Suppose y varies Inversely with x, and y = -1 when x = 3. What Inverse variation equation relates x and y?

Answer:

k = 1

Step-by-step explanation:

Discriminant

[tex]b^2-4ac\quad\textsf{when }\:ax^2+bx+c=0[/tex]

[tex]\textsf{when }\:b^2-4ac > 0 \implies \textsf{two real roots}[/tex]

[tex]\textsf{when }\:b^2-4ac=0 \implies \textsf{one real root}[/tex]

[tex]\textsf{when }\:b^2-4ac < 0 \implies \textsf{no real roots}[/tex]

As we need to determine the value of k that will give one solution, set the discriminant to zero.

Given equation:

[tex]y=kx^2-4x+4[/tex]

Therefore:

Substitute these values into the discriminant and solve for k:

[tex]\begin{aligned}b^2-4ac & = 0\\\implies (-4)^2-4(k)(4) & = 0\\16-16k & = 0\\16k & = 16\\\implies k & = 1\end{aligned}[/tex]

Answer:

The Answer is 50 or 50x

Answer: 15x^2+35x ✅

Step-by-step explanation:

Hii, do you need to distribute [tex]\boldsymbol{5x(3x+7)}[/tex]? No problem! (:

We can solve problems like this one by using what is known as the "distributive property". What it says is: If you have a term that comes before the parentheses, you multiply it times every single term in the parentheses. Let me show you what I mean...

[tex]\twoheadrightarrow\sf 5x(3x+7)[/tex]

[tex]\bullet[/tex] Multiply 5x tmes 3x and 7 - you will obtain

[tex]\twoheadrightarrow\sf 15x^2+35x[/tex] (if we multiply x times x we obtain x²)

Voila! There's our solution, cheers! (:

--

Hope that this helped! Best wishes.

[tex]\it Reach\quad far.\:Aim\quad high. \,Dream\quad big.[/tex]

[tex]\bigstar\underbrace[/tex]

--

Answer:

105.6397

ROUNDED ANSWER:

105

The word problem for given equation is : When 3 is multiplied with x and subtracted by 2 multiplied by y , the number obtained is 13. Solve the equation for x =1 .

The complete equation will be 3x - 2y =13

When an algebraic expression is equated by an equal sign to a constant or any other algebraic expression , then an equation is formed .

The equation given in the question is

3x-2y =13

When 3 is multiplied with x and subtracted by 2 multiplied by y , the number obtained is 13. Solve the equation for x =1 .

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Answer: (1, -4) or y = -4

Step-by-step explanation:

    Given:

y = 3x - 7

    Plug in the value of 1 for x - given to us by "(1, ?)

y = 3x - 7

y = 3(1) - 7

    Multiply:

y = 3 - 7

    Subtract:

y = -4

               y = -4

Answer:

2y - 9x

Step-by-step explanation:

2y + 3 ( x - 4x )

First, solve the brackets.

2y + 3x - 12x

Combine like terms.

2y - 9x

Answer:

[tex]\sf 2y-9x[/tex]

Step-by-step explanation:

Hi There Student! Let me help you out on this question.

________________________________________________________

In this problem, we are given an expression [tex]\longmapsto\pmb{2y+3(x-4x)}[/tex], and asked to simplify it.

                                    ↪

First, we can perform the operation inside the parentheses, x-4x:

[tex]\longmapsto\sf 2y+3(-3x)}[/tex].

Now we can multiply 3 times -3x:

[tex]\longmapsto\sf 2y-9x[/tex]

And that is our final answer, because 2y and -9x are not like terms.

Hope that this helped! Have a good day ahead.

Best Wishes!

[tex]\star\bigstar\overline{\overline{\underline{\underline{\textsf {Reach far. Aim high. Dream big.}}}}}\bigstar\star[/tex]

 ◆◈-Greetings!-◈◆

-______________________________

Opposite values are those values which on the number line has the same distance between them and zero. The temperature in each city is PoT=-PhT and PhT =+PoT.

Opposite values are those values which on the number line has the same distance between them and zero. Although the sign on the values may be difference. For example if the first value is 4, then its opposite value is -4.

In general, the temperature equation for Portland, Maine is stated mathematically as

PoT=-PhT

As it is given in the question that the Portland, Maine and Phoenix, Arizona had opposite values. Also, the temperature in Portland is lower than in Phoenix. Therefore, the temperature in each city can be written as,

PoT=-PhT

PhT =+PoT

Hence, the temperature in each city is PoT=-PhT and PhT =+PoT.

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The graph of [tex]\mathbf{y=\sin{3x}}[/tex] is given by,

Here given the function is [tex]y=\sin{3x}[/tex]

when [tex]x=0\Rightarrow y=\sin{3\times 0}=\sin0=0[/tex], then it passes through the origin (0,0).

When [tex]x=\frac{\pi}{6}\Rightarrow y=\sin{3\times\frac{\pi}{6}}=\sin\frac{\pi}{2}=1[/tex]

Since we know that, [tex]-1\leq\sin{x}\leq1,\forall x[/tex], then the function has maximum height at [tex]x=\frac{\pi}{6}[/tex].

