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.
Complete the point-slope equation of the line through (8,−8) (9,8) Use exact numbers. y-8=
Answer:
y-8=16(x-9)
Step-by-step explanation:
slope m=y2-y1/x2-x1
m=8+8/9-8 ⇒ m=16
y-8=m(x-x1)
y-8=16(x-9)
The equation of the line that is passing through (8, −8) and (9, 8) will be y = 16x − 120.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
Let the equation of the line pass through (x₁, y₁) and (x₂, y₂).
Then the equation of the line is given as,
[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]
The points are given below.
(8, −8) and (9, 8)
The equation of the line that is passing through (8, −8) and (9, 8) will be given as,
(y + 8) = [(8 + 8) / (9 − 8)](x − 8)
Simplify the equation, then we have
(y + 8) = [(8 + 8) / (9 − 8)](x − 8)
(y + 8) = 16(x − 8)
y + 8 = 16x − 128
y = 16x − 120
The equation of the line that is passing through (8, −8) and (9, 8) will be y = 16x − 120.
More about the line passing through two points link is given below.
https://brainly.com/question/12740817
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Mark currently works part time with a salary of $8000 per year mark plans to quit working and attend college for four years if his college cost will total $64,000 how long will it take Mark to recover his investment assuming he has a salary of $32,000 upon graduating
The correct answer for this question is: If his college costs will total $64,000, it take Mark to recover his investment assuming he has a salary of $32,000 upon graduating for "2 years."
= 64,000 / 32, 000
= 2 years
Assuming that there'll be no additional costs in the middle of his college.
If you found this please brainliest it :)
Answer:
it is not 2 years
Step-by-step explanation:
Solve for y
4x + 7y +5
Write a slope-intercept equation for a line passing through the point (5,-5) that is parallel to the line x = -2. Then write a second equation for a line passing through the point (5,-5) that is perpendicular to the line x=-2.
Answer:
1. y=-2x+5
2. y=1/2x-7.5
Step-by-step explanation:
you plug in the cordinates for the y intercept and you already have the slope.
y=mx+b
m= slope which is -2
Find the value of x.
Answer:
x = 10
Step-by-step explanation:
(segment piece) x (segment piece) = (segment piece) x (segment piece)
6*x = 12*5
6x = 60
Divide by 6
6x/6 = 60/6
x = 10
Answer:
[tex]\huge\boxed{x = 10}[/tex]
Step-by-step explanation:
According to chord-chord theorem:
(x)(6) = (5)(12)
6x = 60
Dividing both sides by 6
x = 10
Use linear regression to predict the length of a 40-month-old animal. The ages and lengths of several animals of the same species are recorded in the following table: (2 points)
Answer:
Aw what animal
Step-by-step explanation:
Srry I need pointse
please help i'm having a very hard time understanding this!
Hi there!
check the pic
#YoghurtCup!
Answer: F
Step-by-step explanation:
Put all numbers with 1 exponent.
[tex](\sqrt{8^4} *\sqrt{6^4} )^{\frac{3}{2} }\\\\=(2^{\frac{3*4}{2} }*(2^{\frac{4}{2} }*3^{\frac{4}{2}} )\ )^{\dfrac{3}{2} }\\\\\\=(2^6*2^2*3^2)^{\dfrac{3}{2} }\\\\=2^{8*\frac{3}{2} }*3^{2*\frac{3}{2}} \\\\\\\boxed{=2^{12}*3^3}\\\\\\Answer\ F[/tex]
Find the area of the following shape. Please show work.
Answer:
Step-by-step explanation:
The area of a triangle is given by the formula:
● A = (b×h)/2
b is the base and h is the heigth.
■■■■■■■■■■■■■■■■■■■■■■■■■■
Draw the heigth. This gives you two small right triangles.
Let's focus on the right one containing 45°.
● sin 45° = h/8
● h = sin 45° × 8 = 4√(2)
■■■■■■■■■■■■■■■■■■■■■■■■■■
Replace h by its value in the area formula. The base is 17
● A = (17× 4√(2))/ 2
● A = 34√(2)
● A = 48.08
Round to the nearest unit
● A = 48
Answer:
Area = 48 sq. units
Step-by-step explanation:
will make it short and simple.
area of a triangle = 1/2 * a * b * sinФ
area = 1/2 * 17 * 8 * sin(45°) = 48 sq. units
Using the right triangle below, find the tangent of angle B.
시
A
600
0
3-13
300
B
Answer:1&3
Step-by-step explanation:
HELP ASAP!!!
What is the geometric mean of 7 and 56?
