The point slope form of the equation of the line through the given point with the given slope is y - 4 = -2(x + 1).
The equation in slope intercept form is y = -2x + 2.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the points.At data point (-1, 4), a linear equation of this line can be calculated in point-slope form as follows:
y - y₁ = m(x - x₁)
y - 4 = -2(x - (-1))
y - 4 = -2(x + 1)
Next, we would rewrite the equation in slope-intercept form as follows;
y - 4 = -2(x + 1)
y = -2x - 2 + 4
y = -2x + 2
Read more on slope here: brainly.com/question/3493733
#SPJ1
An artist invests in a mutual fund account paying 5% and $5000 more than four times as much in a mutual fund account paying 4%. Her total annual interest income from the investments is $1145. How much does she invest at each rate?
The artist invests $4500 in the 5% account and $23000 in the 4% account.
Let's call the amount invested in the 5% account x. Then, the amount invested in the 4% account is 4x + 5000.
The total annual interest income from the investments is 1145, so we can write an equation:
0.05x + 0.04(4x + 5000) = 1145
Expanding the second term:
0.05x + 0.04(4x) + 0.04(5000) = 1145
0.05x + 0.16x + 200 = 1145
0.21x + 200 = 1145
0.21x = 945
x = 4500
So the artist invests $4500 in the 5% account and $18000 + 5000 = $23000 in the 4% account.
To learn more about interest click here:
brainly.com/question/25857212
#SPJ1
Evaluate the indefinite integral. (Use C for the constant of integration.) sin(16x) J 1 + cos2(16x) - dx -tan-|(16x)I+C
The indefinite integral of sin(16x) with respect to x cannot be expressed in terms of elementary functions.
LaTeX, you can display powers using the caret (^) symbol. For example, to display x raised to the power of 2, you would write:
[tex]$x^2$[/tex]
And to display x raised to the power of y, you would write:
[tex]$x^y$[/tex]
To solve this integral, we would typically use numerical or approximate methods, or special functions such as the sine integral or Fresnel integrals.
The indefinite integral of [tex](1 + cos^2(16x))[/tex] with respect to x can be evaluated using the substitution u = cos(16x). The derivative of cos(16x) with respect to x is -16sin(16x), so the integral becomes:
[tex]∫ (1 + cos^2(16x)) dx = ∫ (1 + u^2) du[/tex]
[tex]= 1/3 u^3 + u[/tex]
[tex]= 1/3 cos^3(16x) + cos(16x) + C[/tex]
where C is the constant of integration.
To learn more about indefinite integral please click on below link.
https://brainly.com/question/28036871
#SPJ4
What is the difference in marcel and Stephanie tax burdens ?
Answer:
Marcel's and Stephanie's taxable incomes are less than their annual salaries because they both have a series of tax deductions
Step-by-step explanation:
Try This question out and I’ll give you brainliest
The horizontal distance rounded to the nearest hundredth will ve 139.5 feet. Then the correct option is A.
What are the roots of the equation?Let the equation be ax² + bx + c = 0. Then the roots of the equation will be given as,
[tex]\rm x = \dfrac{-b \pm \sqrt{b^2 - 4 a c }}{2a}[/tex]
Paulo hit a baseball. The path of the ball was h = - 0.01d² + 1.37d + 3.5.
Then the horizontal distance is given as,
h = 0
- 0.01d² + 1.37d + 3.5 = 0
0.01d² - 1.37d - 3.5 = 0
Solve the equation by formula, then we have
d = [-(-1.37) ± √{(-1.37)² - 4 × 0.01 × (-3.5)}] / (2 × 0.01)
d = (1.37 ± 1.42) / 0.02
For the plus sign, then we have
d = 2.79 / 0.02
d = 139.5 feet
The horizontal distance rounded to the nearest hundredth will ve 139.5 feet. Then the correct option is A.
