Answer:
n≥5
Step-by-step explanation:
what is 30 divided into the ratio of 7:8
Lines a b c and d are shown below. Which lines are parallel? Which line are perpendicular? Explain and jutsify your answer using slopes
Answer:
Lines A and C are parallel
Lines B and D are perpendicular
Step-by-step explanation:
Given
See attachment for lines A to D
Required
Determine the parallel and perpendicular lines
To start with, we calculate the slope of each line.
Line A
The points on line A are:
[tex](x_1,y_1) = (3,-4)[/tex]
[tex](x_2,y_2) = (-1,2)[/tex]
Calculate the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{2 - (-4)}{-1 - 3}[/tex]
[tex]m = \frac{2 +4}{-4}[/tex]
[tex]m = \frac{6}{-4}[/tex]
[tex]m_1 = -\frac{3}{2}[/tex]
Line B
[tex](x_1,y_1) = (-1,8)[/tex]
[tex](x_2,y_2) = (2,6)[/tex]
Calculate the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{6 - 8}{2 -(-1)}[/tex]
[tex]m = \frac{-2}{2 +1}[/tex]
[tex]m_2 = -\frac{2}{3}[/tex]
Line C
[tex]y - 9 = -\frac{3}{2}(x + 8)[/tex]
Open bracket
[tex]y - 9 = -\frac{3}{2}x -\frac{3}{2}* 8[/tex]
[tex]y - 9 = -\frac{3}{2}x -3* 4[/tex]
[tex]y - 9 = -\frac{3}{2}x -12[/tex]
Make y the subject
[tex]y = -\frac{3}{2}x -12+9[/tex]
[tex]y = -\frac{3}{2}x -3[/tex]
The slope intercept of an equation is: [tex]y = mx + b[/tex]
Where
[tex]m = slope[/tex]
By comparison:
[tex]m_3 = -\frac{3}{2}[/tex]
Line D
[tex]12x - 8y = 40[/tex]
Subtract 12x from both sides
[tex]12x-12x - 8y = -12x+40[/tex]
[tex]- 8y = -12x+40[/tex]
Divide through by -8
[tex]\frac{- 8y}{-8} = \frac{-12x}{-8}+\frac{40}{-8}[/tex]
[tex]y= \frac{12x}{8}-\frac{40}{8}[/tex]
[tex]y= \frac{3}{2}x-5[/tex]
The slope intercept of an equation is: [tex]y = mx + b[/tex]
Where
[tex]m = slope[/tex]
By comparison:
[tex]m_4 = \frac{3}{2}[/tex]
So, the slopes of the lines are:
[tex]m_1 = -\frac{3}{2}[/tex] [tex]m_2 = -\frac{2}{3}[/tex] [tex]m_3 = -\frac{3}{2}[/tex] [tex]m_4 = \frac{3}{2}[/tex]
Lines with the same slope are parallel.
So:
Lines A and C with slope of [tex]-\frac{3}{2}[/tex] are parallel
Lines with the following relationship are perpendicular:
[tex]m * M = -1[/tex]
Lines B and D are perpendicular because:
[tex]-\frac{2}{3} * \frac{3}{2} = -1[/tex]
[tex]-\frac{6}{6} = -1[/tex]
[tex]-1 = -1[/tex]
A rock is thrown down from a cliff that is 180 m high. The function
h(t) = -5t^2 – 10t + 180 gives the approximate height of the rock
above the water, where h(t) is the height in metres and t is the time
in seconds. When will the rock reach a ledge that is 105 m above
the water?
Answer:
t = 3
Step-by-step explanation:
105 = -5t^2 -10t + 180
-75 = -5t^2 -10t
15 = t^2 +2t
t^2 +2t -15 = 0
(t+5)(t-3)
t = -5, 3
There's no such thing as negative time so you use the positive answer
Please help me with this
Answer:
m=9 cm; n=4 cm
Step-by-step explanation:
The area of the rectangle is m*n, and the area of the square is 6*6. We are told that the areas of the rectangle and square equal each other, so:
[tex]m*n=36[/tex]
We are told that m is 5 cm longer than n, so we know that:
[tex]m = 5+n[/tex]
Therefore, we can solve for n using substitution.
[tex]m*n=36\\(5+n)n = 36\\5n+n^2 = 36\\n^2 + 5n -36 = 0\\(n+9)(n-4)=0[/tex]
We now have two answers for n: -9 and 4. However, the side length cannot be negative; that simply wouldn't make any sense. Therefore, n = 4.
Next, using the same equation, plug in 4 for n and solve for m.
[tex]m*n=36\\m*4=36\\m=9[/tex]
What is the measure of _R?
A. 40
B. 640
C. Cannot be determined
D. 32°
Answer:
D hope it helpzStep-by-step explanation:
Thats all i know
Name an independent variable that's used for a laptop computer to work.
Answer:
The FitnessGram PACER Test is a multistage aerobic capacity test that progressively gets more difficult as it continues. The test is used to measure a student's aerobic capacity as part of the FitnessGram assessment. Students run back and forth as many times as they can, each lap signaled by a beep sound.
