The term that is the −20,155,392 in the sequence is a₁₀.
How to solve sequence?The sequence below is a geometric sequence.
Therefore, a geometric sequence can be represented as follows:
nth term = arⁿ⁻¹
where
a = first termn = number of termsr = common ratioTherefore, let's find which term is −20,155,392 for the sequence.
2, -12, 72, -432
r = -12 / 2 = 72 / -12 = -432 / 72 = -6
a = 2
Hence,
nth term = arⁿ⁻¹
−20,155,392 = 2 × -6ⁿ⁻¹
−20,155,392 / 2 = -6ⁿ⁻¹
- 10077696 = -6ⁿ⁻¹
6ⁿ⁻¹ = 10077696
6ⁿ⁻¹ = 6⁹
n - 1 = 9
n = 9 + 1
n = 10
Therefore, it's the 10th term.
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The term −20,155,392 is the tenth in the given geometric sequence.
The given sequence is below which is in a geometric pattern
2, -12, 72, -432
Here first term (a) = 2
The common ratio (r) = -12 / 2
The common ratio (r) = -6
We know that the nth term of the geometric sequence is
Tₙ = arⁿ⁻¹
Here Tₙ = −20,155,392
⇒ −20,155,392 = arⁿ⁻¹
Substitute the values of a and r in the above equation,
⇒ −20,155,392 = 2 × -6ⁿ⁻¹
⇒ −20,155,392 / 2 = -6ⁿ⁻¹
Apply the division operation,
⇒ - 10077696 = -6ⁿ⁻¹
⇒ 6ⁿ⁻¹ = 10077696
⇒ 6ⁿ⁻¹ = 6⁹
Equating exponents of the base
⇒ n - 1 = 9
⇒ n = 10
Therefore, the term −20,155,392 would be the tenth in the given sequence.
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what is the volume of a cube with sides 3 cm.be sure to include correct units with your answer
Answer:
27 cubic feet
Explanation:
The volume of a cube with side length L is given by
[tex]V=L^3[/tex]Now in our case, L = 3 ft; therefore, the volume is
[tex]V=3^3[/tex]which simplifies to give
[tex]\boxed{V=27\text{ ft}^3.}[/tex]which is our answer!
Hence, the volume of the cube with the side length of 3 cm is 27 cubic cm.
i need help solving this and also what does the 2 that's on the top of some letters mean
given the expression :
[tex]a-bc^2[/tex]We need to evaluate the expression when :
[tex]\begin{gathered} a=3 \\ b=2 \\ c=-1 \end{gathered}[/tex]So, substitute with a , b and c at the expression
The result will be :
[tex]\begin{gathered} a-bc^2 \\ =3-2\cdot(-1)^2 \\ =3-2\cdot1 \\ =3-2 \\ \\ =1 \end{gathered}[/tex]There is another expression :
[tex]c^2+a^2b[/tex]By substitute with the values of a, b and c
so, the result will be :
[tex]\begin{gathered} c^2=(-1)^2=1 \\ a^2=3^2=9 \\ \\ c^2+a^2b=1+9\cdot2=1+18=19 \end{gathered}[/tex]At which of the following points do the two equations f(x)=3x^2+5 and g(x)=4x+4 intersect?A. (0,5)B. (1,8)C. (0,4) D. (8,1)
Given the equations:
[tex]\begin{gathered} f(x)=3x^2+5 \\ \\ g(x)=4x+4 \end{gathered}[/tex]Let's find the point where both equations intersect.
To find the point let's first find the value of x by equation both expression:
[tex]3x^2+5=4x+4[/tex]Now, equate to zero:
[tex]\begin{gathered} 3x^2+5-4x-4=0 \\ \\ 3x^2-4x+5-4=0 \\ \\ 3x^2-4x+1=0 \end{gathered}[/tex]Now let's factor by grouping
[tex]\begin{gathered} 3x^2-1x-3x+1=0 \\ (3x^2-1x)(-3x+1)=0 \\ \\ x(3x-1)-1(3x-1)=0 \\ \\ \text{ Now, we have the factors:} \\ (x-1)(3x-1)=0 \end{gathered}[/tex]Solve each factor for x:
[tex]\begin{gathered} x-1=0 \\ Add\text{ 1 to both sides:} \\ x-1+1=0+1 \\ x=1 \\ \\ \\ \\ 3x-1=0 \\ \text{ Add 1 to both sides:} \\ 3x-1+1=0+1 \\ 3x=1 \\ Divide\text{ both sides by 3:} \\ \frac{3x}{3}=\frac{1}{3} \\ x=\frac{1}{3} \end{gathered}[/tex]We can see from the given options, we have a point where the x-coordinate is 1 and the y-coordinate is 8.
