5. The picture below shows the five houses on Maple Street and the five houses on Oak
Street.
6 Maple St.
_innnnn
Maple St.
4 Oak St.
SASA
Oak St.
. Each house number on Maple Street is six more than the house number to its left.
• Each house number on Oak Street is eight more than the house number to its left.
How much greater is the house number of the last house on Oak Street than the house
number of the last house on Maple Street
Answers
The last house on Oak Street has a house number 8 greater than the last house on Maple Street.
The correct answer is option C.
Let's denote the house numbers on Maple Street as M1, M2, M3, M4, and M5, where each house number is six more than the one to its left. Similarly, on Oak Street, denote the house numbers as O1, O2, O3, O4, and O5, where each house number is eight more than the one to its left.
For Maple Street:
M2 = M1 + 6
M3 = M2 + 6
M4 = M3 + 6
M5 = M4 + 6
For Oak Street:
O2 = O1 + 8
O3 = O2 + 8
O4 = O3 + 8
O5 = O4 + 8
Now, let's find the difference between the last house on Oak Street (O5) and the last house on Maple Street (M5):
The difference is (O4 + 8) - (M4 + 6) = (O3 + 8 + 8) - (M3 + 6 + 6) = (O2 + 8 + 8 + 8) - (M2 + 6 + 6 + 6) = (O1 + 8 + 8 + 8 + 8) - (M1 + 6 + 6 + 6 + 6).
Simplifying the expression, the constant terms cancel out, leaving:
The difference is O1 - M1 + (8 + 8 + 8 + 8) - (6 + 6 + 6 + 6) = O1 - M1 + 32 - 24 = O1 - M1 + 8.
So, the house number of the last house on Oak Street is 8 greater than the house number of the last house on Maple Street.
The question probable may be;
The picture below shows 5 houses on maple street anf the five houses on oak street.
Each house number on maple street is six more than the house number to its left. Each house number on oak street is eigth more than the house number to its left.
How much greater is the house number of the last house on oak street than the house number of the last house on maple street?
2
6
8
10
Related Questions
Two pipes are connected to the same tank. When working together., they can fill the tank in 10hrs. The larger pipe, working alone, can fill the tank in 15 hrs less time than the smaller one. How long would the smaller one take, working alone, to fill the tank
Answers
Answer:
30 hours
Step-by-step explanation:
Let the small pipe take time "t" to fill up the tank alone
Since larger pipe takes 15 HOURS LESS, so it will take "t - 15" time to fill up the tank alone
Let the whole tank be equal to "1" and each pipe fills up a fraction of the tank.
Smaller Pipe fills up 10/t, and
Larger Pipe fills up 10/(t-15)
Totalling "1". So we can write:
[tex]\frac{10}{t}+\frac{10}{t-15}=1[/tex]
Now, we solve for t. First, we multiply whole equation by (t)(t-15), to get:
[tex]t(t-15)*[\frac{10}{t}+\frac{10}{t-15}=1]\\(t-15)(10)+10t=t(t-15)[/tex]
Now we multiply out and get a quadratic and solve by factoring. Shown below:
[tex](t-15)(10)+10t=t(t-15)\\10t-150+10t=t^2-15t\\20t-150=t^2-15t\\t^2-35t+150=0\\(t-30)(t-5)=0\\t=5,30[/tex]
Since, this time is for the smaller pipe (which takes longer than 15 hours), so we disregard t = 5 and take t = 30 as our solution. So,
Smaller pipe takes 30 hours to fill up the tank alone
The smaller pipe takes 30 hours to fill the tank on its own, determined by solving the equation derived from the combined and individual rates at which each pipe fills the tank.
Since they can jointly fill the tank in 10 hours, we can use the rates at which they fill the tank to set up the equation: 1/x + 1/(x - 15) = 1/10. To find the solution, we multiply each term by 10x(x - 15) to clear the denominators, which gives us 10(x - 15) + 10x = x(x - 15). This simplifies to 20x - 150 = x^2 - 15x. Rearranging the terms yields x^2 - 35x + 150 = 0, which can be factored into (x - 30)(x - 5) = 0. Thus, x could be either 30 hours or 5 hours. Since x - 15 must also be positive, x = 30 hours is the correct solution, meaning the smaller pipe takes 30 hours to fill the tank alone.
