System of equations is represented by the matrix below is 2x + 3y = 2 and 12x = -24
[2 3 2]
[12 0 -24]
This means 2x + 3y = 2 and 12x = -24
How matrix is used to solve system of equation?
The matrix can be used to solve system of equation. it can be 3 by 3 matrix or 2 by 2 matrices.
The first rows of the matrix above represent the coefficient of the first equation and second row represents the second equation of the system of equations.
Matrices is the plural form of matrix, which is a rectangular array or table with rows and columns of numbers or elements. They can have as many columns and rows as they want. Matrix operations include addition, scalar multiplication, multiplication, transposition, and others.
Matrices, the plural form of matrix, are the arrangements of numbers, variables, symbols, or expressions in a rectangular table with varying rows and columns. They are rectangular arrays with defined operations such as addition, multiplication, and transposition. The elements of the matrix are the numbers or entries in it. The horizontal entries of matrices are referred to as rows, while the vertical entries are referred to as columns.
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What is the value of −163 − 18 − (−215)?
Answer:
34.
Step-by-step explanation:
-163 - 18 = -181
-181 - (-215) = 34.
Answer:
34
Step-by-step explanation:
-163-18-(-215)
-163-18+215
-181+215
34
(I tried my best, is this what your question was?)
what is 11.273.26 in word form
Answer:one million one hundred and twenty-seven thousand three hundred and twenty-six
Step-by-step explanation:
the table shows the maximum and minimum account balances for three college students for one month Giovanni claimed that he had the least variation from maximum to minimum in his account balance that month is he correct? write a mathematical argument to justify your solution
Yes, it should be that.Giovanni's account balance has the least variation from maximum to minimum that month.
How to illustrate the information?It should be noted that the formula for calculating the variation is;
Balance difference = Maximum balance - Minimum balance.
For Jordan;
Maximum balance = $145.
Minimum balance = $-25
Balance difference = 145 - (-25) = $170
For Giovanni;
Maximum balance = $168.
Minimum balance = $15.
Balance difference = 168 - 15 = $ 153.
For Elisa;
Maximum balance = $152.
Minimum balance = $-10
Balance difference = 152 -(-10) = $162.
Therefore, for the data it is clear that the minimum account variation is for Giovanni which is $153.
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Brian ran 17 miles in 2.5 hours. What was brian’s rate in miles per hour .
It takes you 53 seconds to walk from the first (ground) floor of a building to the third floor. How long will it take you to walk from the first floor to the sixth floor (at the same pace, assuming all floors have the same height)?
The time taken to walk from first floor to sixth floor at same pace, assuming
all floors have the same height is 318 seconds or 5 minutes 18 seconds.
It takes you 53 seconds to walk from the first (ground) floor of a building to the third floor.
There are 60 seconds in every minute, so converting seconds to minutes is simple. Just divide the number of seconds by 60 to get your answer. Every 60 seconds a full minute has passed. Dividing a number tells you how many times one number "fits" in the other. Oftentimes the number of seconds will not perfectly convert into minutes. This decimal represents the number of seconds left over.
Walking one floor takes 53 seconds.
So, walking six floors at same pace = 53 seconds * 6
=> 318 seconds or 5 minutes 18 seconds.
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help
25:4 and 45:10 as a complex fraction
Complex fraction of 25 : 4 is 6 1/4.
Complex fraction of 45 : 10 is 4 5/10.
What is the Ratio?
A ratio is an ordered pair of numbers x and y, written x / y where b ≠ 0.
The ratios are given as;
25 : 4 and 45 : 10
Now, To write the ratios in complex fraction we use division method as;
25 : 4 = 25/4
_____
4 ) 25 ( 6
- 24
-----------
1
Hence, Complex fraction of 25 : 4 is 6 1/4.
And, For ratio 45 : 10;
45 : 10 = 45/10
10 ) 45 ( 4
- 40
---------
5
Hence, Complex fraction of 45 : 10 is 4 5/10.
