Using the triangle pictured, find the measure of side AB. Round your answer to the nearest tenth. A) 1.6 B) 2.2 C) 2.7 D) 3.3
Answers
Answer:
Option B (AB = 2.2 units).
Step-by-step explanation:
The diagram shows that there are two sides given and one angle is given. Therefore, the sine rule must be used to solve the question. The sine rule can be written as:
sin ABC / AC = sin BAC / BC.
Plugging ABC=72 degrees, AC=2.5, and BC=2.1 in the sine rule gives:
sin 72 / 2.5 = sin BAC / 2.1.
Cross multiplying gives:
sin BAC = (2.1*sin 72)/2.5.
sin BAC = 0.79888747368.
Taking sin inverse on both sides gives:
BAC = arcsin (0.79888747368) = 53.0239949 degrees.
To find AB, first, the angle ACB is required. To find that angle, use the triangular law of angles. All the three angles sum up to 180 degrees. Therefore ACB = 180 - 72 - 53.0239949 = 54.9760051 degrees.
Now applying the Sine Rule to find AB:
sin ACB / AB = sin ABC / AC.
sin (54.9760051) / AB = sin 72 / 2.5.
AB = (2.5*sin (54.9760051))/sin (72) = 2.2 (to the nearest tenth).
Therefore, AB = 2.2 units, i.e. Option B!!!
Related Questions
Answer this question thanks
Answers
First divide 6 to both sides to isolate q. Since 6 is being multiplied by q, division (the opposite of multiplication) will cancel 6 out (in this case it will make 6 one) from the right side and bring it over to the left side.
18 ≥ 6q
18 ÷ 6 ≥ 6q ÷ 6
3 ≥ 1q
3 ≥ q
For the graph will you have a empty or colored in circle?
If the symbol is ≥ or ≤ then the circle will be colored in. This represents that the number the circle is on is included.
If the symbol is > or < then the circle will be empty. This represents that the number the circle is on is NOT included.
Which direction will the ray go?
If the variable is LESS then the number then the arrow will go to the left of the circle.
If the variable is MORE then the number then the arrow will go to the right of the circle.
In this case your inequality is:
3 ≥ q OR q ≤ 3
aka 3 is greater then q OR q is less then 3
This means that the graph will have an colored circle and the arrow will go to the left of 3. Look at image below.
Hope this helped!
~Just a girl in love with Shawn Mendes
You flip 3 coins 20 times and record the number of heads. The results are listed below. 2, 1, 0, 2, 2, 0, 2, 2, 3, 2, 1, 2, 1, 2, 1, 1, 2, 1, 3, 1 Complete the frequency table. a = ; b = ; c = ; d = Based on these results, which of these statements are true? You would expect to get 0 heads and 3 heads about the same number of times. You would expect to get 1 head and 2 heads about the same number of times. This would be a good experiment to use to find the probability that a family has a dog or a cat. This would be a good experiment to use to find the probability that a family with 3 kids has 1 boy.
Answers
The true statements about the result of the coin toss experiment described are :
You would expect to get 0 heads and 3 heads about the same number of times. You would expect to get 1 head and 2 heads about the same number of timesNumber of heads :__0 __ 1 __ 2 __ 3
Frequency _____ :_ 2___7___9___2
Expected Number of 0 heads = 2 Expected Number of 3 heads = 2Expected Number of 1 head = 7Expected Number of 3 heads = 9Therefore, expected Number of 3 and 0 heads are the same. And the expected number of 1 and 2 heads are almost the same.
The experiment cannot be used to model the events in the options as it only gives the number of occurence of a single event.
Hence, only statements 1 and 2 are true.
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The frequency of 0, 1, 2, and 3 heads in the experiment is 2, 7, 10, and 1 respectively. Statement 2 is the most accurate regarding long-term expectations, while statement 4 can be considered conditionally true. Statements 1 and 3 are not related to the probability outcomes of the experiment.
