Answers
This directly proportional relationship between p and q is written as p∝q where that middle sign is the sign of proportionality. The value of y can be found as shown below.
What is the directly proportional and inversely proportional relationship?Let there are two variables p and q
Then, p and q are said to be directly proportional to each other if
p = kq
where k is some constant number called the constant of proportionality.
This directly proportional relationship between p and q is written as
p∝ q where that middle sign is the sign of proportionality.
In a directly proportional relationship, increasing one variable will increase another.
Now let m and n be two variables.
Then m and n are said to be inversely proportional to each other if
[tex]m = \dfrac{c}{n} \\\\ \text{or} \\\\ n = \dfrac{c}{m}[/tex]
(both are equal)
where c is a constant number called the constant of proportionality.
This inversely proportional relationship is denoted by
[tex]m \propto \dfrac{1}{n} \\\\ \text{or} \\\\n \propto \dfrac{1}{m}[/tex]
As visible, increasing one variable will decrease the other variable if both are inversely proportional.
1.) The relation can be written as,
y ∝ x
y = kx
27 = k × 3
k = 9
Value of y, when x=4 is,
y = 9 × 4 = 36
2.) The relation can be written as,
y ∝ x²
y = k x²
160 = k × 4²
160 = k × 16
k = 10
Value of y, when x=6 is,
y = 10 × 36 = 360
3.) The relation can be written as,
y ∝ (1/x)
y = k/x
16 = k × (1/2)
k = 32
Value of y, when x=17 is,
y = 32 × (1/17) = 1.8823
4.) The relation can be written as,
y ∝ (1/x²)
y = k(1/x²)
64 = k × (1/4²)
64 = k × (1/16)
k = 1024
Value of y, when x=7 is,
y = 1024 × (1/49) = 20.8979
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Related Questions
On. map with a scale of 1:75 000 the distance between a hotel and the airport is 3 cm
What is the actual distance I'm km?
a. 2.25
b. 2.5
c. 22.5
d. 25 km
please help
Answers
Answer:
a. 2.25 km
Step-by-step explanation:
the scale on a map means how many units in the mapp corresponds to how many units in reality.
in this case
1 cm on the map = 75000 cm in reality =
= 75000/100 m = 750 m =
= 750/1000 km = 0.75 km
3 cm = 3×1 cm = 3 × 0.75 km = 2.25 km
If f(x)=x^2 then evaluate (2+3i)
Answers
Answer:
-5 + 12 i
Step-by-step explanation:
(2 + 3i)^2 = 4 + 6i + 6i + 9i^2
= 4 + 12 i + 9(-1)
= - 5 + 12 i
What is the average rate of change for this exponential function for the
interval from X.= 0 to x = 2?
Answers
Answer:
1.5
Step-by-step explanation:
The average rate of change is 1.5
when x=0 , the value of y =1
when x=2 the value of y = 4
average rate of change formula = [tex]\frac{f(b)-f(a)}{b-a}[/tex]
a= 0 , f(a)=1
b=2, f(b)= 4
4 - 1 / 2 - 0 = 3/2 = 1.5
which is an incorrect rounding for 53.864
A.54
B.53.87
C.53.9
D.50
Answers
The incorrect rounding for 53.864 is 53.87
How to approximation a decimal?The decimal to be approximated is as follows;
53.864
The first option rounded the decimal to 2 significant figures or a whole number.
The second option is incorrect because they rounded it wrongly to 2 decimal places. The correct 2 decimal round is 53.86.
The third option is approximated rightly to one decimal place.
The last option is rounded to the closes tens term.
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Another way to write g(h(x)) is
(gOh)(x)
(hog)(x)
Answers
Answer:
A. Another way to write g(h(x)) is (g×h)(x)
Step-by-step explanation:
Hope this helps!
If not, I am sorry.
y’all help find the area and perimeter
Answers
Answer:
área is 15 perimeter is B
Is this pattern a net for the three-dimensional figure?
no
yes
Answers
Answer:
no
Step-by-step explanation:
the bet displays 3 hexagonal bases when in the figure there is only 2 bases.
Answer:
No.
Step-by-step explanation:
Examples of three-dimensional figures are: Cuboid, Cube, Cylinder, Sphere, Pyramid, and a Cone.
Susan makes purple paint by mixing red and blue paint in the ratio 2:3
She has 12ml of red and 15ml of blue
What is the maximum amount of purple she can make?
Answers
A ratio shows us the number of times a number contains another number. The maximum amount of purple that Susan can make is 25 ml.
What is a Ratio?A ratio shows us the number of times a number contains another number.
