Answer:
Sally is 30 and Suki is 20
Step-by-step explanation:
x = Sally's age
y = Suki's age
x = 10 + y
(x - 5) + (y - 5) = 40
x = 30, y = 20
help me please !!! :)
Answer:
A
Step-by-step explanation:
f(x) = x+4 when x is equal to or less than - 2. f(-4)=0
4 of 204 of 20 Questions
Question 4
What is the equation of the line that is parallel to y−5=−13(x+2) and passes through the point (6,−1)?
Answer:
y= -13x+77
Step-by-step explanation:
Parallel lines do not share any points but have the same slope.
First, put the equation y-5=-13(x+2) into slope-intercept form.
y= -13x-21
Slope= -13x
Y-Intercept= (0,-21)
Now that we know the slope...
y-(-1)=-13(x-6)
becomes
y+1=-13x+78
y-1=-13x+78-1
y=-13x+77
I'm doing a task which involves magic v's, a maths pattern which has the rule of having the same total on each side. For e.g.
6 5
3 4
2
Is a magic v because each side adds up to 11. I need to make magic V's with the number 2-6 and 3-7. There are 24 possibilities for each number set.
Answer:
--1-- (of set 23456)
2 4
5 3
6
--2-- (of set 23456)
2 3
5 4
6
--3-- (of set 23456)
2 5
6 3
4
--4-- (of set 23456)
2 3
6 5
4
--5-- (of set 23456)
3 5
4 2
6
--6-- (of set 23456)
3 2
4 5
6
--7-- (of set 23456)
3 6
5 2
4
--8-- (of set 23456)
3 2
5 6
4
--9-- (of set 23456)
3 5
6 4
2
--10-- (of set 23456)
3 4
6 5
2
--11-- (of set 23456)
4 5
3 2
6
--12-- (of set 23456)
4 2
3 5
6
--13-- (of set 23456)
4 6
5 3
2
--14-- (of set 23456)
4 3
5 6
2
--15-- (of set 23456)
5 4
2 3
6
--16-- (of set 23456)
5 3
2 4
6
--17-- (of set 23456)
5 6
3 2
4
--18-- (of set 23456)
5 2
3 6
4
--19-- (of set 23456)
5 6
4 3
2
--20-- (of set 23456)
5 3
4 6
2
--21-- (of set 23456)
6 5
2 3
4
--22-- (of set 23456)
6 3
2 5
4
--23-- (of set 23456)
6 5
3 4
2
--24-- (of set 23456)
6 4
3 5
2
--1-- (of set 34567)
3 5
6 4
7
--2-- (of set 34567)
3 4
6 5
7
--3-- (of set 34567)
3 6
7 4
5
--4-- (of set 34567)
3 4
7 6
5
--5-- (of set 34567)
4 6
5 3
7
--6-- (of set 34567)
4 3
5 6
7
--7-- (of set 34567)
4 7
6 3
5
--8-- (of set 34567)
4 3
6 7
5
--9-- (of set 34567)
4 6
7 5
3
--10-- (of set 34567)
4 5
7 6
3
--11-- (of set 34567)
5 6
4 3
7
--12-- (of set 34567)
5 3
4 6
7
--13-- (of set 34567)
5 7
6 4
3
--14-- (of set 34567)
5 4
6 7
3
--15-- (of set 34567)
6 5
3 4
7
--16-- (of set 34567)
6 4
3 5
7
--17-- (of set 34567)
6 7
4 3
5
--18-- (of set 34567)
6 3
4 7
5
--19-- (of set 34567)
6 7
5 4
3
--20-- (of set 34567)
6 4
5 7
3
--21-- (of set 34567)
7 6
3 4
5
--22-- (of set 34567)
7 4
3 6
5
--23-- (of set 34567)
7 6
4 5
3
--24-- (of set 34567)
7 5
4 6
3
Step-by-step explanation:
This javascript code is extremely brute-force, but it does the job:
function checkIfInSet(i, set) {
return i.toString().split('').sort().join('') === set;
}
function checkIfMagic(s) {
return (parseInt(s[0]) + parseInt(s[1]) == parseInt(s[3]) + parseInt(s[4]))
}
function printMagic(s) {
console.log(`${s[0]} ${s[4]}`);
console.log(` ${s[1]} ${s[3]}`);
console.log(` ${s[2]}\n`);
}
function checkSet(set) {
let counter = 1;
for(let i=1; i<99999; i++) {
if (checkIfInSet(i, set) && checkIfMagic(i.toString())) {
console.log(`--${counter++}-- (of set ${set})`);
printMagic(i.toString());
}
}
}
checkSet('23456');
checkSet('34567');
In the equation $\frac{1}{j} + \frac{1}{k} = \frac{1}{3}$, both $j$ and $k$ are positive integers. What is the sum of all possible values for $k$?
