z varies directly as x⎯⎯√ and inversely as y2. If z=182 when x=25 and y=8, find z if x=64 and y=3.

Answer: 3(4-x) + 6x = 4x + 12 - x

Step-by-step explanation:

For the solution to be all real numbers, the left hand has to be identical to the right hand side.

1) [tex]4(3-x)+7x=12-4x+7x=12+3x[/tex], so wrong.

2) [tex]4(4-x)+6x=16-4x+6x=16+2x[/tex], so wrong.

3) [tex]3(4-x)+6x=12-3x+6x=12+3x=4x+12-x[/tex], so correct.

4) Wrong variable, so eliminate immediately.

Answer: it should be this M=kb^3/B^2

Step-by-step explanation:

[tex]\large\displaystyle\text{$\begin{gathered}\sf \frac{2x-20}{3}=2x \end{gathered}$}[/tex]

Multiply both sides of the equation by 3.

[tex]\large\displaystyle\text{$\begin{gathered}\sf 2x-20=6x \end{gathered}$}[/tex]

Subtract 6x on both sides.

[tex]\large\displaystyle\text{$\begin{gathered}\sf 2x-20-6x=0 \end{gathered}$}[/tex]

Combine 2x and −6x to get −4x.

[tex]\large\displaystyle\text{$\begin{gathered}\sf -4x-20=0 \end{gathered}$}[/tex]

Add 20 to both sides. Any value plus zero results in its same value.

[tex]\large\displaystyle\text{$\begin{gathered}\sf -4x=20 \end{gathered}$}[/tex]

Divide both sides by −4.

[tex]\large\displaystyle\text{$\begin{gathered}\sf x=\frac{20}{-4} \end{gathered}$}[/tex]

Divide 20 by −4 to get −5.

[tex]\large\displaystyle\text{$\begin{gathered}\sf x=-5 \ \ \to \ \ \ Answer \end{gathered}$}[/tex]

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation: }[/tex]

[tex]\mathbf{\dfrac{2x - 20}{3} = 2x}[/tex]

[tex]\huge\textbf{SIMPLIFY IT or DISTRIBUTE:}[/tex]

[tex]\mathbf{\dfrac{2}{3}x - \dfrac{20}{3} = 2x}[/tex]

[tex]\huge\textbf{SUBTRACT 2x to BOTH SIDES:}[/tex]

[tex]\mathbf{\dfrac{2}{3}x - \dfrac{20}{3} - 2x = 2x - 2x}[/tex]

[tex]\huge\textbf{SIMPLIFY IT!}[/tex]

[tex]\mathbf{- \dfrac{4}{3}x - \dfrac{20}{3} = 0}[/tex]

[tex]\huge\textbf{ADD }\boxed{\rm{\bf \dfrac{20}{3}}}\huge\textbf{ to BOTH SIDES:}[/tex]

[tex]\mathbf{-\dfrac{4}{3}x - \dfrac{20}{3} + \dfrac{20}{3} = 0 + \dfrac{20}{3}}[/tex]

[tex]\huge\textbf{SIMPLIFY IT!}[/tex]

[tex]\mathbf{-\dfrac{4}{3}x = \dfrac{20}{3}}[/tex]

[tex]\huge\textbf{MULTIPLY }\boxed{\rm \bf {\dfrac{3}{-4}}}\huge\textbf{ to BOTH SIDES:}[/tex]

[tex]\mathbf{\dfrac{3}{-4}\times\dfrac{-4}{3}x = \dfrac{3}{-4}\times\dfrac{20}{3}}[/tex]

[tex]\huge\textbf{SIMPLIFY IT!}[/tex]

[tex]\mathbf{x = -5}[/tex]

[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{x = -5}}}\huge\chekmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

Step-by-step explanation:

A relation is a function if there is only one y-value for each x-value. If you can draw a vertical line on the graph that intersect more than one point, the relation is not a function. (This is the "vertical line test.")

Graph A: there are 3 y-values associated with x=2. Not a function.

Graph B: passes the vertical line test: A function.

Graph C: there are 2 y-values at each of x=1 and x=2. Not a function.

Answer:

See below

Step-by-step explanation:

=  (-7)(11)(√(3*10) ) =  - 77 √(30)  

Answer: y = -1

Step-by-step explanation:

When x = 0, y = -1

Also, you can think about it as when the graph of the line passes the y axis

By de Moivre's theorem,

[tex]\left(\cos\left(\dfrac\pi6\right) + i \sin\left(\dfrac\pi6\right)\right)^{18} = \cos\left(\dfrac{18\pi}6\right) + i \sin\left(\dfrac{18\pi}6\right) \\\\ ~~~~~~~~ = \cos(3\pi) + i \sin(3\pi) = \boxed{-1}[/tex]

The value of the given complex number is -1

Given the polar form of a complex number expressed as:

[tex](cos\theta + isin\theta)^n\\[/tex]

This can also be expressed according to the de moivre's theorem as;

[tex]=(cos\theta + isin\theta)^n\\\\=(cosn\theta+isinn\theta)[/tex]

Given the expression below;

[tex](cos\frac{\pi}{6} + isin\frac{\pi}{6} )^{18}\\(cos18\cdot\frac{\pi}{6} + isin18\cdot\frac{\pi}{6} )\\(cos3\pi + isin3\pi)\\=-1[/tex]

Hence the value of the given complex number is -1

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Answer:

90 grams

Step-by-step explanation

Full = 120

half filled + empty = 150

half of 120 = 60

Therefore, a jar weighs 150 - 60

= 90 grams

Answer:

D

Step-by-step explanation:

Subtracting 2 from both sides and then dividing both sides by 3 gives that x² = -2/3, which indicates the roots are complex.

