The solution of the pairs of lines are as follows,
(1) Line 1 and line 2 are perpendicular to each other.
(2) Line 1 and line 3 are parallel to each other.
(3) Line 2 and line 3 are perpendicular to each other.
The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
Here,
Calculate the slope of each line,
LIne 1
3y = 2x + 5
y = 2/3x + 5/3
Compared with the standard equation of line y = mx + c,
Slope m = 2/3
Similarly.
The slope of line 2 = -3/2
The slope of line 3 = 2/3
Now. properties of pair of lines state that the slope of parallel lines is equal and the slope of perpendicular lines are negative reciprocal of each other,
So
Slope of line 1 = slope of line 3
But,
The slope of line 2 is the negative reciprocal of the slope of lines 1 and 3.
Thus, the solution of the pair of lines has been shown above.
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In 2015, 120000 people voted. The number of viewers who voted in 2015 was 20% more than those in 2014. Calculate the numbers of viewers who voted in 2014
Answer:
Given;
120,000 people voted in 2015.
In 2015, 20% more people voted than 2014.
Therefore:
How many more people voted in 2015 = 20% of 120,000
= 24,000
Total number of people voted in 2014 = 120,000 - 24,000
= 96,000
Ans) 96,000 people voted in 2014.
You have two exponential functions. One has the formula h(x) = 3x – 2. The other function, g(x), has the graph shown below.
Which inequality below is true for all points on the indicated interval?
A g( x) ≥ h( x) on the interval –3 ≤ x ≤ 3
B g( x) ≥ h( x) on the interval –2 ≤ x ≤ 2
C g( x) ≤ h( x) on the interval –3 ≤ x ≤ 3
D g( x) ≤ h( x) on the interval –2 ≤ x ≤ 2
The correct statement regarding the exponential functions g(x) and h(x) is given as follows:
B g( x) ≥ h( x) on the interval –2 ≤ x ≤ 2.
What is an exponential function?The standard definition of an exponential function is given as follows:
y = ab^x.
In which the coefficients of the function are described as follows:
a is the y-intercept, the value of y at which the function crosses the y-axis.b is the rate of change of the exponential function.Function h(x) is defined as follows:
h(x) = 3^x - 2.
For the graphed function g(x), when x = 0, y = 4, hence the intercept of the function is given as follows:
a = 4.
When x = 1, y = 5, hence the rate of change of the function is obtained as follows:
b = 5/4.
b = 1.25.
Then function g(x) is given as follows:
g(x) = 4(1.25)^x.
Due to the higher intercept, g(x) ≥ h( x) at x = 0. This will change when they intersect, which from the image given at the end of the answer is at x = 1.906, which is approximately 2, hence statement B is correct.
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help me please and thank you!!!
Answer:
-3/4
Step-by-step explanation:
I used a calc called desmos graphing calc. It is very helpful
Answer:
The answer is B.-3/4
Step-by-step explanation:
What is X the distance between a and a?
20 points and brainliest for whoever answers this correctly
Solve for x: −2(x + 3) = −2x − 6
Group of answer choices
0
3
All real numbers
No solution
Answer:
All real numbers
Step-by-step explanation:
Wthen you simplify the equation,it converts to -2x-6=-2x-6. Since they are the same on each side,any real number can be used for x to make the equation equal.
Answer:
the answer I belive is 3.
Explain how to find a measure of angle ACD
without repositioning the protractor
Answer:
60 degrees
Step-by-step explanation:
ACD and ACB are complementary angles. Find ACB=30 degrees. Subtract 30 from 90 degrees. ACD=60 degrees.
Answer:
ACD=60
BCA=30
BCD=90
90-30=60
Find the missing side
Answer:
x = 71.5 in
Step-by-step explanation:
Remember the SOHCAHTOA rule
Soh...
Sine = Opposite / Hypotenuse
...cah...