Answer:
Hello,
answer 22
Step-by-step explanation:
[tex]\dfrac{1}{j} +\dfrac{1}{k} =\dfrac{1}{3} \\\\\dfrac{k+j}{j*k} =\dfrac{1}{3} \\\\\\3k+3j=j*k\\\\k(3-j)=-3j\\\\k=\dfrac{3j}{j-3} \\\\k=\dfrac{3j-9+9}{j-3} \\\\k=3+\dfrac{9}{j-3} \\\\\\j-3\ must\ be \ a divisor\ of\ 9 ==> 1,3,9\\\\j-3=1 ==> j=4 , k=3+\dfrac{9}{1} =12\\\\j-3=3 ==> j=6 , k=3+\dfrac{9}{3} =6\\\\j-3=9 ==> j=12 , k=3+\dfrac{9}{9} =4\\\\\sum\ k=12+6+4=22\\[/tex]
The sum of all possible values for k is 22.
What is fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
1/j + 1/k= 1/3
Simplifying the fraction
(k+ j)/ kj= 1/3
3k + 3j = kj
k(3- j) = -3j
k = -3j/ (3- j)
k= 3j/ (j-3)
k = 3j + 9 - 9 / (j-3)
k = 3 + 9/ (j-3)
Since (j-3) must be divisor of 9.
j- 3 = 1---> j=4, k= 3 +9 = 12
j- 3 = 3---> j=6, k= 3 +9/3 = 6
j- 3 = 9---> j=12, k= 3 +9/9 = 4
So, The sum is = 12+ 6 + 4 = 22
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Given the figure, what is the angle of rotational system?
Answer it should be 72° as the figure is a 5 fold.
360/5 = 72
Angle of rational symmetry is 72°
Must click thanks and mark brainliest
An equilateral triangle has a perimeter of 15x3 + 33x5 feet. What is the length of each side?
