A system of equations is shown:
2x = -y + 6
--4x + 3y = 8
What is the solution to this system of equations?
0 (-1,-4)
O (1.4)
(4, 1)
(-4,-1)
Answers
[tex]\large\underline{\bf \red{Step \:by\: Step \:Explanation:}}[/tex]
Given two equations are :
2x = - y + 6.-4 x + 3y = 8 .We may write them as ,
2x + y - 6 = 0 .................(i) 4x - 3y + 8 = 0 ...............(ii)Multiplying equⁿ (i) by 2 :
⇒ 2(2x + y - 6 ) = 0.
⇒ 4x + 2y - 12 = 0 .....................(iii) .
Subtract equⁿ (ii) from equⁿ (iii) :-
⇒ 4x + 2y - 12 = 0
ㅤ- 4x + 3y - 8 = 0 [ Sign changes ]
__________________
⇒ 5y - 20 = 0.ㅤㅤㅤㅤㅤ
⇒ 5y = 20.
⇒ y = 20/5.
⇒ y = 4
Put this value in (i) to obtain x .
⇒ 2x + y - 6 = 0.
⇒ 2x +4 - 6 = 0.
⇒ 2x - 2 = 0.
⇒2x = 2 .
⇒ x = 2/2.
⇒ x = 1 .
Hence the value of x is 1 & y is 4.
[tex]\boxed{\purple{\bf\pink{\dag}\:Hence\:the\: correct\: option\:is\:[b]\:(1,4)}}[/tex]
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You measure the mass of a book and it’s 420.0890g how many significant digits are in the measurement
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Answer:
7
Step-by-step explanation:
All of the digits in the given number are significant. There are 7 significant digits.
__
Comment on other cases
When there are non-zero digits to the left of the decimal point in a number with a decimal point, all of the digits are significant.
When there are no non-zero digits to the left of the decimal point, leading zeros are not significant. All digits following the leading zeros are significant.
In a number with no decimal point, the leading and trailing zeros are not significant.
If the number is written in scientific notation, all digits of the mantissa are significant. (This can be a way to ensure the correct number of significant digits is known in a number with trailing zeros.)
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Solving a word problem using a 3x3 system of linear equations....
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Find the midpoint of the line segment joining the points R(,) and S(,).
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montha
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Step-by-step explanation:
Homework Weekend Create a short story.
All the fudge machines at a chocolate factory work at the same rate. Six machines working simultaneously can complete a big order in 22 hours.
a
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Step-by-step explanation:
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Complete the following statement to estimate the root of 75 to the nearest tenth. Use numbers that are closest to the root of 75
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Molly has 9 cups of flour. If this is 3/4 of the number she needs to make bread, how many cups does she need?
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Answer:
She needs 12 cups of flour to make bread
Step-by-step explanation:
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what is the value of x,if x=9-9/4
Answers
Answer:
X=6 3/4
Step-by-step explanation:
IF X=9-9/4(X=9-2 1/4) THEN X=6 3/4. HOPE THIS HELPS
You decide to purchase a bond for $500. It pays 5% simple interest per year and matures in 5 years. How much interest will you earn once the bond matures? Round your answer to the nearest dollar.
Do NOT round until you have calculated your final answer.
Answers
Answer:
$625
Step-by-step explanation:
You start with $500
The interest per year is 5% or 500 x 0.05 = $25
If it matures 5 years and each year has an increase of $25 then
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Year 3 - $575
Year 4 - $600
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Answer:
Step-by-step explanation:
We express the interest rate r in decimal form, so we have r=5%=5100=0.05. The principal is P=500 and the time in years is t=5. So, the interest is I=Prt=(500)(0.05)(5)=$125. The interest earned is $125.
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Answer: 1. 2x-3y=-1 y=x-1 2. y=6x-11 -2-3y=-7 3. y=3x+5 5x-4y=-3
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#2. y=6x-11 and -2x-3y=-7
#3. y=-3x+5 and 5x-4y=-3
convert 0.00633 to a scientific notation
Answers
Answer:
6.33 × 10⁻³
Step-by-step explanation:
Scientific Notation: x.xx × 10ⁿ
We simply follow the base 10 decimal system to put anything in scientific notation. Since we are moving the decimal place 3 places to the right, we would have it as 10⁻³ multiplying our standard form.
Answer:
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Step-by-step explanation:
** The negative three is supposed to be an exponent **
What is the value of 4(x - 2)(x + 3) + 7(x - 2)(x - 5) - 6(x - 3)(x - 5) when x = 5?
Answers
Answer:
96Step-by-step explanation:
Put x = 5 to the expression 4(x - 2)(x + 3) + 7(x - 2)(x - 5) - 6(x - 3)(x - 5)
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Felicia is making trail mix. The recipe calls for 3 cups pretzels and 1.5 cups of m&m's.
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Answers
Answer:
81 Cups of Pretzels and 40.5 Cups of M&M's
Step-by-step explanation:
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The following are a list of variables that will almost certainly vary across students in a large undergraduate introductory statistics course.
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Answers
Step-by-step explanation:
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age
Handedness (e.g., left or right handed)
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Answer:
?
Step-by-step explanation:
A deep sea diver descended from a rock that is 45 feet below
Answers
A deep sea diver descended from a rock that is 45 feet below sea level to a coral reef that is 88 feet below sea level.
