What is the solution of the system of linear equations graphed below ? PLEASE HELP
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A linear equation is the equation of a straight line. The solution to the system of linear equations is infinitely many solutions.
There are two straight lines on the attached graph. The lines are:
The black lineThe red lineAnd both lines lie on one another,
This means that, both lines have the following features:
The same slopeThe same interceptsWhen lines have the above features to be the same, it means the equations of both lines are the same.
And as such, the solution to the system is infinitely many solutions.
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Related Questions
Could someone help me?
(50 Points)
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Answer:
.
Step-by-step explanation:
.............................
Refer to the attachment and answer these questions.
( 1 ). Find the first counting number 'x' in group n.
( 2 ). Find the sum S of all counting numbers in group n.
Please also show your work too so others and I can understand. Thanks in advance!
Answers
Answer:
[tex]\displaystyle \text{(1)}\\x=1+\sum_{k=1}^{n-1}2k\\\\\text{(2)}\\\displaystyle \frac{\displaystyle \sum_{k=1}^{n}2k\left(1+\displaystyle \sum_{k=1}^{n}2k \right)}{2}-\frac{\displaystyle \sum_{k=1}^{n-1}2k\left(1+\displaystyle \sum_{k=1}^{n-1}2k \right)}{2}[/tex]
Step-by-step explanation:
Notice that Group 1 starts with 1 and we keep counting up by 1.
Part 1:
The total number of numbers from Group 1 to Group [tex]n[/tex] can be found by:
[tex]\displaystyle \sum_{k=1}^{n}2k[/tex]
To find the first number in a certain group [tex]g[/tex], we'll find the total number of numbers from Group 1 to Group [tex]g-1[/tex], then add 1.
Here's why.
Let's say we want to find the first number of Group 3, which we can clearly see is 7. Take advantage of the fact that the sequence of numbers counts up by 1, starting from 1. We will use the formula above to to find the total number of numbers from Group 1 to Group 2, which is 6, then add 1 to achieve the number of 7.
Therefore, the first number in group [tex]n[/tex] must be:
[tex]\boxed{\displaystyle 1+\sum_{k=1}^{n-1}2k}[/tex]
Part 2:
Recall that the sum of the numbers from [tex]1[/tex] to positive integer [tex]n[/tex] inclusive is given by [tex]\displaystyle\frac{n(n+1)}{2}[/tex].
Therefore, if we find the total number of numbers from Group 1 to Group [tex]n[/tex], we can simply substitute that value into the formula above to find the total sum of the numbers from Group 1 to Group [tex]n[/tex].
To find the total sum of the numbers exclusively in Group [tex]n[/tex] simply subtract the sum of numbers from Group 1 to Group [tex]n-1[/tex].
Short example on how that works:
The sum of all numbers in Group 3 is equal to the sum of the numbers from Group 1 to Group 3 minus the sum of the numbers from Group 1 to Group 2.
We've already found the formula for the total number of numbers from Group 1 to Group [tex]n[/tex] in the previous part, so convert this concept into summation notation like such:
[tex]\boxed{\displaystyle \frac{\displaystyle \sum_{k=1}^{n}2k\left(1+\displaystyle \sum_{k=1}^{n}2k \right)}{2}-\frac{\displaystyle \sum_{k=1}^{n-1}2k\left(1+\displaystyle \sum_{k=1}^{n-1}2k \right)}{2}}[/tex]
Given 1/f=1/v+1/u. make v the subject of the relation
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Answer:
v = [tex]\frac{fu}{u-f}[/tex]
Step-by-step explanation:
Given
[tex]\frac{1}{f}[/tex] = [tex]\frac{1}{v}[/tex] + [tex]\frac{1}{u}[/tex]
Multiply through by fuv to clear the fractions
uv = fu + fv ( subtract fv from both sides )
uv - fv = fu ← factor out v from each term on the left side
v(u - f) = fu ← divide both sides by (u - f)
v = [tex]\frac{fu}{u-f}[/tex]
2+4(7+2²)
--------------
4×2+5×3
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Answer:
[tex] \frac{46}{23} [/tex]
Step-by-step explanation:
[tex] \frac{2 + 4(7 + {2}^{2} )}{4 \times 2 + 5 \times 3} [/tex]
[tex] \frac{2 + 4(7 + 4)}{4 \times 2 + 5 \times 3} = \frac{2 + 4(7 + 4)}{8 + 5 \times 3} [/tex]
[tex] \frac{2 + 4(7 + 4)}{8 + 15} = \frac{2 + 4 \times 11}{8 + 15} [/tex]
[tex] \frac{2 + 4 \times 11}{23} = \frac{2 + 44}{23} [/tex]
[tex] = \frac{46}{23} [/tex]
Answer:
2+4(7+2)^2/4×2+5×3= 46/23
Sixteen is equal to 7 increased by the product of 3 and a number.
Answers
Answer:
number is 3
Step-by-step explanation:
let the number be n then the product of 3 and the number is 3n , so
16 = 7 + 3n ( subtract 7 from both sides )
9 = 3n ( divide both sides by 3 )
3 = n
That is the number is 3
Solve the equation.
2(3x+5)=46
Answers
x=6
Step-by-step explanation:
2(3x + 5) = 46,6x + 10 = 46,6x = 36,x = 6
The solution to the equation is x = 6.
Given is an equation 2(3x + 5) = 46, we need to solve it,
Let's start by gradually simplifying both sides of the problem in order to find the answer:
2(3x + 5) = 46
First, multiply 2 with each term included in parentheses to apply the distributive property:
6x + 10 = 46
Next, remove 10 from both sides to isolate the variable term:
6x = 46 - 10
That amounts to:
6x = 36
Lastly, find x by multiplying both sides by 6:
x = 36 / 6
x = 6
Consequently, x = 6 is the answer to the equation.
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12 - 5 + 6 × 3 + 20 ÷ 4
Answers
Answer:
30
Step-by-step explanation:
12 - 5 + 6 × 3 + 20 ÷ 4
12 - 5 + 6 × 3 + 5
12 - 5 + 18 + 5
7 + 18 + 5
25 + 5
30
Find the slope of the line passing through the points (-8,-3) and (-3,4).
Answers
Answer:
2.333333
Step-by-step explanation:
Answer:
[tex]slope = \frac{y2 - y1}{x2 - x1} \\ = \frac{4 - - 3}{ - 3 - - 8} \\ = \frac{4 + 3}{ - 3 + 8} \\ = \frac{7}{5} = 1.4 \\ thank \: you[/tex]
“reflection across y= -1” HELP
Answers
Answer:
the orange line is the reflection y=-1
To plot the reflection of a function across the line y = -1, you'll need to follow these steps:Understand Reflection Across a Line: Reflection across a line involves flipping the points of the original function over the given line.
For reflection across the line y = -1, you'll be swapping the positions of the points above the line with those below it.
Choose a Function: Let's say you want to plot the reflection of a function f(x) across y = -1. Choose a function that you want to reflect. For demonstration purposes, let's consider a simple quadratic function, [tex]f(x) = x^2.[/tex]
Calculate the Reflected Points: To calculate the reflected points, follow these steps for each point (x, y) on the original function:
a. Find the vertical distance between the point and the reflection line (y = -1). This distance is the difference between the original y-coordinate and -1: distance = y - (-1) = y + 1.
b. The reflected y-coordinate (y') will be -1 minus the distance calculated in the previous step: y' = -1 - distance = -1 - (y + 1) = -2 - y.
c. The x-coordinate remains the same: x' = x.
d. The reflected point is (x', y').
Plot the Reflected Points: Plot the original function f(x) and then plot the reflected points (x', y') that you calculated in the previous step. This will show you the reflection of the function across y = -1.
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Errrrrrrrrrrrrrrrrr
Answers
Answer:
st and wx
Step-by-step explanation:
bc they are on oppostite sides
What is an equation of the line that passes through the point (3,-1)(3,−1) and is parallel to the line 5x+3y=65x+3y=6?
Answers
Step-by-step explanation:
5x+3y = 6
5x = 6 - 3y
5x = 3(2-y)
5x/3 = 2 - y
y = 2 - (5x/3)
slope = x coefficient.
= - 5/3
Perpendicular slopes must be opposite reciprocals of each other: m1 * m2 = –1
new slope = 3/5
the equation formula
y = mx + b
m = new slope = 3/5
y = (3x/5) + b
From the point given (3 , -1 )
x = 3.
y = -1
-1 = (9/5) + b
b =( -5/5) - (9/5)
b = - 14 / 5
[tex]y = \frac{3}{5} x - \frac{14}{5} [/tex]
F(x)=2+4 hurry I need it know guys
Answers
Answer:
f(x) = 6
simple as me haha
Step-by-step explanation:
please give brainliest i need it
what did the boy candy say to the girl candy
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Step-by-step explanation:
Ahh!! that question is complicated....
I didn't realize that candy had genders.
How do I solve 4/9x - 10 > x/3 - 12 word for word steps?
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the answer is in the photo
The sales tax for an item was 29.70 and it cost 330 before tax. Find the sales tax rate. Write your answer as a percentage
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Then move the decimal 2 places to the right & you get 9% sales tax.
9% is the answer.
