ANSWER
P'(-12, 21.5)
EXPLANATION
We are given the cordinates of P as:
P(-9, 10.5)
Cordinate points are given as A(x, y)
We want to translate it 3 units left and 11 units up.
That means that we are moving it 3 units towards the negative side of the x axis and 11 units towards the positive side of the y axis.
Therefore, we will subtract 3 from the x cordinate and add 11 to the y cordinate.
Therefore, the translation is:
P(-9, 10.5) => P'(-9 - 3, 10.5 + 11)
=> P'(-12, 21.5)
The cordinates of P have been translated.
Andre is looking at apartments with 1 of his friends. They want the monthly rent to be no more than $1000. If the roommates split the rent evenly among the two of them, what is the maximum rent each will pay?
We have the next inequality
[tex]2x\le1000[/tex]where x is the rent of each person
[tex]\begin{gathered} x\le\frac{1000}{2} \\ x\le500 \end{gathered}[/tex]The maximum rent each will pay is $500
Bobby says the dilation can be represented by (1\3X, 1,\3Y)Betty says the dilation can be represented by (3X, 3Y)who is correct and why?
Bobby is right because the measurements were made smaller so the dilation factor must be a number less than 1, and 1/3 is less than 1
Given the following five-number summary, find the IQR.
2.9, 5.7, 10.0, 13.2, 21.1.
The IQR of the given series 2.9, 5.7, 10.0, 13.2, 21.1 is 15.4
In the given question, a five number summary is given as follows
2.9, 5.7, 10.0, 13.2, 21.1
We need to find the IQR
So, first we'll find the median of the given series
The middle value in a sorted, ascending or descending list of numbers is known as the median, and it has the potential to describe a data collection more accurately than the average does.
So, the given series is already in ascending order. And the middle value is 10.0. So the median is 10.0
Now to find the IQR the given formula will be used,
IQR = Q3 - Q1
Where Q3 is the last term in lower series and Q1 is the last term in upper series
Lower series - 2.9, 5.7
Upper series - 3.2, 21.1
Q3 = 5.7 , Q1 = 21.1
IQR = Q3 - Q1 = 21.1 - 5.7 = 15.4 ( IQR is always positive)
Hence, the IQR of the given series 2.9, 5.7, 10.0, 13.2, 21.1 is 15.4
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Instructions: Complete the following table, computing each students' mean, median, mode, and range: Math Test Scores ( picture attached ) What is the mean score for Test 2? What is the mode of Test 7? ________What is the median score of Test 4? ________What is the range of Test 6? ________
The completed worksheet is the following:
This worksheet involves three measures of central tendency: Mean, Median, Mode and Range
Mean: To get the mean of a dataset, add up all the data and divide by the number of datum (or inputs)
Median: To get the median of a dataset, sort the data in ascending order, and choose the central datum.
For example, if you have a dataset with 7 inputs, sort it in ascending order and select the 4th datum, as there would be 3 values above and 3 below (Hence it being the central datum).
Mode: The mode is the most repeated value of a dataset.
Range: The range is the difference between the biggest and smallest values of a dataset.
Simplify by combining like terms,8t3 + 8y + 7t3 + 6y + 9t2
The simplification of the expression will be; 15t³ + 9t² + 14y
What are equivalent expressions?Those expressions that might look different but their simplified forms are the same expressions are called equivalent expressions. To derive equivalent expressions of some expressions, we can either make them look more complex or simple.
Given that the expression as 8t³ + 8y + 7t³ + 6y + 9t²
Now combining like terms;
8t³ + 7t³ + 9t² + 8y + 6y
Simplify;
15t³ + 9t² + 14y
It cannot be solved further because of unlike terms in the expression.
Therefore, the simplification of the expression will be; 15t³ + 9t² + 14y
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f(x) = x ^ 3 + 3x ^ 2 + 4x + 5 and g(x) = 5 , then g(f(x)) =
we have the functions
[tex]\begin{gathered} f\mleft(x\mright)=x^3+3x^2+4x+5 \\ g(x)=5 \end{gathered}[/tex]so
g(f(x))=5Use compatible numbers to determine if 455+ 229 is more than 650
Step 1
compatible numbers are the numbers that are easy to add, subtract, multiply, or divide mentally.