More about the roots of the equation link is given below.
https://brainly.com/question/12029673
#SPJ1
help would be great
The number of cakes that Andy, Betty, and Colin have will be 13, 52, and 16, respectively.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Andy has x cakes, Betty has 4x cakes, and Colin has x + 3. Then the equation is given as,
0.65(x + 4x + x + 3) = £52.65
Simplify the equation, then we have
0.65(x + 4x + x + 3) = £52.65
6x + 3 = 81
6x = 78
x = 13
Then the number of cakes that Betty has is given as,
4x = 4 (13)
4x = 52
Then the number of cakes that Colin has is given as,
x + 3 = 13 + 3
x + 3 = 16
The number of cakes that Andy, Betty, and Colin have will be 13, 52, and 16, respectively.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
#SPJ1
30 boys and 36 girls were split into teams for a volleyball tournament. The same number of girls and the same number of boys were on each team. What is the greatest number of teams they could have made?
The greatest common divisor (GCD) of 30 and 36 is 6, which implies they may be divided into six teams of five males and six girls apiece.
What is expression?An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression in mathematics is a collection of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) Expressions and phrases are similar in structure.
Here,
To get the greatest number of teams, each team should have the smallest number of players possible. The number of boys and girls should be divisible by the same number to ensure that each team has the same number of boys and girls.
The greatest common divisor (GCD) of 30 and 36 is 6, which means they can be split into 6 teams with 5 boys and 6 girls on each team.
So the greatest number of teams they could have made is 6.
To know more about expression,
https://brainly.com/question/30091997
#SPJ1
which of the following are equivalent to 85%? choose all that apply, (multiple choices)
A.0.085
B.0.85
C.85/100
D.19/20
Answer:
B.0.85
C.85/100
Step-by-step explanation:
pls, tell me if wrong have a good day/night<3
_ / 6 < 9/6 what is the missing number?
The complete expression is 8/6 < 9/6
How to complete the expressionFrom the question, we have the following parameters that can be used in our computation:
_ / 6 < 9/6
Express properly
So, we have the following representation
_ / 6 < 9/6
Represent the blank with x
x / 6 < 9/6
Multiply both sides of the expression by 6
So, we have the following representation
x < 9
This means that x is any value less than 9
An instance is 8
Hence, the solution to the expression is 8/6 < 9/6
Read more about expression at
brainly.com/question/15775046
#SPJ1
data from what length of time are represented on a climograph? view available hint(s)for part b data from what length of time are represented on a climograph? 30 years 300 years it varies from one climograph to another; there is no standard length of time. 30 days 30 months submit
Option b is the correct answer. It varies from one climograph to another; there is no standard length of time.
A climograph is a graphical representation of climate data that shows the average temperature and precipitation patterns over a certain period of time. The length of time represented on a climograph can vary and there is no set standard. It could be a few months, a year, several years, or even decades. It depends on the specific data and purpose of the climograph. Some climographs may show data from the last 30 years, while others might show data from the last 300 years. The important thing to remember is that the length of time represented on a climograph will vary and there is no set rule for how long it should be.
To learn more about climograph, refer:
https://brainly.com/question/4412811
#SPJ4
The complete question is:
data from what length of time are represented on a climograph? view available hint(s)for part b data from what length of time are represented on a climograph?
a. 30 years 300 years
b. it varies from one climograph to another
c. there is no standard length of time.
d. 30 days 30 months submit
Michael has $16 and wants to buy a mixture of cupcakes and fudge to feed at least 4 siblings. Each cupcake costs $4, and each piece of fudge costs $2.
This system of equations models the scenario:
4x + 2y ≤ 16
x + y ≥ 4
Part A: Describe the graph of the system, including shading and the types of lines graphed. Provide a description of the solution set. (4 points)
Part B: Is the point (2, 3) included in the solution area for the system? Justify your answer mathematically. (3 points)
Part C: Choose a different point in the solution set and interpret what it means in terms of the real-world context. (3 points)
The graph is attached, the point (2, 3) included in the solution area for the system and (4, 0) is the solution of area for the system.
