Answer:
[tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right] = \left[\begin{array}{ccc}3\\2\\\end{array}\right][/tex]
Solution of the given system of equations
x = 3 and y= 2
Step-by-step explanation:
Step(i):-
Given system of equations are
4x - y = 10 ...(i)
8x +5y = 34...(ii)
The matrix form
A X = B
[tex]\left[\begin{array}{ccc}4&-1\\8&5\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] = \left[\begin{array}{ccc}10\\34\\\end{array}\right][/tex]
Step(ii):-
By using matrix inversion method
[tex]A^{-1} = \frac{1}{|A|} adj A[/tex]
|A| = ad-b c = 4(5) - 8(-1) = 20+8 = 28
Given matrix
[tex]A = \left[\begin{array}{ccc}4&-1\\8&5\\\end{array}\right][/tex]
[tex]AdjA = \left[\begin{array}{ccc}d&-b\\-c&a\\\end{array}\right][/tex]
[tex]A djA = \left[\begin{array}{ccc}5&1\\-8&4\\\end{array}\right][/tex]
Inverse of the matrix
[tex]A^{-1} = \frac{1}{|A|} adj A[/tex]
[tex]A^{-1} = \frac{1}{|A|} A djA =\frac{1}{28} \left[\begin{array}{ccc}5&1\\-8&4\\\end{array}\right][/tex]
Step(iii):-
The solution of the given system of equations by using matrix inversion method
X = A⁻¹ B
[tex]X = A^{-1}B =\frac{1}{28} \left[\begin{array}{ccc}5&1\\-8&4\\\end{array}\right]\left[\begin{array}{ccc}10\\34\\\end{array}\right][/tex]
[tex]X = A^{-1}B =\frac{1}{28} \left[\begin{array}{ccc}5X10+1X34\\-8X10+4X34\\\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right] =\frac{1}{28} \left[\begin{array}{ccc}84\\56\\\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right] = \left[\begin{array}{ccc}3\\2\\\end{array}\right][/tex]
Final answer:-
Solution of the given system x = 3 and y= 2
One grain of this sand approximately weighs 6 x 10^-6g.
b) How many grains of sand are there in 7200 kg of sand?
Give your answer in standard from.
Answer:
1.2×10¹² grainsStep-by-step explanation:
1 grain = 6×10⁻⁶ g
7200 kg = 7200000 g = 7.2×10⁶ g = 7.2×10⁶ ÷ 6×10⁻⁶ = (7.2÷6)×10⁶⁻ ⁽⁻⁶⁾ =1.2×10¹² grainsis it one to one or onto? why?
Answer:
Step-by-step explanation:
Given quadratic function is,
f(x) = -x² - x + 1
Range of the function has been defined as (-∞, [tex]\frac{5}{4}[/tex] ]
Domain of the function is a set of all real numbers.
From the graph of this function,
At x = -3 and x = 2, value of y = -5
But for one to one functions, every x value should map to a different value of y.
Therefore, function is not one to one.
Since, every value of domain (x-value) maps the range (y-value) in the given range (-∞, [tex]\frac{5}{4}[/tex] ], function will be defined as onto.
Therefore, this function is ONTO, but NOT ONE TO ONE.
Function w gives the weight of a cat, in kilograms, when it is m months old.
Which statement represents the meaning of the equation w(7) = 4 in this situation?
A) The cat weighs 7 killograms when it is 4 months old.
B) The cat weighs 4 kilograms when it is 7 months old.
C)The weight of the cat has been 7 kilograms for 4 months.
D) The cat weighs 4 kilograms when it is 7 years old.
Option B) The cat weighs 4 kilograms when it is 7 months old. is correct answer.
Given that:w gives weight of cat, in kgs, when it is m months old.
To find:What does w(7) = 4 represents.
Explanation:It is already given that w gives weight in kilograms.
It outputs weight when we tell the age in months, thus, this is what we treat as input.
w(7) means weight when cat is 7 months old.
and w(7) = 4 represents that the cat weighs 4 kilogram when the age of cat is 7 months.
Thus, Option B) The cat weighs 4 kilograms when it is 7 months old. is correct answer.
Learn more about functions here:
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The correct option is Option B) The cat weighs 4 kilograms when it is 7 months old.