Step 2
Math problem
455 + 229
Compatible numbers
455 + 225 = 680
680 is close to 455+229 = 684
Step 3:
Hence
By compatible numbers, 455 + 229 is more than 650.
xin uses 20 yards of fencing to build the walls of a square Chicken Coop which equation and solution represents x, the length, in yards, of each wall of the square coop?A: [tex]x + 4 = 20 \\ x = 16[/tex]b:[tex]x + 4 = 20 \\ x = 24[/tex]c:[tex]4x = 20 \\ x = 80[/tex]d:[tex]4x = 20 \\ x = 5[/tex]
Since the coop is in square shape The fencing is in the shape of a square
So equation is 4x=20, x=5
Given that 4 is a zero of the polynomial function f(x), find the remaining zeros.f(x) = x³ - 6x² + 25x - 68List the remaining zeros (other than 4).4(Simplify your answer. Type an exact answer, using radicals and i as needed. Use a cc
ANSWER
[tex]\begin{gathered} x=1+4i \\ x=1-4i \end{gathered}[/tex]EXPLANATION
Given:
[tex]\begin{gathered} f(x)=x^3-6x^2+25x-68 \\ \end{gathered}[/tex]Also,
One of the zeros: x = 4
Desired Outcome:
List the remaining zeros using radicals and i.
Simplify the polynomial using x - 4 = 0
Determine the remaining polynomials by simplifying x^2 - 2x + 17 = 0 using the quadratic formula
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]where:
a = 1,
b = -2
c = 17
Substitute the values
[tex]\begin{gathered} x=\frac{-(-2)\pm\sqrt{(-2)^2-4(1)(17)}}{2(1)} \\ x=\frac{2\pm\sqrt{4-68}}{2} \\ x=\frac{2\pm\sqrt{-64}}{2} \\ x=\frac{2\pm\sqrt{64\times-1}}{2} \\ x=\frac{2\pm(\sqrt{64}\times\sqrt{-1})}{2} \\ x=\frac{2\pm8\sqrt{-1}}{2} \\ x=1\pm4\sqrt{-1} \\ \text{ Recall: }\sqrt{-1}\text{ = }i \\ x=1\pm4i \\ x=1+4i\text{ }or \\ x=1-4i \end{gathered}[/tex]
In a certain country, the probability that a baby that is born is a boy is 0.52 and the probably that a baby that is born is a girl is 0.48. A family has two children. If X is the number of girls born to a family, find the probability that the family has 0, 1, or 2 girls.(a) Draw a tree diagram showing the possibilities for each outcome.(b) Create the binomial distribution table for p(X)
Given:
The probability that a baby that is born is a boy is 0.52.
The probability that a baby that is born is a girl is 0.48.
To find:
The probability that the family has 0, 1, or 2 girls.
Explanation:
Using the binomial distribution,
[tex]P(X=x)=^nC_xp^x(1-p)^{n-x}[/tex]Here,
[tex]\begin{gathered} n=2 \\ P(Birth\text{ of girls\rparen=}p=0.48 \\ P(B\imaginaryI rth\text{ of boys\rparen=}1-p=0.52 \end{gathered}[/tex]The probability that the family gets 0 girl child is,
[tex]\begin{gathered} P(X=0)=^2C_0(0.48)^0(0.52)^2 \\ =0.2704 \end{gathered}[/tex]The probability that the family gets 1 girl child is,
[tex]\begin{gathered} P(X=1)=^2C_1(0.48)^1(0.52)^1 \\ =0.2496 \end{gathered}[/tex]The probability that the family gets 2 girl children is,
[tex]\begin{gathered} P(X=2)=^2C_2(0.48)^2(0.52)^0 \\ =0.2304 \end{gathered}[/tex]So, the probability that the family has 0, 1, or 2 girls is,
[tex]\begin{gathered} P(E)=0.2704+0.2496+0.2304 \\ =0.7504 \end{gathered}[/tex]a) The tree diagram is,
b) The binomial distribution table for p(X) is,
Karen has 5 more quarters than dimes. She has $3.70. How many quarters and dimes she have?
A dime is 10% of a dollar = 10/100 x 100 cent = 10 cents
A quater is 25% of a dollar = 25/100 x 100 cent = 25 cents
Since Karen has 5 more quaters than dimes
let quaters = q
let dimes = d
Then Karen has 5q : d = $ 3.70
$ 3.70 = 3.70 x 100 cents = 370 cents
True or False. The graph is linear, but not proportional.