Help me thank y'all so much
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Answer:
15 p - 3 is the answer....
x is 5 years older than y.Z is 6 years older than x how old are each person if the sum of their ages is 31
Answers
x= 5+y
(Adding 5 years to y will make both equal)
z is 6 years older than x
z= 6+x
In terms of y:
z= 6 + (5+y)
x+y+z = 31
(5+y) + y + 6 + (5+y) = 31
16 + 3y =31
3y = 15
y= 5
The three ages are
y= 5
x= (5+y) = 10
z= (6+5+y)= 16
16+10+5= 31
solve for x
the area if the triangle is 50 and the one angle is 61, what is x
Answers
6
Step-by-step explanation: that’s math
HELP DUE IN 10 MINS!
Solve for x.
x + 1 / x + 5 = 7/6
Answers
Answer:
[tex]x = ( - 29)[/tex]
Step-by-step explanation:
[tex] \frac{x + 1}{x + 5} = \frac{7}{6} \\ use \: \: \: cross \: \: multipication \\ 7(x + 5) = 6(x + 1) \\ 7x + 35 = 6x + 6 \\ 7x - 6x = - 35 + 6 \\ x = - 29[/tex]
hope this helps you.
At the grocery store a Sprite costs $0.85, a 6 pack of Sprite is $4.08, and a 12 pack of Sprite is $8.52. Which is the better buy.
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Answer:
it's better to buy the six pack
Step-by-step explanation:
4.08/6 is 0.68
8.52/12 is 0.71
making the 6 pack the better deal
hi guys can l ask...... A BABY IS 3WEEKS AND 4 DAYS OLD. WHAT IS THE AGE OF THE BABY IN DAYS
Answers
Answer:
25 days old
Step-by-step explanation:
7 days = 1 week
3 x 7 = 21
21 + 4 = 25
25 days old
How do you find the slope of (-2,-2) and (4,1) the line passing through the points
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You just do rise/run.
How do I change 5/11 to a decimal,please explain
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Step-by-step explanation:
5/11 as a decimal is 0.45454545454545
Answer:
5/11 as a decimal is 0.45454545454545
Step-by-step explanation:
What are the intercepts of the function? The x-intercepts are
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Answer:
-1,0 and -11,0 because you already factored and solved.
When working with integers, when do you add?
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Answer: Ello mate, this image I provided below should help you out, let me know if you need anything else.
Step-by-step explanation:
NEED HELP ASAP!!!!
Anna has a bag that contains orange chews, apple chews, and peach chews. She
performs an experiment. Anna randomly removes a chew from the bag, records the
result, and returns the chew to the bag. Anna performs the experiment 41 times. The
results are shown below:
A orange chew was selected 7 times.
A apple chew was selected 22 times.
A peach chew was selected 12 times.
Based on these results, express the probability that the next chew Anna removes from
the bag will be a flavor other than orange as a fraction in simplest form.
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Answer:
I think its P= 34/41. sorry
Answer:
34/41 yuuhhhh
Step-by-step explanation:
Brian spends 1/4 of his wages on rent and 1/3
on food. If he makes £480 per week, how much money does he have left?
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Answer:
200
Step-by-step explanation:
Which number is a counting number? Can you do both of them plz
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Question 4 is: C. the counting number is 4. Hope this helped :)
Please Help!!
f(x) = square root of x plus 7 ; g(x) = 8x -11
Find f(g(x))
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I'm not sure if you mean ( [tex] \sqrt{x + 7} [/tex] ) or ( [tex] \sqrt{x} + 7[/tex] ) I solved it both ways .
[tex]f(x) = \sqrt{x + 7} \\ \\ f( \: g(x) \: ) = \sqrt{(8x - 11)+ 7} \\ = \sqrt{8x - 11 + 7} \\ = \sqrt{8x - 4} \\ = 2 \sqrt{2x - 1} [/tex]
____o_____o______
[tex]f(x) = \sqrt{x} + 7 \\ \\ f( \: g(x) \: ) = \sqrt{(8x - 11)} + 7 \\ = \sqrt{8x - 11} + 7\\ [/tex]
I hope I helped you^_^
Find the distance between the points (0,-5) and (6,-3)
Answers
Answer:
up 11 and left 2
Step-by-step explanation:
Answer:
x1=0 x2=6 y1 =-5 y3=-3
Distance^2 = Square Root [(x2 - x1)^2 + (Y2 -Y1)^2]
Distance^2 = Square Root [(6 -0)^2 + (-3 --5)^2]
Distance^2 = Square Root [6^2 + 2^2]
Distance^2 = Square Root [36 + 4]
Distance = 6.3245553203
To check the answer go here: https://www.1728.org/distance.htm
Step-by-step explanation:
