Solve the system of linear equations using any method you choose:
-6x + 3y = 18
10x - y = 4
Answers
9514 1404 393
Answer:
(x, y) = (1.25, 8.5)
Step-by-step explanation:
I choose to put these equations into reduced general form, then use the "cross multiplication method" to solve.
2x -y +6 = 0
10x -y -4 = 0
d1 = 2(-1) -10(-1) = 8
d2 = -1(-4) -(-1)(6) = 10
d3 = 6(10) -(-4)(2) = 68
Solutions are ...
x = d2/d1 = 10/8 = 1.25
y = d3/d1 = 68/8 = 8.5
The solution is (x, y) = (1.25, 8.5).
_____
Additional comment
I like a graphing calculator for a quick and easy solution. When the values are not integers, I like an algebraic solution to see what the exact values are.
__
The "cross multiplication method" is similar to Cramer's rule in that determinants of pairs of coefficients are computed. If you look up this method, videos will show you a variation that is slightly different. Here, we determined d1, d2, and d3 as the 2×2 determinant of the coefficients in adjacent columns of the array you get from the general form equations with the first column repeated:
[tex]\begin{array}{cccc}2&-1&6&2\\10&-1&-4&10\end{array}[/tex]
In each pair, the determinant is the difference between the product of numbers on the down-diagonal and the product of numbers on the up-diagonal.
The determinants relate to the x- and y-values by ...
1/d1 = x/d2 = y/d3 ⇒ x = d2/d1, y = d3/d1
There is a Vedic solution method for linear equations that is similar to this, but starts from equations in standard form. As a consequence, the cross-differences are done in a different order.
__
Standard form: ax +by = c
General form: ax +by +c = 0
Related Questions
calculate the Geometric mean for the
distribution 8, 6, 3, 5 and 4
Answers
Answer:
Step-by-step explanation:
The geometric mean is the average of the 5 numbers
8 + 6 + 3 + 5 + 4 Just add.
Total = 26
There are 5 elements, so the average = 26/5 = 5.2
Here’s a freebie for the lucky people who answer this
79 - 10 =
A. 70
B. 7
C. 69
D. 6.9
430 - 10 =
A. 469
B. 421
C. 4.2.0
D. 420
Answers
Answer:
The answer is C.
The answer is D.
Step-by-step explanation:
Thank you:)
please help me !
• don’t use this for points, or send any gross links.
• if you actually KNOW the answer, please do comment / help me!
this is: KS3 — YEAR 8 ! ❤️
Answers
TICKET MONEY for age 16 and over,
155-49 =106
1 person pays £18.60
106 = 106 × £18.60
=£1,971.6
TICKET MONEY for under 16
1 person pays £12.80
49 people =49 × £12.80
= £627.2
TOTAL NUMBER OF TICKETS
£ 1,971.6 + £6272.2
= £2,598.8
3x + 3y = 9
-3x + 2y = 1
Answers
Answer:
X=1
Y=2
Step-by-step explanation:
put 1 in for X
3(1)+3(y)=9
-3(1)+2(y)=1
now put 2 for Y
3(2)+3(2)=9
-3(1)+2(2)=1
3•1= 3
3•2=6
3+6=9
-3•1=-3
2•2=4
-3+4=1
60 is the product of Javier's age and 5
Translate this sentence into an equation
Answers
Answer:
J= Javiers age
5J=60
5J/5= 60/5
J= 12
Check:
5(12)= 60
60=6p
Step-by-step explanation:
see answer
hope this helps
Azad wants to Buy a book he has 25,000 dinars which is 9000 dinars less than she needs does the book cost 34,000 Dinars or 16,000 dinars
Answers
Answer: 34,000 Dinars
Step-by-step explanation: As 25,000 + 9000 is 34,000
A number n is a prime factor of 28 and 63
Answers
Answer:
7
Step-by-step explanation:
The factors of 28 and 63 are
28 : 1, 2, 4, 7, 14, 28
63 : 1, 3, 7, 9, 21, 63
The common factors are 1 and 7
7 is a prime factor of both 28 and 63
5 div by 4=25 div by y
Answers
[tex]\dfrac 54 = \dfrac{25} y\\\\\\\implies \dfrac 14 = \dfrac 5y\\\\\implies y = 4 \times 5 =20[/tex]
Can someone help me with this please?
