![Find The Value Of X That Will Make L||M.2x - 3MX + 4x = [?]](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/QwRpuDLYyyIrvlCGBxv67CBqVdanuOqX.jpeg)
Answers
We can say that Line L and Line M are parallel to each other if, when cut by a transversal line, the corresponding angles, the alternate exterior angles, and the alternate interior angles are congruent.
In the figure shown, we have a pair of alternate exterior angles. Therefore, the two angles must be equal to each other. With that, we have the following equation:
[tex]2x-3=x+4[/tex]From that equation, we can solve x by joining like terms on either side of the equation.
[tex]\begin{gathered} 2x-x=4+3 \\ x=7 \end{gathered}[/tex]Therefore, x = 7. When asked, the measure of the two angles are 11 degrees.
Related Questions
Find the solution of the system of equations. 3x + 3y = 6 9x - 5y = -24
Answers
3x + 3y = 6 (eq. 1)
9x - 5y = -24 (eq. 2)
Multiplying equation 1 by 3,
3(3x + 3y) = 3*6
3(3x) + 3(3y) = 18
9x + 9y = 18 (eq. 3)
Subtracting equation 2 to equation 3,
9x + 9y = 18
-
9x - 5y = -24
---------------------
14y = 42
y = 42/14
y = 3
Replacing this result into equation 1,
3x + 3(3) = 6
3x + 9 = 6
3x = 6 - 9
3x = -3
x = -3/3
x = -1
how do I find the central angle for turn b?
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We will to use the formula to a sector areaa, which is given for:
[tex]A=r^2\theta/2[/tex]Where r is the radius and θ is the central angle.
We can rewrite the formula to obtain the central angle like this:
[tex]\theta=\frac{2A}{r^2}[/tex]We replace with the values of the track:
[tex]\theta=\frac{2\ast51\pi}{20\ast3^2}=\frac{17\pi}{30}[/tex]Then we change radians to degrees:
[tex]\frac{17\pi}{30}\ast\frac{180}{\pi}=102\text{ \degree}[/tex]Then the correct answer is 102°.
Ron bought two comic books on sale. Each comic book was discounted $1 off the regular price r. Write an expression to find what Ron paid before taxes. If each comic book was regularly $2.50, what was the total cost before taxes?
Answers
Step 1
Given;
[tex]\begin{gathered} A\text{ regular price of r for a comic book on sale} \\ A\text{ discount of \$1 before tax} \end{gathered}[/tex]Required; To
1) write an expression to find what was paid by Ron before taxes
2)Find the total cost before taxes of the comic books, if each one costs $2.50
Step 2
Write the expression of what Ron paid before taxes
[tex]\begin{gathered} \text{\$}2(r-1) \\ \text{Note; One book costs \$(r-1)} \\ \text{\$}(2r-2) \end{gathered}[/tex]Step 3
If each book was regularly $2.50, find the total cost before taxes
[tex]\begin{gathered} r=\text{\$}2.50 \\ \text{Total cost=\$(2(2.50)-2)} \\ \text{Total cost=\$(5-2)=\$}3 \end{gathered}[/tex].............................
Answers
step 1
Find out the expected value
In this game, the total possible outcomes are 12
The probability of a win is P=1/12
The probability of loss is P=11/12
so
EV=(1/12)*(30-20)-(11/12)*30
EV=(1/12)*(10)-(11/12)*30
EV=(10/12)-(330/12)
EV=-320/12
EV=-26.67p ----> is negative because is a loss for the players
If 60 people play the game
26.67*60=1,600
therefore
The school expect to raise for charity 1,600p
Divide by 100
1,600p/100=$16According to the histogram, what is the least number of broken light bulbs received in a shipment?
Responses
A 0
B 1
C 10
D 50
I GIVE YOU BRAINEST PLEASE ANWER UNDER 30 MIN
Answers
The graph of y = –2/x lies in ____.A. Quadrant I and IIIB. Quadrant I and IIC. Quadrant II and IVD. Quadrant III and IV
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In order to find the quadrants of y = -2/x, let's choose a positive and a negative value of x, then we calculate the corresponding values of y and check the quadrants:
[tex]\begin{gathered} x=-2\colon \\ y=-\frac{2}{-2}=1 \\ \\ x=2\colon \\ y=-\frac{2}{2}=-1 \end{gathered}[/tex]The point (-2, 1) is in quadrant II (negative x and positive y) and the point (2, -1) is in quadrant IV (positive x and negative y).
