Suppose z varies directly with x and inversely with y . If z is 1.5 when x is 9 and y is 4 , what is z when x is 6 and y is 0.5 ?

Answer:

4*12=48

48*8=384

384 square inches

The inverse function returns the original value for which the output of a function was given.

The inverse the function y = 2x + 1 is [tex]y^{-1[/tex] = x + 1/ 2.

Every logarithmic function has an exponential inverse, and vice versa.

An exponential function is a mathematical function with the formula f(x) = ax, where "x" is a variable and "a" is a constant that is called the function's base and must be greater than zero.

The transcendental number e, which is approximately equal to 2.71828, is the most commonly used exponential function base.

Let the equation be y = 2x + 1

y = 2x + 1

simplifying the equation, we get

⇒ 2x = y+1

⇒ x = y+1/ 2

Therefore, the inverse is [tex]y^{-1[/tex] = x+1/ 2

Let the composition function be

[y ₀ [tex]y^{-1[/tex]] (x) = y (x+1/2)

simplifying the above equation

[y ₀ [tex]y^{-1[/tex]] (x) = 2 (x+1/2)-1

[y ₀ [tex]y^{-1[/tex]] (x) = x

The inverse of y is the image of y in the line y = x.

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Work Shown:

five hundredths = 5/100 = 0.05

Answer: $86.67

Step-by-step explanation:

34 x 7% OR 34 x .07 = 2.38

Skirt = $36.38

47 x 7% = 3.29 47+3.29 = 50.29

50.29+36.38=86.67

by using the operation of multiplication, we get that 21 days is equal to 3 weeks, 504 hours, 30240 minutes and 1,814,400 seconds.

We are given the total number of days as 21.

Now, we know that:

In 1 week, we have 7 days.

So, in 3 weeks = 7 × 3 = 21 days.

Also, 1 day has = 24 hours.

So, by using multiplication, we get that:

21 days = 24 × 21 hours

= 504 hours

Also,

1 hour = 60 minutes

504 hours will be calculated again by using multiplication.

504 hours = 504 × 60 = 30240 minutes

30240 hours = 1,814,400 seconds.

Therefore, by using the operation of multiplication, we get that 21 days is equal to 3 weeks, 504 hours, 30240 minutes and 1,814,400 seconds.

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Your question was incomplete. Please refer the content below:

21 days is equal to:

a) 3 weeks

b) 504 hours

c) 30240 minutes

d) 1,814,400 seconds

e) 1081404 seconds

Select all the correct options that apply.

x = 9 is not an extraneous solution of the equation.

√x=√(x-8) + 2

Squaring both the sides of the equation, we get

(√x)² = (√(x-8)+2)²

x = (✓(x - 8))² + 2² + 2(✓(x - 8))(2)

x = x - 8 + 4 + 2(✓(x - 8))(2)

Subtracting x on both the sides of the equation, we get

- 4 + 2(✓(x - 8))(2) = 0

Adding 4 on both the sides of the equation, we get

4(✓(x - 8)) = 4

Dividing both sides of the equation by 4, we get

(✓(x - 8)) = 1

Squaring again on both the sides of the equation

x - 8 = 1

x = 9

Check for extraneous solution by putting the value of x = 9 in the original equation, we get

✓9 = ✓(9 - 8) + 2

✓9 = ✓1 + 2

3 = 1 + 2

3 = 3

⇒ LHS = RHS

∴ x = 9 is not an extraneous solution of the equation.

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The 50% probability that a student chosen randomly from the class does not play a sport.

According to the statement

We have to find that the probability.

So, For this purpose, we know that the

Probability is that the branch of mathematics that studies the possible outcomes of given events along with the outcomes' relative likelihoods and distributions.

From the given information:

In a class of scholars, the subsequent data table summarizes what percentage students play an instrument or a sport.

Then

In total, there are 8 + 7 + 3 + 12 = 30 students.

And Of this total, 3 + 12 = 15 don't play a sport.

Then

Probability = 15/30

Probability = 0.5

Then

50% probability that a student chosen randomly from the class does not play a sport.

