[tex]\bold{\huge{\underline{ Solution }}}[/tex]
Given :-Here, We have given two equations that is ,[tex]\sf{ x + 2y = 13\:\: and\:\: x + 5y = 28}[/tex]To Find :-We have to find the value of x and y.Concept used :-Linear equations are those equations which having highest power of degree as 1 .Linear equations can be solved by subsitute method, elimination method and cross multiplication method. Here, I have used substitution method to make calculation easier. In subsitute method, you have to subsitute the value of one variable of eq(1) in eq(2) .Let's Begin :-Here,
We have two equations, let consider these two equations as eq(1) and eq(2) that is,[tex]\sf{ x + 2y = 13 ...eq(1)}[/tex]
[tex]\sf{ x + 5y = 28 ...eq(2)}[/tex]
By solving eq(1) :-
[tex]\sf{ x + 2y = 13 }[/tex]
[tex]\sf{ x = 13 - 2y ...eq(3)}[/tex]
Subsitute eq(3) in eq(2) :-
[tex]\sf{ (13 - 2y) + 5y = 28 }[/tex]
[tex]\sf{ 13 - 2y + 5y = 28 }[/tex]
[tex]\sf{ 13 + 3y = 28 }[/tex]
[tex]\sf{ 3y = 28 - 13 }[/tex]
[tex]\sf{ 3y = 28 - 13 }[/tex]
[tex]\sf{ 3y = 15 }[/tex]
[tex]\sf{ y = }{\sf{\dfrac{ 15}{3}}}[/tex]
[tex]\sf{ y = }{\sf{\cancel{\dfrac{ 15}{3}}}}[/tex]
[tex]\bold{ y = 5 }[/tex]
Thus, The value of y is 5
Now,Subsitute the value of y in eq(1) :-
[tex]\sf{ x + 2(5) = 13 }[/tex]
[tex]\sf{ x + 10 = 13 }[/tex]
[tex]\sf{ x = 13 - 10 }[/tex]
[tex]\bold{ x = 3 }[/tex]
Hence, The value of x and y are 5 and 3 .
[tex]\bold{\huge{\underline{ Let's \: Verify }}}[/tex]
Equation 1 :-[tex]\sf{ x + 2y = 13 }[/tex]
[tex]\sf{ 3 + 2(5) = 13 }[/tex]
[tex]\sf{ 3 + 10 = 13 }[/tex]
[tex]\sf{ 13 = 13 }[/tex]
[tex]\bold{ LHS = RHS }[/tex]
Equation 2 :-[tex]\sf{ x + 5y = 28 }[/tex]
[tex]\sf{ 3 + 5(5) = 28 }[/tex]
[tex]\sf{ 3 + 25 = 28 }[/tex]
[tex]\sf{ 28 = 28 }[/tex]
[tex]\bold{ LHS = RHS }[/tex]
Let's use elimination method
Subtract eq(2) from eq(1)We get
[tex]\\ \rm\Rrightarrow 2y-5y=13-28[/tex]
[tex]\\ \rm\Rrightarrow -3y=-15[/tex]
[tex]\\ \rm\Rrightarrow y=\dfrac{-15}{-3}[/tex]
[tex]\\ \rm\Rrightarrow y=5[/tex]
Putting on eq(1)
[tex]\\ \rm\Rrightarrow x+2y=13[/tex]
[tex]\\ \rm\Rrightarrow x+2(5)=13[/tex]
[tex]\\ \rm\Rrightarrow x+10=13[/tex]
[tex]\\ \rm\Rrightarrow x=13-10[/tex]
[tex]\\ \rm\Rrightarrow x=3[/tex]
(x,y)=(3,5)[tex]\LARGE{\underbrace{\underline{\rm{Verification:-}}}}[/tex]
[tex]\\ \rm\Rrightarrow x+2y=13[/tex]
[tex]\\ \rm\Rrightarrow 3+2(5)=13[/tex]
[tex]\\ \rm\Rrightarrow 3+10=13[/tex]
[tex]\\ \rm\Rrightarrow 13=13[/tex]
And
[tex]\\ \rm\Rrightarrow x+5y=28[/tex]
[tex]\\ \rm\Rrightarrow 3+5(5)=28[/tex]
[tex]\\ \rm\Rrightarrow 3+25=28[/tex]
[tex]\\ \rm\Rrightarrow 28=28[/tex]
Hence verified!