Since we have a solution of x = 1.
Let's plug in 1 in both function and check if the result with be 8.
[tex]\begin{gathered} f(1)=3(1)^2+5=8 \\ \\ g(1)=4(1)+4=8 \end{gathered}[/tex]We can see the results are the same.
Therefore, the point where the two equations meet is:
(1, 8)
ANSWER:
B. (1, 8)
Determine the angle of rotation of the conic section given by: 32x2 +50xy + 7y2 = 100 (round your answer to the nearest tenth of adegree).
The formula to obtain the angle of rotation is as follows:
[tex]\cot 2\theta=\frac{A-C}{B}[/tex]Compare the given equation to the general equation of a conic.
[tex]Ax^2+Bxy+Cy^2+Dx+Ey+F=0[/tex]Thus, the values of A, B, and C are as follows.
[tex]\begin{gathered} A=32 \\ B=50 \\ C=7 \end{gathered}[/tex]Substitute the values into the equation.
[tex]\begin{gathered} \cot 2\theta=\frac{32-7}{50} \\ \cot 2\theta=\frac{25}{50} \\ \cot 2\theta=\frac{1}{2} \end{gathered}[/tex]Find the value of the θ.
[tex]\begin{gathered} \frac{1}{\tan 2\theta}=\frac{1}{2} \\ \tan 2\theta=2 \\ 2\theta=\tan ^{-1}(2) \\ 2\theta\approx63.4349 \\ \theta\approx31.7 \end{gathered}[/tex]The Adventure Club has scheduled a trip to hike a nearby mountain. Since the group started hiking, they gained 456 feet in altitude from their start position. The current altitude is 437 feet, but there is no record of their starting altitude.write a equation to represent this situation Explain what your variable representssolve your equation please someone help me ill give you a star anything please ♡
Let h be the altitude of the starting position.
Since the group has gained 456 feet from the start position, then the current altitude is:
covert 6\10 into decimal number and then see if it's a repeating or terminating
We are asked to determine wheater 6/10 in decimal form is repeating or terminating. To do that we need to divide 6 over 10. To do that, we proceed as follows:
We need to find a number that when multiplied by 10 gives 6. That number is 0.6, because:
[tex]0.6\times10=6[/tex]Therefore 6/10=0.6 Since the numbers after the radix point do not repeat, this is a terminating decimal.
Is P(A and B) ≠ 0? Explain.
A.) No. P(A and B) = 0.
B.) Yes. Even if P(A) = 0 or P(B) = 0, P(A and B) will always be non-zero.
C.) No. Because both P(A) and P(B) are not equal to 0, P(A and B) = 0.
D.) Yes. Because both P(A) and P(B) are not equal to 0, P(A and B) ≠ 0. (b)
The right option is D as P(A and B) ≠ 0 only for the independent probability events for A and B.
What is an independent event in probability?Two events say A and B are said to be independent if the probability of the intersection of A and B is equal to the product of their respective probability, But same events are said to be mutually exclusive if the probability of the intersection of A and B is equal to zero(0).
In the given question, P(A and B) ≠ 0 can only be true if A and B are independent event and P(A) and P(B) are not equal to zero such that
P(A and B)=P(A)× P(B)≠ 0.
Hence, we can deduce from the axiom of independent events of probability that because both P(A) and P(B) are not equal to 0, P(A and B) ≠ 0.
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the points E,F,G and H all lie on the same line segment, in that order, such that ratio of EG:FG:GH is equal to 4:1:5. If EH=10, find EG
You have that the ratio of EG:FG:GH = 4:1:5.
Moreover, segment EH = 10.
