We get the value of f ( - 1 ) as - 5 for the function f (x) = x + 4 x³.
We are given a function:
f (x) = x + 4 x³
A function from a set X to a set Y assigns to each element of X exactly one element of Y.
We need to find the value of f ( - 1 )
We will do this by substituting the value of x as - 1
Put x = -1, we get that:
f ( x = -1 ) = ( - 1 ) + 4 ( - 1 )³
f ( - 1 ) = - 1 + 4 ( - 1 )
f ( - 1 ) = - 1 - 4
Simplifying the function:
f ( - 1 ) = - 5
Therefore, we get the value of f ( - 1 ) as - 5 for the function f (x) = x + 4 x³.
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Please I need help ASAP what’s the distance between the 2 points
Answer:
7 grids
Step-by-step explanation:
-start at one of your points
-count up or down the y-axis to the other point.
-count along the x-axis to your other point.
-add the 2 lengths.
can anyone solve -6(4-x)<-4(x+1)
Answer: x<2
Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.
hope this was helpful!! - hailey_ <3 :)
How many centimeters are in 7 feet given that 1 inch is 2.5 cm
Answer: 210 cm
Step-by-step explanation:
1 inch=2.5 cm
1 foot=12 inches
1 foot*12 inches*2.5 cm=30 cm
1 foot=30 cm
7 feet=30*7=210 cm
an isosceles trapezoid has legs of length 30 cm each, two diagonals of length 40 cm each and the longer base is 50 cm. what is the trapezoid’s area?
768 cm'^2 is the trapezoid’s area.
What is isosceles trapezoid?
Isosceles trapezoids have equal length non-parallel sides, hence the name "isosceles" which means "equal legs". The "legs" are another name for these equal sides.
Let 50 cm = the bottom base
We can find the area of one of the triangles that comprise the area of the trapezoid.....its sides are 30, 40 and 50 cm
Let s be the semi-perimeter of one of the triangle = [ 50 + 40 + 30 ] / 2 = 60 cm
And the area of of this triangle = sqrt [ s ( s - a) (s - b) ( s -c) ] where a,b, c are the sides
So...we have sqrt [ 60 ( 60 - 30) (60 - 40) (60 - 50) ] = sqrt [ 60 * 30 * 20 * 10 ] =
sqrt [ 1800 * 200] = sqrt [ 3600 * 100] = 60 * 10 = 600 cm ^2
Now the base of this triangle = 50 and the height can be found as
follows :
Area = (1/2) 50 * height
600 = 25 * height
height = 24 cm and this is the height of the trapezoid
Now....the top base can be found as 50 - 2 sqrt [ 30^2 - 24^2 ] = 14 cm
So....the area of the trapezoid = (1/2) height ( sum of the bases) = (1/2) (24) ( 50 + 14) = 12 ( 64) = 768 cm'^2
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3.66 x 10^1 in standard form
36.6 in standard form will be [tex]3.66 * 10^{1}[/tex]
As per the question statement, we are given standard form of a number i.e., [tex]3.66 * 10^{1}[/tex].
We have to find the number whose standard form is [tex]3.66 * 10^{1}[/tex]
For solving this, we should be knowing about standard form conversion from any given number which is written by raising the number to power of 10.
[tex]3.66 * 10^{1}[/tex][tex]= 3.66 *10 = 36.6[/tex]
Therefore 36.6 is the number whose standard form is [tex]3.66 * 10^{1}[/tex]
Standard form: A number can be expressed in a fashion that adheres to specific standards by using its standard form. Standard form refers to any number that may be expressed as a decimal number between 1.0 and 10.0 when multiplied by a power of 10.To learn more about Standard form, click on the link given below:
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Help with 4 I don’t get it
you need to draw the exact graph of f(x), but moved 3 units to the right and 5 units up.
How to graph the given function?First, we know the graph of f(x), and now we want to find the graph of the function:
f(x - 3) + 5.
Remember that a horizontal translation of N units is written as:
f(x + N)
If N > 0, the translation is to the left.if N < 0, the translation is to the right.Remember that a vertical translation of N units is written as:
f(x + N)
If N > 0, the translation is upif N < 0, the translation is downwards.Then the function:
f(x - 3) + 5
Is a translation of 3 units to the right and 5 units upwards.