To complete the frequency table based on the given results, we will count the occurrences of each number of heads (0, 1, 2, or 3) in the 20 trials. The frequencies are:
0 heads (a): 2 times1 head (b): 7 times2 heads (c): 10 times3 heads (d): 1 timeBased on these results, we can discuss the truthfulness of the provided statements:
You would not expect to get 0 heads and 3 heads about the same number of times because the probability of getting 0 or 3 heads is lower than 1 or 2 heads when flipping three coins.You would expect to get 1 head and 2 heads about the same number of times in the long term, according to the law of large numbers, which states that as the number of trials increases, the empirical relative frequency of the outcomes approaches the theoretical probability.This would not be a good experiment to use to find the probability that a family has a dog or a cat, as the outcomes of coin flips do not correlate to pet ownership statistics.This could be a relatively good experiment to use to find the probability that a family with 3 kids has 1 boy, assuming that the gender of each child is independent and that the probability of being born a boy is equal to that of being born a girl (each coin flip can represent the birth of a child, with heads representing boys). At a certain electronics company, the daily output Q is related to the number of people A on the assembly line by Q=600+√(A+41). Determine how many people are needed on the assembly line if the daily output is to be 621.
Answers
Answer:
[tex]A=400\ people[/tex]
Step-by-step explanation:
we have
[tex]Q=600+\sqrt{A+41}[/tex]
where
Q -----> is the daily output
A -----> is the number of people
For Q=621
Find the value of A
substitute and solve for A
[tex]621=600+\sqrt{A+41}[/tex]
Subtract 600 both sides
[tex]621-600=\sqrt{A+41}[/tex]
[tex]21=\sqrt{A+41}[/tex]
squared both sides
[tex]21^{2} ={A+41}[/tex]
[tex]441={A+41}[/tex]
Subtract 41 both sides
[tex]441-41=A[/tex]
Rewrite
[tex]A=400\ people[/tex]
You work in a hospital that has 9 floors. You need to see 3 patients on each floor. How many patients do you need to see in all?
Answers
Answer:
The answer is 27 patients.
Step-by-step explanation:
There are 3 patients per floor. There are 9 floors.
3 x 9 = 27
There are 27 patients in all.
I hope this helped! :)
What is the equation for a geometric sequence with a first term of 5 and a second term of −10?
an = 5(−2)n − 1
an = 5(2)n − 1
an = 5(−15)n − 1
an = 5(15)n − 1
Answers
Answer: A is correct, an = 5(−2)n − 1
Step-by-step explanation:
The formula for geometric sequences is an=a(r)^n-1
a is the first term, which is 5 in this case
r is the common ratio, which is -2 because (5)(-2)=-10
Find the product. -2 xa (-4 xb - 2 x 3 + 5 x )
Answers
Answer:
[tex]8x^{a+b}+4x^{3+a}-10x^{a+1}[/tex]
Step-by-step explanation:
We need to find the product of: [tex]-2x^{a}(-4x^{b}-2x^{3}+5x)[/tex]
We have that:
[tex]-2x^{a}(-4x^{b}-2x^{3}+5x)[/tex] = [tex]8x^{a+b}+4x^{3+a}-10x^{a+1}[/tex]
We can't simplify more the expression, therefore, the solution is:
[tex]8x^{a+b}+4x^{3+a}-10x^{a+1}[/tex].
Efficient Homemakers Ltd. makes canvas wallets and leather wallets as part of a money-making project. For the canvas wallets, they need two yards of canvas and two yards of leather. For the leather wallets, they need four yards of leather and three yards of canvas. Their production unit has purchased 44 yards of leather and 40 yards of canvas. Let x be the number of leather wallets and y be the number of canvas wallets. If the profit on a canvas wallet is $25 and the profit on a leather wallet is $40, write a function for the total profit for both wallets.
Answers
To find the total profit for both wallets sold by Efficient Homemakers Ltd., use the equation P = 40x + 25y, where x is the number of leather wallets and y is the number of canvas wallets sold.
Explanation:The question involves writing a function for the total profit from selling canvas wallets and leather wallets made by Efficient Homemakers Ltd.
To calculate the total profit, we denote x as the number of leather wallets and y as the number of canvas wallets.
The company makes a profit of $40 for each leather wallet, and $25 for each canvas wallet.
