Answer:
The percentage change is 140%
Step-by-step explanation:
Given
[tex]L= 3W_1[/tex] ---- initial dimension
[tex]W_2 = 6m[/tex] --- new width
[tex]A_2 = 45m^2[/tex] --- new dimension
Required
The percentage increment
The length remains constant because only the width is extended.
The new area is:
[tex]Area =Length * Width[/tex]
[tex]A_2=L * W_2[/tex]
Make L the subject
[tex]L = \frac{A_2}{ W_2}[/tex]
Substitute values for A and W
[tex]L = \frac{45m^2}{6m}[/tex]
[tex]L = \frac{45m}{6}[/tex]
[tex]L = 7.5m[/tex] --- this is the length of the garden
Calculate the initial width:
[tex]L= 3W_1[/tex]
Make W1 the subject
[tex]W_1 = \frac{1}{3} * L[/tex]
[tex]W_1 = \frac{1}{3} * 7.5[/tex]
[tex]W_1 = 2.5[/tex]
So, the initial area is:
[tex]A_1 = L_1 * W_1[/tex]
[tex]A_1 = 2.5 * 7.5[/tex]
[tex]A_1 = 18.75[/tex]
The percentage change in area is:
[tex]\%A = \frac{A_2 - A_1}{A_1}[/tex]
[tex]\%A = \frac{45 - 18.75}{18.75}[/tex]
[tex]\%A = \frac{26.25}{18.75}[/tex]
[tex]\%A = 1.4[/tex]
Express as percentage
[tex]\%A = 1.4*100\%[/tex]
[tex]\%A = 140\%[/tex]
3x<11.75 solve for x please, with step on how you got to that answer!
Answer:
See below
Step-by-step explanation:
3x < 11.75
11.75 / 3 = 3.92
x < 3.92
Find the second derivative of the function.
Answer:
[tex] \displaystyle d)\frac{d ^{2} y}{d{x}^{2} } = 2 + \frac{ 42}{ {x}^{4} }[/tex]
Step-by-step explanation:
we would like to figure out the second derivative of the following:
[tex] \displaystyle y = \frac{ {x}^{4} + 7}{ {x}^{2} } [/tex]
we can rewrite it thus rewrite:
[tex] \displaystyle y = {x}^{2} + 7 {x}^{ - 2} [/tex]
take derivative in both sides:
[tex] \displaystyle \frac{dy}{dx} = \frac{d}{dx}( {x}^{2} + 7 {x}^{ - 2} )[/tex]
by sum derivation we obtain:
[tex] \displaystyle \frac{dy}{dx} = \frac{d}{dx}{x}^{2} + \frac{d}{dx} 7 {x}^{ - 2}[/tex]
by exponent derivation we acquire:
[tex] \displaystyle \frac{dy}{dx} = 2{x}^{} - 14 {x}^{ - 3}[/tex]
take derivative In both sides once again:
[tex] \displaystyle \frac{d ^{2} y}{d{x}^{2} } = \frac{d}{d x } (2{x}^{} - 14 {x}^{ - 3})[/tex]
use difference rule which yields:
[tex] \displaystyle \frac{d ^{2} y}{d{x}^{2} } = \frac{d}{d x } 2{x}^{} - \frac{d}{dx} 14{x}^{ - 3}[/tex]
use exponent derivation which yields:
[tex] \displaystyle \frac{d ^{2} y}{d{x}^{2} } = 2 + 42{x}^{ - 4}[/tex]
by law of exponent we get:
[tex] \displaystyle \frac{d ^{2} y}{d{x}^{2} } = 2 + \frac{ 42}{ {x}^{4} }[/tex]
hence, our answer is d)
Triangle ABC ~ Triangle DEF. Measure of angle A = 30 degrees and measure of angle F = 65 degrees. AB=20, DE = 35, EF= 28.
Find measure of angles B, E, D and C and the length of BC.
Answer:
< B = 180-30-65=85°
< E = 85°
< D = 30°
< C = 65°
BC = 20/35 × 28 = 16
Please help fast for question A and B I’d appreciate it
Step-by-step explanation:
a) Since the precision of the ruler is 1 mm, the uncertainty associated with this ruler is +-0.5mm. So the tire tread has a depth of 7.0 mm +- 0.5mm. The amount of tire thread that has worn off is
11.2 mm - (7.0 mm +- 0.5 mm) = 4.2 +- 0.5 mm
b) The tire thread can anywhere between 3.1 mm and 3.5 mm. Since the lower limit has gone below the legal limit of 3.2 mm, it's time to change the tire.
