Answer:
see explanation
Step-by-step explanation:
consider the left side
(x + 2)² + (x - 2)² ← expand factors using FOIL
= x² + 4x + 4 + x² - 4x + 4 ← collect like terms
= 2x² + 8 ← factor out 2 from each term
= 2(x² + 4)
= right side , thus proven
The amount of charge on a capacitor in an electric circuit decreases by 30% every second. Assume the original charge on the capacitor is
1
millicoulombs. A) What is the charge
0.06
seconds after that. B) Set up and solve the equation to find when the charge is
0.1
millicoulombs.
The amount of charge on the capacitor after 0.06 seconds = 0.042 millicoulombs
What is an electric circuit?An electric circuit is defined as the device that aids in transmission of electricity generated by a battery or a generator.
A capacitor is defined as the device that has the ability to store energy in an electric circuit.
The amount of charge in a capacitor decreases in one second by = 30%
The original charge on the capacitor = 1 millicoulombs
30 % of 1millicoulombs = 30/100 * 1 = 0.3
1millicoulombs - 0.3 millicoulombs = 0.7 millicoulombs .
If 0.7 millicoulombs = 1 second
X millicoulombs = 0.06 second
Make X millicoulombs the subject of formula;
X millicoulombs = 0.06 × 0.7 = 0.042 millicoulombs.
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help me out *warning* its hard jk
Answer:
0.321 repeating 1
Step-by-step explanation:
Explain each step in the space provided below.
Answer:
1) multiply and divide by 2 on right hand side
2) multiply by 24 on both sides ( LHS and RHS)
3) divide by -1 on both sides so that negative sign on RHS will be cancelled
What is the equation of the line that passes through the point (-8,6) and has a slope of 1/4
The equation of the line is 4y = x + 32 which passes through the point (-8,6) and has a slope of 1/4.
We have been given the required line that passes through the point (-8,6) and has a slope of 1/4.
What is the slope of the line?The slope of a line is defined as the angle of the line. It is denoted by m
Slope m = (y₂ - y₁)/(x₂ -x₁ )
Let the required line would be as
⇒ y - y₁ = m (x - x₁ )
The required line passes through the point (-8,6)
Here x₁ = -8 and y₁ = 6 and m = 1/4
Substituting these inputs into the above equation obtains the line equation.
⇒ y - 6 = 1/4 (x - (-8))
⇒ y - 6 = 1/4 (x + 8)
⇒ 4y - 24 = x + 8
⇒ 4y = x + 8 + 24
⇒ 4y = x + 32
Thus, the equation of the line is 4y = x + 32 which passes through the point (-8,6) and has a slope of 1/4.
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how do i factor 12x² - 48 ?
Answer:
144x - 24
Step-by-step explanation:
4 Which statement about the expression -4/9 x - 3/8 is true? 9 A. The product is greater than 1. B. The product is less than both factors. C. The product is less than D. The product is a positive number.
Given data:
The given expression is -4/9 x=3/8
The given expression can be written as,
[tex]\begin{gathered} -\frac{4}{9}x=\frac{3}{8} \\ x=-\frac{27}{32} \end{gathered}[/tex]The product is less than both the factors.
Thus, option C) is correct.
I need help with this math question all parts please
we have the function
[tex]P(t)=\frac{60(1+0.4t)}{0.01t+3}[/tex]Part A
For t=0
substitute
[tex]\begin{gathered} P(t)=\frac{60(1+0.4(0))}{0.01(0)+3} \\ \\ P(t)=\frac{60(1)}{3} \\ \\ P(t)=20 \end{gathered}[/tex]The initial population was 20 insectsPart B
For t=5 years -------> Convert to months
t=60 months
substitute
[tex]\begin{gathered} P(t)=\frac{60(1+0.4(60))}{0.01(60)+3} \\ \\ P(t)=\frac{60(1+24)}{0.6+3} \\ \\ P(t)=\frac{1500}{3.6} \\ \\ P(t)=416.67 \end{gathered}[/tex]The answer is 417 insectsPart C
Determine horizontal asymptote
[tex]\begin{gathered} P(t)=\frac{60\left(1+0.4t\right)}{0.01t+3} \\ \\ rewrite \\ P(t)=\frac{60+24t}{0.01t+3} \end{gathered}[/tex]The horizontal asymptote is given by the ratio of
[tex]\frac{24}{0.01}=2,400[/tex]P(t)=2,400 ---------> horizontal asymptote
that means
as the value of time t increases ------> the value of the population tends to 2,400 insects
the population cannot be greater than 2400 insects
The range for the function P(t) is the interval [20, 2400)
All real numbers greater than or equal to 20 insects and less than 2400 insects
Part D
Using a graphing tool
Which expression is equivalent to 2x ^ 2 - 2x + 7 ?