Thus, the total profit P can be represented by the equation:
P = 40x + 25y
This equation represents the total profit as a function of the number of leather wallets (x) and the number of canvas wallets (y) sold.
x=4 is a solution to the equation
2
= x - 8
True
O False
Answers
Answer:
False
Step-by-step explanation:
2 = x - 8
Add 8 to each side
2+8 = x-8+8
10 = x
x=4 is not a solution
For this case we have the following equation:
[tex]2 = x-8[/tex]
If we add 8 to both sides of the equation, we have:
[tex]2 + 8 = x-8 + 8\\10 = x[/tex]
Thus, the solution of the equation is [tex]x = 10,[/tex] therefore[tex]x = 4[/tex]is not a solution of the given equation.
Answer:
[tex]x = 4[/tex] is not a solution to the given equation.
False
What is 692,119 rounded to the nearest thousand
Answers
In order to get the answer to this problem you will have to go to the thousands place value and look at the number next to the place value and if the number is greater then 5 then you round up which will give you your answer.
[tex]692,119[/tex]
[tex]2,119[/tex]
[tex]1<5[/tex]
[tex]= 2000[/tex]
[tex]= 692,000[/tex]
Which means your answer is "692,000."
Hope this helps.
The value 692,119 is rounded to the nearest thousand is 692,000. The nearest thousand for the given number is 2000.
How to round off a number?A number (integer or decimal) is rewritten to the nearest place value (ones, tens, hundreds, thousands, and so on). The rewritten number is said to be the rounded value of the given number. A number is rounded off at any of its place values on the basis of the digit after the digit which is to be rounded.I.e., if the digit after that place is less than 5 (< 5) then round the number down, or if the digit after that place is greater than or equal to 5 ( ≥ 5) then round the number up. If the digit is less than 5, then all the digits after the required place value are rounded as zerosIf the digit is more than 5 or equal to 5, then add 1 to the digit in the required place value and round all the other digits after it as zeros.Rounding the given number to the nearest thousand?The given number is 692,119
The digit in the thousands place of the given number is 2.
The digit after 2 is 1 which is less than 5. So, the digits after the thousand place is rounded as zeros. I.e., 2119 to 2000.
Therefore, the rounded number is 692,000.
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A stock loses 10% of its value on Monday. On Tuesday it loses 20% of the value it had at the end of the day on Monday. What is the overall percent loss in value from the beginning of Monday to the end of Tuesday?
Answers
Answer: The overall percent loss is 28%.
Step-by-step explanation: Given that a stock loses 10% of its value on Monday and on Tuesday it loses 20% of the value it had at the end of the day on Monday.
We are to find the overall percent loss in value from the beginning of Monday to the end of Tuesday.
Let x represents the value of a stock at the beginning of Monday.
Then, the value of the stock at the end of Monday is given by
[tex]x-10\%\times x=x-\dfrac{10}{100}x=x-\dfrac{x}{10}=\dfrac{9}{10}x.[/tex]
So, the value of the stock at the beginning of Tuesday is [tex]\dfrac{9}{10}x.[/tex]
Therefore, the value of the stock at the end of Tuesday is given by
[tex]\dfrac{9}{10}x-20\%\times\dfrac{9}{10}x\\\\\\=\dfrac{9}{10}x-\dfrac{20}{100}\times\dfrac{9}{10}x\\\\\\=\dfrac{9}{10}-\dfrac{9}{50}x\\\\\\=\dfrac{36}{50}x\\\\\\=\dfrac{18}{25}x\\\\\\=x-\dfrac{7}{25}x\\\\\\=x-\dfrac{28}{100}x\\\\\\=x-28\%x.[/tex]
Thus, the overall percent loss is 28%.
-2,10,-50 next two numbers geometric sequence
Answers
Answer:
250, -1250
Step-by-step explanation:
Geometric Sequence is a hint to think multiplication:
What can you multiply to -2 to get 10
or what is 10/-2
I hope you said -5.
So just multiply -5 to a term to get the term right after!
So
-50(-5)=250
250(-5)=-1250
Can someone please help
Answers
Check the picture below.
