Answers
Answer:
The gradient of line perpendicular to AB is: m = [tex]\frac{1}{2}[/tex]
The equation of line passing through point A and perpendicular to AB is [tex]\mathbf{y=\frac{1}{2}x+6}[/tex]
Step-by-step explanation:
The line on the graph passes through the points A (0,6) and B (3,0)
b) Find the gradient of a line perpendicular to AB
First we will find gradient (slope) of AB
The formula used to find Slope is: [tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
We have [tex]x_1=0, y_1=6, x_2=3, y_2=0[/tex]
Putting values and finding slope:
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{0-6}{3-0}\\Slope=\frac{-6}{3}\\Slope=-2[/tex]
So, we get slope: m = -2
Now, the gradient of line perpendicular to AB will be opposite to the slope of AB
The gradient of line perpendicular to AB is: m = [tex]\frac{1}{2}[/tex]
c) Find the equation of line passing through point A and perpendicular to AB
The equation of line can be found using slope m = [tex]\frac{1}{2}[/tex] and y-intercept b
We need to find y-intercept b:
Using slope m = [tex]\frac{1}{2}[/tex] and point A (0,6)
y=mx+b
6= [tex]\frac{1}{2}[/tex] (0)+b
6=0+b
b=6
So, y-intercept is b =6
So, Equation of line with slope m = [tex]\frac{1}{2}[/tex] and y-intercept b =6 is:
[tex]y=mx+b\\y=\frac{1}{2}x+6[/tex]
So, The equation of line passing through point A and perpendicular to AB is [tex]\mathbf{y=\frac{1}{2}x+6}[/tex]
Related Questions
△RST ~ △RYX by the SSS similarity theorem.
Which ratio is also equal to StartFraction R T Over R X EndFraction and StartFraction R S Over R Y EndFraction?
StartFraction X Y Over T S EndFraction
StartFraction S Y Over R Y EndFraction
StartFraction R X Over X T EndFraction
StartFraction S T Over Y X EndFraction
Answers
Answer:
Answer would most likely be option D. StartFraction S T Over Y X EndFraction
Explanation:
Take care..
Help me out with this, homes
Answers
Answer:
2
Step-by-step explanation:
2
In the chemical formula 2SO2, how many total atoms of oxygen (O) are there?
Answers
Answer:
4
Step-by-step explanation:
2 molecules of SO2
each molecule contains 2 atoms of Oxygen
Answer:
Step-by-step explanation:
Can y’all help me with this
Answers
Answer:
24.45cm squared
Step-by-step explanation:
(9 x 12) - ((6 x 3.14) / 2)
Consider two people where one person is 25% taller than the other but proportion in exactly the same way That the taller person looks like a lager version of the shorter person Suppose the shorter person has a 36%-inch waist what size is the the taller person's waist?
Answers
Answer:
46.8 inches
Step-by-step explanation:
Taller person = 30% more than height of shorter individual
Waist size of shorter person = 36 inches
Since they are proportioned in the same way:
Waist size of the taller person will be 30% larger than the waist size of the shorter person :
30% increase in size 36
(100 + 30)% of 36
130% of 36
(130 / 100) * 36
1.3 * 36
= 46.8 inches
Mini made a recipe that yields 4 and 1 over 2 cups. If each serving is 1 over 2 cup, which expression will help Mini determine the number of servings her recipe will yield?
Answers
Answer:
1/2x = 4 1/2
Where x = Number of servings = 9 servings
Step-by-step explanation:
Mini made a recipe that yields 4 and 1 over 2 cups.
1 recipe = 4 1/2 cups
1 serving = 1/2 cups
1/2 cups = 1 servings
4 1/2 cups = x servings
Cross Multiply
1/2 × x = 4 1/2
x = 4 1/2 ÷ 1/2
x = 9/2 ÷ 1/2
x = 9/2 × 2
x = 9 servings.
