After Multiplying 3 with the eq. (i) we will add this to eq. (ii)
[tex] \sf 18x - 6y + 3z = - 2[/tex]
[tex] \sf2x + 3y - 3z = 11[/tex]
_______________________[tex]⇒ \sf20x - 3y = 9 \: \: .........(iv)[/tex]
After Multiplying 2 with the eq. (iv) we will add this to eq. (iii)
[tex] \sf \: x + 6y = 31[/tex]
[tex] \sf40x - 6y = 18[/tex]
_________________[tex] \sf \: 41x = 49[/tex]
[tex]⇒ \sf \: x = \frac{49}{41} [/tex]
After putting the value of x in the eq. (iii)
[tex] \sf \frac{49}{41} + 6y = 31[/tex]
[tex]⇒ \sf6y = 31 - \frac{49}{41} [/tex]
[tex] \sf \: ⇒ 6y = \frac{1271 - 49 }{41} [/tex]
[tex]⇒ \sf6y = \frac{1222}{41} [/tex]
[tex]⇒ \sf \: y = \frac{1222}{41 \times 6} [/tex]
[tex]⇒ \sf \: y = \frac{611}{123} [/tex]
After putting the value of x and y into eq. (i)
[tex] \sf6 \times \frac{49}{41} - 2 \times \frac{611}{123} + z = -2 [/tex]
[tex]⇒ \sf\frac{294}{41} - \frac{1222}{123} + 2 = - z[/tex]
[tex]⇒ \sf \frac{882 - 1222 + 246}{123} = - z[/tex]
[tex]⇒ \sf - \frac{94}{123} = - z[/tex]
[tex]⇒ \sf \: z = \frac{94}{123} [/tex]
Hence,
[tex] \bf • \: The \: value \: of \: x = \frac{49}{41}
[tex] \bf • \: The \: value \: of \: x = \frac{49}{41} [/tex]
[tex] \bf • \: The \: value \: of \: y = \frac{611}{123}
[tex] \bf • \: The \: value \: of \: y = \frac{611}{123}[/tex]
[tex] \bf• \: The \: value \: of \: z \: = \frac{94}{123}[/tex]
Vaughn paints his porch floor and also the porch floors of 9 neighbors. Each floor is a rectangle that is 8.2 feet long and 6.7 feet wide. What is the exact total area of all the porch floors that Vaughn paints? Enter your answer in the box.
(My little sister needs help but I can't help her right now)
Answer:
494.46 feet²
Step-by-step explanation:
So the area of one porch floor is
=l×w
=8.2×6.7 feet²
=54.94 feet²
So he paints 9 porch floors
So the exact total area of all the porch floors that Vaughn paints is
=54.94×9 feet²
=494.46 feet²
·A long distance runner started on a course running at an average speed of 6
mph. One hour later, a second runner began the same course at an average
speed of 8 mph. How long after the second runner started will the second
runner overtake the first runner? I also need the work pls help!
Identify a solution to this system of equations:
[-4+3y=23]
[x-y=-7]
Answer:
solution for -4 + 3y = 23
3y = 23+4
3y = 27
y = 9
solution for X - y = -7
X = 1
y = 8
Answer: x = 2; y = 9
[tex]\left \{ {{-4+3y=23} \atop {x-y=-7}} \right.\\\\<=>\left \{ {{3y=27} \atop {x=y-7}} \right.\\\\<=>\left \{ {{y=9} \atop {x=y-7}} \right.\\\\<=>\left \{ {{y=9} \atop {x=2}} \right.[/tex]
Step-by-step explanation:
What is the value of y?
A. 10
B. 110
C. 85
D. 55
Answer:
D. 55°
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Geometry
All angles in a triangle add up to 180°Step-by-step explanation:
Step 1: Set Up Equation
40° + (y + 30)° + y° = 180°
Step 2: Solve for y
Combine like terms: 2y° + 70° = 180°Isolate y term: 2y° = 110°Isolate y: y° = 55°John and his best friend found some money. They split the money evenly, each getting $14. How much money did they find?
Answer:
$28
Step-by-step explanation:
John and his best friend each got $14, so in total there are $14+$14=$28.
Answer:
$28
Step-by-step explanation:
If they split the money evenly then both of them got half.