[tex]\bf \stackrel{\textit{triangles' area}}{\cfrac{1}{2}(6)(1)+\cfrac{1}{2}(6)(1)}+\stackrel{\textit{front side}}{(6\cdot 2)}+\stackrel{\textit{left and right sides}}{(4\cdot 2)+(4\cdot 2)}\implies 3+3+12+8+8[/tex]
If it takes 45 manage to go to pale city from Heflin then it takes another hour and nine minutes to drive back to Ranburne Alabama how long will it take
Answers
Answer:
1 hour 54 minutes
Step-by-step explanation:
1 hour and 9 minutes + 45 minutes gives your answer. However, since 45+9=54, this is convenient, since now we don't need to carry. Thus, 1 hour and 54 min is your answer.
Hope this helps!
Answer: 114 minutes or 1 hour and 54 minutes.
Step-by-step explanation:
You need to analyse the exercise.
You know that it takes 45 minutes from Helflin to Pale City.
Driving back to Alabama takes 1 hour and 9 minutes. You need to remember that there are 60 minutes in an hour, therefore, this time in minutes is:
[tex]60\ minutes+9\ minutes=69\ minutes[/tex]
To find the total time, you need to add 45 minutes and 69 minutes. Then you get:
[tex]Total=45\ minutes+69\ minutes=114\ minutes[/tex] or 1 hour and 54 minutes.
Compare the graph of f (x) with the graph of k (x) = 2 (x-8)2
Answers
The graph of k(x)=2(x-8)², a quadratic function, will be an upwards-opening parabola with a vertex at (8,0). To compare it with the graph of f(x), we need more details about f(x), which could be linear, quadratic, or a different type of function entirely. The comparison can focus on attributes like shape, orientation, position, steepness, continuity, differentiability, or periodicity.
Explanation:The function k (x) = 2 (x-8)² is a quadratic function where 2 is the coefficient, and 8 is the amount that the graph is shifted to the right in the x coordinate. This graph will be a parabola that opens upwards, with a vertex at the point (8,0) due to the transformation in the x term (x-8).
To compare the graph of f(x) with the graph of k(x), we first need to understand the characteristics of f(x). For example, if f(x) is also a quadratic function, we can compare their shapes, orientations (upward or downward opening), positions (based on vertex and line of symmetry), and steepness (determined by the absolute value of the coefficient -- in this case, 2).
If f(x) is a linear function, it will be a straight line and we can compare the orientation, steepness (slope), and position (y-intercept). Or if f(x) is a different type of function entirely, the comparison will focus more generally on attributes like continuity, differentiability, periodicity, etc. Therefore, without additional details about f(x), a complete comparison isn't possible.
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Divide. Reduce the answer to lowest terms. 3/4 ÷ 1/3
Answers
To divide fractions, multiply the first fraction by the reciprocal of the second fraction. In this case, the answer is 9/4.
Explanation:To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. In this case, the reciprocal of 1/3 is 3/1. So, we have:
3/4 ÷ 1/3 = 3/4 * 3/1 = 9/4.
The answer, 9/4, cannot be further reduced to lowest terms since 9 and 4 do not have any common factors other than 1.
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In the number 409.21 what digit is in the ones place
Answers
Answer: The number before the decimal
Step-by-step explanation:
The digit in the ones place is 9, in the given number 409.21.
What is the place value?There are only 10 digits in the number system. They are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The digits in a number have values depending on their place. Those values are called place values. According to the number system, the place values are ones, tens, hundreds, thousands, and so on. For a decimal number, after the decimal point, the place values are tenths, hundredths, thousands, and so on.A number is obtained by adding the product of digits with their place values.Expanding the given number according to place values:The given number is 409.21
⇒ 400 + 00 + 9 + 2×(1/10) + 1×(1/100)
⇒ 4×100 + 0×10 + 9×1 + 2×(1/10) + 1×(1/100)
So, the digit in ones place is 9.
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Find the distance of the line segment joining the two points (5, 4) and (−2, 1)
Answers
The distance of the line segment joining the points (5, 4) and (-2, 1) is found using the distance formula. Substituting the given points into the formula, we calculate the distance to be approximately 7.62 units.