Therefore the correct option is C.
Find the area of the region enclosed by f(x) and the x-axis for the given function over the specified interval. x2 + 2x + 2 x2 The area is 54 (Type an integer or a simplified fraction.)
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To find this area, it is necessary to solve an integral, actually the sum of 2 integrals
[tex]\int (x^2+2x+2)dx+\int (3x+4)dx[/tex]The first one must be evaluated from -3 to 2 and the second one from 2 to 3
[tex]\begin{gathered} \int (x^2+2x+2)dx+\int (3x+4)dx \\ (\frac{x^3}{3}+x^2+2x)+(\frac{3x^2}{2}+4x) \\ \end{gathered}[/tex]Evaluate the first integral
[tex]\begin{gathered} \frac{x^3}{3}+x^2+2x\text{ (From -3 to 2)} \\ (\frac{2^3}{3}+2^2+2\cdot2)-(\frac{(-3)^3}{3}+(-3)^2+(2\cdot-3)) \\ \frac{8}{3}+4+4-(-\frac{27}{3}+9-6) \\ \frac{35}{3}+5=\frac{50}{3} \end{gathered}[/tex]Evaluate the second integral
[tex]\begin{gathered} \frac{3x^2}{2}+4x\text{ (From 2 to 3)} \\ (\frac{3\cdot(3^2)}{2}+4\cdot3)-(\frac{3\cdot(2^2)}{2}+4\cdot2) \\ (\frac{27}{2}+12)-(\frac{12}{2}+8) \\ \frac{15}{2}+4=\frac{23}{2} \end{gathered}[/tex]Now, solve the sum
[tex]\begin{gathered} \frac{50}{3}+\frac{23}{2} \\ \frac{100+69}{6}=\frac{169}{6} \end{gathered}[/tex]The area is 169/6
Alex is 12 years older than George, Carl is three times older than Alex, The sum of their ages is 68. Find the ratio of George's age to Carl's age to Alex's age.
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Firstly, let x represent Alex's age, y represent George's age and z represent Carl's age.
from the question;
Alex is 12 years older than George, So;
[tex]x=y+12\ldots\ldots\ldots\ldots.1[/tex]Carl is three times older than Alex, So;
[tex]z=3x\ldots\ldots\ldots..2[/tex]The sum of their ages is 68, So;
[tex]x+y+z=68\ldots\ldots\ldots\ldots\ldots3[/tex]Now we have three equations and three unknowns, so it is solvable.
Let us substitute equation 2 into equation 3; that is replace z with 3x in equation 3.
[tex]\begin{gathered} x+y+3x=68 \\ 4x+y=68\ldots\ldots\ldots\ldots\ldots\ldots4 \end{gathered}[/tex]Next, let us substitute equation 1 into equation 4. that is replace x with y+12 in equation 4.
[tex]\begin{gathered} 4(y+12)+y=68 \\ 4y+48+y=68 \\ 5y+48=68\ldots\ldots\ldots.5 \end{gathered}[/tex]we can now solve for the value of y from equation 5.
[tex]\begin{gathered} 5y+48=68\ldots\ldots\ldots.5 \\ \text{subtract 48 from both sides.} \\ 5y+48-48=68-48 \\ 5y=20 \\ y=\frac{20}{5} \\ y=4 \end{gathered}[/tex]let us now replace y with 4 in equation 1 to get the value of x. since y = 4;
[tex]\begin{gathered} x=y+12\ldots\ldots\ldots\ldots.1 \\ x=4+12 \\ x=16 \end{gathered}[/tex]then, since x =16 let us replace x with 16 in equation 2 to get z.
[tex]\begin{gathered} z=3x\ldots\ldots\ldots..2 \\ z=3(16) \\ z=\text{ 48} \end{gathered}[/tex]so we have;
[tex]\begin{gathered} \text{Alex's age = x = 4 years} \\ George^{\prime}sage_{}=y=16\text{ years} \\ Carl^{\prime}sage=z=48\text{ years} \\ \end{gathered}[/tex]We now need to find the ratio of George, Carl and Alex's age.