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
Given that Michael has $16 and wants to buy a mixture of cupcakes and fudge to feed at least 4 siblings.
Each cupcake costs $4, and each piece of fudge costs $2.
4x + 2y ≤ 16
x + y ≥ 4
The graph for system of inequalities is attached.
The point (2, 3) included in the solution area for the system
4(2)+2(3)≤ 16
14≤ 16 is true.
2+3≥ 4 is true.
Point (2, 3) included in the solution area for the system.
From the graph (4, 0) is the solution of area for the system.
Hence, the graph is attached, the point (2, 3) included in the solution area for the system and (4, 0) is the solution of area for the system.
To learn more on Inequality click:
https://brainly.com/question/28823603
#SPJ1
Mr Saver invests $X at t = 0 in an account that pays a nominal rate of R convertible
quarterly. The interest he earns during t = 0.5 to t = 1.5 is 1.0816 times the interest
he earns during t = 0 to t = 1. Find the exact value of R.
Let X be the amount Mr Saver invests at t = 0.
The interest he earns during t = 0 to t = 1 can be expressed as:
Interest = X * R * (1/4)
The interest he earns during t = 0.5 to t = 1.5 can be expressed as:
Interest = X * R * (3/4)
Since the interest he earns during t = 0.5 to t = 1.5 is 1.0816 times the interest he earns during t = 0 to t = 1, we can set up the following equation:
X * R * (3/4) = 1.0816 * (X * R * (1/4))
Solving for R, we get:
R = 4.3264 Therefore, the exact value of R
For the function defined here, find f(0), ƒ(2), and f(4) by using the graph below.
x² - 1
f(x) = {¹
-x+1
if
if
x < 2
x > 2
The values of the functions are f(0) = 2, f(2) = 0 and f(4) = -2
How to evaluate the piece-wise functionThe graph that completes the question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we can see that the first curve is a quadratic function,
Also, it has an open circle at x = 1
So, we have:
x² + 2 if x < 1
Next, we have a linear equation with a closed circle at x = 1
So we have:
y = -x + 2 for x ≥ 1
This means that
f(0) = 0^2 + 2 = 0f(2) = -2 + 2 = 0f(4) = -4 + 2 = -2Read more about piecewise functions at:
brainly.com/question/3628123
#SPJ1
8) Mrs. Smith drove 20 miles at a speed of 55 mph. She then drove 40 miles at a spe)ed of 60 mph. How
far did Mrs. Smith drive?
The total distance travelled by Mrs. Smith was 60 miles
What is an equation?An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.
Speed is the ratio of the total distance travelled to total time taken. It is given by:
Speed = distance / time
Mrs. Smith drove 20 miles at a speed of 55 mph. She then drove 40 miles at a speed of 60 mph. Hence:
Total distance = 20 miles + 40 miles = 60 miles
The total distance travelled was 60 miles
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
please someone help me quick
Answer:
Top one is (SAS) Middle one is (AAS) Bottom one is (AAA)
Step-by-step explanation:
I hope these were helpful.
ank the following functions in increasing order of (asymptotic) magnitude dragged and dropped options will be automatically saved. for keyboard navigation...show more press space or enter to grab [math] log {3} n [/math] press space or enter to grab [math] n log (3 n) [/math] press space or enter to grab [math] 3 n [/math] press space or enter to grab [math] n^{3} [/math] press space or enter to grab [math] (3!)^{3} [/math] press space or enter to grab [math] 3^{n} [/math]
The order of asymptotic magnitude is (3!)3 < 3n < n log(3n) < n3 < 3n < 3n.
The order of asymptotic magnitude is (3!)3 < 3n < n log(3n) < n3 < 3n < 3n. This means that the function with the smallest asymptotic magnitude is (3!)3, while the function with the largest asymptotic magnitude is 3n.