Geometric Mean = √(ab)
a = 7
b = 56
Geometric mean = √(7×56)
After prime factorization of 56 we get 2 × 2 × 2 × 7
√(7×7×2×2×2)
7×2√2
14√2
Therefore the answer is option d
Must click thanks and mark brainliest
Answer:
I'll add this so that u can give that person brainliest ^^
Find the value of x if 2x-1÷3 is greater than 1-3x÷4 by 1
[tex]\\ \sf\longmapsto \dfrac{2x-1}{3}-\dfrac{1-3x}{4}=1[/tex]
[tex]\\ \sf\longmapsto \dfrac{4(2x-1)-3(1-3x)}{12}=1[/tex]
[tex]\\ \sf\longmapsto 8x-4-3+9x=12(1)[/tex]
[tex]\\ \sf\longmapsto 17x-7=12[/tex]
[tex]\\ \sf\longmapsto 17x=12+7[/tex]
[tex]\\ \sf\longmapsto 17x=19[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{19}{17}[/tex]
1. Look at the numbers listed below. Which numbers are rational? Select all that apply.
9.1874639...
424, 489
121
5/3
if n(p(a)) = 256. find n(a)
n(p(a)) = 256
256 = 2^8
n(a) = 8
Must click thanks and mark brainliest
I really need an answer as soon as possible. 10 pts worth it
Answer:
A. Correct: When we plug in g(x) for the x in f(x), we get H(x).
B. Correct: When we plug in g(x) for the x in f(x), we get H(x).
C. Correct: When we plug in g(x) for the x in f(x), we get H(x).
D. Correct: When we plug in g(x) for the x in f(x), we get H(x).
Step-by-step explanation:
Brainliest, please!
can someone plzz answer dis ma braincells dont seem to work
Answer:
Good luck undersatnding.
Step-by-step explanation:
1.
A) 27 (over) 4
B) 97 (over) 117
2.
C) 8
D) -243 (over) 32
3.
Square root of 25 is 5
Square root of 16 is 4
Square root of 9 is 3
Square root of 1 is 1
4.
E) 553 (over) 72
F) 11 (over) 56
G) 65 (over) 18
H) 28 (over) 9
5.
E) 35941
F) 81130
G) 79567.75
H) 20525.857
I dont know 7-8
9.
E) Negative
F) Positive
G) Positive
H) Negative
10.
Square root of 25 is 5
Square root of 64 is 8
Square root of 121 is 11
Square root of 225 is 15
I couldn't post images for 6, it wont let me.
how to change mixed fraction into improper fraction and improper to proper fraction easy way
Answer with Step-by-step explanation:
To change the mixed fraction into improper fraction you multiply the denominator with the whole and add to numerator.
For example: 4 1/5 = (5*4)+1/5=21/5
To change improper into proper mixed fraction,
Divide the numerator by denominator and write the remainder on numerator
For example: 7/2= 3 1/2
WILL GIVE BRAINLIEST PLS HELP
Answer:
Hello
Step-by-step explanation:
[tex]y=2x^2-12x+19\\=2(x^2-6x)+19\\=2(x^2-2*3*x+9)+19-18\\=2(x-3)^2+1\\\\Vertex\ is\ (3,1)\\\\Axis\ of\ symmetry\ is\ x=3\\\\y-intercept\ is \\\\y=2(0-3)^2+1=19\\[/tex]
5000 x 10 x 10 x 50
Answer:
5000 x 10 x 10 x 50 = 25000000
Step-by-step explanation:
you can just use a calculator....
Answer:
25000000
Step-by-step explanation:
Need help with 1 and 2
Answer:
1a. 128
1b. 81
1c. 64
1d. 25
1e. 343
1f. 100000
1g. 64
1h. 0
1i. 13
1j. 1
2a. 243
2b. 64
2c. 36
2d. 625
2e. 1331
2f. 10000000
2g. 81
2h. 0
2i. 17
2j. 1
the set is points indicated by 12.is the ___ of the angle
Answer:
Vertex
Step-by-step explanation:
The vertex is the point were two rays meet to form an angle.
If my answer is incorrect, pls correct me!
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-Chetan K
Use slope-intercept form, y = mx + b, to find the value for the y-intercept (b) of a line that has a slope of 6 and passes through the point (3, –5)
Answer:
y=6x-23
Step-by-step explanation:
-5=6(3)+b
-5=18+b
b=-23
If this helps, plz give brainly, I rlly need it!