A section of the dining room has 3 tables with 6 chairs at each table determine which expressions represent the situation and which do not
(3)-(6)
3x6
(3)(6)
3/6
3+6
6+6+6
Represent the situation or do not represent the situation
Answers
Do:
3x6
(3)(6)
6+6+6
Do not:
(3)-(6)
3/6
3+6
The cost of 5 squash and 2 zucchini is $1.32. Three squash and 1 zucchini cost $0.75. Find the cost of each vegetable.
Answers
Final answer:
By solving a system of equations, we find that the cost of one squash is $0.18 and the cost of one zucchini is $0.21.
Explanation:
The question involves solving a system of linear equations to determine the cost of each vegetable. Let's define x as the cost of one squash and y as the cost of one zucchini. We have the two equations based on the information provided:
5x + 2y = $1.323x + y = $0.75We can solve this system using either substitution or elimination methods. For this example, I'll use the substitution method:
Solve the second equation for y: y = $0.75 - 3x.Substitute the expression for y in the first equation: 5x + 2($0.75 - 3x) = $1.32.Simplify and solve for x: 5x + $1.50 - 6x = $1.32, which simplifies to x = $1.50 - $1.32, so x = $0.18.Substitute x back into the equation for y: y = $0.75 - 3($0.18), so y = $0.75 - $0.54, thus y = $0.21.Therefore, the cost of one squash is $0.18 and the cost of one zucchini is $0.21.
Final answer:
To find the cost of each vegetable, a system of linear equations was set up and solved, revealing the cost of one squash to be $0.18 and the cost of one zucchini to be $0.21.
Explanation:
The cost of 5 squash and 2 zucchini is $1.32, and the cost of 3 squash and 1 zucchini is $0.75. To find the cost of each vegetable, we can set up a system of linear equations and solve for the unknowns.
Let 's' represent the cost of one squash and 'z' represent the cost of one zucchini. We can then create two equations based on the information given:
5s + 2z = $1.32
3s + 1z = $0.75
Now, we need to solve this system of equations. An effective way to do this would be using the substitution or elimination method. For simplicity, let's use the elimination method:
Multiply the second equation by 2 to align the coefficients of z:
6s + 2z = $1.50
Now subtract the modified second equation from the first:
(5s + 2z) - (6s + 2z) = $1.32 - $1.50
-s = -$0.18
s = $0.18
With the cost of one squash known, substitute 's' back into one of the original equations to find 'z':
3(0.18) + z = $0.75
0.54 + z = $0.75
z = $0.75 - $0.54
z = $0.21
So, one squash costs $0.18, and one zucchini costs $0.21.
Factor the expression completely: x^3−27y^3
Answers
1 Point
Roberto has $37 to buy baseballs for his little league team. Each baseball
costs $7. How many baseballs can he buy? Do not include units in your
answer.
Answers
Answer:
he can only buy 5
Step-by-step explanation:
7x5=35
he has 2 bucks left
Answer:
5
Step-by-step explanation:
5 times 7 is 35. 5 times 8 is 40 which is 3 dollars more than he has therefore he can only buy 5.
Write an expression for the area of a square with a side length of 4a squared. Simplify the expression.
Answers
Answer:
16a^4
Step-by-step explanation:
You do 4a^2*4a^2= 16a^4 because area of square is length times width and we know that that length and width in a square is equal.
4*4= 16
a^2*a^2= a^4 (because when you multiply powers with the same base like a in this case, you add the powers up. So in this example it would be 2+2= 4)
Put them together to give you 16a^4
Final answer:
The area of a square with a side length of 4a² is A = 16a⁴, showcasing the area's proportionality to the fourth power of side length a.
Explanation:
The expression for the area of a square with a side length of 4a squared is found by squaring the side length. Since the side of the square is 4a², the area A is given by:
A = (4a²) × (4a²) = 16a⁴
The simplified expression for the area is 16a to the fourth power, which indicates that the area is proportional to the fourth power of the side length a.
please help before 2pm :/ THANKSSSS
Answers
Answer:
C = [tex]$ \frac{1}{10} $[/tex]
D = [tex]$ \frac{1}{10^2} $[/tex]
Step-by-step explanation:
78.09 = 7 [tex]$ \times A + 8 \times B + 0 \times C + 9 \times D $[/tex]
78.09 = 7 [tex]$ \times 10^1 + 8 \times 10^0 + 0 \times \frac{1}{10} + 9 \times \frac{1}{10^2}[/tex]
⇒ C = [tex]$ \frac{1}{10} $[/tex]
D = [tex]$ \frac{1}{10^2} $[/tex]
Hence, the answer.
