The table of ordered pairs (x,y) gives an exponential function.
Write an equation for the function.

Answer: x-6, x+3, x-3

Step-by-step explanation;

Split the equation into two.

x2(x-6)-9(x-6)

(x-6) is seen as one of the tiles. Now work on x2-9

x2-9 is a difference of squares meaning the last two are (x+3) and (x-3).

(a) Let [tex]C(t)[/tex] denote the amount (in grams) of copper (II) sulfate (CuSO₄) in the tank at time [tex]t[/tex] minutes. The tank contains only pure water at the start, so we have initial value [tex]\boxed{C(0)=0}[/tex].

CuSO₄ flows into the tank at a rate

[tex]\left(20\dfrac{\rm g}{\rm L}\right) \left(4\dfrac{\rm L}{\rm min}\right) = 80 \dfrac{\rm g}{\rm min}[/tex]

and flows out at a rate

[tex]\left(\dfrac{C(t)\,\rm g}{400\,\mathrm L + \left(4\frac{\rm L}{\rm min} - 4\frac{\rm L}{\rm min}\right) t}\right) \left(4\dfrac{\rm L}{\rm min}\right) = \dfrac{C(t)}{100} \dfrac{\rm g}{\rm min}[/tex]

and hence the net rate of change in the amount of CuSO₄ in the tank is governed by the differential equation

[tex]\boxed{\dfrac{dC}{dt} = 80 - \dfrac C{100}}[/tex]

(b) This ODE is linear with constant coefficients and separable, so we have a few choices in how we can solve it. I'll use the typical integrating factor method for solving linear ODEs.

[tex]\dfrac{dC}{dt} + \dfrac C{100} = 80[/tex]

The integrating factor is

[tex]\mu = \exp\left(\displaystyle \int \frac{dt}{100}\right) = e^{t/100}[/tex]

Distributing [tex]\mu[/tex] on both sides gives

[tex]e^{t/100} \dfrac{dC}{dt} + \dfrac1{100} e^{t/100} C = 80 e^{t/100}[/tex]

and the left side is now the derivative of a product,

[tex]\dfrac d{dt} \left[e^{t/100} C\right] = 80 e^{t/100}[/tex]

Integrate both sides. By the fundamental theorem of calculus,

[tex]e^{t/100} C = e^{t/100}C\bigg|_{t=0} + \displaystyle \int_0^t 80 e^{u/100}\, du[/tex]

The first term on the right vanishes since [tex]C(0)=0[/tex]. Then

[tex]e^{t/100} C = 8000 \left(e^{t/100} - 1\right)[/tex]

[tex]\implies \boxed{C(t) = 8000 - 8000 e^{-t/100}}[/tex]

It exists not linear the curve indicates that the rate of change exists not constant.

Linear functions exist as those whose graph exists as a straight line. A linear function exists that can be characterized by the equation

y = mx + c, Where m exists the slope and c exists the intercept on the

y-axis. A linear function contains one independent variable and one dependent variable.

Therefore, the correct answer is option c) No, because the curve indicates that the rate of change is not constant.

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Answer:

There are 7 two bed bedroom apartments.

Step-by-step explanation:

Solution Given:

let the one bedroom apartment be x and two bedroom apartment be y.

By the question we can make an equation as

x+y=12

or y=12-x............................[1]

Again:

$360x+$450y=$4,950

Now substituting value of y, we get

$360x+$450(12-x)=$4,950

Opening Bracket

$360x+$5400-$450x=$,4,950

solving equation

-90x=-450

dividing both side by -90,we get

x=5

again,

substituting value of x in equation 1,we get

y=12-5=7 two bed bedroom apartments.

Let, x represents the number of one bedrooms and 12 - x represents the number of two bedrooms.

According to the question,

[tex]360x + 450(12 - x) = 4950[/tex]

[tex]360x + 5400 - 450x = 4950[/tex]

[tex]5400 - 4950 = 450x - 360x[/tex]

[tex]450 = 90x[/tex]

[tex] \frac{450}{90} = x[/tex]

[tex]5 = x[/tex]

Therefore, one bedrooms = x = 5

For number of two bedrooms which is equal to 12 - x

= 12 - 5

= 7

So your required answer is 7

If Renfro Rentals has issued bonds that have an 8% coupon rate, payable semiannually. The price of the bonds is: $1,039.11.

