Based on the equation,the equation which is not an inverse variation is f(x) = kx
Inverse variationf(x) = kx
= k × x
f(x) = 2k/x
= k(2/x)
f(x) = -kx/z
= k(-x/z)
Inverse variation is given by:
y = k(1/x)
where,
k = constant of proportionalityTherefore, f(x) = kx is not an inverse variation.
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A customer buys a different book that has an original selling price of $38. The book is discounted 25%. The customer must pay a 6% sales tax on the discounted price of the book.
What is the total amount, in dollars, the customer pays for the discounted book? Explain and SHOW how you arrived at your answer.
Answer:
$30.21
Step-by-step explanation:
100% -25%= 75%
Discounted price of the book
= 75% ×$38
= $28.50
Since the customer must pay an additional 6% of the discounted price,
percentage of discounted price paid
= 100% +6%
= 106%
Total amount paid
= 106% × $28.50
= $30.21
_________________________________
Alternative working:
Original selling price= $38
Since the book is discounted 25%,
100% ----- $38
1% ----- $0.38
75% ----- 75 ×$0.38= $28.50
Since the sales tax is based on the discounted price, we let the discounted price be 100%.
100% ----- $28.50
1% ----- $0.285
106% ----- 106 ×$0.285= $30.21
∴ The total amount the customer pays for the discounted book is $30.21.
The 12th term of GP whose
1
first term is 1/8 and second
term is 1/2is
Answer:
jjanation:jdgjdjgdjgjkdkidjgjghdjjghhkd
Point B has coordinates (4,2). The x-coordinate of point A is - 1. The distance between point A and
point B is 13 units. What are the possible coordinates of point A?
Answer:
A (-1,-10) ; A (-1,14)
Step-by-step explanation:
[tex]\sqrt{(-1-4)^2 + (y-2)^2} = 13 \\ 25 + y^2 + 4 -4y = 169[/tex]
y^2 -4y - 140 = 0
Δ/4 = 4 + 140 = 144
y1 = 2 + 12 = 14
y2 = 2 -12= -10
I’m suppose to find the measure of each angle. Thank you
Answer:
E) π/9
Step-by-step explanation:
The angles are complementary meaning they add up to 90°.
Convert radians to degrees:
7π/18 · 180/π = 70°
Now we know that we need the radian equivalent of 20°.
Convert degrees to radians:
70 · π/180 = π/9
Therefore, the measure of the missing degree is π/9.
Explain why the work is not correct.
[tex]8 \times {2}^{n + 2} = 32[/tex]
What is the value of n
Step-by-step explanation:
2³×2^n+2=32
2^3+n+2=2⁵
n+5=5
n=0
[tex]_____________________________________[/tex]
[tex]\sf\huge\underline\red{ANSWER:}[/tex]
[tex]\tt n = 0[/tex]
[tex]\sf\huge\underline\red{SOLUTION:}[/tex]
[tex]\tt8 \times {2}^{n + 2} = 32 \\ = \tt {2}^{3} \times {2}^{n + 2} = 32 \\ = \tt {2}^{n + 5} = 32 \\ = \tt {2}^{n + 5} = {2}^{5} \\ = \tt n + 5 = 5 \\ = \tt n = 5 - 5 \\ = \large\boxed{\tt{\green{n = 0}}}[/tex]
[tex]_____________________________________[/tex]
[tex]\large\boxed{\sf{\green{CarryOnLearning}}}[/tex]
[tex]\large\boxed{\sf{\red{MathDemonQueenシ︎✌︎}}}[/tex]
[tex]\large\boxed{\sf{\green{ItsMoreFunInThePhilippines✌︎}}}[/tex]
NEED HELP ASAP
So for this problem I got 10.8 by multiplying 0.60 x 18. However it stated that my answer is incorrect. How do I go about this problem because I am not sure what else to do?
We are looking for the total amount of the solution. We only know part of it, that there are 18 milliliters of the alcohol. We also know that the alcohol makes up only 60% of the solution.
To find the whole, we can set up a proportion using the information given.
60 / 100 <--- This is our percentage, which we were given.
18 / x <--- This is the part (alcohol - 60%) over the whole, which we don't know and which also corresponds to the 100.
Therefore, our proportion is as such:
60 / 100 = 18 / x
To solve, cross-multiply.
100 * 18 = 60 * x
1800 = 60x
x = 30 total milliliters of the solution
Hope this helps!
upandover has a great solution. Here's a slightly different approach.
x = total amount of solution (consisting of water and alcohol mixed)
0.60x = 60% of x = amount of pure alcohol
0.60x = 18 since we have 18 mL of pure alcohol
Divide both sides by 0.60 to isolate x
0.60x = 18
x = 18/0.60
x = 30
Answer: 30 mL of total solution (alcohol + water).
If "u" varies directly with "v," and u = 6
when v = -7, what is "u" when v = 4
9514 1404 393
Answer:
u = -3 3/7
Step-by-step explanation:
The new value of v is 4/-7 = -4/7 of the old value. Because u varies directly, its new value will also be -4/7 of the old value.
u = -4/7(6) = -24/7
u = -3 3/7
A cone has a diameter of 4 inches and a height of 9 inches. Find the volume of the cone. Use 3.14 for \large \pi.
Answer:
37.68 in.^3
Step-by-step explanation:
diameter = 4 in.
radius = diameter/2 = 2 in.
height = 9 in.
[tex] V = \dfrac{1}{3}\pi r^2 h [/tex]
[tex] V = \dfrac{1}{3}(3.14)(2~in.)^2(9~in.) [/tex]
[tex] V = \dfrac{1}{3}(3.14)(2~in.)^2(9~in.) [/tex]
[tex] V = \blue{37.68~in.^3} [/tex]
Susan was posting gifts to her family. She weighed three envelopes before posting them. Geace Envelope A Envelope B Envelope C • Envelope A weighed x grams. Envelope B was 50 grams lighter than Envelope A. • Envelope C was three times as heavy as Envelope A. If the total weight of the three envelopes was 840 grams, write an equation in x and solve it to find the weight of Envelope A. (
Answer:
5x+50
Step-by-step explanation:
you have one x. An x plus fifty. And 3 mire x's. So 5 x's and a 50.
A bacteria culture is growing at a rate of
r(t) = 7e^0.6t
thousand bacteria per hour after t hours. How much did the bacteria population increase during the first two hours? (Round your answer to three decimal places.)
Answer:
[tex]{ \bf{r(t) = 7e {}^{0.6t} }} \\ { \tt{r(2) = 7 {e}^{0.6 \times 2} }} \\ = { \tt{7 {e}^{1.2} }} \\ = 23.241 \: thiusand bacteria \: per \: hour[/tex]
Pls help I’m need to get my grade up
Answer:
38
Step-by-step explanation:
So, we know the formula is:
D=rt or D=r*t
We only need 2 of the 3 sets of values given in the table, one to find our answer, and the other to double check our answer.
Here are the two sets we can look at:
t=2, d=76
t=3, d=114
Lets plug these in and solve:
76=r*2
Divide both sides by 2 to get r alone:
38=r
Now lets check if this is true by pluggin in 38 for r in the second set, and seeing if it works:
D=r*t
114=38*3
=
114=114
So 38 is our answer.
Hope this helps!
The length of a rectangle should be 20 meters longer than 8 times the width. If the length must be
between 116 and 180 meters long, what are the restrictions for the width, z?
Write the solution set as an algebraic inequality solved for the variable
Answer:
The width of the rectangle lies between 12 and 20.
Step-by-step explanation:
Let the width of the rectangle is w.
length of the rectangle,
L = 8 w + 20
116 < L < 180
So,
116 < 8 w + 20 < 180
96 < 8 w < 160
12 < w < 20
So, the width of the rectangle lies between 12 and 20.
X+ 5
If m(x) =x-1 and n(x) = x-3, which function has the same domain as (mon)(x)?
X+5
O (x)=
11
11
o h(x)=
X-1
11
O (X)=
X-4
11
Oh(x) =
X-3
Answer:
third option
Step-by-step explanation:
m(n(x)) =
[tex] \frac{x - 3 + 5}{x - 3 - 1} = \frac{x + 2}{x - 4} [/tex]
the domain of this is R/(4)
so as the third option
The function that has the same domain as (m o n)(x) is
h(x) = 11 / (x - 3)
Option D is the correct answer.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
m(x) = (x + 5)/ (x - 1) and n(x) = x - 3,
Now,
(m o n)(x)
= m (n(x)
= m (x - 3)
= (x - 3 + 5) / (x - 3 - 1)
= (x + 2) / (x - 3)
We can not have x = 3.
So,
The domain can not have x = 3.
From the options,
h(x) = 11 / (x - 3) can not have x = 3.
Thus,
The function that has the same domain as (m o n)(x) is
h(x) = 11 / (x - 3)
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3.42x16.5 show your work plz
Answer:
= 56.43
Step-by-step explanation:
= 3.42 × 16.5
multiply the numbers= 56.43
There are 400 animals that live at a zoo. You find that 22 of 65 randomly chosen animals are
monkeys. About how many animals in the entire zoo are likely to be monkeys?
Answer:
About 135.
Step-by-step explanation:
As the sample is random the number of monkeys likely to be in the zoo
= (22/65) * 400
= 135.38
What is the probability of flipping a coin 10 times and getting heads 5 times? Round your answer to the nearest tenth percent.
The Probability is 1/2 or .5, .5 rounded to the nearest tenth would be irregular because .5 is already in the tenth place but according to the law of rounding since ut is five it would be rounded up giving the whole number 1
Use the drawing tools to form the correct answer on the graph. Graph this function. - 2 + 8 = Reset ® Delet Undo Drawing Tools Click on a tool to begin drawing. Select Point 10 Line 8 3 6- 4 2 2 4 6 -2 8 10 -4 -10 -8 -6 -2 7071 Frmentum. All rights reserved.
Answer:
we have,AD=x cmBC=AD=x cmAB=2AD=2x cmDC=4 cm+AB=(4+2x)cmPerimeter of the trapezium, p=38 cm
The graph of [tex]f(x) = -2x + 8[/tex] has a slope of -2, and a y-intercept of 8
The function is given as:
[tex]f(x) = -2x + 8[/tex]
The above function is a linear function.
A linear function is represented as:
[tex]y =mx + c[/tex]
Where:
m represents the slope, and c represents the y-intercept.
So, by comparison;
[tex]m =-2[/tex]
[tex]c = 8[/tex]
This means that the graph of [tex]f(x) = -2x + 8[/tex] has a slope of -2, and a y-intercept of 8
See attachment for the graph of the function
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If 12 girls can sweep a room in 20hours, how many hours will it take 8 girls to perform the same task, assuming they are sweeping at the same rate?
Answer:
30 hour
Step-by-step explanation:
girls time
12 20 hour
8 x(let)
now,
12/8=x/20
12×20=8×x
240=8x
x=240/8
x=30,,
Write down the equation of the function whose graph is shown.
will mark brainliest
Answer:
y = 1(x - 5)² + 3
Step-by-step explanation:
The general formula of a quadratic equation is written as;
y = a(x − h)² + k
Where (h, k) are the x and y coordinates at the vertex.
Our vertex coordinate is (5, 3)
Thus;
y = a(x - 5)² + 3
Now,we are given another coordinate as (8, 12)
Thus;
12 = a(8 - 5)² + 3
12 = 9a + 3
9a = 12 - 3
9a = 9
a = 9/9
a = 1
Thus,the equation is;
y = 1(x - 5)² + 3
13. Find the length of X (in the picture)
Answer:
x=2
Step-by-step explanation:
the sides are proportional due the angles being equal
since the hypotonuse is 5 on the bigger one and 2.5 on the small one we can infer there is a ×2 difference
so 4÷2=x
x=2
Suppose b is any integer. If b mod 12 = 7, what is 4b mod 12? In other words, if division of b by 12 gives a remainder of 7, what is the remainder when 4b is divided by 12? Fill in the blanks to show that the same answer will be obtained no matter what integer is used for b at the start. Because b mod 12 = 7, there is an integer m such that b = 12m + . Multiply both sides of this equation by 4 and then simplify the right-hand side to find values of q and r such that 4b = 12q + r with 0 ≤ r < 12. The result is q = and r = . Now 0 ≤ r < 12, and q is an integer because ---Select--- . So the uniqueness part of the quotient remainder theorem guarantees that the remainder obtained when 4b is divided by 12 is . Need Help?
Answer:
4b mod 12 = 4
Step-by-step explanation:
Since b mod 12 = 7, it implies that there is an integer, m such that
b = 12m + 7.
We desire to find 4b mod 12
So, multiplying b by 4, we have
4b = 4(12m + 7)
4b = 4 × 12 m + 4 × 7
4b = 4 × 12 m + 28
4b = 4 × 12 m + 24 + 4
4b = 4 × 12 m + 12 × 2 + 4
Factorizing 12 out, we have
4b = 12(4m + 2) + 4
Since m is an integer 4m + 2 is an integer since the operation of adding and multiplication is closed for the set of integers.
comparing 4b = 12q + r with 4b = 12(4m + 2) + 4,
q = 4m + 2 and r = 4
So 4b mod 12 = 4, that is the remainder when 4b is divided by 12 is 4.
In this exercise we have to calculate the value of the unknown, so we have:
the value is 4
we know that the equation will be given as:
[tex]b = 12m + 7\\[/tex]
we need to multiply both sides by 4 to become another known equation, like this:
[tex]4b = 4(12m + 7)\\4b = 4 * 12 m + 4 * 7\\4b = 4 * 12 m + 28\\4b = 4 * 12 m + 24 + 4\\4b = 4 * 12 m + 12 * 2 + 4[/tex]
So factoring this equation we will find that:
[tex]4b = 12(4m + 2) + 4[/tex]
Thus, when making a comparison between the two equations, we have that:
[tex]4b = 12q + r \\4b = 12(4m + 2) + 4\\q = 4m + 2\\r = 4[/tex]
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Find the lowest common multiple of 10 and 12
Neglecting air resistance and the weight of the propellant, determine the work done in propelling a five-ton satellite to a height of (a) 100 miles above Earth and (b) 300 miles above Earth.
Answer:
a) the work done in propelling a five-ton satellite to a height of 100 miles above Earth is 487.8 mile-tons
b) the work done in propelling a five-ton satellite to a height of 300 miles above Earth is 1395.3 mile-tons
Step-by-step explanation:
Given the data in the question;
We know that the weight of a body varies inversely as the square of its distance from the center of the earth.
⇒F(x) = c / x²
given that; F(x) = five-ton = 5 tons
we know that the radius of earth is approximately 4000 miles
so we substitute
5 = c / (4000)²
c = 5 × ( 4000 )²
c = 8 × 10⁷
∴ Increment of work is;
Δw = [ ( 8 × 10⁷ ) / x² ] Δx
a) For 100 miles above Earth;
W = ₄₀₀₀∫⁴¹⁰⁰ [ ( 8 × 10⁷ ) / x² ] Δx
= (8 × 10⁷) [tex][[/tex] [tex]-\frac{1}{x}[/tex] [tex]]^{4100}_{4000[/tex]
= (8 × 10⁷) [tex][[/tex] [tex]-\frac{1}{4100}[/tex] [tex]+\frac{1}{4000}[/tex] [tex]][/tex]
= (8 × 10⁷ ) [ 6.09756 × 10⁻⁶ ]
= 487.8 mile-tons
Therefore, the work done in propelling a five-ton satellite to a height of 100 miles above Earth is 487.8 mile-tons
b) For 300 miles above Earth.
W = ₄₀₀₀∫⁴³⁰⁰ [ ( 8 × 10⁷ ) / x² ] Δx
= (8 × 10⁷) [tex][[/tex] [tex]-\frac{1}{x}[/tex] [tex]]^{4300}_{4000[/tex]
= (8 × 10⁷) [tex][[/tex] [tex]-\frac{1}{4300}[/tex] [tex]+\frac{1}{4000}[/tex] [tex]][/tex]
= (8 × 10⁷ ) [ 1.744186 × 10⁻⁵ ]
= 1395.3 mile-tons
Therefore, the work done in propelling a five-ton satellite to a height of 300 miles above Earth is 1395.3 mile-tons
the single discount of two successive discounts 10% and 5% is
Answer:
14.5%
Step-by-step explanation:
Use the number 100 as an example to find the single discount.
Take a 10% discount off of this:
100(0.9)
= 90
Take a 5% discount:
90(0.95)
= 85.5
So, after the successive discounts, $14.5 was discounted.
This means that the single discount is 14.5%.
So, the answer is 14.5%
To solve the equation 6x + 3 = 9 for x, what operations must be
performed on both sides of the equation in order to isolate the variable
x?
Answer:
Subtraction, and then division.
Step-by-step explanation:
We would subtract 3 on each side to undo the '3', and then divide by 6 on both sides to isolate 'x'.
[tex]6x+3 = 9\\\\6x + 3 - 3 = 9 - 3\\\\ 6x = 6\\\\\frac{6x=6}{6}\\\\\boxed{x=1}[/tex]
Hope this helps.
To solve the equation 6x + 3 = 9 for x, the operations that must be performed on both sides of the equation in order to isolate the variable x are subtraction and then division.
What is a linear equation?A linear equation in one variable has the standard form Px + Q = 0. In this equation, x is a variable, P is a coefficient, and Q is constant.
How to solve this problem?Given that 6x + 3 = 9.
First, we have to separate variable and constants. So, we have to subtract 3 from both sides.
6x + 3 - 3 = 9 - 3
i.e. 6x = 6
Now, to solve this equation, we use division.
x = 6/6 = 1
i.e. x = 1
Therefore, to solve the equation 6x + 3 = 9 for x, the operations that must be performed on both sides of the equation in order to isolate the variable x are subtraction and then division.
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Finding the Area of a Circle Given the Radius Th It The area in terms of pi isi mi? The approximated value for the area is A circle has a radius of 3 miles. Use the work shown below to identify the area in terms of pi and the approximate area of the circle. Use 3.14 for a and round the answer to the nearest tenth. A = 2 A= T(3 mi) A = 3.14(9 mi)
Answer:
I'd use A = πr^2
The area is 28.3 if we're using 3.14 as pi (rounded to the nearest tenth)
pleaseeeee solve thissss pleaseeee
Answer:
a.) 15 feet
b.) 3.25 seconds
c.) 17.1125 feet
d.) 12.5 seconds
Step-by-step explanation:
a
This is just asking for the y intercept
to get this just do h(0)= 15
b
This is asking for the x value of the vertex
solve that through -b/2a
-1.3/(2*-.2)= 3.25
c
This is asking for the y value of the vertex
to solve this plug in the x value from b
-.2*3.25²+1.3*3.25+15= 17.1125
d
This is asking for an x intercept
using the quadratic formula...
[tex]\frac{-b(+-)\sqrt{b^2-4*a*c}}{2a}=\frac{-1.3(+-)\sqrt{1.3^2-4*-.2*15}}{2*-.2}= -6, 12.5[/tex]
*note the (+-) before the radical is ± *
logic will tell us that a negative x intercept doesn't make any sense so we only take the positive value, 12.5
PLS HELP ITS DUE AT 11:10
Answer:
Scalene.
Step-by-step explanation:
It's scalene because non of the triangle's sides are congruent.
Select all the numbers that are rational.
Answer:
-14/2 , 1/3 and 0.325 are the rational numbers
