The points that will lie on the line will be (0, 0) , (1, - 25) , (- 1, 25).
What is the general equation of a straight line?The general equation of a straight line is : y = mx + c.
[m] is called slope and it tells the unit rate of change in [y] with respect to [x].
[c] is called the [y] - intercept.
We have some points that lie on a line that passes through the origin with a slope of −25.
The equation of a straight line that passes through the origin and has slope of -25 will be -
y = - 25x
The points that will lie on the line will be -
(0, 0) , (1, - 25) , (- 1, 25)
Therefore, the points that will lie on the line will be (0, 0) , (1, - 25) , (- 1, 25).
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Find the Maclaurin series of the following functions.
(b) g(x) = sin(3x^2)
The Maclaurin series of sin(3x²) up to n = 3 is
[tex]=3x^2-\dfrac{9}{2}x^6+\frac{81}{40}x^{10}+\ldots[/tex]
The function is given in the question as
g(x) = sin(3x²)
Taylor (Maclaurin) series of sin(3x²) up to n = 3
A Maclaurin series is given by f(x),
[tex]f\left(x\right)=f\left(a\right)+\frac{f^'\left(a\right)}{1!}\left(x-a\right)+\frac{f^{''}\left(a\right)}{2!}\left(x-a\right)^2+\frac{f^{'''}\left(a\right)}{3!}\left(x-a\right)^3+\ldots[/tex]
[tex]f\left(x\right)=f\left(0\right)+\frac{f^'\left(0\right)}{1!}\left(x\right)+\frac{f^{''}\left(0\right)}{2!}\left(x\right)^2+\frac{f^{'''}\left(0\right)}{3!}\left(x\right)^3+\ldots[/tex]
We need to do to get the desired polynomial is to calculate the derivatives, evaluate them at the given point, and plug the results into the given formula.
f⁽⁰⁾(x) = f(x) =sin(3x²)
Evaluate the function at the point: f(0)=0
1st derivative: f(1)(x)=(sin(3x²))′ = 6xcos(3x²)
1st derivative at the given point: (f(0))′=1
2nd derivative: f(2)(x)=(f(1)(x))′=(6xcos(3x²))′=−36x2sin(3x2)+6cos(3x²)
Evaluate the 2nd derivative at the given point: (f(0))′′=6
3rd derivative: f(3)(x)=(f(2)(x))′=(6xcos(3x²))′=−36x2sin(3x²)+6cos(3x²)
Evaluate the 3rd derivative at the given point: (f(0))′′′=0
Now, use the calculated values to get a polynomial:
[tex]g(x)=0+\frac{0}{1!}x+\frac{6}{2!}x^2+\frac{0}{3!}x^3+\frac{0}{4!}x^4+\frac{0}{5!}x^5[/tex]
Thus, the Maclaurin series of sin(3x²) up to n = 3 is
[tex]=3x^2-\dfrac{9}{2}x^6+\frac{81}{40}x^{10}+\ldots[/tex]
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PLEASE HELP WILL GIVE BRAINLIST -3(0.5+3p)=-6(p-5.9) show ur full work in liner questions form i will get my alt and answer to get u brainliST
50 POINTS!!
Answer:
p = - 123/10 = -123/10 = -12.3
Step-by-step explanation:
-3(0.5 + 3p) = -6(p - 5.9)
Use the distributive property to multiply -3 by 0.5 + 3p
-1.5 - 9p = -6 (p - 5.9)
Use the distributive property to multiply -6 by p - 5.9
-1.5 - 9p = -6p + 35.4
Add 6p to both sides
-1.5 - 3p = 35.4
Add 1.5 to both sides
-3p = 35.4 + 1.5
Add 35.4 and 1.5 to get 36.9
-3p = 36.9
Divide both sides by -3
p = 36.9/-3
Expand 36.9/-3 by multiplying both numerator and the denominator by 10.
p = 369/-30
Reduce the fraction 369/-30 to lowest terms by extracting and canceling out 3.
p = -123/10
10 = 2(x - 2)
How would I solve for X?
Answer:
x = 7Step-by-step explanation:
10 = 2(x - 2)
How would I solve for X?
10 = 2(x - 2)
10 = 2x - 4
14 = 2x
x = 7
--------------------
check
10 = 2(7 - 2)
10 = 2 x 5
10 = 10
the answer is good
Answer:
x=7
Step-by-step explanation:
Given:
A linear equation is given as:
[tex]10=2(x-2)[/tex]
To Find:
The objective is to solve the equation and find the value of x.