x3 feet
5 + 11x2 feet
5x2 + 11 feet
5x3 + 11x5 feet
Answer:
the answer is 5×3+11×5 feet
Answer:
4th option
Step-by-step explanation:
An equilateral triangle has 3 congruent sides
Divide the perimeter by 3 for length of side
[tex]\frac{15x^3+33x^5}{3}[/tex]
= [tex]\frac{15x^3}{3}[/tex] + [tex]\frac{33x^5}{3}[/tex]
= 5x³ + 11[tex]x^{5}[/tex] ← length of 1 side
points V W X Y and Z are collinear, VZ= 52, XZ =20, and WX=XY=YZ find the indicated length
21.) WX 22.) VW 23.) WY 24.) VX 25.) WZ 26.) VY
Answer:
WX=10; VW=22; WY=20; VX=32; WZ=30;VY=42
Step-by-step explanation:
1)WX=XY=XZ/2=20/2=10
2)VW=VZ-WX-XY-YZ=VZ-3*WX=52-3*10=52-30=22
3)WY=WX+XY=2*WX=2*10=20
4)VX=VW+WX=22+10=32
5)WZ=WX+XY+YZ=3*WX=3*10=30
6)VY=VZ-YZ=52-10=42
The points V, W, X, Y and Z are collinear. The indicated lengths are
[tex]WX=10\\VW=22\\WY=20\\VX=32\\WZ=30\\VY=42[/tex]
Given :
points V, W, X, Y and Z are collinear, VZ= 52, XZ =20, and WX=XY=YZ
Lets make diagram using the given information
The diagram is attached below
XY=YZ
XZ=20, so [tex]XY+YZ=20\\Both XY and YZ are same\\XY+XY=20\\2XY=20\\Divide \; by \; 2\\XY=10[/tex]
[tex]WX=XY=YZ \\XY=10\\WY=10\\YZ=10\\[/tex]
Now we find out VW
[tex]VW+WX+XY+YZ=52\\VW+10+10+10=52\\VW+30=52\\Subtract \; 30\\VW=52-30\\VW=22[/tex]
Now we find the indicated length
[tex]WX =10[/tex]
[tex]VW=22\\WY=WX+XY=10+10=20\\VX=VW+WX=22+10=32\\WZ=WX+XY+YZ=10+10+10=30\\VY=VW+WX+XY=22+10+10=42[/tex]
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Someone pls help me . I will mark you brainliest !! thank you sm .
Answer:
first one is 27.89, the second is 20.
Step-by-step explanation:
1. So the 340 dollars is determined by 9.50 multiplied by the amount of hours you show up (which we will call x), plus the 75 dollars.
Your equation will be set up like this : 9.50x +75 = 340
So, to get x, we must isolate it. so subtract 75 from both sides
9.50x +75 -75 = 340 -75 9.50x = 265
Now, since we know that 9.50 multiplied by x equals 265, to isolate and find out x (the hours worked during the pay period), we divide both sides by 9.50
9.50x/9.50 = 265/9.50 so, x = 27.89473684, but based off of the answers there, you would just round to x = 27. 89 hours worked.
2. So now the 120 chips are determined by 6 chips multiplied by the minutes, since 6 chips are eaten every minute, with the minutes represented as x, like this: 6x = 120
So this time, you don't subtract or add anything, you would just divide by 6 to isolate x.
6x/6 = 120/6 so, x = 20 minutes.
The city plans a roadway to have trees every mile. If the path is miles long, how many trees will the city need?
30 trees
31 trees
32 trees
33 trees
Answer:
32
Step-by-step explanation:
the country would need 30 to 33 trees
Questions attached below (❁´◡`❁)
Problem 2
Josh forgot to apply the square root to 16 when he went from [tex](x-3)^2 = 16[/tex] to [tex]x-3 = 16[/tex]
Also, he forgot about the plus/minus.
This is what his steps should look like
[tex]x^2 - 6x - 7 = 0\\\\x^2 - 6x = 7\\\\x^2 - 6x +9= 7+9\\\\(x-3)^2= 16\\\\x-3= \pm\sqrt{16}\\\\x-3= 4 \text{ or } x-3= -4\\\\x= 7 \text{ or } x= -1\\\\[/tex]
There are two solutions and they are x = 7 or x = -1. To check each solution, you plug it back into the original equation
Let's try out x = 7
x^2 - 6x - 7 = 0
7^2 - 6(7) - 7 = 0
49 - 42 - 7 = 0
0 = 0 ... solution x = 7 is confirmed. I'll let you check x = -1
====================================================
Problem 3
We will have
a = 1, b = -4, c = 3
plugged into the quadratic formula below to get...
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-4)\pm\sqrt{(-4)^2-4(1)(3)}}{2(1)}\\\\x = \frac{4\pm\sqrt{4}}{2}\\\\x = \frac{4\pm2}{2}\\\\x = \frac{4+2}{2} \ \text{ or } \ x = \frac{4-2}{2}\\\\x = \frac{6}{2} \ \text{ or } \ x = \frac{2}{2}\\\\x = 3 \ \text{ or } \ x = 1\\\\[/tex]
The two solutions are x = 3 or x = 1. You would check this by plugging x = 3 back into the original expression x^2 - 4x + 3. The result should be zero. The same applies to x = 1 as well.