Explanation:The distance between two points (x1, y1) and (x2, y2) in a 2-dimensional Cartesian plane is given by the distance formula: √[(x2-x1)² + (y2-y1)²].
Substituting the given points (x1, y1) = (5, 4) and (x2, y2) = (-2, 1), we get:
Distance = √[(-2 - 5)² + (1 - 4)²] = √[( -7)² + (-3)²] = √[49 + 9] = √58 ≈ 7.62.
Therefore, the distance of the line segment joining the two points (5, 4) and (-2, 1) is approximately 7.62 units.
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Seth bought a T-shirt that costs $21.00. If the tax rate was 8%, what was the total cost of the t-shirt?
Answers
Answer:
$22.68
Step-by-step explanation:
21×.08= 1.68
21+1.68=22.68
Total cost =$22.68
Answer:
22.68
Step-by-step explanation:
The first step is to find the amount of tax
tax = original cost * tax rate
= 21 * 8%
= 21 * .08
=1.68
Then we add the tax to the original cost to find the total cost
total cost = original cost + tax
= 21 + 1.68
=22.68
One serving of Chad's favorite cereal contains 1 1/4 ounces. How many servings are in a 15 1/3 ounce box
Answers
so namely how many times does 1¼ go into 15⅓?
let's firstly convert the mixed fractions to improper fractions and then divide.
[tex]\bf \stackrel{mixed}{1\frac{1}{4}}\implies \cfrac{1\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{5}{4}}~\hfill \stackrel{mixed}{15\frac{1}{3}}\implies \cfrac{15\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{46}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{46}{3}\div\cfrac{5}{4}\implies \cfrac{46}{3}\cdot \cfrac{4}{5}\implies \cfrac{184}{15}\implies 12\frac{4}{15}[/tex]
What is the value of x in this system of equations? Express the answer as a decimal rounded to the nearest tenth.
-5x - 12y = -8
5x + 2y = 48
Answers
Answer:
x = 11.2
Step-by-step explanation:
-5x - 12y = -8
5x + 2y = 48
you can combine all like terms from both equations together:
0x-10y=40
simplified:
-10y=40
y=-4
now you plug in the value of y into either equation:
5x+2(-4)=48
simplify
5x-8=48
add 8
5x=56
divide by 5
x=56/5=11.2
what is the 17th term in the arithmetic sequence in which a6 is 101 and a9 is 83
Answers
Answer:
The 17th term in arithmetic sequence is 68
Step-by-step explanation:
The general formula of arithmetic sequence is:
aₙ = a₁ + (n – 1)d.
We are given a₆ = 101 and a₉ = 83 and we need to find a₁₇
To find the term a₁₇ we should know a₁ and d. So we would find both
a₆ = a₁ +(6-1)d
101 = a₁ +(5)d
101 = a₁ +5d eq(1)
and
a₉ = a₁ +(9-1)d
83 = a₁ + 8d eq(2)
Subtracting eq(2) from eq(1)
101 = a₁ +5d
83 = a₁ + 8d
- - -
__________
18 = -3d
=> d = 18/-3
=> d = -6
Putting value of d in eq(1)
101 = a₁ + 5d
101 = a₁ + 5(-3)
101 = a₁ -15
=> a₁ = 101+15
=> a₁ = 116
Now finding a₁₇:
aₙ = a₁ + (n – 1)d.
a₁₇ = 116 +(17-1)(-3)
a₁₇ = 116+(16)(-3)
a₁₇ = 116 - 48
a₁₇ = 68
So, the 17th term in arithmetic sequence is 68
the quotient of 1 and 2/3 divided by 4/5
Answers
Answer:
[tex]\frac{15}{8}[/tex]
Step-by-step explanation:
"the quotient of 1 and 2/3 " expressed mathematically is,
1 ÷ [tex]\frac{2}{3}[/tex] = [tex]\frac{3}{2}[/tex]
"divided by 4/5"
[tex]\frac{3}{2}[/tex] ÷ [tex]\frac{4}{5}[/tex]
=[tex]\frac{3}{2}[/tex] x [tex]\frac{5}{4}[/tex]
= [tex]\frac{15}{8}[/tex]
Which of the following numbers has the greatest value?