In order to find EG you consider the following ratios:
EG/FG = 4/1
FG/GH = 1/5
Furthermore, EH = EG + FG + GH
A survey was given asking whether they watch movies at home from Netflix, Redbox, or a video store.Use the results to determine how many people use Redbox.60 only use Netflix64 only use Redbox24 only use a video store 8 use only a video store or Redbox38 use only Netflix or Redbox 35 use only a video store or Netflix5 use all three24 use none of these
SOLUTION
We will use a Venn Diagram for this problem.
Let N represent those that use Netflix, R represent those that use Redbox and V represent those that use video store. The Venn Diagram is shown below
From the Venn Diagram above, the number in each part of a circle, represents the information
Now, how many people use Redbox?
The number of those that use Redbox is represented by the circle R, so we add all the numbers in this circle, we have
[tex]n(R)=38+64+5+8=115[/tex]Hence the answer is 115
rewrite 2x+5y=10 in slope intercept form then graph them
The slope intercept of a line is:
[tex]y=mx+b[/tex]We re-write the equation given:
[tex]\begin{gathered} 2x+5y=10 \\ 5y=-2x+10 \\ y=\frac{-2x+10}{5} \\ y=\frac{-2x}{5}+\frac{10}{5} \\ y=-\frac{2}{5}x+2 \end{gathered}[/tex]The graph of this line is shown below:
The points (-6, -10) and (23, 6) form a line segment.
Write down the midpoint of the line segment.
Answer:
(8.5, - 2 )
Step-by-step explanation:
given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
here (x₁, y₁ ) = (- 6, - 10 ) and (x₂, y₂ ) = (23, 6 ) , then
midpoint = ( [tex]\frac{-6+23}{2}[/tex] , [tex]\frac{-10+6}{2}[/tex] ) = ( [tex]\frac{17}{2}[/tex] , [tex]\frac{-4}{2}[/tex] ) = (8.5, - 2 )
Refer to the diagram below to prove that the exterior angle equals the
To prove that the sum of the remote interior angles and the exterior angle have the same value, we recall 2 things:
1.- the inner angles of a triangle add up 180 degrees
2.- angle 3 and angle 4 are supplementary which means that they add up 180 degrees.
[tex]\begin{gathered} \measuredangle1+\measuredangle2+\measuredangle3=180^{\circ} \\ \measuredangle3+\measuredangle4=180^{\circ} \\ \Rightarrow \\ \measuredangle1+\measuredangle2+\measuredangle3=\measuredangle3+\measuredangle4 \\ \Rightarrow \\ \measuredangle1+\measuredangle2=\measuredangle4 \end{gathered}[/tex]Answer:
They are linear pair and therefore supplementary.
Triangle sum theorem.
Substitution.
Subtraction property of equality.
Model Real Life You have 3 toy bears. Yohave more yo-yos than toy bears. How mamore yo-yos do you have?
Solution
Step 1
Let the number of yo-yos than toy bears = x
A number between 280 and 380 when rounded to the nearest hundred is 45 less than the original number what number is the original number
If the unknown number is an integer between 280 and 349;
When rounded to the nearest hundred, the unknown number is 300.
If the unknown number is an integer from 350-380;
When rounded to the nearest hundred, the unknown number is 400.
If the approximation is 45 less than the original number, thus it cant be in the range of 350-380.
But;
[tex]300+45=345[/tex]When 345 is rounded to the nearest hundred, it is 300.
And the difference between the approximated value and the original value is 45.
Hence, 345 is the original number.
CORRECT ANSWER: 345
Megan's text messaging plan cost $15 for the first 600 messages and 5¢ for each additional text message. If she owes $24.60 for text messaging in the month of October, how many text messages did she send that month
Megan sent 792 text messages in the month of October .
In the question ,
it is given that
Cost for first 600 messages = $15
additional text message charge = $0.05
Amount owed by Megan for the month of October = $24.60
Let the number of Additional messages be x.
So, according to the question
15 + 0.05x = 24.60
0.05x = 24.60-15
0.05x = 9.6
x = 9.6/0.05
x = 192
number of extra messages = 192
total messages = first 600 messages + extra messages
= 600+192
= 792
Therefore , Megan sent 792 text messages in the month of October .
