Answer:
x= 15 and y= 11
Step-by-step explanation:
The goal here is to solve
x + y =26 and
3x + y =56 for the variables x and y.
First, let's work on your first equation, x + y =26
After this initial survey of the equations, the system of equations we'll set out to solve is:
x+y = 26 and 3x+y = 56
Let's start by solving x+y = 26 for the variable x.
Move the y to the right hand side by subtracting y from both sides, like this:
From the left hand side:
y - y = 0
The answer is x
From the right hand side:
The answer is 26-y
Now, the equation reads:
x = 26-y
To isolate the x, we have to divide both sides of the equation by the other variables
around the x on the left side of the equation.
and this is the final solution to your equation.
Next, let's solve 3x+y = 56 for the variable y.
Move the 3x to the right hand side by subtracting 3x from both sides, like this:
From the left hand side:
3x - 3x = 0
The answer is y
From the right hand side:
The answer is 56-3x
Now, the equation reads:
y = 56-3x
To isolate the y, we have to divide both sides of the equation by the other variables
around the y on the left side of the equation.
and this is the final solution to your equation.
Now, plug the earlier result, x=26-y, in for x everywhere it occurs in
y=56-3x.
This gives y=56-3(26-y). Now all we have to do is solve this for y,to have our first solution.
26-y evaluates to 26-y
Multiply 3 by 26-y
we multiply 3 by each term in 26-y term by term.
This is the distributive property of multiplication.
Multiply 3 and 26
1
3 × 26 = 78
Multiply 3 and -y
Multiply 1 and y
The y just gets copied along.
y
3 × -y = -3y
3*(26-y) evaluates to 78-3y
56 - 78 = -22
The answer is -22+3y
56-3*(26-y) evaluates to -22+3y
Move the 3y to the left hand side by subtracting 3y from both sides, like this:
From the left hand side:
y - 3y = -2y
The answer is -2y
From the right hand side:
3y - 3y = 0
The answer is -22
Now, the equation reads:
-2y = -22
To isolate the y, we have to divide both sides of the equation by the other variables
around the y on the left side of the equation.
The last step is to divide both sides of the equation by -2 like this:
To divide y by 1
The y just gets copied along in the numerator.
The answer is y
-2y ÷ -2 = y
-22 ÷ -2 = 11
The solution to your equation is:
y = 11
Lastly, to find the solution for x, we plug this answer for y into the earlier result that
x=26-y.
This gives x=26-(11). Now, simplify this.
26-(11) evaluates to 15
x= 15
So, the solutions to your equations are:
x= 15 and y= 11
Answer:
(15, 11 )
Step-by-step explanation:
Given the 2 equations
x + y = 26 → (1)
3x + y = 56 → (2)
Subtract (1) from (2) term by term to eliminate y, that is
2x = 30 ( divide both sides by 2 )
x = 15
Substitute x = 15 into either of the 2 equations and solve for y
Substituting into (1)
15 + y = 26 ( subtract 15 from both sides )
y = 11
solution is (15, 11 )
One year ago, Lindsey deposited $250 into a savings
account. Her balance is now $253. Two years ago, Jenn
deposited $250 into a savings account. Her balance is
now $257.50. Which account has the greater simple
interest rate? Explain.
Answer:
Jenn's account
Step-by-step explanation:
Given that:
LINDSAY'S ACCOUNT :
Principal = amount deposited = $250
Final Amount after 1 year = $253
Period (t) = 1 year
JENN'S ACCOUNT :
Principal = amount deposited = $250
Final Amount after 2 years = $257.50
Period (t) = 2 year
Using the relation :
A = P(1 + rt)
A = final amount ; r = interest rate ; t = time
Lindsay :
253 = 250(1 + r(1))
253 = 250 + 250r
253 - 250 = 250r
3 = 250r
r = 3/250
r = 0.012 ; (0.012 * 100) = 1.2%
Jenn:
257.50 = 250(1 + r(2))
257.50 = 250 + 500r
257.50 - 250 = 500r
7.50 = 500r
r = 7.50/500
r = 0.015 ; (0.015 * 100) = 1.5%
Hence, JENN'S deposit has the greater interest rate. (1.5 > 1.2)%
Answer:Sample response:Lindsay’s interest is $3 for one year. Using the formula for interest, I = prt, Lindsey’s money is earning at a rate of 1.2%. Jenn has earned $3.75 for one year. Her money is earning at a rate of 1.5%, which is a higher interest rate.
Step-by-step explanation: please make me brainliest
A boat traveled 12 miles in 30 min. At this rate, how many miles will the boat travel in 3 hours?