Susan makes purple paint by mixing red and blue paint in a ratio of 2:3. Now, if Susan wants to use the complete red paint then,
Purple paint she can make = 2/3 × 6/6 = 12 ml of red paint / 18 ml of blue paint
If Susan wants to use the complete blue paint then,
Purple paint she can make = 2/3 × 5/5 = 10 ml of red paint / 15 ml of blue paint
As per the first condition 18ml of blue paint is needed which is not possible, therefore, the second case is possible.
Thus, Susan needs to mix 10 ml of red paint and 15 ml of blue paint. Therefore, the amount of paint that Susan will make is,
Total Paint = 10ml + 15ml = 25ml
Hence, the maximum amount of purple that Susan can make is 25 ml.
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Please help, I have been trying for a while :(
question on photo
Answers
Answer:
[tex]\frac{x-22}{(x+2)(x-4)}[/tex]
Step-by-step explanation:
multiply the numerator/denominator of the first fraction by (x - 4)
multiply the numerator/denominator of the second fraction by (x + 2)
this ensures that the fractions have a common denominator
[tex]\frac{4}{x+2}[/tex] - [tex]\frac{3}{x-4}[/tex]
= [tex]\frac{4(x-4)}{(x+2)(x-4)}[/tex] - [tex]\frac{3(x+2)}{(x+2)(x-4)}[/tex] ← subtract numerators leaving the common denominator
= [tex]\frac{4x-16-3x-6}{(x+2)(x-4)}[/tex]
=[tex]\frac{x-22}{(x+2)(x-4)}[/tex]
which one is the correct graph
Graph f(x) = -1/2x
Click on the graph until the graph of f(x) = -1/2x appears
Answers
Answer:
The third graph
Step-by-step explanation:
The third graph depicts the function f(x) = -1/2x because for every 1 unit decrease along the y-axis, you travel 2 units on the x-axis.
Also, the two points on the third graph can satisfy the equation.
Point 1: (-2,1)
f(-2) = (-1/2)(-2)
f(-2) = 1
Point 2: (0,0)
f(0) = (-1/2)(0)
f(0) = 0
let pheta be an acute angle. if cos2pheta+cos^2pheta=1, then cospheta=
2/3
1
√6/3
√2/3
Answers
The required value of value of cospheta = √2/3, here correct option is d) √2/3.
The given equation is a Trignomatric Equation,
cos2pheta+cos^2pheta = 1
These are the equation which contains trigonometric operators such as sin, cos.. etc.. In algebraic operation.
cos2pheta + cos^2pheta = 1
Now we know that,
[tex]cos2x[/tex] = [tex]cos^2x -1[/tex]
so, substituting cos2pheta = 2cos^2pheta - 1
2cos^2pheta-1 + cos^2peta = 1
3cos^2peta = 2
cos^2pheta = 2/3
cospheta = √2/3
Thus, the required value for the cospheta = √2/3.
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Can somebody please help answer this word problem using grass method? And showing how u get the answer thanks!!!
WILL MARK BRAINLIEST FOR WHOEVER ANSWERS THIS !!! :DD
Answers
Answer:3/20
Step-by-step explanation:
Fraction of total area mowed = (3/5) + (1/4) = 17/20
Therefore fraction of total area left = 1 - (17/20) = (20/20) - (17/20) = 3/20
Question 1 of 25
Which estimate at a 95% confidence level most likely comes from a small
sample?
Answers
It is possible that a small sample size contributed to the 82% (±24%) estimate at a 95% confidence level.
A proportional confidence interval is provided by
[tex]\pi \pm z \sqrt{\frac{\pi (1-\pi )}{n} }[/tex]
Where π is the sample proportion, z is the critical value and n is the sample size.
The margin of error is represented by
[tex]z \sqrt{\frac{\pi (1-\pi )}{n} }[/tex]
As a result, smaller sample sizes result in wider margins of error. Option A has the greater margin of error in this scenario, so it most likely employed the smallest sample size.
Therefore we can conclude It is possible that a small sample size contributed to the 82% (±24%) estimate at a 95% confidence level. Option A is correct.
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A camper ties a rope from a tree to the ground to help build a shelter. The rope is 8 feet long, and it is tied 6 feet up the tree. How far from the tree is the rope anchored to the ground? Use the Pythagorean theorem to find the answer.
Answers
Answer:
≈5.3 feet,63.6 inches
Step-by-step explanation:
36+b²=64
-36 -36
b²=28
if we square root both sides we can get the radical/exact answer or the rounded one
radical: 4√7
rounded to the nearest tenth: 5.3 feet
48 + what gives you 180
Answers
Answer:
132
Step-by-step explanation:
180-48=132
Answer: 132
Step-by-step explanation:
let x = unknown amount
48 + x = 180
————————————————————————
Solve for x by subtracting 48 from both sides
48 - 48 + x = 180 - 48
x = 132
help me with a maths question thanks a lot!!