The given question is incomplete , the complete question is
Megan's text messaging plan cost $15 for the first 600 messages and 5¢ for each additional text message. If she owes $24.60 for text messaging in the month of October, how many text messages did she send that month ?
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Question 5The table below shows the coordinates of a figure that was transformed.Pre-ImageImageA(5,2)B(6, 1)A'(0,0)B'(1, -1)C'(-1,3)C(4,5)Which is a correct description of the transformation?
You have the following A, B and C points, which are transformed to the points A', B' and C', jus
Enter an equation that passes through the point (12, 7) and forms a system of linear equations with no solution when combined with the equation y=−3/4x+8.
To answer this question, we need to know that two linear equation that does not have solutions must not cross to each other, that is, they do not have a common point. For this case, both lines must be parallel lines. So in the question, we need to find a parallel line to the given line. Two parallel lines have the same slope.
Then, we have that the line must pass through (12, 7), and, because it is parallel to y = -3/4x + 8, and the slope for this line is m = -3/4, then, the line equation is, applying the point-slope form of the line:
[tex]y-y_1=m(x-x_1)[/tex]And
x1 = 12
y1 = 7
m = -3/4
Then
[tex]y-7=-\frac{3}{4}(x-12)\Rightarrow y-7=-\frac{3}{4}x+\frac{3}{4}\cdot12\Rightarrow y-7=-\frac{3}{4}x+\frac{36}{4}[/tex][tex]y-7=-\frac{3}{4}x+9\Rightarrow y=-\frac{3}{4}x+9+7\Rightarrow y=-\frac{3}{4}x+16[/tex]Then, the line equation is y = -3/4 x + 16.
We can check this if we use the elimination method as follows:
This is a FALSE result, and we do not have solutions for this system. Therefore, the line equation is y = -3/4 x + 16.
consider the function f(x) = x^1/2 and the function G, shown below. g(x)= f(1/4 • x) = (1/4 •x)^1/2how will the graph of the function g differ from the graph of the function f?
ANSWER
The graph of function g is the graph of function f stretched horizontally by a factor of 4.
EXPLANATION
Function g(x) is a transformation of function f(x), obtained by multiplying the variable, x, by 1/4. This is described as a horizontal stretch by a factor of 4.
Hence, the graph of function g is the graph of function f stretched horizontally by a factor of 4.
The table shows a linear relationship between x and y. Drag and drop the options provided into the correct boxes to complete the equation. х 1 0 6 -4 41 у 9 -39 The equation that represents the relationship Is y = -8 -41 ON 9 4 O?
To calculate the equation first we need to choose two points of the table
P1 (1,1)=(x1,y1)
P2(0,9)=(x2,y2)
then we calculated the slope m
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]substituting the points we have
[tex]m=\frac{9-1}{0-1}=\frac{8}{-1}=-8[/tex]then we can calculate the equation
[tex](y-y1)=m(x-x1)[/tex][tex](y-1)=-8(x-1)[/tex][tex]y-1=-8x+8[/tex][tex]y=-8x+8+1[/tex]the equation is
[tex]y=-8x+9[/tex]20g of radioactive substance decays by 1/2 of it's original
amount every 30 days. How much is left after 10 days.
The amount of radioactive after 10 days with the same rate of change of decay will be 16.67 g.
What is the rate of change?The rate of change is the change of a quantity over 1 unit of another quantity.
Most of the time the rate of change is the change with respect to time.
For example the speed 3meter/second.
As per the given,
Radioactive decays by 1/2 of its original in 30 days.
1/2 of original → 30 days.
Divide both sides by 3
1/6 of original → 10 days
Therefore, in 10 days amount of decays will be,
1/6 of 20 ⇒ 20/6 = 3.33
The amount left = 20 - 3.33 = 16.67.
Hence "The amount of radioactive after 10 days with the same rate of change of decay will be 16.67 g".
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10. If you invest $2000 at 6% compounded monthly, how long will it take the account to double in
value?
If I invest $2000 at 6% interest compounded monthly, it will take 11.58 years by the account to double in value.
What is compound interest?
The practice of adding interest to the principal amount of a loan or deposit is known as compound interest, sometimes known as interest on principal and interest. It happens when interest is reinvested, added to the lent capital rather than paid out, or required to be paid by the borrower, resulting in interest being created the next period on the principal amount plus any accrued interest. Compound interest is a prominent concept in finance and economics.