There are 1125 members in a mountaineering club. The club's secretary surveys 72 randomly selected members and finds that 63 members are in favor of holding a used-gear sale. About how many of the club members would be in favor of holding a used-gear sale?
63
72
984
1053
Answers
984 members of club would be in favor of used-gear sale based on results of survey.
Step-by-step explanation:
Number of people surveyed = 72
People in favor of sale = 63
Percentage of people in favor = [tex]\frac{People\ in\ favor\ of\ sale}{No.\ of\ people\ surveyed}*100[/tex]
Percentage of people in favor = [tex]\frac{63}{72}*100 = \frac{6300}{72}\\[/tex]
Percentage of people in favor = 87.5%
It means that 87.5% members of club will be in favor of sale.
Total members of club = 1125
Total members in favor = 87.5% of total members
[tex]Total\ members\ in\ favor=\frac{87.5}{100}*1125 = \frac{98437.5}{100}\\Total\ members\ in\ favor=984.3[/tex]
Rounding off to nearest whole number
Total members in favor = 984
984 members of club would be in favor of used-gear sale based on results of survey.
Keywords: percentage, division
Learn more about percentage at:
brainly.com/question/2367554brainly.com/question/2821386#LearnwithBrainly
(-511) + (+709) = solve.
Answers
Answer:
198
Step-by-step explanation:
-511 + (+709) =
709 - 511 = 198
Answer:
-511 + 709 = 198
Step-by-step explanation:
-511+709 is the same as 709-511
(2x^3+6x-1)+(3x^2-7x)
Answers
For this case we must simplify the following expression:
[tex](2x ^ 3 + 6x-1) + (3x ^ 2-7x)[/tex]
We eliminate the parentheses taking into account that:
[tex]+ * + = +\\+ * - = -[/tex]
So, we have:
[tex]2x ^ 3 + 6x-1 + 3x ^ 2-7x =[/tex]
We add similar terms taking into account that:
Different signs are subtracted and the sign of the major is placed:
[tex]2x ^ 3 + 3x^2-x-1[/tex]
Answer:
[tex]2x ^ 3 + 3x^2-x-1[/tex]
What's 4 3×7 + 2 1×3
Answers
Answer: 90
Step-by-step explanation: You equation is 4(3*7) + 2(1*3). To solve this, you first solve what is on the inside of the parenthesis. so 3 times 7 is 21. And 1 times 3 is 3. So now your equation looks like this 4(21) + 2(3). 4 times 21 is 84 and 2 times 3 is 6. So now your equation is 84 + 6 which equals 90.
Answer:
90
Step-by-step explanation:
4(3*7)+2(1*3)=4(21)+2(3)=84+6=90
Section #1: Solvi
1) Find the solution to each equation.
A) 4(2x - 1) = -3x + 32
Section
Answers
1) Find the solution to each equation.
A) 4(2x - 1) = -3x + 32
Answer:The solution to the equation 4(2x - 1) = -3x + 32 is x = 3.273
Solution:Need to find the solution of following equation
4(2x - 1) = -3x + 32
Let use BODMAS rule to solve the expression
According to Bodmas rule, if an expression contains brackets ((), {}, []) we have to first solve or simplify the bracket followed by of (powers and roots etc.), then division, multiplication, addition and subtraction from left to right.
On opening the bracket of left hand side we get
[tex]4 \times 2x-4 \times 1=-3 x+32[/tex]
Now perform multiplication,
8x – 4 = -3x + 32
On bringing terms having variable x in left hand side and constant term on right hand side we get
8x + 3x = 32 + 4
=> 11x = 36
On dividing both sides by 11, we get
[tex]\begin{array}{l}{\Rightarrow \frac{11 x}{11}=\frac{36}{11}} \\\\ {\Rightarrow x=\frac{36}{11}=3.273}\end{array}[/tex]
Hence solution of equation 4(2x - 1) = -3x + 32 is 3.273
1. A relation is plotted as a linear function on a coordinate plane starting at point C at (3, –2) and ending at point D at (–2, 3). What is the rate of change for the linear function and what is its initial value?
The rate of change is ______ and the initial value is ______.