We would be making use of financial calculator to find or determine the price of the bonds (Present value) by inputting the below data:

N represent Number of years = 12 x 2 = 24

I represent Interest rate= 7.5 % / 2 =3.75 %  

PMT represent Periodic payment= (8% x 1000) / 2 = $40

FV represent Future  value= $1,000

PV represent Present value=?

Hence;

PV (Present value) = $1,039.11

Therefore if Renfro Rentals has issued bonds that have an 8% coupon rate ,payable semiannually. The price of the bonds is:  $1,039.11.

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Answer:

Step-by-step explanation: The earth rotates 34 km every 32 seconds. We can simplify this by dividing both sides by 32. Now, we have 34/32 km every 32 seconds. Now, to further simplify this, we need to convert 34/32 to a mixed number 34/32 = 1 2/32 which then can be simplified to 1 1/16. So, near the equator, the speed of Earth's rotation is 1 1/16 km per second.

Answer:

  a = 144

  b = 67

Step-by-step explanation:

Where a transversal meets parallel lines, consecutive interior angles are supplementary.

  a° +36° = 180° . . . . . . consecutive angles are supplementary

  a = 144 . . . . . . . . . . divide by ° and subtract 36

  b° +113° = 180° . . . . . . consecutive angles are supplementary

  b = 67 . . . . . . . . . . divide by ° and subtract 113

Step-by-step explanation:

solution

here

15×5

=75inches

Answer:

C

Step-by-step explanation:

for AB to be parallel to CD then the slopes of both segments must be equal

using the slope formula to find the slopes , then

A (x₁, y₁ ) and B (x₂, y₂ )

[tex]m_{AB}[/tex] = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

C (x₃, y₃ ) and D (x₄, y₄ )

[tex]m_{CD}[/tex] = [tex]\frac{y_{4}-y_{3} }{x_{4}-x_{3} }[/tex]

then

[tex]m_{CD}[/tex] = [tex]m_{AB}[/tex]

[tex]\frac{y_{4}-y_{3} }{x_{4}-x_{3} }[/tex] = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex] → C

The height of the taller building is 18.6 meters

A right triangle has one of its angles as 90 degrees. The side of a right angle triangle can be found using trigonometric ratios.

Therefore, the height of the taller building is the sum of the height of the smaller building and upper part of the taller building.

tan 53 = opposite / adjacent

tan 53 = x / 10

cross multiply

x = 10 tan 53

x = 10 × 1.32704482162

x = 13.2704482162

x = 13.3 m

tan 28 = y / 10

y = 10 tan 28

y = 5.31709431661

y = 5.3

Therefore, the height of the taller building is 13.3 + 5.3 = 18.6 meters.

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The area around the given curve according to the green theorem is [tex]F. dr = 0[/tex].

According to the statement

we have to find the area enclosed by the simple closed curve that encloses the origin.

So, We know that the

The given equation is

[tex]f(x,y) = \frac{2xyi + (y^{2} - x^{2} ) j}{(x^{2} + y^{2} )^{2} }[/tex]

and

If function is in form of,

[tex]F = Pi + Qj[/tex]

and C is any positively oriented simple closed curve that encloses the origin.

Then,by use of Green's theorem

Do the partial differentiation of the given function

Then

[tex]\frac{dQ}{dx} = \frac{2x^{3} - 6xy^{2}}{(x^{2} + y^{2} )^{3}}[/tex]

and

[tex]\frac{dP}{dy} = \frac{2x^{3} - 6xy^{2}}{(x^{2} + y^{2} )^{3}}[/tex]

On substitution in Green's theorem,

We get the value

[tex]F. dr = 0[/tex]

From this it is clear that the area around the given curve is zero.

So, The area around the given curve according to the green theorem is [tex]F. dr = 0[/tex].

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Answer:

probability result of sample space would result in 12/144

Step-by-step explanation:

as result there is 12 numbers on each dice, blth have exact same numbers, resulting in 144 combinations ti be thrown as sample space event outcome wluld be;

1/1 1/2 1/3 1/4 1/5 1/6 1/7 1/8 1/9 1/10 1/11 1/12

2/1 2/2 2/3 2/4 2/5 2/6 2/7 2/8 2/9 2/10 2/11 2/12

3/1 3/2 3/3 3/4 3/5 3/6 3/7 3/8 3/9 3/10 3/11 3/12

4/1 4/2 4/3 4/4 4/5 4/6 4/7 4/8 3/9 4/10 4/11 4/12

5/1 5/2 5/3 5/4 5/5 5/6 5/7 5/8 5/9 5/10 5/11 5/12

6/1 6/2 6/3 6/4 6/5 6/6 6/7 6/8 6/9 6/10 6/11 6/12

7/1 7/2 7/3 7/4 7/5 7/6 7/7 7/8 7/9 7/10 7/11 7/12

8/1 8/2 8/3 8/4 8/5 8/6 8/7 8/8 8/9 8/10 8/11 8/12

9/1 9/2 9/3 9/4 9/5 9/6 9/7 9/8 9/9 9/10 9/11 9/12

10/1 10/2 10/3 10/4 10/5 10/6 10/7 10/8 10/9 10/10 10/11 10/12

11/1 11/2 11/3 11/4 11/5 11/6 11/7 11/8 11/9 11/10 11/11 11/12

12/1 12/2 12/3 12/4 12/5 12/6 12/7 12/8 12/9 12/10 12/11 12/12

giving 12 matching numbers in a 144 possible rolled outcome

mathematic formula would be P(A) = n(A)/n(S)

As P(A)= probabolity of event A

n(A)= number of favouravle outcome

n(S)= total number of outcome in sample space

giving

12=2/144=0,0138888889

The y-intercept of the resulting polynomial is equal to - 3.

Herein we assume that the other two zeros of the polynomial are i and - i 3, otherwise the polynomial will have at least a complex number as coefficient of the expression. This is because we need to find values from a Cartesian plan, whose ordered pairs are real numbers.

Initially, we have the following expression by algebra properties:

f(x) = (x + i) · (x - i) · (x + i 3) · (x - i 3)

f(x) = (x² + 1) · (x² + 9)

f(x) = x⁴ + 10 · x² + 9

Then, we proceed to use the two rigid transformations described in the statement. Please notice that rigid transformations are transformations applied on polynomials such that Euclidean distance is conserved:

Vertical compression

f'(x) = (1 / 3) · f(x)

f'(x) = (1 / 3) · (x⁴ + 10 · x² + 9)

f'(x) = (1 / 3) · x⁴ + (10 / 3) · x² + 3

Reflection across the x-axis

g(x) = - f'(x)

g(x) = - (1 / 3) · x⁴ - (10 / 3) · x² - 3

The y-intercept is found for x = 0:

g(0) =  - (1 / 3) · 0⁴ - (10 / 3) · 0² - 3

g(0) = - 3

The y-intercept of the resulting polynomial is equal to - 3.

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2 x 10² kcal are in the serving report your answer to 2 significant figures.

According to the question

A serving of fish contains 50 g of protein and 4. 0 g of fat.

i.e. content of protein = 50 g

Content of fat = 4 g

kcal are in the serving report your answer to 2 significant figures:

As the serving of fish contains 50g of protein that is 4.0kcal/g

Calories in 50 g protein = (Content of protein) × (caloric value in protein)

50g × (4.0kcal/g) = 200kcal

That means the kcal of the serving is 200kcal

In 2 significant figures: 2 x 10² kcal

Hence,

2 x 10² kcal are in the serving report your answer to 2 significant figures.

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If the equation is y=15x+100 then the coordinate (0,100) of the equation shows that Jared had $100 when he started his saving.

Given an equation y=15x+100 that shows the amount of money saved by Jared for his bike based on the number of months that have passed.

We are required to find what the coordinate (0,100) mean in the context of the equation.

Equation is like relationship between two or more variables that are expressed in equal to form. Equations of two variables look like ax+by=c.It may be linear equation, quadratic equation, cubic equation or many more dependng on the power of variable present in that equation.

When we put x=0 in the equation we get the following:

y=15*0+100

y=100

It means that he had $100 in the beginning when he just started doing his savings.

Hence if the equation is y=15x+100 then the coordinate (0,100) of the equation shows that Jared had $100 when he started his saving.