Cosine = Adjacent / Hypotenuse
...toa
Tangent = Opposite / Adjacent
In this case, we use: CAH.
cos(52) = 44/x
x = 44/cos(52)
x = 71.5 inches
An independent set in a graph is a set of vertices S⊆V that contains no edge (so no pair of neighboring vertices is included). The max independent set problem is to find an independent set of maximum size in a graph G. (a) Write the max independent set problem as an integer linear program. (b) Write an LP relaxation for the max independent set problem. (c) Construct an example (a family of graphs) to show that the ratio LP-OPT / OPT can be at least cn where c>0 is some absolute constant and n is the number of vertices of the graph. (d) What is the (exact) relation between the size of a max independent set and the size of min vertex cover of a graph? (e) Using this relation, what does the 2-approximation algorithm for vertex cover imply for an approximation algorithm for max independent set?
The independent set in a graph is a set of vertices that contain no edges. So, no neighboring vertices are included. The max independent set problem is to get an independent set of maximum size in graph G.
The solution for this question is discussed below:
a) The integer linear program for the max independent set problem is as follows:
maximize ∑x_i Subject to: x_i+x_j ≤ 1 {i,j} ∈ E;x_i ∈ {0, 1} ∀i. The variable x_i can represent whether the ith vertex is in the independent set. It can take on two values, either 0 or 1.
b) The LP relaxation for the max independent set problem is as follows:
Maximize ∑x_iSubject to:
xi+xj ≤ 1 ∀ {i, j} ∈ E;xi ≥ 0 ∀i. The variable xi can take on fractional values in the LP relaxation.
c) The family of graphs is as follows:
Consider a family of graphs G = (V, E) defined as follows. The vertex set V has n = 2^k vertices, where k is a positive integer. The set of edges E is defined as {uv:u, v ∈ {0, 1}^k and u≠v and u, v differ in precisely one coordinate}. It can be shown that the size of the max independent set is n/2. Using LP, the value can be determined. LP provides a value of approximately n/4. Therefore, the ratio LP-OPT/OPT is at least c/4. Therefore, the ratio is in for a constant c>0.
d) The size of a max-independent set is equivalent to the number of vertices minus the minimum vertex cover size.
e) The 2-approximation algorithm for vertex cover implies a 2-approximation algorithm for the max independent set.
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IT IS URGENT PLEASE HELP ME
AND SHOW YOUR WORK SO I CAN BETTER UNDERSTAND!!!!
I will mark brainliest
This is due in an hour please help!
Answer:
x=7
Step-by-step explanation:
both of these triangles are about equivalent so we just have to imagine that triangle NMK is turned like the TRP
The corresponding side for TR is NM so we can set them equal to each other
3x-1=20
+1. +1
3x=21
/3. /3
X=7
Hopes this helps please mark brainliest
In testing a certain kind of missile, target accuracy is measured by the average distance X (from the target) at which the missile explodes. The distance X is measured in miles and the sampling distribution of X is given by:X 0 10 50 100P(X) 1⁄12 1⁄6 1⁄3 5⁄12Calculate the mean and variance of this sampling distribution.a) mean = 60.00; variance = 2600.00b) mean = 55.00; variance = 37.64c) mean = 61.08; variance = 37.64d) mean = 60.00; variance = 1416.67e) mean = 61.08; variance = 1416.67
The value of mean is 59.8 and the variance of the sampling distribution is 1440.46
Given,
In the question:
The distance X is measured in miles and the sampling distribution of X is given by;
X :- 0 10 50 100
P(X) : - 1 /12 1/6 1/3 5/12
Calculate the mean and variance of this sampling distribution.
Now, According to the question:
The variance of a random variable provides an idea of the dispersion of the random variable with respect to its hope. It is then defined as shown in the image.
Then you first calculate E [x] and E [\(x^{2}\)], and then be able to calculate the variance.