To confirm this, let's calculate the growth rate of each function. The growth rate of (3!)3 is 3!3 ≈ 216, which is less than the growth rate of 3n (3n) = 3n, which is greater than the growth rate of n log(3n) (n log3n) = n log3n, which is greater than the growth rate of n3 (n3) = n3, which is greater than the growth rate of 3n (3n) = 3n, which is greater than the growth rate of 3n (3n) = 3n.
Therefore, we can conclude that the order of asymptotic magnitude is (3!)3 < 3n < n log(3n) < n3 < 3n < 3n.
Learn more about asymptotic magnitude here:
https://brainly.com/question/9347873
#SPJ4
Answer:The order of asymptotic magnitude is (3!)3 < 3n < n log(3n) < n3 < 3n < 3n
Step-by-step explanation:
Solve.
4 There are 42 tubes of oil paint on trays. Each tray
holds 6 tubes. How many trays of tubes are there?
Show your work.
7
Answer: 7
Step-by-step explanation:
Since there are 42 tubes and each tray can hold 6 tubes, it will be 42/6 which is 7.
PLEASE HELP 10 Points
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{4(2y + 1)}\\\mathsf{= 4(2y) + 4(1)}\\\mathsf{= 8y + 4}\\\mathsf{\rightarrow 4y + 4y + 4}\\\mathsf{\rightarrow 2(4y + 2)}\\\\\huge\text{Therefore your answer should be:}\\\huge\boxed{\mathsf{Option\ A. \ 4y + 4y + 4}}\huge\checkmark\\\\\huge\boxed{\mathsf{Option\ B. \ 4y + 4y + 4}}\huge\checkmark\\\\\huge\boxed{\mathsf{Option\ E.\ 8y + 4}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
A baker is packaging her cupcakes into single serve boxes for a special event. Each
cube-shaped box has side lengths 3.5 inches (in.). The smaller boxes are then packed into a
larger box with dimensions of 10.5 in. x 7 in. x 7 in.
Please help me I have my math class tomorrow and tomorrow is also when it is due!!!
Answer: Sure! I'd be happy to help you with this.
To find the number of cupcake boxes that fit in the larger box, we need to find the volume of the larger box and divide it by the volume of one cupcake box.
The volume of the larger box is 10.5 x 7 x 7 = 572.5 cubic inches.
The volume of one cupcake box is 3.5 x 3.5 x 3.5 = 42.375 cubic inches.
Dividing the volume of the larger box by the volume of one cupcake box, we get 572.5 / 42.375 = 13.5.
So, 13.5 cupcake boxes will fit in the larger box.
Step-by-step explanation:
7. Higher Order Thinking A bagel is cut
into same-size pieces. Some
friends share the bagel.
Each friend gets one piece.
How many friends share
the bagel?
friends
The number of friends sharing the bagel will be n.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
A bagel is cut into same-size pieces. Some friends share the bagel. Each friend gets one piece.
Let the same size pieces of the bagel be 1/n. Then the number of friends who share the bagel is given as,
⇒ 1 / (1/n)
⇒ 1 x n / 1
⇒ n
The number of friends sharing the bagel will be n.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ1
what is -7 + 3x = 8 - 2x
Answer: x = 3
Step-by-step explanation: -7 + 9 = 8 - 6
Not understanding this question, question 2
The domain of the composite function (f o g)(4) for f(x) = 4x - 3 and g(x) = x³ + 2x is equal to -59.
What is composite functionA function is composite when the co-domain of the first mapping is the domain of the second mapping
We shall evaluate the domain of the function (f - g)(4) as follows:
(f - g) = 4x - 3 - (x³ + 2x)
(f - g) = 4x - 3 - x³ - 2x
(f - g) = 2x - 3 - x³
(f - g)(4) = 2(4) - 3 - (4)³
(f - g)(4) = 8 - 3 - 64
(f - g)(4) = -59
Therefore, the domain of the composite function (f o g)(4) for f(x) = 4x - 3 and g(x) = x³ + 2x is equal to -59.
