Answer:
I have solved it in elimination method if you need it in another method let me know.
Step-by-step explanation:
3x+y=21
-x-y=5
2x=26
x=13
-3×13-3y=15
y= -18
What are the 7 types of functions?
The eight categories are power, quadratic, rational, exponential, logarithmic, sinusoidal, polynomial, and linear.
what is functions ?The subject of mathematics includes quantities and their variations, equations and related structures, forms and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A relationship between inputs and outputs in which each input leads to a single, distinct result is known as a function. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.
given
The eight categories are power, quadratic, rational, exponential, logarithmic, sinusoidal, polynomial, and linear.
Functions can be roughly categorized into four sorts. Based on the element, the following relationships are possible: One to One Function, Many to One Function, Onto Function, One to One and Into Function. Based on the following domains: logarithmic functions, trigonometric functions, and algebraic functions.
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If y varies directly as the square of x and y = -54 when x = 9, then y = -1 1/3 when x = 6
Therefore , the solution of the given problem of equation comes out to be k1 = - 0.67 and k2 = -0.1.
Describe equation.A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A scientific statement that verifies the equality of two formalisms is known as an equation in algebra. For instance, the pieces ptdc + 6 and 12 are separated by an equal sign in the solution obd + 6 = 12. The relationship between the two phrases on either flank of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 4x – 4 = 0.
Here,
If y varies in this case simply also as square of x
k is the proportionality constant, and
y = kx² in mathematics.
Considering y = -54 and x = 9,
y = kx²
k = y/ x²
k = -54/ 9²
k = -54/81
k1 = - 0.67
Moreover, if y=-11/3 and x=6,
k = y/x²
k = -3.667/ (6)²
k = -3.667/36
k2 = -0.1
Therefore , the solution of the given problem of equation comes out to be k1 = - 0.67 and k2 = -0.1.
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Which has exactly 12 angles?
A dodecagon or 12-gon is a twelve-sided polygon.
One of the polygonal shapes with 12 sides, 12 vertices, and 12 angles is the dodecagon. A dodecagon is a two-dimensional plane figure, just like other polygons. 12 equal sides and 12 equal angles make up a standard dodecagon polygon.
Dodecagons that are irregular have uneven sides and angles. Dodecagons can also be concave or convex polygons. The dodecagon's inner angles add up to 1800° in total.
The word dodecagon is derived from Greek words, ‘dodeka‘ which means ‘twelve’, and ‘gon‘ means ‘sides’.
Thus, A dodecagon or 12-gon is a twelve-sided polygon.
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What is a line of latitude Class 6 short answer?
latitude are lines from east to west
when we looks at the line from equator it appears that the line are from east to west or either way round and longitude are the lines which are from north to south
we are defining another concept of equator above equator is northern hemisphere and lower part is southern hemisphere
which are filled by water most of the parts of Earth but in the northern part on the top polar caps are available because of the cold whether of northern hemisphere of the Earth
this is a simple definition but if we go into deeply there is another concept emerges of degrees or location and time management
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How do you graph and write function rules from piecewise defined functions?
A piecewise defined function is a function that is defined by different rules for different parts of its domain.
To graph a piecewise defined function, we must first identify the different pieces of the domain and the corresponding function rules for each piece.
(1) Identify the different pieces of the domain: Each piece of the domain is defined by an inequality or an equation that separates it from the other pieces.
(2) Write the function rule for each piece: For each piece of the domain, write the equation that defines the function.
(3) Graph the function: For each piece of the domain, graph the corresponding equation by plotting points and connecting them with a line. Be sure to use different colors or styles for the different pieces of the graph to make it clear where each piece starts and ends.
(4) Label the different parts of the graph: Label each part of the graph with the corresponding inequality or equation that defines it.
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Find the measure of angles 1 and 2.
Explain your reasoning as to how you determined the measurements of angles 1 and 2.
