, the opposite of 5 is located at point k and can be calculated by substituting 5 for x in the equation and solving for y. -5 = y, therefore y = -5. The opposite of 5 is therefore -5. To calculate the opposite of any of the other numbers marked on the number line, the same equation can be used. The answer to the question is d) c and l; f and h.
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At a baseball game, a vender sold a combined total of 135 sodas and hot dogs. The number of sodas sold was two times the number of hot dogs sold. Find the number of sodas and the number of hot dogs sold.
Answer:
vendor sold 90 sodas and 45 hot dogs
Step-by-step explanation:
Let x = number of sodas sold
Let y = number of hot dogs sold
We have x = 2y (1)
( The number of sodas sold was two times the number of hot dogs sold)
We also have x + y = 135 (2)
( sold a combined total of 135 sodas and hot dogs.)
Substituting x = 2y we get
2y + y = 135
3y = 135
y = 135/3
y = 45
Therefore x = 135 - 45
x = 90
Therefore vendor sold 90 sodas and 45 hot dogs
A company sells concrete in batches of 5 cubic yards. The probability distribution of X, the number of cubic yards sold in a single order for concrete from this company, is shown in the table. The expected value of the probability distribution of X is 19.25 and the standard deviation is 5.76. There is a fixed cost to deliver the concrete. The profit Y, in dollars, for a particular order can be described by Y = 75X - 100. What is the standard deviation of Y?
answer choices
O $332.00
O $432.00
O $532.00
O $1,343.75
O $1,400.00
The standard deviation of Y is $432.00 and this can be determined by using the formula of standard deviation and the given data.
Given :
A company sells concrete in batches of 5 cubic yards.
The probability distribution of X, the number of cubic yards sold in a single order for concrete from this company, is shown in the table below.
The expected value of the probability distribution of X is 19.25 and the standard deviation is 5.76.
There is a fixed cost to deliver the concrete. The profit Y, in dollars, for a particular order can be described by (Y = 75X - 100).
The formula to obtain the standard deviation is given below:
SD(Y) = SD(75X - 100)
Simplify the above expression by substituting the value of SD(X) and SD(100) in the above expression.
SD(Y) = 75SD(X) - SD(100)
SD(Y) = 75 SD(X) - 0
SD(Y) = 75×5.76
SD(Y) = $432
Therefore, the correct option is B.
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Find the area of the shaded region shown below and choose the appropriate result.
92 Square inches is the area of the shaded region shown below
What is Area?The area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.
Given a rectangle, that has a length of 12 inches and 9-inch width
Since,
Area = length * width
Area of the given triangle = 12 * 9
Area of the given triangle = 108 square inch
There is also one square inside this rectangle of side 4 inch
Since the area of square = side * side
Thus in our case,
Area of square = 4 * 4 = 16 square inch
As we can see in the figure:
Area of shaded region = complete area of rectangle - area of square
Area of shaded region = 108 - 16
Area of shaded region = 92 square inch
Therefore, The area of the shaded region is 92 Square inches.
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Complete question:
The average yearly cumulative rainfall in Tucson by month is shown in the graph below. Does this
graph represent cumulative rainfall as a function of the day? Why or why not? What is the average
annual cumulative rainfall in Tucson? What is the approximate average rainfall in December? During
which month is average rainfall the greatest? How do you know?
The average annual cumulative rainfall is 1 inch per month. During month of August average rain fall is greatest because slope in this month is maximum.
What is the average?In maths, the average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values. When we need to find the average of a set of data, we add up all the values and then divide this total by the number of values.
The graph does not represent cumulative rainfall as a function of day.
Because they have average all values for month Total cumulative rainfall is 12 inches.
Total period is 12 month
So, average annual cumulative rainfall is
12/12 =1 inch per month
Average rainfall in the month of December= (average cumulative rainfall in December - average cumulative rainfall in November)
= 12-11
= 1 inch
Therefore, during month of August average rain fall is greatest because slope in this month is maximum.
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Can someone tell me if this is right? If not please tell me the actual answer.
Answer:
That is correct.
Step-by-step explanation:
The greater the absolute value of a negative number, the lesser (farther left from zero) it is. The greater the absolute value of a positive number, the greater (farther right from zero) it is.
Thus,
-6 < -2 < 0 < 4 < 8
and
-5.5 < -5.2 < -5 < -2.5 < 5.5
Notice also how it is easier to compare numbers when they are converted to the same form—in this case decimal form.