Answer:
(x² -5x +13) + (x² +3x -6)
Step-by-step explanation:
(x² -5x +13) + (x² +3x -6)
x² -5x +13 + x² +3x -6
|x² + x²| |-5x + 3x| |+13 -6|
2x² -2x +7
luke says that "three divided by 21" is the same AS "twenty one divided by three". Is Luke correct? Explain why or why not.
Answer: He is incorrect
Step-by-step explanation:
3/21 = 0.142857142857143
21/3 = 7
They are two different equations with different answers.
Answer:
He is not correct
Step-by-step explanation:
Luke is not correct because 3/21 is 0.142 while 21/3 is 7.
Please solve in the substitution method only 3x + 2y = 12x = 2/3 y
To solve the system of equation using substitution method only, here are the steps.
1. Since the 2nd equation has been equated already into x = or y = , we can use this value to substitute the "x" value in the first equation.
[tex]\begin{gathered} 3x+2y=12 \\ 3(\frac{2}{3}y)+2y=12 \end{gathered}[/tex]2. Then, solve for y.
a. Eliminate first the parenthesis by multiplying the number outside it to the number inside it. (3 x 2/3y = 2y)
[tex]\begin{gathered} 2y+2y=12 \\ \text{Add similar terms.} \\ 4y=12 \\ \text{Divide both sides of the equation by 4.} \\ \frac{4y}{4}=\frac{12}{4} \\ y=3 \end{gathered}[/tex]Therefore, the value of y is 3.
3. Plug in the value of "y" to either of the equation to solve for x. For this solution, we will plug it in to the second equation.
[tex]\begin{gathered} x=\frac{2}{3}y \\ x=\frac{2}{3}(3) \\ x=2 \end{gathered}[/tex]The value of x = 2.
To check whether these values are true for both equations, we can plug them in.
[tex]\begin{gathered} 3x+2y=12 \\ 3(2)+2(3)=12_{} \\ 6+6=12 \\ 12=12 \end{gathered}[/tex][tex]\begin{gathered} x=\frac{2}{3}y \\ 2=\frac{2}{3}(3) \\ 2=\frac{6}{3} \\ 2=2 \end{gathered}[/tex]Indeed, the values of x and y are true to both equations. The solution x = 2, y = 3 correct.
4. Find f(x) - g(x) * (3 Points)
f(x) = 7x³ - 3x² + 5x+1 and g(x) = 5x³+x²-x-3 Enter Result in Standa
2x³ -5x² +10
02²-4² + 6x +4
-2x²-5r-8.
2²-6r+14
The value of f(x) - g(x) = 2x³ - 4x² + 6x + 4
What is Function?
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
Given,
f(x) = 7x³ - 3x² + 5x+1
g(x) = 5x³+x²-x-3
We have to find the value of:
f(x) - g(x)
Substituting the value of f(x) and g(x)
f(x) - g(x) = (7x³ - 3x² + 5x+1 ) - (5x³+x²-x-3)
Now, open the brackets
f(x) - g(x) = 7x³ - 3x² + 5x+1 - 5x³ - x²+ x + 3
Now, arranging them by like terms
f(x) - g(x) = 7x³ - 5x³ - 3x² - x² + 5x + x +1 + 3
= 2x³ - 4x² + 6x + 4
Hence, f(x) - g(x) = 2x³ - 4x² + 6x + 4
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Thanks to whoever helps
Answer:
Step-by-step explanation:
erm
A triangle is 180 degrees
Add both angles then subtract by 180
an article suggests that a poisson process can be used to represent the occurrence of structural loads over time. suppose the mean time between occurrences of loads is 0.4 year. (a) how many loads can be expected to occur during a 4-year period? loads (b) what is the probability that more than twelve loads occur during a 4-year period? (round your answer to three decimal places.) (c) how long must a time period be so that the probability of no loads occurring during that period is at most 0.3? (round your answer to four decimal places.) yr
The probability of no loads occurring during that period is at most 0.3 exists 3.2 years.
