Because the variable has an even power, we will see that:
As x approaches -∞, h(x) approaches -∞
As x approaches ∞, h(x) approaches -∞.
Here we have h(x) = -4x^2 + 11
Notice that the variable is squared, this means that the sign does not matter, the outcome of:
-4x^2 will always be negative. So in both ends (when x tends to infinity and negative infinity), we will have the same end behavior.
When we take that limit, -4x^2 will just tend to negative infinity, then in both cases, the function tends to negative infinity.
So we have:
As x approaches negative infinity, h(x) approaches negative infinity.
As x approaches positive infinity, h(x) approaches negative infinity.
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find the prime factorization of 85
The prime factors of 85 is 5 and 17
Prime factorisation:
Finding the prime factors of a given number, such as a composite number, is done through the process of prime factorization. The prime numbers are the only components in these factors. A number with just the number itself and factor 1 is said to be a prime number.
Factor:
the quantities that are multiplied to produce new quantities are called Factor.
Prime factors:
A prime factor is a factor that is a prime number and not a composite number.
85=5×17
Therefore,The prime factors of 85 is 5 and 17
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solve 9x + 7 = 12x - 3
and 4 1/2x = 3x - 1
find x please show your work!!
a car radiator contains 10 liters of a 30% antifreeze solution. how many liters will have to be replaced with pure antifreeze if the resulting solution is to be 50% antifreeze?
4 liters of pure antifreeze is needed.
What is an linear equation in math?
An algebraic equation of the form y=mx+b is referred to as a linear equation. m is the slope, and b is the y-intercept, and all that is involved is a constant and a first-order (linear) term.
The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
Let the amount of pure antifreeze required be x + 10 liters. Thus, total solution amount will be
0.30 (10) + 1.00(x) = 0.50 ( x + 10 )
3.00 + x = 0.50x + 5.00
0.50x = 2.00
x = 4
Thus, 4 liters of pure antifreeze is needed.
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Can someone help(explain how)
Answer:a,8
when you do this in the graph its quite clear that in won't turn into a square so I think you should imagine it as a triangle.
There are 60 people in a choir.
Half of the people in the choir are women.
The number of women in the choir is 3 times the number of men in the choir.
The rest of the people in the choir are children.
the number of children in the choir : the number of men in the choir
= n : 1
Work out the value of n.
Answer:
There are 60 people in the chior so we will be dividing that number up to see how many women men and children there are. Half of them are women, which mean divide 60 by 2 which equals 30. There are 30 women in the choir. The number of women is 3 times compared to men. Since its 3 times we use the commutative property of division. 30 divided by 3 is 10. There are 10 men in the choir. The rest are children. To find the rest of them we will take how many people in the choir we know so far and then subtract from the total: 60. there are 30 women and 10 men which adds up to 40. 60 minus 40 equals 20. There are 20 children in the choir.
Since n = number of men and children:
n = 30
30 : 1
Step-by-step explanation:
Hope it helps! =D
Help me pleaseesesese
Answer:
21
Step-by-step explanation:
35x18 is 630/30 is 21.
Does anybody dirt bike??
Answer:
Yes, some
Step-by-step explanation:
how to use coordinates to compute the distance between two points on the coordinate plane
Answer:
d = √[(x2 x 2 − x1 x 1 )2 + (y2 y 2 − y1 y 1 )2]
Step-by-step explanation:
research looks at how variables vary with each other, while research looks at how one variable causes a change in another variable. descriptive; correlational correlational; experimental experimental; descriptive experimental; correlational
"Correlational" research looks at how variables vary with each other, while "experimental" research looks at how one variable causes a change in another variable.
What is correlational research?Research is a form of non-experimental methodology in which a researcher measures 2 factors and analyzes and evaluates the statistical relationship among them without the influence of any other variable.