[tex]\begin{gathered} 16\colon48\colon4 \\ \text{dividing through by 4 we have;} \\ 4\colon12\colon1 \end{gathered}[/tex]So the ratio of their ages are;
[tex]4\colon12\colon1[/tex]Find a quadratic function with the given vertex ans passing through the given point vertex forn E Vertex (4,5): passes through (1, 2)
Answers
The quadratic function forms a parabola. The vertex form of the equation is expressed as
y = a(x - h)^2 + k
Where
h and k are the x and y coordinates of the parabola's vertex. Given that the vertex is (4, 5),
h = 4, k = 5
Substituting these values into the above equation, it becomes
y = a(x - 4)^2 + 5
Given that the parabola passes through the point, (1, 2), we would substitute x = 1 and y = 2 into y = a(x - 4)^2 + 5. It becomes
2 = a(1 - 4)^2 + 5
2 = a * 9 + 5
2 = 9a + 5
9a = 2 -5
9a = - 3
a = - 3/9 = - 1/3
Substituting a = - 1/3 into y = a(x - 4)^2 + 5, the equation would be
[tex]y\text{ = -}\frac{1}{3}(x-4)^2\text{ + 5}[/tex]Consider the rectangle. IT 4 x+1 Which two expressions represent the area of the rectangle?
Answers
sides of the rectangle:
4
x+1
Area of the rectangle = product of the sides
4 (x+1 )
Apply distributive property:
4(x)+4(1)
4x+4
So, the correct options are:
C. 4x+1
E.4x+4
A sociology teacher asked her students to complete a survey at the beginning of the year. One survey question asked, "How responsible are you?" Another question asked, "How many siblings do you have?" Irresponsible Responsible O siblings 6 3 1 sibling 4 5 What is the probability that a randomly selected student has 0 siblings and is irresponsible? Simplify any fractions.
Answers
Answer: Probability is 1/3
Step by step explanation:
The probability (P) of an event is:
[tex]P=\frac{\text{Number of ways it can happen}}{\text{Total number of outcomes}}[/tex]The probability that a randomly selected student has 0 siblings and is iiresponsible is:
[tex]P=\frac{6}{6+3+4+5}=\frac{6}{18}=\frac{1}{3}[/tex]How many ounces of water must be added to 85oz of a 40% salt solution to make a solution that is 17% salt?
Answers
Okay, here we have this:
Considering the provided information, we are going to calculate the requested value, so we obtain the following:
Accordingly, since the amount of salt remains the same, then we have the following equality, where x represents the amount of water that must be added:
0.4(85)=0.17(x+85)
Let's solve for x:
34=0.17x+14.45
0.17x=34-14.45
0.17x=19.55
x=19.55/0.17
x=115
Finally we obtain that must be added 115 ounces of water to make a solution that is 17% salt.
I need help describing the sequence of transformations for 12 and 13.
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12. For the first part we rotate 90° and reflect on the y-axis
Then we reflect on the x-axis
13. First we reflect on the y-axis, then we rotate 90° and finally we reflect on the x-axis
i need help trying to write a system of linear equations for the graph below
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We need to find the equation in slope-intersect form
[tex]y=mx+b[/tex]of the given lines.
For the horizontal line, we can see that it passes through points
[tex]\begin{gathered} (x_1,\text{y}_1)=(0,7) \\ (x_1,y_2)=(4,6) \end{gathered}[/tex]the its slope (m) is given by
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{6-7}{4-0}=\frac{-1}{4}=-\frac{1}{4}[/tex]Then, the line equation has the form
[tex]y=-\frac{1}{4}x+b[/tex]where b is the y-intercept. From the picture, we can see that the line crosses the y-axis at y=7, therefore, b=7. Then, the line equation for the horizontal line is
[tex]y=-\frac{1}{4}x+7[/tex]Similarly, we can apply the same procedure for the other line. We can see that it passes through points
[tex]\begin{gathered} (x_1,\text{y}_1)=(0,-2) \\ (x_2,\text{y}_2)=(4,6) \end{gathered}[/tex]Then, the slope (m) of this line is given by
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{6-(-2)}{4-0}=\frac{6+2}{4}=\frac{8}{4}=2[/tex]Then, the line equation has the form
[tex]y=2x+b[/tex]Since this line crosses y-axis at y=-2 then b=-2. Hence, the equation is
[tex]y=2x-2[/tex]In summary, the system of linear equations is:
[tex]\begin{gathered} y=-\frac{1}{4}x+7 \\ y=2x-2 \end{gathered}[/tex]what is 10•(-1/2)= ??
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For this problem, we are given a product between an integer and a fraction.
