Calculate Sse for the arithmetic sequence {a,}5sequence {1,3 ={}+}=Ο Α. 1463OB. 91220 C. 8,6716D. 9,26767
Answers
Answer:
[tex]\frac{8,671}{6}[/tex]Explanation:
Here, we want to get the sum of the 58 terms in series
Mathematically, we have the formula to use as:
[tex]S_n\text{ = }\frac{n}{2}(a\text{ + L)}[/tex]where a is the first term and L is the last term
The first term is when n is 1
We have this calculated as:
[tex]\text{ a}_{}\text{ = }\frac{5}{6}+\frac{1}{3}\text{ = }\frac{5+2\text{ }}{6}\text{ = }\frac{7}{6}[/tex]The last term is the 58th term which is:
[tex]\text{ a}_{58}\text{ = }\frac{290}{6}\text{ + }\frac{1}{3}\text{ = }\frac{292}{6}[/tex]We finally substitute these values into the initial equation
Thus, we have it that:
[tex]S_{58}\text{ = }\frac{58}{2}(\frac{292}{6}+\frac{7}{6})\text{ = 29(}\frac{299}{6})\text{ = }\frac{8671}{6}[/tex]
Related Questions
[tex] - x \div 4 \geqslant 2[/tex]That's the Math problem
Answers
give a reason that justifies each statement for questions 4-9.
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4.
The angles ∠6 and ∠8 are congruent because they are alternate interior angles.
5.
The angles ∠4 and ∠5 added are equal to 180° because they are supplementary angles.
6.
If ∠1 is equal ∠7, then they are alternate exterior angles, therefore the lines p and q need to be parallel.
7.
The angles ∠1 and ∠2 are congruent because they are vertically opposite angles.
8.
If ∠2 and ∠6 are supplementary, they are consecutive interior angles, therefore the lines p and q need to be parallel.
9.
The angles ∠6 and ∠9 are congruent because they are corresponding angles.
Find two consecutive whole numbers that 11 lies between.
Answers
The number 11 is a whole number that lies between the whole numbers 10 and 12.
Therefore, the two consecutive whole numbers that 11 lies between are 10 and 12
What is the slope of a line perpendicular to the line whose equation is 3x-5y=45. Fully simplify your answer
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The slope of a line perpendicular to the line whose equation is 3x-5y=45 is -5/3.
So first of all, we have to find the slope of the given line. Convert it into Slope-Intercept Form.
The Slope - Intercept Form is : y = mx + c
Converting the given equation, we get :
3x - 5y = 45
5y = 3x + 45
y = (3/5)x + 15
Perpendicular Lines
The lines having opposite reciprocal slopes are perpendicular. That means you flip the sign (+/-) and flip the numerator and denominator. The slope of the line perpendicular to this one is -5/3.
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A committee must be formed with 5 teachers and 4 students. If there are 6 teachers to choose from, and 15 students, how many different ways could the committee be made?
Answers
There are 6 teachers and 15 students to choose from
To form a committee of 5 teachers and 4 students
The combination rule will be applied
From 6 teachers, The number of ways 5 teachers can be selected is
[tex]^6C_5[/tex]From 15 students, the number of ways 4 students can be selected is
[tex]^{15}C_{4^{}}[/tex]Therefore, the total number of ways a committee of 5 teachers and 4 students can be formed from 6 teachers and 15 students is
[tex]^6C_5\times^{15}C_{4^{}}[/tex]Simplifying this gives
[tex]^6C_5\times^{15}C_{4^{}}=\frac{6!}{(6-5)!\times5!}\times\frac{15!}{(15-4)!\times4!}[/tex]This further gives
[tex]\begin{gathered} ^6C_5\times^{15}C_{4^{}}=\frac{6!}{1!\times5!}\times\frac{15!}{11!\times4!} \\ ^6C_5\times^{15}C_{4^{}}=\frac{6\times5!}{1\times5!}\times\frac{15\times14\times13\times12\times11!}{11!\times4\times3\times2\times1} \end{gathered}[/tex]Cancel out common factors
[tex]\begin{gathered} ^6C_5\times^{15}C_{4^{}}=6\times\frac{15\times14\times13\times12}{4\times3\times2\times1} \\ ^6C_5\times^{15}C_{4^{}}=6\times\frac{32760}{24} \\ ^6C_5\times^{15}C_{4^{}}=6\times1365 \\ ^6C_5\times^{15}C_{4^{}}=8190 \end{gathered}[/tex]Therefore, the number of ways the committee can be formed is 8190 ways
Express 2x-3y=-6 into y=mx+b
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For this problem, we are given a certain expression and we need to write it in the "y=mx+b" form.