Therefore, the expression tha will help Mini to determine the number of servings her recipe will yield is
1/2x = 4 1/2
Where x = Number of servings = 9 servings
i dont know plz help
Answers
Consider the volume of a rectangular pyramid, one whose base is not square. Does changing one of the three variables (length, width, or helght)
by a given fraction have a greater effect on the volume of the pyramid than changing either of the other two variables? That is, which variable, if
any, has the largest influence on the volume? Assume that the other two variables remain constant. Explain your answer.
Answers
Answer:
dobt worry il heñp il solve
I REALLY NEED HELP ON THIS!!!!!! I WILL MARK BRAINLIEST
Answers
Answer:
y = 2,500x + 5,000
Rate of change = $2500 a year
Initial value = $5000
Step-by-step explanation:
We have 3 values to figure what is the function here, the rate of change, and the initial value.
To find the initial value, find where y is located where x is 0. In this case it's $5000, so that's the initial value.
Now the rate of change. Find y where x is 1. That is $7,500. Subtract $5000 from to get the rate of change, since it's the same. It's constant because of a straight diagonal line.
$7,500 - $5,000 = +$2,500/year
Now the equation. This is not proportional, because y's starting point is not 0. It's greater than that, so an addition sign is in the equation. Do you remember our initial value? That's right! It was $5,000, so put that after the addition sign.
y = ????x + 5,000
You also need to remember the rate of change, which was 2,500. Put that on the left of the addition sign and there's your equation!
y = 2,500x + 5,000
Answer:
y=2500x + 5000
2500
5000
Step-by-step explanation:
if the mean of 6 7 13 and 10 is 8 find the range
Answers
Answer:
hope this hlo u
Step-by-step explanation:
range =highest observation-lowest observation
range=10-6
=4
13-8
5
The equation of a curve is
[tex]y = 4x {}^{3} + 4px {}^{2} + 16x - 9[/tex]
Find the range of values of p such that y is an increasing function.
Answers
Let's solve for p.
[tex]y=4x3+4px2+16x−9[/tex]
Step 1: Flip the equation.
[tex]4px2+4x3+16x−9=y[/tex]
Step 2: Add -4x^3 to both sides.
[tex]4px2+4x3+16x−9+−4x3=y+−4x3[/tex]
[tex]4px2+16x−9=−4x3+y[/tex]
Step 3: Add -16x to both sides.
[tex]4px2+16x−9+−16x=−4x3+y+−16x[/tex]
[tex]4px2−9=−4x3−16x+y[/tex]
Step 4: Add 9 to both sides.
[tex]4px2−9+9=−4x3−16x+y+9[/tex]
[tex]4px2=−4x3−16x+y+9[/tex]
Step 5: Divide both sides by 4x^2.
4px² / 4x² = −4x³ − 16x + y + 9 / 4x²
Answer:
p = −4x³ − 16x + y + 9 / 4x²
Please help me with this question!!
Answers
Step-by-step explanation:
according to pythagoras theorem
Hypotenuse2 = Perpendicular2 + Base2
c2 = a2 + b2
therefore,
x2 = (4)2 + (4)2
x2 = 16 + 16
x2 = 32
x = √32
hence, x = 4√2
A is what percent of B? Pls help???
Answers
Answer:
If you want to know what percent A is of B, you simple divide A by B, then take that number and move the decimal place two spaces to the right. That's your percentage!
Step-by-step explanation: There is no exact answer and it would be null. You didn't even give an image
What is the slope of the line with equation y - 3= -1/2(x - 2)
Answers
Answer:
-1/2
Step-by-step explanation:
according to what I learnt, the general form of every equation is y=mx+c where y is the y value, x is the x value, m is the slope and c is the y-intercept so the equation y-3= -1/2(x - 2) in the general form wil be :
y= -x/2+4 and so m= -x/2 ,that is -1/2
Find the slope of the line through each pair of points
(-20,-4), (-12,-10)
Answers
Answer:
is it just the slope of those points? if so -3/4
Step-by-step explanation:
i think. if not correct me
Answer:
[tex]-\frac{3}{4}[/tex]
Step-by-step explanation:
The slope of a line is given by:
[tex]m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}[/tex]
Therefore, the slope of the line that passes through these points is:
[tex]m=\frac{-10-(-4)}{-12-(-20)}=\frac{-6}{8}=\fbox{$-\frac{3}{4}$}[/tex].
Find the Values of y
Y ² = 169
Answers
Answer:
Y= 13,-13
Step-by-step explanation:
Subract the sum of 3a^4b-4b^3+c^2 & 6a^4b+3b^3-6c^2 from the sum of 6a^4b-4b^3-4c^2 & 2a^4b+4b^3+7c^
Answers
Answer:
-a^4b + b^3 - 8c^2
Step-by-step explanation:
Sum of
3a^4b-4b^3+c^2 + 6a^4b+3b^3-6c^2
= 3a^4b + 6a^4b - 4b^3 + 3b^3 + c^2 - 6c^2
= 9a^4b - b^3 - 5c^2
Sum of
6a^4b-4b^3-4c^2 + 2a^4b+4b^3+7c^
= 6a^4b + 2a^4b - 4b^3 + 4b^3 - 4c^2 + 7c^2
= 8a^4b + 3c^2
Subtract
8a^4b + 3c^2 - (9a^4b - b^3 - 5c^2)
= 8a^4b + 3c^2 - 9a^4b + b^3 + 5c^2
= 8a^4b - 9a^4b + b^3 + 3c^2 + 5c^2
= -a^4b + b^3 - 8c^2
3 (m+6) +7 (m-2)
7(6x + 5) - 8
4(3x + 5) - 13
Answers
Answer:SAME SIGNS 1. Add.
2. Sum is positive if both are positive; negative if both are negative.
5 + 8 = 13 –5 + (–8) = –13
DIFFERENT SIGNS
1. Subtract the absolute values.
2. Answer is sign of the integer with the greater absolute value.
5 + (–8) = –3 –5 + 8 = 3
Find each sum. 1. –4 + (–8)
–12
4. –16 + 11 –5
7. –49 + (–32)
–49 –81 –32 –81
2. 14 + 16 30
5. 28 +(–42) –14
8. 23 + (–23) 0
3. –43 + (–12) –55
6. 75 + (–5) 70
9. 86 + (–18)
86 68–18 68
Integers
Multiplying & Dividing
RULE
EXAMPLES
1. Multiply or divide.
2. The answer is positive if the signs are the same (both positive or both negative); negative if the signs are different (one positive and one negative).
–5 x(–8) = 40 40 4 = 10
16 x(–3) = –48 –20 10 = –2
Find each product or quotient.
1. –3 x (–8) 24
4. 0 x (–121)
0 5 –13
2. –5 x (–5) 25
3. –15 x 3 –45
5. –35 (–7)
6. –65 5
7. 240 (–4) 8. 36 12 9. (–49 7) x 8 –7 x 8
–60 3
–56
Step-by-step explanation:
share $180 between anna and barry so that Anna share to barry share is in the ratio 4:5
Answers
Answer:
Anna: $80
Barry: $100
Step-by-step explanation:
total of 9 shares
each 20 dollars
4(20) = 80
5(20) = 100
Please help!!
How do I rewrite this expression into radical form??
Answers
PLEASE HELP MEEEE!!!!!!!
Answers
Answer:
its a black picture...?
Step-by-step explanation:
Albert, bill, claire, and David are all siblings. Bill was born 2 years after Albert. Claire's favourite colour is orange and she is currently half the age of Albert. David enjoys golf and swimming and he is 3 times older than Bill.
The total of their age is 113 using algebraic methods find out their exact age
what is their exact age
Answers
Answer:
Albert = 22
Bill = 22 - 2 = 20
Claire = 22/2 = 11
David = 3(20) = 60
Step-by-step explanation:
Let Albert's age = x
Bill = x - 2
Claire = x/2
David = 3(x - 2)
Total sum of their ages = 113
x + x - 2 + 0.5x + 3(x - 2) = 113
x + x - 2 + 0.5x + 3x - 6 = 113
x + x + 3x + 0.5x -2 - 6 = 113
5.5x - 8 = 113
5.5x = 113 + 8
5.5x = 121
x = 121 / 5.5
x = 22
Albert = 22
Bill = 22 - 2 = 20
Claire = 22/2 = 11
David = 3(20) = 60
Convert the following repeating decimal to a fraction in simplest form.
