solve these simultaneous linear equation
3x - 4y = 1
6x + 7y = 13
Answers
9514 1404 393
Answer:
(x, y) = (59/45, 11/15) ≈ (1.311, 0.733)
Step-by-step explanation:
A graphing calculator shows us the solution is not integer values, so we may find it easiest to solve these equations using the "cross-multiplication method."
Writing the equations in general form, we have ...
3x -4y -1 = 0
6x +7y -13 = 0
Then we can form an array of the coefficients, repeating the first column:
[tex]\begin{array}{cccc}3&-4&-1&3\\6&7&-13&6\end{array}[/tex]
Forming differences of cross products involving adjacent pairs of columns gives ...
d1 = (3)(7) -(6)(-4) = 45
d2 = (-4)(-13) -(7)(-1) = 59
d3 = (-1)(6) -(-13)(3) = 33
Then the solutions are found from ...
1/d1 = x/d2 = y/d3
or
x = d2/d1 = 59/45
y = d3/d1 = 33/45 = 11/15
The solution is (x, y) = (59/45, 11/15) ≈ (1.311, 0.733).
_____
Additional comment
This takes longer to explain than to do. One reason we like it is that the number of math operations is slightly smaller than the number of math operations required for substitution or elimination. It is especially nice when the solution is not a pair of integers.
Related Questions
The browns are moving across the counrty. Mr. Brown leaves 2.5 hours before Mrs. Brown, if he averages 75 mph and she averages 85 mph, how many hours will it take Mrs. Brown to catch up to Mr. Brown?
Answers
Answer:
the time taken by Mrs Brown to catch up is 18.75 hours
Step-by-step explanation:
Given;
average speed of Mr Brown = 75 mph
average speed of Mrs Brown, = 85 mph
time first traveled by Mr Brown = 2.5 hours
The distance traveled by Mr Brown before Mrs Brown start her own Journey;
D = speed x time
D = 75 mph x 2.5 h
D = 187.5 miles
Let the time taken by Mrs Brown to catch up = t
(85 - 75)t = 187.5
10t = 187.5
t = 18.75 hours
Check:
after 18.75 hours: Mrs Brown will travel ⇒ 18.75 x 85 = 1593.75 miles
after (2.5 h + 18.75h) : Mr Brown will travel ⇒ 21.25 x 75 = 1593.75 miles
Challenge. Add a number to the original data set based on the instructions below:
Original data set:
3, 10, 8, 3, 10, 1, 10,
A)
Fill in the blank with a number that would make the range of the data set 20.
3, 10, 8, 3, 10, 1, 10,
B)
Fill in the blank with a number that would make the mean of the data set 15.
3, 10, 8, 3, 10, 1, 10,
C)
Fill in the blank with a number that would make the standard deviation smaller.
3, 10, 8, 3, 10, 1, 10,
Answers
Answer:
A) 23
B) 75
C) 6.30
Step-by-step explanation:
A) Range = highest value - least value
Range = 20
least value = 3
Thus,
20 = highest value - 3
highest value = 20 + 3
= 23
The number that would make the range of the data set 20 is 23.
B) Let the number be represented by x, so that;
15 = [tex]\frac{3 + 10 + 8 + 3 + 10 + 1 + 10 + x}{8}[/tex]
cross multiply to have
15 x 8 = 45 + x
120 - 45 = x
x = 75
The number that would make the mean of the data set 15 is 75.
C) The given data plus a number that is close to the mean would reduce the standard deviation.
mean of the data set = [tex]\frac{3+10+8+3+10+1+10}{7}[/tex]
= 6.43
The required number could be 6.30
The number of subsets that can be created from the set {1, 2, 3} is:
Answers
Answer:3
Step-by-step explanation:
Answer:
Step-by-step explanation:
Subset : {} ; {1} ; {2} ; {3} ; {1,2} ; {2,3} ; {1, 3} ; {1,2,3}
Number of subsets = 8
PLEASEEEEEEEEEEEEEE HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answers
Answer:
rhombus
Step-by-step explanation:
What is the distance between the following points?
Answers
Which one goes where?:( WILL GIVE BRAINLIEST!<33
Answers
Answer:
1 pair of parallel sides: B
2 pairs of parallel sides: A, D
3 pairs of parallel sides: C
Step-by-step explanation:
When two lines are parallel, they will never intersect.
Please answer thanks! Brainliest
Answers
Step-by-step explanation:
The last two answers is correct
Answer:
4
Step-by-step explanation:
The answer to T - H is negative
The area of a triangle is 92 and its height is 23 what is its base?
Answers
Answer:
7.36
Step-by-step explanation:
Area=92
Height=23
Base=?