We need to isolate the "y" variable on the left side to solve this problem. We have:
[tex]\begin{gathered} 2x-3y=-6\\ \\ 2x-3y-2x=-6-2x\\ \\ \frac{-3y}{-3}=\frac{-6}{-3}-\frac{2x}{-3}\\ \\ y=2+\frac{2}{3}x\\ \\ y=\frac{2}{3}x+2 \\ \\ \end{gathered}[/tex]The expression is y = (2/3)x+2.
I need geometry help please.
Answers
Lets remember the property "alternative-interior angles" when we have parallels lines:
Given two paralles lines, the following is true:
In our question, we have:
We know that the angles J + P + K=180
So, the triangles have all the angles the same, so they are similar by angle-angle-angle, and they have one side congruent, AC=CD, so the triangles are congruents.
In December, 64 teams qualify for a basketball tournament. After each round, half of the teams are eliminated.
Which exponential function can be used to find the number of teams left after a rounds, where is a whole number?
O f(x) = (64)
O f(x) =
(x)64
O f(x) = 64 (¹)
○ f(x) = x(¹)
Answers
The exponential function is f(x) = 64·(1/2)ˣ which can be used to find the number of teams left after a round.
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
Given that 64 teams qualify for a basketball tournament. After each round, half of the teams are eliminated.
Because it is an exponential function, f(x) will reach 0 as x increases, allowing us to construct the following table of values:
x f(x)
0 64
1 32
2 16
3 8
4 4
5 2
6 1
At that point, 64 teams are in the tournament, and the total number of teams (from this point forward)
Therefore, half of the teams are eliminated after each round and the exponential function is:
f(x) = 64·(1/2)ˣ
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Mr. Bensoua buys 3 bags of Flaming Hot Cheetos for every 4 bags of Takis. He buys a total of 14 bags of chips. If the Flamin Hot Cheetos cost $2 per bag and the Takis cost $2.50 per bag, how much did Mr. Bensoua spend on all of the chips
Answers
Statement Problem: Mr. Bensoua buys 3 bags of Flaming Hot Cheetos for every 4 bags of Takis. He buys a total of 14 bags of chips. If the Flamin Hot Cheetos cost $2 per bag and the Takis cost $2.50 per bag, how much did Mr. Bensoua spend on all of the chips?
Solution:
When Mr. Bensoua buys 4 bags of Takis, he buys 3 bags of Flaming Hot Cheetos.
When he buys another 4 bags of Takis, he buys 3 bags of Flaming Hot Cheetos.
At the end, he buys 8 bags of Takis and 6 bags of Flaming Hot Cheetos and that makes it a total of 14 bags of chips.
The cost of Takis per bag is $2.50, the cost of 8 bags of Takis is;
[tex]\text{2}.50\times8=20[/tex]The cost of Flaming Hot Cheetos per bag is $2., the cost of 6 bags of Takis is;
[tex]2\times6=12[/tex]Hence, the total amount Mr. Bensoua spends is;
[tex]20+12=32[/tex]CORRECT ANSWER: $32
Use Pythagorean theorem to find right triangle side lengthsFind the value of c in the triangle shown below.682Choose 1 answer:A = 28B= 64=9= 10
Answers
EXPLANATION
Given the Right Triangle, we can apply the Pythagorean Theorem in order to get the value of x as shown as follows:
[tex]\text{Hypotenuse}^2=Short_-leg^2+Long_-leg^2[/tex]Replacing terms:
[tex]x^2=6^2+8^2[/tex][tex]x^2=36+64=100[/tex]Applying the square root to both sides:
[tex]x=\sqrt[]{100}=10[/tex]Hence, the solution is x=10
Samantha drinks 2/3 gallon of water everyday.At this rate , how much water does Samantha drink in 30 days ?