Answer:
135 degrees
Step-by-step explanation:
You use Alternate interior angles to get angle 2, then vertical angles to find angle 1
Red is alternate interior angles
Yellow is vertical angles
Step-by-step explanation:
when a line intersects 2 or more parallel lines, it must have the same intersection angles with each of the parallel lines. otherwise the lines are not parallel after all, because parallel lines imitate each other's properties and behaviors exactly except for the actual location.
so,
angle 1 = 135°
the intersection angles between 2 lines must be the same in each side of each line, they are just left-right mirrored.
so,
angle 2 = angle 1 = 135°
Why do we calculate residuals?
The difference between the value predicted by the regression and the observed value for a given data point is known as the residual. The residual calculation offers a useful indicator of how well your model matches the given data set.
What is residual?The discrepancies between actual and expected data values are known as residuals in statistical or machine learning models.
They serve as a diagnostic tool for evaluating a model's quality. They are also called mistakes.
The table below's main column, Inflation, displays information on US inflation for each month of 2017. The Predicted column displays forecasts from a model that aims to forecast the pace of inflation.
The residuals are calculated as follows: Residual = Inflation - Predicted. They are displayed in the Residual column. In the instance of the data for January 2017, the model projected 1.8%, but the observed inflation was 0.5%, leaving a residual of -1.3%.
Hence, The residual calculation offers a useful indicator of how well your model matches the given data set.
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The function a(n)= 2n-5 represents the value of the nth term in a sequence. What is the sum of the 2nd and 3rd terms of the sequence?
The sum of the second and third terms of the arithmetic progression is equal to 0.
How to analyze arithmetic progressionsArithmetic progressions are sets whose terms are generated by expressions of the form:
y = a + r · (n - 1)
y = r · n + (a - r)
Where:
a - Value of the first term.r - Common raten - Index of the n-th term of the progression.
The sum of the second and third elements is:
n = 2
y = 2 · 2 - 5
y = - 1
n = 3
y = 2 · 3 - 5
y = 1
S = - 1 + 1
S = 0
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Jack wants to buy a coat that costs $74.95. The sales tax rate in his city is 612%
. What is the total cost for the coat? Round to the nearest cent.
Answer:
The total amount that will be paid for the coat would be; $79.95 to the nearest cent.
Step-by-step explanation:
What is income tax?
Income tax is a tax applied on individuals or entities concerning income or profit earned by them.
Given that Jack wants to buy a coat that costs $74.95. The sales tax rate in his city is 6 and 1/2 percent.
Thus, the total cost for the coat can be calculated as;
The amount that will be paid for the coat will be;
= Amount of shirt + Tax
= $74.95 + (6.5% × $74.95)
= $74.95 + (6.5/100 × $74.95)
= $74.95 + $4.80
= $79.95
The total amount that will be paid for the coat would be; $79.95 to the nearest cent.
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The total cost for the coat is $79.55
The total cost of the coat is the sum of the cost of the coat and the sales tax. To find the sales tax, Jack needs to multiply the cost of the coat by the sales tax rate as a decimal.
$74.95 x 0.0612 = $4.60452
To find the total cost, he would add this amount to the cost of the coat:
$74.95 + $4.60452 = $79.55452
Rounding to the nearest cent , the total cost of the coat is $79.55. It means Jack has to pay $79.55 including the sales tax, which is $4.60452 on the original price of $74.95 for the coat.
The total cost of the coat is $79.55.
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1. At Franklin High School, there are 480 male students, 320 female students, and 40
teachers. Find the following ratios and write them as a fraction in simplest form.
1A. Female students to male students
2. Teachers to male students
Write out the form of the partial fraction decomposition of the function (as in this example). Do not determine the numerical values of the coefficients. 1 /x^2 + x^4
The partial fraction decomposition of the function is[tex]\\& \Rightarrow \frac{1}{x^2+x^4}=\frac{A}{x}+\frac{B}{x^2}+\frac{C x+D}{x^2+1}\end{aligned}[/tex]
In algebra, a rational fraction—that is, a fraction where the numerator and denominator are both polynomials—can be partially decomposed or expanded by adding a polynomial (potentially zero) and one or more fractions with a lower denominator to the original fraction.