A) .1
B) .47
C) .049
D) .192
E) .0864
Answers
Answer: B) .47
Step-by-step explanation: As all of those numbers have a decimal with no whole number, we look past the decimal. Then you realize 4 is greater than 1, 0, 1 and 0. You ignore the numbers past it and read it from left to right all the time.
The greatest value is 0.47. Then the correct option is B.
What is the greatest value?Let the number will be a, b, c, d, and e.
If the value of the arbitrary constant d has a maximum value then the greatest value will be of d.
The numbers are given below.
0.1, 0.47, 0.049, 0.192, and 0.0864.
Then the greatest value is 0.47.
Then the correct option is B.
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Solve for x
(x + 10)(x + 10) = 0
Answers
[tex](x + 10)(x + 10) = 0\\x+10=0\\x=-10[/tex]
ANSWER
[tex]x = - 10[/tex]
EXPLANATION
We have the quadratic equation
[tex](x + 10)(x + 10) = 0[/tex]
This quadratic equation is in the factored form.
According to the zero product principle either the first factor is zero or the second is zero.
We apply the zero product principle to obtain:
[tex](x + 10) = 0 \: \: or \: \: (x + 10) = 0[/tex]
This is a repeated factor therefore,
[tex]x = - 10[/tex]
is the repeated root.
The density of a American white oak tree is 752 kilograms per cubic meter. If the trunk of an American white oak tree has a circumference of 4.5 meters and a height of 8 meters, what is the approximate number of kilograms of the trunk?
1. 13
2. 9694
3. 13,536
4. 30, 456
Answers
Check the picture below.
[tex]\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\ \cline{1-1} C=4.5 \end{cases}\implies 4.5=2\pi r\implies \cfrac{4.5}{2\pi }=r \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} h=8\\ r=\frac{4.5}{2\pi } \end{cases}\implies V=\pi \left( \cfrac{4.5}{2\pi } \right)^2(8)\implies V=\begin{matrix} \pi \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} \cdot \cfrac{20.25}{\begin{matrix} 4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}\underset{\pi }{\begin{matrix} \pi^2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} }}(\stackrel{2}{\begin{matrix} 8 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}})[/tex]
[tex]\bf V=\cfrac{40.5}{\pi }~cm^3~\hspace{9em} \stackrel{\textit{since density is }752kg~per~cm^3}{density\implies 752\left( \cfrac{40.5}{\pi } \right)}\qquad \approx ~~9694[/tex]
Option 2 is correct. The approximate weight of the trunk of an American white oak tree with a circumference of 4.5 meters and a height of 8 meters is calculated by finding the volume of the trunk and multiplying it by the tree's density, resulting in approximately 9,694 kilograms.
To calculate the approximate weight of the trunk of an American white oak tree, we first need to estimate its volume and then multiply it by the tree's density. Since the tree trunk is cylindrical, we can use the formula for the volume of a cylinder, [tex]V = \(pi \times r^2 \times h\)[/tex], where r is the radius of the base and h is the height of the cylinder. The circumference is given by C = 2 times pi times r, so we can solve for r by rearranging the formula: [tex]\(r = \frac{C}{2 \times \\pi}\)[/tex]. With a circumference of 4.5 meters, the radius is [tex]\(r = \frac{4.5 \text{m}}{2 \times \pi}\approx 0.716m\)[/tex]. Plugging the radius and the height (8 m) into the volume formula gives V approx pi times (0.716m)^2 times 8 m approx 13.07 m^3.