Answer:
6x-23
Step-by-step explanation:
PLEaSE HELP!!!!!! will give brainliest to first answer
Answer:
The coordinates of A'C'S'T' are;
A'(-7, 2)
C'(-9, -1)
S'(-7, -4)
T'(-5, -1)
The correct option is;
B
Step-by-step explanation:
The coordinates of the given quadrilateral are;
A(-3, 1)
C(-5, -2)
S(-3, -5)
T(-1, -2)
The required transformation is T₍₋₄, ₁₎ which is equivalent to a movement of 4 units in the leftward direction and 1 unit upward
Therefore, we have;
A(-3, 1) + T₍₋₄, ₁₎ = A'(-7, 2)
C(-5, -2) + T₍₋₄, ₁₎ = C'(-9, -1)
S(-3, -5) + T₍₋₄, ₁₎ = S'(-7, -4)
T(-1, -2) + T₍₋₄, ₁₎ = T'(-5, -1)
Therefore, the correct option is B
Talia spent \dfrac34 4 3 start fraction, 3, divided by, 4, end fraction of this week's allowance on candy. Of the money she spent on candy, \dfrac56 6 5 start fraction, 5, divided by, 6, end fraction was spent on gummy bears.
Answer:
15/24
Step-by-step explanation:
Talia spent 3/4 of this week's allowance on candy. Of the money she spent on candy, 5/6 was spent on gummy bears.
What fraction of this week's allowance did Talia spend on gummy bears?
Answer: Let this weeks allowance be x. Talia spent 3/4 of the weeks allowance on candy, therefore the money spent on candy = (3/4)x.
Out of the money spent on candy, 5/6 was spent on gummy bears. Therefore the money spent on gummy bears = 5/6 × (3/4)x = (15/24)x.
This means that the fraction of money spent on gummy bears was 15/24 of the weeks allowance.
congruent complements theorem
Answer:
Congruent Complements Theorem If 2 angles are complementary to the same angle, then they are congruent to each other.
HOPE THIS HELPS
MARK IT BRAINLIEST!!!!
Quickly please help
Answer:
6
Step-by-step explanation:
f(x)=2x^3-5x when x=2. So f(2)=6
if one square yard of carpet costs $15.40, how much will 45.5 square yards cost? ( value only, no commas, dollar signs, symbols, or units)
Work Shown:
1 square yard = 15.40 dollars
45.5*1 square yard = 45.5*15.40 dollars
45.5 square yards = 700.70 dollars
In the second step, I multiplied both sides by 45.5 to turn the "1 square yard" into "45.5" square yards.
The perimeter of a triangle is 24 cm.If it’s area is 24cm2 and it’s one of the three sides is 10 cm,find the sides of remaining
Answer:
The other sides are 6cm and 8cm
Step-by-step explanation:
Let the other 2 sides be x and y.
Using herons formula, we have an equation
24=sqrt(12*2*(12-x)*(12-y))
Since the perimeter is given, we have x+y=24-10=14. Solving it we have x=6,8 and y=8,6.
A researcher performs a hypothesis test to test the claim that for a particular manufacturer, the mean weight of cereal in its 18 ounce boxes is less than 18 ounces. He uses the following hypotheses: H 0: μ = 18 vs H A: μ < 18 and finds a P-value of 0.01. Draw a conclusion about the cereal box weight at a significance level of 0.05.
Answer:
We conclude that the mean weight of cereal in its 18-ounce boxes is less than 18 ounces.
Step-by-step explanation:
We are given that a researcher performs a hypothesis test to test the claim that for a particular manufacturer, the mean weight of cereal in its 18-ounce boxes is less than 18 ounces.
Let [tex]\mu[/tex] = mean weight of cereal in its 18-ounce boxes.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 18 {mean that the mean weight of cereal in its 18-ounce boxes is equal to 18 ounces}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 18 {mean that the mean weight of cereal in its 18-ounce boxes is less than 18 ounces}
Also, it is given that the P-value is 0.01 and the level of significance is 0.05.
The decision rule based on the P-value is given by;
If the P-value of our test statistics is less than the level of significance, then we have sufficient evidence to reject our null hypothesis as our test statistics will fall in the rejection region.If the P-value of our test statistics is more than the level of significance, then we have insufficient evidence to reject our null hypothesis as our test statistics will not fall in the rejection region.Here, clearly our P-value is less than the level of significance as 0.01 < 0.05, so we have sufficient evidence to reject our null hypothesis as our test statistics will fall in the rejection region.
Therefore, we conclude that the mean weight of cereal in its 18-ounce boxes is less than 18 ounces.
Briefly explain how you would graph an equation such as y=7x-2
Answer:
put a mark at negative 2 on the graph then you would go up seven rigght one until you cant then you would go back to -2 and go down seven left one until you cant
Step-by-step explanation:
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
B is correct
Step-by-step explanation: