By applying Cramer's rule as solution method, the solution of the linear system 3 · x + 2 · y = 5 and x + 3 · y = 4 is equal to the set (x, y) = (1, 1).
How to solve a system of two linear equations with two variables
Determinants are constructions studied in linear algebra and related to matrices, one of the most common applications of determinants is the solution of linear equations, whose simplest form is known as the Cramer's rule.
Now we proceed to use this rule to get the solution of the linear system:
[tex]x = \frac{\left|\begin{array}{cc}5&2\\4&3\end{array}\right| }{\left|\begin{array}{cc}3&2\\1&3\end{array}\right|}[/tex]
[tex]x = \frac{(5)\cdot (3)-(4)\cdot (2)}{(3)\cdot (3) -(1)\cdot (2)}[/tex]
x = 1
[tex]y = \frac{\left|\begin{array}{cc}3&5\\1&4\end{array}\right| }{\left|\begin{array}{cc}3&2\\1&3\end{array}\right|}[/tex]
[tex]y = \frac{(3)\cdot (4) - (5)\cdot (1)}{(3)\cdot (3) - (1)\cdot (2)}[/tex]
y = 1
By applying Cramer's rule as solution method, the solution of the linear system 3 · x + 2 · y = 5 and x + 3 · y = 4 is equal to the set (x, y) = (1, 1).
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What is the factored form of X^9+27 A (x^3-3)(x^6+3x^3+9) B(x^3+3)(x^6-3x^3+9) C(x-3)^3(x^6+3x^3+9) D(x+3)^3(x^6-3x^3+9)
Answer:
D
Step-by-step explanation:
Graph the equations to solve the system y=x+4 y= -x - 6
Answer:
(-5, -1)
General Formulas and Concepts:
Algebra I
Functions
Graphing
Reading a Cartesian PlaneCoordinates (x, y)Solving systems of equations by graphing
Step-by-step explanation:
Where the 2 equations intersect is the solution to the systems of equations.
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A researcher reports that the standard deviation in population is A is q= 2.3 and the standard deviation in population B is q=4.3. Which population is associated with the highest power to detect an effect?
Answer:
Population A
Step-by-step explanation:
Usually in statistics, the more we increase the sample size, the more the standard deviation decreases. Similarly, the more we decrease the sample size, the more the standard deviation increases.
Finally, the more the standard deviation or error of Variance the lesser the power to detect an effect.
In this question, Population B has a greater standard deviation and thus would not have as much power as Population A in detecting an effect.
Thus Population A with standard deviation of 2.3 will have highest power to detect an effect.
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Find the measure of angle B
Explain and show work!
Answer:
B = 135
Step-by-step explanation:
You take A and subtract 180 to find B.
As it is a parallelogram opposite sides are same
[tex]\\ \sf\longmapsto <B=<D[/tex]
[tex]\\ \sf\longmapsto <A=<C[/tex]
<A=45[tex]\\ \sf\longmapsto <C=<A=45°[/tex]
What value of b completes the function f(x)=-x^2+bx+1?
Answer:
Step-by-step explanation:
It is hard to guess the coordinates of any points, because the graph doesn't go through any intersections of the grid.
Fortunately, I can tell that the axis of symmetry is x=2.
Put the equation into vertex form by completing the square.
axis of symmetry = b/2
b/2 = 2
b = 4
Which of the following can be used to prove that AABC = AADC?
Answer:
AAS postulate
Step-by-step explanation:
Answer:
i hope it help u:))
Step-by-step explanation:
i think that it will be ASA postulate
In a sale the price of a bike is reduced by 40% the sale price of the bike is £192 how much did the bike cost before the sale?
Answer:
£268.8
Step-by-step explanation:
192 = 100%
19.2= 10%
19.2 x 4 = 76.8
76.8 = 10%
76.8 + 192 = 268.8
I hope this helped :)
Kiran scored 223 more points in a computer game than Tyler. If Kiran scored 409
points, how many points did Tyler score?