Area=1/2*base*height
92=1/2*23*height
92=12.5*height
920/125=height
7.36=height
Pleae mention unit in answer
Mark me as brainliest
Figure 2 was constructed using figure 1. For the transformation to be defined as a rotation, which statements must be true? Selext three options.
Answers
Answer:
The segment connecting the center of rotation, C, to a point on the pre-image (figure 1) is equal in length to the segment that connects the center of rotation to its corresponding point on the image (figure 2).
The transformation is rigid.
Every point on figure 1 moves through the same angle of rotation about the center of rotation, C, to create figure 2.
If figure 1 is located 360° about point C, it will be mapped onto itself.
Step-by-step explanation:
Simplify the expression. –(10)–2
100
–100
Answers
Answer:
-12, 0
Step-by-step explanation:
5m - 3n = 19; m - 6n = -7 /pls. help me solve this linear equation with two variables.
Answers
Answer:
m = 5, n = 2
Step-by-step explanation:
[tex]5m - 3 n = 19\\m - 6n = - 7 \ => m = -7 + 6n\\\\Substitute \ m \ in \ 5m - 3n = 19\\\\5(-7 + 6n) - 3n = 19\\-35 + 30n -3n = 19\\27n = 19 + 35 \\27n = 54 \\n = 2\\\\Substitute \ n = 2 \ in \ m = -7 + 6n\\\\m = -7 + (6 \times 2) = -7 + 12 = 5[/tex]
f^3+11g-4hf 3 +11g−4hf, cubed, plus, 11, g, minus, 4, h when f=3f=3f, equals, 3, g=2g=2g, equals, 2 and h=7h=7h, equals, 7.
Answers
Given:
The expression is:
[tex]f^3+11g-4h[/tex]
The given values are [tex]f=3,\ g=2,\ h=7[/tex].
To find:
The value of the given expression for the given values.
Solution:
We have,
[tex]f^3+11g-4h[/tex]
After substituting [tex]f=3,\ g=2,\ h=7[/tex], we get
[tex]f^3+11g-4h=(3)^3+11(2)-4(7)[/tex]
[tex]f^3+11g-4h=27+22-28[/tex]
[tex]f^3+11g-4h=49-28[/tex]
[tex]f^3+11g-4h=21[/tex]
Therefore, the value of the given expression is 21.
Eighty percent of students surveyed said they feel more focused after exercising. Nine hundred fifty students were surveyed.
Students Who Feel More Focused after Exercise
20%
20%
20%
20%
20%
How many students said they feel more focused after exercising?
Answers
Answer:
760
Step-by-step explanation:
A career-placement test eliminates a profession when a person receives a score of 18 or less. The score is equal to the formula 2x - 3y, where x is the number of positive responses and y is the number of negative responses. Which graph represents the range of test results that would be eliminated under this scenario (all points may not apply to the scenario)?
Answers
Answer:
ITS D GOT 100 ON QUIZE
Step-by-step explanation:
Answer:
its d
Step-by-step explanation:
bc i said so
What is the slope of the line that contains these points?
Answers
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]\boxed{m=8}[/tex]
»»————- ★ ————-««
Here’s why:
[tex]\boxed{\text{The Slope Formula:}}\\\\m = \frac{y_2-y_1}{x_2-x_1}\\------------\\m - \text{slope}\\\\(x_1,y_1) \text{ and }(x_2,y_2) - \text{points in the given function}[/tex]
⸻⸻⸻⸻
[tex]\text{\underline{Choosing two points from the table and applying the formula...}}\\\\m = \frac{34-26}{2-1}\\\\\boxed{m = \frac{8}{1}}[/tex]
⸻⸻⸻⸻
[tex]\text{The slope is 8.}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
What are the possible values of x in x2 + 3x + 3 = 0?
Answers
Answer:
Step-by-step explanation:
Answer:
=3
Step-by-step explanation:
given the general form ax2 +bx+c=0
there exist two solutions where: a=1,b=3andc=3
What value of b will cause the system to have an infinite number of solutions? y=6x-b -3x+1/2y=-3
Answers
Answer:
b = 6
Step-by-step explanation:
solve the second equation for 'y':
-3x + 1/2y = -3
add 3x to each side to get:
1/2y = 3x - 3
multiply all terms by 2 to eliminate the denominator to get:
y = 6x - 6
now compare '6x-6' with '6x-b'
you want both expressions to be equal because then there are an infinite number of solutions:
b = 6
please help step by step how do I solve this
Answers
Answer:
my suggested answer (576)
Step-by-step explanation:
i chose the wrong answer :(
3. Find the measure of each indicated arc or the measure of an inscribed angle.
b. Find the measure of Arc BAD
Answers
Answer:
Step-by-step explanation:
Arc BAD is intercepted by inscribed angle BCD which measures 110. The rule is that an intercepted arc is twice the measure of the angle that intercepts it. Therefore, arc BAD is 110(2) which is 220.
