Answer:
[tex]\begin{Vmatrix}1 & 0 & 0& 46/41 &180/41\\0 & 1 & 0&1/41 &-5/41\\0&0 & 1 & -8/41& -42/41\end{Vmatrix}[/tex]
Step-by-step explanation:
From the question we are told that
System of equations given as
x₁ + 3x₂ + x₃ + x₄ = 3;
2x₁ - 2x₂ + x₃ + 2x₄ = 8;
x₁ - 5x₂ + x₄ = 5
Matrix form
[tex]\begin{Vmatrix}1 & 3 & 1&1&3\\2 & -2 & 1&2&8\\0&1 & -5 & 1& 5\end{Vmatrix}[/tex] [tex]\begin{Vmatrix}x_1\\x_2\\x_3\\x_4\end{Vmatrix}[/tex]
Generally the echelon reduction is mathematically applied as
[tex]\begin{Vmatrix}1 & 3 & 1&1&3\\2 & -2 & 1&2&8\\0&1 & -5 & 1& 5\end{Vmatrix}[/tex]
Add -2 times the 1st row to the 2nd row
[tex]\begin{Vmatrix}1 & 3 & 1&1&3\\0 & -8 & -1&0&2\\0&1 & -5 & 1& 5\end{Vmatrix}[/tex]
Multiply the 2nd row by -1/8
[tex]\begin{Vmatrix}1 & 3 & 1&1&3\\0 & 1 & 1/8&0&-1/4\\0&1 & -5 & 1& 5\end{Vmatrix}[/tex]
Add -1 times the 2nd row to the 3rd row
[tex]\begin{Vmatrix}1 & 3 & 1&1&3\\0 & 1 & 1/8&0&-1/4\\0&0 & -41/8 & 1& 21/4\end{Vmatrix}[/tex]
Multiply the 3rd row by -8/41
[tex]\begin{Vmatrix}1 & 3 & 1&1&3\\0 & 1 & 1/8&0&-1/4\\0&0 & 1 & -8/41& -42/41\end{Vmatrix}[/tex]
Add -1/8 times the 3rd row to the 2nd row
Add -1 times the 3rd row to the 1st row
[tex]\begin{Vmatrix}1 & 3 & 0&49/41&165/41\\0 & 1 & 0&1/41 &-5/41\\0&0 & 1 & -8/41& -42/41\end{Vmatrix}[/tex]
Add -3 times the 2nd row to the 1st row
[tex]\begin{Vmatrix}1 & 0 & 0& 46/41 &180/41\\0 & 1 & 0&1/41 &-5/41\\0&0 & 1 & -8/41& -42/41\end{Vmatrix}[/tex]
1. 6 divided by 8/9 SHOW YOUR WORK AND EXPLAIN
Answer:
6.75 is the answer
Step-by-step explanation:
6(8/9)
=6.75
Answer: 6.75
Step-by-step explanation:
1. Multiply the whole number by the denominator
6x9=54 (The denominator stays the same)
Which gives us 54/8 (the answer to 6 divided by 8/9 in fraction form is 54/8)
The answer to 6 divided by 8/9 is 6.75 in decimal form.
Eli had 12 goals on the season. If he played in 8 games, how many goals did he average per game? Your answer
Answer:
1.5 goals
Step-by-step explanation:
12 divided by 8= 1.5
Use the following information for the question. Male players at the high school, college and professional ranks use a regulation basketball that weighs 22.0 ounces with a standard deviation of 1.0 ounce. Assume that the weights of basketballs are approximately normally distributed. Roughly what percentage of regulation basketballs weigh more than 23.1 ounces
Answer:
13.567%
Step-by-step explanation:
We solve the above question, using z score formula
z = (x-μ)/σ, where
x is the raw score = 23.1 ounces
μ is the population mean = 22.0 ounces
σ is the population standard deviation = 1.0 ounce
More than = Greater than with the sign = >
Hence, for x > 23.1 ounces
z = 23.1 - 22.0/1.0
= 1.1
Probability value from Z-Table:
P(x<23.1) = 0.86433
P(x>23.1) = 1 - P(x<23.1)
P(x>23.1) = 1 - 0.86433
P(x>23.1) = 0.13567
Converting to percentage
= 0.13567 × 100
= 13.567%
Therefore, the percentage of regulation basketballs that weigh more than 23.1 ounces is 13.567%
A fraction is shown.
What fraction is shown on the number line?
Answer:
d. 5/8
Step-by-step explanation:
the number line is split into eighths because 1 would be 8/8.
