[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!
The volume of a child’s model plane is 1200cm3. The volume of the full size plane is 4050m3. Find the scale of the model in the form 1:n.
the scale of the airplane is 1/3 the size of its counter part
X-3y-7=0. 3x-3y-15=0 elimination method
Answer:
X=−8+3x
y=−5+x
Step-by-step explanation:
0=x^2-8x-32 solve by completing the square
Answer:
x = 4.65 or x = -0.65 (to 2 d.p)
Step-by-step explanation:
To complete the square, use the formula x² + bx + c = (x + b/2)² - (b/2)² + c
In this case, x² - 8x - 32 = (x - 4)² - 16 - 32This simplifies to (x - 4)² - 48 = 0To solve this:
First, add 48 to both sides → (x - 4)² = 48Next, square root both sides → x - 4 = ± √48 (remember that the square root of a number always has a positive and negative value)Finally, add 4 to both sides → x = 4 ± √7x has 2 solutions
x = 2 + √7 or x = 2 - √7
x = 4.65 or x = -0.65 (to 2 d.p)
Hope this helps!
Answer:
x = 4 ± 4[tex]\sqrt{3}[/tex]
Step-by-step explanation:
x² - 8x - 32 = 0 ( add 32 to both sides )
x² - 8x = 32
to complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 4)x + 16 = 32 + 16
(x - 4)² = 48 ( take square root of both sides )
x - 4 = ± [tex]\sqrt{48}[/tex] = ± 4[tex]\sqrt{3}[/tex] ( add 4 to both sides )
x = 4 ± 4[tex]\sqrt{3}[/tex]
"Twice the reciprocal of a number plus six equals two thirds." Create an equation and find the number.
Answer:
1/x + 6 = 2/3
x is the number, so there it has to be switched if a reciprocal happens. :) hope this helps
Find the slope and y intercept
Answer:
find the angle of the 90 and divide by 5
Step-by-step explanation:
Calculate the surface area of the object above.
Please help ASAP. Will give brainliest if correct!
What is 0.15...(repeating decimal) as a fraction in simplest form?
Clearly show your work.
Answer:
0.15 as a fraction in simplest form is 3/20.
Step-by-step explanation:
0.15 is the same thing as 15/100, divide both the numerator and denominator by 5 and your result is 3/20.
Answer:
0.15 as a fraction in simplest form is 3/20.
Step-by-step explanation:
0.15 is the same thing as 15/100, divide both the numerator and denominator by 5 and your result is 3/20.
A group of friends is going ice skating. The price of admission is $3.25. As a group, they spent $14 on refreshments. If they spent a total of $30.25 on refreshments, how many friends went ice skating
what is the slope of y = 15x + 5
Answer:
15
Step-by-step explanation:
from equation y= mx+c
we can equate m (slope/gradient) to 15
Answer the question below:
Answer:
5 students did.
Step-by-step explanation:
20 students. 1/4 of 20 is 5
Are the triangles similar? If so, how do you know?
Select the two expressions that equivalent to 4 + w + 12w
A. 4+13w
B. 13w2 + 4
C. 2(2+6w)+w
D. 16 + 2w
W. 2(2+6w2)
Answer:
A and C :)
Have an amazing day!!
Please rate and mark brainliest!!
need some help I'm stuck on this question in the image
thank you
If y x w= 0, what can be said about the two vectors y and w?
=
One of the vectors is 0.......
PLSPLSPLSPLSPLSPLSPLSPLS
Answer:
reason
1. symmetrical property
sides can be interchanged and its still true
statement
1. if triangle kjm is congruent to klm
then klm is congruent to klm
reason
2. reflexive property
triangle is congruent to itself
statement
2. triangle kjm is congruent to triangle kjm
reason
3. transitive property
if the 1st 2 triangles are congruent to each other and congruent to a third
then the first triangle is congruent to the third triangle
statement
3. if kjm is congruent to klm and
klm is congruent to abc then
kjm is congruent to abc
The function h defined by h (t) = 4.9 (10+t) (10 - t) models the height, in meters, of an object t seconds after it is dropped from a
helicopter
Answer:
(a) 10 seconds
(b) 490 meters
Step-by-step explanation:
(A)When the object hits the ground, it shows that the height is 0. Hence, h(t) = 0.