Explanation:
[tex]10=2(x-2)\\[/tex]
⇒ [tex]\frac{10}{2}=x-2[/tex]
⇒[tex]5=x-2[/tex]
⇒ [tex]x=7[/tex]
Final Answer :
The value of x is 7.
4.40x2.50
i really need this please
Answer:
11
Step-by-step explanation:
If it is correct, could you please give me brainliest? I would really appreciate it! Thank you!
40! points Which expression is equivalent to 2x + 7y + 4x - 3y * 1 point
6x + 10y
6x - 10y
6x + 4y
6x - 4y
What does the slope tell you?
◄ 0.25 ounce of salad costs $1.
25 ounces of salad costs $1.
A salad costs $0.25 per ounce.
A salad costs $25 per ounce.
Answer: what is the answer?
Step-by-step explanation:
a salad costs $0.25 per ounce!:)
find the inverse of
f(x) = 4x + 2 over 3
Answer: f^-1(x)=(3x-2)/4
Step-by-step explanation:
1. Change the x and y
y=(4x+2)/3 → x=(4y+2)/3
2. Swap sides (optional)
x=(4y+2)/3 → (4y+2)/3=x
3. Multiply the equation by 3 on both sides
(4y+2)/3=x → (3)*(4y+2)/3=x*(3)
4. Subtract 2 from both sides
(3)*(4y+2)/3=x*(3) → 4y=3x-2
5. Divide 4 from both sides
4y=3x-2 → y=(3x-2)/4
6 Substitute f^-1(x) for y
y=(3x-2)/4 → f^-1(3x-2)/4
|6y-7|=-1 solve please
Answer:
no solution
Step-by-step explanation:
You want the solution to the absolute value equation |6y -7| = -1.
AnalysisThe expression on the left side of the equal sign is the output of the absolute value function. That output can never be negative: all negative input values are transformed to positive output values by the absolute value function.
The expression on the right side is negative. There is no value of the variable that will make the absolute value function give a negative output. There can be no solution.
The functions f(x) and g(x) are shown in the graph. What is g(x)?
NO LINKS!! You have 4 contestants in the second heat of the big race:
The equations for the contestants are:
1. Mr. Pace: y= 3/4x + 4
2. Mr. Glintz: y= 2/3x + 7
3. Ms. Liskey: y= 3x
4. Mr. Brininger: y= 1/2x + 10
Answer:
Part (c):
1st Place: Ms. Liskey2nd Place: Mr. Glintz3rd Place: Mr. Pace4th Place: Mr. BriningerPart (d):
1st Pass: Mr Pace Time: 1.78 s (2 d.p.)2nd Pass: Mr Glintz Time: 3 s3rd Pass: Mr Brininger Time: 4 sPart (e):
y = 3x + 2Step-by-step explanation:
Given equations:
[tex]\textsf{1.\;\;Mr.\;Pace}: \quad y = \dfrac{3}{4}x + 4[/tex]
[tex]\textsf{2.\;\;Mr.\;Glintz}: \quad y = \dfrac{2}{3}x + 7[/tex]
[tex]\textsf{3.\;\;Ms.\;Liskey}: \quad y = 3x[/tex]
[tex]\textsf{4.\;\;Mr.\;Brininger}: \quad y = \dfrac{1}{2} + 10[/tex]
Plot the lines on the given coordinate plane.
(See attachment).
Draw a line at y = 25 to represent the distance at the finish line.
Find the points of intersection of the linear equation of each contestant and the finish line equation y =25. The point with the smallest x-value is the contestant who is first place.
Mr Pace
[tex]\begin{aligned}\implies 25&= \dfrac{3}{4}x + 4\\\dfrac{3}{4}x&=21\\x&=28\; \sf seconds\end{aligned}[/tex]
Mr Glintz
[tex]\begin{aligned}\implies 25&= \dfrac{2}{3}x + 7\\\dfrac{2}{3}x&=18\\x&=27\; \sf seconds\end{aligned}[/tex]
Mr Liskey
[tex]\begin{aligned}\implies 25&= 3x\\x&=8.33\; \sf seconds\;(2\;d.p.)\end{aligned}[/tex]
Mr Brininger
[tex]\begin{aligned}\implies 25&= \dfrac{1}{2}x + 10\\\dfrac{1}{2}x&=15\\x&=30\; \sf seconds\end{aligned}[/tex]
Therefore, the order in which the contestants reached the finish line is:
1st Place: Ms. Liskey2nd Place: Mr. Glintz3rd Place: Mr. Pace4th Place: Mr. BriningerFrom inspection of the attached graph, Ms Liskey (red line) passes all three contestants. To find the time at which she passes the other contestants, substitute her equation into the contestant's equation and solve for x.