Answers
Explanation:
We are told that Samantha drinks 2/3 gallon of water daily
We are then asked to find the volume of water that she will drink in 30 days
To do so, we will have:
[tex]\begin{gathered} if\text{ } \\ \frac{2}{3}gallons\text{ =1 day} \\ for\text{ } \\ 30\text{ days, this will be} \\ \frac{2}{3}gallons\text{ per day}\times30days\text{ =}\frac{60}{3}=20gallons \end{gathered}[/tex]Therefore, in 30 days, she will drink 20 gallons of water
The answer is 20 gallonsans
May I please get help with this. I have tried multiple times but still could not get the correct answer or at least answer to them
Answers
SOLUTION:
Step 1:
In this question, we have the following:
Step 2:
The details of the solution are as follows:
Parallelogram:
a) Two pairs of parallel sides: Yes
b) Only one pair of parallel sides: NO
c) Four right angles: NO
d) All sides congruentnt: NO
Rectangles:
a) Two pairs of parallel sides: Yes
b) Only one pair of parallel sides: NO
c) Four right angles: Yes
d) All sides congruentnt: NO
Trapezoid:
a) Two pairs of parallel sides: NO
b) Only one pair of parallel sides: NO
c) Four right angles: NO
d) All sides congruentnt: NO
16. Given the graph below, write the equation of the line graphed. Equation:
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We have the following:
The equation has the following form
[tex]y=mx+b[/tex]where m is the slope and b is y-intercept
The slope formula is as follows
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]The point are (-4, 8) and (6, -4)
replacing:
[tex]m=\frac{-4-8}{6-(-4)}=\frac{-12}{10}=-\frac{6}{5}[/tex]In the graph we can see that the y-intercept is equal to 4, therefore, the equation would be
[tex]y=-\frac{6}{5}x+4[/tex]Solve for a: a = 10.
a = , ,
Answers
Answer:
a=10 and a=-10
Step-by-step explanation: its absolute value
for each triangle list the sides in order from shortest to longest explain your reasoning with words or numbers for the order
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a. For the first triangle ,
Two angles are given. To determine the third angle apply the property of triangle which is sum of the angles of the triangle is 180 degree.
[tex]27^{\circ}+82^{\circ}+\angle T=180^{\circ}[/tex][tex]\angle T=180^{\circ}-27^{\circ}-82^{\circ}=71^{\circ}[/tex]The triangle angles and sides relationship-
The longest side of a triangle is opposite the biggest angle measure.
The shortest side of a triangle is opposite the smallest angle measure in a triangle.
Therefore,
The shortest side is side opposite to the smallest angle that is MT.
The largest side is side opposite to the largest angle that is AT.
Hence the order for the sides from shortest to largest is
[tex]MTb. The triangle is given . First determine the value of x and find the angle using the property of triangle which is sum of the angles of the triangle is 180 degree.
[tex]8x-1+3x+4+3x+9=180^{\circ}[/tex][tex]14x+12=180[/tex][tex]14x=168[/tex][tex]x=12[/tex]The angles obtained are
[tex](8x-1)=95,(3x+4)=40,(3x+9)=45[/tex]We know that the longest side of a triangle is opposite the biggest angle measure.
The shortest side of a triangle is opposite the smallest angle measure in a triangle.
Hence the shortest side is JK and largest side is JL.
Hence the order for the sides from shortest to largest is
[tex]JKThree lakes lost water during a drought. Lake Jensen lost one ninth of its water, Lake Parlow lost 10% of its water, and Lake Stockton lost twenty one two hundredths of its water. Which lake lost the least amount of water?
Lake Jensen
Lake Parlow
Lake Stockton
All three lakes lost the same amount of water.
Answers
The lake that lost the least amount of water during the drought is Lake Parlow.
Which lake lost the least amount of water?The amount of water lost by Lake Jensen is written as a fraction. A fraction is a non-integer that is made up of a numerator and a denominator. An example of a fraction is 1/8.
The amount of water lost by Lake Parlow is written as a percentage. Percentage is the fraction of an amount that is written as a number out of 100.
The amount of water lost by Lake Stockton is written as a decimal. A decimal is the standard form used to write non-integers.
twenty one two hundredths = 21 / 200 = 0.105.
In order to compare the water lost by the three lakes, convert the fraction and the decimal to percentage.