E[x] = 0 × 1/12 + 10 × 1/6 + 50 × 1/3 + 100 × 5/12
E[x] = 1.6 + 16.6 + 41.6
Mean/ E[X] = 59.8
So E[X]²= 59.8² = 3576.04
On the other hand
E[\(x^{2}\)] = \(0^2\) × 1/12 + \(10^2\) × 1/6 + \(50^2\) × 1/3 + \(100^2\) × 5/12
E[\(x^{2}\)] = 0 + 16.6 + 833.3 + 4166.6
E[\(x^{2}\)] = 5016.5
Then the variance will be:
Var[x]= E[\(x^{2}\)] - E[X]²
Var[x] = 5016.5 - 3576.04
Var[x] = 1440.46
Hence, The value of mean is 59.8 and the variance of the sampling distribution is 1440.46
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true or false: if v 1 and v 2 are eigenvectors of a 4 x 4 matrix a with eigenvalues 1 and 2 respectively, then v1 and v2 are orthogonal to each other.
False. Just because two vectors are eigenvectors of the same matrix with different eigenvalues, it does not mean they are orthogonal to each other.
Eigenvectors of a matrix are vectors that, when the matrix is multiplied by them, the vector remains the same except for a scaling factor. Eigenvalues are the scaling factors of the eigenvectors. If two eigenvectors, v1 and v2, of a 4x4 matrix a have eigenvalues 1 and 2 respectively, it does not mean that they are orthogonal (i.e. at a 90 degree angle) to each other. Orthogonality is a property of two vectors that is independent of the matrix and can only be determined by calculating the dot product of the two vectors. Therefore, two eigenvectors of the same matrix with different eigenvalues may or may not be orthogonal to each other.
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isolate the variable on the following problem. show your work.
-2=-4+x
Answer:
x=2
Step-by-step explanation:
Add 4 to both sides:
-2=-4+x
-2+4=-4+4+x
2=x
Answer:
\(x = 2\)
Step-by-step explanation:
First we must add 4 to both sides.
\(-2 = -4 + x\)
+4 +4
-4 + 4 = 0
-2 +4 = 2
Isolating a variable means that it is alone on its side of the eqation.
\(2 = x\)
x is now isolated and we also have the solution for it.
\(x = 2\)
What is the solution to this system of linear equations x â 3y â 2 x 3y 16?
The solution to this system of linear equations is (7, 3).
What is equation?
In mathematics, an equation is a formula that expresses the equivalency of two expressions, by connecting them with the equals sign =
Main body:
x - 3y = -2
x = 3y - 2 ….. (1)
x + 3y = 16 …… (2)
Let us solve the system of linear equations using the substitution method.
Substituting x in equation (2)
3y - 2 + 3y = 16
6y = 16 + 2
6y = 18
Divide both sides by 6
y = 3
Substituting the value of y in equation (1)
x = 3 (3) - 2
x = 9 - 2
x = 7
Therefore, the solution is (7, 3).
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The tangent ration! helpp!!
Answer:
13.5
Step-by-step explanation:
Given
tan34° = \(\frac{x}{20}\) ( multiply both sides by 20 )
20 × tan34° = x , then
x ≈ 13.5 ( to the nearest tenth )
Solve for c.
c+38=113
Enter your answer as a fraction in simplest form in the box.
c =
Answer:
c = 75
Hope this helps!
Step-by-step explanation:
c + 38 = 113
c + 38 - 38 = 113 - 38
c = 113 - 38
c = 75
The difference between 45 and y is 9
Answer:
y = 36
Step-by-step explanation:
1.8 - 3.7 x = -4.2 x + 0.3
Answer:
X= -3
Step-by-step explanation:
1.8-3.7x=-4.2x+0.3 given equation
1.8= -4.2x+0.3+3.7x add 3.7x to both sides
1.8-0.3=-4.2x+3.7x subtract 0.3 from both sides
1.5=-0.5x combine like terms
x= -3 divide both sides by -0.5
Answer:
\(x=-3\)
Step-by-step explanation:
\(1.8 - 3.7 x = -4.2 x + 0.3\)
\(- 3.7 x+4.2x = 0.3-1.8\)
\(0.5x=-1.5\)
\(0.5x/0.5=-1.5/0.5\)
\(x=-3\)
Identify which property you would use first to solve the following equation.