Mr Pace
[tex]\begin{aligned}\implies 3x&= \dfrac{3}{4}x + 4\\\dfrac{9}{4}x&=4\\x&=1.78\; \sf seconds\;(2\;d.p.)\end{aligned}[/tex]
Mr Glintz
[tex]\begin{aligned}\implies 3x&= \dfrac{2}{3}x + 7\\\dfrac{7}{3}x&=7\\x&=3\; \sf seconds\end{aligned}[/tex]
Mr Brininger
[tex]\begin{aligned}\implies 3x&= \dfrac{1}{2}x + 10\\\dfrac{5}{2}x&=10\\x&=4\; \sf seconds\end{aligned}[/tex]
Therefore:
1st Pass: Mr Pace Time: 1.78 s (2 d.p.)2nd Pass: Mr Glintz Time: 3 s3rd Pass: Mr Brininger Time: 4 sIf you want to win the race, either:
increase the slope of Ms Liskey's equation: y = 4xor add a value to Ms Liskey's equation: y = 3x + 2If a person weighs 290 lbs, how much of a dosage should they get every 4 hours if they need to be
administered 11.9 mg/kg? Round to 1 decimal.
290 lbs is the same as 131.542 kg.
So, they should be administeted (131.542)(11.9) mg, which is about 15.65 mg.
HELP ME OUT THANSKSSSSS SO MUCH
Answer:
10.59
Step-by-step explanation:
SOLVE FOR P
-2p = -3p + 8
P=
Answer:
P= 8
Step-by-step explanation:
-1 (-2p = -3p + 8)
2p = 3p - 8
-p = -8
p = 8
to check this...
-2(8) = -3(8) + 8
-16 = -24 + 8
-16 = -16
Solve the following quadratic
function by factoring:
f(x)=x²-10x+9
Enter the number that belongs in the green box.
x = 9; x = [?]
Answer:
1
Step-by-step explanation:
x²-10x+9 = 0
(x-9)(x-1) = 0
x-9 = 0 => x=9
x-1 = 0 => x=1
Given the function R(x) = x-7/x+2 find the values of a that make the function less than or equal to zero. Write the solution in interval notation
The solution for the function R(x) = x - 7 / x + 2 ≤ 0 is −2<x≤7 or x (-2, 7].
What is function?Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and co-domain, respectively.
Given:
The function R(x) = x - 7 / x + 2
The given condition x - 7 / x + 2 ≤ 0
Solve the inequality as shown below
Here, the critical points are x = 7 and x = -2
Check the denominator for the critical point, x = -2 will not be suitable for the function as it becomes undefined,
Thus
−2<x≤7 or x (-2, 7]
Therefore, the solution for the function R(x) = x - 7 / x + 2 ≤ 0 is −2<x≤7 or x (-2, 7].
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please help please I need i real bad
Answer:
C
Step-by-step explanation:
Answer:
I think the Answer choice = C
Step-by-step explanation:
Dance lessons are offered at two studios. The cost of dance lessons at each studio is shown. • Studio Q charges a $30 registration fee plus $80 per month. . Studio R charges a $105 registration fee plus $65 per month. after how many months will the total cost of the dance lessons be equal at the two studios? What will the cost be?
Answer:
5 months and the cost is $430
Step-by-step explanation:
Let's start by figuring out the equations for both dance studios.
Q : 30 registration fee plus 80 per month.
R : 105 registration fee plus 65 per month.
We can use the variable m for months.
Registration is a flat fee, so that will be it's own term. Plus the costs per month. We will multiply the costs per month times months, m.
Q : 30 + 80m
R : 105 + 65m
Now, if we want to find out how many lessons until the costs are equal, we need to make the two equations equal to each other.
80m + 30 = 65m + 105
Now, we work backwards to find out what m is.
Subtract 30 on both sides.