The following information should be considered:
The equation is w(7) = 4.Here car weight should be 4 kilograms at the time of 7 months old. Since w denotes the weight of the cat and m denotes the months.Learn more: https://brainly.com/question/4804019?referrer=searchResults
SOMEONE PLS HELP ME ON ALL THESE ASAP!!!!!
Answer:
4Q a). angle1=55°
angle2=23°
angle3=63°
angle4=125°
5Q. x=35°
6Q. y=15°
8Q. C. 28°
9Q. Yes, they are congruent by S.S.S. congruence
10Q. A.A.S.
11Q. S.S.S.
12Q. Not possible
13Q. S.A.S.
14Q. S.S.S.
15Q. 66°
16Q. 24°
I hope it will be useful.
Step-by-step explanation:
7Q. angle1=angle3 (Alternate Interior Angles)
angle2=angle4 (A.I.A.)
angleXWZ=angleXYZ (opposite angles of a parallelogram)
By A.A.A. congruence criteria, they are congruent.
8Q. Hint: Make the diagram first!
AngleC is halved since M is the mid-point.
angleA=angleB (Property of an isosceles triangle)
which implies, angleAMC=angleBMC=90°
Thus, CM is perpendicular to AB.
I hope it will be useful.
Given: f(x) = 2x^2 - 2x - 4
a.explain how to create a table value for f(x) and make a table for f(x).
b. Explain how to graph using the table and graph f(x).
Write the algebraic expression for... 16 less than a number n
Answer: n-16
Step-by-step explanation:
The algebraic expression for 16 less than a number n is thesame thing as subtracting 16 from n which will be represented as: n - 16.
Therefore, the algebraic expression for 16 less than a number n will be = n - 16
The class has 12 girls and 16 boys. What is the ratio of total students to boys in simplest form?
Answer:
7:4 is the simplest form.
Step-by-step explanation:
total number of students is 28 and number of boys is 16 which makes the ratio 28:16
when we simplyfy it we get 7:4.
Solve the equation:
-4x - 12 = 8
-4x - 12 = 8
+ 12 +12
-4x = 20
-4 -4
x = -5
To ensure that x equals -5, let's substitute the negative integer with x.
-4 x -5 - 12 = 8
-20 - 12 = 8
8 = 8
Therefore, the answer is x = -5 because we confirmed our answer by substituting x with -5 and solving the equation and got the both sides of the equation equal.
The solution to the equation -4x - 12 = 8 is x = -5.
To solve the equation -4x - 12 = 8, we'll isolate the variable x by performing the necessary steps.
First, we'll add 12 to both sides of the equation to eliminate the constant term on the left side:
-4x - 12 + 12 = 8 + 12
This simplifies to:
-4x = 20
Next, we'll divide both sides of the equation by -4 to isolate x:
(-4x)/-4 = 20/-4
This yields:
x = -5
Hence, the solution to the equation -4x - 12 = 8 is x = -5.
By performing the necessary operations of addition, subtraction, and division, we have determined that x is equal to -5, satisfying the equation. This can be verified by substituting x = -5 back into the original equation and confirming that both sides are equal.
To learn more about the linear equation;
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is 0.21 greater than 0.27
Answer:
no
Step-by-step explanation:
0.27 is greater than 0.21
hope it helps
hi can anyone plz help me with this and can you explain how you got it
Answer:
x = 62
Step-by-step explanation:
Since the 2 legs of the triangle are congruent, both 6 , then the triangle is isosceles and the base angles are congruent, that is
x = [tex]\frac{180-56}{2}[/tex] = [tex]\frac{124}{2}[/tex] = 62
ssssssssssssssssssssssssssshhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhStep-by-step explanation:
Help needed ASAP! Please
Answer:
r =5
Step-by-step explanation:
How can you tell if a table represents a proportional relationship?
Answer:
from my knowledge i have made a sample here it is:
To see if multiple ratios are proportional, you could write them as fractions, reduce them, and compare them. If the reduced fractions are all the same, then you have proportional ratios.
Step-by-step explanation:
brainliest?
How much should be added to the sum of 25 1/6 and 7 2/5 to get 60?
Answer:
3.77 should be added
hope it helps.
Answer:
823/30
or 27 13/30
decimal: 27.43
Step-by-step explanation:
(25+7)+ (1/6 + 2/5)
32+ (5/30 + 12/30)
32+ 17/30
= 32 17/30
60- 32 17/30
= 1800/30 - 977/30
= 823/30
= 27 13/30
Anybody know the answers to this
Answer:
no sorry
Step-by-step explanation:
I need help I would really appreciate it !!