The circumference of a roll of party streamers is 11 inches. The circumference decreases by 3 inches after you use the streamers to decorate for a birthday party. Find the diameter of the roll after the decrease. Round your answer to the nearest hundredth.
Answer:
2.54 inches
Step-by-step explanation:
Vic bought a new plasma TV for $2400. He made a down payment of $200 and then financed the balance through the store. Unfortunately, he was unable to make the first monthly payment and now pays 6% interest per month on the balance (while he watches his TV).
This question is incomplete, the complete question is;
Vic bought a new plasma TV for $2400. He made a down payment of $200 and then financed the balance through the store. Unfortunately, he was unable to make the first monthly payment and now pays 6% interest per month on the balance (while he watches his TV).
What is Vic's Monthly interest payment ( Assume interest rates are 1/12 of annual interest rates)
Answer: Vic's Monthly interest payment is $132
Step-by-step explanation:
Given that;
Purchase cost of plasma Tv = $2400
down payment made = $200
so,
Balance financing from store = $2400 - $200 = $2,200
also given that Interest rate is 6% per month6
Now Monthly interest payment will be;
⇒ financing amount × interest rate
⇒ 2200 × (6/100) = 132
Therefore, Vic's Monthly interest payment is $132
Apply the distributive property to factor out the greatest common factor. 30 + 42
Answer:
The answer is 6(5+7)
Step-by-step explanation:
Alice walks 6/10 miles every day. how many miles does she walks 5 days?
3 miles
6 / 10 × 5 = 30 / 10
30 / 10 = 3
Please help I am having a really bad day and crying all the time.
Answer:
7 dollars
Step-by-step explanation:
I hope this helps and i hope you have better days and stop crying because life is way to short for all of that and i dont know you but you dont deserve to cry all the time you should be happy if you want to talk about anything im here!
multiply the binomials (2x-7)(x-5)
(PLEASE HELP ASAP)
A plumber has a 12-foot piece of pipe. He needs 8 feet, 6 inches of pipe to repair a leak in a water line. How many inches of pipe will he have left after he makes the repair?
Answer:
3ft 6in or 42 inches in total
Step-by-step explanation:
hope this helps
4. If Nick goes swimming 7 times, what would he need to pay with each payment plan? Which is
the best payment method for him?
5. If Nick goes swimming 9 times, what would he need to pay with each payment plan? Which is
the best payment method for him?
6. If Nick goes swimming 13 times, what would he need to pay with each payment plan? Which is
the best payment method for him?
Answer:
number 4 and plz thank me if this is right plz
Graphing Polynomial Functions
Graph the following functions by making a table
of values
f(x)=x^5-3x^4+9x^3-x^2+2
Answer:
table and graph attached
Step-by-step explanation:
help me plz One line of text on a page uses about 4/15 of an inch. There are 0.5-inch margins at the top and bottom of a page. Write and solve an inequality to find the number of lines that can be typed on a page that is 17 inches long.
Answer:
60 lines can be typed in the page
Step-by-step explanation:
Given:
Length of the page = 17 inches
Length of the margin = 0.5-inch
length of one line = 4/15
To Find:
The number of lines that can be typed on a page
Solution:
Let the number of line that can be typed be n
then
n <=
the top and bottom margins are 0.5 inches each
so we will be having
=>
=>
=>
=>
=>
Tanya’s gross pay this pay period is $2,100. She is expecting $300 to come out for taxes and insurance. What should her net pay be on her paycheck?
Answer:
1800
Step-by-step explanation:
if 300 is all that is being subtracted from her gross pay then it should just be 2100-300=netpay
After deducting the tax and insurance from the gross pay, the net pay that will be on Tanya's paycheck is $1,800.
Given parameters:
Tanya's gross pay = $ 2,100
Estimated amount for tax and insurance = $300
To find:
the net pay on her paycheckTanya's net pay after deducting the tax and insurance is calculated as;
The net pay = Gross pay - tax and insurance
The net pay = $ 2,100 - $300The net pay = $1,800Thus, the net pay that will appear on Tanya's paycheck is $1,800.
Learn more here: https://brainly.com/question/16555855
What is the simplest way to explain scale drawings for middle school math?
Answer:
The simplest way to teach middle school math scale drawings is to use real pictures to relate to each other to explain the concept. For example, scaling a red ball of 1" to a ball of 2" and so on. This will show how the ball increases by size by adding 1" each time.
Nine times the sum of a number and ten is the difference of a number and six
Answer:
The answer is -2.
hey this subjects really hard for me can someone answer please its 50 points
plz solve for brainlyest
Answer:
1.80
Step-by-step explanation:
Simplify the following expression. Rationalize all denominators.
