Which of the following equations is NOT an example of inverse variation?
I. f(x)=kx
II. f(x)=2kx
f
(
x
)
=
2
k
x
III. f(x)=−kxz

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!

Answer:

jjanation:jdgjdjgdjgjkdkidjgjghdjjghhkd

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]

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).

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

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)

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.

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

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

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

Read more about linear functions at:

https://brainly.com/question/15602982

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

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.

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.

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.

Learn more about linear equations here -

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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]

Answer:

= 56.43

Step-by-step explanation:

= 3.42 × 16.5

= 56.43

Answer:

-14/2 , 1/3 and 0.325 are the rational numbers

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.

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)

Learn more about functions here:

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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

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

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,,

Answer:

Scalene.

Step-by-step explanation:

It's scalene because non of the triangle's sides are congruent.

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]

See more about factoring at brainly.com/question/6810544

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.

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]

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

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.

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

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%

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.