Solve the system of linear equations by elimination. 12x - 7y = -2 8x + 11y = 30
Answers
Steps:
The solutions for the the system of equations are given as x = 1 and y = 2 respectively.
What is a system of linear equations?A system of linear equations is a group of equations having same number of variables and degree.
For the n number of variables n number of equations are required.
On the basis of number of solutions a system of equations can be classified as consistent and inconsistent.
The given system of linear equations are as follows,
12x - 7y = -2 (1)
8x + 11y = 30 (2)
In order to solve by elimination, multiply equation (1) by 2 and (2) by 3 and then subtract to obtain,
2(12x - 7y) - 3(8x + 11y) = 2 × -2 - 3 × 30
=> -14y - 33y = -94
=> -47y = -94
=> y = 2
Substitute y = 2 in equation (1) to get,
12x - 7 × 2 = -2
=> 12x = -2 + 14
=> x = 12/12 = 1
Hence, the given system of linear equations is solved by elimination to give x = 1 and y = 2 respectively.
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Related Questions
-90 divided by (-9) can somebody help me please and also do it STEP BY STEP please this is Algebra 1 please STEP BY STEP
Answers
Answer:
10
Step-by-step explanation:
It is a one step equation
just divide 90 / 10 like you would regularly do, don’t forget about the negatives though.
your answer is +10
when you divide two negatives, your answer will always be positive
$500 deposit over 20 years with an interest rate of 5%
Answers
Answer: $1,104
Step-by-step explanation:At the end of 20 years, your savings will have grown to $1,604.
You will have earned in $1,104 in interest.
Given the triangle that has a base of five less than triple the height. The height is 2x+6.
Part A: Determine the expression that represents that area of the triangle.
Answers
Answer:
A = 0.5(2x+6)(6x+13) = 6x² + 49x + 78Step-by-step explanation:
H = 2x+6 - the hight
3H = 3(2x+6) - triple the hight
3H-5 = 3(2x+6) - 5 - five less than triple the height
Area of triangle: A = 0.5BH
B = 3(2x+6)-5 = 6x + 18 - 5 = 6x + 13
H = 2x+6
So:
A = 0.5(2x+6)(6x+13) = (x+6)(6x+13) = 6x² + 13x + 36x + 78
A = 6x² + 49x + 78
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ASK YOUR TEACHER
According to the Bureau of Labor Statistics, in a recent year, there were 16,359,000 women aged 25 to 34 who were employed and 5,309,000
who were unemployed but looking for work. What is the rate per 1,000 women aged 25 to 34 who were employed? Round to the nearest whole
number.
Answers
Answer:
The rate of employed per 1000 women is 754
Step-by-step explanation:
Given
Employed = 16,359,000
Unemployed = 5,309,000
Required
Rate per 1000 women of employed
In this case, Rate is calculated by dividing employed by total women
i.e.
[tex]Rate = \frac{Employed}{Employed + Unemployed}[/tex]
[tex]Rate = \frac{16359000}{16359000 + 5309000}[/tex]
[tex]Rate = \frac{16359000}{21668000}[/tex]
Represent the denominator as a factor of 1000
[tex]Rate = \frac{16359000}{21668 * 1000}[/tex]
Divide
[tex]Rate = \frac{754.288086}{1000}[/tex]
Approximate
[tex]Rate = \frac{754}{1000}[/tex]
Hence, the rate of employed per 1000 women is 754
Sara is 7 years older than Sushil. June is 4 years younger than Sushil. If the total of their ages is 87, how old is the eldest of them?
Answers
Answer:
76
Step-by-step explanation:
Answer:
We have:
a) Sushi+7=Sara
b) June=Suhi-4
c) Sushi+Sara+June=87
3 equations with 3 variables, we can solve it.
we can introduce in a) and b) in c) and we get: Sushi+Sushi+7+ Sushi-4=87
3 sushi+3=87 which gives:
3 sushi= 87-3=84
sushi=84/3=28
Sara= sushi+7 (from b)= 35
June= sushi-4=24
We can check 24+35+28=87 All good
Step-by-step explanation:
True or False: A slope of 0 means the line dosen't move up or down, it is flat
Answers
Answer:
Step-by-step explanation: yes
Seven more than the product of five and a number is 45.