Ruth is touring New York City with her family. They want to visit the Empire State Building, Central Park, and Times Square before their dinner reservations at 7:10 P.M. They want to spend 1 hour and 25 minutes at the Empire State Building, 2 hours and 5 minutes in Central Park, and 50 minutes in Times Square. What is the latest time Ruth's family can start their tour in order to make it to dinner on time?
Pls help :)
Answer:
The latest time Ruth's family can start their tour in order to make it to dinner on time is 2:50 P.M
Step-by-step
Change:
7h10= 430 mins
1 hour and 25 minutes= 85 mins
2 hours and 5 mintues= 125 mins
- Total time Ruth wants to do before his dinner reservations:
85+ 125+ 50= 260 (mins)
- The latest time Ruth's family can start their tour in order to make it to dinner on time:
430- 260= 170 (mins)
Change: 170 mins= 2 hours and 50 minutes
Good luck!
Consider the perfect square trinomial identity:
a2 + 2ab + b2 = (a + b)2.
For the polynomial x2 + 10x + 25,
and b =
a =
Answer:
a = x
b = 5
Step-by-step explanation:
for the polynomial x² + 10x + 25, b = 5 and a = x.
In the polynomial x² + 10x + 25, we can observe that the first term, x², is the square of x, and the last term, 25, is the square of 5. This suggests that the polynomial follows the perfect square trinomial identity.
The middle term, 10x, can be rewritten as 2ab, where a represents x and b represents a term that when squared equals the last term, 25.
In this case, b = 5, because 5² = 25.
To find a, we can take the square root of the first term, x². The square root of x² is x, so a = x.
Therefore, for the polynomial x² + 10x + 25, b = 5 and a = x.
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Find the equation of the linear function represented by the table below in slope-intercept form.
Answer:
y = 3x+1
Step-by-step explanation:
First find the slope
m = ( y2-y1)/(x2-x1)
= (13-4)/(4-1)
= 9/3
= 3
Slope intercept form is
y = mx+b where m is the slope and b is the y intercept
y = 3x+b
Using a point from the table
10 = 3(3)+b
10 =9+b
10-9 =b
1=b
y = 3x+1
12. Write 0.8 as a fraction,
Pls explain in full detail.
Answer:
8/10
Step-by-step explanation:
10x10 is 100 8x10 would be 80 so 80/100=8/10
Answer:
8/10 = 4/5
Step-by-step explanation:
0.8 is 8-10th which means 8 divided by 10
reducing 8/10 to its lowest term since 8 and 10 has 2 as common factor, then
(8=2*4)/(10=2*5)
if 2 cancels out, then you are left with 4/5
David is the caption of the school soccer team. Last year, the team won four more games than it lost. If the team won 46 games, how many games did it lose?
Answer:
C
Step-by-step explanation:
Games lost=Games won - 4
Games lost=46-4=42
-4(2x-3) simplified
Answer:
-8x + 12
Step-by-step explanation:
Distribute -4 to the parentheses:
-4(2x - 3)
-4(2x) = -8x
-4(-3) = 12
-8x + 12
Answer:
-8x +12
Step-by-step explanation:
-4(2x-3)
Distribute
-4* 2x -4 *-3
-8x +12
if set a is 12345 and Set B is 23 find a union B and find a intersection b
Answer:
a union b= {1,2,3,4,5}
a intersection b ={2,3}
Step-by-step explanation:
The union of two sets A and B is a set that contains all the elements of A and B and is denoted by A U B
the set composed of all elements that belong to both A and B is A intersection B (A ∩ B)
please tell me the right answer
when the point ( k, 3 ) lies on each of these lines, find the value of k y= 3x+1 , y= 4x-2 , y=1/2x - 1 and 2x+3y=4
Answer:
see explanation
Step-by-step explanation:
Since (k, 3) lies on each of the lines, the point satisfies the equations.