A water pail in your backyard has a small hole in it. You notice that it has drained a total of 2.5 liters in 4 days. What is the average change in water volume each day?
Answer:
0.625 liters
Step-by-step explanation:
Given data
volume drained= 2.5Liters
Time= 4 days
Now the if 4 days leakage will produce a volume of 2.5Liters
Then 1 day will produce a volume of x liters
cross multiply
4x= 2.5
x= 2.5/4
x= 0.625 liters per day
Hence, each day will produce 0.625 liters
Expand and simplify:
(x + 1)(2x - 3)
with the explaining the steps
====================================
Work Shown:
(x+1)(2x-3)
y(2x-3)
2xy - 3y
2x( y ) - 3( y )
2x( x+1 ) - 3( x+1 )
2x^2+2x - 3x-3
2x^2 - x - 3
Explanation:
In the second step, I replaced all of (x+1) with y. Afterward, I distributed that y term through. A few steps later, I replaced y with x+1 to help finish up the distributions. You could use the FOIL rule as an alternative approach.
solve for q: plz help
Answer:
-0.67 rounded to hundredths
Step-by-step explanation:
3×(q + 4/3) = 2
q + 4/3 = 2/3
q = -2/3 = -0.666666666666...
How do you factor the quadratic equation 3x^2 + 8x + 3 to find the roots?
Answer:
Step-by-step explanation:
Hope this helps u!!
solve the inequality 2-x<7
Answer:
x>-5
Step-by-step explanation:
2-x<7
Subtract 2 from each side
2-x-2<7-2
-x<5
Multiply each side by -1, remembering to flip the inequality
x>-5
Please can someone help me ?
Answer:
Step-by-step explanation:
1/(3x+5)(3x-5) - 1/2(3x+5)
2 - (3x-5)
2(3x+5)(3x-5)
2-3x+5
2(3x+5)(3x-5)
-3x + 7
2(3x+5)(3x-5)
The point-slope form of the equation of a line that passes through points (8. 4) and (0, 2) is y-4 = (x-8). What
is the slope-intercept form of the equation for this line?
O y= 2 x - 12
O y=-x-4
o y=+*+2
O y=x+6
Answer:
answer y=x-4
Step-by-step explanation:
slope intercept from is y=mx+b
m=slope b=y intercept
convert current equation to slope intercept
y-4=x-8
add 4 to both sides
y=-x-4
determine the slope between -2,6 3,4
Simplify...................
Answer:
(a+b)/2(a-b)
Step-by-step explanation:
Explained in the paper
Goodluck
URGENT PLEASE HELP: Simplify
Answer:
cot (x)
Step-by-step explanation:
cot x
---------------
cos x sec x
We know that sec = 1/ cos
cot x
---------------
cos x 1/ cos x
cot x
---------------
1
cot (x)
Answer:
You're clicking on the correct answer, it's cot with that symbol, I dont have the symbol.
Pls, help me with this geometry question.
Answer:
x=45 degree
Step-by-step explanation:
x+135=180 degree (0pposite angles of a inscribed quadilateral in a circle are supplement of eaach other)
x=180-135
x=45 degree
write and solve an equation given the following information. Angles 1 and 2 are complementary. the measure of angle 2 is 18 larger than the measure of angle 1.
A.) x + (x + 18) = 90, x = 36
B.) x + (x + 18) = 180, x = 81
C.) 2x + 72 = 90, x = 9
D.) x + (x - 18) = 90, x = 54
Will give brainlist!!
List all the possible numbers for ALL 4 Quadrants (in terms of negative, positive).
What Quadrant would the following numbers be in:
-4, -6 ______
+5, +5______
-4, +1 ______
+3, -7 _____
Two basketballs are thrown along different paths. Determine if the basketballs’ paths are parallel to each
other, perpendicular or neither. Explain your reasoning.
o The first basketball is along the path 3x + 4y = 12
o The second basketball is along the path -6x – 8y = 24
Answer:
Since the slopes of the two equations are equivalent, the basketballs' paths are parallel.
Step-by-step explanation:
Remember that:
Two lines are parallel if their slopes are equivalent. Two lines are perpendicular if their slopes are negative reciprocals of each other. And two lines are neither if neither of the two cases above apply.So, let's find the slope of each equation.
The first basketball is modeled by:
[tex]\displaystyle 3x+4y=12[/tex]
We can convert this into slope-intercept form. Subtract 3x from both sides:
[tex]4y=-3x+12[/tex]
And divide both sides by four:
[tex]\displaystyle y=-\frac{3}{4}x+3[/tex]
So, the slope of the first basketball is -3/4.
