If the equation of a line is [y = (12x + 2)], then the slope of a line parallel to this line will be (Tan θ = 12) and, slope of a line perpendicular to this line will be [Tan θ = [tex](\frac{-1\1}{12})[/tex]].
As per question statement, the equation of a line is [y = (12x + 2)].
We are required to find out the slope of a line parallel to this line and the slope of a line perpendicular to this line.
To solve this question, firstly, we need to know about the standard equation of a line which goes as [tex][y = (mx +c)][/tex] where, "m" is the slope of the line and "c" is the y-intercept.
Comparing our given equation [tex][y = (12x +2)][/tex] with the above mentioned standard equation of [tex][y = (mx +c)][/tex], we get (m = 12) and (c = 2).
Hence, slope of our concerned line is 12. And since slopes of all parallel lines are equal, therefore, the slope of any line parallel to the line [tex][y = (12x +2)][/tex] will be 12 or (Tan θ = 12).
Also, we know that, the product of the slopes of two perpendicular lines, (say m₁ and m₂) is equal to (-1), i.e., [m₁*m₂ = (-1)].
Therefore, the line perpendicular to [tex][y = (12x +2)][/tex] will have a slope of [tex](\frac{-1}{m})[/tex], i.e., ([tex]\frac{-1}{12}[/tex]).
Equation: An equation is a mathematical statement that consists of two separate expressions, connected by an equal signSlope: Slope of a line is defined as the inclination of the line along the positive (x- axis) and is calculated by the formula [tex][m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}} ][/tex] where (x₁, y₁) and (x₂, y₂) are two points on the line.To learn more about Slopes (of Lines), click on the link below.
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5-2/5f+3/2f=f-1/2f+4
Answer:
[tex]f=-\frac{5}{3}[/tex]
Step-by-step explanation:
Six less than a number is four more than one-third of the number. Find the number.
Answer:
x - 6 = 1/3x + 4
x = 15
Hope this helps :)
Hope this helps :)Explanation and Check part below.
Step-by-step explanation:
1. Get the variable on one side by subtracting x.
x - 6 = 1/3x + 4
- 1 x - 1 x
- 6 = - 2/3x + 4
2. Subtract 4 which is the inverse operation of addition.
- 6 = - 2/3x + 4
- 4 - 4
- 10 = - 2/3x
3. Divide by - 2/3 which is the invers eoperation of multiplication.
- 10 = - 2/3x
- 2/3 - 2/3
(Keep,Change,Change - KCC method)
- 10 ÷ - 2/3 = - 10 × - 3/2 = 30/2 = 15
- 10 = - 2/3x
- 2/3 - 2/3
15 = x → x = 15
Check:
15 - 6 = 1/3(15) + 4
9 = 15/3 + 4
9 = 5 + 4
9 = 9
True statement.
Question
If A {3,7,9,13, 22}, B = {5,7,14, 23, 31), and C= {8, 9, 15, 23, 25, 31, 33), then what is (AUB) nC?
Provide your answer below:
whats 901513115/10293371972328287 X 1/2039 winner gets brainlist
Challenge: A scuba diver has 30 cubic feet of air in his tank and dives under the water at
3:15pm. When he resurfaced at 3:30pm, he had 12 cubic feet of air left. How many cubic
feet of air per minute did he use?
The cubic feet of air the scuba diver used per minute is 1.2 cubic feet of air per minute
Unit rateQuantity of air in his tank = 30 cubic feetTime he dives in = 3:15pmTime he resurfaced = 3:30pmQuantity of air remaining in the tank = 12 cubic feetCubic feet of air used per minute = Difference in quantity of air in his tank / difference in time
= (30 - 12) / (3:30pm - 3:15pm)
= 18 / 15
= 1.2 cubic feet of air per minute
Therefore, the cubic feet of air the scuba diver used per minute is 1.2 cubic feet of air per minute
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1. 4(-20) 2. (-8)(-5)
3. (-10)(0) 4. (-9)(-21)
5. 11(-1) 6. 18(-4)
Kingwood's zoo has two elephants. The male elephant weighs 5/8 of a ton and the female elephant weighs 1/2 of a ton. How much more does the male weigh than the female?
Harper desires to invest in a single mutual fund or ETF. She wants the fund to invest
50%-70% in stocks and the rest in bonds. Which fund or ETF would you recommend?
Harper should invest his funds in Hybrid Mutual Funds.
What are Hybrid Mutual Funds?Hybrid funds are mutual funds or exchange-traded funds (ETFs) that invest in securities other than stocks and bonds. They enable investors to own a combination of different elements that are typically found in two or more funds while investing in a single mutual fund. Hybrid Funds are mutual fund schemes that invest in more than one asset class, such as equity, debt, and other asset classes, depending on the scheme's investment objective. These funds invest in a variety of asset classes in order to diversify the portfolio and reduce risk.Therefore, Harper should invest his funds in Hybrid Mutual Funds.