What is the value of the expression below? 52 + (8 – 6)
Answer:
54
Step-by-step explanation:
2 3/4 as an improper fraction
ZX is perpendicular bisector of WY if WY=24 what is WX
Answer:
12
Step-by-step explanation:
Find the distance between the points. Round your answer to the nearest tenth. (6, -1) and (-2,-6)
Answer:
9.433981
Step-by-step explanation:
d=(−2−6)2+(−6−(−1))2−−−−−−−−−−−−−−−−−−−−−√
d=(−8)2+(−5)2−−−−−−−−−−−−√
d=64+25−−−−−−√
d=8–√9
d=9.433981
Warren Anderson's annual salary is $54,500. His personal exemptions total $1,500. The annual tax
withheld is: 1.5 percent of the 1st $1,000, 3.0 percent of the next $2,000, 4.5 percent of the next $2,000, and
5.0 percent over $5,000. How much is deducted annually for state income tax?
A. $2,400
B. $2,565
C. $2,725
D. $2,890
Answer:
B. $2,565
Step-by-step explanation:
"find the length indicated"
Answer:
huh??
Step-by-step explanation:
A department store buys200 shirts at a cost of $ 5400 and sells them at a selling price of $30 each. Find the percent markup
200 shirts x $30 = $6000
Total sales would be $6000
Profit = 6000 - 5400 = $600
Divide profit by cost:
600/5400 = 0.1111
Multiply by 100 for percentage:
0.111 x 100 = 11.1%
Rounding to nearest percent would be 11% markup
Answer:
is it 2.00?
Step-by-step explanation:
Which relation is NOT a function a: y=5x b: y=x2 c: x=3 d: y= 6x
Answer:
C. x = 3
Step-by-step explanation:
because it is not a function, it's an answer. The other equations are all equal to y, which you can find the x and the y for a coordinate, but for c you have just x, and without y you can't have a function.
Answer:
x = 3
Step-by-step explanation:
Think about an archery practice. One target can get hit by multiple archers, but an archer can only shoot one arrow. Therefore its x = 3, because the same x value can not hit every y. Hope this helps, its for more visual learners.
Archers (x) Targets (y)
X O
X O
X O
X O
-3(1)+(-3)(-1) =
+()]
-3(1) + (-3)(-1)=-3[0]
-3(1)+(-3)(-1) =
_
+(-3)(-1) =
+
Answer:
³⅜
Step-by-step explanation:
⁴⁵⅖
+⁷⅝×⅖i
I HOPE IT HELP TYSM
Answer:
i dunno
Step-by-step explanation:
This extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the extreme values of the function subject to the given constraint.
f(x, y) = xy; 4x2 + y2 = 8
Answer: minimum value of f = -2 and maximum value of f = 2
Step-by-step explanation:
Given that;
f(x, y) = xy; 4x² + y² = 8
S(x,y) = xy + λ(4x² + y² - 8)
dS/dλ = 4x² + y² - 8 = 0
dS/dx = y + 8λx = 0 -> y = -8λx
dS/dy = x + 2yλ = 0 -> x + 2λ(-8λx) = x(1 - 16λ²) = x(1-4λ)(1+4λ) = 0
-> x = 0 , λ = 1/4 , λ = -1/4
x = 0 -> y = 0 -> it doesn't satisfy 4x² + y² = 8
λ = 1/4 -> y = -8λx = -2x -> 4x² + y² = 8x² = 8 -> x = -1 , 1 -> y = 2 , -2
λ = -1/4 -> y = -8λx = 2x -> 4x² + y² = 8x² = 8 -> x = -1 , 1 -> y = -2 , 2
we have 4 critical points:
(-1, 2) -> f = -2
(1, 2) -> f = 2
(-1, -2) -> f = 2
(1 , -2) -> f = -2
Therefore; minimum value of f = -2 and maximum value of f = 2
If sec theta>0 and tan theta<0, the terminal side of angle theta must lie in
Answer:
the last one
Step-by-step explanation:
super easy bro tell me if its right
what is 22 to the power of 34?
Answer:
4.3890563e+45!!
Step-by-step explanation:
-10 -(-5) can someone answer dis for me please
.
Answer:
-5
Step-by-step explanation:
yw
Answer:
-5
Step-by-step explanation:
the two minus signs next to each other make it a plus sign so the equation would become
-10 + 5
which is -5
Which line has a constant of proportionality between y and x of 5/4
Answer:
B
Step-by-step explanation:
Because under the six there's a line so the line is there then you look at the four and equal it to it and that's how you know it's B
You're welcome
Given that
R
=
2
x
+
2
y
Find
y
when
x
=
9
and
R
=
29
Give your answer as an improper fraction in its simplest form.
Answer: y=11/2
Step-by-step explanation:
r = 2x + 2y
29=2(9) + 2y
29=18 + 2y
11 = 2y
11/2 = y
How much cinemeters is 5 inches
Answer:
5 inches is equal to 12.7 centimeters.
Step-by-step explanation:
There is 2.54 centimeters in an inch so just multiply that by 5 and you get 12.7.