The second basketball is modeled by:
[tex]-6x-8y=24[/tex]
Again, let's convert this into slope-intercept form. Add 6x to both sides:
[tex]-8y=6x+24[/tex]
And divide both sides by negative eight:
[tex]\displaystyle y=-\frac{3}{4}x-3[/tex]
So, the slope of the second basketball is also -3/4.
Since the slopes of the two equations are equivalent, the basketballs' paths are parallel.
Some angles are shown. Complete each of the 2 activities for this Task. Activity 1 of 2 The measure of angle NOP is 140°. Which of these equations could be used to find the measure of angle NOQ? A. 23+x=140 B. x−23=140 C. 23×x=140 D. 140÷23=x Activity 2 of 2 What is the measure, in degrees, of angle NOQ?
Answer:
A. 23+x=140
Step-by-step explanation:
The angle addition postulate states that the measure of a larger angle formed by two or more smaller angles placed side by side is the the sum of the smaller angles. The angle addition postulate states that if B is in the interior of AOC , then:
m∠AOB + m∠BOC = m∠AOC.
From the image:
∠NOP = ∠NOQ + ∠QOP
∠NOP = 140, ∠NOQ = x, ∠QOP = 23
substituting:
140 = x + 23
x = 140 - 23 = 117
∠NOQ = 117°
Taxi A charges a fee of $3.50, plus $1.75 per mile. Taxi B charges a few of $1.25, plus $2.00 per mile. At what distance would the taxi cost the same?
Please someone help i'm struggling with this work!
Answer:
5es7tc6fz8s5exf UFO zd5d 3azyfxf6f,a3
Step-by-step explanation:
It is abe
SOMEONE PLEASE HELP ME!!!!
Answer:
Step-by-step explanation:
scale factor=17/36
A rectangle has a length of 30 and A diagonal that measures 34. What is the width of the rectangle? (Round your answer to the nearest tenth)
Answer:
45.34
Step-by-step explanation:
you have to use the pythagorean theorem
a cylinder and sphere both have the same diameter and the same volume. if the height of the cylinder is 36cm,
find their common radius?
Answer:
27
Step-by-step explanation:
V_cylinder = pi r^2 h
h = 36
V_cylinder = 36 pi r^2
V_Sphere = 4/3 * pi * r^3
But the volumes are given as equal
36pi r^2 = (4/3) pi r^3 divide by pi r^2
36 = 4/3 r Multiply both sides by3/4
36 * 3/4 = r
r = 27
x^2 times x^2 times 5
Answer:
5x^4
Step-by-step explanation:
Re-order terms so constants are on the left
x^2*x^2*5
5x^2*x^2
Combine exponents
5x^2*x^2
5x^4
(PLS GIVE brainliest)Which pairs of angles in the figure below are vertical angles?
Check all that apply
Answer:
[see below]
Step-by-step explanation:
Vertical angles are simply opposite angles that are made from intersecting lines.
The most appropriate pairs would be vertical pairs:
∠NSI and ∠TSW
∠NST and ∠ISW
The angles are opposite of each other and formed from the two lines.
Hope this helps.
Estimate 28 x 31 x 3
Answer:
2604
Step-by-step explanation:
Answer:
2600 as a estimate but it is 2604
Step-by-step explanation:
if x= 3-2^2 then find the value of x^2+1÷x^2
X = 3-2^2
Simplify x:
3-4 = -1
X = -1
Replace x in the equation and solve:
(-1) ^2 + 1 /(-1)^2
(-1)^2 = 1
Simplify to get 1 + 1/1 = 1+ 1 = 2
The answer = 2
Help please help 50 points!!!!! no links or i will report if you know how to solve just answeer pllllease !!
Answer:
39.6 degrees
Step-by-step explanation:
There are 176 baseball answers out of 1600
There are 360 degrees in a circle
Multiply the fraction of baseball responses by the degrees in a circle
176/1600 * 360
198/5
39.6 degrees
A business purchases a computer system for $3,000. The value of the
system decreases at a rate of 15% per year. What is the computer system
value after 5 years?
Answer: $6335.76
Step-by-step explanation:
you would do 3,000 times 105% = 3450
then you would do 3450 times 105% = 3967.5 then you would do 3967.5 times 105% = 4562.62 then you would do 4562.62 times 105% = 5247.01 next you would do 5247.01 times 105% = 6034.06 finally you would do 6034.06 times 105% = 6335.76