The required values for a 95 percent confidence interval for population standard deviation are CI₈² = [1.1894, 5.221]
CI₈ = [1.0906, 2.2849]
n = 16, Standard Deviation = 1.4764, Var = 2.1796
X²₀.₀₂₅,₁₅ = 6.26, X²₀.₉₇₅,₁₅ = 27.49
CI₈² = [(15ₓ2.1796/27.48),(15ₓ2.1796/6.26)] = [1.1894, 5.221]
CI₈ = [[tex]\sqrt{15*2.1796/27.48} , \sqrt{15*2.1796/6.26}[/tex]] = [1.0906, 2.2849]
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factor this polynomial completely[tex]10 {x}^{2} - 11x + 3[/tex]
Given:
There are given the equation:
[tex]10x^2-11x+3=0[/tex]Explanation:
According to the question:
we need to find the factor of the given equation:
So,
From the equation:
[tex]\begin{gathered} 10x^{2}-11x+3=0 \\ 10x^2-6x-5x+3=0 \\ (2x-1)(5x-3)=0 \end{gathered}[/tex]Final answer:
Hence, the factor of the given equation is shown below:
[tex](2x-1)(5x-3)=0[/tex]rotate the figure 90 degrees clockwise around the origin?indentify the coordinates of the vertices of the rotated figure?
first write the coordinates
A (5,8)
B(9,8)
C(9,5)
D(5,5)
to rotate 90 degrees clockwise you must swap coordinates I mean change x for y and change the sign of the secon term or the new y
A(5,8)-->A'(8,-5)
B(9,8)-->B'(8,-9)
C(9,5)-->C'(5,-9)
D(5,5)-->D'(5,-5)
Rewrite 20 − 4x3 using a common factor.
Using a common factor, 20 - 4x³ can be rewritten as 4(5 - x³).
What is a Common Factor?A common factor of two or more numbers is any number that the two numbers can be divided by and will leave no remainder.
For example, a common factor of 4 and 8 is 2. This is because:
2 into 4 will give us 2 without a remainder.
2 into 8 will give us 4 without a remainder.
To rewrite the expression, 20 - 4x³ using a common factor, find the factor that will go into each of the terms without a remainder.
4 into 20 will give us 5 without a remainder.
4 into 4x³ will give us x³ without a remainder.
Therefore, we can factor out the common factor from the expression to rewrite 20 - 4x³ as 4(5 - x³).
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The log flume ride lasts 8 minutes. This amount of time is one minute more than twice the length of time for the teacup ride.
How long does the teacup ride last?
The time for the teacup to last is D. m = 3.5 minutes.
What is an expression?An expression is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Let the number of minutes be m.
The amount of time is one minute more than twice the length of time for the teacup ride. This will be:
= (2 × m ) + 1 = 8
2m - 1 = 8
Collect like terms
2m = 8 - 1
2m = 7
Divide
m = 7/2
m = 3.5
The correct option is D.
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Answer:
d) m = 3.5 minutes
Step-by-step explanation:
Now we have to,
→ find the time the teacup ride last.
Forming the equation,
→ 2m + 1 = 8
Then the value of m will be,
→ 2m + 1 = 8
→ 2m = 8 - 1
→ m = 7/2
→ [ m = 3.5 min ]
Hence, ride lasts for 3.5 min.
Please help me, it is important
Examining the given figure it can be calculated that
GI = 15 unitsm< IEH = 65 degrees How to get the required angel and length of side in the given figureGiven that
EI = 2x + 1
FH = 3x + 9
m< FIG = 50 degrees
The length of diagonals of rectangles are equal and when they bisect each other the divide each other into equal halves
EI is the half of FH, therefore we have that
( 3x + 9 ) / 2 = 2x + 1
3x + 9 = 2(2x + 1)
3x + 9 = 4x + 2
9 - 2 = 4x - 3x
7 = x
GI = EI (half diagonal of rectangle are equal)
GI = 2 * 7 + 1
= 15
m< FIG = 50 degrees = m< EIH (vertical opposite angles)
m< EIH + m< IEH + m< IHE = 180
m< IEH = m< IHE = y (base angles of isosceles triangle)
m< EIH + 2y = 180
50 + 2y = 180
2y = 180 - 50
2y = 130
y = 65 degrees
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Rewrite the following calculation so it involves addition only and then determine the result. Show your work.