Substitute x = k, y = 3 into each and solve for k
y = 3x + 1
3 = 3k + 1 ( subtract 1 from both sides )
2 = 3k ( divide both sides by 3 )
k = [tex]\frac{2}{3}[/tex]
-------------------------------------------------------
y = 4x - 2
3 = 4k - 2 ( add 2 to both sides )
5 = 4k ( divide both sides by 4 )
k = [tex]\frac{5}{4}[/tex]
--------------------------------------------------------
y = [tex]\frac{1}{2}[/tex] x
3 = [tex]\frac{1}{2}[/tex] k ( multiply both sides by 2 to clear the fraction )
k = 6
---------------------------------------------------------
2x + 3y = 4
2k + 3(3) = 4
2k + 9 = 4 ( subtract 9 from both sides )
2k = - 5 ( divide both sides by 2 )
k = - [tex]\frac{5}{2}[/tex]
Please help I’ll mark brainliest
Answer:
Step-by-step explanation:
The rule that makes a relation NOT a function is if there are shared x values. This function has 2 points with the same x value:
(7, 4) and (7, 6). The sharing of these x-values (or the repeating of them) within the same relation makes this NOT a function. The last choice is the one you want. Just remember that a relation is only a function if there are no shared x-values. The y-values don't matter to this at all. A relation would be a function if it were made up of the following coordinates:
(1, 2), (2, 2), (3, 2), (4, 2), (5, 2), etc. Again, as long as the x-values don't repeat, the relation is a function.
For the rational equation,[tex]\frac{x^{2}+5x+6}{x+3}=1[/tex] , what is a valid value of x?
Answer:
-3 or -1 is a valid value for x
Step-by-step explanation:
We start by cross multiplying;
So the expression becomes;
x^2 + 5x + 6 = 1(x + 3)
x^2 + 5x + 6 = x + 3
x^2 + 5x -x + 6-3 = 0
x^2 + 4x + 3 = 0
x^2 + x + 3x + 3 = 0
x(x + 1) + 3(x + 1) = 0
(x + 3)(x + 1) = 0
x + 3 = 0 or x + 1 = 0
x = -3 or x = -1
Calculate YZ if WY = 25, XY = 23, and VZ = 35
Answer:
WY= 25
XY= 23
VZ=36
so,
WY/XY = YZ/VZ
25/23 = YZ/25 (then do cross multiply)
25×25 = 23 × YZ
625= 23 × YZ
625/23= YZ
27,17= YZ
#i'm indonesian
#hope it helps.
Answer:
[tex]\huge \boxed{13.04}[/tex]
Step-by-step explanation:
The triangles are congruent, we can use ratios to solve.
WY/XY = (WY+YZ)/VZ
Let the length of YZ be x.
25/23 = (25+x)/35
Cross multiply.
23(25+x) = 25 × 35
575 + 23x = 875
Subtract 575 from both sides.
575 + 23x - 575 = 875 - 575
23x = 300
Divide both sides by 23.
(23x)/23 = 300/23
x = 13.0434782609...
Circles in the Coordinate Plane
Acellus
Complete the equation of this circle:
A
1
Answer: [tex](x-3)^2 + (y-2)^2 = 16[/tex]
Explanation:
The center of this circle is point A(3,2). These coordinates are the (h,k) values.
The radius is r = 4
Plug those three items into the template [tex](x-h)^2 + (y-k)^2 = r^2[/tex] to arrive at the final answer shown above.
Please answer this question now
Hello!
Answer:
[tex]\huge\boxed{V = 60 m^{3}}[/tex]
Formula for the volume of a triangular pyramid:
V = 1/3(bh)
The base is a triangle, so b = 1/2(b · h)
Solve for the base:
b = 1/2(8 · 5)
b = 1/2(40)
b = 20 m²
Solve for the volume:
V = 1/3(20 · 9)
V = 1/3(180)
V = 60 m³.
Hope this helped you!
Answer:
60 cubic meters
Step-by-step explanation:
I used the formula V = 1/3 AH to figure it out
john always wears a shirt, pants, socks, and shoes. he owns 12 pairs of socks, 3 pairs of shoes, 5 pairs of pants, and 5 shirts. how many different outfits can john make? PLEASE ANSWER
Answer:
900 outfits
Step-by-step explanation:
You just have to multiply them all together :)
The generic version was basedOn the brand name and was 2/3 the size of the brand name. If the generic television set is 12 inches by 24 inches what are the dimensions of the brand name television
Answer:
18 inches by 36 inches.
Step-by-step explanation:
Since we have given that
The generic version was basedOn the brand name and was 2/3
And given Dimensions of generic version is given by 12inches ×24inches
If we use the first dimensions of 12inches we have
12=2/3 × brand
12×3/2 = brand
=18inches= brand
we use the first dimensions of 24 inches we have
24=2/3 × brand
24×3/2 = brand
=36 inches= brand
brand= 36 inches
Therefore,the dimensions of brand name will be 18 inches by 36 inches.
I promise i will mark as brainiest
Answer:
A
Step-by-step explanation:
[tex] \frac{2003}{n} = z + \frac{23}{n} [/tex]
where z is an integer
[tex]2003 = nz + 23[/tex]
[tex]nz = 1980[/tex]
[tex]nz = {2}^{2} \times {3}^{2} \times 5 \times 11[/tex]
possible values of n
n= {1980, 990, 660, 495, 396, 330, 198, 180, 165, 132, 99, 90, 60, 45, 36, 30, 20, 18, 15, 5, 3}
cardinality of n=21
Find the co-ordinates of the foot of the perpendicular drawn from the point (6, 3) to the line by
segment joining (4,1) and (8,3).
The coordinates of the foot of the perpendicular drawn from the point (6, 3) to the line by segment joining (4,1) and (8,3). is (6.4, 2.2)
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
The equation of the line passing through (4,1) and (8,3) is:
y - 1 = [(3 - 1)/(8 - 4)](x - 4)
y = 0.5x - 1
The line perpendicular to y = 0.5x - 1 has a slope of -2. It passes the point (6, 3), hence:
y - 3 = -2(x - 6)
y = -2x + 15
The line y = 0.5x - 1 and y = -2x + 15 intersect at point (6.4, 2.2)
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. Two trains leave a train station traveling different directions. The first train travels 12 miles west, then 6 miles north. The second train travels 20 miles east, then 35 miles north. a. The train station is the origin. What is the coordinate of each train? b. Using the train station and the stop point of the first train, what is the slope of the line? Is it horizontal, vertical or neither? Write the equation of the line in slope-intercept form and standard form. c. The city wants to build a second train station 2 miles directly north of the first train station. They are going to build a train track from the second train station that is parallel to the path the first train would've traveled if it had taken a direct route to its stopping point. What would be the equation of the line in slope intercept form of the new track?
Answer:
a. The coordinates of the first train are (-12,6). The coordinates of the second train are (20,35).
b. The slope of the line for the first train is [tex]-\frac{1}{2}[/tex]. The slope is neither horizontal or vertical. It slopes diagonally downward from left to write since the slope is negative. In slope-interdept form, it is written as [tex]y=-\frac{1}{2} x[/tex]. In standard form, it is written as [tex]x+2y=0[/tex]. The slope of the line for the second train is [tex]\frac{7}{4}[/tex]. The slope is neither vertical or horizontal. It slopes diagonally upward from left to right since the slope is positive. In slope-intercept form, it is written as [tex]y=\frac{7}{4}x[/tex]. In standard form, it is written as [tex]-7x+4y=0[/tex].
c. The equarion of a line in slope-intercept form of the new track would be [tex]y=-\frac{1}{2} x+2[/tex].
