The linear equation for the parallel line will be y=6x-3.
What exactly is a linear equation?
The equation is referred to as linear when a variable's maximum power is 1. A one-degree equation is another name for it. A linear equation in one variable has the conventional form Ax + B = 0. This equation has three variables: x, A, and B. A is a coefficient. A linear equation in which there are only two variables typically takes the form Ax + By = C. In addition to the constant C, there are three other constants: the variables x and y, the coefficients A and B, and the variables.
Now,
Line parallel to line y=6x-7 will have same slope which will be m=6
as general equation is y=mx+c where m=slope and c=constant.
For parallel line c will be as it is passing through (2,9)
9=6*2+c
c=9-12
c=-3
then the equation will be y=6x-3
Hence,
The equation for the parallel line will be y=6x-3.
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Given right triangle ABC with altitude
BD drawn to hypotenuse AC. If
AC 36 and DC = 9, what is the length
of BC?
=
C
9
D
36
X
A
B
Can someone please helppp
The measure of the length of x is equal to 20.1246 using the trigonometric ratios of cosine for angle C
What are trigonometric ratiosThe trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.
Considering the right triangles; ∆ABC with hypotenuse = 45 and adjacent = BC, the triangle ∆ADC with hypotenuse = BC and adjacent = 9 with the angle C we can solve for BC as follows:
for ∆ABC;
cosC = 9/BC {adjacent/hypotenuse}
for ∆ADC;
cosC = BC/45 {adjacent/hypotenuse}
9/BC = BC/45
BC² = 9 × 45 {cross multiplication}
BC² = 405
BC = √405 {take square root of both sides}
BC = 20.1246
Therefore, the measure of the length of x is equal to 20.1246 using the trigonometric ratios of cosine for angle C
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The monthly rents (in dollars) paid by 10 people are given below. (Note that these are already ordered from least to greatest.) 865, 970, 985, 1005, 1015, 1035, 1055, 1080, 1095, 1095 Send data to calculator Suppose that one of the people moves. Her rent changes from $1095 to $1045. Answer the following.
The new list of rents, ordered from least to greatest, would be 865, 970, 985, 1005, 1015, 1035, 1055, 1080, 1045, 1095. The median rent would also be changed from $1095 to $1045.
My question is in the picture below
Answer:
j1gru3hek3n
Step-by-step explanation:
bso2jw4usk8
Please help fast!! What is the domain of the relation?
Please explain the answer!
The domain of the relation include the following: C. {-5, -2, 0, 1, 4}.
How to determine of this relation?In Mathematics, the horizontal extent of any graph of a function represents all domain values and they are always read and written from smaller to larger numerical values, and from the left of the graph to the right.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain:
Domain = {-5, -2, 0, 1, 4}.
In conclusion, the domain of this relation are all the x-values (independent value) that are located on the x-axis of the graph, which include {-5, -2, 0, 1, 4}.
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Select the statement that correctly defines continuous and discrete quantitative variables. O A continuous variable has an infinite number of possible values, whereas a discrete variable always has a finite number of possible values. O A continuous variable can take on any real number value within some range, whereas a discrete variable come in countable units. O A continuous variable has a countable number of possible values, whereas a discrete variable has an uncountable number of possible values. O A continuous variable has numerical values, whereas a discrete variable serves to group items into categories.
The statement that correctly defines continuous and discrete quantitative variables is:
"A continuous variable can take on any real number value within some range, whereas a discrete variable come in countable units."
A variable is a quantity that may assume any one of a set of values.
This means that a continuous variable can take on any value within a certain range, which could be infinite, and that it can have decimal values. In contrast, a discrete variable has specific values that are separate and countable, such as integers or categories. For example, the height of individuals is a continuous variable, while the number of siblings someone has is a discrete variable.
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The 8 red markers in a box account for 4% of all markers in the box. How many markers are in the box?.
Answer: 32
Step-by-step explanation: divide 8 into 4/100
Kcf
Keep change flip
Keep the 4/100 change the division sign to multiplication then flip the 8 to 8/1 then just multiply across.
Un capitalista tiene dos capitales que se diferencian en S/. 221 000, el mayor de ellos lo impone al 20% anual y el menor al 16% anual, así al cabo de 3 años, el monto producido por el mayor es el doble de lo que produce el menor. Hallar la suma de los capitales.
The sum of the capitals would be $530400.