Answer:
[tex]\frac{\sqrt{3}x}{2y^{\frac{2}{3} } }[/tex]
Step-by-step explanation:
√3x^6/√2x^4y^3
~Factor
(√3)x^3/(√2)x²y√y
~Cancel
(√3)x/(√2)y√y
~Rationalize
(√6)x/2y^(2/3)
Best of Luck!
36 x - 8y2 when x=3 and y= 6
Step-by-step explanation:
multiply the numbers
36×3=108. 8×6×2=96
subtract the numbers
108-96
=12
great day :)
Answer:
12
Step-by-step explanation:
x = 3
36 x 3 = 108
y = 6
8 x 6 x 2 = 96
= 108 - 96
= 12
What is the slope of the function?
if u have a 30-foot long ribbon and u split it into 7 equal parts how muck woold u get in number plz I need help
Answer:
[tex]Each\ Part = 4.29\ ft[/tex]
Step-by-step explanation:
Given
[tex]Length = 30\ ft[/tex]
[tex]Parts = 7[/tex]
Required
Determine the length of each part
This is calculated as:
[tex]Each\ Part = \frac{Length}{Parts}[/tex]
[tex]Each\ Part = \frac{30\ ft}{7}[/tex]
[tex]Each\ Part = \frac{30}{7}\ ft[/tex]
[tex]Each\ Part = 4.29\ ft[/tex] -- approximated
Hence, the length of each part is approximately 4.29ft
The polygons are similar. Solve for x.
scale factor from A to B = 3:5
Answer:
9
Step-by-step explanation:
if scale factor is 3/5, then
(x+12):35=3:5, ⇒
[tex]\frac{x+12}{35} =\frac{3}{5}; x=21-12; x=9[/tex]
F(-2)=x^2-3x+4; find f(-2)
A package of spaghetti weighs 238 grams. How many ounces does the package weigh? 1 oz = 28 g.
Answer: 8.5
Step-by-step explanation: 238 / 28 = 8.5
8.5 oz
The package of spaghetti weighs 8.5 ounces.
To find out how many ounces the package of spaghetti weighs, we can use the conversion factor that 1 ounce is equal to 28 grams.
Given that:
package of spaghetti weighs 238 grams, we can convert this to ounces by dividing it by the conversion factor:
= 238 grams / 28 g/oz
= 8.5 ounces
Therefore, the package of spaghetti weighs 8.5 ounces.
Learn more about Unit Conversion here:
https://brainly.com/question/28600662
#SPJ6
Help ASAP! And explain!
Answer:
Option (2)
Step-by-step explanation:
Given:
AC is an angle bisector of ∠DAB and ∠DAB
m∠BCA ≅ m∠DCA
m∠BAC ≅ m∠DAC
To Prove:
ΔABC ≅ ΔADC
Solution:
Statements Reasons
1). m∠BCA ≅ m∠DCA 1). Given
2). m∠BAC ≅ m∠DAC 2). Given
3). AC ≅ AC 3). Reflexive property
4). ΔABC ≅ ΔADC 4). ASA property of congruence
Therefore, Option (2) will be the correct option.
Select the point shown on the coordinate plane for each ordered pair. Point is located at (3, 9). Point is located at (9, 3). Point is located at (6, 5). Point is located at (5, 6).
Answer:
A D B C in ORDER
Step-by-step explanation:
Answer:
Point
✔ A
is located at (3, 9).
Point
✔ D
is located at (9, 3).
Point
✔ B
is located at (6, 5).
Point
✔ C
is located at (5, 6).
Step-by-step explanation:
I hope this helps doing the Assignment!
What is the radius of a circle with a diameter of 12 inches?
Answer:6
Step-by-step explanation:
the radius of a circle is half of the length of the diameter
Answer:
diameter of circle=12 inches
radius of circle = half of diameter
=12÷2
=6 inches
Jordan has a checking account. he withdrew $90 from an ATM Tuesday. Thursday he deposited $20. Friday he wrote a check for $15 what was the total change in Jordan account
Answer:
The total change in his account is of -$85, that is, a loss of $85
Step-by-step explanation:
We combine these changes. So
On Tuesday, he withdrew $90 from his account, which means that, the total change, initially of $0, is now of -$90.
On Thusday, he deposited $20, which means that the total change of -$90 is now of -$90 + $20 = -$70
On Friday, he wrote a check of $15, removing 15 from his account, which means the total change will be of -$70 -$15 = -$85
