Solve the system using a matrix,
3x – 2y = 2
6x - 5y = -1
Answers
9514 1404 393
Answer:
(x, y) = (4, 5)
Step-by-step explanation:
The solution to the matrix equation ...
[tex]\left[\begin{array}{cc}3&-2\\6&-5\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right] =\left[\begin{array}{c}2\\-1\end{array}\right][/tex]
is shown in the attachment. It is found by multiplying the equation on the left by the inverse of the coefficient matrix.
[tex]\left[\begin{array}{c}x\\y\end{array}\right] =\left[\begin{array}{c}4\\5\end{array}\right][/tex]
Related Questions
You borrow $600 to buy a canoe. The simple annual interest rate is 5%. You pay off the loan after 4 years of equal monthly payments. How much is each payment?
Answers
Answer:
Amount of each payment = $15 each month
Step-by-step explanation:
Given:
Amount borrow = $600
Simple rate = 5% = 0.05
Number of year = 4 year
Payment method = monthly payment
Find:
Amount of each payment
Computation:
Total amount after 4 year = P + PRT
Total amount after 4 year = 600 + (600)(4)(0.05)
Total amount after 4 year = 600 + 120
Total amount after 4 year = $720
Number of total month = 4 x 12
Number of total month = 48
Amount of each payment = Total amount after 4 year / Number of total month
Amount of each payment = $720 / 48
Amount of each payment = $15 each month
Figure A ~ Figure B
Figure A
Figure B
1 ft
3 ft
V = 6 cu ft
Find the volume of Figure A.
Answers
Answer:
the answer is
162ft3
Step-by-step explanation:
Jayda is watching a movie that lasts 1 hour and 37 minutes. She has watched 52 minutes so far. How many minutes are left in the movie? *
Answers
Answer:
45 minutes
Step-by-step explanation:
97-52 = 45
Mary wants her friend to guess how many cards she has in her hand. She says that if the number of cards in her hand is tripled, and 4 are added, then she has 22 cards.
Answers
Answer:
22 minus 4 = 18
18 divided by 3 is equal to 6
then following from the question now that we got the answer
so she have 6 cards first then it tripled and now it's 18 Then she added four now it's 22
your welcome
Answer:
6
Step-by-step explanation:
let x be the number of cards
3x + 4 = 22
3x = 18
x = 6
Eileen plant a tree that is 2 meters tall in her yard which of the following is equivalent to meters following is equivalent to 2 meters?
(A) 200 mm
(B) 20 cm
(C) 200 km
(D) 2,000 mm
Answers
Answer:
D
Step-by-step explanation:
Answer: (d)
Step-by-step explanation:
Can someone help me pls
Answers
Answer:
AB = 18
Step-by-step explanation:
tan 45° = 18/AB
1 = 18/AB
AB = 18
A box of chocolates was shared evenly between 5 people. Each person received 4 chocolates.
How many chocolates were in the box?
Answers
Answer:
20
Step-by-step explanation:
5x4=20
plz give me a thx! IF I HELPED :)
A movie theater has 940 seats. Tickets were sold for 846 of the seats. For what percent of the seats were tickets sold?
Answers
Answer:
90 percent
Step-by-step explanation:
If a= 35 then find b
Answers
9514 1404 393
Answer:
35
Step-by-step explanation:
All of the marked angles subtend the same arc, so all have the same measure.
a = b = c = d = 35
b = 35
You need a 90% alcohol solution. On hand, you have a 55 mL of a 45% alcohol mixture. You also have 95% alcohol mixture. How much of the 95% mixture will you need to add to obtain the desired solution?
Answers
Answer:
495 milliliters of the 95% mixture are needed.
Step-by-step explanation:
Given that I need a 90% alcohol solution, and on hand I have a 55 ml of a 45% alcohol mixture, and I also have 95% alcohol mixture, to determine how much of the 95% mixture will I need to add to obtain the desired solution, the following calculation must be performed:
55 x 0.45 + 45 x 0.95 = 67.5
25 x 0.45 + 75 x 0.95 = 82.5
15 x 0.45 + 85 x 0.95 = 87.5
10 x 0.45 + 90 x 0.95 = 90
10 = 55
90 = X
90 x 55/10 = X
4,950 / 10 = X
495 = X
Thus, 495 milliliters of the 95% mixture are needed.
Which equation finds the length of side c of this right triangle
Answers
Answer:
Find The Length Of The Side Of A Right Triangle : Example Question #1. Explanation: The Pythagorean Theorem gives us a2 + b2 = c2 for a right triangle, where c is the hypotenuse and a and b are the smaller sides.
Step-by-step explanation:
Answer:
see below
Step-by-step explanation:
Use the Pythagorean Theorem to find c:
a² + b² = c²
√a² + b² = √c²
c = √a² +b²
Tarzan leaned a 100-foot ladder against the side of a building. The
hase of the ladder is 18 feet from the base of the building. The top of
the ladder is 16 feet from the top of the building How tall, to the
narest tenth of a foot, is the building?