1/9 x 100 = 11.11%
0.105 x 100 = 10.5%
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Can you help me, please? I have to find the restrictions on x .Thank you.
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If angle A is greater than angle C, then side BC is greater than side AB.
[tex]\begin{gathered} BC>AB \\ 8-x>4x+48 \end{gathered}[/tex]Then, we solve for x
[tex]\begin{gathered} -4x-x>48-8 \\ -5x>40 \\ x<-\frac{40}{5} \\ x<-8 \end{gathered}[/tex]Hence, the restriction of x is that its value must be less than -8.The function C(x) =17.5x-10 represents the cost (in dollars) of buying x tickets to the orchestra with a $10 coupon.
Answers
a) It represents the discount of $10 coupon
b) It repesetns the cost of each ticket
c) Five tickets cost is:
C(5) = 17.5(5) - 10 = 87.5 - 10 = 77.5
Five tickets cost $77.50
d) 130 = 17.5x - 10
130 + 10 = 17.5x
140 = 17.5x
x = 140/17.5 =8
x = 8
With $130 you can buy 8 tickets
z2=46Use a calculator.Z≈(Round to the nearest tenth as needed. Use a comma to separate answers as needed.)
Answers
The given expression is
[tex]z^2=46[/tex]We can look for a number in which square power is 46 or close to 46.
Notice that, 6 times 6 is 36, and 7 times 7 is 49. This means The number is between 6 and 7.
[tex]z\approx6,-6[/tex]Now, we use a calculator to find the exact solution.
[tex]z=\sqrt[]{46}\approx\pm6.78[/tex]As you can see, the approximated solutions are 6.78 and -6.78.I’m doing this timed assignment and I have no idea how to do it..help
Answers
Step 1
State the MACRS formula
[tex]Original\text{ value\lparen applicable MACRS \% rate\rparen}[/tex]Step 2
The original value=$20000
The depreciation for the first years is shown thus
A figure is made up of three triangles. Each triangle has a baseof 4.5 feet and a height of 4.5 feet. What is the total area of thefigure?
Answers
Area of Compound Figures
A figure is made up of 3 triangles with a base b=4.5 feet and a height h=4.5 feet
The area of a triangle of base b and height h is:
[tex]A=\frac{b\cdot h}{2}[/tex]Substituting the given values:
[tex]A=\frac{4.5ft\cdot4.5ft}{2}=10.125ft^2[/tex]The total area is 3 times the above area, thus:
[tex]A_t=3\cdot10.125ft^2=30.375ft^2[/tex]Answer: a.
You deposit $5000 in an account earning 6% interest compounded continuously. How much will you have in the account in 5 years?
Answers
For us to determine how much the account will be in 5 years at compounded continuously, we will be using the following formula:
[tex]\text{ A = P}_0e^{rt}[/tex]Where,
P = Principal amount (Initial Value)
A = Final amount (Future Value)
r = interest rate (in decimal)
t = time (in years)
e = mathematical constant approximately 2.7183
Given:
P = $5,000
r = 6% = 6/100 = 0.06
t = 5 years
We get,
[tex]\text{ A = P}_0e^{rt}[/tex][tex]\text{ A = (5,000)(2.7183)}^{(0.06)(5)}[/tex][tex]\text{ A = (5,000)(2.7183)}^{0.3}[/tex][tex]\text{ A = (5,000)(}1.34986151469)[/tex][tex]\text{ A = }6,749.30757343\text{ }\approx\text{ \$6,749.30}[/tex]Therefore, in 5 years, at 6% compounded continuously, your account will be $6,749.30
At a college basketball game, the ratio of the number of freshmen who attended to the number of juniors who attended is 3:4. The ratio of the number of juniors who attended to the number of seniors who attended is 7:6. What is the ratio of the number of freshmen to the number of seniors who attended the basketball game?
A) 7:8
B) 3:4
C) 2:3
D) 1:2
Answers
The ratio of the number of freshmen to the number of seniors who attended the basketball game is 7 : 8.
What is the ratio?Ratio is used to show the relationship between two or more numbers. Ratio provides information on the frequency of one value within other values. The sign that is used to represent ratio is :.
The ratio of freshmen to juniors is 3 : 4.
The ratio of juniors to seniors is 7 : 6.
In order to determine the required values, let us make some assumptions.