How long must a time period be so that the probability of no loads occurring during that period?Given: Mean time between occurrence = 0.4 year
A number of loads expected to occur during a 4 year period
Period = 4
Mean time = 0.4
Let the formula = Period/Mean Time
The number of loads expected to occur during a 4-year period
= 4/0.4 = 10 loads
B. Probability that more than 11 loads occur during 4 year period
The expected number of loads during 4-year period = 10 (from A above)
mean = 10
Using Poisson distribution,
P(k events in interval)= (λ^k * e^-k)/k!
where: k = 0, 1, 2,3,4, . . ., 11 and λ = 10.
P(k = 0) = (1[tex]0^0[/tex] × [tex]e^{-10[/tex])/0! = 0.000045
P(k = 1) = (1[tex]0^1[/tex] × [tex]e^{-10[/tex])/1! = 0.000454
P(k = 2) = (10² × [tex]e^{-10[/tex])/2! = 0.00227
P(k = 3) = (10³ × [tex]e^{-10[/tex])/3! = 0.007567
P(k = 4) = (1[tex]0^4[/tex] × [tex]e^{-10[/tex])/4! = 0.018917
P(k = 5) = (1[tex]0^5[/tex] × [tex]e^{-10[/tex])/5! = 0.037833
P(k = 6) = (1[tex]0^6[/tex] × [tex]e^{-10[/tex])/6! = 0.063055
P(k = 7) = (1[tex]0^7[/tex] × [tex]e^{-10[/tex])/7! = 0.090079
P(k = 8) = (1[tex]0^8[/tex] × [tex]e^{-10[/tex])/8! = 0.112599
P(k = 9) = (1[tex]0^9[/tex] × [tex]e^{-10[/tex])/9! = 0.12511
P(k = 10) = (1[tex]0^{10[/tex] × [tex]e^{-10[/tex])/10! = 0.12511
P(k = 11) = (1[tex]0^{11[/tex] × [tex]e^{-10[/tex])/11! = 0.113736
The probability that more than 11 loads occur during a 4-year period is then given by the following Express
1 - [P(k = 0) + P(k = 1) + P(k = 2) + . . . + P(k = 11)]
substitute the values in the above equation, we get
= 1 - [0.000045 + 0.000454 + 0.00227 + 0.007567 + 0.018917 + 0.037833 + 0.063055 + 0.090079 + 0.112599 + 0.12511+ 0.12511 + 0.113736]
simplifying the equation, we get
= 1 - 0.571665 = 0.428335
C. How long must a time period be so that the probability of no loads occurring during that period is at most 0.3
(λ^0 * e^-λ)/0! = 0.3
⇒ e^-λ/1 = 0.3
simplifying the above equation, we get
⇒ e^-λ = 0.3
⇒ -λ = ln 0.3
⇒ -λ = -1.204
⇒ λ = 1.204
The time period = 4 years / 1.204
Time period = 3.2 years
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The equation y = -16x² +96x + 20 models the height, in feet, after a seconds, of a toy rocket
that is launched from a cliff that is 20 feet (ft) above the ground.
Use the above information to answer the questions below. Round all answers to the tenthplace.
Answer:
No questions are shown. See attached graph for more details.
Step-by-step explanation:
See attachment
expand the expression: [tex]-\frac{1}{3}[/tex](-6x+15y) to write an equivalent expression. Use as few terms as possible.
Answer:
2x - 5y
Step-by-step explanation:
Hello!
We can distribute the value outside the parenthesis to the terms inside to simplify the expression.