What is the formula to calculate the simple interest?The formula to calculate the simple interest is -
I = PRT/100
Given is that a capitalist has two capitals that differ in $221,000. The largest of them imposes it at 20% per year and the smallest at 16% per year, so after 3 years, the amount produced by the largest is double what the smallest produces.
We can write the amount produced by largest as -
A = P(1 + rt)
A = 221000(1 + 0.2 x 3)
A = 221000 x 1.6
A = 353600
Amount generated by smallest -
a = 353600/2
a = 176800
Their sum would be -
A + a = 530400
Therefore, the sum of the capitals would be $530400.
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{Question in english -
A capitalist has two capitals that differ in S/. 221,000, the largest of them imposes it at 20% per year and the smallest at 16% per year, so after 3 years, the amount produced by the largest is double what the smallest produces. Find the sum of the capitals.}
Examine the figure below, solve for a, round to the nearest whole number.
T
37
A
46⁰
28
D
The measure of a from the triangle ATD is 27 units. Therefore, the option B is the correct answer.
What is sine rule?Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.
The formula for sine rule is sinA/a=sinB/b=sinC/c
From the given triangle ADT, ∠A=46°, ∠D=84°, AT=37, AD=t and TD=a.
By angle sum property,
∠A+∠D+∠T=180°
46°+84°+∠T=180°
130°+∠T=180°
∠T=50°
sin46°/a=sin84°/37=sin50°/t
0.7193/a=0.9945/37=0.7660/t
0.7193/a=0.9945/37
0.9945a=0.7193×37
0.9945a=26.6141
a=26.6141/0.9945
a=26.76
≈27
0.9945/37=0.7660/t
0.9945t=0.7660×37
0.9945t=28.342
t=28.342/0.9945
t=28.5
Therefore, the option B is the correct answer.
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What is the volume 
The volume of the composite figure is 12 cubic in.
How to calculate the Volume of Composite Shapes?
Composite shapes have a volume that is made up of basic shapes. We can calculate the volume of the composite shapes using the steps listed below:
Step 1: Break down the compound shape into different components.
Step 2: Determine the volume of each basic shape.
Step 3: Combine the volumes of all the basic shapes.
Step 4: Write the solution in cubic units.
Firstly we can divide the figure into two rectangular prisms A and B. Then add these two to total volume the volumes of each prism.
The volume of prism A = length × width × height
V = 4 * 2 * 1
V = 8 cubic in.
The volume of prism B = length × width × height
V = 1 * 2 * 2
V = 4 cubic in.
Total volume = volume of prism A + volume of prism B
= 8 cubic in + 4 cubic in
= 12 cubic in
Hence, the volume of the composite figure is 12 cubic in.
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help me pls and thank you :)
Explanation:
Spreadsheet software is strongly recommended. If you have excel, then it's best to use it since it's used practically everywhere. If you don't have excel, then there are tons of free alternatives such as OpenOffice or LibreOffice.
Enter the data as shown. Then form a third column labeled xy which represents multiplying each x and y pair for any given row. Eg: Tom = xy = 7*2 = 14. Use cell references to quickly compute this new column. I don't recommend manually multiplying each pair of items.
Once the xy column is formed, add up everything in it since [tex]\Sigma[/tex] represents summations. The command called "Sum" or "SUM" does this very quickly. In a cell off to the side type in [tex]=Sum(C2:C10)[/tex] which will add up the elements in cell C2, C3, ... all the way up to C10. Don't forget about the equal sign up front. That's needed to execute the command rather than print out text.
The result of the command should be 350
To verify you can manually add up the values to check the answer is correct.
Answer:
First you have to add :-X = 7+2+5+9+6+10+9+8+4
X= 50
Y = 2+5+7+4+2+9+9+4+10
Y = 52
Now ,
Σ(xy)= 50×52
= 2600
Hope it helpful to you
If a graph of y=-9x + 11 were changed to a graph of y=-9x+14, how would the y-intercept change? OA. The y-intercept of the new graph would shift up 3 units. B. More information is needed to determine the change. C. The y-intercept would remain the same. D. The y-intercept of the new graph would shift down 3 units.
Answer:
Step-by-step explanation:
The y-intercept of a linear equation in slope-intercept form, y = mx + b, represents the point at which the line crosses the y-axis. In this form, "m" represents the slope of the line and "b" represents the y-intercept.
If we have a graph of y = -9x + 11, the y-intercept can be found by setting x equal to 0 and solving for y:
y = -9x + 11
y = -9 * 0 + 11
y = 11
So, the y-intercept of the original graph is (0, 11).
Now, if we have a graph of y = -9x + 14, the y-intercept can be found in the same way:
y = -9x + 14
y = -9 * 0 + 14
y = 14
So, the y-intercept of the new graph is (0, 14).
Comparing the y-intercepts of the two graphs, we can see that the y-intercept of the new graph has shifted up by 3 units, from (0, 11) to (0, 14).
Therefore, the correct answer is A: The y-intercept of the new graph would shift up 3 units.
What is the value of x in l-16l = x
Answer: |-16| =x
- (-16)= x
x = 16
Step-by-step explanation:
thank you
Hercules crawled on fifth of a mile in a one tenth of an hour. find the rate in miles per hour
In linear equation, 2 miles per hour is the rate in miles per hour .
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Divide the distance by the time.
(1/5 miles) / (1/10 hour)
= 10(1/5) miles per hour
= 2 miles per hour
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in a recent survey of 500 people,it was found that 2800 read Concord and 2300 read guardian while 400 read both papers. How many read neither
300 people read neither of the papers.
How to find how many read neither?Set theory is a branch of mathematical logic that studies sets, which are collections of objects. It is a fundamental theory in mathematics and can be used as a foundation for all other areas of mathematics.
Total population n(ξ) = 5000
Number of people reading Concord, n(C) = 2800
Number of people reading Guardian, n(G) = 2300
Number of people reading both = n(C ∩ G)] = 400
Number of people reading any of the newspaper = n(C ∪ G)] = n(C) + n(G) - n(C ∩ G) = 2800 + 2300 - 400 = 4700.
Number of people reading none of them is equal to = Total population - Number of people reading any of the newspaper = 5000 - 4700 = 300
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Janelle has set up bird feeders around the pond behind her house. Each feeder can hold 1/2 a cup of bird food. After measuring, Janelle finds that she has 3 cups of bird food. How many feeders can she fill?
Answer: Janelle can fill 6 feeders.
Step-by-step explanation:
To find the number of feeders Janelle can fill, we need to divide the total amount of bird food she has by the amount of bird food each feeder can hold.
First, let's convert the total amount of bird food from cups to half-cups:
3 cups / 2 = 6 half-cups
So, Janelle has 6 half-cups of bird food, and each feeder can hold 1 half-cup.
Therefore, she can fill:
6 half-cups / 1 half-cup per feeder = 6 feeders.
So, Janelle can fill 6 feeders.
Z-score with the area of 0.0054if the area is halfway between two entry’s use the z score halfway between the corresponding z scores
A chest has a length of 0.8 m, a width of 0.5 m
and a height of 0.6 m. What is the volume of the
chest?
A verbal description of a linear function g is given. Express the function g in the form
g(x) = ax + b.
The linear function g has rate of change −12 and initial value 100.
g(x) =
G is a linear function with a rate of change of -12 and an initial value of 100. Its equation is: g = -12x + 100.
What is a linear function?Straight lines make up the graph of linear functions. The following is the format of a linear function. y = f(x) = a + bx A linear function has a independent variable so one dependent variable.
What does the described linear function look like?As a result of the task's objectives, it is necessary to identify the linear expression that corresponds to the verbal description that has been provided.
Since f(x) = axe + b is the typical slope-intercept form of a linear function,
an is the slope (rate of change), and b is the y-intercept (initial value).
g = -12x + 100 is the necessary linear function, which is what has been presented.
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what’s the equation of the line graphed below i’ll give you brainlist pls help
y=3/2x+4
y=2/3x+4
y=2/3x-6
y=3/2x-6
Answer:
y = 2/3x + 4
Step-by-step explanation:
y-intercept (b) is 4
Use points (-6, 0) and (0, 4) to find the slope (m) = (4-0)/(0--6) = 4/6 = 2/3
y = mx + b = 2/3x + 4
A mailer for posters is a triangular prism as shown. Determine the lateral surface area of the mailer. Draw a net if necessary.
The lateral surface area of the mailer is 234 In²
How to determine the lateral areaIt is important to note that the formula for the lateral area of a triangular prism is expressed as;
A = (a + b+ c) h
Given that the parameters are enumerated as;
A is the lateral area of the triangular prisma is the base sideb is the base sidec is the base sideNow, substitute the values into the equation, we have;
Lateral area, A = (4 + 4 + 5) 18
Add the values
Lateral area = (13)(18)
Multiply the values
Lateral area = 234 In²
Hence, the value is 234 In²
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The median home value in Pennsylvania and Nevada (adjusted for inflation) are shown below.
Year Pennsylvania Nevada
1950 42400 53700
2000 97000 142000
If we assume that the house values are changing linearly,
a) In which state have home values increased at a higher rate?
Nevada
Correct
b) If these trends were to continue, what would be the median home value in Pennsylvania in 2010?
$
c) If we assume the linear trend existed before 1950 and continues after 2000, the two states' median house values will be (or were) equal in what year? (The answer might be absurd)
The year
According to the given statement Nevada's property prices have grown more rapidly , median home value 148,880 and median house values will be 15.6.
What does the median in housing mean?The selling price of the middle property in a list of properties listed by highest sale price through lowest over a predetermined time period is the median house price. Thus, if 71 homes were sold, the median home price would correspond to the sale price of the 36th home.
Rate of change for Pennsylvania [tex]= (97000 - 42400) / (2000 - 1950) = 1092[/tex]
Rate of change for Nevada [tex]= (142000 - 53700) / (2000 - 1950) = 1816[/tex]
As a result, Nevada's property prices have grown more rapidly.
b) Median home value of Pennsylvania in 2010[tex]= 42400 + 1092 * (2010 - 1950) = $148,880[/tex]
c) Pennsylvania[tex]= 42400 + 1092x[/tex]
Nevada[tex]= 53700 + 1816x[/tex]
[tex]42400 + 1092x = 53700 + 1816x\\724x = 11300\\x = 15.6[/tex]
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The inequalities 3x<1 and 6x<2 are equivalent inequalities. Write another inequality that is equivalent to 3x<1 and 6x<2.
One inequality that is equivalent to 3x<1 and 6x<2 is 3x<1/2.
To see why this is true, we can divide both sides of the second inequality by 2, which gives 3x<1/3. However, we want an inequality that is equivalent to both 3x<1 and 6x<2, so we need to find a common solution.
Notice that if 3x<1, then x<1/3. And if 6x<2, then x<1/3 as well (since 1/3 is less than 2/6). Therefore, the intersection of the solutions for these two inequalities is x<1/3.
But we want an inequality in the form of 3x<a, where a is some constant. To find this value, we need to solve for x in the intersection of the two solutions:
x<1/3
Multiplying both sides by 3 gives:
3x<1
So we can choose a=1/2, which gives us the final inequality:
3x<1/2
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angie has reviewed grades of 88, 96, 92, and 93 on her last 4 tests. what grade will she need to receive
The grades that Angie need to receive in her next test so that her average is 92 is 91.
What is average?The average is defined as the mean value a given data set. The formula to calculate the mean of a given data set is:
Average = Sum of the observations / Total number of observations
Assume the marks that Angie needs in her next test is represented by x.
Given that Angie has reviewed grades of 88, 96, 92, and 93 on her last 4 tests. Therefore, the grades she need to receive in her next test so her average is 92 is:
Average = Sum of the grades of all test / Total Number of test
92 = (88+96+92+93+x)/5
460 = 369+x
460 - 369 = x
x = 91
Hence, she needs 91 grades in her next test.
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The complete question is:
Angie has reviewed grades of 88, 96, 92, and 93 on her last 4 tests. what grade will she need to receive in her next test so that her average of all test is 92?
In an isosceles triangle, one angle is 24° greater than each of the other two equal angles.
Find the measure of all three angles.
The two smaller angles are each _____
The two smaller angles are 39 degrees each. The other angle is 106
How to solve for the anglesThe measure of the angles would be found using the formula
2*x + 24 = 180
This is because the sum of angles that are in a triangle is = 180
the two equal angles are x + x = 2x
the other angle is 24 greater than 2x
2x + 24 = 180
2x = 180 - 24
2x = 156
x = 78
eaxh of the two equal angles are 78 degrees
while the other angle is 78 + 24 = 106
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From the picture, find the value of the pawn in each of the following problems, and write the check
Answer:
6) x = 6
7) x = 4
8) x = 4
9) x = 6
10) x = 6
Step-by-step explanation:
This is based on Dr. Henry Borenson's method of using pawns to explain algebraic equations. Frankl I find using variables more intuitive
Let each pawn represent an x in the equations
6.
x + 8 = 10 + 4
x = 10 + 4 - 8
x = 14 - 8 = 6
7.
x + x = 4 + x
2x = 4 + x
2x - x = 4
x = 4
8.
x + x + x + 2 = 7 + 7
3x + 2 = 14
3x = 14 - 2
3x = 12
x = 12/3
x = 4
9.