Answers
Answer:
0.5236 radians or 30 degrees
Step-by-step explanation:
We want to find the angle based on the opposite side and the hypotenuse. Therefore, we need to use the inverse sine function:
Θ = sin[tex]^{-1} (\frac{5}{10})[/tex]
Simplifying the function, we get:
Θ = sin[tex]^{-1} (\frac{1}{2})[/tex]
Inputting this into a calculator, we get Θ = 0.5236 radians or 30 degrees.
Step-by-step explanation:
sin θ = 5cm/10cm
sin θ = ½
sin θ = sin 30°
therefore, θ = 30°.
hope this helps you.
Which statement best explains if the graph correctly represents the proportional relationship y = −2x? A coordinate plane is shown. Points are graphed at negative 2 and 4 and negative 1 and 2. The points are joined by a line. It does not, the points shown would not be part of y = −2x. It does not, proportions cannot be represented on a graph. It does, all proportions can be shown on a graph of this line. It does, the points shown on the line would be part of y = −2x.
Answers
Answer:
d. It does, the points shown on the line would be part of y = −2x.
is the answer let me know if this helped
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
hope i helped
Write the equation of the line that passes through the given points.
(1,2.5) and (0,6.5)
Answers
let's change the decials first off to fractions and get the slope and line
[tex]2.\underline{5}\implies \cfrac{25}{1\underline{0}}\implies \cfrac{5}{2}~\hfill 6.\underline{5}\implies \cfrac{65}{1\underline{0}}\implies \cfrac{13}{2} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{1}~,~\stackrel{y_1}{\frac{5}{2}})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{\frac{13}{2}})[/tex]
[tex]\stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{\frac{13}{2}}-\stackrel{y1}{\frac{5}{2}}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{1}}}\implies \cfrac{~~ \frac{8}{2}~~}{-1}\implies \cfrac{4}{-1}\implies -4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{\cfrac{5}{2}}=\stackrel{m}{-4}(x-\stackrel{x_1}{1})[/tex]
[tex]y-\cfrac{5}{2}=-4x+4\implies y=-4x+4+\cfrac{5}{2}\implies y = -4x+\cfrac{13}{2}[/tex]
last month adhem ate 5 apples , 8 bananas , 7 Peaches , 10 oranges what the ratio of apples to the total of the fruit
Answers
Answer: 5:30
Step-by-step explanation: there are 5 apples and 30 total fruits.
Answer:
5:30 or simplified 1:6
Step-by-step explanation:
There are 30 fruits including the apples, and the apples only make up 5 of the fruits.
Suppose you plan to take a survey of Math 146 students asked about their overall grades at CBC. 22 students were surveyed, and it was found that the average GPA of the 22 sampled students was a 3.2, with a standard deviation of 0.9 points. Suppose you want to re-sample the population to reduce the margin of error. If you plan to calculate a 90% confidence interval for the true mean GPA of Math students, how many samples would be necessary to reduce the margin of error to 0.2 points?
Answers
Step-by-step explanation:
we have the data set given below here and using it, we want to find the sample mean X. Bar, the sample standard deviation S. And constructed 99% confidence interval for the population we knew, assuming the population is normally distributed. So since we have this data we can find expire and s using the appropriate definitions expire, is that some of the data divided by n 2.353 and s. Is the square root of the sum of deviations of the mean square divided by n minus one. In this case 1.3 Now with X. Bar and sample standard deviation S, we can use a student's t distribution to construct this confidence interval. So we can identify the appropriate T score. So for the degree of freedom and minus one equals 14 and critical values um providing probability 140.99 for the confidence interval, to identify T C equals 2.977 Now, with this T. C, we can identify the margin of error E, which is given by this formula plugging in our T C. S and N. We obtain E equals 0.572 And now plugging into our confidence interval formula, which is that new falls between a sample mean minus C, and sampling plus E gives us our confidence interval. That new is between 1.781 and 2.9 to 5 with 99% confidence.