Answer:
186
Step-by-step explanation:
Tyler: 223 less than Kiran
Kiran: 409
409 - 223 = 186
87°
A
74°
C
B
What is mZB?
mZB =
O
using Inscribed Quadrilateral Theorem
Answer:
m<B = 93°
Step-by-step explanation:
Based on the inscribed quadrilateral theorem, the opposite angles of a cyclic quadrilateral are supplementary.
Thus:
m<B + m<D = 180°
Substitute
m<B + 87° = 180°
m<B = 180° - 87°
m<B = 93°
Classmates Joan, Peta, and Linda each received $400 as graduation gift. Joan deposits her money in an account that earns 7% interest compounded annually and keeps the money in the account for three years. Peta deposits her money, plus an extra $70, in an account that earns 8% interest compounded annually and keeps the money in the account for two years. Linda deposits her money in an account that earns 5% compounded'annually and keeps the money in the account for one year.
Who has more money when they close their accounts and why?
A) Joan, because she kept her money in the longest.
B) Linda, because of her interest rate.
C) Peta, because she invests the most.
D) They all make the same amount.
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Answer:
C) Peta, because she invests the most
Step-by-step explanation:
The additional $70 that Peta invests is equivalent to more than 2 years' interest at either of the other rates. Not only does Peta invest more money, she does so at a higher interest rate.
Peta will have the most money in her account when she closes it.
__
The balances will be ...
Joan $490.02
Peta $548.21
Linda $420.00
Help&EXPLAIN
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Help plz
Answer:
diameter = 2.5 feet
Step-by-step explanation:
Circumference of a circle is given as C = πd
Circumference of the tree trunk = 7.85 ft
π = 3.14
Diameter of the tree trunk = d
Thus:
7.85 = 3.14*d
Divide both sides by 3.14
7.85/3.14 = 3.14*d/3.14
2.5 = d
d = 2.5 ft
Fine the slope of the line through (20, -8), (9, -8)
Answer: The slope is 0
Whoever answer is correct gets brainleiest .
Answer:
9/24 for the first and 8/24
Find the vertex of the function. ill mark brainlist
Answer:
(2,-9)
Step-by-step explanation:
Sarah makes $3000 contributions at the end of each half-year to a retirement account for 8 years. For the next 20 years, she makes no additional contributions and no withdrawals. If the account earns 7.5%, compounded semi-annually, find the value of the account after the 28 years.
(b) If the above account is used to set up an annuity that pays her an amount at the beginning of each 6-month period for the next 20 years, how much will each payment be?
Answer:
I think its aa.... I think its aa.... Carrot
Step-by-step explanation:
Jack collected 18 ten dollar bills while selling tickets for a show. He gave 1 over 6 of the bills to the theater and kept the rest. How much money did he keep?
Answer:
150
Step-by-step explanation:
Collected bills: 18 * 10= 180
1/6 of 180 = 30
180-30=150
Answer:
15 ten dollar bills, 150 dollars
Step-by-step explanation:
1/6 of 18 is 3, so he gave 3 bills to the theater and kept the other 15 for himself
Activity
Part A
Match the factors affecting cost to their definitions. Write the name of the factor next to its definition
Answer:
cost of materials - the value of all things needed to create the good or service
opportunity cost - the value of a product given up to produce or obtain another product
fixed cost - costs that are not affected by the level of production
sunk cost - past costs that cannot be recovered
marginal cost - change in total cost that arises when the quantity produced changes by one unit
Step-by-step explanation:
Answer:
cost of materials: the value of all things needed to create the good or service
opportunity cost: the value of a product given up to produce or obtain another product
fixed cost: costs that are not affected by the level of production
sunk cost: past costs that cannot be recovered
marginal cost: change in total cost that arises when the quantity produced changes by one unit
3. If a week is 7 days, what fraction of a week is 2 days?
3
a) The average rainfall of the last week was 35 mm. If the records of daily
rainfall from Sunday to Friday were 45 mm, 22 mm, 28 mm, 36 mm, 30 mm
and 24 mm, find the rainfall on Saturday.