-3+1-7- (-4)+10
URGENT PLEASE HELP FOR HW
The given calculation, -3+1-7- (-4)+10, can be rewritten as (1+4) so that it only involves addition and the result is 5.
According to the question,
We have the following expression:
-3+1-7- (-4)+10
Now, we have to remove all the negative signs from this expression.
So, we will first solve this expression to the step where we have only addition.
Now, we know that the multiplication of two negative integers is always positive.
-3+1-7+4+10
Adding the numbers with the negative sign:
-10+10+1+4
1+4
5
Hence, -3+1-7- (-4)+10 can be rewritten as (1+4) so that it only involves addition and the result is 5.
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Good Morning please help outt
The solution to the inequality given as 3 - x/2x + 1 ≥ 2 is (-oo, -1/2) u [1/5, oo]
How to determine the solution to the inequality?The inequality expression is given as
3 - x/2x + 1 ≥ 2
Cross multiply in the above inequality
So, we have
3 - x ≥ 2(2x + 1)
Open the brackets in the inequality
So, we have
3 - x ≥ 4x + 2
Collect the like terms
4x + x ≤ 3 - 2
Evaluate the like terms
5x ≤ 1
Divide by 5
x ≤ 1/5
Because of the denominator 2x + 1, we have
x > -1/2
This means that the solution is (-oo, -1/2) u [1/5, oo]
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x+6x-5x=x+114 Please help.
combine the like terms to create an equivalent expression -4r - 2r + 5
Answer:8r+7-6r-5Combine the like terms=8r-6r+7-5Thenafter, simplify=2r+2
good luck
Step-by-step explanation:
a restaurant employs 16 people, 8 of whom are women. if five employees are chosen randomly to receive tickets to a concert, what is the probability (to two decimal places) that three of them will be women? use the hypergeometric distribution.
The probability that 3 of the people chosen would be women = 0.36.
Probability is basically a numerical description of how likely an event is supposed to happen. It is a number something between 0 and 1.
total number of people = 16
total number of women = 8
number of chosen employees randomly to receive tickets to a concert = 5
probability to find = that 3 of them will be women
Therefore, we can conclude that the probability of 3 of the chosen people will be women is 0.36.
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What is the slope of this line?
Enter your answer as a whole number or a fraction in simplest form in the box.
Answer:
1/4
Step-by-step explanation:
The points (-4, 5) and (0, 6) lie on the line. Substituting into the slope formula,
[tex]\frac{6-5}{0-(-4)}=\frac{1}{4}[/tex]
z + mx = yx Solve for x
Answer:
[tex]X=\frac{-z}{m-y}[/tex]
Step-by-step explanation:
simplify the expression then write a rule for the pattern (√t)²
The expression of (√t)² is t.
What are square and square roots?A number can be squared, but it can also be divided into its square root. The value we get from multiplying a number by itself yields its square value, whereas the value we get from finding a number that, when squared, yields the original value of the number yields its square root value. In the event that 'a' is the square root of 'b,' then a a = b. Any number has two square roots, one with a positive value and the other with a negative value, because any number's square is always a positive number. As an illustration, the square root of 4 has the values 2 and -2. A number's power 1/2 value is represented by a number's square root. In other words.
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A bag of 5 blue, 3 red, 6 green, 9 orange, and 20 black marbles. what is the ratio of the number of blue marbles to the number of marbles that are orange or green?
The ratio of the number of blue marbles to the number of marbles that are orange or green is 1 : 3.