Again when [tex]x=\frac{\pi}{3}\Rightarrow y=\sin{(3\times\frac{\pi}{3})}=\sin\pi=0[/tex], again the function is 0.

So clearly the function is the Oscillating function with a maximum value of the function as 1 and a minimum value of the function as -1.

Range of the oscilaltion of the function = 1-(-1) = 1+1 = 2

Using graphing calculator we get the graph of function [tex]y=\sin3x[/tex],

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Answer:

[tex]2x^{2}[/tex] - 16x + 14

Step-by-step explanation:

(2x - 4)(x - 6)

= (2x + −4)(x + −6)

= (2x)(x) + (2x)(−6) + (−4)(x) + (−4)(−6)

= [tex]2x^{2}[/tex] − 12x − 4x + 24

= [tex]2x^{2}[/tex] - 16x + 14

The equation gives the measure of the central angle 7/5 times 3 60/2 π.

An angle with its vertex at the center of a circle and with sides that are radii of the circle.

radius= 5 feet.

Circumference of circle,

= 2πr

=2*3.14*5

= 31.4 feet.

Arc length = 7.

Then, the part of circle 7 feet arc have

=7/31.4

=0.2229

Also, 0.2229 * 360 = 80.244°

In radian,

80.244° = 1.4 radians

Hence, 7/5 times 360/2 π.

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Using the binomial distribution, it is found that there is a 0.4096 = 40.96% probability that he answers exactly 1 question correctly in the last 4 questions.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

Considering that there are 4 questions, and each has 5 choices, the parameters are given as follows:

n = 4, p = 1/5 = 0.2.

The probability that he answers exactly 1 question correctly in the last 4 questions is P(X = 1), hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 1) = C_{4,1}.(0.2)^{1}.(0.8)^{3} = 0.4096[/tex]

0.4096 = 40.96% probability that he answers exactly 1 question correctly in the last 4 questions.

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Answer:

Step-by-step explanation:

At noon, the temperatures in Portland, Maine and Phoenix, Arizona had opposite values. is mathematically given as

Generally, the equation  for the temperature at Portland, Maine is mathematically given as

PoT=-PhT

Since  Portland, Maine and Phoenix, Arizona had opposite values. The temperature in Portland was lower than in Phoenix.

In conclusion, the temperature in each city is

PoT=-PhT

PhT =+PoT

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There is no solution for b.

The rule for operations done in exponents are

(a) [tex]a^m*a^n=a^{m+n}[/tex]

(b) [tex]a^m/a^n=a^{m-n}[/tex]

(c)[tex](1/a)^m=a^{-m}[/tex]

Given the expression (one-twelfth) superscript negative 2 b baseline times 12 superscript negative 2 b+2 baseline = 12

the expression (one-twelfth) superscript negative 2 b simplifies that [tex](1/12)^{-2b}[/tex]

12 superscript negative 2b+ 2 simplifies that [tex]12^{-2b+2}[/tex]

so the final expression (one-twelfth) superscript negative 2 b baseline times 12 superscript negative 2 b+2 baseline = 12 will be

[tex](1/12)^{-2b}[/tex] * [tex]12^{-2b+2}[/tex] =12

⇒[tex]12^{-(-2b)}\\[/tex] * [tex]12^{-2b+2}[/tex] =12

⇒[tex]12^{2b[/tex] * [tex]12^{-2b+2}[/tex] =12

⇒[tex]12^{2b-2b+2}[/tex]=12¹

equating the exponts of the both sides

⇒2b-2b+2=1

⇒2=1 (not accepted because un-logic condition)

Therefore there is no solution.

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The required work done is 62400 J.

work done to lift a 1500 N object from the ground to the top of a 40 m building if the cable weighs 3 N per m

work done, is define as the product of force and displacement.

since,
work done to lift 1500N to height of 40 m is:
W= FS
   =  1500 x 40 = 60000J
now work done for rope
  is given by
w = mgΔx(40-x)
w= [tex]\int _0^{40}\left mg(40-x\right)dx[/tex]
w=[tex]3\int _0^{40}\left(40-x\right)dx[/tex]
w= 3[tex][40x-x^2/2]\left \{ {{40} \atop {0}} \right.[/tex]
w= 3[1600-800]
w = 2400
Total work done for lifting 1500N to 40m height
= 6000+2400=62400J

Thus the required work done to lift 1500N weight to 40m is 62400J.

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Answer:

-5

Step-by-step explanation:

Since g(x) is f(x) shifted 5 units down, g(x) = f(x) -5. Therefore k = -5

Answer:

the first answer y = 20x - 15

Step-by-step explanation:

since the correct tangent line must share the same point with the originated function, only a line function that delivers y = 25 for x = 2 can be correct.

only the first answer option provides this (20×2 - 15 = 25).

so, we know, this line goes through the given point, but does it have the correct slope for the tangent ?

the correct slope we get from the first derivative of the original function.

f(x) = (1 + 2x)² = 1 + 4x + 4x²

f'(x) = 4 + 8x

for x = 2 we get the tangent slope at that point as

4 + 8×2 = 20

and the provided line is again

y = 20x - 15

with the slope being the factor of x (20).

so, it fits, and indeed, answer 1 is correct.