Answers
Answer:
7+(5n)=45
n= 7.6
Step-by-step explanation:
Sione just landed a great job as an engineer where he will make $55,000 a year. The company he
will work for guarantees a 3% pay increase each year so it's employees' salaries keep up with
inflation. At the end of the first year Sione will have made $55,000.
RECURSIVE FUNCTION?
Answers
Answer:
m (t) = m (t-1) * 1.03; m(t) = 55,000
Step-by-step explanation:
f(x) = 3x5 – 15x3 + 12x
Answers
Answer:
f(x)=3⋅5−15⋅3+12x
Simplify each term
f(x)=15−45+12x
Subtract 45 from 15
f(x)=−30+12x
HELP ME PLEASEEE. I WILL MARK U BRAINLIESTTTT.
Answers
Edgenuity’s sample response for this question:
Sublimation occurs because the atoms in a solid must gain enough energy to form a gass without passing through the liquid state. Low air pressure and large amounts of energy, often in the form of heat, allow the atoms to move fast enough to overcome the attractive forces between them.
If you need an original response here’s my take!!:
Sublimation happens when a solid turns directly into a gas. For this to happen, there must be low air pressure and immense heat energy. This allows atoms to quickly move and perform sublimation.
Cuánto mide el lado de un cuadrado si su área es de 20 cm
Answers
4 1/8 (3x−4)=33
pls find x thank you
Answers
Answer:x=3 2/3
Step-by-step explanation:
Answer:
the answer is 23.3
Step-by-step explanation:
Which statement describes g(x) as a transformation of
f(x) and identifies an equation for g(x)?
Vertical stretch followed by a translation 1 unit left, so
g(x) = f*(x + 1)).
O Vertical stretch followed by a translation 1 unit right,
so g(x) = 1 + x = 1)).
O Horizontal stretch followed by a translation 1 unit left,
so g(x) = (3x + 2).
O Horizontal stretch followed by a translation 1 unit
right, so g(x) = (4 x - 1)
Answers
Answer:
The correct option is;
Horizontal stretch followed by a translation 1 unit left so g(x) = (3·x + 2)
Step-by-step explanation:
In geometric transformation, a dilation involves the increase in the dimension of the distances between points by a given scale factor.
Therefore, with regards to the question, a dilation can be represented by the product of the initial dimension, x, by a variable, such as an integer
A translation right is represented by an addition to the x value, while a translation left is represented by subtraction from the x value
Therefore, whereby f(x) = x + 1
An horizontal stretch of 3 will be 3 × (x + 1) = 3·x + 3
Followed by an a translation 1 unit left will be;
3·x + 3 - 1 = 3·x + 2;
Therefore;
g(x) = (3·x + 2).
Answer:
The answer is D on e2020
Step-by-step explanation:
Which equation represents a line which is parallel to the line y=-3/4 x -2
Answers
Answer: Any equation that is of the form y = -3/4x + b, where b is a real number, will be parallel to y = -3/4x - 2.
Step-by-step explanation:
A parallel line has the same slope as the original line. Therefore, if the equation of the original line is y = mx+b, m (the slope) will remain the same, while b can change.
The equation y = -3/4x - 2 has the same slope -3/4, represents a line which is parallel to the line y=-3/4 x -2
What is a linear function?A function that can be represented in the form of y =mx +c, is called a Linear Function. where m is the slope and c is the y-intercept.
The slope of the given line can be found as;
A parallel line has the same slope as the original line. Thus, if the equation of the original line is y = mx+b, m (the slope) will remain the same, while b can change.
Any equation that is of the form y = -3/4x + b,
where b is a real number, will be parallel to the equation.
y = -3/4x - 2.
m = -3/4
The equation y = -3/4x - 2 has the same slope -3/4, represents a line which is parallel to the line y=-3/4 x -2
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Help! 13 points!:) Geometry
Answers
Answer:
For part A its called a ray.For part B it would be EA.
Step-by-step explanation:
Part A would be called a ray because B is the endpoint while C is continuous and a ray has only one endpoint.Part B is EA because E would be the endpoint while A would be continuous
I NEED HELP ASAP
Evaluate the expression for r = –3.
15 + 6r =
Answers
Answer: -3
Step-by-step explanation:
Since we are given the value of r, we can plug that value into the expression and solve.
15+6(-3) [multiply]
15-18 [subtract]
-3
Now, we know that the expresison is equal to -3.
how do I do this :( I tried but I can’t figure out how to
Answers
Answer:
Step-by-step explanation: got you
slope 2/3
x | y
0 -1
2/3 0
Use implicit differentiation to find the slope of the tangent line at the given point:
Answers
Answer:
[tex]\displaystyle \frac{dy}{dx}\Big|_{(1, 1)}=0[/tex]
Step-by-step explanation:
We are given the equation:
[tex](x^2+y^2)^2=4x^2y[/tex]
And we want to find the slope of the tangent line at the point (1,1).
Recall that the slope of the tangent line to a point of a function is given by the function's derivative.
Thus, find the derivative of the equation. Take the derivative of both sides with respect to x:
[tex]\displaystyle \frac{d}{dx}\left[(x^2+y^2)^2\right]=\frac{d}{dx}\left[4x^2y\right][/tex]
Let's do each side individually.
Left:
We can use the chain rule:
[tex](u(v(x))'=u'(v(x))\cdot v'(x)[/tex]
Let v(x) be x² + y² and u(x) is x². Thus, u'(x) is 2x. Therefore:
[tex]\displaystyle \frac{d}{dx}\left[(x^2+y^2)^2\right]=2\left(x^2+y^2\right)\left(\frac{d}{dx}\left[x^2+y^2\right]\right)[/tex]
Differentiate:
[tex]\displaystyle \frac{d}{dx}[(x^2+y^2)^2]=2(x^2+y^2)\left(2x+2y\frac{dy}{dx}\right)[/tex]
Factor. Therefore, our left side is:
[tex]\displaystyle 4(x^2+y^2)\left(x+y\frac{dy}{dx}\right)[/tex]
Right:
We have:
[tex]\displaystyle \frac{d}{dx}\left[4x^2y\right][/tex]
We can move the constant multiple outside:
[tex]\displaystyle =4\frac{d}{dx}\left[x^2y\right][/tex]
We will use the Product Rule:
[tex]\displaystyle =4\left(\frac{d}{dx}\left[x^2\right]y+x^2\frac{d}{dx}\left[y\right]\right)[/tex]
Differentiate:
[tex]\displaystyle =4\left(2xy+x^2\frac{dy}{dx}\right)[/tex]
Therefore, our entire equation is:
[tex]\displaystyle 4(x^2+y^2)\left(x+y\frac{dy}{dx}\right)=4\left(2xy+x^2\frac{dy}{dx}\right)[/tex]
To find the derivative at (1,1), substitute and evaluate dy/dx when x = 1 and y = 1. Hence:
[tex]\displaystyle 4((1)^2+(1)^2)\left((1)+(1)\frac{dy}{dx}\right)=4\left(2(1)(1)+(1)^2\frac{dy}{dx}\right)[/tex]
Evaluate:
[tex]\displaystyle 4((1)+(1))\left(1+\frac{dy}{dx}\right)=4\left(2+\frac{dy}{dx}\right)[/tex]
Further simplify:
[tex]\displaystyle 8\left(1+\frac{dy}{dx}\right)=8+4\frac{dy}{dx}[/tex]
Distribute:
[tex]\displaystyle 8+8\frac{dy}{dx}=8+4\frac{dy}{dx}[/tex]
Solve for dy/dx:
[tex]\displaystyle 4\frac{dy}{dx}=0\Rightarrow \frac{dy}{dx}=0[/tex]
Therefore, the slope of the tangent line at the point (1, 1) is 0.
Please answer the equation in the attachment.
Answers
Answer:
the missing value is 9.33.
Step-by-step explanation:
given,
length (l) = 3x+2
breadth (b) = 4
perimeter(P) = 68 cm
now,
P = 2(l+b)
or, 68 = 2× ( 3x+2+4)
or, 68 = 2× ( 3x+ 6)
or, 68 = 6x+12
or, 68 - 12= 6x
or, 56 = 6x
or, 6x = 56
or, x = 56/6
or, x = 9.33
what is 6/6 in a reduced fraction
Answers
Answer:
1
Step-by-step explanation:
Step 1:
6 ÷ 6
Answer:
1
Hope This Helps :)
Find the midpoint between
(3,8)
and
(-10,5)
Answers
Answer:
(-3.5,6.5)
Step-by-step explanation:
See the photo for step-by-step explanation
Answer:
(6.5,1.5)
Step-by-step explanation:
scale factor 0.1 is it en large preserve or reduce
Answers
Answer:
Stay the same
Step-by-step explanation:
1 * x = x it will stay the same
a classroom has 24 desks. if the students arrange the desks to 4 rows how many desks will be in each row explain.
Answers
6 desk in a row
Explanation:
There is 24 desks total divided by 4 rows which equals 6. And if you want to check if this is correct reverse the operation by multiplying 6 x 4.
2x + 3 = 7
I'm confused
Answers
The answer is x=2
move all terms that dont contain x to the right side and then solve.
Answer:
x=2
Step-by-step explanation:
Sorry the picture is sideways, I was trying to fit everything in lol.
It will take five builders 62 days to complete a particular project. At this rate, how long would the project take if there were only two builders?(SHOW WORK)
Answers
Answer:
2 builder complete work = 155 days
Step-by-step explanation:
Given:
5 builder complete work = 62 days
So,
1 builder complete work = 62 days × 5
if,
2 builder complete work = [62 days × 5] / 2
2 builder complete work = 155 days
An investor purchased a house 8 years ago for $48,000 This year it was appraised at $73,500 Complete parts (a) through (d) below. (a) A linear equation V=mt+b,0
Answers
Answer:
b = $48000, m = $3187.5 / year
Step-by-step explanation:
The equation of a linear function is given as y = mx + b, where m is the rate of change, b is the value of y when x = 0, y = dependent variable and x = dependent variable.
Given that V = mt + b:
b = initial price of the house at 0 years = $48000
V = mt + 48000, At 8 years the house is appraised at $73,500
73500 = 8m + 48000
8m = 73500 - 48000
8m = 25500
m = 3187.5
please help soon!!!
find the sum of the series
30
Z = (2k-1)
k=3
Answers
Oceanside bike rental shop charges 11 dollars plus 6 dollars an hour for renting a bike. Joan paid 35 dollars to rent a bike . How many hours did she pay to have the biked checked out?
Answers
Answer:
4 hours
Step-by-step explanation:
Which equation can be represented using the number line?
A number line going from to 1 in increments of one-eighths. Arrows go from each mark on the line to the next up to three-fourths.
Three-fourths divided by one-eighth = 6
One-eighth divided by three-fourths = 6
6 divided by three-fourths = one-eighth
6 divided by one-eighth = three-fourths
Answers
Answer:
a
Step-by-step explanation:
The equation which can be represented using the picture displayed on the number line is Three-fourths divided by one-eighth = 6
The distance between each marked line on the number line is 1/8The length of the number line is 3/4The number of steps or marked points can be obtained using the relation :
Length of line ÷ Distance between each marked points
3/4 ÷ 1/8 = 6
Therefore, the expression which represents the scenario on the number line is 3/4 ÷ 1/8 = 6
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what is 9b = 8b − 16
Answers
Answer:
b = -16
Step-by-step explanation:
9b = 8b - 16
9b - 8b = -16
b = -16