The expression is shown below:
[tex]10\cdot(\frac{-1}{2})[/tex]To solve this problem, we need to multiply the two numerators and denominators, then simplify the fraction:
[tex]\frac{-10}{2}=-5[/tex]The result is -5.
If the line joining the points (a,4) and (2,-5) is parallel to the line with given equation 2x-3y=12 find the value of a
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Parallel lines have the same slope, thus, using the equation of the parallel line, we can find out the slope of the line that passes through the given points.
To find the slope of a line given its equation, we have to put the equation into the slope-intercept form, whcih we can do by solving the equation for y:
[tex]\begin{gathered} 2x-3y=12 \\ -3y=-2x+12 \\ y=\frac{-2}{-3}x+\frac{12}{-3} \\ y=\frac{2}{3}x-4 \end{gathered}[/tex]The slope of the line is the coefficient multiplying x, which is 2/3 in this case.
So, let's name the slope m:
[tex]m=\frac{2}{3}[/tex]Since the lines are parallel, both have the same slope m.
Also, if we want to find the slope given two numbers on the line, we can use the following equation:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]So, we have the points (a, 4) and (2, -5) and we have the slope m = 2/3. Substituting these, we have:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1}_{} \\ \frac{2}{3}=\frac{-5-4}{2-a} \\ \frac{2}{3}=\frac{-9}{2-a} \\ 2(2-a)=3\cdot(-9) \\ 4-2a=-27 \\ -2a=-27-4 \\ -2a=-31 \\ a=\frac{31}{2} \end{gathered}[/tex]Thus, the value of a is 31/2.
The taxes on a house assessed at 90,000 are $3420 a year. If the assessment is raised to 119,000 and the tax rate did not change, how much would the taxes be now?
Answers
The amount of tax to be paid on the assessment of the house is $4522.
How to calculate the tax?Given that the taxes on a house assessed at 90,000 are $3420 a year, the tax rate will be:
= Tax / Total value.
= 3420 / 90000
= 3.8%
Therefore, when the assessment is raised to 119,000 and the tax rate did not change, the value of the tax will be:
= Tax percentage × New assessment
= 3.8% × 119000
= $4522
The tax is $4522.
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- Gross pay: $38,550; married,
2 dependents; state income tax rate:
3 percent.
Answers
Answer:
Step-by-step explanation:
This is 0% of your total income of $0. 0% would also be your average tax rate. Your income puts you in the 0% tax bracket. At higher incomes, exemptions, many deductions and many credits are phased out. This increases your tax bill and your marginal tax rate. With these phase outs, adding $1,000 to your income would result in a 0% marginal tax rate.
The table represents the cost to eat at a buffet-style restaurant.Number ofPeople (p)2Cost (C)(including tax)27.5441.3155.0868.85345682.62Which equation could be used to calculate the cost. C, for any number of people, p, to eat at the restaurant?
Answers
We need to take the values of the table and check which of the options fit with the results.
In the first line of the table we have p=2 and C=27.54.
Using the equation in option A, for p=2 we would get:
[tex]\begin{gathered} C=p+27.54 \\ C=2+27.54 \\ C=29.54 \end{gathered}[/tex]Which is not value for C in the table. Thus we discard option A.
Using the equation for option B, for the value of p=2, we would get:
[tex]\begin{gathered} C=13.77p \\ C=13.77(2) \\ C=27.54 \end{gathered}[/tex]Which is indeed the value of the table.
To confirm, we try now with the next value of p, p=3, and check if we get the same result with equation B as with the table:
[tex]\begin{gathered} C=13.77p \\ C=13.77(3) \\ C=41.31 \end{gathered}[/tex]Which is also the value for C in the table.
Thus we confirm that option B is the correct equation
What is the quotient in simpilest form? 3/4÷5/16
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the given expression is
[tex]\frac{\frac{3}{4}}{\frac{5}{16}}[/tex][tex]\frac{3\times16}{5\times4}=\frac{12}{5}=2.4[/tex]so the quotient will be 2.4
Question 9, on which interval is the graph negative ?
