The solution of the given system of linear equation would be x = 1, y = 1, and z = 0.
What is a linear equation?A linear equation is one in which the greatest power of the variable is always one.
The given system of linear equation as:
-2x+2y+3z=0 ...(i)
-2x-y+z=-3 ...(ii)
2x+3y+3z=5 ...(iii)
Adding the third equation to the (i) and (ii), we get
5y+6z=5
2y+4z=2
Multiplying the equation(ii) by -6/4 and after adding to get
⇒2y=2
Dividing both sides by 2.
⇒y=1
Substitute the value of y=1 into 2y+4z=2, and we get
⇒2+4z=2
Subtracting 2 from both sides, we get
⇒ z = 0
Substitute the values of y=1 and z=0 into -2x-y+z=-3, we get -2x-1+0=-3
By adding 1 to both sides, we get -2x=-2
By dividing both sides by -2, we get x=1
Therefore, the solution of the given system of linear equation would be x = 1, y = 1, and z = 0.
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Consider the type of clothes dryer (gas or electric) purchased by each of five customers at a certain store. A. If the probability that at most one of these purchases an electric dryer is 0.428 what is the probability that at least two purchase an electric dryer?
One- third of a number is five-sixths. Find the number
Another common multiple of 30 and 42 besides 210
divide 300 g^2 0.0005 g and express using scientific notation
Answer:
[tex]\Rightarrow 6\times 10^5\ g[/tex]
Step-by-step explanation:
Given : Divide two number and write as scientific notation.
Scientific notation:
[tex]\Rightarrow k\times 10^n[/tex]
Number 1: 300 g²
Number 2: 0.0005 g
Divide [tex]=\dfrac{300\ g^2}{0.0005\ g}[/tex]
[tex]\Rightarrow \dfrac{30\times 10}{5\times 10^{-4}\ g{2-1}[/tex]
[tex]\Rightarrow 6\times 10^{1+4}\ g[/tex]
[tex]\Rightarrow 6\times 10^5\ g[/tex]
Scientific notation:
[tex]\Rightarrow k\times 10^n[/tex]
Hence, The result of division is [tex]\Rightarrow 6\times 10^5\ g[/tex]
A taxi service charges a flat fee of $4.20 per ride plus an additional $.80 per mile.
If a taxi ride costs $6.60, how many miles did the taxi travel?
Answer:
3.
Step-by-step explanation:
How many combinations of four different odd numbers whose sum is 30 can you find?
Evaluate the exponential function ƒ(x) = 8x + 1.
the answer, by putting 1/3 in the place of x the answer comes out to 3.
You spend $28 on ingredients to make cookies. You charge $4 per container of cookies. How many containers do you need to sell to earn $20 in profit?
Complete the equation below by writing an equation equivalent to height h of a cylinder
what is -0.38,-3/8,-0.04 in order from least to greatest
smamantha deposits ＄300 in a bank account thats earns an annual rate of 2.5%.after 9months,she computes the simple interest what is the correct amount of simple interest after 9 months
Evaluate –32 + (2 – 6)(10).
Final answer:
The expression –32 + (2 – 6)(10) evaluates to –72, by first calculating the operation within the parentheses, multiplying it by 10, and then adding it to –32.
Explanation:
To evaluate the expression –32 + (2 – 6)(10), we must follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). Firstly, we calculate the value inside the parentheses (2 – 6), which equals –4. Then we multiply this value by 10 to get –40. Finally, we add the result to –32 which gives us –32 + (–40) = –32 – 40 = –72.
Final answer:
The expression –32 + (2 – 6)(10) evaluates to –372 after performing the operations inside the parentheses and then multiplying and adding as per the order of operations.
Explanation:
To evaluate the expression –32 + (2 – 6)(10), we start by performing the operation inside the parentheses first. We subtract 6 from 2, getting –34. Then we multiply this result by 10 to get –340.
Next, we add this result to –32: –32 + (–340) = –372. So the final answer to the expression is –372.
A silo composed of a cylinder topped by a half-sphere. The height of the cylinder is 6.2 meters and the radius of both the cylinder and the half-sphere is 1.6 meters. Use 3.14 for pi. Find the volumes of the half-sphere, the cylinder, and the entire silo to the nearest tenth. Explain how you found the volume of the silo.
Answer:
55.88
Step-by-step explanation:
On a bike across the United States rodney notes that he covers about 190 miles every 4 days if he continues
at this rate use a ratio table to determine how many miles he could buy in 6 days
The highest point in Texas ,Guadalupe peak is 8749 feet high the highest point in California Mount Whitney is 14497 feet high. How much higher is Whitney then Guadalupe?