Some key features regarding the correlational research are-
The correlation coefficient (a statistical technique that determines the strength of the connection between two variables) shows this same correlation between two variables, with a value ranging from -1 to +1. A positive correlation exists between the two variables so when correlation coefficient is close to +1. If the value is close to -1, the two variables have a negative correlation. Whenever the value is close to zero, the two variables have no relationship.To know more about the correlational research, here
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The endpoints of segment AB are A (-7, 3) and B (1, 0). Find the coordinates of the midpoint M. SHOW WORK
Answer:
We can now solve for B(x2, y2):
-14 = -3 + x2 and 16 = 6 + y2
-11 = x2 ... and... 10 = y2
Therefore B(x2, y2) = (-11, 10)
Step-by-step explanation:
Swati played eight basketball games this season. her point totals for each game were 8, 14, 4, 7, 6, 14, 4, and 7. what was the mean number of points she scored per game? 7 8 9 10
The Mean number of points she scored per game is 8.
Mean is defined as the average value of the given set of data .
mean is calculated by dividing the (sum of all observations) with (total number of observations).
For Example , Smith scored 8,6,10 out of 10 in his three tests.
so the mean score of smith will be [tex]\frac{8+6+10}{3} =\frac{24}{3} =8[/tex].
In the given question
Points for each game = 8, 14, 4, 7, 6, 14, 4, and 7.
Sum of all the points = 64.
Total number of basketball games =8
[tex]Mean= \frac{Sum of all the points }{total number of games} \\ \\ Mean=\frac{64}{8} =8.[/tex]
Therefore , the mean number of points Swati scored per game is 8.
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Answer:
it is 8 the mean is 8
Step-by-step explanation:
Make a conjecture about each value or geometric relationship.the relationship between AP and PB if M is the midpoint of AB and P is the midpoint of AM
The geometric relationship between AP and PB such that M is the midpoint of AB and P is the midpoint of AM is PB = 3AP.
What is a line segment?A line section that can connect two places is referred to as a segment.
In other words, a line segment is just part of a big line that is straight and going unlimited in both directions.
Given that,
M is the midpoint of AB and P is the midpoint of AM
Let's suppose AP = x
Then,
AB = AM + MB
Since M is the midpoint so AM =
MB = AM
AB = AM + AM = 2AM
Since P is the midpoint of A and M
So,
AP = PM
AM = AP + PM
So,
AM = 2AP = 2x
So,
MB = 2x
So,
AP = x and PB = 3x
PB = 3AP
Hence "The geometric relationship between AP and PB such that M is the midpoint of AB and P is the midpoint of AM is PB = 3AP".
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25 points plus brainliest
Answer:
y = 3x - 6
Step-by-step explanation:
to find the answer we must first find the slope
the slope must be 3x because the two lines must be parallel
so
y = 3x + b
we must plug in x and y to find b
so
9 = 3(5) + b
9 = 15 + b
b = -6
that is your b
so
y = 3x - 6
that is your equation
Answer: I'd say C (y = 3x - 6)
Step-by-step explanation:
1. I mean, it is quite obvious as a parallel line needs to go the same way
2. But a parallel line doesn't mean the line is the same one, since the coordinate says that the other line passes through (5,9).
3. Also because looking at a graphing calc, you can see it for yourself, the equation on C is the correct answer
17/3 as a mixed number
Answer:
5 2/3
Step-by-step explanation:
because 17/3= 5 so 5 then they is 2 left so the answer is 5 2/3
a. statistics 201 is a course taught at a university. professor rauch has taught nearly 1,500 students in the course over the past 5 years. you would like to know the average grade for the course.
The information illustrated about the statistics 201 is a sample.
What is a sample?A sample is an analytical subset of a larger population in statistics. Researchers can conduct their studies more quickly and with more manageable data by using samples. If the sample size is large enough, there won't be any bias, but getting such a sample might be costly and time-consuming.
The entire group about whom you want to make conclusions is referred to as a population. The particular group from which you will gather data is known as a sample. The sample size is always smaller than the population as a whole.