Identify the figure and denote it by its appropriate symbol
ОА.
Half Line, AB
OB.
Ray
AB
O C. Line, AB
OD
Line Segment AB
Answers
Rays are a linear formation that start at a point and continue forever in a direction. The photo shows a point on one end, and an arrow on the other indicating that it starts at the point and continues forever past the arrow.
Use technology to find the P-value for the hypothesis test described below.
The claim is that for a smartphone carrier's data speeds at airports, the mean is p = 19.00 Mbps. The sample size is n = 21 and the test statistic is t= 1.401
P-value = (Round to three decimal places as needed)
Answers
Using the t-distribution, it is found that the p-value is of 0.177.
At the null hypothesis, it is tested that for a smartphone carrier's data speeds at airports, the mean is 19 Mbps, that is:
[tex]H_0: \mu = 19[/tex]
At the alternative hypothesis, it is tested if the mean is different than 19 Mbps, that is:
[tex]H_1: \mu \neq 19[/tex]
We are testing if the mean is different from a value, hence it is a two-tailed test.The test statistic is t = 1.401.Sample size of n = 21, hence there are 21 - 1 = 20 df.Inputting this information into a calculator, the p-value is of 0.177.
A similar problem is given at https://brainly.com/question/13873630
Order the following numbers from least to greatest.
|-1 1⁄2|, 1 3⁄4, |-1 1⁄5|, 1 2⁄5
Answers
Answer:
|- 1 1/5|, 1 2/5, |-1 1/2|, 1 3/4
Step-by-step explanation:
Please Help Me With this question.
Answers
Answer:
Y=76x
Step-by-step explanation:
if you divide 3 and 228 it is 76. if you divide 5 and 380 it is 76.if you divide 532 and 7 it is 76. and if you divide 11 and 836 it is 76.
Answer:
Step-by-step explanation:
The trick is to get rid of b in y = mx + b. The way to do that is to take 2 values and subtract them
(380 - 228) / (5 - 3) = 152/2 = 76
Not all problems work out this nicely.
The answer is
y = 76x
In this case you can be a little more direct. m = 380 ÷ 5 = 76, but not all equations are this well behaved and doing it the long way is the best way.
3. Marilyn hit a golf ball on the ground with her driver. Use
the general function for a projectile to write a function
that shows the height in feet of her golf ball as a function
of time. The ball was hit with an initial vertical velocity of
130 feet per second.
h(t) = -16t2 + 130t
a) How long will Marilyn's ball stay in the air?
b) What was the maximum height of the ball?
Answers
It will take the ball 4.0625secs to stay in the air
The maximum height of the ball is 264.0625m
Given the function representing the height reached by the golf expressed as;
h(t) = -16t^2 + 130t
The velocity function is expressed as:
v(t) = -32t + 130
At maximum height, the velocity of the ball will be zero, i.e v(t) = 0
0 = -32t + 130
32t = 130
t = 130/32
t = 4.0625
Hence it will take the ball 4.0625secs to stay in the air
b) Substitute t = 4.0625 into the height function to have:
h(t) = -16t^2 + 130t
h(t) = -16(4.0625)^2 + 130(4.0625)
h(4.0625) = -264.0625 + 528.125
h(t) = 264.0625m
Hence the maximum height of the ball is 264.0625m
Learn more on velocity function here: https://brainly.com/question/10962624
Work out the area of the parallelogram.
13 cm
790
21 cm
Answers
Answer:
Step-by-step explanation:
please try to provide a more accurate information 13cm of what? 790?