A. 1 and -1
B. -1 and 1
C. 5 and -2
D. -2 and 5
2. Ava drove her car at a constant rate to the train station. At the train station, she waited for the train to arrive. After she boarded the train, she traveled at a constant rate, faster than she drove her car. She entered the taxi and traveled at a constant speed. This speed was equal to the speed at which she had driven her car earlier. After some time, she arrived at her destination.
Which graph represents Ava’s travel plans? (First 3 graphs are the options to this question.)
Answers
1. The rate of change is -1 and the initial value is 1.
2. The graph represents Ava’s travel plans is graph (I).
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
1. We have the coordinates as C(3, -2) and D(-2, 3).
So, the rate of change of linear function is
= 3 - (-2) / (-2 -3)
= 3+ 2 / (-5)
= 5/ (-5)
= -1.
and, the initial values is where the independent variable is zero which is (1, 0).
2. The graph represented for Ava journey is (A).
This, is because the speed of Ava car and speed of taxi is equal which is shown in graph 1 clearly.
Learn more about Rate of change here:
https://brainly.com/question/2419308
#SPJ3
1. The rate of change is -1 and the initial value is 1 (Option B). 2. The graph represents Ava’s travel plans is: option A (Graph 1).
What is the rate of change of a linear function?The rate of change for a linear function is given by the slope of the line. The slope (m) can be calculated using the formula:
m = change in y / change in x
In this case, using the given points C (3, -2) and D (-2, 3):
[tex]\[ m = \frac{{3 - (-2)}}{{(-2) - 3}} = \frac{{5}}{{-5}} = -1 \][/tex]
So, the rate of change is -1.
The initial value of a linear function is the y-intercept, which is the y-coordinate when x = 0. Substituting (x, y) = (-2, 3) and m = -1 into y = mx + b, find b (initial value):
3 = -1(-2) + b
3 = 2 + b
3 - 2= b
b = 1.
Therefore, the correct answer is:
B. The rate of change is -1, and the initial value is 1.
2. The graph depicting Ava's journey is labeled as (A) because it clearly illustrates that Ava's car and the taxi have the same speed, as shown in Graph 1.
Learn more about linear function on:
https://brainly.com/question/4025726
#SPJ3
What are the coordinates of 2x-4y=6 and 3x+y=-5 ?
Answers
Answer:
The coordinates are x = -1 and y = -2.
Step-by-step explanation:
Given:
Equations are 2x-4y=6 and 3x+y=-5.
Now, to find the coordinates.
[tex]2x-4y=6[/tex]...........(1)
[tex]3x+y=-5[/tex]...........(2)
So, first we solve the equation 1 to get the value of [tex]x[/tex].
[tex]2x-4y=6[/tex]
Subtracting both sides by [tex]-4y[/tex] we get:
[tex]2x=6+4y[/tex]
Dividing both sides by 2 we get:
[tex]x=3+2y[/tex]
Now, we put the value of [tex]x[/tex] in equation 2 to get [tex]y[/tex].
[tex]3x+y=-5[/tex]
[tex]3(3+2y)+y=-5[/tex]
[tex]9+6y+y=-5[/tex]
[tex]9+7y=-5[/tex]
On solving the whole equation we get :
[tex]y=-2[/tex]
And, now putting the value of [tex]y[/tex] in equation (1) we get [tex]x[/tex]:
[tex]2x-4y=6[/tex]
[tex]2x-4(-2)=6[/tex]
[tex]2x+8=6[/tex]
[tex]2x=6-8[/tex]
[tex]2x=-2[/tex]
on solving we get:
[tex]x=-1[/tex]
Therefore, the coordinates are x=-1 and y=-2.
In TVW if VW is three meters longer than TV, TW is 20 meters shorter than the sum of VW and TV, and the perimeter of TVW is 74 meters, find the length of VW.
PLEASE EXPLAIN STEPS!!!
