Answer:
We're asked to solve this system of equations:
\begin{aligned} 2y+7x &= -5\\\\ 5y-7x &= 12 \end{aligned}
2y+7x
5y−7x
=−5
=12
We notice that the first equation has a 7x7x7, x term and the second equation has a -7x−7xminus, 7, x term. These terms will cancel if we add the equations together—that is, we'll eliminate the xxx terms:
\begin{aligned} 2y+\redD{7x} &= -5 \\ +~5y\redD{-7x}&=12\\ \hline\\ 7y+0 &=7 \end{aligned}
2y+7x
+ 5y−7x
7y+0
=−5
=12
=7
Solving for yyy, we get:
\begin{aligned} 7y+0 &=7\\\\ 7y &=7\\\\ y &=\goldD{1} \end{aligned}
7y+0
7y
y
=7
=7
=1
Plugging this value back into our first equation, we solve for the other variable:
\begin{aligned} 2y+7x &= -5\\\\ 2\cdot \goldD{1}+7x &= -5\\\\ 2+7x&=-5\\\\ 7x&=-7\\\\ x&=\blueD{-1} \end{aligned}
2y+7x
2⋅1+7x
2+7x
7x
x
=−5
=−5
=−5
=−7
=−1
The solution to the system is x=\blueD{-1}x=−1x, equals, start color #11accd, minus, 1, end color #11accd, y=\goldD{1}y=1y, equals, start color #e07d10, 1, end color #e07d10.
We can check our solution by plugging these values back into the original equations. Let's try the second equation:
\begin{aligned} 5y-7x &= 12\\\\ 5\cdot\goldD{1}-7(\blueD{-1}) &\stackrel ?= 12\\\\ 5+7 &= 12 \end{aligned}
5y−7x
5⋅1−7(−1)
5+7
=12
=
?
12
=12
Yes, the solution checks out.
If you feel uncertain why this process works, check out this intro video for an in-depth walkthrough.
Example 2
We're asked to solve this system of equations:
\begin{aligned} -9y+4x - 20&=0\\\\ -7y+16x-80&=0 \end{aligned}
−9y+4x−20
−7y+16x−80
=0
=0
We can multiply the first equation by -4−4minus, 4 to get an equivalent equation that has a \purpleD{-16x}−16xstart color #7854ab, minus, 16, x, end color #7854ab term. Our new (but equivalent!) system of equations looks like this:
\begin{aligned} 36y\purpleD{-16x}+80&=0\\\\ -7y+16x-80&=0 \end{aligned}
36y−16x+80
−7y+16x−80
=0
=0
Adding the equations to eliminate the xxx terms, we get:
\begin{aligned} 36y-\redD{16x} +80&=0 \\ {+}~-7y+\redD{16x}-80&=0\\ \hline\\ 29y+0 -0&=0 \end{aligned}
36y−16x+80
+ −7y+16x−80
29y+0−0
=0
=0
=0
Solving for yyy, we get:
\begin{aligned} 29y+0 -0&=0 \\\\ 29y&=0 \\\\ y&=\goldD 0 \end{aligned}
29y+0−0
29y
y
=0
=0
=0
Plugging this value back into our first equation, we solve for the other variable:
\begin{aligned} 36y-16x+80&=0\\\\ 36\cdot 0-16x+80&=0\\\\ -16x+80&=0\\\\ -16x&=-80\\\\ x&=\blueD{5} \end{aligned}
36y−16x+80
36⋅0−16x+80
−16x+80
−16x
x
=0
=0
=0
=−80
=5
The solution to the system is x=\blueD{5}x=5x, equals, start color #11accd, 5, end color #11accd, y=\goldD{0}y=0y, equals, start color #e07d10, 0, end color #e07d10.
Want to see another example of solving a complicated problem with the elimination method? Check out this video(Opens in a new window).
Step-by-step explanation:
Kaya invests £4000 for 8 years
The investment gets compound interest of x% per annum
At the end of 8 years the investment is worth £6872.74
Work out the value of x
To find the interest rate on the investment for 8 years is equal to 0.7%
Given the following data:
Principal = £4000Future value = £6872.74Time = 8 years
To find the interest rate on the investment for 8 years:
Mathematically, compound interest is given by the formula:
[tex]A = P(1 + r)^{t}[/tex]
Where;
A is the future value.P is the principal or starting amount.r is annual interest rate.t is the number of years for the compound interest.Substituting the given parameters into the formula, we have;
[tex]6872.74 = 4000(1 + r)^{8}\\\\(1 + r)^{8}=\frac{6872.74}{4000} \\\\(1 + r)^{8}=1.7182\\\\1+r=\sqrt[8]{1.7182} \\\\1+r =1.07\\\\r=1.07-1\\\\r=0.7[/tex]
Interest rate, r = 0.7%
Read more: https://brainly.com/question/22339845
Select Correct or Incorrect for each equation.
Equation
−1−1=−1 Correct Incorrect
−1+1−1=−1 Correct Incorrect
Answer:
-1-1=-1 is incorrect.
-1+1-1=-1 is correct.
Step-by-step explanation:
Add them all up and if they do not equal what is on the other side of the equal sign, then it is incorrect. If it does add up to what is on the other side of the equal sign, then it is correct.
Find the next two terms. 2, 10, 50, ?, ?
Hi there!
The next 2 terms are 250 and 1,250.
We have a geometric sequence, which means we use multiplication or division to get to the next term.
Here, we multiply by 5 to get to the next term.
So we multiply 50 by 5:
50*5=250
We multiply 250 by 5 to get to the next term:
250*5=1,250
And we're done!
Therefore, the next two terms are: 250 and 1,250.Hope this helps!
~Just a felicitous girlie
#HaveASplendidDay
[tex]SilentNature :)[/tex]
Answer:
250, 1250
Step-by-step explanation:
This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by 5 gives the next term.
Hope that helps!
someone please help, how many do i split the shape into.
Answer:
The sum is 1260°.
Step-by-step explanation:
Find the quotient.
593
÷
60
A.
10 R7
B.
9 R53
C.
9 R3
D.
9 R93
Answer:
b
Step-by-step explanation:
b
The answer is. B.) 9 R53
I used long division
The graph of g(x) is a transformation of the graph of f(x)=3^x.
Enter the equation for g(x) in the box.
g(x) =
Transformation involves changing the position of a graph
The equation of g(x) is [tex]\mathbf{g(x) = 8(2)^x}[/tex]
A geometric function is represented as:
[tex]\mathbf{y =ab^x}[/tex]
The graph of g(x) passes through (-1,4) and (-2,2)
So, we have:
[tex]\mathbf{2 =ab^{-2}}[/tex]
[tex]\mathbf{4 =ab^{-1}}[/tex]
Divide both equations
[tex]\mathbf{\frac{4}{2} =\frac{ab^{-1}}{ab^{-2}}}[/tex]
Divide
[tex]\mathbf{2 =b}[/tex]
Rewrite as:
[tex]\mathbf{b =2}[/tex]
Substitute 2 for b in [tex]\mathbf{4 =ab^{-1}}[/tex]
[tex]\mathbf{4 = a2^{-1}}[/tex]
Multiply both sides by 2
[tex]\mathbf{8 = a}[/tex]
Rewrite as:
[tex]\mathbf{a = 8}[/tex]
Substitute 2 for b and 8 for a in [tex]\mathbf{y =ab^x}[/tex]
[tex]\mathbf{y = 8(2)^x}[/tex]
Express as a function
[tex]\mathbf{g(x) = 8(2)^x}[/tex]
Hence, the equation of g(x) is [tex]\mathbf{g(x) = 8(2)^x}[/tex]
Read more about function transformation at:
https://brainly.com/question/13810353
Answer:
g(x)=8(2)^x
Step-by-step explanation:
A 30 ft building casts a shadow that is 75 ft. long. A nearby tree casts a shadow that is 35 ft. long. How tall is the tree?
Answer:
The tree is 14 ft. tall.
Step-by-step explanation:
Height of the building/ Height of the tree = Shadow of building/ Shadow of tree
30/x = 75/35 Cross multiply
75x = (30)(35)
75x = 1050
x = 1050/75
x = 14
ahh help !!
im bad at math ;-;
Answer:
To be honest I think it is D
Step-by-step explanation:
A car is traveling is at a speed of 99 km/h. what is the car speed in kilometers per minute how many kilometers for the car travel in 2 minutes do not round your answers.
Answer:
1.65 kilometers a minute and you would travel 3.3 kilometers in two minuets
Step-by-step explanation:
Im pretty sure that is the answer because 99/60 = 1.65 and 1.65 * 2 = 3.3
I can run 5km in 30 minutes. How long would it take me to run 30km?
Answer:
3 hours
Step-by-step explanation:
5km = 30m
-------------------
5
1km = 6m
*30 *30
30km = 180 m
30k = 3 hours
The history museum charges a $20 fee plus S8 per student for a field trip. The aquarium charges a $50 fee plus $5 per student. The lines in the graph represent the cost of each field trip. For what number of students will the total cost of each field trip be the same, and what will that cost be? Field Trip Costs 120 110 100 90 80 70 y = 50 - 5x (s) jsou y = 20 + 8x 50 30 20 10 1 2 3 4 5 G 7 8 9 10 11 12 Number of students A. 110 students; $12 B. 12 students: $110 O c. 10 students; $100 *C O D. 100 students: $10
Answer:
C
Step-by-step explanation:
took test
Answer: C!
Step-by-step explanation: if you look at where the lines intersect, it lands on 10 students and 100 dollars.
Need help thank you…
Answer: 48 degrees
Step-by-step explanation: the sum of all the angles in a triangle has to be 180 degrees. 180-(62+70)=48
What is 1,234.7(578)/345
it should be
2068.56985507
Answer:
2068.56985507
Step-by-step explanation:
1234.7 x 578 = 713656.6
713656.6/345 = 2068.56985507
Have a great day!
Describe the Function
f(x) = 3x² + 2
2 + y + y + y + y + y + 3 ?
Answer:
5 + 5y
Step-by-step explanation:
2 + y + y + y + y + y + 3
Combine like terms
2+3 + y + y + y + y + y
5 + 5y
Using the distributive property write an expression equivalent to -7(7-x)
Answer:
-49+7x
Step-by-step explanation:
-7*7=-49
-7*-x=7x
How many meals can you buy with $60 if one meal in the college cafeteria costs $6
Answer:
10
Step-by-step explanation:
60/6=10
Please help me with this question?
Answer:
x + 1/2
Step-by-step explanation:
1/2 x + 3/4 + 1/2 x - 1/4
= 1/2 x + 1/2 x + 3/4 - 1/4
= 2/2 x + 2/4
= x + 1/2
What is the cost to get into a Green Cab?
Answer:
$5
Step-by-step explanation:
The graph shows the green cab costs $5 even if you don't go anywhere (miles = 0).
The cost to get into a green cab is $5.
Answer:
15
Step-by-step explanation:
because it's the where the green lines cross the graph.
Solve this equation
2x-3=7
2x -3 = 7
Add 3 to both sides:
2x = 10
Divide both sides by 2:
X = 5
Answer:
x = 5
Step-by-step explanation:
2x - 3 = 7
=> 2x = 7 + 3
=> 2x = 10
=> x = 5
I need this answer.
Answer:
0.5
Step-by-step explanation:
isabel is buying 6 anglefish, and she wants her total cost to be no more than 2$ above or below 36$. what inequalty models the cost in Dollers of an angle fish
Answer:
c<2$
c>36$
Step-by-step explanation:
._.
Working together, Edward and Frances can wallpaper an apartment in 12 hours. It would take Frances 30 hours to do the same job by herself. How long would it take Edward to do it alone?
Answer:
Step-by-step explanation:
Givens
together: 12 hours
Frances: 30 hours
Edward: x
Formula
The formula is an odd one that shows up in physics as well.
1/Frances + 1 / Edward = 1/Together.
Solution
1/30 + 1/x = 1/12
LCD for 12 and 30
12: 2 * 2 * 3
30:3 * 2 * 5
LCD: 2*2*3*5
LCD: 60
2/60 + 1/x = 5/60 Subtract 2 / 60 from both sides
1/x = 5/60 - 2/60
1/x = 3/60 Cross Multiply
3x = 60*1 Divide by 3
3x/3 = 60/3
x = 20
So Edward (doing it alone) takes 20 hours to do the job.
8. Which symbol makes this number sentence true?
38.21 O 38.023
Answer:
>
Step-by-step explanation:
if Angle 4 = 6x+8 and Angle 3 = 20x+16 find the measure of all Four Angles
Answer:
40 on edge
Step-by-step explanation:
2021
Due in 30 mins!!
Thank you!
Answer:
Domain: (-∞, ∞)
Range: (0,∞)
Step-by-step explanation:
Exponential functions are curves which approach a horizontal asymptote usually at y=0 or the x-axis unless a value has been added to it. If it has, the curve shifts. This function has addition on the exponent but not to the whole function so it does not change the asymptote. Its y - values remain between 0 and ∞. This is the range, the set of y values.
However, the range of exponentials can change based on the leading coefficient. If it is negative the graph flips upside down and its range goes to -∞. This doesn't have it either.
The addition to 1 on the exponent shifts the function to the left but doesn't change the range.
In exponential functions, the x values are usually not affected and all are included in the function. Even though it shifts, the domain doesn't change either. Its domain is (-∞, ∞).
Domain: (-∞, ∞)
Range: (0,∞)
Answer:
try graphing it to see the domain and range easier (desmos or a graphing calculator is useful)
hello i really need help pls ASAP
Answer:
1. D
2. A
3. picture isn’t clear
4. B
5. C
Step-by-step explanation:
2. Anything to the power of 0 is = 1
1^-1 = 1/1 = 1
real answer : study hard
Frank has a student loan of $55,780.
This loan has a simple interest rate of
9% per year. What is the amount of
interest that Frank will be charged on
this loan at the end of one year?
Answer: $6197.77 would be the right answer
hope it helps :]
a help with my mathhh i give brainliest <3
Answer: -36
Step-by-step explanation:
Answer is -36
if you don't understand why ask
man pays $225 each month into an account to pay his bills. How much does he pay into the account in three years?
Answer:
$8100
Step-by-step explanation:
There are 36 months in 3 years.
225 x 36 = $8100