0 = 4.9(10+t)(10-t)
0 = (10+t)(10-t)
t = 10, -10
Since time cannot be negative, t = -10 will be rejected.
Therefore, t = 10 seconds
(B)Based on the question, "t seconds after the object is dropped from a helicopter", means that the time starts right after the object is dropped from the helicopter, this shows that t = 0.
h(0) = 4.9(10+0)(10-0)
= 4.9(100)
= 490 meters
Ralphie is taking a ten-question multiple choice test. Each question has five choices. If Ralphie answers a question
correctly, he earns one point; if he answers incorrectly, he loses half a point. Ralphie answers the first six questions
correctly, then guesses on the last four. What is the expected value of his test score? Round the answer to the nearest
whole percent.
Using the binomial distribution, it is found that the expected value of his test score is of 6.8.
What is the binomial probability distribution?It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The expected value of the binomial distribution is:
E(X) = np
In this problem, the parameters are given as follows:
For the first 6 questions, n = 6 and p = 1.For the last 4 questions, n = 4 and p = 1/5 = 0.2.Hence, the expected score is given by:
E(X) = 6 x 1 + 4 x 0.2 = 6.8.
More can be learned about the binomial distribution at https://brainly.com/question/24863377
Answer:
A.
Step-by-step explanation:
Apples cost $1.99 per pound how much do 3 1/4 pounds of apples cost
Answer:
6.47
Step-by-step explanation:
1.99/1 lb= x/3.25lb
3 1/4=3.25
Cross multiply
X=(1.99)(3.25)=6.47
If you put $5000 in a savings account that
pays 2% annual interest, the amount
of money you will have at the end of the year
is?
Answer:
$5100.
Step-by-step explanation:
2% annual interest is the same as multiplying a number by 0.02, then adding that number to the original number. Using this information, we can do the following steps:
5000 x 0.02 = 1005000 + 100 = 5100You will have $5100 at the end of the year.
Answer:
$5100
Step-by-step explanation:
$5000 is put into the account originally. If you multiply this number by 0.02 you will get your answer. All the best. -Crispin
Select all the expressions that describe the area of this rectangle.
Answer:
a, c, d
Step-by-step explanation:
This is because there share the same answer:
12x + 6
hope this helps =)
Find the error in the calculations below, if there is one:
Line (1): -5 ≤ 2x +7<9
Line (2):-12 ≤ 2x < 2
Line (3): -6 ≤ x < 1
Line (4):
-6
1
The error ocurred from Line (1) to Line (2).
O The error ocurred from Line (3) to Line (4).
There are no errors.
O The error ocurred from Line (2) to Line (3).
A baker mixes 8\frac{3}{4}8
4
3
cups of white flour with 2\frac{1}{2}2
2
1
cups of rye flour for a bread recipe.
How many cups of white flour does the baker mix for every 11 cup of rye flour?
Fractions are written as the ratio of two integers. 3 1/7 cups white flour will be needed for every 11 cup of rye flour
Ratio and proportionFractions are written as the ratio of two integers. If a baker mixes 8 3/4 cups of white flour with 2 1/2 cups of rye, the number of cups of rye needed for 1 cup ofwhile flour will be:
For 1 cup of flour = (2 1/2)/(8 3/4)
For 1 cup of flour = (5/2)/(35/4)
For 1 cup of flour = 5/2 * 4/35
For 1 cup of flour = 2/7 cups of rye
For 11 cups:
For 11 cup of rye flour = 11 * 2/7
11 cup of rye flour = 22/7=3 1/7 cups
Hence 3 1/7 cups white flour will be needed for every 11 cup of rye flour
Learn more on ratio and proportion here:https://brainly.com/question/2914376
Spencer cut a square cake vertically to make two rectangle slices. Each rectangle had a perimeter of 27 inches. How long is each side of the original square cake?Solve on paper.Each side of the original square cake is 9 in. What is the area of the original square cake?