Simplify:[tex]-\frac13(-6x + 15y)[/tex][tex]-\frac13(-6x) -\frac13(15y)[/tex][tex]\frac{-6x}{-3} - \frac{15y}{3}[/tex][tex]2x - 5y[/tex]The simplified expression is 2x - 5y.
When creating a graph, it is important to _____ the x and y axis?
"When creating a graph, it is important to assign the x and y axis."
Assigning the x and y axes is crucial when making a graph because the x-axis is referred to as the line on a Cartesian coordinate system that runs horizontally. A point or line's separation from the y-axis can be determined using the x-axis. The y-axis displays a point's location on a Cartesian plane in the y (vertical) direction. Additionally, it serves as the origin (zero) point for calculating how far a point is from the x-axis.
What is Graph?A graph is a structure that resembles a set of objects in mathematics, more specifically in graph theory, in which some pairs of the objects are conceptually "related." The objects are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.
What is x and y axis?Two parallel lines, known as axes (pronounced AX-eez), that are perpendicular to each other make up a coordinate grid. Typically, the term "x-axis" refers to the horizontal axis. The y-axis is the common name for the vertical axis. The origin is the location where the x- and y-axes intersect.
"When creating a graph, it is important to assign the x and y axis."
Because the x-axis is referred to as the line on a Cartesian coordinate system that runs horizontally, determining the x and y axes is essential when creating a graph. The x-axis can be used to calculate a point or line's distance from the y-axis. A point's position on a Cartesian plane is shown on the y-axis in the y (vertical) direction. It also acts as the origin (zero) point for determining a point's distance from the x-axis.
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Find the measure of angle L. Round youranswer to the nearest degree.
Given the triangle KLM, you can find the measure of angle L by using the Law of Sines. This states that:
[tex]\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}[/tex]Where "a", "b" and "c" are sides of the triangle, and "A", "B", and "C" are the angles.
In this case, you can set up this equation:
[tex]\frac{sinK}{k}=\frac{sinL}{l}[/tex]Knowing that:
[tex]\begin{gathered} m\angle K=22\text{\degree} \\ k=56 \\ l=26 \end{gathered}[/tex]You can substitute values into the equation and solve for "L". Remember the use the Inverse Trigonometric Function Arcsine, in order to solve for the angle:
[tex]\frac{sin(22°)}{56}=\frac{sinL}{26}[/tex][tex]\frac{26\cdot sin(22°)}{56}=sinL[/tex][tex]sin^{-1}(\frac{26\cdot sin(22°)}{56})=L[/tex][tex]m\angle L\approx10°[/tex]Hence, the answer is:
[tex]m\angle L\approx10°[/tex]A data set has these values: 13, 15, 15, 17, 17, 17, 17, 19, 19, 21. A histogram
of the distribution is shown.
Frequency
4
3
2
0
12 14 16 18 20 22
Which statement does not describe the data set?
A. It has a median of 17.
OB. It has a mode of 17.
OC. It is symmetric.
D. It has a range of 22.
The correct option is option D) it has range of 22
What is the range of a dataset?
It the difference between the minimum and maximum value of the dataset.
We are given a dataset with a histogram and we are asked to find out which of the given options does not describe the data
We find the answer by eliminating the correct option
Our given dataset contains 10 points
Hence the median will be the average of 5th and 6th element
Here the 5th and 6th elements are 17
Hence the median of the dataset is 17
Similarly 17 is repeated 4 times in the dataset. i.e highest number of times
Hence 17 is the mode of the dataset
If you look clearly at the histogram from median it is symmetrical that is left side equal to the right side
But if you look at the range the minimum value is 13 and maximum value is 21
Hence the range of the function is 21-13=8
And not 22
Hence the correct option is option D)
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The graph shows the printing rate of Printer A. Printer B can print at a rate of 25 pages per minute.
How does the rate for Printer B compare to the rate for Printer A? Use the drop-down menus to explain your answer.
The unit rate of Printer B = 25 pages per minute, which is greater than the unit rate of Printer A that is 15 pages per minute.
How to Find the Unit Rate of a Linear Graph?The unit rate of a graph can b determined by using any point, (x, y), on the graph and solve by finding, m, which is the ratio of y to x, if x and y represents the variables of the relationship that is graphed.