Einstein's theory of Relativity E=mc²
Answer:
Einstein went on to present his findings mathematically: energy (E) equals mass (m) times the speed of light (c) squared (2), or E=mc2.
The secret the equation revealed—that mass and energy are different forms of the same thing—had eluded scientists for centuries.
×
E=mc2
In Einstein's first paper about energy and mass, E=mc2 doesn't actually appear anywhere—he originally wrote the formula as m=L/c2. What happened? Einstein was using "L" (for Lagrangian, a general form of energy) instead of "E" for energy. Later, he replaced "L" with "E," rearranged the variables, and the famous form of the equation emerged.
The implications of E=mc2 are profound. For centuries, scientists had considered energy and mass to be completely distinct and unrelated to each other. Einstein showed that in fact, energy and mass are different forms of the same thing. Einstein himself was surprised by the finding, calling it "amusing and enticing" and wondered "whether the Lord is laughing at it and has played a trick on me."
Write a second equation for the system so it has infinitely many solutions.
Write a second equation whose graph goes through (0,2) so that the system has no solutions.
Write a second equation whose graph goes through (2,2) so that the system has one solution at (4,3).
Answer:
See below ↓
Step-by-step explanation:
Our equation :
y = 3/2x - 3(A) Infinitely Many Solutions
y = 3/2x - 3The slope and y-intercept have to be equal in order for it to have infinitely many solutions(B) No solution
y = 3/2x + 1The slope has to be equal and the y-intercept has to be different in order for it to have no solution(C) One solution at (4, 3)
x has to equal 4y = 3/2x - 3 and y = 2x - 1In both of these equations, (4, 3) is a solution"All rational functions have asymptotes and points of discontinuity." Katlyn wants to put this statement in her math book. Is this statement true? Explain, for her benefit, using 2 examples
Answer:
Not true.
Step-by-step explanation:
A rational function is like P(x) / Q(x) where P and Q are polynomials.
Examples would be x^2 / (x^2 - 2) and x^2 / (x^2 + 2).
Now the first one will have a vertical asymptote at x = √2 because this value would make the denominator zero.
The second one will have no asymptotes because the only value that would make x^2 + 2 = zero is not real (it would be √2i). So the domain of this is all real numbers , and no asymptotes.
one side of a triangle is 8 inches long and another side is 4 inches long. The third side is opposite an obtuse angke. What is a possible length of the third side? Explain
Answer:
it should be over 8 inches long
Step-by-step explanation:
by the instructions
a side of a triangle is 8 inches and other one is 4 inches
and the OPPOSITE of OBTUSE angle is the 3 Rd one
As the Third side which connect the 1st and 2nd side ( of the obtuse angle) it should be over 8 inches.
What percent of the utterances in the sample need to be 1 word in length in order to use Nelson's or Bloom's One-Word Utterance Analyses
The percent of the utterances in the sample need to be 1 word in length is 13.3%.
How to calculate the percentage?Your information is incomplete. Therefore, an overview will be given. Let's assume that the number if 1 word is 12 and the total number of words given is 90.
Therefore, the percentage will be:
= 1 word/Total words × 100
= 12/90 × 100.
= 13.3%
In conclusion, the percentage is 13.3%.
Learn more about percentages on:
https://brainly.com/question/24877689
Use the GCF to factor 9x+54
9(x+6)
Solution:The GCF stands for Greatest Common Factor.We need to factor out the GCF of this binomial (expression with two terms)In order to factor out the GCF, we need to divide both terms by the GCF and place it outside the parentheses, like so:9x+549x÷9=x54÷9=6x+69(x+6)Hope it helps.
Do comment if you have any query.
“Use distributive property to rewrite each expression.”
3(a + 10)
Answer:
The answer is
3a+30
Step-by-step explanation:
I hope this helped
Pythagorean Theorem
(Rounding)
Find the length of the third side. If necessary, round to the nearest tenth.