Answer:
The rainfall on Saturday was of 60 mm.
Step-by-step explanation:
Average rainfall:
The average rainfall is given by the total rainfall divided by the number of days(7). So
If the records of daily rainfall from Sunday to Friday were 45 mm, 22 mm, 28 mm, 36 mm, 30 mm and 24 mm
On Saturday it was of x mm. So
[tex]35 = \frac{45 + 22 + 28 + 36 + 30 + 24 + x}{7}[/tex]
[tex]185 + x = 245[/tex]
[tex]x = 245 - 185[/tex]
[tex]x = 60[/tex]
The rainfall on Saturday was of 60 mm.
Helen makes 6 friendship bracelets . She gave 1/3 of the bracelets to sami which expression can i use
Answer:
6 x 1/3 = 2
Step-by-step explanation:
There are two squares.ONe has a side length of 12 inches and the other has a side length of 14 inches.What is he total area of both squares?
Answer:
340 in^2
Step-by-step explanation:
1. First square
A = l*w = 12^2 OR 12*12 = 144
2. Second square
A = l*w = 14^2 OR 14*14 = 196
3. Combined Area
144+196=340
The area of a square is found by squaring the side length, which is the same as multiplying two of the sides together.
Square 1: 12 x 12 = 144 square inches.
Square 2: 14 x 14 = 196 square inches.
Total area = 144 + 196 = 340 square inches.
what's the answer! Consider having a personal loan that spans 5 years. The loan was only taken out for $6000, but the interest rate was a higher fixed percentage of 5.99%. How much interest will you have paid after it is paid off?
Answer: $179.70
Step-by-step explanation:
The simple interest will be:
= (Principal × Rate × Time) / 100
= ($6000 × 5.99% × 5) / 10
= ($6000 × 0.0599 × 5) / 10
= $1797 / 10
= $179.70
Therefore, the total interest on the loan is $179.70
Question 1
Select all expressions that are equivalent to 64.
A. 2 to the power of 6
B.2 to the power of 8
C.4 to the power of 3
D. 8 to the power of 2
E. 16 to the power of 4
F. 32 to the power of 2
As a percentage, $9.00 is equal to
What % of $20.00.
Answer:
45%
Step-by-step explanation:
let's say 20 is 100%
10 is 50%
then 10 divided by 5 (to get 10%) is 2
so 1 is 5%
then we wanna get 9 so we do 10-1 which equals the percentages 50-5 to get 45%
1)1/4+1/2
2)7/10-3/5
3)1/2-2/6
With lowest term
Thank you who answer my question
p -> q is false and p is true.
q is
True
False
Answer:
q is false
Step-by-step explanation:
Answer:
q is false
Step-by-step explanation:
for a conditional statement, if the first part (if....) is true and second part is false, then p->q will be false. This is THE ONLY CASE IN CONDITIONAL STATEMENT where the truth value is false.
In this figure what is the value of v
50 points!!!! Assuming all parabolas are of the form y = ax^2+ bx + c, drag and drop the graphs
to match the appropriate a-value.
Answer:
Step-by-step explanation:
a > 0 for an up-opening parabola, so a = 0.25 for the third graph.
The greater the magnitude of a, the skinnier the parabola.
|-1| < |-4|, so a = -4 for the first graph.
Which triangle can be used to find the slope of the line shown? explain your answer
Answer:
A right triangle contains a right angle, so it must have two sides that are perpendicular. If the slopes of two sides can be shown to be negative reciprocals of each other, then it can be concluded that a right angle is formed. If a triangle contains a right angle, then it is a right triangle
Step-by-step explanation:
to determine if a triangle is a right triangle using slopes, you have to understand perpendicular slopes/negative reciprocals.
You can calculate the slope of all 3 sides of the triangle and if two of the slopes are negative reciprocals, then those two lines intersect creating a right angle/right triangle.
Let's say there's triangle ABC.
If the slope of AB is 1/2
and the slope of BC is 2/5
and the slope of CA is -2/1
then AB and CA intersect resulting in a right angle (triangle).