Thus, unit rate (m) = y/x.
The printing rate for Printer A is represented by the graph. To find the unit rate for Printer A, use a point on the graph, (2, 30) to find the unit rate, m.
Printer A's Unit rate (m) = y/x = 30/2
Printer A's unit rate (m) = 15 pages per minute.
The printing rate for Printer B is given as 25 pages per minute. 25 pages per minute is a greater unit rate compared to 15 pages per minute.
Therefore, we can conclude that Printer B has a greater printing rate than Printer A, because the unit rate of 25 pages per minute is greater than 15 pages per minute.
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all you need is in the photo PLEASE DON'T DO STEP BY STEP BECAUSE IS SO CONFUSING PUT ONLY THE ANSWER
A) The ball in the ground is represented by h(t)=0, that is, the height is equal to 0, the reference level.
Then, we can find for which values of t we have h(t).
We equal h(t) to 0 and calculate t as:
[tex]\begin{gathered} h(t)=-16t^2+64t=0 \\ 64t-16t^2=0 \\ 16t(\frac{64}{16}-t)=0 \\ t_1=0\text{ (first solution)} \\ t_2=\frac{64}{16}=4\text{ (second solution)} \end{gathered}[/tex]The ball is in the ground at time t=0 (an instant before it is kicked) and then again at time t=4, that is the value we are looking for: the ball landed again in the ground 4 seconds after kicked.
B) The maximum height can be find in two ways:
- By finding the t-value of the vertex, that in this case will be correspond to the maximum height as this is a concave down parabola with only one extreme point.
- Deriving the function and equaling to 0 and finding t.
If we apply the first method, we have:
[tex]\begin{gathered} h(t)=-16t^2+64x=-16(x^2-4x) \\ -16(x^2-4x) \\ -16(x^2-4x+4-4) \\ -16((x-2)^2-4) \\ -16(x-2)^2+64\longrightarrow\text{Vertex:}(2,64) \end{gathered}[/tex]As the vertex is at time t=2 seconds, the maximum height happens at t=2.
Answer: A) t = 4 seconds B) t = 2 seconds
NOTE for Part B:
If we derive the expression, we get:
[tex]undefined[/tex](30 points) need help asap
Answer:
I don't know the value of X. The question says it's in question 2.
Step-by-step explanation:
Explanation on picture
On Saturday, 108 people hiked around Lake E. Find the total distance walked by the group.Use the standard algorithm to solve.
(I’ll give brainyest)
Answer:
1655.64 miles
Step-by-step explanation:
because 108 people times 15.33 miles for all the total people would be 1655.64 miles
HELP MATH SUCKSSSSSS 7 and 8
Answer:
Step-by-step explanation:
Under his cell phone plan, Rahul pays a flat cost of $36 per month and $4 per
gigabyte. He wants to keep his bill under $95 per month. Which inequality
can be used to determine g, the maximum number of gigabytes Rahul can use
while staying within his budget?
The inequality of the function is 36 + 4x < 95 and Rahul can use 14 gigabyte while staying within his budget
How to determine the inequality of the function?The given parameters are:
Flat cost = $36 per monthRate per gigabyte = $4 per gigabyteRahul's bill = Under $95The above means that;
The total charges per month is
C(x) = Flat cost + Rate per gigabyte x Number of gigabyte
So, we have
C(x) = 36 + 4x
For the bill to be under $95, we have
36 + 4x < 95
Solving further, we have
4x > 59
Divide by 4
x < 14.75
Hence, the inequality is 36 + 4x < 95
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the shape of the density curve for a dataset is like a triangle. that is, as we move to the left of the horizontal axis, it starts from zero height, then rises linearly until some peak, then declines linearly until reaches zero, then stays zero from there onward. if we standardize this dataset by calculating the standard scores, what is the geometrical shape of the density curve for the standardized dataset?
It will be similar to the original triangle.
The shape of the density curve for a dataset is like a triangle, that is, as we move to the left of the horizontal axis, it starts from zero height, then rises linearly until some peak, then declines linearly until reaches zero, then stays zero from there onward. If we standardize the dataset by calculating the standard scores, the geometrical shape of the density curve will more or less be the same. i.e., similar to the original triangle. Scale of it will be just changed.