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The intervals where the graph is negative are those where it goes below the x-axis. With the figure we can easily identify the following negative portion of the graph:
As you can see, these negative values are located for all the points within (-5, -1), this is equivalent to the interval -5 < x < -1. Then option B is the correct answer
hello I am having difficulty on this problem please help thank you
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we have a system of inequalities
Inequality A
[tex]-4x+3y<6[/tex]Isolate the variable y
[tex]\begin{gathered} 3y\lt6+4x \\ y<\frac{4}{3}x+\frac{6}{3} \\ y\lt\frac{4}{3}x+2 \end{gathered}[/tex]The solution to the first inequality is the shaded area below the dashed line y=(4/3)x+2
Inequality B
[tex]4x+7y\leq-7[/tex]Isolate the variable y
[tex]\begin{gathered} 7y\leqslant-7-4x \\ y\leqslant\frac{-7}{7}-\frac{4x}{7} \\ \\ y\leqslant-\frac{4}{7}x-1 \end{gathered}[/tex]The solution to the second inequality is the shaded area below the solid line y=-(4/7)x-1
therefore
The solution to the system of inequalities is the shaded area below the dashed line y=(4/3)x+2 and below the solid line y=-(4/7)x-1
Using a graphing tool
see the attached figure below
Remember that
If an ordered pair is a solution to the system of inequalities
then
the ordered pair must lie in the shaded region of the solution
so
the point (-2,-2) is a solution to the system of inequalities
see the figure below
Cara has 42.5 pounds of coffee. If she splits the coffee into 2.5 pound bags, how many bags will she need?A)17B)19C)21D)23
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could i have a fast answer please? if not it’s ok
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Given:
Strip diagrams are given.
Option D represents the 175% .
Option D is the correct answer.
choose the expression that is represented by the following phrase:"the square of Y decreased by the quotient of 8 and y"
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a pet store has c tanks of fish. Each tank has 24 fish. Using c, write an expression for the total number of fish in the store
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a pet store has c tanks of fish. Each tank has 24 fish. Using c, write an expression for the total number of fish in the store
the equation is equal to
Multiply the number of tanks by 24
so
24c
the answer is 24cPart 2
1/13 is the reciprocal of 13
because
(13)(1/13)=1
a number multiplied by its reciprocal is equal to 1
Determine the domain and range Express your answer in interval notation
Answers
The domain of a function is the set of all values that the x-variable can take.
On the other hand, the range of the function is the set of all values that the function takes when it is evaluated at elements of the domain.
For the given expression:
[tex]p(x)=-\frac{1}{(x-1)^2}[/tex]The denominator is (x-1)^2. Since the denominator must be different from 0, then:
[tex]\begin{gathered} (x-1)^2\ne0 \\ \Rightarrow x-1\ne0 \\ \Rightarrow x\ne1 \end{gathered}[/tex]Then, the only restriction for the variable x is not to be equal to 1. Then, the domain of p(x) is the set of all real numbers except 1, which can be written using interval notation as:
[tex](-\infty,1)\cup(1,\infty)[/tex]Since the exponent of the denominator is 2, then the denominator is always positive. Since the coefficient of the term 1/(x-1)^2 is -1, then the whole expression must always be negative. Additionally, there is no way in which the expression can be equal to 0.
Then, the range of the function is the set of all negative numbers, which can be expressed using interval notation as:
[tex](-\infty,0)[/tex]Therefore, the answers are:
[tex]\begin{gathered} \text{ Domain: }(-\infty,1)\cup(1,\infty) \\ \\ \text{ Range: }(-\infty,0) \end{gathered}[/tex]The price of televisions has dropped dramatically over the last three years. Three years ago, a 32 inch television was $500. This year the tv was on sale for $199. What is the percent change?
it is due today!!! 7th honers
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The percent change in the price of television from initial price $500 to final price $199 is 60.2.
What are Percentages?
The term 'per cent' means 'out of a hundred'.
Percentage is a way to define parts of a whole.
To convert fraction to a percentage, first convert fraction to decimal,
then multiply decimal value with 100, with '%' sign.
So, Percentage change = [tex]\frac{initial-final}{initial}[/tex]×100%
Percentage change = { ( $500 - $199 ) / $500 } × 100%
= { $301 / $500 } × 100%
= .602 × 100%
= 60.2%
Hence, the percentage change in tv price is 60.2%.
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A segment has endpoints A and C. What are two names for the segment? Choose the correct answer below O AC and CA OAC and CA O AC and CA O AC and CA
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Given that endpoints of a segment: A and C
The two names for the sgment will be:
AC and CA
ANSWER:
AC and CA
If f(x) = x2 + x, find f(-3).-123O6
Answers
To find f(-3) we have to substitute x = -3 in the equation.
[tex]\begin{gathered} f(-3)=(-3)^2+(-3) \\ f(-3)=9-3 \\ f(-3)=6 \end{gathered}[/tex]