Answer:
81 square inches. square have equal length for all sides area for square is any side times another side so 9x9=81
Farm A has 120 sheep. of the sheep have lambs. Some of the sheep have 1 lamb and some of the sheep
have 2 lambs. The ratio of the sheep who have 1 lamb to the sheep who have 2 lambs is 3:5.
(a) What fraction of the sheep who have lambs on farm A have 2 lambs?
Answer:
75/120 = 15/24 = 5/8
Step-by-step explanation:
3 + 5 = 8 There are 8 parts
120 / 8 = 15
15 X 5 = 75
There are 75 sheeps with 2 lambs
The total number of sheep having 2 lambs in farm A is [tex]0.625[/tex].
To find the fraction of the sheep who have lambs on farm A have 2 lambs, we need to have the total number of sheep having 2 lambs in farm A.
How to determine the fraction of sheep?
According to the question, the ratio of the sheep having 1 lamb and 2 lambs is [tex]3:5[/tex] and the total number of sheep is 120.
So, the total number of sheep having 2 lambs in farm A is calculated as-
[tex]L_2=\dfrac{5}{3+5}\times 120\\=5\times 15\\=75[/tex]
Now, the fraction of the total number of sheep having 2 lambs in farm A is-
[tex]F=\dfrac{75}{120}\\=0.625[/tex]
Thus, the total number of sheep having 2 lambs in farm A is [tex]0.625[/tex].
Learn more about fractions here- https://brainly.com/question/10354322
#SPJ2
answer needed please
Answer:
the top answer should be stretched
how many degrees is 7/9 of a semicircle
Answer:
140
Step-by-step explanation:
A semicircle is 180 degrees
7/9x180=140
Answer: 7/9 degrees = 0.00216 cir
Step-by-step explanation:
The angle in circles is equal to the degrees divided by 360. ( For example, here's how to convert 500 degrees to circles using the formula above.500° = (500 ÷ 360) = 1.388889 cir)
of money Itzel has left over after buying p bottles
of nail polish
What does the constant 25 represent in this
context?
Welcome to the brainiest championship answer the question and you win a brainiest.
Answer:
d
Step-by-step explanation:
Answer: d
Step-by-step explanation:
solve for x -3(x + 5) = -9
Answer:
[tex]\tt x=-2[/tex]
Step-by-step explanation:
[tex]\tt -3(x + 5) = -9[/tex]
Step (1) :- Distribute
[tex]\tt -3x-15=-9[/tex]
Step (2) :- Add 15 to both sides
[tex]\tt -3x-15+15=-9+15[/tex]
Step (3) :- Simplify
[tex]\tt -3x=6[/tex]
Step (4) :- Divide both sides by -3:-
[tex]\tt \cfrac{-3x}{-3}=\cfrac{6}{-3}[/tex]
[tex]\tt x=-2\;\; \bf Answer[/tex]
____
[tex] \sf:\implies \quad {\pmb{\sf x = -2}} [/tex]
Solution:Let's solve the given problem step by step :
[tex]:\implies \quad \sf - 3(x + 5) = - 9[/tex]
First, distribute the given problem :
[tex]:\implies \quad \sf - 3(x + 5) = - 9[/tex]
[tex] \sf:\implies \quad - (3 \times x) - (3 \times 5) = - 9[/tex]
Add 15 to both sides :
[tex] \sf:\implies \quad - 3x - 15 = - 9[/tex]
[tex] \sf:\implies \quad - 3x - 15 + 15 = - 9 + 15[/tex]
On simplifying :
[tex] \sf:\implies \quad -3x-15+15 = -9+15[/tex]
[tex] \sf:\implies \quad - 3x = 6[/tex]
Dividing both sides with same factor :
[tex] \sf:\implies \quad - 3x = 6[/tex]
[tex] \sf:\implies \quad \dfrac{ - 3x}{ - 3} = \dfrac{6}{ - 3} [/tex]
[tex] \sf:\implies \boxed{ \pmb{ \sf\quad x = - 2}}[/tex]
A prince has arrived to rescue a princess standing in a tower balcony 18 meters up across a
moat 12 meters wide. He knew the princess was high up and there was a moat, so he
brought the longest ladder in the kingdom, a 20-meter monster. Is the ladder long enough?
