Select the correct answer.
Use the inverse matrix to solve this system of equations:
(4x + 3y = 7.5 7x+9z=14. 4y-z=8.3
Answers
Answer:
The answer is C.
Step-by-step explanation:
4(.032) + 3(2.458) = 7.502
7(.032) + 9(1.531) = 14.003
4(2.458) - 1.531 = 8.301
The solutions to the system of equation are x = 0.032, y = 2.458, z = 1.531 after using the inverse matrix method option (C) is correct.
What is the matrix?It is defined as the group of numerical data, functions, and complex numbers in a specific way such that the representation array looks like a square, rectangle shape.
We have a system of equations:
4x + 3y = 7.5
7x + 9z = 14
4y - z = 8.3
First we have to write above system of equation in the form of:
AX = B
[tex]\rm X = A^{-1}B[/tex]
Where A, X and B are the matrix such that:
[tex]\rm A = \left[\begin{array}{ccc}4&3&0\\7&0&9\\0&4&-1\end{array}\right][/tex]
[tex]\rm X = \left[\begin{array}{c}x\\y\\z\end{array}\right][/tex]
[tex]\rm B = \left[\begin{array}{c}7.5\\14\\8.3\end{array}\right][/tex]
[tex]\rm \left[\begin{array}{ccc}4&3&0\\7&0&9\\0&4&-1\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] \rm = \left[\begin{array}{c}7.5\\14\\8.3\end{array}\right][/tex]
Now find the determinant of matrix A
|A| = -123
[tex]\rm A^{-1}= \dfrac{Adj(A)}{Det(A)}[/tex]
After calculating, we will get:
x = 0.032, y = 2.458, z = 1.531
Thus, the solutions to the system of equation are x = 0.032, y = 2.458, z = 1.531 after using the inverse matrix method
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Related Questions
Dedra polled people at the mall to determine which types of movies
they preferred to watch. She displayed the results in a circle graph.
Of the people polled, 120 preferred to
to watch action movies. Use this information and
the graph to answer these questions.
a) What is the total number of people
Dedra polled?
Answers
The total number of people Dedra polled is 400.
Given,
Number of people preferred to watch action movies = 120
We have to find the total number of people Dedra polled:
According to the given circle graph:
Percentage of people preferred to watch action movies = 30%
Now,
The total number of people polled = x
Then,
30% of x ix 120.
So,
x = (120 × 100) / 30
x = 4 × 100
x = 400
Therefore the total number of people Dedra polled is 400.
Lets check the others also:
Comedy: 35%
∴ (400 × 35) / 100 = 4 × 35 = 140
140 people preferred to watch comedy movies.
Drama: 20%
∴ (400 × 20) / 100 = 4 × 20 = 80
80 people preferred to watch drama movies.
Fantasy: 10%
∴ (400 × 10) / 100 = 4 × 10 = 40
40 people preferred to watch fantasy movies.
Horror: 5%
∴ (400 × 5) / 100 = 4 × 5 = 20
20 people preferred to watch horror movies.
The total number of people Dedra polled is 400
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XZ is the perpendicular bisector of segment WY. Solve for k. Enter a NUMBER only.
Answers
3K + 17 = 7K - 7
17 = 4K - 7
24 = 4K
24/4 = K
6 = K
K = 6
Is the work below correct? If not, explain the mistake
Answers
Answer:
the answer is correct just switch the sign to less than or equal to
Step-by-step explanation:
PLZ HELP!!
A family is trying to decide between two apartments, before signing a lease agreement they
are considering the cost compared to the size of the apartment. Apartment A is 1,500 square
feet for a monthly rent of $2,875 and Apartment B is 1,200 square feet for a monthly rent of
$2,425. Based on this information which apartment costs the least per square foot?
A. Apartment A
B. Apartment B
Answers
PLSSS HELP ANSWER, THE QUESTION IS IN THE SCREENSHOT
Answers
Answer:
72
Step-by-step explanation:
Let f(x)=x³.
[tex]f(-2)=-8 \\ \\ f(0)=0 \\ \\ f(2)=8 \\ \\ f(4)=64 \\ \\ \\ \implies \int^{4}_{-2} x^3 \text{ } dx \approx -8+64+2(0+8)=72[/tex]
Divide and simplify.
(-7)+(-7)
=
Answers
Step-by-step explanation:
=-7-7
=-14
HOPE THIS HELPS
(40 points please explain your answer)
If triangle ABC is reflected over the y‐axis, reflected over the x‐axis, and rotated 180 degrees, where will point A' lie?
(−1, 2)
(−2, 1)
(1, −2)
(2, −1)
Answers
A is reflected over the y‐axis, reflected over the x‐axis, and rotated 180 degrees
A' is (-2,1)
Given :
A triangle ABC is reflected over the y‐axis, reflected over the x‐axis, and rotated 180 degrees.
