Solve the following system of linear equations by graphing.{5x - 2y = 10 {x - y = -1 Graph the equations on the same set of axes.Note: Use different points on each line when plotting the graphs.The solution point is: (_, _)
Answers
Kindly Check below
1) The first thing we need to do in this question, is to pick the method we are going to use to solve this system. Let's use the Elimination Method.
2) So, let's solve this system analytically (algebraically):
[tex]\begin{gathered} 5x-2y=10 \\ x-y=-1\:\:(\times-2) \\ \\ 5x-2y=10 \\ -2x+2y=2 \\ ------- \\ 3x=12 \\ \\ \frac{3x}{3}=\frac{12}{3} \\ \\ x=4 \end{gathered}[/tex]Now, let's plug into the 2nd original equation x=4 and solve it for y:
[tex]\begin{gathered} x-y=-1 \\ \\ 4-y=-1 \\ \\ -y=-1-4 \\ \\ y=5 \end{gathered}[/tex]So we know the solution is (4,5).
3) Now, let's graph these equations by setting two t-tables. Let's rewrite those equations from the Standard form to the Slope-intercept form.
5x-2y=10 -2y=10-5x, y=-5+5/2x
x-y=-1,-y=-1-x, y=x+1
4) Now, let's plot those points and trace the lines through them
(-2,-10), (-1,-7.5), (0,-5), (1,-2.5), (2,0)
(-2,-1), (-1,0), (0,1), (1,2), (2,3)
Related Questions
To mail the envelope first class do US post office charges $.39 for the 1st ounce and $.22 for each additional ounce . use inequality to find the maximum number of whole ounce of that can be mailed for $7.24
Answers
Let N be the total amount of whole ounces that are mailed.
Since mailing the first ounce has a cost of $0.39, then there will be N-1 ounces charged for $0.22 each.
The total cost of mailing N ounces will be:
[tex]0.39+0.22\times(N-1)[/tex]If that cost cannot exceed $7.24, then:
[tex]0.39+0.22\times(N-1)\le7.24[/tex]Solve the inequality for N:
[tex]\begin{gathered} \Rightarrow0.22\times(N-1)\le7.24-0.39 \\ \Rightarrow0.22N-0.22\le6.85 \\ \Rightarrow0.22N\le6.85+0.22 \\ \Rightarrow0.22N\le7.07 \\ \Rightarrow N\le\frac{7.07}{0.22} \\ \Rightarrow N\le32.136\ldots \end{gathered}[/tex]Since N must be a whole number, the maximum value of N that satisfies the inequality is 32.
Therefore, the maximum number of whole ounces that can be mailed for $7.24 is:
[tex]32[/tex]What are the coordinates of the point on the directed line segment from (3,-3) to (7,5) thar oartitions the segment into a ratio of 5 to 3?
Answers
Answer:
(x, y) = (5.5, 2)
Explanation:
The coordinates of a point that divide the segment from point (x1, y1) to (x2, y2) into a ratio of a:b can be found using the following equations:
[tex]\begin{gathered} x=x_1+\frac{a}{a+b}(x_2-x_1) \\ y=y_1+\frac{a}{a+b}(y_2-y_1) \end{gathered}[/tex]So, replacing (x1, y1) by (3, -3), (x2, y2) by (7, 5) and the ratio a:b by 5:3, we get that the coordinates of the point are:
[tex]\begin{gathered} x=3+\frac{5}{5+3}(7-3) \\ x=3+\frac{5}{8}(4) \\ x=3+2.5=5.5 \\ y=-3+\frac{5}{5+3}(5-(-3)) \\ y=-3+\frac{5}{8}(5+3) \\ y=-3+\frac{5}{8}(8) \\ y=-3+5=2 \end{gathered}[/tex]Therefore, the coordinates of the point are (x, y) = (5.5, 2)
Which equation has a solution of 34 for y?Select all the correct answers.A.8y=9B.y−1=−14C.4y=6D.7−y=614E.12y=9F.214+y=4
Answers
SOLUTION
We want to know which of the options would give us
y = 34,
Let's try A. 8y = 9
This becomes
[tex]\begin{gathered} 8y=9 \\ to\text{ get y, we divide both sides by 8} \\ \frac{8y}{8}=\frac{9}{8} \\ y=1\frac{1}{8} \end{gathered}[/tex]We didn't get y = 34, hence A is incorrect.