3(2y+5) = 8y - 23
Answer:
Distributive property
Step-by-step explanation:
In order to solve this equation we first need to distribute 3 into 2y+5, we use the distributive property to do this.
Given 300mL of a gas at 17.0 degrees Celsius, what is the volume at 10 degrees Celsius if the pressure remains constant?
Answer:
292.75mL
Step-by-step explanation:
From the ideal gas equation
PV= nRT
With each symbols having standard meaning
For pressure remaining constant the equation for two states can be written as
\(\frac{V_1}{T_1}=\frac{V_2}{T_2}\)
Given V_1 = 300mL, T_1 = 17° C = 290K and T_2 = 10°C or 283K
Now plugging values in above equation to find V_2
\(\frac{300}{290} =\frac{V_2}{283}\\V_2 =\frac{300}{290}\times283 = 292.75mL\)
Therefore, the volume at 10 degrees Celsius = 292.75mL
A risk profile from PrecisionTree lists
a. all possible outcomes and tneir corresponding utility,
b. the full probability distribution,
c. the nodes and branches for each possibe outcome
d. all oprions and their possible outcomes
A risk profile from PrecisionTree lists: A. all possible outcomes and their corresponding utility.
What is a decision tree?In Mathematics and Statistics, a decision tree is sometimes referred to as PrecisionTree and it can be defined as a tree-like model that is used by mathematicians, statisticians, and researchers as a decision support tool, in order to graphically display decisions with respect to their potential outcomes, consequences, utility, and resource costs.
This ultimately implies that, a decision tree is used for making decisions in business management by graphically displaying all the possible (expected) outcome of a decision in layers.
What is a risk profile?A risk profile can be defined as a distribution that is associated with a specific action. This ultimately implies that, a risk profile lists all the possible economic outcomes (monetary values) and provides the corresponding probability or utility of each.
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Complete Question:
A risk profile from PrecisionTree lists"
a. all possible outcomes and their corresponding utility.
b. the full probability distribution,
c. the nodes and branches for each possible outcome
d. all options and their possible outcomes
Different hotels in a certain area are randomly​ selected, and their ratings and prices were obtained online. Using​ technology, with x representing the ratings and y representing​ price, we find that the regression equation has a slope of 130 and a​y-intercept of −389.
Complete parts​ (a) and​ (b) below.
a. What is the equation of the regression​ line? Select the correct choice below and fill in the answer boxes to complete your choice.
A. y^ =_____ + ( _____ ) x^
B. y^ = ____ + ( ____) x
C. y = ____ + (____) x^
D. y + ____ + (____) x
b. What does the symbol y ​represent?
A. The symbol y^ represents the predicted value of price.
B. The symbol y^ represents the average price of hotels in the area.
C. The symbol y^ represents the expected price when the​ hotel's rating is 0.
D. The symbol y^ represents the amount that price increases with a​ 1-point increase in rating.
The regression equation is given by y^ = -389 + 130x^ and the symbol y^ represents the predicted value of price.
It is given to us that -
x = ratings
y = y-intercept
It is also given that the regression equation has -
Slope = 130
y-intercept = -389
We have to find out -
(a) the equation of the regression line
(b) what symbol y represents
We know that, regression analysis is used to predict continuous variables explained by single or multiple independent or explanatory variables.
There are various regression techniques that can be used to create predictive models, including simple regression, multiple regression, and logistic regression.
Here, we have -
Slope = 130
y-intercept = -389
(a) So, the regression equation can be represented as -
y^ = -389 + 130x^
(b) The symbol y^ is the dependent variable in the regression equation. Here, the symbol y^ represents the predicted value of price.
Thus, the regression equation is given by y^ = -389 + 130x^ and the symbol y^ represents the predicted value of price.
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An angle measures 10 more than four times a number. It’s supplement is two more than three times the number. What is the measure of each angle in degrees
Answer:
4x +10 + 3x +2 = 180 (since they're supplementary, the angles together =180)
7x +12 =180 (combine like terms on left side, and subtract 12 from both sides)
7x = 168 (divide both sides by 7 to isolate x)
x= 24
angle 1 = 4(24)+10 (plug x into the expression for each angle, and solve)
..................96 +10
angle 1 = 106 degrees (the measure of the first angle)
angle 2 = 3(24) +2
..................72 +2
angle 2 = 74 (the measure of the second angle)
106 +74 =180 (the two add up to 180, so they're supplementary)
Step-by-step explanation:
I hope this helps :)
A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 4 large boxes and 8 small boxes has a total weight of 125 kilograms. A delivery of 2 large boxes and 3 small boxes has a total weight of 57 kilograms. How much does each type of box weigh?
Answer:
weight of large box = x kg=18.25kg
weight of small box =y kg=15.5kg
Step-by-step explanation:
weight of large box = x kg
weight of small box =y kg
2 large boxes and 3 small boxes has a total weight of 83 kilograms.
2x+3y=83--------- eq 1
4 large boxes and 8 small boxes has a total weight of 197 kilograms.
4x+8y =197 -------eq 2
multiply eq 1 with -2
-4x-6y =-166
now add both equations
-4x-6y=-166
4x+8y=197
______________________
2y= 31
y=15.5
substitute value of y=17 in eq 1
2x+3y=83
2x+3(15.5)=83
2x+46.5=83
2x =36.5
x=18.25
weight of large box = x kg=18.25kg
weight of small box =y kg=15.5kg
hope this helps :)
In your English class you are given a list of 12 books you want to choose three books to read over the summer how many groups of three books are available from the list of 12
Answer:
4
Step-by-step explanation:
2 Points
Chelsea saw an advertisement for a loan that offered 6 months, same as
cash. If she takes the loan, which of these scenarios is most likely to occur?
O
A. Chelsea won't be charged interest for the first 6 months of the
loan, but she will have to make payments for the first 6 months.
O
B. Chelsea will be charged interest for the first 6 months of the loan,
and she will also have to make payments for the first 6 months.
O
C. Chelsea will be charged interest for the first 6 months of the loan,
but she won't have to make payments for the first 6 months.
D. Chelsea won't be charged interest for the first 6 months of the
loan, nor will she have to make payments for the first 6 months.
Based on the information provided regarding same as cash loans, Chelsea won't be charged interest for the first 6 months of the loan, nor will she have to make payments for the first 6 months. (Option D)
A Same-As-Cash Loan refers to a short-term lending solution in which no interest or monthly payment are required to be paid during a set “Same-As-Cash” period. At the end of a predetermined period, the loan is paid off. Hence, the customer owes no interest or monthly payments during a set promotional period and pays the same amount on the loan as they would have paid up front with cash. These are interest deferred loans in which the loans interest still accrues during that promotional period, however if the customer pays off the entire principal balance before the period ends, they are not required to pay that interest. The advantage of these loans is that customers may spend the same amount they would have if they had paid with cash up front. Hence, if Chelsea opts for loan that offered 6 months, same as cash, there would be no requirement of payment or interest charged for the 6 months.
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What is the correct equation for the table below?
i need help plzz
Answer:
ummmm sorry i dont know
Step-by-step explanation:
if a student is chosen at random, what is the probability that the student prefers the zoo or the water park?
Without specific data on the number of students who prefer each option, we cannot calculate the probability.
To determine the probability that a student prefers the zoo or the water park, we need to know the total number of students and the number of students who prefer each option. Without this information, it is not possible to calculate the probability accurately.