Answer:
True.
The graph is linear, but not proportional.
Explanation:
Given the graph in the attached image;
The graph is linear because it is a straight line graph.
A linear graph is always straight.
A proportional relationship in which the two components have a constant ratio.
The proportional graph is a straight line graph that passes through the origin (0,0).
Since the given graph does not pass through the origin, it is not a proportional graph.
Therefore, The graph is linear, but not proportional.
What did the student do incorrectly in this problem? Thanks for the help!
Solution
We have the function
[tex]f(x)=\frac{(5x-2)(x-1)}{(x-1)(x+2)}[/tex]The graph of the function is
To prepare for disinfection of hard nonporous surfaces against canine parvovirus, mix a solution of bleach in 2.5 gallons of water at the rate of ¾ cup of bleach per 1 gallon of water. What is the volume of bleach added to the 2.5 gallons of water? a. 30 fl. oz b.15 fl. oz c.1 ¾ cups d.1 ½ cups and 2 tbsp
Answer:
b. 15 fl. oz
Explanation:
From the question, we are told that 3/4 cup of bleach is needed per 1 gallon of water.
Thus:
[tex]\begin{gathered} 1\text{ gallon of water requires }\frac{3}{4}\text{ cup of bleach} \\ \implies2.5\text{ gallons will require }\frac{3}{4}\times2.5\text{ cups of bleach} \\ \frac{3}{4}\times2.5=1\frac{7}{8}\text{ cups} \end{gathered}[/tex]Next, we represent the result in the form of the given options:
Using the standard rate of conversion: 1 cup = 8 fl. oz
[tex]\begin{gathered} 1\text{ cup}=8\text{ fl.oz} \\ \implies1\frac{7}{8}\text{ cups}=8\times1\frac{7}{8}floz=8\times\frac{15}{8}=15fl.oz \end{gathered}[/tex]The volume of bleach added to 2.5 gallons of water is 15 fl. oz.
The population of a school of fish decreases at a rate of 18% per month. There are currently500 fish in the school. How many fish will there be in 3 months?
Population decreasing rate is
18% monthly
Actual population = 500
Then
In 1 month decreases (500/100)• 18 = 90
Population = 500-90= 410
No find (410/100)•18 = 73.8
410-73.8= 336.2
In 3 months
(336.2/100) •18 = 60.5
336.2 - 60.5 = 276 fishes
ANSWER IS 276 fishes remain
In 2005 there were 744 radio stations, by 2015 that number had increased by 13.8%. How many radio stations in 2015?
Answer: We have to find the radio stations in 2015, which is 13.8% more than the radio stations in 2005 which were 744:
[tex]\begin{gathered} x=\text{ Radio stations in 2015} \\ \\ x=(1.138)\times(744) \\ \\ x=846.672 \\ \\ x\approx847 \end{gathered}[/tex]Antonio has a balance of $4273.56 on a credit card with an annual percentage rate of 21.1%. He decides to not make any additional purchases with his card until he has paid off the balance. a) Many credit cards require a minimum monthly payment of 2% of the balance. What is Antonio's minimum payment on the balance of $4273.56? b) Find the amount of interest charged this month
a) To calculate the minimum payment of the balance, you calculate the 2% of $4273.56. You proceed as follow:
(2/100)(4273.56) = 85.47
Hence, the mimum payment of the balance is $85.47
b) You calculate the amount of interest charged this month as follow:
convert the annual percentage rate to decimal form:
21.1/100 = 0.211
divide the previous result by 12 to get the monthly interest rate:
0.2111/12 = 0.0175
multiply the previoues result by the balance:
0.0175 x 4273.56 = 75.143 ≈ 75.14
convert the monthly rate to a percentage:
0.0175 x 100 = 1.75%
Hence, the amount of interest was $75.14, which corresponds to a 1.75%
Find the degree measure of the central angle for sector C. (image attached)
We will determine the angle as follows:
We know that the whole circle contains 360°, so we determine the angle of 0.35 as follows:
[tex]C=\frac{0.35\ast360}{1}\Rightarrow C=126[/tex]So, the measure of the central angle for sector C is 126°.