In symbols, the partial fraction decomposition of a rational fraction of the [tex]{\textstyle {\frac {f(x)}{g(x)}},}[/tex]
[tex]{\displaystyle {\frac {f(x)}{g(x)}}=p(x)+\sum _{j}{\frac {f_{j}(x)}{g_{j}(x)}}}[/tex]
Where p(x) is a polynomial, [tex]g_{j}[/tex] for each j is a power of an irreducible polynomial (which cannot be factored into polynomials of positive degrees), and [tex]f_{j}[/tex] for each j is a polynomial with a smaller degree than this irreducible polynomial's degree.
The numerical values of the coefficients is [tex]\frac{1}{x^2+x^4}$[/tex].
Now,
[tex]$\begin{aligned} x^2+x^4 & x^2+x^4 \\ = & x^2\left(1+x^2\right)\end{aligned}$[/tex]
Therefore, the form of the partial fraction decomposition is
[tex]\begin{aligned}& \frac{1}{x^2\left(1+x^2\right)}=\frac{A}{x}+\frac{B}{x^2}+\frac{C x+D}{x^2+1} \\& \Rightarrow \frac{1}{x^2+x^4}=\frac{A}{x}+\frac{B}{x^2}+\frac{C x+D}{x^2+1}\end{aligned}[/tex]
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Darnell can buy a particular brand of fruit juice in a 6-ounce bottle or a 10-ounce bottle. The juice in a 10-ounce bottle contains 150 calories. How many calories are in the juice in a 6-ounce bottle
Answer:
90 calories in a 6 ounce bottle
Step-by-step explanation:
6oz/x
10oz/150
150 divided by ten is 15
15 times 6 equals 90
Answer: 90 calories is in 6 ounce bottle which is 90
In a bag of apples and oranges, the ratio of apples to oranges is 4:3.
The bag contains 70 apples and oranges, how many oranges are there?
Only possible answers
35
30
25
40
Answer:
30 Oranges
Step-by-step explanation:
The ratio of apples to oranges is 4:3. For every 4 apples there are 3 organges. We can write that as 4A/3O, where A and O are Apples and Oranges. This can be rewritten as percentages of each fruit. A bag of 7 would have 4 Apples (4/7) or 0.5715 [57.15%] and 3 Oranges (3/7) or 0.4285 [42.85%].
A bag of 70(A and O) can be determined to have:
Apples: 70*(0.5715) = 40 Apples, and
Oranges: 70*(0.4285) = 30 Oranges
An ice chest contains 8 cans of apple juice, 6 cans of grape juice, 7 cans of orange juice, and 6 cans of mango juice. Suppose that you reach into the container and randomly select three cans in succession. Find the probability of selecting three cans of apple juice.
The probability of selecting three cans of apple juice is 0.01915
What is the probability?Probability determines the odds that a random event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability of selecting three cans of apple juice = (number of apple cans / total number of cans) x {(number of apple cans / total number of cans) -1 }x {(number of apple cans / total number of cans) -1}]
total number of cans = 8 + 6 + 7 + 6 = 27
The probability of selecting three cans of apple juice = (8/27 x 7/26 x 6/25 = 0.01915
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Write the inequality represented on each graph. Use n for the variable.
Graphs 1 and 2's respective inequalities are n14 and n14.
What exactly is inequality?"Inequality" is the term used in mathematics to describe a connection between two expressions or values that is not equal to one another.
the first graph
line excluding number 14 is extending to the left.
The disparity is as;
n < 14.
Within Graph 2,
The number 14 is part of a line that is diverging to the right.