SOMEONE PLEASE HELP ME ILL GIVE YOU BRAINLIST ANSWER AND POINTS!!!!
IMAGE DOWN BELOW!!
An airplane flies with a constant speed
of 680 miles per hour. How long will it
take to travel a distance of 2720 miles?
4 hours
T= d/s
= 2720/680
= 4
Hope this helps!
3. Write 6x - 2y = 0 in slope-intercept form, if possible.
Answer:
y=3x
Step-by-step explanation:
Answer:
y = 3x
Step-by-step explanation:
subtract 6x to the other side
divide by -2
there is no y-intercept because it's 0
A 48-fluid-ounces container of orange juice costs $.2.40.A 60-fluid -ounces container of orange juice costs $3.60.Which is the better coast
Answer:
48/2.40 = 60/360
Step-by-step explanation:
do a proportion chart
Please help me with this problem I’m very confused and cannot figure it out
HELP I NEED IT
NO LINKS!!
Answer:
option c
Step-by-step explanation:
Area of triangle:
a = 2 and c = 3
base = 6ac²
= 6 *2 * 3 * 3
= 108 cm
height = base + 3
= 108 + 3
= 111 cm
[tex]\boxed{\text{Area of a triangle = $ \dfrac{1}{2}*base*height$}}[/tex]
[tex]=\dfrac{1}{2}*108*111\\\\\\= 54*111\\\\=5994 \ cm^{2}[/tex]
Answer:
5,994 cm²
Step-by-step explanation:
Formula
Area of the triangle = 1/2 x base length x heightGiven
Base length = 6ac² cmHeight = 6ac² + 3 cma = 2c = 3Solving
Area = 1/2 x 6ac² x (6ac² + 3)Area = 1/2 x 36a²c⁴ + 18ac²Area = 9ac² (2ac² + 1)Substitute the values of a and c⇒ Area = 9 x 2 x 3² (2 x 2 x 3² + 1)⇒ Area = 162 (36 + 1)⇒ Area = 162 x 37⇒ Area = 5,994 cm²find a, b, and c please and thank u
Which shows the correct solution to the inequality StartFraction 7 over 10 EndFraction greater-than-or-equal-to 1 and StartFraction 5 over 8 EndFraction + p? StartFraction 7 over 10 EndFraction greater-than-or-equal-to 1 and StartFraction 5 over 8 EndFraction + p. StartFraction 7 over 10 EndFraction minus 1 and StartFraction 5 over 8 EndFraction + p. StartFraction 28 over 40 EndFraction minus 1 and StartFraction 25 over 40 EndFraction greater-than-or-equal-to p. p less-than-or-equal-to negative 1 and StartFraction 3 over 40 EndFraction. StartFraction 7 over 10 EndFraction greater-than-or-equal-to 1 and StartFraction 5 over 8 EndFraction + p. StartFraction 7 over 10 EndFraction minus 1 and StartFraction 5 over 8 EndFraction greater-than-or-equal-to 1 and StartFraction 5 over 8 EndFraction minus 1 and StartFraction 5 over 8 EndFraction + p. StartFraction 28 over 40 EndFraction minus 1 and StartFraction 25 over 40 EndFraction greater-than-or-equal-to p. p greater-than-or-equal-to negative 1 and StartFraction 3 over 40 EndFraction. StartFraction 7 over 10 EndFraction greater-than-or-equal-to 1 and StartFraction 5 over 8 EndFraction + p. StartFraction 7 over 10 EndFraction minus 1 and StartFraction 5 over 8 EndFraction greater-than-or-equal-to 1 and StartFraction 5 over 8 EndFraction minus 1 and StartFraction 5 over 8 EndFraction + p. StartFraction 28 over 40 EndFraction minus 1 and StartFraction 25 over 40 EndFraction greater-than-or-equal-to p. p less-than-or-equal-to negative StartFraction 37 over 40 EndFraction. StartFraction 7 over 10 EndFraction greater-than-or-equal-to 1 and StartFraction 5 over 8 EndFraction + p. StartFraction 7 over 10 EndFraction minus 1 and StartFraction 5 over 8 EndFraction greater-than-or-equal-to 1 and StartFraction 5 over 8 EndFraction minus 1 and StartFraction 5 over 8 EndFraction + p. StartFraction 28 over 40 EndFraction minus 1 and StartFraction 25 over 40 EndFraction greater-than-or-equal-to p. p greater-than-or-equal-to negative StartFraction 37 over 40 EndFraction.