Knowing the volume, we can find the mass of the trunk by multiplying the tree's volume by its density. The density of American white oak is given as 752 kilograms per cubic meter. The mass (m) is then [tex]m = V \times \ext{density} = 13.07 m^3 \times 752 \frac{kg}{m^3} \approx 9,832.64 kg.[/tex] Rounding off gives us approximately 9,694 kilograms, which is option 2 and is the closest answer provided in the question.
how to solve a system of three equations using the elimination method
Answers
Answer:
1. Write all the equations in standard form, leaving out decimals or fractions.
2. Select the variables to be eliminated; And then you take two of these equations, and you eliminate the variables.
3. Select a different set of two equations and eliminate the same variables as in step 2.
4. Solve two equations containing two variables from steps 2 and 3.
5. Substitute the answer to step 4 into any equation that contains the remaining variables.
6. Check the solution with three original equations.
To solve a system of three equations using the elimination method, pair up the equations, eliminate a variable from each pair, solve for the remaining variable and substitute this value into other equations to find the values of other variables.
Explanation:To solve a system of three equations using the elimination method, the process involves eliminating one variable at a time to eventually have one equation with one variable left, which you can then solve.
Pair up the equations. You can pair the first and second equation together, and then pair the second and third equation together. Eliminate one variable from each pair. This can be done by adding or subtracting the equations. For instance, if you have these equations: Qd = 16 - 2P, and Qs = 2 + 5P, subtracting the second equation from the first gives you Qd - Qs = 14 - 7P, thus eliminating the P variable. Solve for the remaining variable. This usually involves rearranging the equation and solving for the variable in question. Once you obtain the value for one variable, substitute this value into the other equations so as to solve for the other two variables. Learn more about Solving Systems of Equations here:
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What equation best represents the following sentence?
The sum of a number and two is twice the number.
n +2 = 2n
n + 2 = 2n
n +2=n
2n = n
Answers
Answer: n + 2 = 2n
Step-by-step explanation:
sum = add
number and two = n, 2
twice the number = 2 x n
Answer: n + 2 = 2n
Step-by-step explanation:
The sum of two numbers is 28. The first number, x, is three
times the second number, y.
Answers
Answer:
x=21
y= 7
Step-by-step explanation:
x+y = 28
x = 3y
Substitute the second equation into the first
3y+y = 28
4y = 28
Divide by 4
4y/4 = 28/4
y = 7
Now we need to find x
x = 3*y
x = 3*7
x = 21
Graph the following piecewise function.
Answers
Step-by-step explanation:
[tex]for\ 2<x\leq4-\text{the horizontal segment}\ y=2\\\\for\ 4<x<8\to y=x+3\\\\\text{put}\ x=4,\ \text{and}\ x=8\ \text{to the equation}\\\\y=4+3=7\to(4,\ 7)\\y=8+3=11\to(8,\ 11)\\\\for\ x\geq8\to y=2x\\\\\text{put}\ x=8,\ and\ x=9\ \text{to the equation}\\\\y=2(8)=16\to(8,\ 16)\\y=2(9)=18\to(9,\ 18)\\\\==========================[/tex]
[tex]<,\ >\ -\ \text{op}\text{en circle}\\\\\leq,\ \geq\ -\ \text{closed circle}[/tex]
2 squares area is 125 yards and 5 yards. how many yards would it take to fence the two squares in separately
Answers
Answer:
[tex]24\sqrt{5}\ yards[/tex]
Step-by-step explanation:
Let A1 be the area of one square and A2 be the area of second square
So,
A1 = s^2
where s is side of square
[tex]s^2=125\\\sqrt{s^2}=\sqrt{125}\\s=\sqrt{25*5}\\ s= \sqrt{5^2 * 5}\\ s= 5\sqrt{5}[/tex]
So side of one square is [tex]5\sqrt{5}[/tex]
To calculate the length of fence we need to find the perimeter of the square
So,
P1 = 4 * s
[tex]=4*5\sqrt{5} \\=20\sqrt{5}[/tex]
For second square:
[tex]A_2=s^2\\5=s^2\\\sqrt{s^2}=5\\{s}=\sqrt{5}[/tex]
The perimeter will be:
[tex]P_2 = 4*s\\=4 * \sqrt{5} \\=4\sqrt{5}[/tex]
So the total fence will be: P1+P2
[tex]= 20\sqrt{5}+4\sqrt{5} \\= 24\sqrt{5}\ yards[/tex]