The disparity is as;
n≥14
As a result, graphs 1 and 2's respective inequalities are n14 and n14.
Graph 1 and Graph 2 each have n14 and n14 inequalities.
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In preparation of a company's annual dinner, 450 notebooks and 315 fridge stickers are to be
distributed equally into goodie bags without leftovers.
(a) Is it possible to prepare 21 goodie bags exactly? Explain your answer.
(b) What is the largest number of goodie bags that can be prepared?
(c) Using the answer from (b), how many notebooks and fridge stickers will there be in a goodie bag?
(a) To determine if it is possible to prepare 21 goodie bags exactly, we need to check if 450 notebooks and 315 fridge stickers can be divided equally into 21 goodie bags without any leftovers.
To do this, we can use the greatest common divisor (GCD) of 450 and 315, which is 15. If the GCD is not 1, it means that the two numbers cannot be divided exactly, so it is not possible to prepare exactly 21 goodie bags with 450 notebooks and 315 fridge stickers.
(b) To find the largest number of goodie bags that can be prepared, we can use the least common multiple (LCM) of 450 and 315. The LCM is 990, which means that 990 notebooks and 990 fridge stickers can be divided into the same number of goodie bags without any leftovers. Therefore, the largest number of goodie bags that can be prepared is 990/450 = 990/315 = 2.
(c) Using the answer from (b), we can calculate how many notebooks and fridge stickers will be in a goodie bag. If we divide 990 by 2, we get 495. Therefore, there will be 495 notebooks and 495 fridge stickers in each goodie bag.
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2+sqrt{4-p} = sqrt {2p-4}
Please show work.
The value of the given expressions is p = -1.281, though it is also possible for p = 0.781 to be the value.
what is equation ?Take into consideration the equation 3x + 5 = 14, in which 3x + 5 and 14 are two expressions that are separated by the word "equal." The standard form, slope-intercept form, and point-slope form are the three primary formats for linear equations. In a mathematical expression known as an equation, the equals sign appears. Algebra is used in a variety of equations. When you don't know how much to compute in math, you use algebra to approximate the answer.
given
-4p^2=2p-4
p=(-1-sqrt(17))/4=-1.281
p=(-1+sqrt(17))/4=0.781
The value of the given expressions is p = -1.281, though it is also possible for p = 0.781 to be the value.
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Is triangle FHK similar to triangle GHJ? If so, which postulate or theorem proves these two triangles are similar?
The correct statement regarding the similarity of triangles GHJ and FHK is given as follows:
Triangle FHK is similar to triangle GHJ by the SAS Similarity Theorem.
What are similar triangles?Similar triangles are triangles that share these two features given as follows:
Congruent angle measures.Proportional side lengths.For this problem, the similar triangles are given as follows:
FHK and GHJ.
They are similar because:
They share a common angle, which is angle H.Side length HF is proportional to side length HG.Side length HK is proportional to side length HJ.As they have two proportional side lengths, along with the angle between them, the congruence theroem is the SAS theorem.
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The probability for event a is 0. 3, the probability for event b is 0. 6, and the probability of events a or b is 0. 8.
The events are not mutually exclusive because P(A or B) ≠ P(A) + P(B). The probability of either event happening is not equal to the sum of each event happening.
What are mutually exclusive events?Mutually exclusive events are events that cannot happen at the same time. For example, when you are tossing a coin, you cannot get head and tail at the same time. They are mutually exclusive, also called disjoint events, where P(A and B) = 0.
In mutually exclusive events, it also states that the probability of either event happening is the sum of probabilities of each event happening. It means that P(A or B) = P(A) + P(B).
Your question is incomplete and here is the complete question.
The probability for event A is 0.3, the probability for event B is 0.6, and the probability of events A or B is 0.8. Why are the events not mutually exclusive?
From the information, we have:
P(A) = 0.3P(B) = 0.6P(A or B) = 0.8Let's check if the events are mutually exclusive!