Step-by-step explanation:
what is the gradient of (0,3) and (1,8)
Answer: 5/1 = 5
Step-by-step explanation:
The gradient is the slope of something. The slope = rise/run so you just do 8-3 = 5 is the rise and then 1-0 = the run so its a gradient of 5
what is the answer to this question
Answer:
the height is 4
Step-by-step explanation:
it is a right triangle and also a perfect 3-4-5 right triangle
[tex] {3}^{2} + {h}^{2} \: equals \: {5}^{2} [/tex]
[tex]9 + {h}^{2} \: eqauls \: 25[/tex]
subtract 9 from 25
[tex] {h}^{2} \: equals \: 16[/tex]
then you square root 16
[tex] \sqrt{16} [/tex]
and now you height is 4
15 feet by 120 inches area
Answer:
21600 In.
Step-by-step explanation:
First, turn 15 feet into inches
15*12 is 180
then do 120*180 which equals 21600 In.
1. At a specific time of day, a flagpole has a shadow 40 ft long, at the same time of day
Jose who is 6 ft tall has a shadow of 8ft long. Find the height of the flagpole to the
nearest tenth of a foot if needed.
Please help!! I will be marking brainliest
Answer:
DVDs= $16.2
CDs = $11.9
Cassettes = $11.4
Step-by-step explanation:
A train travels 228km in 4 hours and 45 minutes. What is its average speed in kilometers per hour?
Answer:
48 km/h
Step-by-step explanation:
The average speed is calculated by distance divided by time. So 228 / 4.45 gets the answer.
Simplify the expression d + 11 - 8d.
28 is 12 less than k equation
Multiplying by 1.19 is the same as increasing by
%
Answer:
19%
Step-by-step explanation:
If you mulityply by 1.19 you are giving a result of 119%, thus you either multiply by 1.19 or divide first by 100 and then multiply by 119.
2. Identify the measure of angle x. (Write your answer in number form only, 1 point
for example 8. No degree symbol). *
73
Answer:
17
Step-by-step explanation:
What is the area of the circle? *
10 ft
31.4 square feet
78.5 square feet
314 square feet
15.7 square feetT
Answer:
The answer is 314.159 which can be rounded to 314.
pleaseeeeee someone help i'm in tears
Answer:
the correct answer is 6
Step-by-step explanation:
only reasonable answer
Lena drove 355 miles using 17 gallons of gas. At this rate, how many gallons of gas would she need to drive 284 miles.
Answer:
13.6 gallons
Step-by-step explanation:
Miles Driven = Gallons Burnt * Miles Per Gallon
So if yo drive 20.88 miles on one gallon how many gallons does it take to drive 284 miles. This is 284/20.88 = 13.6 gallons
Whilst the numerical answer is correct the previous answer, it does not maintain the validity of the units - in which things are measured. You will see this is very important in science
What can we learn from this. As an intermediate step we have learnt that the car does 20.88 mpg, lets call it 21. So a car that has a sticker at the show room with an MPG of more than 21 will consume less gas and one that has a smaller mpg will consume more.
What is an equation of the line that contains the point (0, -5) and a slope of 1/4
Answer:
y=1/4x-5
Step-by-step explanation:
Answer:
y = 1/4x - 5
Step-by-step explanation:
y = mx + b is the equation of a straight line.
m = slope, b = y intercept. (y intercept is the point where the line of the graph crosses the y axis)
(0, -5) is the y intercept (if you were to graph this point, it would be on the y axis, fitting the previous description)
the slope is 1/4
replace each variable in the equation, and you get:
y = 1/4x - 5
Hep need please and thanks
Dont need awnser just explain
Answer:
i am just standing here
Step-by-step explanation:
(3) GEOMETRY IMAGE BELOW. 20 POINTS!!
Answer:
option D
Step-by-step explanation:
option D is the correct answer of this question.
the length of the mid segment was 42 option A
( previous question ) according to me and it is right so please recheck your previous answer as it was option A not D
hope this will be helpful to you.
and mark my answer as brainlist plzzzz.
Some number added to -12 is 36. Add this number to -15. Then multiply this
number by 2. What is the final number?
z
Which of the following congruency statements is
correct?
2.4 cm
108
2.4 cm
O AYZX - ABCD
Y
36°
36
Ο ΔΥΖX2 ΔDCB
3.8 cm
Ο ΔZXΥ: ΔDCB
Х
O AYXZ – ACDB
B
3.8 cm
136
2.4 cm
36°
С
1089
2.4 cm
D
Orange
Answer:
the answer is c
Step-by-step explanation:
Please help me! What does X equal?
Answer:
x = 75
Step-by-step explanation:
X = 180 - 78 - 27 = 75
Answer:
The answer is 75
Step-by-step explanation:
I got this answer because i added 78 and 27 then i subtracted it from 180 because that was the interior angle of a triangle and i got 75.
Can someone help me with this please?
Answer:
your awnser would be. 1/4
Answer:
y=3x-2
Step-by-step explanation:
3/1 simp so 3
then pick a point (1,1) I marked were what goes hope that helps you understand
(1)=(3)(1)+b
1=3+b
-3 each side
1-3=-2
-2=b
y=3x-2
Solve the following system of equations for x using elimination
4x + y = 2
x - y = 3
A. -2
B. 1
C. 3.
D.4
Answer:
A
Step-by-step explanation:
A
Answer:
b 1 ksoeoeskmx
Step-by-step explanation:
ksowoxk374
What is the result when 4x^4+17x^3+10x^2-7x+184x
4
+17x
3
+10x
2
−7x+18 is divided by x+2x+2?
Answer:
-5x+18/x+2
Step-by-step explanation:
I'm pretty sure it's the answer
Place the indicated product in the proper location on the grid. (x + 1)(x - 1)