1. Write down the gradient of the line joining the points (2m, n) and (3, -4).
2.Find the value of n if the line is parallel to the X-axis
3.Find the value of m if the line is parallel to the Y-axis.
Answers
Answer:
Step-by-step explanation:
1 . ( n + 4 ) / ( 2m - 3 )
The gradient (slope) is
= ( change in y direction ) / ( change in x direction )
= ( n - (-4) ) / ( 2m - 3 )
= ( n + 4 ) / ( 2m - 3 )
2.
A line parallel to the x-axis will always have the equation of y = #. This is because all along that line, every value of x, y will still equal the same number. For example, a line parallel to the x-axis that crosses the y-axis at 2, will be y = 2. If it is in the negative range, it's the same concept, for example if it crossed the y-axis at -4, the equation would be y = -4.
Example - Computational Knowledge Engine
3.
To understand the slope of a line parallel to y axis, let us consider the figure given below.
1 . The gradient (slope) is ( n + 4 ) / ( 2m - 3 )
2. n = -4
3. m is not defined.
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
Given:
points (2m, n) and (3, -4).
1 . The gradient (slope) is
= ( change in y direction ) / ( change in x direction )
= ( n - (-4) ) / ( 2m - 3 )
= ( n + 4 ) / ( 2m - 3 )
2. A line parallel to the x-axis will always have the equation of y = x.
The line is therefore horizontal so gradient = 0
(n+4) / (2m-3)= 0
n = -4
(iii) Find the value of m if the line is parallel to the y-axis
(n+4) / (2m-3)= gradient
(n+4) / (2m-3)= 1
We know n = -4 from part (ii) then
(-4+4) /(2m-3)= 1
0/(2m-3) = 1
0 = 1 The 'm' vanishes
Hence, m is not defined.
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Related Questions
please help me its hard
Answers
Answer:
1
Step-by-step explanation:
16-9=5t+2t
7=7t
1=t
Answer:
t = 1
Step-by-step explanation:
16 - 2t = 5t + 9
=> 16 - 2t - 9 = 5t
=> 16 - 9 = 5t + 2t
=> 7 = 7t
=> 7/7 = t
=> 1/1 = t
=> 1 = t
Round each to the nearest cent.
$879.190
and
$532.626
Answers
Answer:
$879.190 = $879.19
$532.626 = $532.627
Step-by-step explanation:
You round up for the tenths place if the hundredths place is above five, but you round down for the tenths place if the hundredths place is below five. For example, 0 is below five for $879.190, so I round to 9.
X
( = [?]
DK
x Х
А AK
140°
B
HC
Angles are not drawn to scale
Answers
Answer:
40 degrees
Step-by-step explanation:
Supplementary angles are a pair of angles that add up to 180 degrees
Since ABD and DBC are supplementary, you can make the equation:
180=140+x
Simplify and you get x=40
[tex]\bf \large \implies \: \: x \: + \: 140 \degree \: = \: 180 \degree[/tex]
[tex]\bf \large \implies \: \: x \: = \: 180 \degree - \: 140 \degree[/tex]
[tex]\bf \large \implies \: \: x \: = \: 40 \degree[/tex]
Solve the equation :
-3 • ( 2 - x ) + 4 = 2 • ( 1 - 2x) + 3
thanks :)
Answers
Isolate the variable by dividing each side by factors that don't contain the variable.
x = 1
-6+3x+4=2-4x+3
-8+7x+1=0
7x=7
x=1
Answer:
x=1
Step-by-step explanation:
SEE IMAGE for Solution
3000 dollars is invested in a bank account at an interest rate of 7 percent per year, compounded continuously. Meanwhile, 20000 dollars is invested in a bank account at an interest rate of 5 percent compounded annually.
To the nearest year, when will the two accounts have the same balance?
Answers
9514 1404 393
Answer:
after 89 years
Step-by-step explanation:
For principal p, interest rate r, and number of years t, the two account balances are ...
a = p·e^(rt) . . . . continuous compounding
a = p(1+r)^t . . . . annual compounding
Using the given values, we have
3000·e^(0.07t) . . . . . compounded continuously
20000·1.05^t . . . . . . compounded annually
We want to find t so these are equal.
3000·e^(0.07t) = 20000·1.05^t
0.15e^(0.07t) = 1.05^t . . . . divide by 20,000
ln(0.15) +0.07t = t·ln(1.05) . . . . take natural logarithms
ln(0.15) = t·(ln(1.05) -0.07) . . . . subtract 0.07t
t = ln(0.15)/(ln(1.05) -0.07) ≈ -1.8971/-0.02121 . . . . . divide by the coefficient of t
t ≈ 89.4 ≈ 89
The two accounts will have the same balance after 89 years.