Answer:
The answer is C
Step-by-step explanation:
a certain number is added to 6 and then divided by 10. The result is 3. Find the number
Answer:
let the number be x.
(x+6)/10 = 3
x+6 = 30
x =24
a. translation; four units right and six units down
b. translation; four units left and six units down
c. rotation; 90 degrees
d. reflection; across y=-4
Answer:
b. translation; four units left and six units down
A textbook store sold a combined total of 255 sociology and physiology textbooks in a week. The number of sociology textbooks sold was two times the number of physiology textbooks sold. How many textbooks of each type were sold?
Answer:
75 physiology Textbook was sold and 150 sociology textbook was sold
Step-by-step explanation:
Let x represent textbook
2x + x = 225
⇒3x = 225
⇒[tex] \sf \frac{\sout{3}x}{\sout{3}} = \frac{225}{3}[/tex]
⇒x = 75
75 textbooks for physiology
To find How many textbook for sociology
Multiply 2 by the amount of physiology
⇒2 × 75
⇒150 sociology textbook
Please help me with this!
What is the distance between ( − 2 , − 4 ) and ( 5 , 7 ) ? Use the distance formula, d = √ ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 .
4.24
6.32
10.25
13.03
Answer:
13.03
Step-by-step explanation:
Suppose ( x₁ , y₁ ) = ( − 2 , − 4 ) and (x₂ , y₂ ) = (5 , 7)
In the formula : d = √ [( x₂− x₁ )² + ( y₂ − y₁ )²]
Just replace x₁ by -2
replace y₁ by -4
replace x₂ by 5
replace y₂ by 7
We get ,
d = √ [( 5− (-2) )² + ( 7 − (-4) )²]
Then
d = √ [(7 )² + ( 11 )²]
d = √ [49 + 121]
d = √ [170]
≈ 13.03
look at attachment hurry
Answer:
the top one on the right
Step-by-step explanation:
i used desmos graphing calculator
A line parallel to the graph of (y − 4) = m(x − 7) passes through (−1,−2) and (m, 10). If
m > 0, what is the value of m?
Answer:
Step-by-step explanation:
Givens
These are the givens for the second line. The second line also has m (same value) as the x coordinate of one of the points. I'm not sure why you are given the first line.
x1 = - 1
x2 = m
y1 = - 2
y2 = 10
Second line formula for m
m = (y2 - y1) / (x2 - x1) Substitute values for this equation
Solution
Note that the m you seek is both the slope of the second line, and the x coordinate of one of the points.
m = (10 - - 2) / (m - - 1) Change the double minus, and combine
m = 12 / (m + 1) Multiply both sides by (m + 1)
m(m+1) = 12 Remove the brackets
m^2 + m = 12 Subtract 12 from both sides.
m^2 + m - 12 = 0 Factor
(m + 4)(m - 3) = 0
We are told that m >0
So m- 3 = 0
m = 3
Answer
The value for m = 3. The first line also has a slope of 3
Estimate the value of 96.8 x 9.74
Answer:
1000
Step-by-step explanation:
Let's round!
96.8 can be rounded to 100
9.74 can be rounded to 10
100*10=1000
Hope this helps!
The estimated value of the given product is 970. The given product is (96.8×9.74). This is obtained by using the rounding-off method.
What is estimation?Estimating means finding something close to the actual answer. In other words, it is approximating.Estimating decimal products involves many strategies.General strategy is rounding-off to the nearest value method.Estimating the given product:The given product is (96.8×9.74)
Here the first decimal number in the product is 96.8
Since the digit after the decimal point 8 is nearer to the value of 10, it is rounded to 97. I.e., 96.8≅97
And the second decimal number is 9.74
Since the digit after the decimal 7is nearer to the value of 10, it is rounded to 10. I.e., 9.74≅10
So, the product is 97×10=970
Thus, 96.8×9.74≅970 (approx.)