What is the equation in point slope form of the line passing through (4,0) and (2,6)
What is the best answer to report for (679 × 0.0025) 24.17?
To solve (679 × 0.0025) + 24.17, multiply 679 by 0.0025 to obtain 1.6975, then add this to 24.17 to get the final result, which rounded to the nearest thousandth is 25.868.
To find the best answer to report for the calculation (679 × 0.0025) + 24.17, we first perform the multiplication of 679 by 0.0025. This step is crucial to solve the problem accurately. After carrying out the multiplication, we add the result to 24.17 to find the final answer.
Calculating 679 × 0.0025 gives us 1.6975. The next step is to add this product to 24.17:
1.6975 + 24.17 = 25.8675
Thus, the best answer to report, rounded to the nearest thousandth as is common in many mathematical contexts, would be 25.868.
Complete Question:
What is the best answer to report for: (679 × 0.0025) + 24.17?
Find the amount of money in an account after 10 years if a principal of $2500 is invested at 3.5% interest compounded quarterly
An athlete eats
45
grams of protein per day while training. How much is this in milligrams?
Which method do you prefer to use to find sums__count by tens and ones,use compatible numbers,or use friendly numbers and adjust? Explain why.
A sporting goods manufacturer designs a golf ball having a volume of 2.48 cubic inches.
What is the radius of the golf ball?
If the ball's volume can vary between 2.45 cubic inches and 2.51 cubic inches, how can the radius vary?
identify epsilon and limit
f (1)= 7, f (n)= f (n-1) + 14
The percentage results of a quiz are as follows: 62, 83, 90, 72, 88, 92, 75, 88, 96, 86, 81, 68, 87. About what percent of the class scored below an 80?
Which of the following symbols correctly replaces the question mark (?) in the number comparison below?
0.700 ? 0.7
>
≠
=
<
Answer:
=
Step-by-step explanation:
When solving this, we just have to remember that the zero´s to the right after the decimal point are meaningless, so basically 0.700 is the same as 0.7 so in this case both number are the same, 0.700 and 0.7 are the same number expressed in different ways.
A race car travels at 205 mi/h. How far does the car travel in 3 hours
How many pairs of whole numbers have the sum of 99
If the angle between polaris and the horizon is 40°, what is your approximate latitude?
Polaris is the basis of our calculation having a deviation of 0.7 degrees from the fixed north. So if the angle between Polaris and the horizon is 40 degrees, then it only means that you are at approximately 39.3-40.7 degrees north latitude.
Final answer:
The angle between Polaris and the horizon is approximately equal to the observer's latitude. Therefore, if Polaris is observed at a 40° angle from the horizon, the observer is at approximately 40° North latitude.
Explanation:
When you observe Polaris, the North Star, from your location and find that its angle above the horizon is 40°, this angle is equivalent to your approximate latitude. This is because Polaris is situated nearly directly above the Earth's North Pole.
Therefore, the altitude angle of Polaris, as you observe it from a particular location in the Northern Hemisphere, generally corresponds to that location's latitude. In your case, since Polaris is at a 40° altitude, your latitude is approximately 40° North.
A certain plant grows 1 1/6 inches every week. How long will it take the plant to grow 6 1/6 inches
(b) we often read that iq scores for large populations are centered at 100. what percent of these 78 students have scores above 100? (round your answer to one decimal place.)
IQ scores follow a bell curve distribution where 100 is the mean. About 50% of people score above 100. Therefore, in a group of 78 students, we would expect about 39 students to have IQ scores above 100.
Explanation:The question is asking to determine what percent of 78 students in a population have IQ scores above a 100. Given that the IQ scores in large populations are centered at 100 and follow a bell curve, most people fall within the range of 85 to 115. The percentage of people who score above 100 is the same as those who score below it - about 50%.
According to the nature of a bell curve, approximately 34% of people score between 100 and 115, and about 14% score above 115. Therefore, around 50% (34% + 14%) of the people score above 100.
Applying this percentage to the population of the 78 students, we would expect about 50% of this student population to have scores above 100. So, 50% of 78 students amounts to 39 students. Rounded off to one decimal place, the answer would be 39.0 students. However, students can't be divided, so we conclude that about 39 students from the group of 78 have IQ scores above 100.
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What is 40 1/2 divided by 13 1/2?