Let's try B. y − 1= − 14
This becomes
[tex]\begin{gathered} y-1=-14 \\ \text{collecting like terms } \\ y=-14+1 \\ y=-13 \end{gathered}[/tex]B too is incorrect.
Let's try C. 4y = 6
[tex]\begin{gathered} 4y=6 \\ \text{divide both sides by 4 we have } \\ \frac{4y}{4}=\frac{6}{4} \\ y=\frac{3}{2} \\ y=1\frac{1}{2} \end{gathered}[/tex]C too is incorrect
Let's check D. 7 − y = 614
[tex]\begin{gathered} 7-y=614 \\ \text{collecting like terms we have } \\ y=7-614 \\ y=-607 \end{gathered}[/tex]D too is incorrect
H +6g when 9=g and h=4
Answers
Hey there!
[tex]g+6g\\g=9,h=4[/tex]
[tex]4(h)+6(9(g))[/tex]
[tex]4+6(9)[/tex]
[tex]=58[/tex]
Hope this helps!
A trampoline park charges $2 plus an hourly rate for each hour. The sign to theright gives the prices for up to 3 hours of parking. Which linear equationrepresents the given information where C is the total cost and h is the number ofhours spent at the park?
Answers
Given the following question:
Trampoline park charges $2 plus an hourly rate for each hour (variable h)
Sign gives prices for up to three hours of parking
C = total cost
h = hours
C = total cost
The sign goes up 12 dollars for every hour
The sign goes up to 3 hours
Option A isn't the answer because the sign only goes up to 3 hours
Your answer is option B
Since c represents total cost
2h = 2 +12 which is plus 12 dollars every hour
You bought your first car for $3,000 and make payments of $150 each month. Letting B represent the balance (what still needs to be paid), which function rule represents how much money is still owed (the balance) after m months?
Answers
The function rule represents how much money is still owed is B = 3000 - 150m
What is a function?A function is used to show the relationship between the data given. This can be illustrated with the variables.
Here, the person bought the first car for $3,000 and make payments of $150 each month.
Let B represent the balance.
The function to illustrate this will be:
B = 3000 - 150(m)
B = 3000 - 150m
where B = balance
m = number of months
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Determine whether the following relation is a function. Then state the domain and range of the relation or function.{(7,6), (4,-6), (0,-1), (3,3), (1,1)}Is this relation a function? Choose the correct answer below.A.Yes, because each first component corresponds to exactly one second component.B.No, because each first component corresponds to more than one second component.C.Yes, because each first component corresponds to more than one second component.D.No, because each first component corresponds to exactly one second component.
Answers
A function is a relation in which each possible input value leads to exactly one output value. We say “the output is a function of the input.”
The input values make up the domain, and the output values make up the range.
The relation is given to be:
[tex]\mleft\lbrace(7,6\mright),(4,-6),(0,-1),(3,3),(1,1)\}[/tex]To classify a function, get the input and output values. If each input value leads to only one output value, classify the relationship as a function. If any input value leads to two or more outputs, do not classify the relationship as a function.
The input values are: {7, 4, 0, 3, 1}
The output values are: {6, -6, -1, 3, 1}
Therefore, the relation is a function.
The correct option is OPTION A: Yes, because each first component corresponds to exactly one second component.
The domain is:
[tex]\mleft\{7,4,0,3,1\mright\}[/tex]The range is:
[tex]\mleft\{6,-6,-1,3,1\mright\}[/tex]Determine the sum of the infinite geometric series
1/2-1/3+2/9-…
A. -1/2
B. the sum cannot be determined
C. 1/3
D. 3/10
Answers
We (B) cannot determine the sum of the given infinite geometric series (1/2-1/3+2/9-…).