9(7h−4k)+10k−5(6k−7h)
Answer:
98h - 56k----------------------------
Given expression:
9(7h - 4k) + 10k - 5(6k - 7h)Simplify it in steps below:
9(7h - 4k) + 10k - 5(6k - 7h) = Given 9(7h) - 9(4k) + 10k - 5(6k) + 5(7h) = Distribute63h - 36k + 10k - 30k + 35h = Simplifyh(63 + 35) - k(36 - 10 + 30) = Collect like terms98h - 56k AnswerAnswer:
[tex] \sf \: 98h - 56k [/tex]
Step-by-step explanation:
Given expression,
→ 9(7h - 4k) + 10k - 5(6k - 7h)
Let's simplify the expression,
→ 9(7h - 4k) + 10k - 5(6k - 7h)
→ 63h - 36k + 10k - 30k + 35h
→ (63h + 35h) + (-36k + 10k - 30k)
→ (98h) + (-56k)
→ 98h - 56k
Hence, answer is 98h - 56k.
Two cars are 298 mi apart and traveling toward each other along the same road. They meet in 2 hr. One car is traveling 7 mph slower than the other. What is
the speed of each car?
Part 1/2
The faster car travels at (blank) mph.
The faster car is traveling at 149 mph, and the slower car is traveling at 142 mph.
How to calculate the speed?Speed can be calculated using the following formula: Speed = Distance/Time.Speed is measured in units such as meters per second (m/s), kilometers per hour (km/h), miles per hour (mph), etc.To calculate the speed of an object, you must first measure the distance it has traveled and the time it took to travel that distance. If the object is moving in a straight line, the distance is the length of the line. If it's moving in a circle, the distance is the circumference of the circle.Once you have the distance and time, divide the distance by the time to get the speed of the object. For example, if an object travels 10 meters in 5 seconds, its speed is 10/5 m/s, or 2 m/s.The faster car is traveling at (298 mi / 2 hrs) = 149 mph.The slower car is traveling at (149 mph - 7 mph) = 142 mph.
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1. You are the manager of a small store that specializes in hats, sunglasses, and other accessories. You are considering a sales promotion of a new line of hats and sunglasses. You will offer the sunglasses only to those who purchase two or more hats, so you will sell at least twice as many hats as pairs of sunglasses. Moreover, your supplier tells you that, due to seasonal demand, your order of sunglasses cannot exceed 100 pairs. To ensure that the sale items fill out the large display you have set aside, you estimate that you should order at least 210 items in all. Assume that you will lose $3 on every hat and $2 on every pair of sunglasses sold. Given the constraints above, how many hats and pairs of sunglasses should you order to lose the least amount of money in the sales promotion? [Using Graphic method]
Least cost in the sales promotion is when (140, 70) i.e. Hats = 140 and pair of glasses = 70.
What is meant by Graphic method?To determine if the data support the mixing of two potential sources or the fractionation of a single source, graphical approaches are frequently used.
To better interpret their data, researchers now employ a variety of graphical tools, including scatterplots, box plots, and histograms. Graphs are excellent for illustrating trends, patterns, and correlations between variables as well as for displaying and summarizing vast volumes of numerical data.
Value of cost at (140, 70) is 3 × 140+ 3 × 70
= $630
Consider any point on the feasible line, say (150, 60)
Cost = 3 × 150 + 3 × 60 = $570
Cost is increasing towards the point (210, 0)
Thus, Least cost is when (140, 70) i.e. Hats = 140 and pair of glasses = 70.
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Evaluate the following expression.
3
8
2
(3) ².
8
11
2
(Type an integer or a simplified fraction.)
By calculating, The value of given expression 8 · (2 + 3 )²- 4² is 184
What is Algebraic expression ?
Algebraic expressions are the concept of expressing numbers the use of letters or alphabets with out specifying their actual values. The fundamentals of algebra taught us a way to explicit an unknown price using letters along with x, y, z, etc. those letters are known as right here as variables.
An algebraic expression can be a combination of both variables and constants. Any cost this is positioned before and extended by using a variable is a coefficient.
Given expression ,
= 8 · (2 + 3 )²- 4²
= 8. (5)^2 - 4^2
=8.25 - 16
= 200 - 16
= 184
so, the value of expression is 184.
Therefore, The value go given expression 8 · (2 + 3 )²- 4² is 184
To learn more about Algebraic expression from the given link.
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