So, multiply 14 by 2 to find the answer:
(14)(2) = 28
John and his best friend found a total of $28.
I hope this helps!!
- Kay :)
how many combinations of 3 letters can be made from the word oranges ? what is the probability that these three letters will all be consonants?
The number of all possible combinations of 3 letters can be made from the word 'oranges' = 35
The probability that the three letters will be consonants = 0.114
In this question, we have been given a word 'oranges'
We need to find the number of ways in which the letters of orange can be arranged.
Also, we need to find the probability that these three letters will all be consonants.
The number of letters in the word oranges = 7
So, n = 7
We need combinations of 3 letters.
so, r = 3
The number of all possible combinations of 3 letters would be,
^7C_3 = 7! / (7 - 3)! (3!)
^7C_3 = 35
The number of combinations of 3 letters = 35
We can observe that the consonants in the word 'oranges' are:
r, n, g, s
The number of consonants = 4
The combinations of 3 consonants would be,
^4C_3 = 4! / (4 - 3)! 3!
^4C_3 = 4
The required probability would be,
p = ^4C_3 / ^7C_3
p = 4 / 35
p = 0.114
Therefore, the number of all possible combinations of 3 letters can be made from the word 'oranges' = 35
the probability that the three letters will be consonants = 0.114
Learn more about the probability here:
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Find the m<2 if m<1=127 awnser choice a.106 b.127 c. 90 d.53
how many solutions does
-10x+x=-9x have
A) one solution
B) two solutions
C) No solutions
D) infinite solutions
Answer:
I am not sure but i think B so two solutions
If v2 = u2 + 2as, evaluate a when v = 5,
u = 2 and s = 7.
Answer:
a = 3/2
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define
v² = u² + 2as
v = 5
u = 2
s = 7
Step 2: Evaluate
Subtract u² on both sides: v² - u² = 2asDivide 2s on both sides: (v² - u²)/(2s) = aRewrite: a = (v² - u²)/(2s)Substitute: a = (5² - 2²)/(2 · 7)Exponents: a = (25 - 4)/(2 · 7)Multiply: a = (25 - 4)/14Subtract: a = 21/14Simplify: a = 3/27
Find the slope of a line that passes through the points (-5,3) and (-3, 8)
Answer:
-2/5
Step-by-step explanation:
hope this helps
determine the slope of the lines.
line 1: y=9
line 2: x=-3
are the slopes parallel, perpendicular, or neither?
Which graph shows a non-proportional linear relationship between x and y?
10:Mohan lent altogether 6,600 to Ram and Shyam for 2 years. Ram agreed to
pay simple interest at 15 % p.a. and Shyam agreed to pay compound interest
at the same rate. If Ram paid Rs 112.50 more than Shyam as the interest, find
how much did he lend to each of them?
Answer:
Mohan lent 3600 to Ram and 3000 to Shyam.
Step-by-step explanation:
Given that Mohan lent altogether 6,600 to Ram and Shyam for 2 years.
Let Mohan lent x to Ram and y to Shyam
x+y=6600
Or, x=6600-y ...(i)
As Ram pays simple interest at 15 %=0.15 p.a, so, the interest paid by Ram in 2 years:
[tex]I=x\times 0.15 \times 2 \\\\\Rightarrow I=0.3x \\\\[/tex]
[tex]\Rightarrow I=0.3(6600-y) \\\\[/tex] [by using (i)]
[tex]\Rightarrow I=1980-0.3y \cdots(ii)[/tex]
As Shyam pays compound interest at 15 %=0.15 p.a,
so, the interest paid by Shyam in 2 years, C.I.= Final amount - Initial principal amount
[tex]C.I. = y(1+0.15)^2-y \\\\\Rightarrow C.I. = y(1.15^2-1) \\\\\Rightarrow C.I. = y(1.3225-1) \\\\\Rightarrow C.I. = 0.3225y \cdots(iii)[/tex]
As Ram paid Rs 112.50 more than Shyam as the interest, so by using equations (ii) and (iii),
[tex](1980-0.3y)-0.3225y=112.5 \\\\\Rightarrow 1980-0.3y-0.3225y=112.5 \\\\\Rightarrow 0.6225y=1980-112.5 \\\\\Rightarrow y = 1867.5/0.6225=3000[/tex]
From equations (i),
[tex]x=6600-3000=3600[/tex]
Hence, Mohan lent 3600 to Ram and 3000 to Shyam.
need helpppp i have no idea what to do
Answer:
Line 1 and Line 2: Perpendicular
Line 1 and Line 3: Neither
Line 2 and Line 3: Neither
Step-by-step explanation:
We will write all lines in slope intercept form i.e [tex]y=mx+b[/tex]
where m is slope.
And check
a) If two lines are parallel they have same slope [tex]m_1=m_2[/tex]
b) If two lines are perpendicular they have opposite reciprocal slopes i.e [tex]m_1=-\frac{1}{m_2}[/tex]
Equation for Line 1: [tex]y=-\frac{4}{3}x-4[/tex]
Already in slope-intercept form
Slope for Line 1 m is: [tex]\mathbf{m_1=-\frac{4}{3}}[/tex]
Equation for Line 2: [tex]6x-8y=-6[/tex]
Converting into slope-intercept form:
[tex]6x-8y=-6\\-8y=-6x-6\\y=\frac{-6x-6}{-8}\\y=\frac{-6x}{-8}+\frac{-6}{-8} \\y=\frac{3x}{4}+\frac{3}{4}[/tex]
Slope for Line 2 m is: [tex]\mathbf{m_2=\frac{3}{4}}[/tex]
Equation for Line 3: [tex]-4y=3x+7[/tex]
Converting into slope-intercept form:
[tex]-4y=3x+7\\y=-\frac{3}{4} -\frac{7}{4}[/tex]
Slope for Line 3 m is: [tex]\mathbf{m_3=-\frac{3}{4}}[/tex]
Now, finding answers
Line 1 and Line 2
Checking their slopes: [tex]\mathbf{m_1=-\frac{4}{3}}[/tex], [tex]\mathbf{m_2=\frac{3}{4}}[/tex]
Both lines are perpendicular because they have opposite reciprocal slopes
Line 1 and Line 3
Checking their slopes: [tex]\mathbf{m_1=-\frac{4}{3}}[/tex], [tex]\mathbf{m_3=-\frac{3}{4}}[/tex]
Slopes are neither same, nor opposite reciprocal, so they are neither
Line 2 and Line 3
Checking their slopes: [tex]\mathbf{m_2=\frac{3}{4}}[/tex], [tex]\mathbf{m_3=-\frac{3}{4}}[/tex]
Slopes are neither same, nor opposite reciprocal, so they are neither
The answers are:
Line 1 and Line 2: Perpendicular
Line 1 and Line 3: Neither
Line 2 and Line 3: Neither
The Ratio of number x and four added by two
Answer:
The ratio of a number x and four added to two:
= 4x + 2 = 0
= 4x = -2
= 4x/4 = -2/4
= x = -2/4
= x = -1/2
Step-by-step explanation:
Hope this helped!
4r + 5y = 10
- 1 - 8 = 3y
Answer:
y = -3, r = 25/4
Step-by-step explanation:
4r+5y = 10
-1 - 8 = 3y <--- This can be simplified to:
-9 = 3y
-3 = y
Now we plug -3 into y in the first equation
4r + 5y = 10
4r + 5(-3) = 10
4r - 15 = 10
4r = 25
r = 25/4
Write an explicit formula for each sequence.
3, 7, 11, 15, ...
Answer:
f(n)= f(1)+d(n-1)
Step-by-step explanation:
the aerithmetric explict formula is the one above, but im not sure what the question is asking, your difference is 4 btw
Solve for x
3x-30=4
HELPPPPPPPPPPP
Answer:
x=34/3
Step-by-step explanation:
Please help
I will mark brainlest and theres alot of points :)
Answer:
answer is a
Step-by-step explanation:
5(2)=10+2(7)=24
Pls help I’m stuck on this question and I can’t figure it out! Will give brainliest!
Answer:
A, C, and D
Step-by-step explanation:
Parent function of y = x will be all linear equations that have the x variable with the exponent equal to one.
Answer:
A, C, and D.
Step-by-step explanation:
the other answer is not correct because i pressed on this to help you because my teacher actally just tought me that and so she just tought us (my class)
about this and she used this question for an example and she used that other answer and asked which ones where correct and i said A, C, And D.
and guess what? i got it correct! so trust me, you gotta do A, C, and D. i hope that helps you and please mark me brainlist have a nice day.