This means that you need to draw the exact graph of f(x), but moved 3 units to the right and 5 units up.
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O Zeema gets paid £22,440 per annum. Assuming she gets paid in equal monthly payments, how much does she earn per month?
O Zeema gets paid £1870 per month in equal monthly payments.
The amount paid each month to repay the loan over the course of the loan is known as the monthly payment. When a loan is taken out, not only the principal, or the original amount borrowed, but also the interest that accrues, must be repaid.
Now when the total amount earned in a month is given then the monthly payment is calculated by dividing the total amount by 12 as there are 12 months in a year.
Annual amount earned by O Zeema=£22,440
Therefore monthly amount earned=£22,440 ÷12=£1870
Hence O Zeema earns £1870 per month
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A shop in the mall is 5 meters by 15 meters. How much would it cost to recarpet the shop with carpet that costs $5.00 per square meter?
Work Shown:
The floor area is length*width = 5*15 = 75 square meters
1 square meter = 5 dollars
75*(1 square meter) = 75*(5 dollars)
75 square meters = 375 dollars
The mass of a textbook is approximately 0.00165 metric ton. How is this number written in scientific notation?
Answer: 1.65 × 10⁻³
Step-by-step explanation: hope this helps!!!
Simplify
45 - (31 - 9)
Answer:
23
Step-by-step explanation:
you always do whatever is in the brackets first,
31 - 9 = 22
then the equation would be,
45 - 22
so the answer is 23
hope this helped xx
Need help right now again
Answer:
I gotchu! The answer is 80.
Step-by-step explanation:
To find the mean, you need to add up all the scores and divide it by how many scores there are. In this case, there are 5 scores, so we can first add them all up.
70+75+80+85+90=400
Now, since there are 5 scores, you need to divide 400 by 5.
400/5=80
The mean would be 80.
Hope that helped!
Have a great day!
:D
which sequence of rigid transformations will map the preimage ABC onto image A'B'C'?
The sequence of rigid transformations that will map the preimage ΔABC onto image ΔA'B'C' is Option(a) a reflection across the x-axis, a translation 8 units right, and then a reflection across the x-axis.
What is the sequence of rigid transformations?There are three basic rigid transformations: reflections, rotations, and translations.Reflections, as the name implies, mirror the given shape over a particular line. Translations slide or shift a shape from one location to another, whereas rotations spin a shape about a predetermined center point.Co-ordinates of the points of ΔABC are,
A = (-4, 2)
B = (-6, 2)
C = (-2, 6)
point (x,-y) is the reflection of the point (x,y) across the x-axis.
So, new co-ordinates are,
A = (-4, -2)
B = (-6, -2)
C = (-2, -6)
point (x+8,y) is the translation of the point (x,y) by 8 units right.
So, new co-ordinates are,
A = (4, -2)
B = (2, -2)
C = (6, -6)
Then, the reflection of the point (x,y) across the x-axis is the point (x,-y).
So, new co-ordinates are,
A' = (4, 2)
B' = (2, 2)
C' = (6, 6)
These are the coordinates of ΔA'B'C' so the correct answer is Option(a).
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"The complete question is: Which sequence of rigid transformations will map the preimage ΔABC onto image ΔA′B′C′?
a) a reflection across the x-axis, a translation 8 units right, and then a reflection across the x-axis
b) a translation 4 units down and 10 units to the right
c) a reflection across the line y = x followed by a rotation 90° counterclockwise
d) a rotation 180° clockwise followed by a reflection across the x-axis."
last year, nine hundred forty-nine thousand people visited the museum. what is the number written in standard form?
The number of written in standard form is 9.45 × 10⁵
Writing in Standard formFrom the question, we are to write the given number in standard form
The given number is
Nine hundred forty-nine thousand
That is,
945000
To write a number in standard form, we will write the number as a decimal number between 1.0 and 10.0, multiplied by a power of 10.
The number, 945000, written in standard form is
9.45 × 10⁵
Hence, the number of written in standard form is 9.45 × 10⁵
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The regular price of a photograph printed on a canvas is $18. You have a coupon for 15% off. How much is the discount?
I KNOW ITS 2.70 I JUST NEED TO KNOW HOW TO GET IT PLEASE MY THINGS DUE TONIGHT AND IM VERY BAD AT PERCENTAGES!!