80m = 65m + 75
Subtract 65m on both sides
15m = 75
Divide by 15 on both sides to isolate m.
m = 5
After 5 months, the total cost of the dance lessons will be equal at the two studios. To find out the cost, we must multiply the months back in. We can substitute 5 in for any of the equations as they are equal. I will use 80m + 30.
80(5) + 30 = ?
400 + 30 = ?
430 = ?
The cost for both studios will be equal at 5 months, with a cost of $430.
Which statement is true about the algebraic expression 450 −15t?
A student has 450 marbles. Each of their t friends gives them 15 marbles. The expression represents the total marbles the student has.
A student has 450 marbles. They give t marbles to each of their 15 friends. The expression represents the total marbles the student is left with.
A student has 450 marbles. They give t marbles to one of their friend and 15 marbles to another. The expression represents the total marbles the student is left with.
A student has 450 marbles. One of their friends gives them t marbles and another friend gives them 15 marbles. The expression represents the total marbles the student has.
PLEASE HELP I'M SOOO CONFUSED
The statement that is true about the algebraic expression 450 −15t is B. A student has 450 marbles. They give t marbles to each of their 15 friends. The expression represents the total marbles the student is left with.
What is the definition of an algebraic expression?In mathematics, an algebraic expression is an expression composed of variables and constants as well as algebraic operations (addition, subtraction, etc.). Terms combine to form expressions.
In this case, when a student has 450 marbles. They give t marbles to each of their 15 friends.
The expression represents the total marbles the student is left with will be:
= 450 - (15 × t)
= 450 - 15t
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Can someone please help me with my math homework (m^2+2m-8)/(m+4) thanks and have a good day/night/evening.
Answer:
Below
Step-by-step explanation:
The numerator factors , so you have this:
(m+4)(m-2) / (m+4) the (m+4) 's cancel and you are left with (m-2)
The dinner bill comes to $30, and you want to leave a 20% tip. What is the total cost of the bill?
Answer:
$36
Step-by-step explanation:
First, let us make an expression to solve this using the given information.
For that let the total cost be x.
Amount of the bill tip total cost
100 ⇒ 20 ⇒ 120
30 ⇒ 20 ⇒ x
Accordingly,
100 ⇒ 120
30 ⇒ x
Use cross multiplication and solve for x.
100x = 120 × 30
100x = 3600
Divide both sides by 100.
x = $ 36
A positive integer is 6 less than another. If the sum of the reciprocal of the smaller and twice the reciprocal of the larger is frac(5,9), then find the two integers.
The two integers are equal to 1 and 7 respectively.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Let x represent the smaller number. Then the given relationships say ...
1/x + 2/(x+6) = 9/7
Multiplying by 7x(x+6), we have ...
7(x+6) +14x = 9x(x+6)
9x² +54x = 21x +42 . . . . .eliminate parentheses, swap sides
9x² +33x = 42 . . . . . . . . ...subtract 21x
3x² +11 -14 = 0 . . . . . . . . . .subtract 42 and divide by 3
(3x +14)(x -1) = 0 . . . . . . . . factor
Values of x that make this true are x = 1 and x = -14/3. Then for the positive integer x=1, the other integer is x+6=7.
Therefore, the two integers are equal to 1 and 7 respectively.
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Will mark brainliest :)
Answer:
hope it helps!
Step-by-step explanation:
Answer:
See below
Step-by-step explanation:
8y ≤ 10x Divide both sides by 8
y ≤ 5/4x Simplified
See the attached picture. This is crossing the y axis at 0. If you start at (0,0) and go up 5 and to the right 4. You will see the second point graphed. This demonstrates the slope of the line. ≤ tells us that we are including everything below the line.
You should check out Desmos. It is a free graphing program. It is cool.
Which set of rational numbers is arranged from least to greatest? (4 points) a −3.5, negative 1 over 4 , 2, 1 over 3 b −3.5, negative 1 over 4 , 1 over 3 , 2 c 2, 1 over 3 , negative 1 over 4 , −3.5 d negative 1 over 4 , 1 over 3 , 2, −3.5
The set of rational numbers arranged from least to greatest is -3.5, -1/4, 1/3, 2, which is option (b).
What is a rational number?Any number that can be represented as the ratio of two integers and where the denominator is not zero is referred to as rational.
The given sets of rational numbers are:
(a) -3.5, -1/4, 2, 1/3
(b) -3.5, -1/4, 1/3, 2
(c) 2, 1/3, -1/4, -3.5
(d) -1/4, 1/3, 2, -3.5
Note that 1/4 = 0.25 and 1/3= 0.33
Therefore, the set of rational numbers arranged from least to greatest is -3.5, -1/4, 1/3, 2, which is option(b).