P(A or B) = P(A) + P(B)
P(A or B) = 0.3 + 0.6
P(A or B) = 0.9
0.8 ≠ 0.9
P(A or B) ≠ P(A) + P(B)
The probability of A or B is not equal to the sum of the individual probabilities. It proves that A and B are not mutually exclusive.
Hence, A and B are not mutually exclusive because the probability of A or B is not equal to the sum of the individual probabilities.
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a light year is defined as 5.88 times 10^12 miles: the distance that light travels in 1 year. How far will light travel in 3 years?
The distance that light will travel in 3 years, given the speed it travels in one year is
How to find the speed travelled ?The notion of a Light Year allows us to quantity the distance that light travels in an entire year. This has allowed scientists to quantify with more ease, the distance to other galaxies and planets.
The distance that light travels in a year is 5. 88 x 10¹² miles.
In 3 years therefore, the distance would be:
= 3 x ( 5.88 x 10 ¹²)
= 17.64 x 10 ¹² miles
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PLEASE HELP
is this equation an exponential decay of 40% or 30%
y=0.4(0.7)^t
Answer:
30%
Step-by-step explanation:
The level of decay is determined by the number raised to the power.
y = 0.4(0.7)^t
If you had 1^t, there would be no decay or growth since 1^t is always 1.
Instead, you have 0.7^t
As t increases, 07^t decreases. That is where the decay comes from.
Now look at 0.7
In the general decay equation, you have
y = a(1 - r)^t
r is the rate of decay.
Here we have 0.7
0.7 = 1 - 0.3
the rate of decay is 0.3 or 30%
Answer:
The equation y = 0.4(0.7)^t represents an exponential decay of 30%. The decay rate is determined by the value in the parentheses, which in this case is 0.7. To calculate the decay rate, you can subtract this value from 1, giving you 1 - 0.7 = 0.3, or 30%.
Step-by-step explanation:
Can you PLSS help me answer these question?
AND PLS GIVE A EASY + DETAILED STEP BY STEP ON HOW U GOT THE ANSWER BC IM SLOW LOL
Use a trigonometric ratio to solve for z. Round to two decimal places as necessary!!
HELP, and can someone explain how to get the answer?
According to the response to the question, the trigonometric ratios will be tan Y = 8/15, tan X = 15/8, and sin Y = 8/17.
What Are Trigonometric Ratios?Trigonometric functions, which are real functions, are used in mathematics to connect the angle of a right - angled triangle to the proportion of the lengths of its two sides. They are widely utilized in a variety of fields connected to geometry, including celestial mechanics, solid mechanics, and geodesy. Trigonometric ratios are all trigonometric values based on the values of the right triangle's aspect ratio. The trigonometric ratio of the opposite sides of a right triangle reduced by any extreme angle is one.
Here,
Because X is actually 8/17,
the right response to this question is not X.
TanX = 15/8 = Opp
Sin x = 8/17 is accurate.
Incorrect cos Y = 8/17.
tan X = 8/15 is a valid assertion.
Sin x = 15/8
Cos Y = 8/17
According to the response to the question, the trigonometry proportions will be tan Y = 8/15, tan X = 15/8, and sin Y = 8/17.
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6÷3+9
2
−4=6, divided by, 3, plus, 9, squared, minus, 4, equals
Answer:
6÷3=2+9=11
11square == 22 22-4
18
the answer is 18
I need to find the rise over run
Calculate the rise between the two points and divide it by the difference in the horizontal direction to arrive at the answer (run).
How do you find the rise over run?An indication of how steep a line is is its slope. When calculating slope mathematically, "rise over run" is used (change in y divided by change in x). Calculate the rise over the run ratio of a line going through the points (-7,3) and (4, 2). With this in mind, the rise over run ratio of the line joining the two points is -1/11. Decide on the coordinates of two spots along the line.