Answers
Answer:
The length of VW is [tex]25\ m[/tex]
Step-by-step explanation:
we know that
The perimeter of triangle TVW is equal to
[tex]P=VW+TV+TW[/tex]
we have
[tex]P=74\ m[/tex]
so
[tex]74=VW+TV+TW[/tex] -----> equation A
[tex]VW=TV+3[/tex] ----> equation B
[tex]TW=(VW+TV)-20[/tex] ----> equation C
substitute equation B in equation C
[tex]TW=(TV+3+TV)-20[/tex]
[tex]TW=2TV-17[/tex] ----> equation D
substitute equation B and equation D in equation A
[tex]74=(TV+3)+TV+(2TV-17)[/tex]
solve for TV
[tex]74=4TV-14[/tex]
[tex]4TV=74+14[/tex]
[tex]4TV=88[/tex]
[tex]TV=22\ m[/tex]
Find the value of VW
[tex]VW=TV+3[/tex] -----> [tex]VW=22+3=25\ m[/tex]
Find the value of TW
[tex]TW=2TV-17[/tex] -----> [tex]TW=2(22)-17=27\ m[/tex]
What’s the slope of (-2,1) and (3,-3)
Answers
Answer:
-4/5
Step-by-step explanation:
slope = m = (difference in y)/(difference in x) = (-3 - 1)/(3 - (-2)) =-4/5
-8(4+4n)=8(n+6)
what is the answer for this? please thank you :)
Answers
Answer:
n = -2
Step-by-step explanation:
Distribute first.
-32 - 32n = 8n + 48
Subtract 8n.
-32 - 40n = 48
Add 32
-40n = 80
n = -2
Answer: download Photomath is the best!! The answer is n=-2
Step-by-step explanation:
A boat goes 50 km downstream in the same time that it takes to go 30 km upstream. The speed of the stream is 3km/hour. Find the speed of the boat in still water.
Answers
Answer:
12 km/h
Step-by-step explanation:
Given: Distance covered by boat downstream = 50 km
Distance covered by boat upstream = 30 km
Time taken by boat in down stream and upstream are equal.
Speed of the stream = 3 km/h
Let x be the speed of boat in still water.
∴ Speed of boat in downstream [tex](s_1)[/tex] = [tex](x+3)\ km/h[/tex]
Speed of boat in upstream [tex](s_2)[/tex] = [tex](x-3)\ km/h[/tex]
As we know, [tex]Time = \frac{Distance}{speed}[/tex]
And time remain same for both upstream and downstream
∴ [tex]\frac{50}{(x+3)} = \frac{30}{(x-3)}[/tex]
Now, cross multiply both side
⇒ [tex]50\times (x-3) = 30\times (x+3)[/tex]
⇒ [tex]50x-30x = 150+90[/tex]
∴ [tex]x= 12\ km/h[/tex]
∴ Speed of boat in still water is 12 km/h
Help!!!! Plssss!!! ASAP
Answers
Answer:
The y-intercept is (0,-26)
Step-by-step explanation:
Given two points P(a,b) and Q(c,d), the line that passes for both points can be found with the expression
[tex]\displaystyle y-b=\frac{d-b}{c-a}(x-a)[/tex]
We'll take the first two points P(34,-52) and Q(51,-65) to find
[tex]y=-\frac{13}{17}(x-34)-52\\ \\y=-\frac{13}{17}x-26[/tex]
Let's verify if the third point is on the line:
[tex]y=-\frac{13}{17}68-26=-52-26=-78[/tex]
It belongs to the line. To find the y-intercept of the line, we set x to 0
[tex]y=-\frac{13}{17}(0)-26=-26[/tex]
The y-intercept is (0,-26)
Put in simplest fraction form:
3,628,800/55
Answers
It’s because if you divide the top and the bottom of 3628800 over 55 by 5 it would be 725,760 over 11.
to find the product 3 3/8 * 4 1/9.tara rewrote 3 3/8 as 17/8 amd 4 1/9 as 13/9. she multiplies the fractions to find the product 221/72. what error did she make
Answers
Answer:
The error Tara made is she rewrote incorrectly 3 3/8 as 17/8 and 4 1/9 as 13/9,
the corrected number can be rewrote as 3 3/8 as 27/8 and 4 1/9 as 37/9.
Step-by-step explanation:
To find the Product of:
[tex]3\frac{3}{8}\times 4\frac{1}{9}[/tex]
The Number can be rewrote as,
[tex]\frac{3\times8+3}{8}\times \frac{4\times9+1}{9}\\\\\frac{24+3}{8}\times \frac{36+1}{9}\\\\\frac{27}{8}\times \frac{37}{9}[/tex]
Tara made error here she rewrote the number incorrectly 3 3/8 as 17/8 amd 4 1/9 as 13/9.
Now multiplying the fraction we get
[tex]\frac{999}{72}[/tex]
Because she rewrote incorrectly which led her answer to multiplication of fraction, the product too was incorrect which she wrote as 221/72.