2x + 4 = x + 10
2x - x = 10 - 4
x = 6
10
3x = x + 10 + 2
3x = x + 12
3x - x = 12
2x = 12
x = 6
2. Determine the area of each composite figure below.
Answer:
[tex]6\pi[/tex]
Step-by-step explanation:
There's two things to note here, we're dealing with a semi-circle and also a semi-circle that has some area taken out of it.
Area of a Circle:The area of a circle can be calculated using the formula: [tex]A=\pi r^2[/tex] where "r" is the radius, equal to half the diameter.
Since we're dealing with the semi-circles, we can just divide this area by two to get: [tex]A=\frac{\pi r^2}{2}[/tex]
Now as noted, we have some of the area taken out, but fortunately it's just another semi-circle. We can simply calculate the area of the entire semi-circle, and then calculate the area of the semi-circle inside and subtract them.
So the diameter of the entire thing is just 8 ft, so the radius is half of this, equal to 8 ft. That means the area is: [tex]A=\frac{\pi (4)^2}{2}=A = \frac{\pi * 16}{2} = 8\pi[/tex]
One mistake that may be made here, is assuming the radius of the smaller semi-circle is just two, as provided in the image. It's actually the radius of the inner semi-circle plus two which gives us the radius of the outer circle, of 4 feet. Now luckily in this case, it actually still results in 2 ft (since 2 + 2 = 4), but in other examples, that may noe be the case.
So now let's calculate the area of the inner semi-circle: [tex]A=\frac{\pi (2)^2}{2}=2\pi[/tex]
Now let's just subtract the areas: [tex]8\pi - 2\pi = 6\pi[/tex], so the area is 6 pi
2.63 divied by 0.5 standard way
Answer: 5.26
Step-by-step explanation:
Answer:
= 0.190
Solution:
Change the divisor 2.63 to a whole number by moving the decimal point 2 places to the right. Then move the decimal point in the dividend the same, 2 places to the right.
We then have the equations:
50 ÷ 263 = 0.190
and therefore:
0.5 ÷ 2.63 = 0.190
Both calculated to 3 decimal places.
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The records of a casualty insurance company show that, in the past, its clients have had a mean of 1.7 auto accidents per day with a standard deviation of 0.04. The actuaries of the company claim that the standard deviation of the number of accidents per day is no longer equal to 0.04, Suppose that we want to carry out a hypothesis test to see if there is support for the actuaries' claim. State the null hypothesis H, and the alternative hypothesis H, that we would use for this test. P KQ 0 Oso X X a Р S 00 020
The null hypothesis H0 in this case would be that the standard deviation of the number of accidents per day is equal to 0.04, while the alternative hypothesis Ha would be that the standard deviation of the number of accidents per day is not equal to 0.04.
The null hypothesis represents the status quo or the default assumption, which is that there has been no change in the standard deviation of the number of accidents per day. The alternative hypothesis represents the claim made by the actuaries, which is that there has been a change in the standard deviation.
Mathematically, the null and alternative hypotheses can be expressed as follows:
H0: σ = 0.04
Ha: σ ≠ 0.04
where σ represents the standard deviation of the number of accidents per day.
The hypothesis test would be used to determine whether there is evidence to support the actuaries' claim that the standard deviation has changed, or whether there is not enough evidence to reject the null hypothesis that the standard deviation remains equal to 0.04.
Help please! Which of the following tables represents a relation that is a function? Explained answer please
A
B
C
D
Answer:
Step-by-step explanation:
THE ANSWER TO YOUR QUESTION IS C.
Describe how you know whether an equation will be true for all values of x or true for no values of x
Answer:
Step-by-step explanation:
Generally an equation which will be true for all values of x have some statement which can be simplified into another state which will always be true.
So for example: [tex]x+4=x+4[/tex], is kind of a bit obvious to tell it's going to be true for all values as the two expressions have the same exact terms, but we can subtract "x" from both sides leading us to the statement: [tex]4=4[/tex] which is always true.
One important thing to note is you must be cautious at times, for example: [tex]\frac{x-2}{x-2}=\frac{x-2}{x-2}[/tex] may seem to be true for all values, and x-2 over x-2 is the same thing, so it simplifies to one and same thing on the right side: [tex]1=1[/tex] thus the statement should be true for all values right? Not completely, it's true for most values, except for x=2, and this is because 1=1 isn't exactly the same expression. In the original fraction the denominator has an x-2, and if we plug in x=2, we get 2-2 resulting in division by one, which of course isn't definable. So that's just one important thing to note as simplifying expressions may result in expressions that look equal, but are slightly different in a way.