16
100
18
Answers
Answer:
is 16 foot a part from the building
Which table shows ordered pairs that satisfy the function y = x + 1?
А
X
12
0
2
- 4
1
4
B
-2
0
2
5
0
5
С
X
y
5
-2
0
2.
1
5
D
x
y
-24
0 2
2 4
Answers
Answer:
Knowledge Check The table of ordered pairs (x, y) gives an exponential function. Write an equation for the function. x y -1 6 0 12 1 1 24 2. 48 88 O х ? I Don't ...
Step-by-step explanation:
Un círculo tiene una circunferencia de 18.4 m. Determina el valor del radio. (Utiliza el valor de π = 3.14)
Answers
Answer: 2.92
Step-by-step explanation:
De la circunferencia del círculo, se encuentra que su radio es de 2.93m.
El circunferencia de un círculo de radio r es dada por:
[tex]C = 2\pi r = 2(3.14)r = 6.28r[/tex]
En este problema, la circunferencia es de 18.4. Así, es posible aplicar la fórmula de la cincumference para encontrar su radio, puesto que [tex]C = 18.4[/tex].
[tex]C = 6.28r[/tex]
[tex]6.28r = 18.4[/tex]
[tex]r = \frac{18.4}{6.28}[/tex]
[tex]r = 2.93[/tex]
El radio es de 2.93m.
Un problema similar es dado en https://brainly.com/question/24562611
Find the area of each figure.
Answers
1536in (for rectangle). 288in (for triangle)
Area of rectangle: 48in* 32in = 1536 in
Area of triangle: 48in*12in÷1/2= 576/2=288in
Formula of area of triangle is b*h divided by 2
Formula of area of rectangle is length*width
Hope this helps!
3 When 25 x+2y-* x-12y+3) x-1ży+3) is simplified, what is the resulting expression? 1 Tox+23y+6 7. x+23y+6 x+85y+8 1 Tox+4*x+3
Answers
Answer:
B
Step-by-step explanation:
I pick a ball from a bag, replace it and then pick
another. I keep doing this until I have chosen 40 balls. If I picked out 12 yellow balls, estimate the probability of not picking out a yellow ball.
Answers
Answer:
It should be 50%
Step-by-step explanation:
It should be 50% because there are 12 yellow balls, so it should be 50%.
Hope it helps you
Which category do both of these shapes belong to
Answers
Answer:
D. Parallelogram
Step-by-step explanation:
Answer:
The answer is Parallelgram(D)
two pairs of parallel sides in a quadrilateral
hope it helps...
I need questions 1 , 2 ,3 answered please :)
Answers
9514 1404 393
Answer:
54°both are 73°x = 12Step-by-step explanation:
Some useful relations are ...
A triangle inscribed in a semicircle is a right triangle.
Acute angles in a right triangle are complementary.
An inscribed angle is half the measure of the arc it intercepts.
The sum of arcs around a circle is 360°; 180° around a semicircle.
__
1. Arc DF is twice the marked inscribed angle, so is 126°. Arc FE is supplementary to that, so is ...
arc FE = 180° -126°
arc FE = 54°
Alternate solution: arc FE is twice angle D, which is the complement of 63°.
2(90° -63°) = 2(27°) = 54° = arc FE
__
2. Arc GJ = 360°-68° -31° -115° = 146°
angle GHJ = angle GIJ = 146°/2 = 73°
__
3. arc UT = 2(90° -43°) = 94°
9x -14 = 94
9x = 108 . . . . . add 14
x = 12 . . . . . . . . divide by 9
In a large city school system with 20 elementary schools, the school board is considering the adoption of a new policy that would require elementary students to pass a test in order to be promoted to the next grade. The PTA wants to find out whether parents agree with this plan.
a. If they put a big ad in the newspaper asking people to log their opinions on the PTA Web site what kind of bias might they encounter.
1. response bias due to desire to give acceptable answers
2. nonresponse bias
3. bias due to the use of a voluntary response sample
4. bias due to a poor sampling frame resulting in undercoverage
5. no bias
b. If they randomly select one of the elementary schools and contact every parent by phone, what kind of bias is there?
1. bias due to the use of a voluntary response sample
2. response bias due to desire to give acceptable answers
3. undercoverage bias due to a poor sampling frame
4. no bias
5. nonresponse bias
c. Suppose they randomly select 20 parents from each elementary school. Send them a survey, and follow up with a phone call if they do not return the survey within a week. What kind of sampling was done?
1. stratified sampling
2. convenience sample
3. simple random sampling
4. voluntary response sample
Answers
Two catalysts may be used in a batch chemical process. Twelve batches were prepared using catalyst 1, resulting in an average yield of 84 and a sample standard deviation of 3. Fifteen batches were prepared using catalyst 2, and they resulted in an average yield of 90 with a standard deviation of 2. Assume that yield measurements are approximately normally distributed with the same standard deviation.
(A) Is there evidence to support the claim that catalyst 2 produces higher mean yield than catalyst 1? Use alpha = 0.01.