The number of freshmen is 21
The number of juniors is 28.
Given the two above assumption, the number of seniors = (28 x 6) / 7 = 24
The ratio of freshmen to seniors = number of freshmen : number of seniors
21 : 24
Express the ratio in its simplest form - 7 : 8.
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Prof. Glatt likes 2% milk (2% fat) for her cereal in the morning. Her parents only buy wholemilk (3.5% fat) and non-fat milk (0% fat). While she is visiting her parents, how much of eachtype of milk does she need to mix to get 3 cups of 2% milk. The answer can be rounded to thenearest tenth.linear systems solving algebraically
Answers
It is given that there are two types of milk.
One is 3.5% and one is 0%.
Let the number of cups of 3.5% milk be x and the number of cups of 0% milk used be y.
The total should be 3 cups so it follows:
[tex]x+y=3\ldots(i)[/tex]It is also known that the resulting milk is 2% so it follows:
[tex]\begin{gathered} \frac{3.5}{100}x+\frac{0}{100}y=\frac{2}{100}(x+y) \\ \frac{3.5}{100}x=\frac{2}{100}(x+y) \end{gathered}[/tex]Multiply by 100 on both sides to get:
[tex]\begin{gathered} 3.5x=2(x+y) \\ 3.5x=2x+2y \\ 1.5x=2y \\ x=\frac{2}{1.5}y \\ x=\frac{2\times2}{1.5\times2}y \\ x=\frac{4}{3}y \end{gathered}[/tex]Substitute the value of (ii) in (i) to get:
[tex]\begin{gathered} x+y=3 \\ \frac{4}{3}y+y=3 \\ \frac{4+3}{3}y=3 \\ \frac{7}{3}y=3 \\ \frac{3}{7}\times\frac{7}{3}y=\frac{3}{7}\times3 \\ y=\frac{9}{7} \end{gathered}[/tex]Hence the quantity of 0% milk is 9/7 cups.
The quantity of 3.5% milk is given by:
[tex]\begin{gathered} x=\frac{4}{3}y \\ x=\frac{4}{3}\times\frac{9}{7} \\ x=\frac{12}{7} \end{gathered}[/tex]Hence the quantity of 3.5% milk is 12/7 cups.
Find the slope of the line that passes
through these two points.
Point 1 Point 2
(3,5)
(4,2)
X1 У1
X2 Y2
m =
3
=
y2-91
X2-X1
[?]
Enter
Answers
Answer:
-3
Step-by-step explanation:
The slope of a line is the steepness of the line and is given by the formula below:
[tex]\boxed{\text{Slope} = \frac{y_1 - y_2}{x_1 - x_2} }[/tex], where [tex](x_1,y_1)[/tex] is the 1st coordinate while [tex](x_2,y_2)[/tex] is the 2nd coordinate
The two coordinates given are: (3, 5) and (4, 2)
Slope of line
[tex] = \frac{5 - 2}{3 - 4} [/tex]
[tex] = \frac{3}{ - 1} [/tex]
= -3
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Red Tickets: 50 tickets for $37.50A sign at the fair advertises ticket prices for the carnival games,Blue Tickets: 20 tickets for $16.00Yellow Tickets: 5 tickets for $5.00Find the price per ticket for each:Red ticketBlue Ticket:Yellow Ticket:How much would 40 red tickets costs?123456 7 10
Answers
The price per ticket can be calculated as follows;
[tex]\begin{gathered} \operatorname{Re}d=\frac{\text{Price}}{No\text{ of tickets}} \\ \operatorname{Re}d=\frac{37.50}{50} \\ \operatorname{Re}d=0.75 \\ \text{Blue}=\frac{16}{20} \\ \text{Blue}=0.8 \\ \text{Yellow}=\frac{5}{5} \\ \text{Yellow}=1.00 \end{gathered}[/tex]The price per ticket for each is given as;
Red tickets = $0.75
Blue tickets = $0.80
Yellow tickets = $1.00
Therefore, 40 red tickets would cost
40 Red = 0.75 x 40
40 Red tickets = $30.00
3. Solve the system using elimination (not substitution or matrices). negative 2 x plus y minus 2 z equals negative 8A N D7 x plus y plus z equals negative 1A N D5 x plus 2 y minus z equals negative 91. If the system has a single solution, write the solution as an ordered triple, (x, y, z).2. If the system has infinite solutions, write the solutions IN TERMS OF z.The solution should look something like left parenthesis 3 minus 3 z comma space minus 1 plus 7 z comma space z right parenthesis but not like left parenthesis negative 6 plus 3 y comma space y comma space 2 minus 5 y right parenthesis or not like left parenthesis x comma space 3 plus 5 x comma space minus 1 plus 4 x right parenthesis. None of these are the solution, they are just examples of what the answer could look like and not look like.3. Be sure to show all appropriate work. Extraneous work may be counted against you. Your handwritten work should include the steps used to find the solution. You should label your steps with how you combined your equations, like 2E1+E3. Solutions with no work will receive no credit.