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Solve the equation 2a²3a-27=0
Answer:
[tex]a = \frac{ \sqrt[3]{36} }{2} [/tex]
Simplify the expression 15.6 + -13.5 .
Answer:
2.1
Step-by-step explanation:
15.6 + (-13.5) + = 2.1
Remove Parentheses (-a) = -a
Subtract the numbers: 15.6 - 13.5 = 2.1
= 2.1
The distribution of the number of hours that a random sample of people spend doing chores per week is shown in the pie chart. Use 32 as the midpoint
for "30+ hours." Make a frequency distribution for the data. Then use the table to estimate the sample mean and the sample standard deviation of the
data set
Click the icon to view the pie chart
First construct the frequency distribution.
Class Frequency, f
0-4
5-9
10-14
15-19
20-24
25-29
30+
CIB
4
The frequency distribution for the given data is:
0-4: 0.0349.5-9: 0.1512.10-14: 0.2558.15-19: 0.1977.20-24: 0.1628.25-29: 0.1512.30: 0.0465.Treating the frequency distribution as a discrete distribution, we have that:
The mean is of 16.71.The standard deviation is of 10.95.What is the missing information?The pie chart is missing, but is given at the end of the answer.
What is a relative frequency?A relative frequency is given by the number of desired outcomes divided by the number of total outcomes.
A frequency distribution is composed by the relative frequencies of each outcome. From the pie chart, we have that there is a total of 3 + 13 + 22 + 17 + 14 + 13 + 4 = 86 people, hence the frequency distribution is given as follows:
0-4: 3/86 = 0.0349.5-9: 13/86 = 0.1512.10-14: 22/86 = 0.2558.15-19: 17/86 = 0.1977.20-24: 14/86 = 0.1628.25-29: 13/86 = 0.1512.30: 4/86 = 0.0465.What are the mean and the standard deviation of a discrete distribution?The mean of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.The standard deviation of a discrete distribution is given by the square root of the sum of the differences squared between each observation and the mean, multiplied by their respective probabilities.This is relevant because we want to treat the frequency distribution as a discrete distribution, taking the midpoint of each interval, hence:
P(X = 2): 0.0349.P(X = 7): 0.1512.P(X = 12): 0.2558.P(X = 17): 0.1977.P(X = 22): 0.1628.P(X = 27): 0.1512.P(X = 32): 0.0465.Hence the mean is:
E(X) = 0.0349 x 2 + 0.1512 x 7 + 0.2558 x 12 + 0.1977 x 17 + 0.1628 x 22 + 0.1512 x 27 + 0.0465 x 32 = 16.71.
The mean is of 16.71.
The standard deviation is found as follows:
S(X) = sqrt[0.0349 x (2 - 16.71)² + 0.1512 x (7 - 16.71)² + 0.2558 x (12 - 16.71)² + 0.1977 x (17 - 16.71)² + 0.1628 x (22 - 16.71)² + 0.1512 x (27 - 16.71)² + 0.0465 x (32 - 16.71)²] = 10.95.
The standard deviation is of 10.95.
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I need to know the answer to this ASAP, which of these aren’t equivalent please help.
Answer:
b
Step-by-step explanation:
cuz remember () and no parentheses has a different meaning
Pablo necesita
7
8 de litro de leche para preparar una bebida. La jarra que usa tiene graduadas las medidas de 1
1
2 litros y
3
4 de litro, como se observa en esta figura.
Answer:
i don't speak Spanish but I think it's 3
A board game has 6 blue spaces,29 yellow spaces ,12 green spaces, and 18 red spaces. If you are equally likely to land on each space, what is the probability of landing on a green space? Give your answer as decimal rounded to the nearest thousandth.
Answer:
If you're equally likely to land on each space then you're 1 in number of spaces to land on a specific space=1/(6+29+12+18) = 1/65
there are 12 green spaces so chance of a green space is 12/65=0.185 rounded to a nearest thousandth
Use the information given to find a convenient class width. Then list the class boundaries that can be used to create a relative frequency histogram. (Round your class width up to the nearest multiple of 5. Use the minimum value as the smallest class boundary. Enter your class boundaries as a comma separated list.) 8 classes for n = 75 measurements; minimum value = 50; maximum value = 205
Class boundaries list: 50,70,90,110,130,150,170,190,210
1. Calculate the range.
range= maximum value - minimum value= 205 - 50 =155
2. Divide the range by the number of classes.
width= [tex]\frac{155}{8}[/tex] =19.375
3. Round this number up to the nearest multiple of five.
width = 20
class boundaries: smallest class boundry= minimum value =50
difference between two class boundries= width
class boundaries list: 50,70,90,110,130,150,170,190,210
The range is the difference between the highest and lowest values within a set of numbers. To calculate range, subtract the smallest number from the largest number in the set.The statistical distributions' characteristics are described by the terms mean, median, mode, and range. The set of all potential values for terms that indicate predetermined events is known as a distribution in statistics. A term's value stated as a variable is referred to as a random variable.