(B) Find a 99% confidence interval on the difference in mean yields that can be used to test the claim in part (a). (e.g. 98.76).
Answers
Answer:
Step-by-step explanation:
From the given information:
Let assume:
[tex]\mu_1 =[/tex] population mean for catalyst 1
[tex]\mu_2 =[/tex] population mean for catalyst 2
Then:
Null hypothesis: [tex]\mu_1 \ge \mu_2[/tex]
Alternative hypothesis: [tex]\mu_1 <\mu_2[/tex]
[tex]\alpha= 0.01[/tex]
By using MINITAB software to compute the 2 sample t-test, we have:
Two-Sample T_Test and CI
Sample N Mean StDev SE Mean
1 12 94.00 3.00 0.87
2 15 90.00 2.00 0.52
Difference = [tex]\mu_1(1)-\mu_2(2)[/tex]
Estimate of difference: -6.00
99% upper bound for difference: -3.603
T-test of difference: 0 (vs <): T-value = -6.22
P.value = 0.000
DF = 25
Both use Pooled StDev = 2.4900
From above result
the test statistics = -6.00
p-value = 0.00
Decision Rule: To reject [tex]H_o\ \ if \ \ p \le \alpha[/tex]
Conclusion: Provided that p-value is < ∝, we reject [tex]H_o[/tex]. Hence, there is sufficient evidence to support the given claim.
b) From the MINITAB;
The 99% C.I on the difference in the mean yields that can be applied to test the claim in part (a) is:
[tex]\mathbf{\mu_1 -\mu_2 \le -3.60}[/tex]
g(x) = 2x – 4
h(x)=x²-3
Find (g.h)(5)
Answers
Answer:
40
Step-by-step explanation:
This is asking you to plug in the value of h(5) into g(x). First solve for h(5)
x^2-3 = h(x)
5^2-3= 22
h(5) = 22
h(5) is 22. So now, plug that into g(x).
g(h(5)) = 2(22)-4
44-4=40
(g.h)(5) is 40.
Can someone help me pls
Answers
Answer:
Okay so for this one use the Pythagorean theorem
Step-by-step explanation:
A^2 + 28^2 = 128^2
You are trying to find A.
So 28^2 is 784
128^2 is 16384
Now you will subtract 784 from both sides of the equation your new equation should be this: a^2 = 15600
Now you find the square root of both sides which gives you: A= 124.89 round it to 125
Please help .. would be appreciated
Answers
Answer:
x = 30
Step-by-step explanation:
[tex] \triangle JLK\sim\triangle PQR[/tex] (given)
[tex] \therefore \frac{JL}{PQ}=\frac{LK}{QR} [/tex]
(corresponding sides of similar triangles)
[tex] \therefore \frac{20}{x}=\frac{22}{33} [/tex]
[tex] \therefore \frac{20}{x}=\frac{2}{3} [/tex]
[tex] \therefore x=\frac{20\times 3}{2} [/tex]
[tex] \therefore x=\frac{60}{2} [/tex]
[tex] \therefore x=30 [/tex]
Or using scale factor:
Scale factor = 33/22 = 3/2
x = 20*3/2
x = 10*3
x = 30
Give the system, X + y = 15 3x - y = 9, find the value of x and y
Answers
Answer:
(x,y)=(9/77,684/77)
Step-by-step explanation:
X + y = 15 3x - y = 9
=154x=18
x=9/77
9/77+y=9
y=684/77
=(x,y)=(9/77,684/77)
what is the slope of the line shown?
Answers
Additional Activities
BRAIN-COMPATIBLE
Activity 3
Directions: Determine the variable and constant in the given algebraic expression and
equation. Write your answer in your notebook.
Algebraic Expression and Equation
Variable
Constant
1) three more than y
2) p multiplied by 7
3) the quotient of x and four
4) sixteen subtracted from ten times k
5) twice the difference between twenty and
9
6) six times p decreased by twelve
7) twenty taken from eight-timesh
8) four times the sum of five and x
9) f multiplied by fifteen
10) twice d added to forty
Answers
Answer:
1. C: three | V: y
2. C: 7 | V: p
3. C: four | V: x
4. C: sixteen, ten | V: k
5. C: two, twenty | V: g (I believe that's a "g" and not a "9" due to OCR scanning! and even logically that should be a letter to represent the variable so that the expression is correct)
6. C: six, twelve | V: p
7. C: twenty, eight | V: h
8. C: four, five | V: x
9. C: fifteen | V: f
10. C: two, forty | V: d
Evaluate the expression.
-2.035 – 1.008 - 3.04 + 0.008
Answers
Answer:
-6.075
Step-by-step explanation:
simple addition/subtraction
we multiply all the terms by "-1"
we add the first three terms then subtract the last from it
Which of the following is the closest to the value of x
Answers
a customer asked for 48 oz of turkey lunch meat and 64 oz of cheese.How many pounds of lunch meat did the customer buy in total
Answers
Answer:
in order to get the total you must add add 48 + 64 whereby you get 112
Step-by-step explanation:
the the customer bought 112 pounds of meat hope that helps