Amy has 20 quarters.sodas cost $.75 write an expression for how many quarters Amy has left after buying D amount of sodas
Answers
The expression x=20-3D will present the amount Amy has left after buying D sodas.
Step-by-step explanation:
Given,
Total amount = 20 quarters
Cost of sodas = $0.75 = 0.75*100 = 75 cents
25 cents = 1 quarter
1 cent = [tex]\frac{1}{25}\ quarter[/tex]
75 cents = [tex]\frac{1}{25}*75[/tex] = 3 quarters
Amount of D sodas = 3D
Let x be the amount left with Amy.
Amount left = total amount - Amount of D sodas
[tex]x=20-3D[/tex]
The expression x=20-3D will present the amount Amy has left after buying D sodas.
Keywords: fractions, subtraction
Learn more about subtraction at:
brainly.com/question/2977815brainly.com/question/3071107#LearnwithBrainly
A manufacturing plant earned $80 per man-hour of labor when it opened. Each year, the plant earns an additional 5% per man-hour.Write a function that gives the amount A(t) that the plant earns per man-hour t years after it opens.
Answers
A function that gives the amount that the plant earns per man-hour t years after it opens is [tex]\mathrm{A}(\mathrm{t})=80 \times 1.05^{\mathrm{t}}[/tex]
Solution:Given that
A manufacturing plant earned $80 per man-hour of labor when it opened.
Each year, the plant earns an additional 5% per man-hour.
Need to write a function that gives the amount A(t) that the plant earns per man-hour t years after it opens.
Amount earned by plant when it is opened = $80 per man-hour
As it is given that each year, the plants earns an additional of 5% per man hour
So Amount earned by plant after one year = $80 + 5% of $80 = 80 ( 1 + 0.05) = (80 x 1.05)
Amount earned by plant after two years is given as:
[tex]=(80 \times 1.05)+5 \% \text { of }(80 \times 1.05)=(80 \times 1.05)(1.05)=80 \times 1.052[/tex]
Similarly Amount earned by plant after three years [tex]=80 \times 1.05^{t}[/tex]
[tex]\begin{array}{l}{\Rightarrow \text { Amount earned by plant after } t \text { years }=80 \times 1.05^{t}} \\\\ {\Rightarrow \text { Required function } \mathrm{A}(t)=80 \times 1.05^{t}}\end{array}[/tex]
Hence a function that gives the amount that the plant earns per man-hour t years after it opens is [tex]\mathrm{A}(t)=80 \times 1.05^{t}[/tex]
Direct variations need help
Answers
Answer:
Part 11) The table represent a direct variation. The equation is [tex]y=18x[/tex]
Part 12) The table represent a direct variation. The equation is [tex]y=0.4x[/tex]
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin
Part 11)
For x=0.5, y=9
Find the value of k
[tex]k=y/x[/tex] -----> [tex]k=9/0.5=18[/tex]
For x=3, y=54
Find the value of k
[tex]k=y/x[/tex] -----> [tex]k=54/3=18[/tex]
For x=-2, y=-36
Find the value of k
[tex]k=y/x[/tex] -----> [tex]k=-36/-2=18[/tex]
For x=1, y=18
Find the value of k
[tex]k=y/x[/tex] -----> [tex]k=18/1=18[/tex]
For x=-8, y=-144
Find the value of k
[tex]k=y/x[/tex] -----> [tex]k=-144/-8=18[/tex]
The values of k is the same for each ordered pair
therefore
The table represent a direct variation
The linear equation is
[tex]y=18x[/tex]
Part 12)
For x=-5, y=-2
Find the value of k
[tex]k=y/x[/tex] -----> [tex]k=-2/-5=2/5=0.40[/tex]
For x=3, y=1.2
Find the value of k
[tex]k=y/x[/tex] -----> [tex]k=1.2/3=0.40[/tex]
For x=-2, y=-0.8
Find the value of k
[tex]k=y/x[/tex] -----> [tex]k=-0.8/-2=0.4[/tex]
For x=10, y=4
Find the value of k
[tex]k=y/x[/tex] -----> [tex]k=4/10=0.4[/tex]
For x=20, y=8
Find the value of k
[tex]k=y/x[/tex] -----> [tex]k=8/20=0.4[/tex]
The values of k is the same for each ordered pair
therefore
The table represent a direct variation
The linear equation is
[tex]y=0.4x[/tex]
A graph with a line running through coordinates (0,0) and coordinates (30,24)
Item 3
Carl's new car gets 27 miles per gallon. What is the equation that represents y, the total miles driven on x gallons of gas?