Step-by-step explanation:
a. The way to find the coordinates is either to picture a coordinate grid in your head or to have one out in front of you for a visual. The first train travels 12 miles west, or 12 units to the left (-12), and 6 miles north, or 6 units up (6). On a coordinate plane, that would be marked as (-12,6). The second train travels 20 miles east, or 20 units to the right (20), and 35 miles north, or 35 units up (35). On a coordinate plane that would be marked as (20,35). This means that the coordinates of the first train would be (-12,6), and the coordinates of there second train would be (20,35).
b. The way to find slope is to find [tex]\frac{delta "x"}{delta "y"}[/tex]. "Delta" means "the change in". The equation would be [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]. So, let's find the slope of the first train's travel path. We'll use the origin, (0,0), and the stopping point, (-12,6), as our coordinates to find the slope. [tex]\frac{0-6}{0-(-12)}=\frac{0-6}{0+12}=\frac{-6}{12}=\frac{-1}{2}=-\frac{1}{2}[/tex]. That makes the slope of the first train's travel path to be (-1/2). Now, let's find the slope of the second train's travel path. We'll use the origin, (0,0), and the stopping point, (20,35), as our coordinates to find the slope. [tex]\frac{0-35}{0-20}=\frac{-35}{-20}=\frac{35}{20}=\frac{7}{4}[/tex]. That makes the slope of the second train's travel path to be (7/4). They want to know the equation of the travel path line in slope-intercept form and in standard form, and what the line looks like. To start off, any vertical line would be undefined, and that would be if the slope was a fraction with a denominator of zero, which doesn't occur for either train path. A horizontal line would be if the slope was zero itself and the trains were not moving, but the trains are moving, so that's not possible either. The way to determine theway a slope is diagonally is to look at whether the slope is positive or negative. The first train's path slopes negatively, so it moves diagonally downward from left to right, or diagonally upward from right to left (both the same thing). The second train's path slopes positively, so it moves diagonally upward from left to right, or diagonally downward from right to left. Finally, the equations for this part of the question. For both trains, the origin is the y-intercept, so the y-intercept does not have to be written in the slope-intercept equation. The slope-intercept form of an equation of a line is [tex]y=mx+b[/tex] where "m" is the slope and "b" is the y-intercept. The "b" value is 0, so that will not be written. The slope for the first train is (-1/2), so the slope-intercept form of the first train's travel path is y=(-1/2)x. The slope of the second train is (7/4), so the slope-intercept form for this train's path is y=(7/4)x. As for standard form, subtract the "mx" value from both sides, and set the equation equal to 0. Also, get rid of any fractions. So, for the first train, standard form would be x+2y=0. And for the second train, standard form would be -7x+4y=0.
c. Parallel means having the same slope but a different y-intercept. The second train station would be placed two miles north, or two units up, from the first train station. The first train station is at (0,0), so the second train station would be placed at (0,2). That makes 2 the y-intercept for if the first train had taken the second train station's travel route. The slope for the intitial route was (-1/2), so that will stay the same. Therefore, the equation of thr route taken if the first train had come out of the second train station, if it was already built, would be y=(-1/2x)+2.
SP=2x+3, and LN=5x−14. Find SP. A. 20 B. 86 C. 43 D. 50
Answer:
C
Step-by-step explanation:
A segment joining the midpoints of two sides of a triangle is half the length of the third side.
SP is a midline segment, thus
SP = [tex]\frac{1}{2}[/tex] LN , that is
2x + 3 = [tex]\frac{1}{2}[/tex] (5x - 14) ← multiply both sides by 2
4x + 6 = 5x - 14 ( subtract 4x from both sides )
6 = x - 14 ( add 14 to both sides )
20 = x
Thus
SP = 2x + 3 = 2(20) + 3 = 40 + 3 = 43 → C