Therefore, the estimated value is 970.
Learn more about estimation here:
https://brainly.com/question/3639595
#SPJ2
Evaluate 49x - 2 when x = 1
Answer:
49(1) - 2 =
49x1=49
49 - 2 = 47 is your answer
Answer:
47
__________________________________________________________
SolveIf the variable, x has an assigned value, you must multiply the number behind x by the assigned value.
[tex]49 * 1 = 49[/tex]
Lastly, subtract by 2
[tex]49 - 2 = 47[/tex]
________________________________________________________
Questions?Ask me in the comments box.
What is the scale factor of this dilation?
Answer:
I am not sure but I thing it is -2.
Step-by-step explanation:
Hope it helps! (Please mark brainliest if it does!)
1.6667
Step-by-step explanation:
the lengths are the same on both sides which makes the triangles equilateral
therefore the scale=5/3
=1.6667
how do i find the vertex of y= -4x^2-16x+1 ?
Answer:
(-2, 17)
Step-by-step explanation:
the first step you can do to find the vertex is to find the axis of symmetry
the equation for that is -b/2a
-(16) / 2(-4)
-16 / 8 = -2
the axis of symmetry is x =-2 so you plug in -2 to the equation
-4(-2)^2 - 16(-2) + 1
-4(4) + 32 + 1
-16 + 33
17
the vertex is (-2, 17)
Which object would weigh closest to 1 ton? A.Car B.Toothbrush C.Notebook D.Dog
help!!!!!!! hurry and help me pls!
Answer:
(2, 4)
Step-by-step explanation:
A reflection across the y-axis, will simply change the sign of your x-coordinate to positive rather than negative, this gives you a new point (2,4).
PLEASE HELP!! 50 POINTS!!
Part A
[tex]\sf{ change \ of \ base \sf \ : \ \ \ \log _{b} a=\dfrac{\log _{d} a}{\log _{d} b}}[/tex]
Part B
Some common choices for base:
2310Part C
[tex]\longrightarrow\ \sf \log _{2} 3=\dfrac{\log _{3} 3}{\log _{3} 2}}[/tex]
[tex]\longrightarrow\ \sf \log _{2} 3=\dfrac{1}{0.631}}[/tex]
[tex]\longrightarrow\ \sf \log _{2} 3=\dfrac{1}{0.630929}}[/tex]
[tex]\longrightarrow\ \sf \log _{2} 3=1.584962501[/tex]
[tex]\longrightarrow\ \sf \log _{2} 3 = 1.58[/tex]
1.58 is the value when rounded to nearest hundredth.
The table is shaped like a trapezoid. The sum of the lengths of both bases is 90 inches. The area is
1,170 square inches. Write an equation to find the height of the table.
HELPP
Answer:
Step-by-step explanation:
Formula (Normal Area Trapezoid)
A = (b1 + b2 ) * h / 2
Formula (Trapezoid Modified for the question)
b1 + b2 is given as 90
Area = 90*h / 2
Givens
b1 + b2 = 90
Area = 1170
h = ?
Solution
Area = 90 * h / 2 Substitute the givens into the formula
1170 = 90 * h/ 2 Divide by 2 on the right.
1170 = 45 * h Divide both sides by 45
1170 / 45 = 45 * h/45
Answer: h = 45 inches.
You text your friend for 15 minutes on friday night and for 25 minutes on saturday night. what is the percent of increase? (round to nearest whole percent)
Answer:
66%
Step-by-step explanation:
This doesn't really require any equations, it's just brain work.
15 can be easily divided into 3 parts, each part consisting of 5 units. Here, it will be 5 minutes, then, if it's 5 minutes for each 33%(this number is rounded), then, that means that for 10 minutes, it will be 66%. You can understand this because the amount of increase in minutes is 10 minutes, and if each 5 minutes = 33% of increase, then 33+33=66, so hence, our answer is 66%.
----------------------------------------------------------------------------------------------------------"The beautiful thing about learning is that no one can take it away from you!" B.B.King
Thanks!
Have a great day!
Mark me brainliest!
~ms115~
:D