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What are the distances from the point (x, y) to the focus of the parabola and the directrix?
Select two answers.
distance to the focus: √(x+3)²+(y-3)²
distance to the directrix: |y+4|
distance to the focus: √(x+3)²+(y-2)²
distance to the focus: √(x-2)²+(y+3)²
distance to the directrix: |y-4|
distance to the directrix: |x-4|
The distances from the point (x,y) are given as follows:
Distance to the focus: √(x+3)²+(y-2)².Distance to the directrix: |y - 4|.How to obtain the distance between two points?Suppose that we have two points with coordinates given by [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].
The shortest distance between them is given by the equation presented as follows:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
The coordinates of the focus of the parabola are given as follows:
(-3,2).
Hence the distance of the point (x,y) to the focus of the parabola is given as follows:
√(x+3)²+(y-2)².
The equation that defines the directrix is given as follows:
y = 4.
The y-coordinate of the point is of:
y.
Hence the distance is of:
|y - 4|.
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Solve the system of equations using any method
y = x^2 + 4
y = 2x + 4
The solution of the system of equation is as follows;
x = 2y = 8How to solve system of equation?System of equation can be solved using different method such as elimination method, substitution method and graphical method.
Let's solve the system of equation using substitution method as follows:
y = x² + 4
y = 2x + 4
Therefore,
2x + 4 = x² + 4
x² - 2x = 0
x² = 2x
x = 2
Let's find y
y = 2x + 4
y = 2(2) + 4
y = 4 + 4
y = 8
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How do I solve this?
11) (Level 2):
I believe if you just multiply the shaded area (10x6), then maybe subtract the non-shaded area (20cm and 10 cm). After doing this process, I believe you will get: 200-60 = 140! (But then again I could be wrong, I’ll admit it I’m not a pro but at least I gave effort!)
Fraction: 14/10
Decimal: 1.4
Percent: 140%
12) (Level 3):
I have absolutely no idea about this question and I don’t want to guess! Sorry!
Write 50.001 in word form
Edna bought a cube-shaped jewelry box that has 7-inch sides. The volume of a cube with side s is s3. What is the volume of the jewelry box?
The volume of the jewelry box will be;
⇒ 343 inch³
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
Edna bought a cube-shaped jewelry box that has 7-inch sides.
And, The volume of a cube with side s is s³.
Now,
Since, Edna bought a cube-shaped jewelry box that has 7-inch sides.
Hence, The volume of the jewelry box = 7³
= 7 × 7 × 7
= 343 inch³
Thus, The volume of the jewelry box will be;
⇒ 343 inch³
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What does the term rhetorical situation refer to?
• A. Ideals
that a speaker uses to guide a speech no matter who the
audience is
• B. A specific occurrence in ancient Greece when politicians bullied
the people
• C. The relationship between the speaker, the speaker's style of
address, and the audience's expectations
• D. Parents, teachers, and other adults who are on social networking
sites
Answer:
Step-by-step explanation:
This term refers to any set of circumstances that involves at least one person using some sort of communication to modify the perspective of at least one other person.
Answer: c
Step-by-step explanation:
j took the quiz on apex
helppppp plsssssss
what is the average rate of change of the function on the interval from x = 3 to x = 5? f(x)=10(2)x Enter your answer in the box.
The average rate of change of the function on the interval from x = 3 to x = 5 is 40.
What is meant by average rate of change?In mathematics, the average rate of change is a measure of how much a dependent variable (such as y) changes in proportion to a change in the independent variable (such as x). It is calculated by dividing the change in the dependent variable by the change in the independent variable during a certain time period. If the value of y rises by 5 units when the value of x rises by 2 units, the average rate of change is 5/2 Equals 2.5 per unit change in x. Calculus students frequently use this idea to compute the slope of a line on a graph or to calculate the rate at which a function changes. It is a crucial idea in several domains.
How to solve?
f(x) = 10(2)x,the interval is from x = 3 to x = 5
At x = 3, 10(2)3 = 80
at x = 5, 10(2)5 = 160
total change over the interval from x = 3 to x = 5 is 160 - 80 = 80.
the length of the interval is 5 - 3 = 2,
average rate of change is 80 / 2 = 40.
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