Since there are many students, a sample will be used.
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For the following questions, would you collect information using a sample or population
a. statistics 201 is a course taught at a university. professor rauch has taught nearly 1500 students in the course over the past 5 years. you would like to know the average grade for the course
A company that teaches self-improvement seminars is holding one of its seminars in hillsboro. the company pays a flat fee of $388 to rent a facility in which to hold each session. additionally, for every attendee who registers, the company must spend $11 to purchase books and supplies. each attendee will pay $15 for the seminar. once a certain number of attendee register, the company will be breaking even. what will be the company's total expenses and revenues? how many attendees will that take?
The total number of attendees who attended the seminar was 97. While the total cost and revenue generated are given to be $1455 each. This problem is solved using the knowledge of linear equations.
What is a linear equation?
It is the equation in which the degree of a variable is always one i.e. the greatest power of a variable is one. Linear equations consist of two major types, linear equations in one variable and linear equations in two variables. The general form of a linear equation in one variable is ax + b = 0, while for two variables is ax + by + c = 0
Calculation of the total number of attendees of seminar and total revenue generated
Let us assume x as the number of attendees and C(x) as the cost function for the company
According to the given conditions,
C(x) = 11x + 388
As the company pays $11 for every person, thus the total amount for x attendees is given by 11x, further $388 is added up to attain overall dollars.
Further, let the revenue be R(x) being equal to $15 per person i.e.
R(x) = 15x
The company will be breaking even when the cost and revenue are the same, R(x) = C(x)
15x = 11x + 388
15x - 11x = 388
4x = 388
x = 97
Thus, the total number of people attending the seminar is 97.
Now, calculate the total expense, C(x) and revenue, R(x)
C(x) = 11(97) + 388
= $1455
R(x) = 15(97)
= $1455
The cost and revenue are $1455 for each.
Hence, the total number of attendees who attended the seminar is 97. Total cost and revenue are given to be $1455 each.
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how would ninteen billion,eighty-seven thousand,three hundred fourteen be written in standard form
Answer: 190,870,314
Step-by-step explanation:
It would be 190,870,314
answer with show work!
continuing question.
What pattern would have 64 squares?
Write down an expression, in terms of n, for the number of squares in Pattern n.
Answer:
Pattern 8 would have 64 squares.
Step-by-step explanation:
Ok, I understand, Pattern 4 would have 16 squares, so we have to continue adding the pattern.
5 = 25, 6 = 36, 7 = 49, and 8 = 64. The key to this is each pattern number is multiplied BY ITSELF.
Hope this helps!
Sorry for being a little rude previous question, I didn't have a reference.
The pie chart below shows information about
the electronic devices that a shop sold in
January.
The shop sold 900 electronic devices in total in
January.
In February, the shop sold the same numbers of
tablets, desktop computers and laptops as in
January, but sold 40% more mobile phones.
If a second pie chart was drawn showing the
shop's sales in February, what would the central
angle of the mobile phones section be?
Give your answer in degrees (°) to 1 d.p.
Electronic devices sold in January
70°
84
60
146°
Key
Desktop computer
Laptop
Tablet
Mobile phone
Not drawn accurately
The central angle of mobile phones section in February be 91°
Given,
The total number of electronic devices sold by a shop in January = 900
According to pie chart
900 implies 360°. Therefore, 900/360 = 2.5
Now lets check the number of devices sold in January:
Desktop = 60° ⇒ 60 × 2.5 = 150
Laptop = 146° ⇒ 146 × 2.5 = 365
Tablet = 84° ⇒ 84 × 2.5 = 210
Mobile = 70° ⇒ 70 × 2.5 = 175
Its given that in February, all other numbers are same except Mobile phones.
40% more mobile phones are sold in February than in January.
So, number of mobile phones sold in February = 175 × (140/100) = 245
Now lets calculate the total number of devices sold in February:
900 - 175 = 725
725 + 245 = 970
970 devices sold in February.