Pls help. I’m begging you.
Answer:
n=6
Step-by-step explanation:
Which trigonometric functions have a domain of [–1, 1]?
A.) y = arcsinx and y = arccosx
B.) y = arccosx and y = arctanx
B.) y = arcsinx and y = arctanx
D.) y = arcsecx and y = arccscx
Answer:
The answer is A. y = arcsinx and y = arccosx
Step-by-step explanation:
Need help answer ASAP
Answer:
.1i01390
Step-by-step explanation:
What is the equation of the given linear function? x y 0 8 1 17 2 26 -3 -19
A. f(x)=8x+9
B. f(x)=9x+8
C. f(x)=9x
D. f(x)=17x
Answer:
Step-by-step explanation:
If you were to use the substitution method to solve the following system, choose the new
equation after the expression equivalent to x from the second equation is substituted into the
first equation.
2x – 3y = -29
x + 4y = 13 (6 points)
1) 2(4y + 13) – 3y = -29
2) 2(-4y + 13) – 3y = -29
3) 2x - 3(4y + 13) = -29
O4) 2x - 36-4y + 13) = -29
Answer:
Option 2
Step-by-step explanation:
We will use the substitution method, as the question asks for. The second equation (where x or y is isolated on one side) will be susbstituted as the x or y in the first equation.
2x-3y=-29
x+4y=13
let's isolate x onto one side in the second equation.
Subtract 4y from both sides
x=-4y+13
now we can substitute the expression as x in the first equation
2(-4y+13)-3y=-29
it's the 2nd option
Hope this helps!
Solve the system of equations:
y = 2x
y=x2-3
A. (-1,2) and (3, 2)
B. (-2, -4) and (2, 4)
C. (-2, 1) and (2, 1)
D. (-1, -2) and (3, 6)
Answer:
D. (-1, -2) and (3, 6)
Step-by-step explanation:
y = 2x
y = x² - 3
2x = x² - 3
x² -2x - 3 = 0
(x + 1)(x - 3) = 0
x = -1 or x = 3
y = -2 or y = 6
help this is geometry
Answer:
a=corresponding sides of congruent triangles
b= by SAS condition ( ac=ce, acb=oce,oc=cb)
Find the value of x in the proportion. Check your answer.
30
15
14
Х
x=0
what is x?
Answer:
Step-by-step explanation:
OREGON TRAIL! (pls help)
So far you have completed 816 miles
which is 54% of the trail.
Can you find about how many miles for the total trip?
How would I divide decimals by a whole number?
Answer:
divide the two numbers ignoring the decimal point and then place the decimal point in the quotient in the same position as in the dividend
Jimmy walked 5 miles east from his campsite. Then from his current location he decided to walk 3 miles south. Determine Jimmy’s Bearing From his current location to his campsite
The length, l, of the shadow cast by an object varies directly as the height, h, of the object. If k is the constant of variation, which equation represents this situation?
A.
l + h = k
B.
lh = k
C.
l = hk
D.
l = h + k
Answer:
C. l = hk
Step-by-step explanation:
the equation for direct variation is y = xk (or y/x = k) so you just replace y and x with l and h
The length of the shadow cast l represents by situation l = hk. Hence, option (C) is correct.
What is the linear relation of an equation?An equation has a linear relation if a variable from that equation varies linearly with the other variable.
for example, x is varied linearly with y then we can write
x ∝ y
x = yk where k will be the constant of variation.
Given that length, l is varies directly as the height h
Hence, l = hk will be the correct representation.
For more information about direct variation.
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please help(lots of pts) which table represents the increasing linear function with the greatest unit rate?
A.
x y
2 16
5 10
B.
x y
2 14
6 12
C.
x y
2 -24
5 -15
D.
x y
2 -12
6 -16
E.
x y
2 -19
6 -17
Answer:
I believe the answer is B
Step-by-step explanation:
Hope this helps :D
Question 3 (4 points)
(04.01 LC)
Which of the following types of rocks are likely to disintegrate by weathering and erosion? (4 points)
a
Igneous rocks only
b
Metamorphic rocks only
c
Both igneous rocks and metamorphic rocks
d
Neither igneous rocks nor metamorphic rocks
1,615×10 to the power of 2