Know more about composite function here:https://brainly.com/question/10687170
#SPJ1
Please help me, it would be helpfull
Answer:
A:[tex]y = 4x + 3[/tex]
ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ
▲
Part 1 of 2
Use the graph to the right to complete the following. For
the graph, tick marks along the axes represent one unit
each.
a. Determine the x-intercepts, if any.
b. Determine the y-intercepts, if any.
a. What is/are the x-intercept(s)? Select the correct
choice below and, if necessary, fill in the answer box to
complete your choice.
A. The x-intercept(s) is/are
(Type an integer or a simpied fraction. Use a
comma to separate answers as needed.)
OB. There is no x-intercept.
O Points: 0
-6
-2
-4
A
Save
Q
x
The x intercept is x = 4 and the y intercept is y = 4.
What is the intercept of a graph?The intercept of a graph is a point at which the graph crosses either the x-axis or the y-axis. For a graph with an x-intercept, the y-coordinate is 0 and the x-coordinate gives the value at which the graph intersects the x-axis.
For a graph with a y-intercept, the x-coordinate is 0 and the y-coordinate gives the value at which the graph intersects the y-axis. In the context of a line or a linear regression model, the intercept is the value of the dependent variable (y) when the independent variable (x) is 0.
Learn more about intercept:https://brainly.com/question/14180189
#SPJ1
A water park keeps track of the number of times each visitor goes down water slides during their visit . The data shows the number of times 12 visitors went down a water slide.
4, 22, 16, 10, 11, 20, 20, 12, 6, 3, 11, 1
Create a histogram of this data.
To create a histogram, hover over each age range on the x-axis. Then click and drag up to plot the data.
Histogram of given data is attached below.
What is histogram?A histogram is a graphical representation of data points organized into user-specified ranges.
Given,
Data shows the number of times, 12 visitors went down a water slide.
4, 22, 16, 10, 11, 20, 20, 12, 6, 3, 11, 1
Histogram can be drawn as below,
Hence, following is the histogram of given data.
Learn more about histogram here:
https://brainly.com/question/30354484
#SPJ1
a restaurant offers delivery for pizzas. The total cost includes $11 per pizza and the delivery fee. A delivery of 5 pizzas costs $58.
Write an equation to represent the total cost, y for x number of pizzas. Use your wquation to find the cost of delivery of 80 pizzas.
Answer:
y=883
Step-by-step explanation:
The total cost includes $11 per pizza and the delivery fee. A delivery of 5 pizzas costs $58.
11 (dollars per pizza) x 5 (pizzas were delivered) = 55 dollars
58 (total cost) - 55 (total cost for pizza) = 3 (fee)
11x+3=y (Equation)
input the 80 pizzas to the equation
11(80)+3=y
y= 883
Hope this helps! I took a similar question 3 years ago! =)
based on a random sample of 50 students, the 90 percent confidence interval for the mean amount of money students spend on lunch at a certain high school is found to be ($3.45, $4.15). which of the following statements is true?
90% of all random samples of 50 students obtained at this high school would result in a 90% confidence interval that contains the true mean amount of money students spend on lunch. Hence, the correct statement is option (d).
A confidence interval is a range of values that are expected to contain the true population parameter with a certain degree of confidence, usually expressed as a percentage. Here, a 90% confidence interval means that if we were to repeatedly take random samples of 50 students and compute a 90% confidence interval for each sample, we would expect that 90% of these intervals would contain the true mean amount of money that all students spend on lunch at this high school.
Read more about Confidence intervals:
brainly.com/question/15712887
#SPJ4
The complete question is -
Based on a random sample of 50 students, the 90 percent confidence interval for the mean amount of money students spend on lunch at a certain high school is found to be ($3.45, $4.15). Which of the following statements is true?
(a) 90% of the time, the mean amount of money that all students spend on lunch at this high school will be between $3.45 and $4.15.
(b) 90% of all students spend between $3.45 and $4.15 on lunch at this high school.
(c) 90% of all random samples of 50 students obtained at this high school would result in a sample mean amount of money students spend on lunch between $3.45 and $4.15.