Therefore, Complex fraction of 25 : 4 is 6 1/4.
Complex fraction of 45 : 10 is 4 5/10.
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Hi can someone please help me with these!
Answer:
64=18
Step-by-step explanation:
A random sample of 40 college professors is selected from all professors at a university. The following list gives their ages.
63, 49, 44, 46, 30, 52, 45, 46, 41, 25, 55, 65, 59, 48, 63,
66, 58, 44, 51, 29, 37, 62, 40, 46, 35, 39, 46, 31, 20, 41,
67, 35, 38, 45, 27, 32, 42, 30, 35, 50.
Construct a stem-and-leaf plot for the data. Complete parts a. and b.
Here is the stem-and-leaf plot
Stem Leaves
2 1, 2, 5, 9
3 1, 1, 2, 3, 4, 5, 6, 8, 9
4 1, 1, 3, 4, 4, 4, 5, 5, 5, 8, 8, 8, 9, 9,
5 0, 0, 3, 3, 8, 9
6 2, 3, 3, 6, 7, 7
The shape reveals that the greatest number of professors are in their 40s.
What is stem-and-leaf plot?A stem-and-leaf plot is a table that is used to display numbers. It is similar to a histogram. A stem-and-leaf plot divides a number into a stem and a leaf. The stem is the first number in the digit while the leaf is the last number. For example in the number 21, 2 would be the stem and 1 would be the leaf.
An advantage of the stem-and-leaf plot is that all the data in the data set are shown. A drawback of a stem-and-leaf plot is that it can only be used for a small dataset.
Looking at the stem-and-leaf plot, it can be seen that the professors in their 40s have the highest frequency. They are 14 professors in their 40s.
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A project is budgeted for 2400 hours and will last 3 weeks. Technicians will cover 25% of the project for the first week and then 60% for the final two weeks. If each technician normally works 40 hours per week, how many technicians are there?*
Using the percentage and hours, the total number of technician that was there is 42.
How to find the number of technicians that are there?The project is budgeted for 2400 hours and will last 3 weeks.
This means the whole project will last for 2400 hours for 3 weeks.
Technicians will cover 25% of the project for the first week and then 60% for the final two weeks.
This simply implies 25% of the project will be completed in the first week. Then 60% of the remainder of the project will be completed the final two weeks.
Each technician normally works 40 hours per week.
Therefore,
Number of hours for the first week = 25 % of 2400
Number of hours for the first week = 25 / 100 × 2400
Number of hours for the first week = 600 hours
Therefore,
number of technicians for the first week = 600 / 40
number of technicians for the first week = 15 technicians
Therefore,
Number of hours for the final two week = 60 % of (2400 - 600)
Number of hours for the final two week = 60 / 100 × 1800
Number of hours for the final two week = 1080 hours
Hence,
number of technicians for the final two week = 1080 / 40
number of technicians for the final two week = 27 technicians
Therefore, the total number of technician that was there is 42.
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The normal price of a laptop’s is 899€.In a sale, it’s price is reduced to 599.95€.How many percent is the discount?
Work Shown:
A = original price
B = final price
C = difference in price
C = A - B
C = 899 - 599.95
C = 299.05 <--- this is the amount you save
D = C/A
D = (299.05)/(899)
D = 0.3326
D = 33.26% approximately
a normal temperature for a certain animal is 73.9 F if a temperature x that differs from the normal
If a temperature differs from normal by x° F it will be 73.9° F ± x° F.
What is a mod function ?A mod function is defined as |x|= a which is x = a or - x = - a.
According to the given question a normal temperature for a certain animal is 73.9 F if a temperature x that differs from the normal it can be
73.9° F + x° F or 73.9° F - x° F which is
73.9° F ± x° F.
Because rise of temperature and fall of temperature is a temperature difference that differs from the normal temperature.
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After his first month he had more than expected to have due to interest bank provided this that Rob come up with a better expression W squared over 25+45W +155 we’re W is the number of weeks how much will you have in one year
Rob will earn in one year $2603.16.