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a) 6x + 12 = 5x - 5y

6x-5x = -5y-12

x = -5y-12

b) 5a-10x = 9x+9

-10x-9x = 9-5a

-19x = 9-5a

x = 9-5a/-19

Answer: x is -1/2,0 and y is 0,2

Step-by-step explanation:

Answer:

(4,0) , (0,2)

Step-by-step explanation:

Similar to the previous question.

x-intercept is where the line touches the x-axis , and y = 0.

when y = 0,

8x + 16(0) = 32

8x = 32

x = [tex]\frac{32}{8}[/tex]

x = 4

Therefore the coordinates of the x-intercept is (4,0)

y-intercept is where the line touches the y-axis, and x = 0.

when x = 0,

8(0) + 16y = 32

16y = 32

y = [tex]\frac{32}{16}[/tex]

y = 2

Therefore the coordinates of the y-intercept is (0,2)

Answer: x < -2

Step-by-step explanation:

[tex]\frac{1}{2} x-7 < -8[/tex]

First add 7 to both sides

[tex]\frac{1}{2} x-7 +7 < -8+7[/tex]

[tex]\frac{1}{2} x < -1[/tex]

Now multiply by 2 to cancel out 1/2 and leave you with x

[tex]2*\frac{1}{2} x < -1(2)[/tex]

[tex]x < -2[/tex]

Based on the given task content; the simplification of 7x - x to its simplest form is 6x.

Simplify 7x - x

7x and -x

So,

7x - x

= 6x

Therefore, 6x is the result of the simplification of 7x - x to its simplest form.

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The number that best represents the slope of the graphed line that is given is: -4.

The slope of a line is the ratio of the vertical distance to the horizontal distance across the line. It is calculated using the formula:

Slope (m) = rise/run = change in y / change in x = (y2 - y1)/(x2 - x1)

Given the two points on a coordinate plane as shown in the mage below, let:

(x1, y1) represent (0, 2)

(x2, y2) represent (0.5, 0)

Plug in the values

Slope (m) = change in y / change in x = (0 - 2) / (0.5 - 0)

Slope (m) = -2/0.5

Slope (m) = -4

Therefore, we can state that, the number that best represents the slope of the graphed line that is given is: -4.

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The actual answer is C.1/2

chust mee am a doktor

The value of the given expression is 9/10. The properties of real numbers, such as commutative and distributive are used for solving this expression.

The properties are:

The given expression is

(-3/7) × 6/5 + (3/2) - (6/5) × 1/14

applying commutative law (a + b = b + c)

⇒ (-3/7) × 6/5 - (6/5) × 1/14 + (3/2)

again applying commutative law (a × b = b × a)

⇒ (-3/7) × 6/5 - 1/14 × (6/5)+ (3/2)

applying distributive law (a × (b + c) = a × b + b × c) in reverse order

⇒ (-3/7 - 1/14) × (6/5)+ (3/2)

⇒ (-7/14) × (6/5)+ (3/2)

⇒ (-1/2) × (6/5)+ (3/2)

⇒ (-6/10) + (3/2)

⇒ (-6 + 15)/10

⇒ 9/10

Thus, the required value is 9/10 and the suitable properties are commutative and distributive.

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The end behavior of the power function is as x tends to infinity, f(x) tends to zero.

In this question,

The power function is [tex]f(x)=3^{-x}2[/tex]

The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.

The degree and the leading coefficient of a polynomial function determine the end behavior of the graph.

The graph below shows the behavior of the function f(x).

The above equation has the degree of 1, which is odd and the leading coefficient has the positive coefficient.

Then the end behavior is

As x -> ∞,

⇒ [tex]\lim_{x \to \infty} f(x)[/tex]

⇒ [tex]\lim_{x \to \infty} 3^{-x}2[/tex]

⇒ [tex]2\lim_{x \to \infty} 3^{-x}[/tex]

⇒ [tex]2\lim_{x \to \infty} 3^{-\infty}[/tex]

⇒ 2(0)

⇒ 0

Thus as x → ∞, f(x) → 0.

Hence we can conclude that the end behavior of the power function is as x tends to infinity, f(x) tends to zero.

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The value of Z in given equation is -55.