According to pie chart:
970 implies 360 = 970/360 = 2.69
Now lets check the degree in pie chart for each devices,
Desktop = 150 ⇒ 150/2.69 = 55.7°
Laptop = 365 ⇒ 365/2.69 = 135.5°
Tablet = 210 ⇒ 210/2.69 = 78°
Mobile = 245 ⇒ 245/2.69 = 91°
That is, the central angle of mobile phones section in February be 91°
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A 48.548.5 -ounce batch of cologne will be used to fill empty bottles. Each full bottle will contain 0.350.35 ounces of cologne. This batch of cologne will fill at most how many bottles full of cologne?
This batch of cologne can fill 138 bottles at most where each bottle has 0.35 ounce of cologne.
We are given that:
The total amount of cologne that we have = 48.5 ounce
Also,
Each bottle requires = 0.35 ounces of cologne.
We need to tell that how many bottles can this batch fill with 48.5 ounce of cologne.
We will do this by dividing the total amount of cologne with the cologne required per bottle.
So, we get that:
Number of bottles that can be filled = 48.5 ounces / 0.35 ounces.
Dividing the values, we get that:
Number of bottles that can be filled = 138.57
Number of bottles that can be filled = 138 bottles.
Therefore, this batch of cologne can fill 138 bottles at most where each bottle has 0.35 ounce of cologne.
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In a test run, a certain car accelerates uniformly from zero to 22.4 m/s in 2.10 s. (a) what is the magnitude of the car's acceleration?
A specific car accelerates consistently from zero to 22.4 m/s in 2.10 seconds during a test session. The car's uniform acceleration is 8.1356 meter/[tex]sec^{2}[/tex].
What is acceleration?The rate at which an object's velocity with respect to time changes is known as acceleration in mechanics. Accelerations are vector quantities (in that they have magnitude and direction). The direction of the net force acting on an object determines its acceleration.
For instance, a car accelerates in the direction of motion when it begins at rest (zero velocity in an inertial frame of reference) and moves at increasing speeds in a straight path. When a vehicle turns, its motion vector is altered and accelerates in the new direction. A linear acceleration is the acceleration of the car in the direction it is moving, and it is this acceleration that the occupants of the car feel.
Calculations:
Acceleration=([tex]\frac{change in speed}{change in time}[/tex])= (24 m/s) / (2.95 s) = 8.1356 meter/[tex]sec^{2}[/tex]
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18. Two rectangles are shown below. Rectangle P has a perimeter of 20 inches. Rectangle Q has a perimeter of [/latex]30[/latex] inches.
What are the values of j and h?
A. j = 3 and h = 3
B. j = 10 and h = 4
C. j = 2 and h = 4
D. j = 9.5 and h = 6.5
In two rectangles, the value of j and h are 2 and 4
The subject of mathematics known as mensuration is concerned with measuring geometric shapes and their various characteristics, such as length, volume, shape, surface area, lateral surface area, etc.
According to the question, we get the equations
The perimeter of rectangle = 2*[base + height]
Rectangle P
Perimeter = 20inches
Perimeter = 2*[j+4+h]
20= 2j+2h+8
2j+2h=12
J + h=6
J=6-h ……….. Equation 1
Rectangle Q
Perimeter = 30 inches
Perimeter = 2*[j+1+3h]
30=2j+6h+2
2j+6h=28
J+3h=14 ……….. Equation 2
Substitute equation (1) in equation (2)
(6-h) +3h=14
2h=8 = H=4
J=6-h
J=6-4 = J=2
Hence, the value of j and h is 2 and 4.
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4+2n = n+8+n
How do you solve this? Help please!!
Answer:
0=4 No solution
Step-by-step explanation:
you combine like terms like n, and n= 2n+8
then subtract 4 from both sides= 2n=2n+4
Last week a painter painted 4 houses in 6 days. what is the productivity of the painter? calculate your answer to 2 decimal places.