How many tiles would be in figure 100? Help :/
Answers
Answer: pretty sure it is 201 tiles
please mark me brainlies. That would be helpful
GIJL is a trapezoid with mid segment of HK. If IJ =7 cm and GL=15 cm, what is the length of HK?
Answers
Consider IJ and GL are the parallel sides of the trapezoid.
Given:
In a trapezoid GIJL, HK is the mid segment, IJ =7 cm and GL=15 cm.
To find:
The length of the mid segment HK.
Solution:
The length of the mid segment of a trapezoid is:
[tex]\text{Midsegment}=\dfrac{b_1+b_2}{2}[/tex]
where, [tex]b_1,b_2[/tex] are two parallel side or bases of the trapezoid.
HK is the mid segment, and the parallel sides are IJ =7 cm and GL=15 cm. So, the length of the mid segment is:
[tex]HK=\dfrac{IJ+GL}{2}[/tex]
[tex]HK=\dfrac{7+15}{2}[/tex]
[tex]HK=\dfrac{22}{2}[/tex]
[tex]HK=11[/tex]
Therefore, the length of HK is 11 units.
What is the length of /AB?
Answers
Answer:
[tex]\sqrt{53}[/tex]
Step-by-step explanation:
HELPPP PLS!! WILL MARK BRAINLIEST!! #plato
Drag each tile to the correct box.
Arrange the entries of matrix A in increasing order of their cofactor values.
Answers
Answer:
a23, a31, a21, a11, a12, a33
Step-by-step explanation: I got it right on Edumentum.
Answer:
a23, a31, a21, a11, a12, a33
Step-by-step explanation:
Which statement best describes why the value of the car is a function of the number of years since it was purchased?
Answers
Answer:
What are the statements?
Step-by-step explanation:
You have to list the statements.
attachment below or above
Answers
Answer:
840
Step-by-step explanation:
600×140% =840 hope this helps
600 × 140/ 100 = 840 grizzly bears
840 - 600 = 240 grizzly bears
A batter gets 6 hits in 12 times at bat. What is the experimental
probability that she will get a hit in her next time at bat?
Answers
Answer:
1/2 or 50% or .5
Step-by-step explanation:
She hits at .500 that's pretty good. I'd take her on my fantasy team.
How much would $500 invested at 6% interest compounded monthly be
worth after 5 years? Round your answer to the nearest cent.
int
A09) P(124
A. $512.63
B. $669.11
C. $674.43
D. $886.41
Answers
Answer:
$669
Step-by-step explanation:
Given data
Principal= $500
Rate= 6%
Time= 5 years
The compound interest formula is given as
A= P(1+r)^t
A=500(1+0.06)^5
A=500(1.06)^5
A=500*1.338
A=$669
What is the radius of a circle with a diameter of 6 meters
Answers
radius = d/2
Hope this helps ;)
Answer:
the radius is 3 m
Step-by-step explanation:
the radius of a circle is always one half of the diameter.
Here the diameter is 6 m, so the radius is 3 m.
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answers
Answer:
Step-by-step explanation:
circumference of circle=2πr
=2*π*9
=18π m
[tex]{ \bf{ \underbrace{Given :}}}[/tex]
Radius of the circle = 9 m.
[tex]{ \bf{ \underbrace{To\:find:}}}[/tex]
The circumference of the circle.
[tex]{ \bf{ \underbrace{Solution :}}}[/tex]
A. C = 18 π ✅
[tex]\sf\orange{The\:circumference \:of\:the\:circle\:is\:18\:π\:m.}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
We know that,
[tex]\sf\purple{Circumference\:of\:a\:circle \:=\:2Πr }[/tex]
[tex] = 2 \: \pi \times 9 \: m \\ = 18 \: \pi \: m[/tex]
Therefore, the circumference of the circle is 18 π m.
[tex]\large\mathfrak{{\pmb{\underline{\blue{Happy\:learning }}{\blue{!}}}}}[/tex]
Find the missing angle measurements of HFG ? , fill in the boxes
Answers
Answer:
Angle HFG = 24 degrees
Step-by-step explanation:
From the diagram, we have the following;
Angle EFH and angle HFG are complementary (they add up to be 90 degrees)
angle EFH + angle HFG = 90
Angle HFG = 90-66
Angle HFG = 24 degrees