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Difference = -45 - ( - 88)
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If that is your question...
Emma is 10 years younger than Joseph. Joseph's age 6 years from
now will exceed twice Emma's age 2 years ago by 3 years.
How old is Em ma and Joseph now?
Answers
Answer:
Step-by-step explanation:
let Emma age be x now
Let Joseph age be y now
If Emma is 10 years younger than Joseph, then x = y-10
six years from now:
Emma will be x+6 years
Joseph will be y+6 years
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y+6 = 2(x+6-2) + 3
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Answers
Answer:
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Step-by-step explanation:
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Answers
Answer:
The coordinates of the midpoint of LB are (1, 3.5)
Step-by-step explanation:
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Let us use this rule to solve the question
∵ M is the midpoint of segment LB
∵ The coordinates of point L are (8, 5)
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∵ The coordinates of point B are (-6, 2)
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→ Remember (+)(-) = (-)
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∴ The coordinates of the midpoint of LB are (1, 3.5)
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Find the slope of the line.
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Enter your answer in the box
Answers
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-2y = 126
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Factorise fully
-x - 8
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Answers
Answer:
-(x+8)
Step-by-step explanation:
-x - 8
-1 *x -1 * 8
Factor out a -1
-1(x+8)
-(x+8)
Answer:
-1(x+8)1(-x -8)Step-by-step explanation:
[tex] - x - 8[/tex]
Factor out common term : -1
[tex] - 1(x + 8)[/tex]
Which shows another way to write 9.54?
O 0.5 + 0.04
O 9+ 0.4 + 0.05
O (9 * 1) + (5 x 0.1) + (4 x 0.01)
O (9 x 0.1) + (5 x 0.01) + (4 x 0.001)
Answers
Answer:
It would be C
Step-by-step explanation:
If A and B are independent events, which equation must be true?
Α.
P(B/A) = P(A)
B.
P(B/A) = P(B)
C.
P(B/A) = P(A) P(B)
D.
P(B/A) = P(A) + P(B)
Answers
Answer:
B. P(B/A)=P(B)
A coin is about to be tossed 50 times. Determine the probability the 8th heads occurs on the 12th toss
Answers
Answer:
0.0806
Step-by-step explanation:
From the given information:
Number of toss = 50
The probability of having a head = 1/2 = 0.5
The Probability of 8th head occur on 12th toss can be computed as :
Pr(8th head occur on 12th toss) = Pr(7 heads in 11 toss) × P(8th head on 12th toss)
Pr(8th head occur on 12th toss) = C(11,7) × 0.5⁷ × (1 - 0.5)⁴ * 0.5
Pr(8th head occur on 12th toss) = [tex]\dfrac{11!}{7!(11-7)!}[/tex] × 0.5⁷ × (1 - 0.5)⁴ × 0.5
Pr(8th head occur on 12th toss) = 0.0806
Answer:
The probability of 8th heads,
That is occurred on 12th toss.
Step-by-step explanation:
A coin is tossed 50 times.
There are two possible outcomes of occurring a head or tail.
Probability of occurring head = no.of head/ possible outcomes
= 1/2
Total number of tossing a coin= 50 times
Probability of 8th heads occurs on 12th toss:
12C8 (1/2)8 (1/2)9 (1/2)10 (1/2)11 (1/2)12
= 12C8 (1/2)8+9+10+11+12
= 12C8 (1/2)50
= 12C8 / 250
= 495 / 1125899906842624
= 4396.48317752 x 10-16
This is the probability of 8th heads,
That is occurred on 12th toss.
In a certain section of Southern California, the distribution of monthly rent for a one-bedroom apartment has a mean of $2,325 and a standard deviation of $270. The distribution of the monthly rent does not follow the normal distribution. In fact, it is positively skewed. What is the probability of selecting a sample of 50 one-bedroom apartments and finding the mean to be at least $2,245 per month
Answers
Answer:
0.982
Step-by-step explanation:
Given that:
Mean (μ) = 2325
Standard deviation (σ) = 270
From the central limit theorem ; the Distribution of 50 sample means will be normally distributed
Finding the mean to be at least $2245 per month;
x = 2245
Using the Z score relation :
Zscore = (x - μ) / (σ/√n)
Zscore = (2245 - 2325) / (270/√50)
Zscore = - 80 / 38.183766
ZSCORE = - 2.0951312
= - 2.1
P(Z > - 2.1) = 0.982 ( from the Z probability Calculator).
8.032×10^-4 in standard form
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Answer:
0.0008032
Step-by-step explanation:
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Answer:
80,320
Step-by-step explanation:
To solve the problem -9 + 18 what is the first step?
a. KCO (keep change fli[p)
b. Subtract 18 - 9
c. Subtract 9 - 18
d. Add 9 + 18
Answers
Answer:
Step-by-step explanation:
How is 5 represented in 6.75
Answers
Answer:
5 is in the hundreths place :))
Step-by-step explanation:
Answer:
0.05
Step-by-step explanation:
since the place value of the five is beyond the decimal point, and it is the second number beyond the decimal point, so it is in the hundredths place.
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Answers
Is 17/5 + square root of 64 greater than 8 + pi?
Answers
Answer:
I'm probably wrong 69??? Yea I'm definitely wrong
Which graph represents a function?