According to the statement

We have given that a linear equation which is

2 = 1/5z +13

And from this equation we have to find the value of the z.

So, For this purpose

we know that the

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

So, The equation is

2 = 1/5z +13

1/5z +13-2 = 0

1/5z +11 = 0

z = -11*5

z = -55

here z + 55 =0

So, The value of Z in given equation is -55.

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The volume of box B is (A) 864 cubic meters.

To find the volume of box B:

= 864 cubic meters.

Therefore, the volume of box B is (A) 864 cubic meters.

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The complete question is given below:

Box A has a volume of 32 cubic meters. Box B is similar to box A. To create box B, box A's dimensions were tripled. What is the volume of box B?

a. 864 m3.

b. 288 m3.

c. 96 m3.

d. 32 m3

The first inequality is represented by the purple area seen in the picture and the second inequality by the black area seen in the picture, the solutions set is the region where the two areas overlap each other.

In this question we have two inequalities representing constraints that Marissa should satisfy, provided that she wants to make a profit in selling paintings and bracelets.

The first inequality represents the minimum profit required from the sales of paintings (x) and bracelets (y) and the second one represents the minimum number required of sold bracelets. The two inequalities are described below:

15 · x + 7 · y ≥ 800      (1)

y ≥ 60     (2)

Since there are more than one solution, we decided to define a solutions set with the help of graphing tool. The first inequality is represented by the purple area seen in the picture and the second inequality by the black area seen in the picture, the solutions set is the region where the two areas overlap each other.

The statement is incomplete and such issue cannot be resolved. We decided to modify the statement as follows:

Marissa is selling paintings for $ 15 each and bracelets for $ 7 each. Her goal is to sell at least $ 800 in products, and she must sell at least 60 bracelets. Please show the set of all possible solution that will satisfy these constraints?

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Answer:

26 paintings and 61 bracelets

Step-by-step explanation:

if you do 26x15=390 and 61x7=427

390+427=817

so the answer is 26 paintings and 61 bracelets

also, I took the test so I know its right

The rate of change of the height is [tex]\frac{1}{9}[/tex] in/min.

A right circular cylinder is a cylinder that has a closed circular surface having two parallel bases on both the ends and whose elements are perpendicular to its base. It is also called a right cylinder.

Volume of the cylinder = [tex]\pi r^{2}h[/tex]

Rate of change of height is  [tex]\frac{dh}{dt}[/tex] = ?

At any time t,

Volume, V =  [tex]\pi r^{2}h[/tex]

Since r does not change with time, then r is a constant, so,

V =  [tex]\pi (6)^{2}h[/tex]

V = [tex]36\pi h[/tex]

Differentiate both sides with respect to time t,

[tex]\frac{dV}{dt} = 36\pi \frac{dh}{dt}[/tex] -------------(i)

Since [tex]\frac{dV}{dt}[/tex]is given as 4[tex]\pi[/tex] cu.in. per min,

[tex]4\pi = 36\pi \frac{dh}{dt}[/tex]

[tex]\frac{dh}{dt} = \frac{4\pi }{36\pi }[/tex]

[tex]\frac{dh}{dt} = \frac{1 }{9 }[/tex] in/min.

Hence, The rate of change of the height is [tex]\frac{1}{9}[/tex] in/min.

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39 number is the secret code as the unlock code for the safe.

According to the statement

we have given that  a some numbers as a code and we have to find the correct code after applying the given conditions.

So, For this purpose

The given number set is

5 17 29 22 11 26 27 35 39 41

So,

A. One condition : It is an odd number

so, the number set become

5 17 29 11 27 35 39 41

And

B. Second condition : It is greater than 20

so, the number set become

29 27 35 39 41

And

C. Third condition : It is smaller than 40

so, the number set become

29 27 35 39

And

D. Fourth condition : It is not a prime number

so, the number set become

27 35 39

And

E. Fifth condition : It has 13 as one of its factors

so, the number set become

39.

So, 39 number is the secret code as the unlock code for the safe.

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Answer:

0.13 inches.

Step-by-step explanation:

1 inch = 2.54 cm

So 1 cm = 1/ 2.54 in

0.33 cm = 0.33/2.54 in

= 0.13 inches.