The initial investment of $2000 at 6% compounded monthly.
Since, the interest rate of 6% is compounding monthly, then the effective annual interest rate will be
= (1+)−1i = (1+rm)m−1
Here, r = interest rate in decimals
= (1+0.0612)12−1i = (1+0.0612)12−1
= 0.061678i = 0.061678
= ×100 = 6.1678%
Now, we are using Rule 72 to calculate the doubling time
Time to double the initial amount = 72 /effective annual interest rate
Time to double the initial amount = 11.58 years
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Swine Flu is attacking Springfield. The function below determines how many people have swine where t=time in days and S=the number of people in thousands.
A.find s(4)
[tex]\begin{gathered} s(4)=9(4)-4 \\ s(4)=36-4 \\ s(4)=32 \end{gathered}[/tex]B. means that in 4 days there will be 32000 infected people
C. find t to S(t)=23
[tex]\begin{gathered} 23=9t-4 \\ 9t=23+4 \\ t=\frac{27}{9} \\ t=3 \end{gathered}[/tex]D. means there will be 23,000 infected people after 3 days
E. Graph
to draw the line we need two points which we already have but we will add another to make a table of 3 values the new value is t=1
[tex]\begin{gathered} s(1)=9(1)-4 \\ s(1)=5 \end{gathered}[/tex]table
graph
Explaining the Converse of the Pythagorean TheoremThe converse of the Pythagorean Theorem states that if the three sides of a triangle work for the equation a^2 + b^2 = c^2, then the triangle is a right triangle. To prove this, you can use what’s called a proof by contradiction. That is, you can prove something is true because it cannot be false.Start by assuming a triangle is not a right triangle and the sides work for the equation a^2 + b^2 = c^2. Here is a diagram of the triangle. Keep this diagram window open as you work on the tasks in this section.Now, create a right triangle with legs a and b. Call the hypotenuse n. Here is a diagram of the triangle. Keep this diagram window open as you work on the tasks in this section.questionsPart ASince triangle 2 is a right triangle, write an equation applying the Pythagorean Theorem to the triangle.Part BSince the equations for both triangles have a^2 + b^2, you can think of the two equations for c^2 and n^2 as a system of equations. Substitute what a^2 + b^2 equals in the first equation for a^2 + b^2 in the second equation. After you substitute, what equation do you get?Part CNow, take the square root of both sides of the equation from part B and write the resulting equation.Part DIs there any way for this equation to be true? How?Part EWhat does this show about the relationship between the two triangles?Part FDoes this mean that triangle 1 is a right triangle? Why or why not?
Part A: Since triangle 2 is a right triangle, write an equation applying the Pythagorean Theorem to the triangle.
Triangle 2 has the following sides: a, b and n
Writing it into an equation will be:
[tex]\text{ a}^2\text{ + b}^2\text{ = n}^2[/tex]The answer is a² + b² = n²
Part B: Since the equations for both triangles have a^2 + b^2, you can think of the two equations for c^2 and n^2 as a system of equations. Substitute what a^2 + b^2 equals in the first equation for a^2 + b^2 in the second equation. After you substitute, what equation do you get?
Equation 1 (Triangle 1): a² + b² = c²
Equation 2 (Triangle 2): a² + b² = n²
Substitute what a^2 + b^2 equals in the first equation for a^2 + b^2 in the second equation, it will be:
[tex]\text{ a}^2\text{ + b}^2\text{ = n}^2[/tex][tex]\text{ c}^2\text{ = n}^2[/tex]The answer is c² = n²
Part C : Now, take the square root of both sides of the equation from part B and write the resulting equation.
[tex]\text{ c}^2\text{ = n}^2[/tex][tex]\text{ }\sqrt{c^2}\text{ = }\sqrt{n^2}[/tex][tex]\text{ c = n}[/tex]The answer is c = n
How come my answer is wrong? It says it’s equal to the correct answer but it’s not the right answer.