Answers
Given the system of equation
[tex]\begin{gathered} -2x+y-2z=-8\ldots\ldots\ldots\text{.}(1) \\ 7x+y+z=-1\ldots\ldots\ldots\text{..}(2) \\ 5x+2y-z=-9\ldots\ldots\ldots\text{.}(3) \end{gathered}[/tex]step 1: Make z the subject of the formula in equations (2)
[tex]z=-1-7x-y\ldots\ldots\ldots(2)[/tex]step 2: Substitute the value of z obtained into equation (1)
10
step 3: Substitute the value of z obtained in step 1 into equation (3)
[tex]\begin{gathered} 5x+2y-(-1-7x-y)=-9 \\ 5x+2y+1+7x+y=-9 \\ 12x+3y=-10\ldots\ldots\ldots\text{.}(5) \end{gathered}[/tex]step 4: Solve equations (4) and (5) simultaneously,
[tex]\begin{gathered} 12x+3y=-10\ldots\ldots\ldots\text{.}(4) \\ 12x+3y=-10\ldots\ldots\ldots\text{.}(5) \\ \text{subtract equation (5) from (4)} \\ (12x-12x)+(3y-3y)=-10-(-8) \\ 0\text{ + 0 = }-10+10 \\ 0=0 \end{gathered}[/tex]Therefore, the system has infinite solutions
The solution in terms of z is
[tex]\begin{gathered} x=-\frac{1}{3}z+\frac{7}{9} \\ y=\frac{4}{3}z-\frac{58}{9} \\ z=z \end{gathered}[/tex]4. Use the graph below to answer the following questions.
Answers
By the concept of set builder notification
(b) 4
(c) 6
(d) -6
What is the set builder notification?In mathematics, the set-builder notation is used to express a set's elements or specify the conditions that each member of the set must meet. for instance The notation for the set builder is A = x Z | x 4 for the supplied set A =..., -3, -2, -1, 0, 1, 2, 3, 4. Sets can also be expressed using an interval or an equation by using the set-builder notation. In many cases, sets with an infinite number of elements have their elements written and represented in this way. These include integers, real numbers, and natural numbers, among other popular forms of numbers. One (or more) variables from these categories are utilized in this.
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Find the value of x to make this equation true. 6x + 1 = 6 + 2x.
Answers
6x + 1 = 6 + 2x.
collect the like term
6x - 2x = 6-1
4x = 5
divide both-side of the equation by 4
4x/4 = 5/4
x=1.25
1.25
Recall that two angles are complementary if the sum of their measures is 90°.
Find the measures of two complementary angles if one angle is 18° more than two times
the other angle.
The smaller angle measures
...
Answers
Complementary angles - The smaller angle is 24 degrees in size.
what are complementary angles?
Angles that add up to a precise 90 degree angle are said to be complementary. For instance, 30 degrees and 60 degrees are complementary angles.
Let x equal the first angle's measurement for the sake of explanation.
Let y be the size of the first angle's complement.
One angle, which we'll refer to as y, is 18 more than twice as large as another, x.
y = 18 + 2x
Complementary angles add up to 90 degrees.
x + 18 + 2x = 90
By substituting for y,
we get x + 18 + 2 x = 90.
Putting like phrases together and taking 18 off on both sides...
3x + 18 = 90
- 18 -18
3x = 72
By dividing both sides by 3, you get
3x/3 = 72/3
24 degrees is the angle between the two that is smaller. and the other angle would be,
y= 18+2x
=18+2(24)= 66 degrees.
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