Instructions: Find the value of the trigonometric ratio. Makesure to simplify the fraction if needed.
sin C = 3/5
Explanation:Given:
CB = 32
AC = 40
AB = 24
To find:
sin C
To determine sinC, we will apply the sine ratio:
[tex]\begin{gathered} sin\text{ C = }\frac{opposite}{hypotenuse} \\ \\ oppoite\text{ =side opposite the angle = AB = 24} \\ hyp\text{ = 40} \end{gathered}[/tex][tex]\begin{gathered} sin\text{ C}=\text{ }\frac{24}{40} \\ \\ sin\text{ C}=\text{ }\frac{3}{5} \end{gathered}[/tex]In class, we determined that 11 peoplewould fit comfortably in a 5 ft by 5 ftsquare. How many square feet wouldeach person require?
We have to first determine the area of the square. The area of a square can be represented as follows
[tex]\begin{gathered} \text{Area of square = L}^2 \\ L\text{ = 5 ft} \\ \text{Area of square = 5}^2 \\ \text{Area of a square = 25 ft}^2 \end{gathered}[/tex]The number of each square feet each person will requre can be calculated as follows
[tex]\begin{gathered} numbers\text{ of each square ft each person require = 25/11} \\ numbers\text{ of each square ft each person require = }2.27272727273ft^2 \\ numbers\text{ of each square ft each person require }\approx\text{ }2.27ft^2 \end{gathered}[/tex]Mary Bought her car for $20,000. After 5 years she decided to sell her car for a 25% increase invalue. What is the price that Mary decided to sell her car for?
Original Car price = $20,000
Price increase after 5 years = 25%
To calculate the price after 5 years, first multiply the original price (20,000) by the percentage increase in decimal form ( divided by 100) to obtain the increase amount:
20,000 x (25/100) = 20,000 x 0.25 = $5000
Finally, add the increase amount to the original price:
20,000+5,000 = $25,000
HELP ASAP
QUESTION IS ATTACHED!
Answer:
(2,8) and (-6,0)Step-by-step explanation:
(3,9)
(-5*3) +( 3*9) > 12
-15 + 27 > 12
12 > 12
not true
(-5,5)
(-5*5) + (3*5) > 12
-25 + 15 > 12
-10 > 12
not true
(3,-6)
(-5*3) + (3*-6) > 12
-15 + -18 > 12
-33 > 12
not true
(-2,-5)
(-5*-2) + (3*-5) > 12
10 + -15 > 12
5 > 12
not true
(2,8)
(-5*2) + (3*8) > 12
-10 + 24 > 12
14 > 12
true(-6,0)
(-5*-6) + (3*0) > 12
30 + 0 > 12
30 > 12
true
Help!
find all zeros of p(x). include any multiplicities greater than one.
The most appropriate choice for polynomial will be given by
1) Zeroes of P(x) = 2, [tex]\frac{2 + \sqrt{2}i}{3}[/tex], [tex]\frac{2 - \sqrt{2}i}{3}[/tex]
where [tex]i = \sqrt{-1}[/tex]
2) Zeroes of P(x) = 3, 2i, -2i
3) Roots are 2i, -2i, [tex]\frac{3}{2}[/tex]
4) Roots are 0, 1, [tex]2 + \sqrt{5}[/tex], [tex]2 - \sqrt{5}[/tex]
What is a polynomial?
An algebraic expression of the form [tex]a_0 + a_1x +a_2x^2 + a_nx^n[/tex] is called a polynomial of degree n.