Given that,
After his first month, he had more than expected to have due to the interest the bank provided.
This let Rob come up with a better expression w²/25+45W +155 where W is the number of weeks how much will you have in one year is to be determined.
The equation is the relationship between variables and represented as y =ax +b is an example of a polynomial equation.
Here,
Given expression,
w² / 25 + 45w + 155
In i year w = 52
= 52²/25 + 45 * 52 + 155
= 2603.16
Thus, Rob will earn in one year $2603.16.
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> Read and try to solve the problem below.
Mei is building a raised bed in her garden to grow lettuce.
She wants the base of the bed to be a square with an area of
2 square meters. Find an approximate side length of the base
of the bed. Plot the value on the number line.
When Mei is building a raised bed in her garden to grow lettuce, it should be noted that the approximate length will be 1.4m.
How to illustrate the information?It should be noted that from the information, Mei is building a raised bed in her garden to grow lettuce and she wants the base of the bed to be a square with an area of 2 square meters.
Therefore, an approximate side length of the base will be the square root of the value will be:
= ✓2
= 1.41 m
Therefore, based on the information, the approximate length will be 1.4m.
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Evaluate 1(8+12)-4)+5. (6-3)
Evaluate 1(8+12)-4)+5. (6-3) = 31
Solution :
PEMDAS rule states that the order of operation starts with the parentheses first or the calculation which is enclosed in brackets. Then the operation is performed on exponents (degree or square roots) and later we do operations on multiplication & division and at last addition and subtraction.
BODMAS, BIDMAS and PEMDAS are acronyms for remembering the order of operations in mathematics. BODMAS stands for Brackets, Orders, Division, Multiplication, Addition and Subtraction. BIDMAS and PEMDAS do exactly the same thing but using different words.
MDAS :
stands for Multiplication, Division, Addition, and Subtraction. It is part of the Order of Operations, a collection of rules that gives a sequence for simplifying mathematical operations. It is used when an expression or equation has more than one operation. According to the Order of Operations, all multiplication or division must occur before addition or subtraction. For example, the expression 6+4×5 involves addition and multiplication. According to MDAS, simplify the multiplication portion of the expression before adding. Since 4×5 equals 20, rewrite the expression as 6+20, which equals 26
= 1(8+12)-4)+5. (6-3)
= 20 - 4+5.3
= 16+15
=31
Answer:
Evaluate 1(8+12)-4)+5. (6-3) = 31
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Use the function to evaluate the indicated expressions and simplify.
f(x) = 4x² + 3
f(x + 2) =
f(x) + f(2)=
The function to evaluate the expression is f(x)+f (2) =4x^2+22.
The function simplify () attempts to "simplify" the input expression by using clever heuristics.
⇒ f(x)=4x^2+3
⇒ f(x+2)=4(x+2)^2+3
by using algebra formula
⇒ f(x+2)=4(x^2+4+4x)+3
⇒ f(x+2)=4x^2+16x+19
by adding f(x)+f (2)
⇒ f(x)+f(2)=4x^2+3+(4×(2)^2 )+3
⇒ f(x)+f(2)=4x^2+3+(4×4)+3
⇒ f(x)+f(2)=4x^2+3+16+3
⇒ f(x)+f(2)=4x^2+22
There is a general function called simplify () that seeks to reduce an expression to its most basic form. Simplify in simply, this function is defined. reduce module.
Hence, the function to evaluate the indicated expressions and simplify f(x)=4x^2+3, f(x+2)=4(x+2)^2+3 and f(x)+f(2)=4x^2+22.
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Please help me solve this !
Answer:
x = -0.25
Step-by-step explanation:
-4 x (2 x 1) = 8x - 2 - 4
-4 x 2 = 8x - 2 - 4
-8 = 8x - 2 - 4
-8 + 4 + 2 = 8x
-2 = 8x
-2/8 = x
x = -0.25
hoped this helped xx
Landscaping boulders weigh 28 pounds each. Using b for the number of boulders and w for the weight, write an equation that relate the two variables.
Equation should begin with b =.
In a unit circle, 0 = 3pi/2. What is the terminal point?
O A. (1,0)
O B. (0,1)
O C. (0, -1)
O D. (-1,0)
Option c - (0 , -1).
Terminal Point on the Unit Circle. To find the terminal point on the unit circle, start at (1, 0), measure the angle in degree or radian on the circle (move counter clockwise if the angle is positive and clockwise if the angle is negative.) The coordinate of the endpoint is called the terminal point.
In a unit circle, θ = 3π/2 radians.
r = 1
Angle θ = 3π/2
The terminal point is (rcosθ, rsinθ)
= (cos3π/2, sin3π/2)
cos3π/2 = 0
sin3π/2 = -1
= (0, -1)
Thus, for the unit circle 3π/2 = 0 ,the terminal points are (0, -1) . So the option C is the correct answer.
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Write a system of equations to describe the situation below, solve using any method, and fill
in the blanks.
At a candy store, Emilia bought 5 pounds of jelly beans and 4 pounds of gummy worms for
$61. Meanwhile, Jessica bought 3 pounds of jelly beans and 4 pounds of gummy worms for
$43. How much does the candy cost?
A pound of jelly beans costs $___
and a pound of gummy worms costs $____
Answer:
The last one
Step-by-step explanation:
A pilot flew a plane from an altitude of 6000 feet to an altitude of 18900 feet. What was the change in altitude?
Answer:
12,900
Step-by-step explanation:
18,900 - 6,000= 12,900
dino has a pizza with a diameter of
Based on the given parameters, the square box is big enough to fit the pizza?
How to determine if the square box is big enough to fit the pizza?The given parameters are:
Diameter of pizza = ten and one third inchesLength of square box = 10.38 inchesRewrite the parameters properly as:
Diameter of pizza = 10 +1/3 inches
Length of square box = 10.38 inches
Express the diameter as a numeral.
So, we have:
Diameter of pizza = 10 + 1/3 inches
Evaluate the sum
Diameter of pizza = 10.33 inches
By comparison:
10.33 inches is less than 10.38 inches
This means that the square box is big enough to fit the pizza
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Complete question
Dion has a pizza with a diameter of ten and one third inches.is a square box of 10.38 inches big enough to fit the pizza?
Marcus dives from the surface of the ocean to a reef 18 meters below sea level .what integer represents Marcus location relative to the surface?How far does Marcus have to go to return to the surface
The integer that represents Marcus location relative to the surface is -18 and Marcus has to go 18 meters to return to the surface
What integer represents Marcus location relative to the surface?The depth is given as
Depth = 18 meters below sea level
Below sea level is represented as negative
So, we have
Depth = -18
Hence, the integer that represents Marcus location relative to the surface is -18
How far does Marcus have to go to return to the surfaceThe distance to return to the surface is
Distance = |Depth|
This gives
Distance = |-18|
Evaluate
Distance = 18
Hence, Marcus has to go 18 meters to return to the surface
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The equations of two lines are given. Determine whether the lines L₁ and L2 are parallel, perpendicular, or neither
4₁: y = x + 1; L₂: y = - 6/5x + 3
The slope of the two equations is required to answer this
What is an equation?
An equation is a formula in mathematics that expresses the equality of two expressions by linking them with the equals sign. The word equation and its cognates in various languages may have somewhat different definitions; for example, in French, an équation is defined as including one or more variables, but in English, an equation is any well-formed formula consisting of two expressions linked by an equals sign.
Given equation
[tex]y=x+1[/tex] has slope [tex]m1=1[/tex]
and the other equation
[tex]-\frac{6}{5}x+3[/tex] has slope [tex]m2 =-\frac{6}{5}[/tex]
For parallel equations, [tex]m1=m2[/tex]
and for perpendicular equations, [tex]m1[/tex]x[tex]m2=-1[/tex]
These two equations are neither parallel nor perpendicular.