.6
Answers
Answer:
2/3
Step-by-step explanation:
Answer:
7/10
Step-by-step explanation:
0.6 is a repeating decimal in this case, so you can round it to .7
From there, you simply put it over ten because you cant break seven down any more than that in a simple fraction.
Can someone please explain to me how I would do this, I cannot figure out how to do this equation at all!!
Answers
Answer:
First, do 4x*4x. then,16x*16x. next, 64x*64x. and,256x*256x. answer:1024x. Divide 1024x by 8x. answer to that is 128.
Answer:
The expression in simplified form:
[tex]\frac{4x^5}{8x}=\frac{x^4}{2}[/tex]
Step-by-step explanation:
Given the expression
[tex]\frac{4x^5}{8x}[/tex]
We need to simplify the expression.
Simplifying the expression
[tex]\frac{4x^5}{8x}[/tex]
Cancel the common factor: 4
[tex]=\frac{x^5}{2x}[/tex]
Cancel the common factor
[tex]=\frac{x^4}{2}[/tex]
Therefore, the expression in simplified form:
[tex]\frac{4x^5}{8x}=\frac{x^4}{2}[/tex]
43 decreased by a number B
Answers
Answer:
43 - B = x
Step-by-step explanation:
When decreasing, you are subtracting, so the equation for this problem would be 43 minus B equals whatever quantity you were given as a solution.
You have 42 coins with a total value of $3.00. Some of the coins are dimes, and the rest are quarters.
Select the two equations that would create the best system of equations to represent this scenario.
Answers
Answer:
1. $3.00+42=$3.42
2. 4 Dimes , 2 Pennies
Step-by-step explanation:
2. 4 Dimes = 40 cents , 2 pennies = 2 cents
1. Add up 3.00+42 and that is how you could get the answer for number 1 .
make x the subject. 4x-5=t(x+m)
Answers
Answer:
x= tm+5/4-t
Step-by-step explanation:
4x-5=t(x+5)
4x-5-=tx+tm distributive
4x-5-tx=tm substract tx from both sides
4x-tx=tm+5 add 5 to both sides
x * 4+ x(-t) =tm+5 factor x out 4x-tx
x(4-t)=tm+5 factor x out x*4 + x(-t)
x(4-t)/4-t= tm/4-t+ 5/4-t divide each term in 4-t
x= tm/4-t + 5/4-t combine the numerators over the common denominator
x=tm+5/4-t
A video game is on sale for $55. If the discount was
14%, what was the original price?
Answers
Answer:
$77
Step-by-step explanation:
i just take 55 x 0.14 which is 7.7 then i moved the decimal 1 place to the right.
Answer:
I believe the answer it 62.70
although I am not completely sure
Step-by-step explanation:
14% of 55 = 7.7
7.7 + 55 = 62.7
= $62.70
HELP I NEED HELP ASAP
Taxi Driver A(x)=1.50x+5 and Taxi Driver B charges B(x)=1.25x+8 where x is the number of miles driven. After how many miles will the cost be the same for each taxi driver?
Answers
Answer:
12 miles
Step-by-step explanation:
1.25x + 8 =1.5x+5
1.25x-1.5x=5-8
-0.25x=-3
-0.25x/-0.25x=-3/-0.25
x= 12
Pleaseee help this is urgent!!! I need it in English! Please show all the work ! 14 points
Answers
Answer:
width = 40 feet, length = 90 feet
Step-by-step explanation:
length = 2w + 10
width = w
Perimeter = 260
Perimeter of rectangle = 2length + 2width
Sub the values into that equation:
260 = 2(2w + 10) + 2(w)
260 = 4w + 20 + 2w
260 = 6w + 20
260 - 20 = 6w
240 = 6w
w = 240/6
w = 40
So now we know the width of the garden is 40 feet.
To find the length, substitute the width into the length equation:
length = 2w + 10
length = 2(40) + 10
length = 90 feet
length = 90 feet, width = 40 feet