When water flows across farmland, some of the soil is washed away, resulting in erosion. Researchers released water
across a test bed at different flow rates and measured the amount of soil washed away. The following table gives the
flow (in liters per second) and the weight (in kilograms) of eroded soil:
The correlation coefficient between flow rate and amount of eroded soil is:
0.967.
Correlation coefficientsThe correlation coefficient is an index that measures correlation between two variables, assuming values between -1 and 1.
If it is positive, the relation is positive, meaning that the variables are direct proportional. If it is negative, the variables are inverse proportional.
If the absolute value of the correlation coefficient is greater than 0.6, the relationship between the variables is strong.
Given a data-set of two points, the correlation coefficient is found inserting points of the data-set into the calculator. In this problem, the points in the data-set are given as follows:
(0.31, 0.82), (0.85, 1.95), (1.26, 2.18), (2.47, 3.01), (3.75, 6.07).
Using a calculator, the coefficient is given as follows:
0.967.
Hence the last option gives the correct coefficient.
Missing informationThe complete problem is given by the image at the end of the answer.
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Becky borrowed $580.00 from the bank. The loan had a 13.5% simple
annual interest rate, and she paid off the bill over 18 months. What was
the total amount, including interest, Becky paid for the loan?
Work Shown:
P = 580
r = 0.135
t = 18 months = 18/12 = 1.5 years
A = P*(1+r*t)
A = 580*(1+0.135*1.5)
A = 697.45
A basketball player scored 24 times during one game. she scored a total of 38 points, two for each two-point shot and one for each free throw. How many two-point shots did she make? How many free throws?
The number of two-points shots made is 14
The number of free throws made is 10
What is the number of two-points shots and free throws made?The first step is to formulate a set of linear equations that represent the information in the question:
x + y = 24 equation 1
2x + y = 38 equation 2
Where:
x = number of two-point shots made y = number of free throws madeThe linear equations would be solved using the elimination method.
In order to determine the value of x, take the following steps:
Subtract equation 1 from equation 2
x = 14
Substitute for x in equation 1
14 + y = 24
Combine similar terms:
y = 24 - 14
Add similar terms together
y = 10
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Answer:
Dependent and independent variables are variables in mathematical modeling, statistical modeling and experimental sciences. Dependent variables are studied under the supposition or demand that they depend, by some law or rule, on the values of other variables.
Step-by-step explanation:
given A(2, 3), B(8, 7), C(6 1), which will make line AB perpendicular to line CD?D(9, 3)D(4, 4)D(3, 3)D(8, 4)
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
A(2, 3), B(8, 7), C(6 1)
Step 02:
Line AB
Slope formula
m = (y2 - y1) / (x2 - x1)
A (2 , 3) x1 = 2 y1 = 3
B (8 , 7) x2 = 8 y2 = 7
[tex]m\text{ = }\frac{7-3}{8-2}=\frac{4}{6}=\frac{2}{3}[/tex]Step 03:
Slope of the perpendicular line, m’
m' = -1 / m
[tex]m\text{'}=\text{ }\frac{-1}{m\text{ }}=\text{ }\frac{-1\text{ }}{\frac{2}{3}}\text{ = -}\frac{3}{2}[/tex]Step 04:
Line CD
m' = (y2 - y1) / (x2 - x1)
C (6 , 1) x1 = 6 y1 = 1
D ( x2, y2) x2 = x2 y2 = y2
[tex]-\frac{3}{2}=\text{ }\frac{y2-1}{x2-6}[/tex][tex]\frac{3}{2}=\frac{1-y2}{6-x2}[/tex]We must test the numerical values to verify equality,
x2 = 9
y2 = 3
[tex]\frac{3}{2}=\frac{1-9}{6-3}\text{ = }\frac{-8}{3}\text{ }[/tex]x2 = 4
y2 = 4
[tex]undefined[/tex]Find the measures of an interior angle and an exterior angle of the indicated regular polygon. Regular 20-gon interior angle exterior angle
Which statement explains whether x=5 is the solution to 5x + 2 = 27? a. Yes, because 5x means x=5.b. No, because 5x doesn't mean x=5.c. No, because when x is replaced by 5 the equation is false. d. Yes, because when x is replaced by 5 the equation is true.
Given
x = 5
5x + 2 = 27
Procedure
d. Yes, because when x is replaced by 5 the equation is true.