A bank loaned out $8200, part of it at a rate of 7.9% per year and the rest of it at a rate of 7.4% per year. The total amount of interest owed to the bank at the end of one year was $614.67.
Find the amount of money that the bank loaned out at 7.9%.
The amount that the bank loaned out at 7.9% is $1,574.00
How do represent the amounts lent at different rates?
On the assumption that x amount was loaned at 7.9% and that the remaining amount, (8,200-x) was loan out at 7.4%, we can determine the interest charged on each loan as the loan multiplied by the interest rate
interest on 7.9% loan=7.9%*x=0.079x
interest on 7.4% loan=7.4%*(8200-x)
interest on 7.4% loan=606.80-0.074x
total interest=0.079x+606.80-0.074x
total interest=0.005x+606.80
total interest on loans=614.67
614.67=0.005x+606.80
614.67-606.80=0.005x
7.87=0.005x
x=7.87/0.005
x=amount loaned at 7.9%=$1,574.00
y=$8200-$1574
y=$6,626.00
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find the solutions to the equation in the interval 0 ≤ theta ≤ ????/2 . enter your answers as a comma-separated list. 2cos(4theta) − 1
The solutions to the equation in the interval are x = π/3, x = 5π/3 and x = π.
What is an equation?A formula for a mathematical equation is one that connects two expressions and expresses their equality using the equals sign (=). In English, an equation is defined as a properly written formula that consists of two expressions connected by an equals sign, however cognates of the word in other languages may have slightly different meanings. For instance, an equation is defined as having one or more variables in French. Finding the variables' values that cause the equality to be true is the first step in solving an equation with variables.
Let's assign a variable to the cosine function, cos(x), and say y = cos (x). Our phrase changes to
4y2 + 2y - 2 = 0
2(2y2 + y - 1) = 0
2y2 + y - 1
= 2y(y+1) - (y + 1)
= (2y - 1)(y + 1)
2(2y-1)(y+1) = 0
y + 1 = 0 = y = -1
The answers cos(x) = 1/2 and cos(x) = -1 result from replacing y with cos(x). Our solutions are x = /3, x = 5/3, and x = on the interval [0, 2], where cos(x) = 1/2 for x = /3 and x = 5/3 and cos(x) = -1.
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Eva left her house at time zero and drove to the store, which is 3 blocks away, at a
speed of 1 block per minute. Then she stopped and went into the store for 3 minutes.
From there, she drove in the same direction at a speed of 1 block every 2 minutes
until she got to the bank, which is 3 blocks away from the store. She stopped at the
bank for 6 minutes. Then she drove home at a speed of 1 block every minute. Make a
graph of showing the number of blocks away from home that Eva is a minutes after
she leaves her house, until she gets back home.
The function f(x), representing the number of blocks Eva is away from her house after x minutes is
[tex]f(x) = \begin{cases} & 0\text{ if } x= 0\\ & x\text{ if } 0 < x\leq 3 \\ & 3\text{ if } 3 < x\leq 6\\ & x/2\text{ if } 6 < x\leq 12\\ & 6\text{ if } 12 < x\leq 18\\ & 24-x\text{ if } 18 < x\leq 24 \\ & 0\text{ if } x > 24 \end{cases}[/tex]
The graph for the same is attached.
In the question, we are asked to form a graph showing the number of blocks, that Eva is away from her home at x minutes, after she leaves her home.
To form the graph, we first try to make a function for x minutes, f(x), showing the number of blocks Eva is away from her home after x minutes.
Since x represents time, it cannot be negative.
At x = 0, f(x) = 0, as she is at her home at 0 minutes.
Then, Eva visits the store, 3 blocks away from her home at a speed of 1 block per minute.
Thus, she moves 1 block every minute up to 3 minutes.
Thus, we get f(x) = x, 0 < x ≤ 3.
After this, she spends 3 minutes at the store, giving f(x) = 3, 3 < x ≤ 6.
Then she moves towards the bank, in the same direction, 3 blocks away at the speed of 1 block every 2 minutes.
Thus, in every minute, she travels 1/2 block.
Thus, the function can be designed as follows:
f(x) = 3 + (1/2)(x - 6), 6 < x ≤ 12,
or, f(x) = x/2, 6 < x ≤ 12.