The two main categories of statistical distributions are as follows. There are discrete random variables in the first category. This indicates that each phrase has a distinct, precise numerical value. A continuous random variable is present in the distribution of the second major kind. An unlimited number the of possible values can be represented by a continuous random variable.
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4m+2mm+m2+m+3m2 simplified
4m^2+7m
I did this before
An Apple Computer store sells computers for $1,234.88. Assuming the computers cost $10,896 per dozen. Find the dollar markup for each computer. Note: Round your answer to the nearest cent. Find the percent markup on cost for each computer. Find the percent markup on selling price for each computer.
If an Apple Computer store sells computers for $1,234.88 and the computers cost $10,896 per dozen, then the dollar markup for each computer is $326.88 and the percentage markup is 36%
Given,
An Apple Computer store sells computers = $1234.88
The cost of computers per dozen = $10896
Cost of one computer = [tex]\frac{10896}{12}[/tex] = $908
Then the dollar markup for each computer = 1234.88-908
=$326.88
Percentage markup = [tex]\frac{326.88}{908}[/tex]×100
=36%
Hence, If an Apple Computer store sells computers for $1,234.88 and the computers cost $10,896 per dozen, then the dollar markup for each computer is $326.88 and the percentage markup is 36%
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Find the difference: 20-√80
O-12√5
O-2√5
02√5
O-2√15
Step-by-step explanation:
maybe you missed something in the problem definition or in the answer options, but the answer options do not contain any right answer to the described problem.
20 - sqrt(80) = 20 - sqrt(16×5) = 20 - 4×sqrt(5) =
= 11.05572809...
it is simple to estimate, in what dimension the result should be : 80 is very close to 81. so the sqrt(80) is also very close to the sqrt(81), which is 9.
20 - 9 = 11.
so, all the negative answer options are wrong by default.
and the only positive one is 2×sqrt(5) = 4.472135955...
additional thoughts :
20 = 4×5 or 4×sqrt(5)×sqrt(5)
so, we could write the problem as
4×sqrt(5)×sqrt(5) - 4×sqrt(5)
which could be simplified to either
4×sqrt(5)×(sqrt(5) - 1)
or
4×(5 - sqrt(5))
Helen is making 3 batches of cupcakes for a bake sale. Each batch is 1 2/3 pounds one cooked and packaged. How heavy will 3 batches be in pounds?
Answer: 5 lbs
Step-by-step explanation: 1 2/3 x 3= 5
Answer:
5 pounds
Step-by-step explanation:
1 2/3 x 3 = 5 :)
& Quinn is reading a book with 788 pages. She is on page 329.
About how many more pages does Quinn have left to read?
Explain your reasoning.
There are about 460 pages left for Quinn to read
About how many more pages does Quinn have left to read?The given parameters are
Pages = 788
Pages read = 329
The number of pages does Quinn have left to read is
Pages left = Pages - Pages read
So, we have
Pages left = 788 - 329
Evaluate
Pages left = 459
Hence, there are about 460 pages left for Quinn to read
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Use formulas to find the lateral area and surface area of the given prism. Round your answer to the nearest whole number.
The side-lengths of a triangle are increased by a scale factor of 4. Predict
how this change will affect the area.
A. The area will be one-fourth the original area.
B. The area will be 4 times greater.
C. The area will be 16 times greater.
D. The area will be increased by 4 units.
If the side-lengths of a triangle are increased by a scale factor of 4 then the area will be 16 times greater.
As given in the question,
Let 'a' be the base of the triangle
and 'h' be the height of the triangle
Area of the triangle = (1/2)×a× h
Side length increased by scale factor 4
New base = 4a
New height=4h
New area=(1/2)×4a×4h
= 16×(1/2)×a ×h
= 16 times the original area
Therefore, if the side-lengths of a triangle are increased by a scale factor of 4 then the area will be 16 times greater.
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5.) Joey is saving money for a car that will cost at least $2500. His grandpa gave him. $460 and he is currently saving $15 each week. Write and solve an inequality to represent the number of weeks it will take Joey to save up for his car.
A certain missing number will result in the expression 20 + 24 when using the Distributive Property. What number must be multiplied by ( 5 + 6 ) to result in the expression: 20 + 24
Answer:
4
Step-by-step explanation:
You want to know what number, multiplied by (5 +6), gives 20 +24.