Answer:
The area of parallelogram can be found by product of its base and height. The calculations are shown below:
Step-by-step explanation:
We know that,
Area of parallelogram = base × height
assume base to be 21 cm.
Then,
sin 79° = [tex]\frac{height}{13}[/tex]
∴ height = 13 × 0.98 = 12.74
Area of parallelogram = 21 × 12.74
= 267.54 [tex]cm^{2}[/tex]
The area of parallelogram is calculated as 267.54 [tex]cm^{2}[/tex]
For their group project, Mia and Ichiro researched
hybrid cars that combine gas and an electric motor.
“Awesome, so it consumes less fuel and emits less
CO2 into the environment,” Ichiro said.
“While hybrid cars are better for the environment,
I’m seeing that some people are hesitant to buy one
because of the higher purchase price,” Mia noted.
They found the graph to the right, which shows the
miles per gallon (MPG) and the annual tons of GHG
produced by 8 different types of cars. If each gallon
of gasoline burned created 20 pounds of GHG, and
the price of gasoline was $2.454 per gallon, how
much money was saved annually on gas by the car
that got 40 miles per gallon when compared to the
car that got 20 miles per gallon? Provide your answer
to the hundredths place. Note: 1 ton = 2,000 pounds. This is from Pg.2 -7th Grade math problem.
Answers
Hybrid cars have lower operational cost and reduce Green House Gases
GHG when journeys are made on a frequent basis.
The amount saved annually on gas by the car that got 40 miles per gallon when compared to the car that got 20 miles per gallon is $1,076.76.Reasons:
The given parameters are;
The mass of Green House Gases GHG created by each gallon of gasoline burned = 20 pounds
The price per gallon of gasoline = $2.454Let A represent the cars that consume 40 MPG and let B represent the cars that consume 20 MPG.
Amount of GHG produced per year by cars A = 4.4 tons
4.4 US tons = 8,800 lbs
Amount of GHG produced per year by cars A = 8.8 tons
8.8 US tons = 17,600 lbs
[tex]\displaystyle Gasoline \ consumed \ per \ year \ by \ car \ A = \frac{8,800 \ lb}{20 \ lb/ gallon} = \mathbf{440 \ gallons}[/tex]
Cost of gasoline consumed per year by car A per year is therefore;
[tex]Cost_A[/tex] = 440 gallons × $2.454 = $1,079.76
[tex]\displaystyle Gasoline \ consumed \ per \ year \ by \ car\ B = \mathbf{\frac{17,600\ lb}{20 \ lb/ gallon}} = 880 \ gallons[/tex]
Cost of gasoline consumed per year by car B per year is therefore;
[tex]Cost_B[/tex] = 880 gallons × $2.454 = $2,159.52
The amount saved annually by car A compared to car B is therefore;
Fuel cost savings by Car A = $2,159.52 - $1,079.76 = $1,079.76
The amount saved on gas by the 40 MPG car = $1,079.76Learn more here:
https://brainly.com/question/14806781
(10 points!!!) AND I’LL GIVE YOU BRAINLIEST IF CORRECT
I ALREADY KNOW THE ANSWER I JUST WANT THE EXPLANATION!!
The answer is ( Jose, $901.31 more)
Janell deposits $2,000 and for 5 years leaves it in an account earning 3% annual interest, compounded quarterly. For 5 years, José saves and deposits $150 per quarter in an account earning 3% interest compounded quarterly. Who will have more money in the account after 5 years? How much more?
Use the table to answer:
Answers
Answer:
2%
Step-by-step explanation:
5) Placido pulls a rope attached to a wagon through a pulley at a rate of q m/s. With dimension as in Figure 5:
(a) Find a formula for the speed of the wagon in terms of q and the variable x in the figure.
(b) Find the speed of the wagon when x=0.6 if q=0.5 m/s.
Answers
The formula for the speed of the wagon can be found by using Pythagoras theorem, and chain rule of differentiation.