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The United States Department of Agriculture (USDA) found that the proportion of young adults ages 20–39 who regularly skip eating breakfast is 0.238 . Suppose that Lance, a nutritionist, surveys the dietary habits of a random sample of size =500 of young adults ages 20–39 in the United States.
Apply the central limit theorem to find the probability that the number of individuals, , in Lance's sample who regularly skip breakfast is greater than 126 . You may find table of critical values helpful.
Express the result as a decimal precise to three places.
(>126)=
Part 2: Apply the central limit theorem for the binomial distribution to find the probability that the number of individuals in Lance's sample who regularly skip breakfast is less than 98 . Express the result as a decimal precise to three places.
(<98)=
Using the normal approximation to the binomial, it is found that there is a 35.57% probability that the number of individuals in Lance's sample is.
What is Normal Probability Distribution?In a normal distribution with mean and standard deviation, the z-score of a measure X is given by:
z = x - [tex]\mu[/tex]/ [tex]\sigma[/tex]
Normal Probability Distribution measures how many standard deviations the measure is from the mean.
In this problem:
The proportion of young adults ages 20–39 who regularly skip eating breakfast is given as 0.238, hence p = 0.238
A sample of 500 hence n = 500
The mean and the standard deviation are given by:
[tex]\mu[/tex] = 500 ( 0.238) = 119
[tex]\sigma[/tex] = 9.5225
The probability that the number of individuals in Lance's sample who regularly skip breakfast will be greater than 122, using continuity correction, then the p-value of Z when X = 122.5.
z = x - [tex]\mu[/tex]/ [tex]\sigma[/tex]
z = 122.5 - 119/ 9.5225
z = 0.37
Then p-value of 0.6443.
1 - 0.6443 = 0.3557.
0.3557 = 35.57%is the probability that the number of individuals in Lance's sample who regularly skip breakfast is greater than 122.
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The ratio 13 to X is equivalent to the ratio 104 to y. Which equation represents y in terms of X?
Answer:
y=8X
Explanation:
The ratio 13 to X = 13:X
The ratio 104 to y = 104:y
If they are equivalent, we have that:
[tex]13\colon X=104\colon y[/tex]We write the ratios in fraction form.
[tex]\frac{13}{X}=\frac{104}{y}[/tex]We then make y the subject of the equation.
[tex]\begin{gathered} 13y=104X \\ y=\frac{104X}{13} \end{gathered}[/tex]We can simplify further to get:
[tex]\begin{gathered} y=\frac{13\times8X}{13} \\ y=8X \end{gathered}[/tex]This is the equation that represents y in terms of X.
Estimate 70⎯⎯⎯⎯√3 to the nearest integer.
Answer:
Step-by-step explanation:
round up
√3 = √4
70-√4= 70-2
=68
SOS PLEASE HELP QUICKLY WILL MARK BRAINLYIST
Submit a picture of your work to the assignment page:
its a two column proof
Prove: If two parallel lines are cut by a transversal then the alternate exterior angles are congruent. Do not use the alternate exterior angles theorem. Use a diagram and the corresponding angles theorem.
Proved that if two parallel lines are cut by a transversal then the alternate exterior angles are congruent.
What is the Exterior Angle of a Triangle Property?An exterior angle of a triangle is equal to the sum of the opposite interior angles.
By the property of alternate interior angles;
From the figure attached;
∠XWY ≅ ∠ZYW
The Property of the alternate angles states that if two parallel lines are cut by a transversal, then the alternate angles are congruent.
Here, ∠XWY and ∠ZYW shows the interior angles between the parallel lines and the transversal.
The interior alternate angles ∠XWY and ∠ZYW will be congruent.
Hence, Proved that if two parallel lines are cut by a transversal then the alternate exterior angles are congruent.
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PLEASE HELP ME!!!!!!!
Answer: 31
Step-by-step explanation:
The numbers are increasing by 1, then 2, then 3, ...
In other words, the second difference is 1.
So, the next number is likely [tex]24+7=31[/tex].