Answers
Answer:
Side b is approximately 4.00064cm or since the question asked for the answer to be up to one decimal point, your answer should be 4 cm
Step-by-step explanation:
First of all, this triangle isn't a right triangle. This can be proven if we assume that the triangle is a right triangle. If it is a right triangle, since, one of its angle is 30 degrees, we can find the last unknown angle to = 60 degrees. Therefore, using the side ratios of a 30-60-90 triangle, and since side b is the smallest side (because it has the smallest angle facing it), its length is one half the length of the hypotenuse, therefore making its length 4. However, the 30-60-90 ration also states that, in this case, side b * sqrt(3) should be equal to the side tha measure 7cm, which is clearly not true. Therefore, proving that this triangle isn't a rigt tirangle.
So now, let's get to solving the question. Since we found out that this isn't a right triangle, we have to use the law of cosines which states
a^2 = b^2 + c^2 - 2bc*cos(A) where A is the angle facing side a
If we do this, it comes to the solution that a is approximately 4.00064cm.
Therefore, side b measures to 4.00064cm.
4. If u = {1,2,3,....10) A = { odd numbers up to 9} B = {numbers less than 7). Write out the members of the following sets: (i) AUB (ii) An B (ii) A(prime) U B
Answers
Answer:
i. {1,2,3,4,5,6,7,9}
ii. {1,3,5}
iii. {1,2,3,4,5,6,8,10}
Step-by-step explanation:
U= {1,2,3,4,5,6,7,8,9,10}
A= {1,3,5,7,9}
B= {1,2,3,4,5,6}
A U B = {1,2,3,4,5,6,7,9}
A n B = { 1,3,5}
A (prime) U B =
A(prime)= {2,4,6,8,10}
Therefore A(prime)= {1,2,3,4,5,6,8,10}
A function is a rule thats assigns each value of the independent variable to exactly ____ value of he dependent variable.
Free response:
Answers
A function assigns the values. A function is a rule that assigns each value of the independent variable to exactly each value of the dependent variable.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The given statement can be completed as given below.
A function is a rule that assigns each value of the independent variable to exactly each value of the dependent variable.
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Richard has a debt of $45. Express it in the form of absolute value.
Answers
The absolute value of debt of $45 is 45 because a balance of $0 on an account means there is no debt, and a negative of 45 value represents the debt.
What is debt?It is defined as the amount one party needs to pay to another party as the first party borrowed an amount that will be credited by the second party. Debt occurs when one party cannot be able to purchase something under normal circumstances.
As we know,
The absolute value of a negative account balance is equal to the amount of debt. A balance of $0 on an account means there is no debt. Credit is shown by a positive account balance.
Richard has a debt of $45.
The negative of 45 value represents the debt.
-$45 = debt
Absolute value = |-45| = 45
Thus, the absolute value of debt of $45 is 45 because a balance of $0 on an account means there is no debt, and a negative of 45 value represents the debt.
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I’ve been stuck in this for almost 20 minutes
help :/
Answers
Answer:
pi/2 units to the left
Step-by-step explanation:
the formula is y = cos(x-b) so when b is negative, the formula will show a plus sign because minus negative is adding. this means the graph is shifted -pi/2 to the right which is really pi/2 to the left
Today an electronics store took
5% off the price of a computer,
and for the next two days, it will
take 5% off the previous day's
price. if the price of the
computer yesterday was
$2000.00, what will be the price
of the computer two days from
now?
Answers
Answer:
$ 1805
Step-by-step explanation:
2000 × 95%
= 1900
1900 × 95%
= 1805
A right rectangular pyramid is sliced parallel to the base, as shown. (100 POINTS)
What is the area of the resulting two-dimensional cross-section?
2 m²
3 m²
9 m²
12 m²
Answers
Step-by-Step Explanation:
We know, the 2-dimensional cross-section is a Rectangle.
Length (l) = 2 m
Breadth (b) = 1 m
Area of the Cross Section = l * b
Therefore,
= lb
= l * b
= 2 * 1
=> 2
Area of the Cross Section = 2 m^2
That shaded region area we need
length=2mBreadth=1mArea
Length×Breadth2(1)2m²two dice are thrown what is the probability of two odd number
Answers
Answer:
6/12 or 1/2 or 50% or 0.5
Step-by-step explanation:
You have two 6-sided dice, and there are 3 odd numbers on each.
So, you put 6 on top, (the total number of odd outcomes) and 12 on the bottom. (12 total outcomes for both dice.) This simplifies to 1/2 or 50% or .5.
analyze the following budget,with an income of $600,to determine how much can be spent on food for the month
Answers
Answer:
C: 80
Step-by-step explanation:
Take 600, and subtract it by the values of 200, 95, 65, and 160.
You get $80 left.
Hope this helps!
Find the equation of the line through point (8,−9) ( 8 , − 9 ) and perpendicular to 3+8=4 3 x + 8 y = 4 .