[tex](a) \ \mathrm{The \ speed \ of \ the \ wagon} , \ \dfrac{dx}{dt} = q -\dfrac{x}{\sqrt{x^2+ 5.76}}[/tex]
(b) When x = 0.6 and q = 0.5 m/s, the speed of the wagon is approximately 0.243 m/s.
Reasons:
(a) The distance from the cart to the pulley, r is given by Pythagoras's
theorem as follows;
r = √((3 - 0.6)² + x²) = √(2.4² + x²)
The speed of the wagon = [tex]\mathbf{\dfrac{dx}{dt}}[/tex]
The speed of the rope, q = [tex]\mathbf{\dfrac{dr}{dt}}[/tex]
By chain rule, we have;
[tex]\dfrac{dr}{dt} = \mathbf{\dfrac{dr}{dx} + \dfrac{dx}{dt}}[/tex]
[tex]\dfrac{dr}{dx} = \dfrac{x}{\sqrt{x^2+ 5.76}}[/tex]
Therefore;
[tex]\dfrac{dr}{dt} = q =\dfrac{x}{\sqrt{x^2+ 5.76}}+ \dfrac{dx}{dt}[/tex]
[tex]\mathrm{The \ speed \ of \ the \ wagon} , \ \dfrac{dx}{dt} = \underline{ q -\dfrac{x}{\sqrt{x^2+ 5.76}}}[/tex]
(b) The speed of the wagon when x = 0.6 if q = 0.5 m/s is given as follows;
[tex]\dfrac{dx}{dt} = 0.5 -\dfrac{0.6}{\sqrt{0.6^2+ 5.76}} =\sqrt{\dfrac{1}{17} } \approx 0.243[/tex]
The speed of the wagon when x = 0.6 and q = 0.5 m/s, [tex]\dfrac{dx}{dt}[/tex] ≈ 0.243 m/s
Learn more here:
https://brainly.com/question/17081984
Two functions f and g are defined on the set R, of real numbers by f : x 2x 3 and
x g : x 1 3x . Find the inverse of the function f and the domain of gof.
Answers
Answer:8
Step-by-step explanation:
50 point question Solve quick i will give branliest
Answers
Answer:
17
Step-by-step explanation:
x + 100 = 4x + 49
100 - 49 = 3x
3x = 51
x = 17
someone help please!!
Answers
Answer:
a - 145
b - 35
c - 145
d - 70
e - 70
f - 110
g - 55
h - 125
i - 55
j - 50
k - 50
l - 130
m - 50
n - 80
o - 50
p - 23
q - 89
r - 68
s - 157
t - 112
u - 48
v - 132
w - 132
x - 48
y - 48
z - 132
A - 48
B - 94
C - 86
D - 94
E - 47
F - 133
how do I do 2÷834
Fourth grade
Answers
Answer:
I honestly don't know why you are on this if your in 4th grade because this is for middle, high, and college school kids.
The answer is anyways 417
Answer:
2 divided by 834 is 1/417 or 417
Step By Step Explanation:
Why is a fourth-grader even on a website for middle, high school, and college...
the area of a square is 36 centimeters. how long is each side of the square?
Answers
Answer:
6cm
Step-by-step explanation:
square root of 36 because the area of a square is base x height and a square has equal sides
Sử dụng phép tính mệnh đề (các luật logic) để chứng minh các biểu thức sau là hằng
đúng:
[p -> (q ∨ r)] ->[(p -> q) ∨ (p ->r)]
Answers
Answer: “P hay Q” là một mệnh đề được
Step-by-step explanation: Các quy tắc tương đương logic: ... Chứng minh biểu thức mệnh đề (¬((r ∨ q) ∧ q) ∨. ¬p)∧ ((¬p
I’m so confused, can someone help me? I’ll give brainlist
Answers
Answer:
16
Step-by-step explanation:
the square root of 16 is 4. (4x itself is 16)
out of the options, that is the only one that has a whole number as the square root.
factorize
1) x²-4y²
2) 27-8y³
Answers
you cant factorise both of them as they have nothing in common