Answer:

D.  domain

Step-by-step explanation:

domain is set of x-values

range is set of y-values

Input is the set of x-values, so it is the domain.

The range of the function the as given in the equation is; -∞ ≤ y < ∞.

It follows from the task content that the function given is; y=3√x+8.

On this note, it follows that the range of the function is the set of all possible outputs, y values and in this case is; -∞ ≤ y < ∞.

It therefore follows that the range of the function is as indicated above as all X-values (domain) must be positive and the square root of x yields a positive or negative real number.

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Answer:

2.7 is the answer!!

Step-by-step explanation:

hope this helps :)

Answer:

4

Step-by-step explanation:

To find f(-1)g(-1) which is f(-1)*g(-1), first, we must find what are values of f(-1) and g(-1) first which can be found by substituting x = -1 in both functions.

[tex]\displaystyle{f(-1)=(-1)^2+1}\\\\\displaystyle{f(-1)=1+1 = 2}[/tex]

Now we know that f(-1) is 2, next, we find g(-1).

[tex]\displaystyle{g(-1) = 3(-1)+5}\\\\\displaystyle{g(-1)=-3+5 = 2}[/tex]

Now we know that g(-1) is 2 too. Since the question wants to find f(-1)g(-1), therefore 2*2 = 4.

Hence, the answer is 4.

Answer:

D) 4

Step-by-step explanation:

Given functions:

f(x) = x² + 1

g(x) = 3x + 5

Here, we're asked to find the value of both functions when the value of x is -1. Then, we multiply the functions in order to find the value of f(-1)•g(-1).

Note: f(-1) • g(-1) is equivalent to (f • g)(-1).

Method 1: f(-1) • g(-1)

Find the value of each function when x = -1.

f(-1) = (-1)² + 1 ⇒ f(-1) = 1 + 1 ⇒ f(-1) = 2

g(-1) = 3(-1) + 5 ⇒ g(-1) = -3 + 5 ⇒ g(-1) = 2

Multiply the functions together.

f(-1) • g(-1) ⇒ 2 • 2 ⇒ 4

Method 2: (f • g)(-1)

First, multiply the functions.

⇒ (x² + 1) • (3x + 5) [ Simplify using the Distributive Property: (a + b) • (c + d) = ac + ad + bc + bd. ]

⇒ x²(3x) + x²(5) + 1(3x) + 1(5)

⇒ 3x³ + 5x² + 3x + 5

Now, substitute -1 as the value of x.

⇒ 3(-1)³ + 5(-1)² + 3(-1) + 5 [ Exponents first. }

⇒ 3(-1) + 5(1) -3 + 5 [ Multiply the numbers. ]

⇒ -3 + 5 - 3 + 5 [ Simplify. ]

⇒ 4

Therefore, the product of both functions when x = -1 is 4.

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a) The point (2, -7/5) is not a point on the graph?

b)  The value of f(x) when x is 1 is -1/3 and the point on the graph is (1, -1/3)

c) The value of x for f(x) = 2 is 22 and the point on the graph is (22, 2)

d) The domain of x is all real values of x ≠ 10

e) The x intercept is -2

f) The y intercept is -1/5

Function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output and not one input for two outputs.

Analysis:

a) To test if the point (2, -7/5) is a point on the graph, we put in x = 2 into the function,

f(2) = 2+2/2-10 = 4/-8  = -1/2 ≠ -7/5. Therefore (2, -7/5) is not a point on the graph.

b) if x = 1, f(1) = 1 +2 / 1-10 =  3/-9 = - 1/3

   The point on the graph is (1, -1/3)

c) if f(x) = 2, then 2 = x+2/x-10

     2(x-10) = x+2

     2x -20 = x+2

      2x-x = 2+20

      x = 22, the point on the graph is (22, 2)

d) The domain of the function is such that the denominator would not be zero.

so if x - 10 ≠ 0

Then the values of x ≠ 10 are the domain of the function.

e) The x intercept of the graph is the point at which f(x) = 0

  0 = x+2/x-10

   x+2 = 0

   x = -2. The x-intercept is -2.

f) the y-intercept is such that x = 0

   0+2/0-10 = 2/-10 = -1/5

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Answer: 841

Step-by-step explanation:

29×29=841

Answer:

  about 8.66 years

Step-by-step explanation:

The multiplier of account value when interest is compounded continuously is ...

  k = e^(rt)

where r is the annual interest rate, and t is the number of years.