[tex]1) P(x ) = 3x^3 -10x^2 + 10x -4\\P(2) = 3(2)^3 - 10(2)^2 +10(2) - 4\\[/tex]
[tex]= 24 -40 + 20 -16\\= 0[/tex]
(x - 2) is a factor of P(x)
[tex]P(x) = 3x^2(x - 2) -4x(x - 2) +2(x-2)\\[/tex]
= [tex](x - 2)(3x^2 - 4x + 2)[/tex]
[tex]=(x-2)(x -a)(x - b)[/tex]
where,
[tex]a = \frac{-(-4)+\sqrt{(-4)^2 - 4\times 3\times 2}}{2\times 3}\\a =\frac{ 4 + \sqrt{-8}}{6}\\a = \frac{4 + 2\sqrt{2} i}{6}\\a = \frac{2(2 + \sqrt{2}i)}{6}\\a = \frac{2 + \sqrt{2}i}{3}[/tex]
[tex]b = \frac{-(-4)-\sqrt{(-4)^2 - 4\times 3\times 2}}{2\times 3}\\b =\frac{ 4 -\sqrt{-8}}{6}\\b = \frac{4 - 2\sqrt{2} i}{6}\\b = \frac{2(2 - \sqrt{2}i)}{6}\\b = \frac{2 - \sqrt{2}i}{3}[/tex]
Zeroes of P(x) = 2, [tex]\frac{2 + \sqrt{2}i}{3}[/tex], [tex]\frac{2 - \sqrt{2}i}{3}[/tex]
where [tex]i = \sqrt{-1}[/tex]
[tex]2) P(x) = x^3 - 3x^2+4x-12\\P(3) = (3)^3 - 3(3)^2 +4(3) -12\\ P(3) = 0[/tex]
(x - 3) is a factor of P(x)
[tex]x^2(x - 3) + 4(x - 3)\\(x - 3)(x^2 + 4)\\(x - 3)(x -a)(x-b)\\[/tex]
where,
[tex]a = \sqrt{-4}\\a = 2i[/tex]
[tex]b = -\sqrt{-4}\\a = -2i[/tex]
Zeroes of P(x) = 3, 2i, -2i
[tex]3) 2x^3 - 3x^2 +8x-12= 0\\[/tex]
x = 2 satisfies the equation
[tex]2x^2(x -\frac{3}{2}) + 8(x-\frac{3}{2})=0\\(2x^2+8)(x - \frac{3}{2}) = 0\\[/tex]
[tex]2x^2 + 8 = 0[/tex] or [tex]x - \frac{3}{2} = 0[/tex]
[tex]x^2 = -\frac{8}{2}[/tex] or [tex]x = \frac{3}{2}[/tex]
[tex]x^2 = -4[/tex] or [tex]x = \frac{3}{2}[/tex]
[tex]x = \sqrt{-4}[/tex] or [tex]x = \frac{3}{2}[/tex]
[tex]x = 2i[/tex] or [tex]x = -2i[/tex] or [tex]x = \frac{3}{2}[/tex]
Roots are 2i, -2i, [tex]\frac{3}{2}[/tex]
4)
[tex]x^4 - 5x^3 +3x^2 +x = 0\\x(x^3 -5x^2 + 3x +1) = 0\\[/tex]
[tex]x = 0[/tex] or [tex]x^3 -5x^2+3x +1 = 0[/tex]
For [tex]x^3 -5x^2+3x +1 = 0[/tex]
x = 1 satisfies the equation
[tex]x^2(x -1) -4x(x-1)-1(x-1) = 0\\(x - 1)(x^2 - 4x -1) = 0\\[/tex]
[tex]x -1 = 0[/tex] or [tex]x^2 - 4x -1 = 0[/tex]
Roots are x = 1 or x = a or x = b
where,
[tex]a = \frac{-(-4) + \sqrt{(-4)^2 - 4\times 1 \times(-1)}}{2\times 1}\\a = \frac{4+\sqrt{20}}{2}\\a = \frac{4 + 2\sqrt{5}}{2}\\a = \frac{2(2 + \sqrt{5})}{2}\\a = 2 + \sqrt{5}[/tex]
[tex]b = \frac{-(-4) - \sqrt{(-4)^2 - 4\times 1 \times(-1)}}{2\times 1}\\b = \frac{4-\sqrt{20}}{2}\\b = \frac{4 - 2\sqrt{5}}{2}\\b = \frac{2(2 - \sqrt{5})}{2}\\b = 2 - \sqrt{5}[/tex]
Roots are 0, 1, [tex]2 + \sqrt{5}[/tex], [tex]2 - \sqrt{5}[/tex]
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Good morning, thanks for helping meHi, can you please help me with my math? Please help me please that's all I'm asking and thank you so much.
6.