The volume of a rectangular prism with a cone shaped hole in it is approximately 163.22cm³ (as shown below).
✏️ What is the height of the cone?
Answers
Answer:
Height of the cone = 5 cm
Step-by-step explanation:
Volume of the rectangular prism with a cone shaped hole = Volume of the rectangular prism - Volume of the cone
Volume of the rectangular prism = Length × Width × Height
= 5 × 5 × 7
= 175 cm³
Volume of the cone = [tex]\frac{1}{3}\pi r^{2}h[/tex]
Here, r = Radius of the cone
h = Height of the cone
Volume of the cone = [tex]\frac{1}{3}\pi (\frac{3}{2})^{2}(h)[/tex]
= 0.75πh cm³
Volume of the rectangular prism with a hole = 163.22 cm³
175 - 0.75πh = 163.22
0.75πh = 175 - 163.22
0.75πh = 11.78
h = 5 cm
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST!!
Answers
Answer:
so the simplest way to find the volume of water is by dividing into different....objects
so when dividing you create a rectangular box that has length of 12 width of 14.5 and height of 5 and another rectangular box with length of 7 (19-12) width of 4 and height of 5
now calculate the volume of each box and add them up
v = length x width x height
box 1 = 12 x 14.5 x 5 = 870 ft^3
box 2 = 7x4x5 = 140
now smash them up together = 870+140=1010ft^3
hope that answers your question
This is my question. These are the options below, does anyone know the simplest form?
Answers
Answer:
B. [tex]2ab^5\sqrt{2ab}[/tex]
Step-by-step explanation:
To simplify, first, simplify the integers. The integers include the number 8. To simplify 8, find out what is the largest perfect square that is a factor of 8. In this case, that is 4. Then, divide 8 by that number. This equals [tex]\sqrt{4} *\sqrt{2}[/tex]. Since the square root of 4 is 2, it can be taken out of under the radical. So, the new expression is [tex]2\sqrt{2a^3b^11}[/tex].
Next, simplify the exponents. To simplify exponents under a radical divide the exponent by the root. For example, 3 divided by 2 is 1 with a remainder of 1. So, take the answer out from under the radical and then leave the remainder in the radical. This looks like[tex]\sqrt{a^3} = a\sqrt{a}[/tex]. Then, do this for the other variable, [tex]\sqrt{b^11} = b^5\sqrt{b}[/tex]. Finally, put everything for the final answer, [tex]2ab^5\sqrt{2ab}[/tex].
A translation is shown on the grid below in which triangle A is the pre-image and triangle B is the image.
x+0
x+6
x-6
x+4
Answers
Answer: x+6
Step-by-step explanation:
The cost of plastering in 4 walls of a room whose length is three times its height as wellas twice its breadth at Rs 5per m^2 is Rs 720. What will be the cost of the carpenting the floor of the room at Rs 250per m^2
Answers
Answer:
please mark me brainlist I really need it
Step-by-step explanation:
Say the height of the room is X metres. So the length is 3X, and the breadth is length/2, or 3X/2.
The area of the 4 walls is then 3x^2 + 3X^2 + 3X^2/2 +3X^2/2 = 9X^2
If the cost of plastering is R5/sq m, then 9X^2 * 5 = 720
Solving this gives X = 4 m - a rather high ceiling
The floor area is then (3*4) * (3*4/2) = 72 sq m
Carpeting is then 250*72 = R18000
I’ve been stuck on this for 3 days today is the last day please help me guys
Answers
y = x^2 - 2x - 3
Factored Form: y = (x - 3)(x + 1)
X-Intercepts: (3, 0) and (-1, 0)
Axis of Symmetry: x = 1
Vertex: (1, -4)
Domain: All Real Numbers (or negative infinity to infinity)
Range: y > -4
Hope this helps!
What am i supposed to type here tho, just look at the photo pls
Answers
slope is just "how much up or down" for one step to the right.
its clearly negative here
only -3 seems to be remotely plausible looking at the graph in your screenshot
Answer:
The slope is [tex]-3[/tex]
Step-by-step explanation:
The slope of a line, [tex]m[/tex], that passes through points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
To find the slope of a line, choose two points that it clearly passes through.
In the given graph, the line clearly passes through points (2, 2) and (0, 8).
Let:
[tex](x_1, y_1)\implies (2, 2)\\(x_2, y_2)\implies (0, 8)[/tex]
Substitute into the slope formula:
[tex]m=\frac{8-2}{0-2}=\frac{6}{-2}=\boxed{-3}[/tex]
Therefore, the slope of the line is -3.
Find the surface area of the
rectangular prism.
2 cm
6 cm
3 cm
[?] sq cm
Enter
Answers
Answer:
72 sq cm
Step-by-step explanation:
Surface area of the cuboid is 2*(lb+bh+lh)=2*(12+18+6)=2*36=72
Answer:
36 sq cm
Step-by-step explanation:
This prism is formed by rectangles, and to find the area of a rectangle you have to multiply its sides. So, to find the surface area, you find the area of each rectangle and after add it all:
3×2 = 6 sq cm, and your have two of this rectangles
6×2 = 12 sq cm, and you also have two of this
3×6 = 18 sq cm, and also have two of this
6 + 12 + 18 = 36 sq cm
Please help me, asap
Answers
Answer:
10
Step-by-step explanation:
(10*2) ÷ (1+1)
Parentheses first
20 ÷2
Then divide
10
Answer:
The answer to the equation is 10.
Step-by-step explanation:
Use PEMDAS/Order of operations.
Parentheses go first.
(10*2) divided by (1+1)
remove the parentheses after working on the equation in them
20 divided by 2
20/2=10
the answer is 10
If you have any questions tell me them in the comments, I will come answer them. Have a good day.
$60 is shared between Ali, Ben and Carol in the ratio of 5 :3 : Z How much does Ben get?
Answers
Answer:
the answer is 100:60:40 hope it helps
which of the following functions are an example of exponential decay???
Answers
Answer:
C. II only
Step-by-step explanation:
iyzgkxhldlufulduo
HIGH POINTS + BRAINLIEST!!!!
Each row shows the tax rate on a specific portion of the taxpayer's taxable income given their filing status. For example, suppose a taxpayer has a filing status of Single and a taxable income of $40,000. This means that the taxpayer owes 10% tax on the first $8,925, 15% tax on the amount over $8,925 up to $36,250, and 25% in the amount over $36,250 up to $ 40,000.
If Abdul and Maria had a filing status of Married Filing Jointly and together have a taxable income of $91,307 in the year 2013, how much did the couple owe for federal income tax?
Do not round any intermediate computations. Round your answer to the nearest dollar.
Answers
Answer:
Step-by-step explanation:
Taxable income = $ 91,307
Tax for $ 17,850 = 10% of 17850 = 0.1*17850 = $ 1785
Tax for $17,850 to $72,500 = 15% of (72,500-17850) = 0.15* 54650 = $ 8197.5
Tax $72,500 to $91,307 = 25% of (91307-72500)=0.25*18807= $ 4701.75
Total tax = 1785 + 8197.5 + 4701.75 = 14684.25
Total tax = $14684
please help me is for my homework
Answers
Answer:
50%
Step-by-step explanation:
so 1 half is colored in so 1/2 is also 50%
Answer:
it's 50% because it's half the circle
Identify the equation of the circle that has its center at (7, -24) and passes
through the origin
A. (x - 7)^2 + (y + 24)^2 = 625
B. (x + 7)^2 + (y - 24)^2 = 25
c. (x - 7)^2 + (y + 24)^2 = 25
D. (x + 7)^2 + (y - 24)^2 = 625
Answers
Answer:
x = 7 e y = -24
Step-by-step explanation:
The equation of the circle that has its centre at (7, -24) and passes through the origin is (x - 7)² + (y + 24)² = 625.
What is an equation of a circle?A circle can be characterized by its centre's location and its radius's length.
Let the centre of the considered circle be at (h,k) coordinate and the radius of the circle be 'r' units.
Then, the equation of that circle would be:
(x-h)²+(y-k)²=r²
The equation of a circle is given as (x-h)²+(y-k)²=r², where (h,k) is the coordinate of the centre of the circle, and r is the radius of the circle.
Since the given circle is needed to pass through the origin and the coordinates of the centre of the circle are (7, -24). Therefore, the distance between the origin and (7, -24) will the radius of the circle.
Therefore, the radius of the circle will be,
Radius = √[(7-0)² + (-24 - 0)²]
= √(49 + 576)
= √(625)
= 25
Now, the equation of the circle that is centred at (7, -24) and has a radius of 25 units is,
(x - h)² + (y - k)² = r²
[x - 7]² + [y - (-24)]² = (25)²
(x - 7)² + (y + 24)² = 625
Hence, the equation of the circle that has its centre at (7, -24) and passes through the origin is (x - 7)² + (y + 24)² = 625.
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Evaluate the expression
Answers
Answer:
Is -15
Step-by-step explanation:
Explain how to combine the terms 5x an 3x
Answers
Answer:
below
Step-by-step explanation:
In short, we will add both coefficients together to combine like terms.
3x + 5x → x(3 + 5) → 8x
If you have a value like 2x and 2, you cannot combine them because they do not have the same variable.
Best of Luck!