Answers
The equation of the line will be 3y + 8x = 165.
What is an equation?
It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
Given that:-
Find the equation of the line through point (8,−9) ( 8, − 9 ) and perpendicular to 3 x + 8 y = 4.The given equation of the line is:-
3 x + 8 y = 4.
The slope of this line will be:-
3 x + 8 y = 4.
8y = -3x + 4
y = -3 /8x + ( 1 / 2)
y = mx + c
m = -3 / 8
Since the line is perpendicular to the other line 3x +8y = 4 so the slope will be inverse and negative for the line.
So the slope of the line will be -8 / 3
The equation of the line passing through the point will be given as:-
y - y 1 = m ( x- x1)
y - (-9) = ( -8 / 3) ( x - 8)
Y + 9 = ( -8 / 3 ) ( x -8 )
3 y = -8x + 165
3y + 8x = 165
Therefore the equation of the line will be 3y + 8x = 165.
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need help on this ASAP! please
Answers
Step-by-step explanation:
x=66°
180-118=62°
180-52+62=66°
hope this helps
Explanation: angles on a line add up to 180, so if part of it is 118 you do 180-118 which is 62. So 62 is the angle on the right, then add the left and right angle which is 52 plus 62 which is 114.
And we know a triangle adds up to 180. So 180 take away 114 equals 66
Hope this helps and hope you can understand it
Here are the dimensions of some rectangles. Which rectangle has an area of 12 square units and a perimeter of 14 units?
a length of 1 unit and a width of 12 units
a length of 6 units and a width of 1 unit
a length of 6 units and a width of 2 units
a length of 3 units and a width of 4 units
Answers
Considering the formulas for the area and the perimeter of the rectangle, the one with the desired measures is given as follows:
a length of 3 units and a width of 4 units.
What are the area and the perimeter of a rectangle?Considering a rectangle of length l and width w, we have that:
A = lw.P = 2(l + w).For a rectangle with a length of 3 units and a width of 4 units, we have that:
A = 3 x 4 = 12 square units.P = 2(3 + 7) = 14 units.Hence it is the correct option.
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If a_1=9a
1
=9 and a_n=-3a_{n-1}a
n
=−3a
n−1
then find the value of a_5a
5
.
Answers
A geometric series is the collection of an unlimited number of terms with a fixed ratio between them. The value of a₅ is -729.
What is geometrical series?A geometric series is the collection of an unlimited number of terms with a fixed ratio between them.
Given the value of a₁=9 and the value of [tex]a_n=-3a_{(n-1)}[/tex]. Therefore, the value of a₅ can be written as,
a₂ = -3(a₁) = -3(9) = -27
a₃ = -3(a₂) = -3(-27) = 81
a₄ = -3(a₃) = -3(81) = -243
a₅ = -3(a₄) = -3(-243) = -729
Hence, the value of a₅ is -729.
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only a genius can solve it !!
[tex] \frac{ \cos(A) }{1 - \sin(A) } + \frac{ \sin(A) }{1 - \cos(A) } + 1 = \frac{ \sin(A) \cos(A) }{(1 - \sin(A)(1 - \cos(A)} [/tex]
Answers
[tex]\text{L.H.S}\\\\=\dfrac{\cos A}{1-\sin A} + \dfrac{\sin A}{1-\cos A} +1\\\\\\=\dfrac{\cos A(1-\cos A) + \sin A(1-\sin A) + (1-\sin A)(1 - \cos A)}{(1-\sin A)(1 -\cos A)}\\\\\\=\dfrac{\cos A - \cos^2 A + \sin A - \sin^2 A + 1 - \cos A - \sin A + \sin A \cos A}{(1 -\sin A)(1 - \cos A)}\\\\\\=\dfrac{-(\sin^2 A + \cos^2A) +1 + \sin A \cos A}{(1 - \sin A)(1 - \cos A)}\\\\\\=\dfrac{-1 + 1 + \sin A \cos A }{(1 - \sin A)((1 - \cos A)}\\\\\\=\dfrac{0+ \sin A \cos A}{(1 - \sin A)(1 - \cos A)}\\[/tex]
[tex]=\dfrac{\sin A \cos A}{(1 - \sin A)(1 - \cos A)}\\\\\\=\text{R.H.S}\\\\\text{Proved.}[/tex]
What is the slope of the line with the equation y-3=-1/2(x-2)?
Answers
Answer: [tex]-\frac{1}{2}[/tex]
Step-by-step explanation:
[tex]y -3 = -\frac{1}{2}(x-2)[/tex]
Write as slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.
[tex]y-3=-\frac{1}{2}x + 1[/tex]
[tex]y = -\frac{1}{2}x+4[/tex]
Therefore, the slope is [tex]-\frac{1}{2}[/tex].