Ratio is defined as the relationship between two quantities. It can be expressed as a to b, a/b, or a : b.
Let a = total number of blue marbles
b = total number of orange and green marbles
If the total number of blue marbles is 5 and the total number of orange and green marbles are 9 and 6, respectively, then the ratio is 5 to (9 + 6).
Simplify the ratio.
5 : (9 + 6) = 5 : 15 = 1 : 3
Hence, the ratio is 1:3.
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please help thank you, due soon
Answer:
8.1
Step-by-step explanation:
just calculate 45 of 18%
FREE BRAINlIEST IF CORRECT: Find an equation of the perpendicular bisector of the segment AB with endpoints A(1, 2) and B(–3, 4). If the perpendicular bisector of AB intersects the x‑axis at point P, what are the lengths of PA and PB ?
The lengths of PA and PB are 3.1622 units if the point is P (0, 5).
What is the distance between two points?The distance between two points is defined as the length of the line segment between two places representing their distance. Most significantly, segments that have the same length are referred to as congruent segments and the distance between two places is always positive.
The formula of the distance between two points exists P(x₁, y₁) and Q(x₂, y₂) is given by:
d (P, Q) = √ (x₂ – x₁)² + (y₂ – y₁) ².
The given points exists A(1, 2) and B(–3, 4).
The perpendicular bisector of AB will pass through the midpoint of AB.
Now the perpendicular bisector of AB will meet the Y-axis at P(0, y).
∴ AP = BP
Applying the distance formula, we get4
⇒ PA² = PB²
⇒ (x₁ – 0)² + (y₁ – y)² = (x₂ – 0)² + (y₂ – y)²
⇒ (1 – 0)² + (2 – y)² = (–3 – 0)² + (4 – y)²
After solving, we get y = 5
Therefore, the point is P (0, 5).
Now calculating the lengths of PA and PB
PA = √(1 – 0)² + (2 – 5)² = 3.1622
PB = √(-3 – 0)² + (4 – 5)² = 3.1622
Therefore, the lengths of PA and PB are 3.1622 units.
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One month Ivan rented 8 movies and 3 video games for a total of $43. The next month he rented 2 movies and 5 video games for a total of $32. Find the rental cost for each movie and each video game.
Given
Let's represent movies with M
Let's represent video with V
[tex]\begin{gathered} 8m+3v=43\ldots\text{Equation 1} \\ 2m+5v=32\ldots\text{Equation 2} \end{gathered}[/tex]Solution
Using substitution method
I will solve your system by substitution.
[tex]\begin{gathered} 8m+3v=43\ldots\text{Equation 1} \\ \text{Make M the subject of the formula} \\ 8m=43-3v \\ \text{Divide both sides by 8} \\ m=\frac{43-3v}{8}\ldots\text{Equation 3} \end{gathered}[/tex]Substitute for m in Equation 2
[tex]\begin{gathered} 2(\frac{43-3v}{8})+5v=32 \\ \\ \frac{43-3v}{4}+5v=32 \\ \end{gathered}[/tex]To clear the fraction multiply all through by 4
[tex]\begin{gathered} \frac{43-3v}{4}\times4+5v\times4=32\times4 \\ \\ \\ 43-3v+20v=128 \end{gathered}[/tex]Separate the similar term
[tex]\begin{gathered} -3v+20v=128-43 \\ 17v=85 \\ \text{Divide both sides by 17} \\ \frac{17v}{17}=\frac{85}{17} \\ \\ v=5 \end{gathered}[/tex]Substitute for v =5 in equation 3
[tex]\begin{gathered} m=\frac{43-3v}{8}\ldots\text{Equation 3} \\ m=\frac{43-3(5)}{8} \\ m=\frac{43-15}{8} \\ \\ m=\frac{28}{8} \\ \\ m=\frac{7}{2}=3.5 \end{gathered}[/tex]The rental cost for each movie
[tex]m=\text{ \$}3.50[/tex]The rental cost for each video game.