What is infinite geometric series?A geometric series is one where each pair of consecutive terms' ratios is a fixed function of the summation index. The ratio is a rational function of the summation index in a more general sense creating what is known as a hypergeometric series.The result of an infinite geometric sequence is an infinite geometric series. There would be no conclusion to this series. The infinite geometric series has the general form a₁ + a₁r + a₁r² + a₁r³ +..., where r is the common ratio and a1 is the first term.So, the sum of 1/2-1/3+2/9-…
We can easily observe that the terms of the following given series are not in a series or in a particular sequence.Then, it is not possible to find the sum of this given series.Therefore, we (B) cannot determine the sum of the given infinite geometric series (1/2-1/3+2/9-…).
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1. The price for a new iPhone today is $829. In 2010 it was $299 for the new iPhone. What is the percent of change in the price of an iPhone from 2010 to today?
Answers
Given:
a.) The price for a new iPhone today is $829.
b.) In 2010 it was $299 for the new iPhone.
To be able to determine the percent change of price, we will be using the following formula:
[tex]\text{ Percent of Change = }\frac{Price\text{ today - Price in 2010}}{\text{Price in 2010}}\text{ x 100}[/tex]We get,
[tex]\text{ = }\frac{\text{ \$829 - \$299}}{\text{ \$299}}\text{ x 100}[/tex][tex]\text{ = }\frac{\text{ \$530}}{\text{ \$299}}\text{ x 100}[/tex][tex]\text{ = 1.77257525084 x 100 = 1.77 x 100}[/tex][tex]\text{ Percent of Change = 177\% ; an increase}[/tex]Therefore, the percent of change in the price from 2010 and today is an increase of 177%.
can you explain this to me what you are supposed to do this
Answers
Solution
If we see the two tirangles given BAC and A'B'C' we can conclude that we have the following congruent angles
< CAB = < C'A'B'
< BCA = < B'C'A'
< ABC = < A'B'C'
10 i You spin the spinner and flip a coin. Find the probability of the compound event. 3 LD t The probability of spinning a number less than 3 and flipping tails is
Answers
Compound probability = probability of first event * probability of second event
Let the spinning of the spinner be event A(First event)
Recall,
Probability = number of favourable outcomes/total number of outcomes
The numbers lesser than 3 are 1 and 2. thus, favourable outcomes = 2
total outcomes = 5
P(A) = 2/5
For event B(second event)
The coin has only head and tail
P(B) = 1/2
Thus, the probability of spinning a number less than 3 and flipping tails is
2/5 * 1/2
= 1/5
four tenths squared minus 19 plus the quantity negative 5 divided by the absolute value of 6.7 minus 9.2 end quantity times 3.81
Answers
The expression has a value of -26.46 when evaluated
How to evaluate the expression?From the question, the expression is given as
four tenths squared minus 19 plus the quantity negative 5.......
Rewrite the expression properly as
0.4² - 19 + (-5)/|6.7 - 9.2| * 3.81
Start by evaluating the exponent
So, we have
0.16 - 19 + (-5)/|6.7 - 9.2| * 3.81
Remove the expression in the bracket
0.16 - 19 - 5/|6.7 - 9.2| * 3.81
So, we have
0.16 - 19 - 5/|-2.5| * 3.81
Remove the absolute bracket
0.16 - 19 - 5/2.5 * 3.81
Divide
0.16 - 19 - 2 * 3.81
Evaluate the products
0.16 - 19 - 7.62
So, we have
-26.46
Hence, the value of the expressions is -26.46
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CALCULATO 11 i You spin the spinner, flip a coin, then spin the spinner again. Find the probability of the compound event. Write your answer as a fraction or percent. If necessary round your answer to the nearest hundredth. 1 2 3 The probability of spinning blue, flipping heads, then spinning a 1 is
Answers
Let:
A = Spinning blue
B = flipping heads
C = Spinning a 1
The probality of spinning blue is given by:
[tex]P(A)=\frac{1}{3}[/tex]The probality of flipping heads is:
[tex]P(B)=\frac{1}{2}[/tex]The probality of spinning 1 is given by:
[tex]P(C)=\frac{1}{3}[/tex]Since they are independent events:
[tex]P(A\cap B\cap C)=P(A)\cdot P(B)\cdot P(C)=\frac{1}{3}\cdot\frac{1}{2}\cdot\frac{1}{3}=\frac{1}{18}[/tex]
Gor trapezoid HJKL, T and S are midpoint of the legs. If HJ = 14 and LK = 42, find TS.
Answers
First, we are going to divide the figure and named new points X and Y as:
Now, we know that TS is the sum of TX and XS.
TS = TX + XS
Adittionally, TX has the same length of HJ, so:
TX = HJ = 14
Now, we want to know the length of YK, and we can calculate it using the following equation:
LK = LY + YK LY is also equal to HJ, so LY = 14
42 = 14 + YK
42 - 14 = YK
28 = YK
Finally, since T and S are midpoints, the length of XS is the half of the length of YK. It means that XS is:
XS = YK/2
XS = 28/2
XS = 14
Therefore, TS is equal to:
TS = TX + XS
TS = 14 + 14
TS = 28
Answer: TS = 28
Give the digits in the ones place and the hundredths place.
12.86
Please help ASAP
Answers
Colin just travelled across Ontario on a road trip. He bought some skis in Blue Mountain for $879.95 plus tax, a boombox in Muskoka for $145.58 including taxes, a souvenir in Niagara Falls for $99.97 plus tax, and some maple syrup in Toronto for $45.14 including tax. Overall, how much HST did Colin pay on his trip? Answer should be rounded off to whole number.
Answers
The Harmonized Sales Tax that Colin paid on this trip was of $152.18.
What is the Harmonized Sales Tax?The Harmonized Sales Tax is a rate that a person pays over the values of their purchases.
In the context of this problem, the person traveled on Ontario, where the HST rate is of 13%.
The purchases of the person are given as follows:
Skis in Blue Mountain for $879.95.Boombox in Muskoka for $145.58.Souvenir in Niagara Falls for $99.97.Maple syrup in Toronto for $45.14.The total value of these purchases is given by:
Total value = 879.95 + 145.58 + 99.97 + 45.14 = $1,170.64.
The HST paid is 13% of this amount, hence it is calculated as follows:
HST = 0.13 x 1170.64 = $152.18.
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How many arrangements of the word NEWFOUNDLAND are there?Page 5 of 12Previous PageNext Page
Answers
Step 1:
Concept
Number of way of arranging n different objects = n!
Step 2:
Word = NEWFOUNDLAND
N = 3
E = 1
W = 1
F = 1
O = 1
U = 1
D = 2
L = 1
A = 1
Step
Number of ways of arranging the word NEWFOUNDLAND
[tex]\begin{gathered} \text{ = }\frac{12!}{3!\text{ 2!}} \\ =\text{ }\frac{12\times11\times10\times9\times8\times7\times6\times5\times4\times3\times2\times1}{3\times2\times1\times2\times1} \end{gathered}[/tex][tex]\begin{gathered} \\ =\text{ }\frac{479001600}{12} \\ =\text{ 39916800 ways} \end{gathered}[/tex]i need the fourth term of one and three all I need is the answers so I can quiz my son.
Answers
The formula for the nth term is expressed as
an = (an - 1)^2 - 3
This is a recursive formula
This means that the second term, a2 is
a2 = (a2 - 1)^2 - 3
a2 = (a1)^2 - 3
a2 = 4^2 - 3 = 16 - 3 = 13
a3 = (a3 - 1)^2 - 3
a3 = (a2)^2 - 3
a3 = 13^2 - 3 = 169 - 3 = 166
a4 = (a4 - 1)^2 - 3
a4 = (a3)^2 - 3
a4 = 166^2 - 3 = 27556 - 3 = 27553
Thus,
a4 = 27553
URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100
POINTS!!!!!
Answers
Answer:
it would be the same since reflection doesn't change the andle
Answer:
A: It would have the same measure as the original angle.
Step-by-step explanation:
Well, reflecting is where you take the original image, which you see now, and flipping it like a mirror image. So, I think the answer would be: A It would have the same measure as the original angle. Because, it is literally the same thing, just in a mirror image. Like, if you look in the mirror, you see yourself, still the same.
3. Two companies charge differently for canoe rentals, as shown below.
Company A: c= 8h+ 10, where cequals the total cost (in dollars) and hequals number of
hours.
Company B: $15 per hour.
a. What is Company A's rate of change? How much would it cost for a 4 hour rental?
b. What is Company B's rate of change? How much would it cost for a 4 hour rental?
c. Which is the better buy? By how much for a 4 hour rental?