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Melissa Jackson, bookkeeper for Kinko Company, cannot prepare a bank reconciliation. The bank statement showed a $2,955.82 balance. Melissa’s checkbook showed a $3,301.82 balance. Melissa placed a $510.19 deposit in the bank’s night depository on June 30. The deposit did not appear on the bank statement. The bank included two DMs and one CM with the returned checks: $690.65 DM for NSF check, $8.50 DM for service charges, and $400.00 CM (less $10 collection fee) for collecting a $400.00 non-interest-bearing note. Check number 811 for $110.94 and check number 912 for $82.50, both written and recorded on June 28, were not with the returned checks. The bookkeeper had correctly written check number 884, $1,000, for a new cash register, but she recorded the check as $1,069. The May bank reconciliation showed check number 748 for $210.90 and check number 710 for $195.80 outstanding on April 30. The June bank statement included check number 710 but not check number 748.
Kinko's checkbook balance: $3,301.82 +Collection on notes receivable: $400,00 -Collection fee: $10.00 Notes-fee- $390.00 Error in recording: $69.00 Balance (Notes-fee)+Error= $3,760.82 -NSF Check: $690.65 -Service Charge: $8.50 Total in deduct: $699.15 Reconciled Balance: $3,061.67
Kinko's bank balance: $2,955.82
+Deposit in transit: $510.19 Balance+DIT= $3,466.01 -Outstanding checks (total): $404.34 Reconciled balance: $3,061.67
What is the simplest form of 5/8 divided by 2 21/3
Answer:
[tex]= \frac{5}{72}[/tex]
Step-by-step explanation:
21/3 = 7
(5/8)÷(2 21/3)
2 21/3 = 2 + 21/3 = 2 + 7 = 9
then:
(5/8)÷(2 21/3) = (5/8)÷9 = 5 ÷ (8*9)
= 5/72
please help:
add: 0.7+0.45
Answer:
1.15
Step-by-step explanation:
Answer 1.15
Step-by-step explanation:
the only thing you had to do is line it up like standard algorithm and add if you need anymore help just tell me.
How many times larger is (1.092 × 101) than (7 × 10−1)?
The answers: A. 0.156 B. 15.6 C. 6.41 D. 6.908
please helpppppppp
The correct option is A. 0.156. The number (1.092×10¹) is 156 times larger than number (7×10⁻¹).
What is defined as the scientific notations?Scientific notation is a method of writing extremely large or extremely small numbers. Whenever a number among 1 and 10 is multiplied by a power of 10, it is written in scientific notation. 650,000,000, for example, can be composed in scientific notation as 6.5× 10⁸.Scientific notation is a method of writing extremely large or extremely small numbers in a way that makes them easier to read as well as work with. A number is expressed as the product of an amount that is equal to one but less than ten and an integral power of ten.For the given number;
The number 1.092×10¹ can be written as; 10.92 after multiplication with 10.
Similarly, the number 7×10⁻¹ can be written as 0.7 after diving with 10.
Now, divide larger number by 0.7
= 10.92/0.7
= 156
Thus, the number 1.092×10¹ is almost 156 time greater than (7×10⁻¹).
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Which is the order from least to greatest of the following: seventh fifths, 0.4, one eighth, seventy five percent?
0.4, seventy five percent, seven fifths, one eighth
one eighth, 0.4, seventy five percent, seven fifths
0.4, one eighth, seventy five percent, seven fifths
seventy five percent, one eighth, 0.4, seven fifths
The order from least to greatest of the numbers will be B. one eighth, 0.4, seventy five percent, seven fifths.
How to oder the numbers?It should be noted that 7/5 = 1.4
It should be noted that 1/8 = 0.125
It should be noted that 75% = 0.75
Therefore, the ordering of the numbers from least to greatest will be one eighth, 0.4, seventy five percent, seven fifths.
In conclusion, the correct option is B.
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Is 635 a perfect cube? Check with your answer.
What is 8.118 divded by 0.615