Help me please!! I cannot do math! :D
Answer:
Dude PDF is not a question
Step-by-step explanation:
3.
=45x-27
=9(5x-3)
4.
=6x+75x²
=3x(2+9x)
17.
22=16+x+3+14+57
5
110=90+x
110-90=x
x=20
The PTO is hosting a donut and coffee day at the shcool. Each box of donuts and costs $9.00 and each cup of
coffee cost $0.50. The PTO spent $63 on the donuts and on the coffee.
What are the unknown quantities in this problem? Select all that apply.
The school where the donut and coffee day will take place.
The cost of each box of donuts.
The cost of each cup of coffee.
The number of boxes of donuts the PTO bought.
The number of cups of coffee the PTO bought.
Answer:
The school where the donut and coffee day will take place.
The number of boxes of donuts the PTO bought.
The number of cups of coffee the PTO bought.
Emmet walks 0.4 miles on each trip to the park. How far will Emmet walk if he makes 4 trips to the park?
Miles
Emmet will walk 1. 6 miles if he makes 4 trips to the park
How to determine the valueFrom the information given, we have that;
Emmy walks 0. 4 miles per tripHe wants to walk 4 tripsIt is important to note that proportion is the mathematical comparison of two numbers or elements
If 0. 4 miles is equivalent to 1 trip
Then x miles is equivalent to 4 trips
cross multiply
x = 0 . 4 × 4
Multiply through
x = 1. 6 miles
Thus, Emmet will walk 1. 6 miles if he makes 4 trips to the park
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Add your CORRECT Please
Answer:
IQR= (16)−(10)=6
Thus, option 'C' is true.
Step-by-step explanation:
Given the data
8, 9, 9, 10, 12, 12, 13, 14, 15, 15, 15, 16, 18, 19, 20
The interquartile range is equal to the difference between the 75th and the 25th percentiles
The 25th percentile is 10
The 75th percentile is 16
Finally,
IQR= (16)−(10)=6
Thus, option 'C' is true.
420 presents in 15 hours at this rate how many presents does Santa deliver in 5 hours
Answer:
140 Presenrs
Step-by-step explanation:
If Santa delivers 420 presents in 15 hours and to get to 5 hours you need to divide 15 to 3, so what you do to one number you must do to the other, so therefore divide 420 by 3 to get 140 presents in 5 hours.
Hi can someone help me with this I’ll mark u as brainliest :)
Answer:
A: [tex]5^2[/tex] times [tex]5^2[/tex]
C: [tex]\frac{1}{5^-^4}[/tex]
Step-by-step explanation:
A:
[tex]5^2[/tex] × [tex]5^2[/tex]
[tex]=5^2^+^2[/tex]
[tex]=5^4[/tex]
C:
[tex]\frac{1}{5^-^4}[/tex]
[tex]=5^4[/tex]
PLEASE HELP ASAP I HAVE A TEST TIME LIMIT EDGE 2020! HELLLLP!
Which statement best illustrates using the vertical line test to determine if the graph below is a function of x?
A. The graph is not a function of x because the line x = 0 intersects the graph at two points.
B. The graph is a function of x because the line x = 5 does not intersect the graph.
C. The graph is not a function of x because the line y = 0 intersects the graph at two points.
D. The graph is a function of x because the line y = 5 does not intersect the graph.
Answer:
A
Step-by-step explanation:
Graph is not a function, so B and D are false.
y = 0 is a horizontal line, not a vertical line, so C is false.
This leaves only A.
Which shape are congruent to shape I in this graph
Which line show the first error in the solution?
3(x−2)=18 (1)
3x−6=18 (2)
3x−6+6=18+6 (3)
3x=24 (4)
x=21 (5)
Line 2
Line 4
Line 5
Line 3
Answer:
Line 3
Step-by-step explanation:
Proper solution step-by-step:
1. 3(x-2)=18
2. 3x - 6 = 18
3. 3x = 18 + 6
4. 3x = 24
5. x = 8
A Cuban restaurant
donates 225 meals each hour. How
many meals does the restaurant
donate in 12 hours?