We want to find t when k=2 and r=0.08. Putting these values in the formula gives ...

  2 = e^(0.08t)

Taking logs of both sides, we have ...

  ln(2) = 0.08t

  t = ln(2)/0.08 = 0.693147/0.08 ≈ 8.66

It takes about 8.66 years to double the amount.

__

Additional comment

If the interest rate is expressed in integer numbers of percentage points (R%), then the doubling time is ...

  t = 100·ln(2)/R ≈ 69.3147/R

Here, that is 69.3147/8 ≈ 8.66.

The "rule of 72" is used to estimate the doubling time for periodically compounded interest at rate R%. That rule tells you the time is t ≈ 72/R. For most interest rates and compounding frequencies in a reasonable range, this gives a time within a reasonable amount of error.

For continuously compounded interest, we have shown the doubling time in years is 69.3147/R. (The exact value of the constant is 100·ln(2).) For the purpose here, a constant of 69.3 gives an estimate accurate to 3 sf.

Answer:c

options A  and B

Step-by-step explanation:

the ratio between the lengths of the two legs of a 30-60-90 triangle

General ration of 30-6- 90 degrees triangle is

x : xsqrt(3) : 2x

When x=1 the ratio becomes 1 : 1 sqrt(3)

when x= 2sqrt(3) the ratio becomes

It becomes

Two sides of 30-60-90 triangle cannot be equal

so option c  and option D are not possible

sqrt(2) is also not possible  because we have sqrt(3) in general ratio

PLS MARK ME AS BRAINLIEST.

A ratio shows us the number of times a number contains another number. The elephant's weight on Planet B is 96 pounds.

A ratio shows us the number of times a number contains another number.

The ratio of the weight of an object on Planet A to the weight of the same object on Planet B is 100 to 3.

Weight on Planet A/ Weight on planet B = 100 / 3

Now, the weight of the elephant on planet A to Planet B will be,

elephant's weight on Planet A/elephant's weight on Planet B = 100 / 3

elephant's weight on Planet B = (3 ×3200)/100

elephant's weight on Planet B = 96 pounds

Hence, the elephant's weight on Planet B is 96 pounds.

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The answer is 90% of the crime is between 48.63 and 51.37

The sd = 5 months

n = 36

Mean length = 50

1- 0.90

= 0.1

Critical value = alpha/2 = 1.645

Margin of error

E = 1.645 x 5/√36

= 1.37

50 -  1.37 + 50 + 1.37

= (48.63, 51.37)

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The y-intercept on the x-y plane is (0, -9).

To get the y-intercept we just need to evaluate in x = 0.

Here we have:

y = 6*(x - 1/2)*(x + 3)

Evaluating the given equation in x = 0 we get:

y = 6*(0 - 1/2)*(0 + 3) = -9

Then the y-intercept on the x-y plane is (0, -9).

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Answer:

-9

Step-by-step explanation:

The true statements are:

The interquartile range is 10.

The data is skewed.

A box plot is used to study the distribution and level of a set of scores

The end of the first whisker represents the minimum number and the end of the second whisker represents the maximum number.

On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile. The interquartile range is the difference between the first and third quartile.

Interquartile range = 9 - (-1) = 10

A box plot is negative skewed because the median is not at the center of the box.

An outlier would be within: (Q1 - 1.5 * IQR or Q3 + 1.5 * IQR).

- 1 - (1.5 x 10 ) = -16

9 + (1.5 x 10) = 24

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Answer:

13.25km

Step-by-step explanation:

25 Litres = 331.25km

1 Litre =

[tex] \frac{331.25}{25} \\ = 13.25km[/tex]

Answer:

13.25 km

Step-by-step explanation:

25 litres = 331.25 km

1 litre =

331.25

25

=13.25 km

Answer:

48 servings

Step-by-step explanation:

3tsp=tbsp

32*3=96

96/2=48

The students in the school would be expected to do household chores for at least two hours every week with 1020 students.

We have given

Time (in hours)                  0–  1    2–3     4–5    6–7

Number of Students         32   64          3        1

A simple random sample is a subset of a statistical population in which each member of the subset has an equal probability of being chosen.

The keyword is at least, this means anything under that number will not qualify.

So that leaves 68 out of the 100 sample students.

So if you want to have the same thing but with 1,500 students.

Take off the 2 zeros at the end of 1500 and multiply by 68 to get your answer.

This is because there are 2 zeros in 100, so to cancel out the 2 zeros in 100, take out the 2 zeros in 1500 making it a lot easier.

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Answer:

c

Step-by-step explanation:

The $1.25 one for 9 Oz box of rice would be the best buy.

To get the best buy among the given items and prices, we need to find the unit price. Thus, the formula is;

Unit price = Price/Quantity

A) Unit Price = 0.90/6 = 0.15

B) Unit Price = 1.93/12 = 0.15083

C) Unit price = 2.42/16

Unit Price = 0.15125

D) Unit Price = 1.25/9 = 0.138

The $1.25 one for 9 Oz box of rice would be the best buy.

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