Answer is 1832.7

step by step

z=kx^3 / y^3

167=27k/1000

k=16700/27

k=6185.2, then

z=6185.2×4^3/6^3

z=6185.2×64/216

z=1832.7

Answer: 2xy

Step-by-step explanation: 2xy is the answer bra

The journal entry on July 24 to record payment of the balance due is $2156

Discount period is the time period given by the supplier to the consumer for getting discount if the payment is made by the due date.

                                                                          Debit                          Credit

Accounts payable (2300-100 )                       2200

Cash (2200 - (2200* 2%))                                                                   2156

Purchase Discount / Merchandise Inventory                                     44

To record the payment of accounts within discount period

Amount Paid = 2300 - 200 -44 = 2156

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Answer:

Gabrielle is 27

Mikhail is 9

Step-by-step explanation:

g = 3m

g + m = 36

since g = 3m we can substitute it in the equation

g + m = 36 as

3m + m = 36

4m = 36

m = 9

3m = 27 which is g

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Answer:

Step-by-step explanation:

hello :

Answer:

The correct option is;

B. Rolling a die; 1 or 2 represents door A, 3 or 4 represents door B, and 5 or 6 represents door C

The answers are as follow:

a) y'= -2x/y

b) y' = -4/y

The technique of implicit differentiation allows you to find the derivative of y with respect to x without having to solve the given equation for y.

Given:

x²y+4y=8

On differentiation

applying product rule

2xy+ x²y'  = 0

2xy = - x²y'  

2y = -xy'

y'= -2x/y

b) equation of the tangent line to the graph when x = 2.

y' = -4/y

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Answer:

516 students eat out 3 times a week

Step-by-step explanation:

22% of 2346 is 516.12 and a person can't be a decimal so it's 516

22 x 2346 = 51612
and 51612÷100 = 516.12

We would expect about 516 WHS students to eat out 3 time

percentage, a relative value indicating hundredth parts of any quantity.

Given that 22% of high school students say they eat out 3 times a week

We need to find the number of students  of the 2346 students who attend WHS would you expect eat out 3 times a week

We can start by using the proportion:

(22/100) = (x/2346)

where x is the number of students we would expect to eat out 3 times a week.

To solve for x, we can cross-multiply:

100x = 22 × 2346

100x = 51612

Divide both sides by 100

x = 516.12

Hence, we would expect about 516 WHS students to eat out 3 time

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The slope of the line that passes through (1, -3) and (0, 2) is: B. m = -5.

Slope (m) = rise / run = change in y / change in x.

Given the points, (1, -3) and (0, 2):

Slope (m) = (-3 - 2)/(1 - 0)

Slope (m) = -5/1

Slope (m) = -5

Therefore, the slope of the line is: B. m = -5.

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Answer:

N. The number of people purchasing coffee each day in a coffee shop

Step-by-step explanation:

A fraction of a person could not buy coffee because every person is a whole person. If something is not a person, it's not a person. Therefore, the only numbers you could add to this value are 0 and 1.

The simplified form of the given expression is [tex]\frac{27}{4x^{12} y^{8} }[/tex].

The given expression is [tex]\frac{4(3x^{2} y^{4} )^{3} }{(2x^{3} y^{5} )^{4} }[/tex].

Exponentiation is a mathematical operation, written as bⁿ, involving two numbers, the base b and the exponent or power n, and pronounced as "b raised to the power of n".

We need to simplify the given expression.

Now, [tex]\frac{4(3^{3}x^{6} y^{12} )}{2^{4} x^{12}y^{20} }[/tex]

⇒[tex]\frac{108x^{6}y^{12} }{16x^{12} y^{20} }[/tex]

⇒[tex]\frac{27}{4x^{12} y^{8} }[/tex]

Therefore, the simplified form of the given expression is [tex]\frac{27}{4x^{12} y^{8} }[/tex].

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The value of minimum usual value is, [tex]\mu-2\sigma=-119.2[/tex]

The value of maximum usual value is, [tex]\mu+2\sigma=1311.2[/tex]

Given the values of the parameters of Binomial Distribution are,

Total number of trials (n) = 1490

probability of success in one trial is (p) = 2/5

The probability of failure in on trial is given by,

[tex]q=1-p=1-\frac{2}{5}=\frac{5-2}{5}=\frac{3}{5}[/tex]

For Binomial distribution we know that,

Mean [tex](\mu)=np=1490\times\frac{2}{5}=596[/tex]

and Standard Deviation [tex](\sigma)=\sqrt{npq}=\sqrt{1490\times\frac{2}{5}\times\frac{3}{5}}=357.6[/tex]

Now, calculating the required measurement we get,

The minimum usual value is given by,

Mean -2 Standard Deviation [tex]=\mu-2\sigma=596-2\times357.6=-119.2[/tex]

The maximum usual value is given by,

Mean + 2 Standard Deviation [tex]=\mu+2\sigma=596+2\times357.6=1311.2[/tex]

Hence the minimum and maximum usual values are -119.2 and 1311.2 respectively.

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