The productivity of the painter is 0.66 up to two decimal places. It is attained by applying the knowledge of the division of two numbers and decimals to the provided problem.
What is decimal?
A decimal is a quantity that is distributed into two components, namely a whole and a fraction. A decimal number represents the numerical value lying in between the two integers. A decimal point (.) is used to segregate the fractional part from the whole part of a number.
E.g. 1.5, 0.06, 7.05, etc.
Calculation of the productivity of the painter
Productivity of the painter is obtained by dividing the number of houses painted by the number of days taken to paint them
The number of houses painted is 4
The number of days taken to paint 4 houses is 6 days
Productivity = 4 ÷ 6
= 0.666
Thus, the productivity of the painter is 0.66 up to two decimal places.
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Plot the points in a coordinate plane and sketch ∠ XYZ. Then classify it as right, acute, or obtuse.
X(5,-3), Y(4,-1), Z(6,-2)
The points X(5,-3), Y(4,-1) and Z(6,-2) can be plotted as given below. From the obtained graph ∠XYZ is the obtuse angle.
The given coordinates are X(5,-3), Y(4,-1) and Z(6,-2).
We need to classify ∠XYZ whether it is right, acute, or obtuse.
How to plot the points in a cartesian plane?A cartesian plane or coordinate plane can be defined as a plane formed by the intersection of two coordinate axes that are perpendicular to each other. The horizontal axis is called the x-axis and the vertical one is the y-axis. These axes intersect with each other at the origin whose location is given as (0, 0). Any point on the cartesian plane is represented in the form of (x, y). Here, x is the distance of the point from the y-axis and y is the distance from the x-axis.
Now, X(5,-3), Y(4,-1) and Z(6,-2) can be plotted as given below:
The given points X(5,-3), Y(4,-1) and Z(6,-2) have positive x-coordinate and negative y-coordinate.
In the cartesian plane, the fourth quadrant positive x-coordinate and negative y-coordinate.
So, all points X(5,-3), Y(4,-1) and Z(6,-2) lie in the fourth quadrant.
From the graph, we can see that the two lines make an obtuse angle, which is more than 180° and less than 360°.
From the obtained graph ∠XYZ is the obtuse angle.
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Eric had 2 picnic baskets. He put 7 apples in each one. How many apples did he put into the picnic baskets.
Answer:
14
Step-by-step explanation:
Answer:
14
Step-by-step explanation:
2 x 7 = 14 apples
Find the indicated one-sided limits, if they exist. (if an answer does not exist, enter dne.)
The limit doesn't exist.
What is a limit?
The value that a function (or sequence) approaches when the input (or index) gets closer to a particular value is known as a limit. Calculus and mathematical analysis are impossible without limits, which are also required to determine continuity, derivatives, and integrals.
In addition to being closely related to limit and direct limit in category theory, the idea of a limit of a sequence is further generalized to include the concept of a limit of a topological net.
A function's limit is typically expressed in formulas as
[tex]\lim_{x \to c } F(x) = L[/tex]
It is typically used to assign values to specific functions at locations where none are defined while maintaining consistency with existing values.
[tex]F(x) = -x+8 ,x\leq 0[/tex]
[tex]F(x) = 4x+9 , if x > 0[/tex]
[tex]\lim_{x \to 0^{+} } F(x) = \lim_{n \to 0^{+} } (4x+9) = 9[/tex]
[tex]\lim_{x \to 0^{-} } F(x) = \lim_{x \to 0^{-} } (-x+8) =8[/tex]
[tex]\lim_{x \to 0^{+} } F(x) \neq \lim_{x \to 0^{-} } F(x)[/tex]
So limit doesn't exist
For limit to exist
[tex]\lim_{x \to 0^{+} } F(x) = \lim_{x \to 0^{-} } F(x) = \lim_{x \to 0} f(x)[/tex]
must be satisfied
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Given that f ( x ) = x 2 + 9 x + 20 f(x)=x 2 +9x+20 and g ( x ) = x + 5 g(x)=x+5, find f ( x ) + g ( x ) f(x)+g(x) and express the result in standard form.