a. x = 27y
b. y = 27x
c. y = 27 + x
d. x = 27 + y
Answers
Answer:
b. y = 27x
Step-by-step explanation:
When you talk about "per" it means multiplication, and 27 is being multiplied by (x) gallons of gas.
an elementary school teacher wants to know if the words in a book are too difficult for her students. She reads the first sentence on the first page in every chapter and finds three words her students would not know. what is the sample in this situation
A.the three words her students would not know
B. the words that she reads that her students would know
c. every word in the book
d.every word in the first sentence of the first page of every chapter<—my answer
Answers
Answer:
d.every word in the first sentence of the first page of every chapter.
Step-by-step explanation
the sample space means the set of total possible outcomes or ALL possible outcomes.so here, the situation is about the teacher reading a sentence.the favorable outcome is the set which has all the words that the students would not know from all the words read by the teacher or simply from the sample space.since the teacher reads the first sentence on the first page in every chapter , all the words in that sentence will be sample in this situation.simplify 5(6x+9) using the distributive property
Answers
Answer:
30x+45
Step-by-step explanation:
5*6x=30x
5*9=45
Answer:
30x + 45
Step-by-step explanation:
We distribute the 5 to the variable 6x and the constant 9:
5(6x+9)
5 x 6x = 30x
5 x 9 = 45
The answer is 30x + 45
what does 500+38+2538+48 equal
Answers
My answer would be 3124 or 3,124
Which statement describes the graph of function g?
f(x) = 2x
g(x) = 2x + 3
A. The graph of g is 3 units above the graph of f.
B. The graph of gis 3 units to the right of the graph of f.
C. The graph of g is 3 units below the graph of f.
D. The graph of g is 3 units to the left of the graph of f.
Answers
Answer: B
Step-by-step explanation: The equation of the line in Slope-intercept form is:
Where "m" is the slope of the line and "b" is the intersection of the line with the y-axis.
For the graph of the line, you can identify that:
And for, you can identify that:
Therefore, you can observe that the slope does not change, but now the line cuts the y-axis at . In other words, it was moved from to (3 units on the y-axis)
Then, it is the graph of translated 3 units upward, which means that the graph of g(x) is 3 units above the graph of f(x).
The graph of g is 3 units above the graph of f(x), the correct option is A.
What is a Graph?The graph is a mathematical representation of the relation between two objects.
It helps in determining the function that fits best for the data obtained.
A function is a mathematical statement that defines a relationship between a dependent and an independent variable.
A function always has a defined range and domain, domain is all the value a function can have as input and range is all the value that a function can give as output.
The function f(x) = 2x
g(x) = 2x+3
Both functions are a straight line, an equation of a straight line is given by y =mx +c, m is the slope of the line and c is the y intercept.
In the function f(x), the slope is 2 and the intercept is 0
In the function g(x), the slope is 2 and the intercept is 3.
As the intercept is 3, the g(x) is 3 units above the graph f(x).
To know more about Graph
brainly.com/question/14375099
#SPJ5
What is a equation of the line that is parallel to y=-5×+6 and passes through the point (-4,-1)
Answers
The equation of the line that is parallel to y = -5x + 6 and passes through the point (-4, -1) in slope intercept form is y = -5x -21
Solution:Given that line passes through the point (-4, -1) and parallel to y = -5x + 6
We have to find the equation of line
Let us first calculate the slope of line having equation as y = -5x + 6
The slope intercept form of line is given as:
y = mx + c ---- eqn 1
where "m" is the slope of line and "c" is the y-intercept
Comparing the given equation of line y = -5x + 6 with slope intercept form y = mx + c,
we get the slope of line "m" = -5
We know that slope of two given parallel lines are always equal
Hence the slope of line which is parallel to line with equation y = -5x + 6 is also -5
Now we have to find the equation of line passing through point (-4, -1) with slope -5
Substitute (x, y) = (-4, -1) and m = -5 in eqn 1 to find "c" intercept
-1 = -5(-4) + c
-1 = 20 + c
c = -21
Substitute c = -21 and m = -5 in eqn 1 to get the equation of line
y = -5x + (-21)
y = -5x -21
Thus the equation of required line is found out as y = -5x -21