Answer:
12.70 cm hope it is right
Step-by-step explanation:
Angel Sanchez has 10 books on a shelf; 5 mysteries, 4 science fiction books, and 1 biography. Determine the probability of each situation below.
a) Selecting one biography and then one mystery, with replacement
b) Selecting one biography and then one mystery, without replacement
a) The probability of selecting one biography and then one mystery, with replacement, is 17
(Type an integer or a simplified fraction)
Answer:
a) 1/10 x 5/10 = 1/20
b) 1/10 x 5/9 = 1/18
Step-by-step explanation:
a) Probability of selecting one biography and then one mystery, with replacement: 1/20
b) Probability of selecting one biography and then one mystery, without replacement: approximately 0.0556 or 5.56%.
The probability of each situation can be calculated as follows:
a) Selecting one biography and then one mystery, with replacement:
With replacement means that after each selection, the book is put back on the shelf before the next selection.
The probability of selecting the biography first is 1 out of 10 books (since there is 1 biography out of 10 books).
The probability of selecting the mystery book next is 5 out of 10 books (since there are 5 mysteries out of 10 books).
The overall probability is the product of the individual probabilities:
Probability = (1/10) * (5/10) = 1/20
So, the probability of selecting one biography and then one mystery, with replacement, is 1/20.
b) Selecting one biography and then one mystery, without replacement:
Without replacement means that after each selection, the book is not put back on the shelf before the next selection.
The probability of selecting the biography first is still 1 out of 10 books.
However, after selecting the biography, there are now 9 books left on the shelf, and the probability of selecting a mystery is 5 out of 9 books (since there are 5 mysteries out of the remaining 9 books).
The overall probability is the product of the individual probabilities:
Probability = (1/10) * (5/9) ≈ 0.0556 or 5.56%
So, the probability of selecting one biography and then one mystery, without replacement, is approximately 0.0556 or 5.56%.
To know more about Probability, refer here:
https://brainly.com/question/27784798
#SPJ2
Paulina has a suitcase full of clothes that weighs 4
4
7pounds. Rebecca has a suitcase full of clothes that weighs
7
8of Paulina's suitcase. How many pounds does Rebecca's suitcase weigh?
Answer:
4 pounds
Step-by-step explanation:
Paulina has a suitcase full of clothes that weighs 4 4/7pounds. Rebecca has a suitcase full of clothes that weighs
7/8 of Paulina's suitcase. How many pounds does Rebecca's suitcase weigh?
Weight of Paulina's suitcase = 4 4/7 pounds = 32/7 pounds
Weight of Rebecca's suitcase = 7/8 of Paulina's suitcase
Hence, the weight of Rebecca's suitcase in pounds = 7/8 of 32/7 pounds
= 7/8 × 32/7
= 4 pounds
Therefore, Rebecca's suitcase weighs 4 pounds.
Find – 8-(-3). -8-(-3) =
Answer:
-5.5
Step-by-step explanation:
Solve the trig identity: csc(x) - sin x
Caitlyn is saving for vacation. She already has $38 and plans to save $18 per week until she reaches her goal of $524. Caitlyn’s total savings, s, can be determined using this equation, where w represents the number of weeks she saves.
s=18w+38
How many weeks will Caitlyn need to save to reach her goal of $524?
Answer:
27.88 can be rounded to whatever the question wants you to, coz it needs to be a whole no.---> so I would say 28 weeks, but it depends on what the question asks
Step-by-step explanation:
18w+38= should equal to $540
rephrasing this in a mathematical way would be-
18w+38=$540
18w=$540-38
18w=502
w=502/18
w=27.88
Answer:
The answer is 27. 88 but if this is like a test and not a open end question than the answer is 27 ;)
I really need help with -8 - 4(5m + 9)
Which binomial could be rewritten as a difference of two squares?
A 2r2 – 4y2
B 9x2 + 16y2
C 3r2 – 10y2
D 4x2 - 25y2
It Snowed 1/2 inch on Saturday and 1 3/5 inches on Sunday. How much did it snow altogether, total?
Answer:
Fraction form: it snowed 2 1/10 inches in total, decimal form: in other words it snowed 2.1 inches.
Step-by-step explanation:
Which table represents a function with a slope of 1/2 and a y-intercept of 4
Answer:D
Step-by-step explanation: trust me ima sophomore use this for help y=1/2x+4 then x value change it to the number in the x section then if the y appears just like in the box the y section it’s correct
Evaluate 5x - 9y if x = 8 and y=-3
Plz help like soon
16. Adam uses a microscope to observe insects in science class. The
microscope enlarges objects to 100 times their actual size. Find the length of
each insect as seen in the microscope.
A=
cm
(Type a whole number or a decimal.)
Answer:
A= 0.5, B=2.2, C=0.12, D=.0.9.
Step-by-step explanation:
What’s the area? Please help :)
Answer:
252 sq. in.
Step-by-step explanation:
divide it into sections like this
12*15=180
3*6=18
6*9=54
then add it all together. sometimes it is more complicated, but as long as none of the divided parts overlap this will be correct for any shape, as long as you account for the whole shape.