The standard form is [tex]x^{3}[/tex] + 15[tex]x^{2}[/tex] + 75x + 125.
We have,
f ( x ) = [tex]x^{2}[/tex]+ 9 x + 20
g ( x ) = x + 5
Now we will simplify f ( x ) + g ( x ) f ( x ) + g ( x ).
On substituting the value of f ( x ) and g ( x ) in this equation, we get
( [tex]x^{2}[/tex]+ 9 x + 20 ) + ( x + 5) ( [tex]x^{2}[/tex]+ 9 x + 20 ) + ( x + 5)
Now we will simplify this equation,
( [tex]x^{2}[/tex]+ 10 x + 25 ) + ( [tex]x^{3}[/tex] + 9[tex]x^{2}[/tex] + 20x + 5[tex]x^{2}[/tex] + 45x + 100 )
⇒ [tex]x^{3}[/tex] + 15[tex]x^{2}[/tex] + 75x + 125
The standard form is [tex]x^{3}[/tex] + 15[tex]x^{2}[/tex] + 75x + 125.
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the mean of the sample group of answer choices can assume any value between the highest and the lowest value in the sample. can never be negative. can never be zero. is always smaller than the mean of the population from which the sample was taken.
The mean of the sample (D) none of these alternatives is correct.
What is a mean?In mathematics, particularly statistics, there are several types of means. Each mean is used to summarize a specific set of data, often in order to better understand the overall value (magnitude and sign) of a given data set.The arithmetic mean, also known as "arithmetic average," of a data set is a central tendency of a finite collection of numbers: specifically, the sum of the values multiplied by the number of values. In two simple steps, we can calculate the mean or average of a data set: add up all of the values to find the sum. Subtract the sum from the total number of values in the data set.Therefore, the mean of the sample (D) none of these alternatives is correct.
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The correct question is given below:
The mean of the sample
a. is always smaller than the mean of the population from which the sample was taken
b. can never be zero
c. can never be negative
d. None of these alternatives is correct.
5. A state began an effort to increase the
deer population. In year 2 of the ef-
fort, the deer population in a state
forest was 2,400. In year 4, the pop-
ulation was 3,456. Write an explicit
rule for the sequence using subscript
notation.
The explicit rule for the sequence using subscript notation is [tex]a_n=2000\times1.2^{n-1}[/tex] .
Explicit expressions are always used to represent any term in a sequence without describing any other term in the sequence. The meaning of "explicit" is direct, something that can be found directly without knowing the other terms in the sequence.A term in a sequence can be uniquely represented by a single expression, an explicit expression. Geometric Sequence: [tex]a_n=ar^{n-1}[/tex], where 'a' is the first term and 'r' is the common ratio.It is given that sequence is G.P
In G.P 2nd and 4th is given by
[tex]a_2=ar[/tex] ...(1) and [tex]a_4=ar^3[/tex] ...(2)
We have given [tex]a_2=2400 , a_4=3456[/tex]
Putting in equation (1) and (2) , we get
[tex]2400=ar[/tex] ...(3) and [tex]3456=ar^3[/tex] ...(4)
On dividing equation (3) by equation (4) , we get
[tex]\frac{2400}{3456} =\frac{ar}{ar^3} \\\\\\ 0.6944=\frac{1}{r^2}\\\\r^2=1.44 \\r=1.2[/tex]
First term will be given by
[tex]a_1=a_2 r^{1-2}\\\\a_1=2400r^{-1}\\\\a_1=\frac{2400}{1.2} \\\\a_1=2000[/tex]
Nth term is given by
[tex]a_n=a_1r^{n-1}\\a_n=2000\times1.2^{n-1}[/tex]
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