(d) 90% of all random samples of 50 students obtained at this high school would result in a 90% confidence interval that contains the true mean amount of money students spend on lunch.
Circles C 1 ,C 2 ,C 3 have their centres at (0,0),(12,0),(24,0) and have radii 1,2 and 4 respectively. Line t 1 is a common internal tangent to C 1 and C 2 and has a positive slope and line t 2 is a common internal tangent to C 2 and C 3 and has a negative slope. Given that lines t 1 and t 2 intersect at (x,y) and that x=p−q√r, where p,q and r are positive integers and r is not divisible by the square of any prime, find p+q+r.a.P+Q+R=26b.P+Q+R=24c.P+Q+R=28d.P+Q+R=27
The sum of p, q, and r is 27.
The point of intersection of the lines t1 and t2, (x,y), can be found by using the equation of the lines. The equation of t1 is y=mx+c, where m is the slope, and c is the y-intercept. The equation of t2 is y=mx+c, where m is the slope, and c is the y-intercept.
The equations of t1 and t2 can be written as y= 1/2 x + 1 and y= -1/4 x + 7/2 respectively.
By setting the two equations equal to each other, we can find the x-coordinate of the point of intersection (x,y).
x=2 - 7/4 =4/4 - 7/4 = -3/4
Since x=p−q√r, we can write -3/4 = p−q√r.
Rearranging this equation, we get p+q+r= 4/3 + 7/3 + 4/3 = 27/3 = 9.
Therefore, P+Q+R=27.
Therefore, the sum of p, q, and r is 27.
Learn more about point of intersection here:
https://brainly.com/question/26496929
#SPJ4
the area of the rectangle is 12^cm2 what is t in cm?
Answer:
t = 9cm
Step-by-step explanation:
area = l*w
2(t-3) = 12
2t - 6 = 12
2t - 6 + 6 = 12 + 6
2t = 16
t = 18/2
t = 9
t = 9cm
applied partial differential equations with fourier series and boundary value problems 5th edition solution
The 5th edition of Applied Partial Differential Equations with Fourier Series and Boundary Value Problems by John D. Fenton covers a wide range of topics related to the use of Fourier series and boundary value problems to solve various partial differential equations.
The solution to the given differential equation is
[tex]$y(x) = \frac{-1}{2 \pi} \sin(4x)$.[/tex]
One example of a solution, to the ODE differential equation
[tex]$\frac{d^2y}{dx^2} + 4y = 0$[/tex]
with the boundary conditions
[tex]$y(0) = 0$[/tex] and [tex]$y(\pi) = 0$[/tex]
is given by the Fourier series
[tex]$y(x) = A \sin(2x) + B \cos(2x) + C \sin(4x) + D \cos(4x)$[/tex]
Where the constants A, B, C, and D are determined by the boundary conditions.
Using the boundary conditions, we find
[tex]$A = 0$[/tex] and [tex]$B = 0$[/tex]
[tex]$C = \frac{-1}{2 \pi}$[/tex] and [tex]$D = 0$[/tex]
Therefore, the solution to the given differential equation is
[tex]$y(x) = \frac{-1}{2 \pi} \sin(4x)$.[/tex]
Learn more about Differential Equations: https://brainly.com/question/9686427
#SPJ4
Solve for the 2 problems below, show your work and submit the answers.
In the isosceles triangle, the value of x for the first figure is 15
for the second figure,
x = 5the missing angle is 110How to find the value of xThe value of x is solved using the knowledge of isosceles triangle
An isosceles triangle has the base angles equal hence
2x - 5 = 35
2x = 35 - 5
2x = 30
x = 15
Second figure
7x = 35
x = 5
let the angle at the peak be p
35 + 35 + p = 180 (sum of angles in a triangle)
70 + p = 180
p = 180 - 70
p = 110
Learn more about isosceles triangle at:
https://brainly.com/question/1475130
#SPJ1