Answers
The rate of change for company A is 8.
The rate of change for company B is 15
Company A is better as it is charging less by a value of $18
What is rate of change?
Rate of change is the changes in the dependent variable when the independent variable changes by a unit value.
We are given 2 companies
A) equation for charges applied by company A is given by c=8h+10
Cost is a function of hours
To find the rate of change we differentiate the function
We get c' = 8
Rate of change for company A is 8
The cost for 4 hour rental is
c= 8(4)+10
c=32+10
c=$42
B) Company B charges $15 per hour
Rate of change for company B is 15
The cost for 4 hour rental is
c= 15(4)
c=$60
C) Company A is better to buy by $18 as the difference between the four hours price between company A and company B is $ 18
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Write a recursive formula for an and the nth term of the sequence 4, 10, 16, 22, ...
Answers
Here we have an arithmetic sequence with a common difference of 6, so the recursive formula is:
Tₙ = Tₙ₋₁ + 6
Where T₁ = 4.
How to find the recursive formula?Here we have the following sequence:
4, 10, 16, 22, ...
This seems to be an arithmetic sequence, to check this, we need to take the difference between consecutive terms and see if this is constant.
10 - 4 = 6
16 - 10 = 6
22 - 16 = 6
So yes, this is an arithmetic sequence and the common difference is 6, this means that each term is 6 more than the previous one, so the recursive formula is:
Tₙ = Tₙ₋₁ + 6
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sarah spent a total of 10 on oranges and apples at the supet market. if she spent 3 dollars less for oranges than she did on apples how much did sarah spend on oranges
Answers
Let's write 2 equations from the two statements given.
Sarah spent 10 dollars on both oranges and apples
Let the price of oranges be "x" and price of apples be "y", thus we can write:
[tex]x+y=10[/tex]Oranges cost 3 less than apples, thus we can say:
[tex]y-3=x[/tex]We can substitute this into the first equation and solve for y:
[tex]\begin{gathered} x+y=10 \\ y-3+y=10 \\ 2y=10+3 \\ 2y=13 \\ y=\frac{13}{2} \\ y=6.5 \end{gathered}[/tex]Thus, let's solve for x now,
[tex]\begin{gathered} x=y-3 \\ x=6.5-3 \\ x=3.5 \end{gathered}[/tex]We want the price of oranges (x), thus,
Price of Oranges = $3.50
Enter an equation that passes through the point (12, 7) and forms a system of linear equations with no solution when combined with the equation y=−3/4x+8.
Answers
To answer this question, we need to know that two linear equation that does not have solutions must not cross to each other, that is, they do not have a common point. For this case, both lines must be parallel lines. So in the question, we need to find a parallel line to the given line. Two parallel lines have the same slope.
Then, we have that the line must pass through (12, 7), and, because it is parallel to y = -3/4x + 8, and the slope for this line is m = -3/4, then, the line equation is, applying the point-slope form of the line:
[tex]y-y_1=m(x-x_1)[/tex]And
x1 = 12
y1 = 7
m = -3/4
Then
[tex]y-7=-\frac{3}{4}(x-12)\Rightarrow y-7=-\frac{3}{4}x+\frac{3}{4}\cdot12\Rightarrow y-7=-\frac{3}{4}x+\frac{36}{4}[/tex][tex]y-7=-\frac{3}{4}x+9\Rightarrow y=-\frac{3}{4}x+9+7\Rightarrow y=-\frac{3}{4}x+16[/tex]Then, the line equation is y = -3/4 x + 16.
We can check this if we use the elimination method as follows:
This is a FALSE result, and we do not have solutions for this system. Therefore, the line equation is y = -3/4 x + 16.
A store charges $140 for every 10 bags of fertilizer a farmer buys. a. Complete the table. Graph the values. 30 40 Fertilizer (bags) 10 Cost ($) 140 280 840 b. How much would a farmer pay for 50 bags of fertilizer? Explain. a. Complete the table. 30 40 Fertilizer (bags) 10 Cost ($) 140 280 840
Answers
Question:
Solution
a) If for every 10 bags the store charges $140 then
1. for 10x2 = 20 bags the store charges 2x$140 = 280.