[tex]v=\text{ \$5}[/tex]Change baseround final answer to nearest ten thousandONLY INCLUDE THE NUMBER OF YOUR FINAL ANSWER
We can solve this by means of the change of base formula:
[tex]a^y=x,y=\log _ax[/tex]By replacing x for y, 3 for a, and 27.3 for x into the above formula, we get:
[tex]x=\log _327.3=3.0101[/tex]Then, x = 3.0101
Write a multiplication problem with two fractions that has a simplified product of 4/5.
A problem that consists of the multiplication of two fractions, and in which the simplified product is 4/5 is presented as follows;
[tex] \displaystyle {\frac{14}{15} \times \frac{6}{7} = \frac{4}{5} }[/tex]
What is a fraction in mathematics?A fraction consists of a number that is expressed as a quotient, such that the numerator is being divided by the value in the denominator.
The multiplication problem with two fractions that ha a simplified product of 4/5 is found as follows;
let the fractions be [tex] \displaystyle \frac{a}{b} [/tex] and [tex] \displaystyle \frac{c}{d} [/tex]
The multiplication product is therefore;
[tex] \displaystyle \frac{a}{b} \times \frac{c}{d} = \frac{a \cdot c}{b\cdot d} = \frac{4}{5}[/tex]
The lowest common multiple of a and c is 4, while the lowest common multiple of b and d is 5
Taking b as 15, and a as 14 and c as 6, while d is taken as 7, such that we have;
[tex] \displaystyle {\frac{14}{15} \times \frac{6}{7} =\frac{2 \times 7}{5 \times 3} \times \frac{2 \times 3}{7} = \frac{2 \times 2}{5 \times 1} =\frac{4}{5} }[/tex]
The multiplication problem is therefore;
[tex] \displaystyle {\frac{14}{15} \times \frac{6}{7} = \frac{4}{5} }[/tex]
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answer pls
1. A surfer paddles out past breaking waves, rides a
wave, paddles back out past the breaking waves,
rides another wave back to the beach. Draw a sketch
of a graph (with labels) that shows the surfer’s
possible distance from the beach over time.
2. For the table, identify the independent and
dependent variables, Represent the relationship
using words, an equation and a graph.
# of cases of
bottled
water, c
# of bottles
of water,
b
1 24
2 48
5 120
10 240
20 480
for this one i only need the graph cannot find it out
3. Sketch a graph of the function shown by the table. Is
its linear or nonlinear?
x y
1 0
2 1
3 8
4 20
5. Write a function rule to represent the situation:
The volume, V, remaining in a 243 ft3 pile of gravel
decreases by .2 ft3 with each shovelful, s, of gravel
spread in a walkway
Tell whether the relation is a function. Explain your
reasoning.
{(-1, 7), (9, 4), (3, -2), (5, 3) , (9, 1)
7. Tell whether the relation is a function. Explain your
reasoning. find graph below
Describe the pattern in the sequence. Find the next
two terms of the difference.
-2, -5, -8, -11,
the graph for 7
Answer:
V = 243 - 0.2s
Step-by-step explanation:
See attached document for questions 1 - 3.
5. Write a function rule to represent the situation:
The volume, V, remaining in a 243 ft3 pile of gravel
decreases by .2 ft3 with each shovelful, s, of gravel
spread in a walkway.
Volume Remaining (V) = Initial - Used
Volume Remaining (V) = 243 ft^3 - (0.2 ft^3/shovel)(s shovels)
V = 243 - 0.2s
6. Tell whether the relation is a function. Explain your
reasoning.
{(-1, 7), (9, 4), (3, -2), (5, 3) , (9, 1)
This is not a function. When x = 8, it results in more than one output.
7. Pattern:
-2
-5
-8
-11
Each step decreases by 3
-14
-17
8.
Use BIMDAS to calculate my fortnightly earnings.
I have two part-time jobs.
3 days per week I work for 6 hours each day and I earn $20.00 per hour. For 2 days per week, I earn $25.00 per hour, working an 8-hour day.
Based on your earnings from each of the part-time jobs, your fortnightly earnings would be $1,520
How to find the earnings?First, find out how much you earn in the first part-time job per week:
= (Number of days per week x Number of hours per day x Pay per hour)
= (3 x 6 x 20)
The find out how much you earn in the second part-time job:
= (Number of days per week x Number of hours per day x Pay per hour)
= (2 x 8 x 25)
In a fortnight (two weeks), your earnings would be:
= (2 weeks x (3 x 6 x 20)) + (2 weeks x (2 x 8 x 25))
= (2 x 360) + (2 x 400)
= 720 + 800
= $1,520
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Fortnightly earnings would be $1,520 based on previous earnings.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that there are two part time jobs.
For first part time
3 days per week I work for 6 hours each day and I earn $20.00 per hour
(3 x 6 x 20)
=360
Second part time
2 days per week, I earn $25.00 per hour, working an 8-hour day.
=2×25×8
=400
Now we need to calculate, the total fortnightly earnings.
= (2 weeks x360) + (2 weeks x 400)
= (2 x 360) + (2 x 400)
= 720 + 800
= $1,520
Hence $1520 is the fortnightly earnings.
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write the linear equation in slope-intercept form passing through the point with the given slope. 1. (0,3):slope = -2 2. (-5,-3); slope = -3/5 3. (-8,6); slope 1/4 write the linear equation in slope-intercept form that passes through the given points. 4.
The equation of each line in slope-intercept form are:
1. y = -2x + 3
2. y = -3/5x - 6
3. y = 1/4x + 8
How to Write the Equation of a Line in Slope-intercept Form?If we are given a point (a, b) and the slope of a line (m), we can write the linear equation in slope-intercept form by first plugging in the given values into y - b = m(x - a), then rewrite it in the slope-intercept form as y = mx + b.
1. Slope (m) = -2
Point (a, b) = (0, 3)
Plug in the values into y - b = m(x - a):
y - 3 = -2(x - 0)
y - 3 = -2x + 0
y = -2x + 0 + 3
y = -2x + 3 [slope-intercept form]
2. Slope (m) = -3/5
Point (a, b) = (-5, -3)
Plug in the values into y - b = m(x - a):
y - (-3) = -3/5(x - (-5))
y + 3 = -3/5x - 3
y + 3 - 3 = -3/5x - 3 - 3
y = -3/5x - 6 [slope-intercept form]
3. Slope (m) = 1/4
Point (a, b) = (-8, 6)
Plug in the values into y - b = m(x - a):
y - 6 = 1/4(x - (-8))
y - 6 = 1/4(x + 8)
y - 6 = 1/4x + 2
y - 6 + 6 = 1/4x + 2 + 6
y = 1/4x + 8 [slope-intercept form]
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Draw a slope triangle, from point B, whose horizontal leg is along the x-axis. What are the lengths of the vertical and horizontal legs of your slope triangle?
Horizontal leg = 6 units
Vertical leg is 4 units
Lets Represent the diagonal as line AB where A and B are the endpoints of the line segment
The coordinates of point A is ( 12,4)
The coordinates of point B is ( 6,0)
Slope = ( Y2 - Y1 ) / (X2 -X1) = (0 - 4) / ( 6 - 12) = -4 / -6 = 2/3
or simply.
slope = rise / run = vertical leg/ horizontal leg = 4/6 = 2/3
ANSWER
Horizontal leg = 6 units
Vertical leg is 4 units
Slope = 2/3
A scientist has 2 3rd liter of solution. He uses 1 halfof the solution for an experiment. Howmuch solution does the scientist use forthe experiment?
SOLUTION
The total amout of solution given is
[tex]\frac{2}{3}\text{liter}[/tex]From thequestion, 1/2 of the solution is used, then the amount of solution used for the experiment will be
[tex]\frac{2}{3}\times\frac{1}{2}=\frac{2\times1}{3\times2}=\frac{2}{6}=\frac{1}{3}\text{liters }[/tex]Hence
The amount of solution the scientist use is 1/3 litres
What is the value of the missing segment? there is a ? , 4., 5 and 10
Step-by-step explanation:
I assume the ? is the left leg of the left triangle.
the middle line (right leg of the smaller left triangle, and the left leg of the larger right triangle) bisects the top angle of the main large triangle (because the top angles left and right from the middle line are equal).
that means per the angle bisector theorem
5 / 4 = 10 / ?
5 = 10×4/? = 40/?
?×5 = 40
? = 40/5 = 8
solve by graphing 6X + 3y equals 12 x + 4y equals 24
The system of equations is:
[tex]\begin{gathered} 6x+3y=12 \\ 8x+4y=24 \end{gathered}[/tex]To solve the system of equations by graphing, we need to make a graph of each equation. For that, we solve for y in both equations:
[tex]\begin{gathered} \text{Solving the first equation for y:} \\ 6x+3y=12 \\ 3x=-6x+12 \\ y=-2x+4 \\ \text{Solving the second equation for y:} \\ 8x+4y=24 \\ 4y=-8x+24 \\ y=-2x+6 \end{gathered}[/tex]We have two equations to graph:
[tex]\begin{gathered} y=-2x+4 \\ y=-2x+6 \end{gathered}[/tex]Comparing with the slope-intercept equation:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
We can see that the slope of the two equations is m=-2, this means that the lines will have the same rate of change of -2 in y for every 1 in x. And one graph will cross the y-axis at 4 and the other at +6.
The graph of the two equations is shown in the following image:
Where the green line is the first equation, and the red line is the second equation.
There is no solution to this system of equations because the lines do not intersect each other.
A given triangle has vertices at (-3, 1) (2, 4) and (5, -3). If the triangle were rotated 180 degrees counterclockwise, the new coordinates would be:
The new coordinates when we rotate the triangle counterclockwise is (3, -1), (-2, -4), (-5, 3).
Given,
The triangle with vertices;
(-3, 1) (2, 4) and (5, -3).
We have to find the new coordinates, when the triangle rotated 180 degrees counter clockwise;
Here,
The vertices;
(-3, 1) (2, 4) and (5, -3).
When we rotate 180 degree counter clockwise, the plane changes not the point.
That is,
(-3, 1) becomes (3, -1)
(2, 4) becomes (-2, -4)
(5, -3) becomes (-5, 3)
That is,
The new coordinates when we rotate the triangle counterclockwise is (3, -1), (-2, -4), (-5, 3).
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The new coordinates when we rotate the triangle counterclockwise is (3, -1), (-2, -4), (-5, 3).
Given,
The triangle with vertices;
(-3, 1) (2, 4) and (5, -3).
We have to find the new coordinates, when the triangle rotated 180 degrees counter clockwise;
Here,
The vertices;
(-3, 1) (2, 4) and (5, -3).
When we rotate 180 degree counter clockwise, the plane changes not the point.
That is,
(-3, 1) becomes (3, -1)
(2, 4) becomes (-2, -4)
(5, -3) becomes (-5, 3)
That is,
The new coordinates when we rotate the triangle counterclockwise is (3, -1), (-2, -4), (-5, 3).
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11.4.4 Set F 10. The area of the trapezoid below is 24 square meters, the altitude is 4 meters, and the length of one base is 2 meters, What is the length, *, of the other base, in meters? 4 H. 10 K, 1211.4.4 Set F 10. The area of the trapezoid below is 24 square meters, the altitude is 4 meters, and the length of one base is 2 meters. What is the length, x, of the other base, in meters?
The length, [tex]x[/tex], of the other base, in meters is 10.
The area of trapezoid = 24 square meters
The altitude = 4 meters
The length of one base = 2 meters
We have to find the length [tex]x[/tex] of the other base in meters.
To find the value of the length [tex]x[/tex] we use formula of area of trapezoid.
We use the area of trapezoid to find the value of length [tex]x[/tex] because we know the value of area of trapezoid, length of one base and altitude.
As we know the formula of area of the trapezoid
[tex]A=\frac{a+b}{2}\times H[/tex]
In the formula,
[tex]A=[/tex] area of trapezoid
[tex]a[/tex] and [tex]b[/tex] are the two length of two different base of the trapezoid
[tex]H=[/tex] height or altitude of the trapezoid
From the given question, [tex]A[/tex] = 24 square meters, [tex]a=x[/tex] meter, [tex]b[/tex] = 2 meters and [tex]h[/tex] = 4 meters.
Now putting the values in the formula.
[tex]24=\frac{x+2}{2}\times 4[/tex]
[tex]24=(x+2)\times 2[/tex]
Divide by [tex]2[/tex] on both side
[tex]\frac{24}{2} =\frac{(x+2)\times 2}{2}[/tex]
[tex]12=x+2[/tex]
Subtract [tex]2[/tex] on both side
[tex]12-2=x+2-2[/tex]
[tex]10=x[/tex]
[tex]x=10[/tex]
Hence, the length, [tex]x[/tex], of the other base, in meters is 10.
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Emilio borrows $1200 from a bank with 8% simple interest per year.How much will he have to pay back total in 2 years
The amount of money that Emilio will pay back in two years is $1392.00.
What is the accrued amount of the loan?The accrued amount includes principal plus interest.
Simple interest formula can be expressed as;
A = P( 1 + rt )
Where A is accrued amount, P is principal, r is rate and t is time elapsed.
Given the data in the question;
Principal P = $1200Simple interest rate r = 8%Time t = 2 yearsAccrued amount A = ?First, converting percent to decimal.
Rate r = 8% = 8/100 = 0.08
Now, plug the given values into the above formula and solve for the accrued amount.
A = P( 1 + rt )
A = $1200( 1 + 0.08 × 2 )
A = $1200( 1 + 0.16 )
A = $1200( 1.16 )
A = $1392.00
Therefore, the accrued amount is $1392.00.
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Solve system of equation by substitution
7y=-2x+5
3x+10y=6
Answer:
x= -8/41
y= 27/41
Step-by-step explanation:
7y=2x+5
3x+10y=6
maybe divide all parts of first equation by 7 to leave y by itself: y=2/7x+5/7
Then plug that in for y in the second equation:
3x+10(2/7x+5/7)=6
Then just solve for x:
x= -8/41
Substitute value of x into first equation:
7y=2(-8/41)+5
Solve for y:
y=27/41
In systems of equations, the values of x and y are -8 and 3, respectively.
Given systems of equations are:
7y=-2x+5 .....(i)
3x+10y=6 .....(ii)
We want both equations to be in standard form (Ax + By = C) so we need to fix the first equation.
For the equation (i), simply add 2x from both sides, so that x & y are on the same side of the equal sign
2x + 7y = 5 .....(i)
3x + 10y = 6 .....(ii)
To get the same x value in both equations (i) and (ii), we must now multiply equation (i) by 3 and equation (ii) by 2.
3(2x + 7y = 5) .....(i)
2(3x + 10y = 6) .....(ii)
Simplify.
6x + 21y = 15 .....(i)
6x + 20y = 12 .....(ii)
Now, subtract equations (ii) from (i)
y = 3
Now, substitute value of y = 3 in equation (i).
2x + 7y = 5 .....(i)
2x + 7(3) = 5
2x + 21 = 5
Then, subtract 21 from both sides.
2x + 21 - 21 = 5 - 21
2x = - 16
Divide both sides by 2.
2x / 2 = - 16 / 2
x = -8
So, x = -8 & y = 3
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