To calculate the probability, we would need to divide the number of students who prefer the zoo or the water park by the total number of students. For example, if there are 50 students in total and 30 prefer the zoo and 20 prefer the water park, the probability would be:
P(prefer zoo or water park) = (30 + 20) / 50 = 50 / 50 = 1
However, without specific data on the number of students who prefer each option, we cannot calculate the probability.
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The number 20,2Δ8 is a 5-digit number with the tens digit covered by a triangle. Given that the number is divisible by 7, what is its tens digit? I GIVE BRAINLIEST!
Answer:
20258. The missing digit is a 5
Step-by-step explanation:
Ok, let's write the number in a more creative way. That's \(21 000 - 700 = 20 300\), minus something else. That something else has to be a multiple of 7, be less than 100, and has to end with a 2. Now start writing down the multiplication table for 7 and find how many of them ends with 2. 42 comes to mind, and that's the only one. (you can go up to 7x14=98 before having one digit too many).
That brings your number to be written as \(21000-700 -42 = 20258.\)
In theory there was a criteria to see if a number was divisible by 7, but I've never learned it.
I agree with the other person. The answer is 5.
Here's how we can check to see if a number is divisible by 7.
Step 1) Remove the units digit to form a truncated (aka shrunken) number.Step 2) Double the digit we removed.Step 3) Subtract that result from the truncated number.If the result of the third step is a multiple of 7, then so is the original value itself. We can repeat the steps to progressively shrink the values down so we have something more manageable.
---------------
Let's use those steps to see if 20,258 is a multiple of 7
Step 1) Remove the '8' from 20258 to to get 2025Step 2) Double the 8 to get 16Step 3) Subtract 16 from 2025 to get 2025 - 16 = 2009It's not clear if 2009 is a multiple of 7 or not; however, we can apply the same three steps to shrink the number down. This process can be repeated as many times as you like.
Step 1) Remove the 9 from 2009 to get 200Step 2) Double the 9 to get 18Step 3) Subtract to get 200-18 = 182Like before, the result 182 is fairly big and it's not clear if we have a multiple of 7. Luckily, we only need to do one more round of those steps.
Step 1) Remove the 2 from 182 to get 18Step 2) Double that value we removed to get 4Step 3) Subtract to get 18-4 = 14The result 14 is a multiple of 7, which means that 182 is also multiple of 7. By a domino-like chain reaction, the values 2009 and 20258 are also multiples of 7.
Notes:
182 = 26*72009 = 287*720258 = 2894*7---------------
We've just verified that 20258 is a multiple of 7. Let's go over an example a non-multiple of 7. I'll add 1 to the number 20258 so we are guaranteed that it cannot possibly be a multiple of 7. Doing the round of steps as shown above should get us to some smaller non-multiple of 7.
Step 1) Remove the 9 from 20259 to get 2025Step 2) Double the 9 to get 18Step 3) Subtract: 2025 - 18 = 2007Repeat the steps until we get something more manageable
Step 1) Remove the 7 from 2007 to get 200Step 2) Double the removed digit: 7*2 = 14Step 3) Subtract: 200-14 = 186Let's do one more round
Step 1) Remove the 6 from 186 to get 18Step 2) Double the digit removed: 2*6 = 12Step 3) Subtract: 18-12 = 6The value 6 is not a multiple of 7, and neither are 186 and 2007 and 20259.
If you have your calculator with you, then you should see that dividing any of those values over 7 will not lead to a whole number result.
186/7=26.57 2007/7=286.71 20259/7=2894.14This is a fairly quick and efficient way to check divisibility by 7 if you are in a hurry.
In a given triangle, one interior angle is 80 degree. Calculate the second interior angle x degree
The other angle of the triangle is 65°.
We know that
Exterior Angle = Sum of two angles opposite to the exterior angle
Here, 145° = 80° + x°
=> x° = (145 – 80)°
=> x° = 65°
Therefore, the value of x in the given figure is 65°
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Complete question:
Convert y+2=-3(x-7) to standard form
Answer:
3x + y = 19
Here to answer any questions as well