2. for 10x3 = 30 bags the store charges 3x$140 = 420.
3. for 10x4 = 40 bags the store charges 4x$140 = 560
4. for 10x6 = 60 bags the store charges 6x$140 = 840
b) According to the previous item, we can conclude that for 10x5 = 50 bags the store charges 5x$140 = 700 then, the farmer must pay $700 for 50 bags.
c)
According to the previous item, we can conclude that for 10x5 = 50 bags the store charges 5x$140 = 700 then, the farmer must pay $700 for 50 bags.
the hypotenuse of a right triangle is 5 ft long. the shorter leg is 1 ft shorter than the longer leg. find the side lengths of the triangle
Answers
the hypotenuse of the right angle triangle is h = 5 ft
it is given that
the shorter leg is 1 ft shorter than the longer leg.
let the shorter leg is a and longer leg is b
the
b - a = 1
b = 1 + a
in the traingle using Pythagoras theorem,
[tex]a^2+b^2=h^2[/tex]put he values,
[tex]a^2+(1+a)^2=5^2[/tex][tex]\begin{gathered} a^2+1+a^2+2a=25 \\ 2a^2+2a-24=0 \\ a^2+a-12=0 \end{gathered}[/tex][tex]\begin{gathered} a^2+4a-3a-12=0_{} \\ a(a+4)-3(a+4)=0 \\ (a+4)(a-3)=0 \end{gathered}[/tex]a + 4 = 0
a = - 4
and
a - 3 = 0
a = 3
so, the longer leg is b = a + 1 = 3 + 1 = 4
thus, the answer is
shorter leg = 3 ft
longer length = 4 ft
hypotenuse = 5 ft
write in point slpoe form an equation of the line that passes through th griven point and has the given slope (1, -3); m = 4
Answers
A linear equation in slope-point form looks like this:
y -y0= m(x-x0)
Where m is the slope of the line and (x0,y0) is a point of the line.
In this case, we know that the slope of the line equals 4 and that the line goes through the point (1, -3), then, we can substitute these values into the general form to get:
y-(-3) = 4(x-(1))
Dave and his friends went out to celebrate his birthday at Chill's in buda. their meal cost $86 and they left a 15% tip how much was the total bill including tip?
Answers
The meal cost is $86
its 15% is:
$86 x 0.15 = $12.9
then the tip was $12.9. Then, the total bill would be:
$86 + $12.9 = $98.9
that is the total bill was $98.9
Find the surface area Formula: SA= p * h + 2 * B
Answers
Given:
For the given figure,
[tex]h=2ft,w=3ft,l=8ft[/tex]The surface area is calculated as,
[tex]\begin{gathered} S=2lh+2wh+2wl \\ S=2\cdot8\cdot2+2\cdot3\cdot2+2\cdot3\cdot8 \\ S=32+12+48 \\ S=92 \end{gathered}[/tex]Answer: surface area is 92 square ft.
the bakers want to sell their house for 145,500.After 2 months,the bakers decided to mark down the price of their house 8% to sell more quickly. How much are the bakers selling their house for now?
Answers
Answer:
133,860
Step-by-step explanation:
The baker was going to sell his house for 145,500 but he found that no one came to buy, so he decreased the amount by "8%".
* No we have our key elements:
- Starting amount = 145,500
- Rate of change = 8%
* We will get the "8%" of the number 145,500
- Firstly, "8%" means 8/100
- So, 0.08 will be our new rate of change.
* 145,500 will be multiplied by 0.08 to find the final answer because when we talk about the percentage of a number, we are going to talk about a part of it.
- 145,500 × 0.08 = 133,860 ; the same as
145,500 × 8/100 = 133,860
The measure of side VT is 60 inches. Find the length of side VProunded to the nearest tenth.
Answers
It is important to notice that side VP is the hypothenuse of the triangle, and VT is the adjacent leg to 30°.
To find VP, we just have to use the cosine function
[tex]\begin{gathered} \cos 30=\frac{VT}{VP} \\ \cos 30=\frac{60}{VP} \\ VP=\frac{60}{\cos 30} \\ VP\approx69.3 \end{gathered}[/tex]Hence, VP is 69.3 inches long.