Now, we are given that she stops at the bank for 6 minutes.
Thus, we get, f(x) = 6, 12 < x ≤ 18.
Now, she drove back home, at the speed of one block every minute.
Thus, we get f(x) = 6 - (x - 18), 18 < x ≤ 24,
or, f(x) = 24 - x, 18 < x ≤ 24.
At the 24th minute, Eva reaches her house back, giving f(x) = 0, x > 24.
Thus, the complete function can be shown as:
[tex]f(x) = \begin{cases} & 0\text{ if } x= 0\\ & x\text{ if } 0 < x\leq 3 \\ & 3\text{ if } 3 < x\leq 6\\ & x/2\text{ if } 6 < x\leq 12\\ & 6\text{ if } 12 < x\leq 18\\ & 24-x\text{ if } 18 < x\leq 24 \\ & 0\text{ if } x > 24 \end{cases}[/tex]
The graph for this function is attached.
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1. Eight less than the product of a
number and 6 is seven less than
that number
2. The product of a number and 2 is the same as the sum of that number and eleven
The values of x are 1/ 5 and 11 respectively.
What are algebraic expressions?Algebraic expressions are expressions that are comprised of terms, constants, coefficients, variables and factors.
They are also made up of arithmetic operations made up of subtraction, addition, multiplication, division.
To determine the expressions, we have;
1. Let the number be x
We have the expression as;
6x - 8 = x - 7
collect like terms
6x - x = - 7 + 8
5x = 1
Make 'x' the subject
x = 1/ 5
2. Let the number be x
2x = x + 11
collect like terms
2x - x = 11
x = 11
Thus, the values of x are 1/ 5 and 11 respectively.
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Please help me, it’s due in 35 mins. Please & thank you *SHOW YOUR WORK*
Answer:
Week 1:
Michelle makes the most with $237.50
Chris made $195 and Alex made $178.50
Week 2:
Michele makes the most with $232
Chris made $192.50 and Alex made $180.83
Week 3:
Alex makes the most with $234.50
Chris made $272.50 and Michelle makes $206
Step-by-step explanation:
For Chris in week 1, multiply 3/100 x 1500 to get what he makes on commission. That equals $45. $150 + $45 = $195
For Michelle in week 1, multiply 15 x 5 = 75. Also multiply 25 x 6.5 = 162.5 to find how much she gets payed by the Pringles. Add it up to get $237.50
For Alex in week 1, multiply 21 x 8.5 = $178.50
For Chris in week 2, multiply 1/40 x 1000 = $25 to get what he makes on commission for the first $1,000. Then multiply 7/200 x 500 = $17.50 to get when he makes on commission for the sales over $1,000. Add it all up and get $192.50
For Michelle in week 2, multiply 10 x 5 = 50 to find how much she gets payed by the Rogers'. Then multiply 28 x 6.5 = 182 to find how much she gets payed by the Pringles. Add it up to get $232
For Alex in week 2, multiply 25 x 7 = 175 to find out how much he earns for 5 hours each day. Then, since Alex worked another 50 minutes, multiply 5/6 x 7 = 5.83. Add it up to get $180.83
For Chris in week 3, multiply 3/200 x 1500 = 42.50 to get what he makes on commission. Then add it with the base salary of 250 to get $272.50
For Michelle in week 3, since the Pringles paid her double, she earned $13 an hour. So, multiply 13 x 12 = 156. Then add it with the $50 she makes from the Rogers' and get $206
For Alex in week 3, multiply 7 by the number of hours he works each day in the week. Get $234.50
can someone help me with all of this and show work pls (I posted this before but I had to create a new acc atm) pls I'm begging bro
Answer:
Step-by-step explanation:
How would you write the name of a segment differently than the name of a line? What
symbols would you use?
The way to write the name of a segment differently than the name of a line is that a line is written with the use of two arrowheads on the ends. While a line segment is just written down by an overbar with endpoints.
What is the line segment about?A line is known to be a kind of a one-dimensional figure that moves from infinitely in 2 directions.
A line segment is seen as a part of a line that is known to be made up of definite attributes where it has two endpoints as well as a fixed length.