The rule for reflection over y axis
(x,y) -> (-x,y)
Reflection over x axis is
(x,y) -> (x,-y)
Rotate by 180 degree
(x,y)->(-x,-y)
The point A lies on (-2,1)
Lets find the coordinate of point after reflection over y axis, x axis and rotation by 180 degree using the rules
Reflection over y axis
(-2,1) -> (2,1)
Reflection over y axis
(2,1)-> (2,-1)
Rotate by 180 degrees
(2,-1)-> (-2,1)
So A' is (-2,1)
Learn more : brainly.com/question/20192008
3/8 divided by 4????
Answers
Answer:
um Yess?
Step-by-step explanation:
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▇╱▏┈┈▇▇▇╱▏▇╱▏
▇╱▏▁┈▇╱▇╱▏▇╱▏▁
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▇▇▇╱┈▇▇▇╱┈▇▇▇╱
Here is another one
5. 1 4/5 × 15
Answers
Answer:
27 i think
Step-by-step explanation:
hi lohith my ff play my iD I'd is opBOYS123123
Answers
Answer:
Step-by-step explanation:
Password
Solve the inequality and express your answer in interval notation. x² + 8x + 3 < 0
Answers
Answer:
Convert the inequality to an equation.
x2+8x+3=0" role="presentation" style="outline: 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 15.47px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">x2+8x+3=0x2+8x+3=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a" role="presentation" style="outline: 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 15.47px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">−b±√b2−4(ac)2a-b±b2-4(ac)2a
Substitute the values a=1" role="presentation" style="outline: 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 17.03px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">a=1a=1, b=8" role="presentation" style="outline: 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 17.03px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">b=8b=8, and c=3" role="presentation" style="outline: 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 17.03px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">c=3c=3 into the quadratic formula and solve for x" role="presentation" style="outline: 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 17.03px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">xx.
-8±82-4⋅(1⋅3)2⋅1" role="presentation" style="outline: 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 15.47px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">−8±√82−4⋅(1⋅3)2⋅1
What is the "quotient" of two numbers?
Answers
Answer:
Result of a division
Step-by-step explanation:
Example
x / y = z
z is the quotient
Write the equation in slope-intercept form of the line that passes through the points (5,4) and (1−6,)
Answers
Answer:
y = 5/2x - 17/2
Step-by-step explanation:
First, find the slope of the equation by using the slope formula:
m = (y2 - y1) / (x2 - x1)
m = (-6 - 4) / (1 - 5)
m = 10/4
m = 5/2
Next, find the y-int by plugging in one of the two points into the equation we have so far:
y = 5/2x + b
(5, 2)
4 = 5/2(5) + b
4 = 25/2 + b
4 - 25/2 = b
b = -17/2
Now you have your final equation:
y = 5/2x - 17/2
Answer:
[tex]y=\frac{5}{2}x-\frac{17}{2}[/tex]
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
Points: (5, 4), (1, -6)
Slope (Calculated): [tex]\frac{5}{2}[/tex]
[tex]y = \frac{5}{2}x+b[/tex]
[tex]-6 = \frac{5}{2}(1)+b[/tex]
[tex]b=-\frac{17}{2}[/tex]
[tex]y=\frac{5}{2}x-\frac{17}{2}[/tex]
Find the value of x. Give reasons to justify your answer.
Answers
10x=180°
180/10x
x=18
6x and 4x are alternate interior angles and they can be added to each other to create a product of 180.
A cashier at the local bank expected to serve 12 customers every hour. In the past 15 minutes he served 4 customers. Assuming that the cashier continues to work at the same rate, will he meet his goal?
Answers
Answer: yes
yes
Step-by-step explanation: he will do more than his goal because 4x3=12 and 15x3= 45
An urn contains 4 black and 5 white balls. A ball is drawn at random and then replaced, and then a second ball is drawn. Find the probability that the first is black and the second iswhite.
Answers
Answer:
[tex]Probability = 0.2470[/tex]
Step-by-step explanation:
Given
[tex]Black = 4[/tex]
[tex]White = 5[/tex]
[tex]Total = 9[/tex] i.e. 5 + 4
Required
Determine [tex]P(Black\ and\ White)[/tex]
In probability;
[tex]P(A\ and\ B) = P(A) * P(B)[/tex]
So:
[tex]P(Black\ and\ White) = P(Black) * P(White)[/tex]
i.e. multiply the probability of selecting black by that of selecting white
[tex]P(Black\ and\ White) = \frac{n(Black)}{Total} * \frac{n(White)}{Total}[/tex]
[tex]P(Black\ and\ White) = \frac{4}{9} * \frac{5}{9}[/tex]
[tex]Probability = \frac{20}{81}[/tex]
[tex]Probability = 0.2470[/tex]
Which graph shows the solution to the systern of linear inequalities? x+3y>6 y>2x+4
Answers
Answer: y>2x+4
Step-by-step explanation:
Dieciocho centésimas a números
Answers
Answer:
.18
Step-by-step explanation:
The sugar sweet company will choose from two companies to transport it's sugar to market the first company charges $4894 to rent trucks plus an additional fee of $175.75 for each ton of sugar the second company charges $5500 to rent trucks plus an additional fee of $125.25 for each ton of sugar
Answers
The sugar sweet company will choose from two companies to transport it's sugar to market the first company charges $4894 to rent trucks plus an additional fee of $175.75 for each ton of sugar the second company charges $5500 to rent trucks plus an additional fee of $125.25 for each ton of sugar
Answer: 12
Does this graph represent a function? Why or why not? 10 22 -10B2 10 8 A. No, because it fails the vertical line test. B. No, because it is not a straight line. C. Yes, because it passes the vertical line test. O D. Yes, because it has two straight lines.
Answers
Answer: I need to see the graph
Step-by-step explanation:
please help asap will give brainliest
Answers
Answer:
of course three units ..
10 times as much as 72.67
Answers
Answer:
726.7 hope this helps
SAY SAUSAGE KEEP IT GOIN' EGGS BACON GRITS
Answers
SAY SAUSAGE KEEP IT GOIN' EGGS BACON GRITS SAUSEGE thanks for the points :D
Georgia goes shopping with $80 to spend on food for a party. She buys 9 pizzas that all cost the same price, $20 worth of soda and $15 worth of ice cream. If she spent all of her money, what was the cost of each pizza?
Answers
Answer:
$5
Step-by-step explanation:
20+15=35
80-35=45
45 divided by 9 = 5
A recipe for fruit salad includes
cups of grapes for 4 servings. How many cups of grapes are needed for 30 servings of this fruit salad? {7.4D}
Answers
Answer:
u need to tell me how many cups of grapes are used for 4 servings for me to be able to answer this
Step-by-step explanation:
Write a function to convert Celsius to Fahrenheit using F=(9/5)C+32. Find the Fahrenheit value when C=56.7 and when C=−89.2. (The record high and low temperatures ever recorded on Earth.)
If x is the given temperature in Celsius, the function to return the equivalent temperature in Fahrenheit it:
f(x) = 9 / 5 * x + 32
f(x) = 9/5x + 32
f(x) = 9/5 * (x + 32)
f(x) = 9/5c + 32
The value in Fahrenheit at C=56.7 (a record high) is:
?
The value in Fahrenheit at C=−89.2 (a record low) is:
?
Using your function, f(C), to convert Celsius to Fahrenheit, compare the difference at C=20 between the function value and the simpler function: g(C)=2C+30. (In other words, is "double and add 30" a reasonable approximation?)
The difference f(C)−g(C) at C=21 (approximate room temperature) is:
?
Answers
The function used to convert Celsius to Fahrenheit is: 5/9(F - 32)
The Fahrenheit value when C = 56.7 is: 134.06
and when C = 89.2, F = -128.56, as found by basic algebra. If x is the given temperature in Celsius, the function used to return the equivalent temperature in Fahrenheit is: f(x) = 9 / 5 * x + 32 (Option A).
What is basic algebra?Numbers, variables, constants, expressions, equations, linear equations, and quadratic equations are all part of the basics of algebra. Additionally, the algebraic expressions contain the basic arithmetic operations of addition, subtraction, multiplication, and division.(1)
Given:
F = 9/5 × (C) + 32
F - 32 = 9/5 × (C)
5/9 × (F-32) = C(2)
For C = 56.7, in the above formula, by basic algebra, we get:
F = 9/5 × (56.7)+32
F = 102.06 + 32
F = 134.06
For C = -89.2, by basic algebra,
we get: F = (9/5) × (-89.2)+32
F = -160.56 + 32
F = -128.56(3)
We are given:
F = 9/5 (C) + 32
If f(x) represents the temperature in Fahrenheit, we get:
f(x) = 9/5 (C) + 32,
which is equivalent to Option A.
Hence, (1) The function used to convert Celsius to Fahrenheit is:
9/5(F-32)
(2) The Fahrenheit value when C = 56.7 is: 134.06 and when C = 89.2, F = -128.56, as found by basic algebra.
(3) If x is the given temperature in Celsius, the function used to return the equivalent temperature in Fahrenheit is: f(x) = 9 / 5 * x + 32 (Option A).
To learn more about basic algebra, refer to the link: https://brainly.com/question/723406
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HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answers
Answer:
just devide the 2 numbers thats there
Six more than seven times a number equals 10 times the number -12
Answers
Answer:
The equation becomes
[tex]7x+6 = 10x-12[/tex]
Thus, the number = x = 6
Step-by-step explanation:
Let 'x' the number
seven times a number = 7x
Six more than seven times a number = 7x+6
10 times the number -12 = 10x-12
Given that Six more than seven times a number equals 10 times the number -12.
Thus, the equation becomes
[tex]7x+6 = 10x-12[/tex]
We can further solve for x
[tex]7x+6 = 10x-12[/tex]
[tex]6+12 = 10x-7x[/tex]
[tex]18 = 3x[/tex]
[tex]x = 6[/tex]
Thus, the number = x = 6
1. What is the place value of the 9 in 0.964?*
Answers
Answer:
0.9
Step-by-step explanation:
remove all the other digits OR
divide by ten after the d. p.
Solve the equation algevraically and check your solution to verify it is correct. YOU MUST SHOW YOUR WORK INSIDE THE PAGE.Place your final answer in the text box below
Answer:
Explain:
Answers
Add 6 to 11
Divide 17 by -5