Find the location of these two points' respective y-coordinate differences (rise). The difference between these two places' x-coordinates should be known (run). In order to calculate the difference in y-coordinates (rise/run or slope), divide it by the difference in x-coordinates. Rise is the quantity you gain or lose when moving from one location to another. That would result in a modification of the y values on the graph.
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Himari invet 200000 yen for 3 year in a aving account paying compound interet. The rate of interet i 1. 8% for the firt year and x% for each of the econd year and the
third year. The value of the invetment at the end of the third year i 209754 yen. Work out the value of x
Give your anwer correct to one decimal place
The interest rate for the second and third years is 0.9%.
The interest rate for the second and third years is 0.9%.
We can use the formula for compound interest to find the value of x:
A = P(1 + r/n)^(nt)
Where:
A is the final amount (209754 yen)
P is the initial amount (200000 yen)
r is the interest rate (x% for the second and third years)
n is the number of times the interest is compounded per year (let's assume it is compounded annually)
t is the number of years the money is invested (3 years)
We know that the interest rate for the first year is 1.8%.
So we can calculate the final amount after the first year using:
A = P(1 + 1.8/100)^1
A = P(1.018)
A = 200000*(1.018) = 203600
So, the total amount after the first year is 203600 yen.
Now let's find the remaining interest rate for the second and third years:
A = P(1 + r/100)^(2)
203600 = 200000(1 + r/100)^2
We can now solve for the value of x by isolating r/100
r/100 = (203600/200000)^(1/2) - 1
x = (r/100)*100
x = (203600/200000)^(1/2) - 1*100
x = 0.9%
x is 0.9%
Hence, the interest rate for the second and third years is 0.9%.
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(Linear Relationships MC) An indoor soccer field can be rented for personal use. The total cost for renting the field can be found by using the equation y=225x + 200 The x-variable is the number of hours the field is being rented, the constant is the flat rate for renting the field, and the y-variable is the total cost, in dollars Which statement is true based on the given equation? The equation shows a linear relationship, but not a proportional relationship The equation shows a linear relationship and a proportional relationship The equation does not show a linear relationship or a proportional relationship The equation shows a proportional relationship but not a linear relationship
first statement is true, the equation shows a linear but not proportional.
what is linear equation?The equation which has two variables with first order term and only a constant available in the equation is termed as linear equation. Example of a linear equation, y =mx + b
Which statement is true for this question?
Given, an equation, y = 225x + 200
where x and y are two variables
x denotes the number of hours the field is being rented
y denotes the total cost
constant 200 implies the flat rate for renting the field.
If we compare this equation to the standard form of linear equation, y = mx + b, where m = slope and b is the y intercept.
we will find that the above two equation is similar and therefore the equation given in question is a linear relationship.
the coefficient 225 is the slope of equation and the constant 200 is the y intercept.
this given equation is not a proportional relationship.
The first statement is true.
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Segment JK has endpoints J(2,4) and K(6,2). You dilate the segment using a dilation centered at the origin with a scale factor of 1/2 and then reflect the image over the x-axis. Where is the final image of K?
The final image of K would be at (3,-1) after the given sequence of transformation Segment JK.
What is Dilation?Dilation is a process for creating similar figures by changing the size.
Segment JK has endpoints J(2,4) and K(6,2).
A dilation by a factor of 1/2 means that each coordinate value will be multiplied by 1/2.
The dilation of segment JK with a scale factor of 1/2 would shrink the segment by half, so the coordinates of K would be (3,1).
Reflecting over the x-axis would change the sign of the y-coordinate, so the final image of K would be at (3,-1).
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What is the slope of the line through (-9,6(−3,9)
Answer:
0.6 cause I got it correct.
x^2 = 361 Which represents the solution of the given equation?
Answer: X=19
Step-by-step explanation:
x^2=361
Square root both sides to get rid of the exponent above x.
[tex]\sqrt{x^2}[/tex]=[tex]\sqrt{361}[/tex]
x=19