So, The 50% probability that a student chosen randomly from the class does not play a sport.

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Answer:

Step-by-step explanation:

Answer:

36792000

Step-by-step explanation:

you look up how many minutes in a year then multiply by 70

Answer:

0.00762

Step-by-step explanation:

According to the question, the given rational expression can be simplified which is shown below:

Rational expression = [tex](\frac{x^{2}+8x+7}{x^{2} -x-12)} /(\frac{x^{2} +2x-8}{x^{2} +13x+24} )[/tex]

To simplify the given rational expression which is also an polynomial expression by the method of factors rule. Performing factors on numerator as well as on denominator. And later divide them with each other.

Rational expression = [tex](\frac{(x+7)(x+1)}{(x-4)(x+3)}) /(\frac{(x+4)(x-2)}{x^{2} +13x+24} )[/tex]

The factors of the denominator term is not possible. Therefore, the given expression cannot be simplified.

What is polynomial expression?

Polynomial expression are those equation whose highest degree is two. It is also called as quadratic equation. And it is simplified by performing the factors on the given expressions.

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Answer:

C. SNL

Step-by-step explanation:

S is a point in the plane, N is a line in the plane, and L is a point on another line in the plane.

Answer: D XLJ

Step-by-step explanation:

Hope that helps

Gracias

The linear equation of the graph is y = x - 5

Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

The graph represents the given parameter

On the graph, we have the following points

(x, y) = (1, -4) and (5, 0)

Calculate the slope (m) using

m = (y2 - y1)/(x2 - x1)

So, we have

m = (0 + 4)/(5 - 1)

Evaluate

m = 1

The equation is then calculated as

y = m(x - x1) + y1

So, we have

y = 1 * (x - 5) + 0

Evaluate

y = x - 5

Hence, the linear equation of the graph is y = x - 5

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Answer:

f(n + 3) = 3n + 13

Step-by-step explanation:

f(x)=3x+4 then f(n+3)=

f(n + 3) = 3(n + 3) + 4

f(n + 3) = 3n + 9 + 4

f(n + 3) = 3n + 13

I hope this helps!

The partial derivatives for this problem are given as follows:

To find the partial derivatives of a function, we apply the same rules that we apply for complete derivatives, just considering the variables for which we are not deriving the function as constants.

For this problem, the function is given as follows:

x² + 4y² + 7z² = 1.

The function for z is given by:

7z² = 1 - x² - 4y²

[tex]z = \sqrt{\frac{1 - x^2 - 4y^2}{7}}[/tex]

As a function of x, the derivative will be given by:

[tex]\frac{\partial z}{\partial x} = -\frac{x}{\sqrt{\frac{1 - x^2 - 4y^2}{7}}}[/tex]

Because the derivative of the inside term as a function of x is of -2x, then we apply the derivative of the root and simplify -2 with 2.

For the derivative as a function of y, we follow the same procedure, with the lone difference being the the inside derivative is of -8y, then:

[tex]\frac{\partial z}{\partial y} = -\frac{4y}{\sqrt{\frac{1 - x^2 - 4y^2}{7}}}[/tex]

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Answer:

y=2880x+26500

Step-by-step explanation:

Basically, this question wants you to write an equation where you can figure out how much money Tony has at any year.

1. They already told us how much the raise was: $2880

2. He started off with $26,500, so we know we have to add that at the beginning. That is our y-intercept.

3. A function is written as y=mx+b. Y is what you are solving for. M is the constant change (x doesn't mean anything, it just tells us which number is m). B is the y-intercept, which is 26,500 in this case. Its what you are starting with. If he had no money, there would be nothing to start with. There would be no y-intercept.

4. Because he gets the same raise every year of 2880, that is constant. It does not change, but it increases constantly.

5. So, y=2880x+26500 is your answer.

[tex] \frac{9}{3} - \frac{1}{6} = \frac{9 \times 2}{3 \times 2} - \frac{1}{6} = \frac{18}{6} - \frac{1}{6} \\ \\ \frac{18 - 1}{6} = \frac{17}{6} = 2 \frac{5}{6} [/tex]

Answer: 2 5/6

Step-by-step explanation:

9/3-1/6 is 2 5/6 what you do is cross multiply 9/3 and 1/6 to get 18/6 and 1/6 then you subtract across

An expression in math is a sentence with a minimum of two numbers/variables and at least one math operation in it. (-6p+1)/7 is an equivalent fraction of -4/7p+(-2/7p)+1/7.