(a)
The slope for the side AB is:
[tex]\begin{gathered} A=(-5,-4)=(x1,y1) \\ B=(5,-2)=(x2,y2) \\ m_{AB}=\frac{y2-y1}{x2-x1}=\frac{-2-(-4)}{5-(-5)}=\frac{2}{10}=\frac{1}{5}=0.2 \end{gathered}[/tex]The slope for the side BC is:
[tex]\begin{gathered} B=(5,-2)=(x1,y1) \\ C=(7,6)=(x2,y2) \\ m_{BC}=\frac{6-(-2)}{7-5}=\frac{8}{2}=4 \end{gathered}[/tex]The slope for the side DC is:
[tex]\begin{gathered} D=(-3,4)=(x1,y1) \\ C=(7,6)=(x2,y2) \\ m_{DC}=\frac{y2-y1}{x2-x1}=\frac{6-4}{7-(-3)}=\frac{2}{10}=\frac{1}{5}=0.2 \end{gathered}[/tex]And the slope for AD is:
[tex]\begin{gathered} A=(-5,-4)=(x1,y1) \\ D=(-3,4)=(x2,y2) \\ m_{AD}=\frac{4-(-4)}{-3-(-5)}=\frac{8}{2}=4 \end{gathered}[/tex](b) According to the previous results:
[tex]\begin{gathered} m_{AB}=m_{DC} \\ so \\ m_{AB}\parallel m_{DC} \end{gathered}[/tex][tex]\begin{gathered} m_{BC}=m_{AD} \\ so\colon \\ m_{BC}\parallel m_{AD} \end{gathered}[/tex](c) Since it has two pairs of parallel sides, also, The opposite sides are of equal length, we can conclude that this figure is a parallelogram
What are the lengths of segments PQ and QR? input the lengths. then click done.
state income tax? Jim Koslo earns $156,200 annually as a plant manager. He is married and supports 3 children. The state tax rate in his state is 3.55% of taxable income. What amount is withheld yearly for state income tax?
Answer:
44,000
Let me know if its wrong
find the value of the 30th percentile of the following set of data
The given data is:
[tex]18,9,7,5,11,7,17,20,19,2,17,12,5,1,13,12,11,15,16,20[/tex]Rearrange the data in ascending order:
[tex]1,2,5,5,7,7,9,11,11,12,12,13,15,16,17,17,18,19,20,20[/tex]The length of a room is twice as its breadth and breadth is 6 cm. If it's height is 4 cm, find the total surface area.
The breadth of the room = 6 cm
Since the length of the room is twice its breadth
Then
Length of the room = 2 times 6cm = 12cm
The height of the room = 4cm
Since the shape of the room is a cuboid
The surface area of a cuboid is given as
[tex]SA=2(lh+lw+hw)[/tex]Substitute l = 12, w = 6 and h = 4 into the formula
This gives
[tex]SA=2(12\times4+12\times6+4\times6)_{}[/tex]Simplify the expression
[tex]\begin{gathered} SA=2(48+72+24) \\ SA=2(144) \\ SA=288 \end{gathered}[/tex]Therefore, the total surface area of the room is
[tex]288cm^2[/tex]Base on table above is the scenario a proportional relationship
No
Explanations:A relationship is called a proportional relationship if it has two variables that are realated by the same ration. In this case there will be a proportionality constant.
In this table:
Let Height be represented as H
Let Time be represented as T
For the relationship to be a proportional relationship, it must obey the relation:
[tex]\begin{gathered} H\propto\text{ T} \\ H\text{ = kT} \\ \text{Where k is the proportionality constant} \end{gathered}[/tex]When T = 3, H = 15
Using H = kT
15 = 3k
k = 15 / 3
k = 5
When T = 6, H = 30
H = kT
30 = 6k
k = 30 / 6
k = 5
When T = 12, H = 45
H = kT
45 = 12k
k = 45 / 12
k = 3.75
Since the constant of proportionality is the the same for the three cases in the table, the scenario is not a proportional relationship
2) Corresponding angles are congruent L1 II L2 (2x + 20) (3x - 10)
Given angles are corresponding angles, they are congruent (have the same measure):
[tex](2x+20)=(3x-10)[/tex]Use the equation above to solve x;
[tex]\begin{gathered} 2x+20=3x-10 \\ \\ \text{Subtract 3x in both sides of the equation:} \\ 2x-3x+20=3x-3x-10 \\ -x+20=-10 \\ \\ \text{Subtract 20 in both sides of the equation:} \\ -x+20-20=-10-20 \\ -x=-30 \\ \\ \text{Multiply both sides of the equation by (-1):} \\ (-1)(-x)=(-1)(-30) \\ \\ x=30 \end{gathered}[/tex]You use the value of x=30 to find the measure of corresponding angles:
[tex]\begin{gathered} 2x+20 \\ 2(30)+20=80 \end{gathered}[/tex]Then, the meaure of the corresponding angles is 80°