Therefore, The way to write the name of a segment differently than the name of a line is that a line is written with the use of two arrowheads on the ends. While a line segment is just written down by an overbar with endpoints.
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5000+200+5000+300+40
Answer:
10,540
Step-by-step explanation:
(5000*2)+(200+300)+40
10,000+500+40=10,500+40=10,540
Hope this helps!
Answer:
10540
Step-by-step explanation:
Suppose that P and Q are points on the number line.
If PQ=10 and Q lies at 13, where could P be located?
If there is more than one location, separate them with commas.
we get that the point P can either lie at - 3 or at 23.
We are given the two points:
P and Q
We are also given the distance between the two points P and Q is:
PQ = 10 units.
Now we have that Q lies at 13.
We have to find the location of P.
We know that
Distance = P ± Q
10 = P ± 13
so, we get that
10 = P + 13 or 10 = P - 13
P = 10 - 13 or P = 13 + 10
P = -3 or P = 23
Therefore, we get that the point P can either lie at - 3 or at 23.
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Options are
A. (2, 2)
B. (8, 2)
C. (3, 11)
D. (5, 1)
Answer: The answer is C(3,11)
Step-by-step explanation:
If you replace x with 3 that will be 3 to the third power 3 x 3 is 9 so 9 plus 2 is 11 you can use 11 in y, therefor your answer is C.(3,11)
Use the following diagram to answer Parts A and B. A(-6,5) B (-6,1) (-2,1 (2.1) (6.1) (6,5) A' Part A: Identify the transformation that took triangle ABC to triangle A'B'C'. Part B: If the same transformation was applied to point J(5, -4), what are the coordinates for J'? Edit View Insert Format Tools Table 12pt Paragraph I BIU 2T²00
Using translation concepts, it is found that:
A. The triangle was reflected over the y-axis.
B. The coordinates for J' are (-5,-4).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
For item a, we have that the rule applied at each vertex is given by:
(x,y) -> (-x,y).
This rule means that the triangle was reflected over the y-axis.
In item b, supposing point J(5,-4), the image is given by:
(5,-4) -> (-5,-4).
The coordinates for J' are (-5,-4).
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There are 3 circles and 9 squares. What is the simplest ratio of circles to squares?
Answer:
1/3
Step-by-step explanation:
3/9 divide both sides by 3 for simplest form
1/3
A professional gamer is preparing for a tournament. in his game he averaged a score of 534 points, every day, for 5 days. then, for the next 3 days he scored a total of 1827 points. finally in another 4 days he averaged a score of 516 points each day. in 12 days how many points in total did this gamer get
In 12 days a professional gamer got 6561 points
We know that average is ratio of the sum of all observations and the number of total observations.
For given question,
A professional gamer averaged a score of 534 points, every day, for 5 days.
⇒ 534 = (total score of 5 days) / 5
⇒ total score of 5 days = 534 × 5
⇒ total score points of 5 days = 2670 points
Then, for the next 3 days he scored a total of 1827 points.
So, the total points of 8 days would be,
total score points of 5 days + total score points of 3 days
⇒ 2670 points + 1827 points = 4497 points.
In another 4 days he averaged a score of 516 points each day.
⇒ 516 = (total score of 4 days) / 4
⇒ total score of 4 days = 516 × 4
⇒ total score points of 4 days = 2064 points
So, the total number of points he did in 12 days:
total score points of 5 days + total score points of 3 days + total score points of 4 days
= 2670 points + 1827 points + 2064 points
= 6561 points
Therefore, in 12 days a professional gamer got 6561 points
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cocoa drank 1/3 milk on monday. on tuseday she drank 1/4 gallon of milk. how much milk did she drank inb all
Identify the a, b and c values from general form:
f(x) = 7x^2 - 10x + 3
a =
b =
c =
Answer:
a = 7
b = -10
c = 3
That is all for this question.
In Exercises 11 and 12, write a rule for the translation of LMN to L'M'N'
The rule for the translation from LMN to L'M'N' is:
(x,y) -> (x + 3, y + 1).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
For this problem, we have that each vertex of LMN was:
Shifted 3 units right, hence x -> x + 3.Shifted 1 unit up, hence y -> y + 1.Thus the rule for the translation from LMN to L'M'N' is:
(x,y) -> (x + 3, y + 1).
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