Distributive propertyFor some number 'a', you want ...
a(5 +6) = (20 +24)
We can solve for 'a' in the usual way.
11a = 44 . . . . simplify
a = 44/11 = 4 . . . . divide by the coefficient of 'a'
The missing number is 4: 4(5 +6) = 20 +24.
__
Additional comment
You can also look at it term by term:
5a = 20 ⇒ a = 4
6a = 24 ⇒ a = 4 . . . . the same factor, as you want it to be
a company makes a table for $15 and sells it for $19 what is the percent of markup
Answer:
126.6667%
Step-by-step explanation:
Using the mileage chart below, find the distance between Sturgis and Hot
Springs.
The distance between the Sturgis and Hot springs is 102 miles.
We have a mileage chart,
We have to estimate the distance between Sturgis and Hot Springs.
What is mileage chart ?A chart showing distances between various points in miles is called mileage chart.
According to the question -
The horizontal row with the name Sturgis intersects the vertical column with the name Hot springs at the block representing 102 miles.
Therefore, the distance between the Sturgis and Hot springs is 102 miles.
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The Johnsons have accumulated a nest egg of $40,000 that they intend to use as a down payment toward the purchase of a new house. Because their present gross income has placed them in a relatively high tax bracket, they have decided to invest a minimum of $2400/month in monthly payments (to take advantage of the tax deduction) toward the purchase of their house. However, because of other financial obligations, their monthly payments should not exceed $3000. If local mortgage rates are 4.5%/year compounded monthly for a conventional 30-year mortgage, what is the price range of houses that they should consider? (Round your answers to the nearest cent.)
Using the monthly payment formula, the price range of houses that they should consider is:
[$513,666.78, $592,083.48].
What is the monthly payment formula?It is given by:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
In which:
P is the initial amount.r is the interest rate.n is the number of payments.For this problem, the parameters are given as follows:
r = 0.045 -> r/12 = 0.045/12 = 0.00375.n = 30 x 12 = 360.The minimum price, discounting the down payment, is found when A = 2400, hence:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]2400 = 0.00375P\frac{(1.00375)^{360}}{(1.00375)^{360} - 1}[/tex]
[tex]P = \frac{2400[(1.00375)^{360} - 1]}{0.00375 \times (1.00375)^{360}}[/tex]
P = $473,666.78.
Considering the down payment, we add $40,000, hence the minimum value of the range is: $513,666.78.
The maximum price, discounting the down payment, is found when A = 3000, hence:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]3000 = 0.00375P\frac{(1.00375)^{360}}{(1.00375)^{360} - 1}[/tex]
[tex]P = \frac{3000[(1.00375)^{360} - 1]}{0.00375 \times (1.00375)^{360}}[/tex]
P = $592,083.48.
Considering the down payment, we add $40,000, hence the maximum value of the range is: $592,083.48.
Hence the price range is:
[$513,666.78, $592,083.48].
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Which formula can be used to describe the sequence?
-2/3, -4, -24, -144,...
The formula that describes the sequence given i.e. [tex]\frac{-2}{3}[/tex],-4,-24,-144 (geometric sequence) is [tex](\frac{-2}{3} )(6)^{n-1}[/tex]
Geometric progression:
A geometric progression or a geometric sequence is a series, in which each word is varied by another by a common ratio. When we multiply the previous term by a constant (which is non-zero), we get the following term in the sequence. It is symbolized by:
A, AR,[tex]AR^{2}[/tex],[tex]AR^{3}[/tex]...
Where A is the first term of the geometric sequence and R is the common ratio of the geometric sequence.
The general term of geometric sequence i.e. nth term =[tex]AR^{n-1}[/tex]
Given that A= [tex]\frac{-2}{3}[/tex] and R=6
As a result the general term of geometric sequence i.e. nth term =[tex](\frac{-2}{3} )(6)^{n-1}[/tex]
Therefore,The formula that describes the geometric sequence given i.e. [tex]\frac{-2}{3}[/tex],-4,-24,-144 is [tex](\frac{-2}{3} )(6)^{n-1}[/tex]
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Solve 2x2 + 5x = 12. (5 points)
A pair of shoes is regularly priced at $80 and is on sale for 20% off. You have a coupon to receive an additional 15% off the sale price. How much will you pay for the shoes?
The customer would pay $54.40 for the shoes
What is the dollar value of the initial discount of 20%?
The dollar worth of the general discount of 20% of the price of $80 is determined as 20% multiplied by the shoe price
dollar worth of initial discount=20%*$80
dollar worth of the initial discount=$16
the price after the initial discount=$80-$16
the price after the initial discount=$64
The fact the customer has a coupon to receive additional 15% off the sale price means the purchase price for the customer is as computed thus:
final sale price=$64*(1-15%)
final sale price=$54.40
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