An expression in math is a sentence with a minimum of two numbers/variables and at least one math operation in it.

The given expression is

-4/7p+(-2/7p)+1/7

In the given expression there is a variable p and a constant.

We have to add the terms which having p.

(-4/7+(-2/7))p+1/7

=(-4/7-2/7)p+1/7

=-6/7p+1/7

=(-6p+1)/7

Therefore (-6p+1)/7 is an equivalent fraction of -4/7p+(-2/7p)+1/7.

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Answer:EVALUATE

(x=3)(x=1) 4−2(x+3) 2(x+1) 3

Step-by-step explanation:

Answer:

2.61625

Step-by-step explanation:

The missing terms in the given factorized expression are:

3x²y + 12xy² + 9xy = 3xy ( x + 4y + 3 )

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation.

We have,

_ x²y + _ y² + 9 _ = 3x _ ( _ + 4y + _ )

We need to fill the boxes and make sure that both sides are equal.

We will remove the bracket on the right side.

i.e 3x _ _ + 12xy_ + 3x_ _

Now,

_ x²y + _ y² + 9 _ = 3x _ _ + 12xy_ + 3x_ _

We will make,

_ x²y  and 3x _ _ equal.

_ y²  and 12xy_ equal.

9 _  and + 3x_ _ equal.

So,

(3)x²y = 3x (x)(y)

(12x)y² = 12xy(y)

9 (xy) = 3x(y)(3)

Thus the missing terms in the given factorized expression are:

3x²y + 12xy² + 9xy = 3xy ( x + 4y + 3 )

3x²y + 12xy² + 9xy = 3x²y + 12xy² + 9xy

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Answer:  D (Interval)

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$30000\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\dotfill &5 \end{cases} \\\\\\ I = (30000)(0.05)(5) \implies I = 7500[/tex]

Answer:

50

Step-by-step explanation:

Answer

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2 answers

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The length is 50. You solve it by making an equation out of the information given. the rectangle's length(l) is 3 times its width(w) and its perimeter(p) is 128. So in order to solve this you need an equation to find the perimeter, isolating w to find l. It'll look something like this:

(3w+8)+(3w+8)+w+w=128

?You combine all like terms turning it into:

2(4w+8)=128

8w+16=128

8w=112

w=14

you use the value of w to solve for l as follows:

l=w*3+8

l=14*3+8

l=42+8

l=50

Answer:

-18 + 30 s - 72 t + 12 u

Step-by-step explanation:

Expand the following:

-6 (3 - 5 s + 12 t - 2 u)

-6 (3 - 5 s + 12 t - 2 u) = -6×3 - 6 (-5 s) - 6×12 t - 6 (-2 u):

-6×3 - 6 (-5) s - 6×12 t - 6 (-2) u

-6×3 = -18:

-18 - 6 (-5) s - 6×12 t - 6 (-2) u

-6 (-5) = 30:

-18 + 30 s - 6×12 t - 6 (-2) u

-6×12 = -72:

-18 + 30 s + -72 t - 6 (-2) u

-6 (-2) = 12:

Answer:  -18 + 30 s - 72 t + 12 u

Answer:

270

Step-by-step explanation:

With a 270 rotation you move 3 boxes

Answer: 53

Given, expression:

Given values: a = -2, b = 5, c = -3

Substitute them inside the expression:

distribute

evaluate

simplify

Step-by-step explanation:

the vertex form is

y = a(x - h)² + k

a is a stretch factor, (h, k) are the coordinates of the vertex of the parabola.

so, the original x-coordinate of the vertex was 4.

when we move it 6 units to the left. we subtract 6 from the x-coordinate.

that makes the new h

4 - 6 = -2

answer B is correct.

and the equation of the translated function is

g(x) = -3(x + 2)² + 5