CAN SOMEBODY HELP ME PLS GIVE THE CORRECT ANSWER IM FAILING BUT ITs PYTHAGOREAN THEOREM
Answers
Answer:
c=65
Step-by-step explanation:
Answer:
c=65
Step-by-step explanation:
c=a2+b2=63
632+162=65
please
[tex] \sin(120) \\ \tan( \frac{3\pi}{4} ) [/tex]
help me I need help
Answers
Answer:
[tex] \sin(120) \\ = \sin(90 + 30) \\ = \cos(30) \\ = \frac{ \sqrt{3} }{2} \\ \\ \tan( \frac{3\pi}{4} ) \\ = \tan(135) \\ = \tan(90 + 45) \\ = - \cot(45) \\ = - 1[/tex]
[tex]\\ \rm\longmapsto sin120[/tex]
[tex]\\ \rm\longmapsto sin(90+30)[/tex]
[tex]\\ \rm\longmapsto cos30[/tex]
[tex]\\ \rm\longmapsto \dfrac{\sqrt{3}}{2}[/tex]
Now
[tex]\\ \rm\longmapsto tan\left(\dfrac{2\pi}{4}\right)[/tex]
[tex]\\ \rm\longmapsto tan135[/tex]
[tex]\\ \rm\longmapsto -1[/tex]
Which two ratios represent quantities that are proportional? A 25/28 and 5/7 B 22/33 and 14/21 C 16/13 and 13/16 D 48/60 and 35/42
Answers
Answer:
Step-by-step explanation:
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
Which ratio is not equivalent to the others?
A. 1:3
B. 36
C. 7 to 14
D. 816
Answers
Answer:
a. 1:3
Step-by-step explanation:
theres a pattern of x^2 but 1:3 is 1x3
HELP!!!!!! so many points for this one!!!!!! x^2+y^2+4x-2y=-1
The equation of a circle in the xy-plane is shown above. What is the radius of the circle
A.2
B.3
C.4
D.9
Answers
Answer:
A. 2Step-by-step explanation:
Given circle:
x² + y² + 4x - 2y = -1Convert the equation into the standard form of (x - k)² + (y - h)² = r²:
x² + 4x + 4 + y² - 2y + 1 = -1 + 4 + 1(x + 2)² + (y - 1)² = 2²As per above:
r = 2Correct choice is A
A.2
Answer:
Solution given:
equation of a circle is:
x²+y²+4x-2y=-1
x²+y²+4x-2y+1=0
Comparing above equation with
ax²+by²+2gx+2fy+c=0
we get
a=1
b=1
g=2
f=-1
c=1
now
radius of a circle (r)=[tex]\sqrt{g²+f²-c}[/tex]
substituting value
r=[tex]\sqrt{2²+(-1)²-1}=2[/tex]
therefore radius of a circle is 2 units
40) what is the area of a rectangular porch measuring 8 ft x 12/f
45) Create a stem and leaf plot to represent this set of data.
30, 62, 32, 63, 43, 77, 48, 78, 49, 82, 51, 84, 60,
please make sure to answer both questions
Answers
[tex]\frac{1}{4}X - 1 = 13[/tex]
Answers
Answer:
x =56
Step-by-step explanation:
1/4 x - 1 =13
Add 1 to each side
1/4x - 1+1 = 13+1
1/4 x = 14
Multiply each side by 4
1/4x * 4 = 14*4
x =56
x = 56
Step-by-step explanation:
1/4x - 1 = 13
Add 1 to both sides
1/4x = 14
Isolate the variable
x = 14/0.25
x = 56
Find the missing side length.
Assume that all intersecting sides meet at right angles.
Be sure to include the correct unit in your answer.
Answers
Answer: 9ft
One side is given 16ft
The other is 7ft
The 7ft is in the same length of the 16ft line
So 16-7 = 9ft
Must click thanks and mark brainliest
Frank can type a report in 2 hours and James takes 7 hours. How long will it take the
two of them typing together?
Answers
Answer: x = 1 hour and 33 minutes
Step-by-step explanation:
Let x = time (hours) it takes typing together
then
x(1/2 + 1/7) = 1
multiplying both sides by 14:
x(7 + 2) = 14
x(9) = 14
x = 14/9
x = 1.56 hours
or
x = 1 hour and 33 minutes
Hope tjis help you!:)
Answer: 14/9 hr
Step-by-step explanation:
If you divide Frank's ability to write 1 report by 2 hours, he could write half a report in an hour. James could write one seventh of the report in a hour after dividing his ability to write 1 report in 7 hours. Find the least common denominator between 2 and 7, which is 14 convert 1/2 to that, which would be 7/14 and 2/14. Add That together and you'd get the amount of report they can write in an hour. If you multiply this by a number equalvilent to flipping 9/14, you'd get 1. This number is 14/9 hours.
