3. The triangles shown are similar. List all the pairs of congruent angles and write the statement of proportionality.

The exponential function shown in the graph is f(x) = 2ˣ

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

The standard form of an exponential function is:

y = abˣ

where a is the initial value and b is the multiplication factor.

The graph shown is an exponential function.

At the point (0, 1):

y = abˣ

substituting:

1 = ab⁰

a = 1

At the point (2, 4):

y = abˣ

substituting x = 2, y = 4 and a = 1:

4 = b²

b = 2

The exponential function is y = 2ˣ

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

The exact value of the trigonometric function sin (A + B) is equal to 1020 / 1189.

In this problem we must determine the exact value of the sine of the sum of two acute angles. There are acute angles in the first quadrant, thus:

sin θ > 0

cos θ > 0

tan θ = sin θ / cos θ

In addition, by trigonometric formulas:

cos θ = √(1 - sin² θ)

cos θ = 1 / √(tan² θ + 1)

Where θ is the angle, in degrees.

sin (α + β) = sin α · cos β + cos α · sin β

If we know that sin A = 40 / 41 and tan B = 20 / 21, then the exact value of sin (A + B) is:

cos A = √[1 - (40 / 41)²]

cos A = 9 / 41

cos B = 1 / √[1 + (20 / 21)²]

cos B = 21 / 29

sin B = √[1 - (21 / 29)²]

sin B = 20 / 29

sin (A + B) = (40 / 41) · (21 / 29) + (9 / 41) · (20 / 29)

sin (A + B) = 1020 / 1189

To learn more on trigonometric formulas: https://brainly.com/question/24377281

#SPJ1

Answer: y+3= 1/7 * (x+8)

Step-by-step explanation:

g⁻¹(x) = ∛(x²/2 + 3)  is the inverse of  the function g(x)= √(2x³-6)

In mathematics, the inverse function of a function g (also called the inverse of g) is a function that undoes the operation of g.

g(x)= √(2x³-6)

Let g(x) = y

So we can say y = √(2x³-6)

We will then make x the subject:

y = √(2x³-6)

y² = 2x³-6

y² + 6 = 2x³

2x³ = y² + 6

x³ = y²/2 + 6/2

x³ = y²/2 + 3

x = ∛(y²/2 + 3)

since x = g⁻¹(y)  = ∛(y²/2 + 3)

Thus, g⁻¹(x) = ∛(x²/2 + 3)      (Replace y with x)

Learn about inverse function on:

brainly.com/question/11735394

#SPJ1

After 10 years at 9% compound interest per annum, The amount will be £393.57.

The amount of money you will have after 10 years can be calculated using the formula for compound interest:

[tex]A = P * (1 + r/n)^{nt}[/tex]

where:

A is the final amount,

P is the initial amount (principal),

r is the interest rate as a decimal,

n is the number of times the interest is compounded per year,

t is the number of years the money is invested.

In this case:

P = £200

r = 9% = 0.09

n = 1 (because interest is compounded annually)

t = 10

So, plugging in the values, we get:

[tex]A = 200 * (1 + 0.09/1)^{1 * 10)} = 200 * (1.09)^{10}[/tex]

[tex]A = 200 * 1.96787 = 393.57[/tex]

So, after 10 years at 9% compound interest per annum, you will have £393.57.

Learn more about compound interest here https://brainly.com/question/14295570

#SPJ4

The two equations form a system of linear equations that has no solution are

y=3x+2

y=3x+(1/2)

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

y=3x+2

y=3x+(1/2)

Equate both the equations to find x

3x+2 =3x+(1/2)

same term 3x cancels out

2=(1/2)

This is not true

So, two equations form a system of linear equations that has no solution are

y=3x+2

y=3x+(1/2)

To learn more about the solution of an equation from the given link

https://brainly.com/question/22688504

#SPJ1

The two equations can be rearranged to get two equations with one variable on each side. The equations become 4a = -9 - 3b and 2a = -1 - 5b. By dividing both sides of the first equation by 4, the equation becomes a = -2.25 - 0.75b. Substituting this value of a into the second equation gives -4.5 - 3.75b = -1. Solving this equation for b gives b = 1.2.

4a + 3b = -9

2a + 5b = -1

4a = -9 - 3b

2a = -1 - 5b

a = -2.25 - 0.75b

-4.5 - 3.75b = -1

b = 1.2

a = -2.25 - 0.75(1.2)

a = -1.95

The given set of equations is a simultaneous equation. This means that both equations have the same two variables, a and b. To solve for a and b, we must rearrange the equations so that each equation has only one variable on one side. We can do this by subtracting 3b from the first equation and 5b from the second equation. This gives us the equation 4a = -9 - 3b and 2a = -1 - 5b.

Next, we divide both sides of the first equation by 4 to get a = -2.25 - 0.75b. We can then substitute this into the second equation to get -4.5 - 3.75b = -1. Solving this equation for b gives us b = 1.2. Finally, we can substitute this value of b back into the first equation to get a = -1.95. This means that the solutions for a and b are a = -1.95 and b = 1.2.

Learn more about equation here

https://brainly.com/question/29657992

#SPJ4

Option C) is the correct graph that best represents the combination of both functions.

The graph, which plots time on the x-axis and temperature on the y-axis, displays an increasing function that depicts the temperature. The graph is divided into two sections: one shows a straight line with a positive slope to reflect the heater's contribution, and the other shows a curve to show the sun's contribution.

Option A) depicts a straight line that illustrates the rise in temperature brought on by the heater, but it omits the sun's influence. The intersection of these two functions is not depicted in this graph.

Option B) displays a curve that depicts the rise in temperature brought on by the sun, but it omits the impact of the heater. The intersection of these two functions is not depicted in this graph.

The sum of the two functions h(t) and s(t), which model the rise in pool temperature, can be written as follows:

c(t) = h(t) + s (t)

The specific functions h(t) and s(t) and their values at various times t would affect the graph of c(t).

Both the function h(t) and the function s(t) model the rise in temperature brought on by the sun and the heater, respectively.

As a result, Option C) is the correct graph that accurately depicts the union of the two functions.

To know more about Graph visit:

brainly.com/question/17267403

#SPJ1

Answer:

Its A.

Step-by-step explanation:

it just looks like a combination of the other 2

The total surface area of the pyramid is 100 + 4 x 50 = 100 + 200 = 300 square inches.

A square pyramid's surface area is calculated by summing the areas of its four lateral sides and base.

Since each side of the base of the pyramid measures 10 inches, the base has an area of 10 x 10 = 100 square inches.

Due to the fact that each lateral face is a triangle with a base of 10 inches and a height of 10 inches each, they each have an area of (1/2) x 10 x 10 = 50 square inches.

Therefore, the total surface area of the pyramid is 100 + 4 x 50 = 100 + 200 = 300 square inches.

To learn more about surface area, visit the link below:

https://brainly.com/question/29101132

#SPJ4

Answer: To find the minimum value of c = x + 3y, you need to solve the optimization problem with a constraint or without any constraint.

Without a constraint:

The minimum value of c = x + 3y without a constraint is achieved when the partial derivatives of c with respect to x and y are equal to zero.

Let's take the partial derivative of c with respect to x:

dc/dx = 1

And with respect to y:

dc/dy = 3

Setting these equal to zero, we have:

1 = 0 and 3 = 0

Since the partial derivatives are not equal to zero, there is no minimum value of c without a constraint.

With a constraint:

If there is a constraint, such as a limit on x or y, then the minimum value of c can be found by using optimization techniques, such as the method of Lagrange multipliers.

Step-by-step explanation:

Answer: X= 5 ;  -11

To solve our problem lets work backwards.

x^2-6x=55. First we must subtract 55 from both sides our equation. That leaves us with x^2-6x-55=0.  

We next need to cancel out the number six. We also need to find two numbers that can be multiplied by one another to equal 55.

This would be 5 and -11. 5 and -11 can be added together to make -6, which is the negative integer for 6. They can also be multiplied together to make the negative integer of 55, which is -55.

This means that our X has two possible solutions.

Hence, X= 5 & -11

I hope this helps & Good Luck <3 !

Answer:

your profit is 400

Step-by-step explanation:

50×225

Answer:

y = 2x + 5

The slope: 2

Y-intercept: 5

Step-by-step explanation:

Slope-intercept form: y = mx + b

m = the slope

b = y-intercept

Our equation

-4x+2y=10

2y = 4x + 10

y = 2x + 5

The slope: 2

Y-intercept: 5

Rudy's timing in the most recent race is 312 minutes.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that Rudy has run many marathons and keeps track of all of his finishing times. At a race last month, he finished in 260 minutes. At his next race, he finished with a time that was 20% longer.

Rudy's timing in the most recent race can be calculated as -

{x} = 260 + 20% of 260

{x} = 260 + (20/100) x 260

{x} = 260 + 20 x 2.6

{x} = 260 + 52

{x} = 312

Therefore, Rudy's timing in the most recent race is 312 minutes.

To solve more questions on functions, visit the link below-brainly.com/question/17613163

#SPJ1

(-5, 0 ) and (0, 5) are the ordered pair satisfies the inequality y < x+5

a relationship between two expressions or values that are not equal to each other is called 'inequality.

The given inequality is y < x+5

First, we have to find the x-intercept which occurs at y = 0

0 < x + 5

x<-5

For y-intercept,

y <  0+ 5

y <5

As a result, the obtained ordered pair is  (-5, 0 ) and (0, 5).

Hence, (-5, 0 ) and (0, 5) are the ordered pair satisfies the inequality y < x+5

To learn more on Inequality click:

https://brainly.com/question/28823603

#SPJ1

The exponential function to model the population of Valley View is [tex]y = 1800(1.012)^t[/tex].

What is an exponential function?

The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

An exponential function is written in the form -

[tex]y=ab^t[/tex]

Here, y is the function, a is the base value b is the rate and t is time period.

The number of people in Valley view is 1800. So, the base is a = 1800.

The function y depicts the towns population.

Each decade the population grows by 12%.

The growth rate per year is = 12 / 10

The growth rate is 1.2%

The value for b will be = 1 + r

b = 1 + 1.2/100

b = 1 + 0.012

b = 1.012

So, the exponential equation will be -

[tex]y = 1800(1.012)^t[/tex]

Therefore, the exponential equation is [tex]y = 1800(1.012)^t[/tex].

To learn more about exponential function from the given link

brainly.com/question/12626186

#SPJ1

The number of ways to select 9 players for the starting lineup from a team of 15 players  is 4862 ways.

The number of ways to select 9 players for the starting lineup from a team of 15 players can be calculated using the formula for combinations, which is given by:

C(n,k) = n! / (k! (n-k)!)

Where n is the total number of items, k is the number of items being selected, ! means factorial, and C(n,k) represents the number of combinations of k items from n.

Using this formula, the number of ways to select 9 players from a team of 15 players is:

C(15,9) = 15! / (9! (15-9)!) = 15! / (9! 6!) = 4,862

So, there are 4,862 ways to select 9 players for the starting lineup from a team of 15 players.

To learn more about combinations click on,

https://brainly.com/question/13480867

#SPJ4

The relative minimum and the relative maximum for the attached graph over the interval [ 1, 5 ] of the function given in graph is equal to -14 and -3 respectively.

Graph is attached.

Function shown in the attached graph over the interval [ 1, 5 ] is :

Representing the parabola function.

Vertex representing lowest point of the graph in the interval [ 1, 5 ] is given by :

( 4.5 , -14 )

Vertex representing highest point of the graph in the interval [ 1, 5 ] is given by :

( 1.5 , -3)

Relative minimum and maximum is represented by the y -coordinate of the graph.

Lowest point gives relative minimum = -14

Highest point gives relative maximum = -3

Therefore, for the function in the graph the relative minimum = -14 and relative maximum= -3.

The above question is incomplete , the complete question is:

what are the relative minimum and relative maximum values over the interval [1, 5] for the function shown in the graph?

Graph is attached.

learn more about function here

brainly.com/question/12431044

#SPJ4

Answer: 2 c squared d + d c + 6 c squared d squared

Step-by-step explanation:   I looked it up

Eliza is 212 feet above the ground as the given sector area of the half of the wheel is 5618 pi ft^2 and ride is stuck at 180 degrees.

Ferris wheel has a shape of a circle

So, we can use this formula

Area = πr²

Sector area of half the circle = πr²/2

From Eliza to the ground is the diameter of the wheel

5618 π ft² = πr²/2

r² = √2×5618ft²

r = 106 feet

The diameter of the wheel is twice the radius

= 2 × 106 feet = 212 feet

Therefore, Eliza is 212 feet above the ground.

Learn more about circles here brainly.com/question/29142813

#SPJ4

The loss percentage on selling an article is, 75%.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

The loss made on selling an article is 25% of the cost price.

Let the cost price = 100

Hence, Selling price is,

⇒ 25% of cost price

⇒ 25% of 100

⇒ 25

Thus, The loss is,

⇒ Loss = cost price - selling price / cost price × 100

           = (100 - 25) / 100 × 100

          = 75%

Thus, The loss percentage on selling an article is, 75%.

Learn more about the percent visit:

https://brainly.com/question/24877689

#SPJ1

The value of a car that depreciates over time can be modeled by the function [tex]J(t)=27000(0.9)^{2t+2}[/tex] has an equivalent form of [tex]J(t) = 21870(0.81)^t[/tex].

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).

The value of the car is given as:

[tex]J(t)=27000(0.9)^{2t+2}[/tex]

The equation can be written as:

[tex]J(t)=27000(0.9)^{2t} (0.9)^2\\\\J(t) = 27000(0.81)^t(0.81)\\\\J(t) = 21870(0.81)^t[/tex]

Hence, the value of a car that depreciates over time can be modeled by the function [tex]J(t)=27000(0.9)^{2t+2}[/tex] has an equivalent form of [tex]J(t) = 21870(0.81)^t[/tex].

Learn more about functions here:

https://brainly.com/question/12431044

#SPJ1

The simplified expression is j^-4k^-12

From the question, we have the following parameters that can be used in our computation:

j^-5k^-5 x jk^-7

Rewrite as

j^-5k^-5 x jk^-7 = j^-5 * j * k^-5k^-7

Apply the law of indices in the products

j^-5k^-5 x jk^-7 = j^-4 * k^-12

So, we have

j^-5k^-5 x jk^-7 = j^-4k^-12

Hence, the expression is j^-4k^-12

Read more about expression at

https://brainly.com/question/15775046

#SPJ1

The length of AB is [tex]2\sqrt{105}[/tex].

An altitude is a line which passes through the vertex of the triangle and meets the opposite side at the right angle. A triangle has three altitudes.

Consider the triangle ABC, with right angle at B,

Let AB = x, BC = y, BD = z.

By pythagoras theorem,

[tex]AC^{2} =AB^{2} +BC^{2}[/tex]⇒[tex]x^{2} +y^{2} = 21^{2}[/tex]----------(1)

From triangle ADB,

[tex]z^{2} +11^{2} =x^{2}[/tex]-------(2)

[tex]z^{2} +10^{2} =y^{2}[/tex]--------(3)

(2)-(3), we get, [tex]x^{2} -y^{2} =21[/tex]-----(4)

subtract (1) and (4) we get,

[tex]x^{2} =420[/tex]

⇒[tex]x=2\sqrt{105}[/tex]

Hence, the length of AB is [tex]2\sqrt{105}[/tex] in simplest radical forms.

Learn more about altitude here:

https://brainly.com/question/14385841

#SPJ1

The value of the expression is 40.64.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

41 + (5/7)t

When t = -1/2

41 + (5/7)t

= 41 + 5/7 x (-1/2)

= 41 - 5/14

= (574 - 5) / 14

= 569/14

= 40.64

Thus,

The value is 40.64.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ1

Therefore, Nolan has 8 dollars left to spend on gift C.

Nolan spent 9 dollars and 34 cents on gift A,

and 3 dollars and 12 cents on gift B,

for a total of

9 + 3 = 12 dollars and

34 + 12 = 46 cents spent so far.

Nolan started with 20 dollars, so he has 20 - 12 = 8 dollars remaining for gift C.

By using wildcards (such as "x" and "y") that are replaced with random values when the quiz is taken, simple calculated questions provide a technique to build individual numerical questions whose response is the result of a numerical formula that contains changeable numerical values.

For such more question on spend

https://brainly.com/question/24188070

#SPJ4

The exponential model is [tex]T(t)=69+(111)e^-^1^3^6^8^3^5^7^0^2^1^t[/tex] and It takes the cake 9.32 minutes to cool to the desired​ temperature

We can solve this by using Newton's Law of cooling,

[tex]T(t)=C+(T_o-C)e^k^t[/tex]

where

T(t) is the temperature at any given time

C is the surrounding temperature

T₀ is the initial temperature

k is a negative constant

t is the time

A cake recipe is baked until the center is 180 °F

T₀=180 ⇒ initial temperature

The room temperature is 69 °F

C = 69 ⇒ surrounding temperature

By using the table, substitute t and T to find the constant k

At t = 5 minutes, T = 125 °F

[tex]125=69+(180-69)e^k^t[/tex]

By subtracting 69 on both sides

[tex]56=(111)e^k^t[/tex]

Dividing both sides by 111

[tex]\frac{56}{111} =e^k^t[/tex]

Add ㏑ for both sides

[tex]ln(\frac{56}{111} )=ln(e^k^t)[/tex]

Dividing both sides by 5

k=- 0.1368357021

The exponential model is  [tex]T(t)=69+(111)e^-^1^3^6^8^3^5^7^0^2^1^t[/tex]

The cake cools at 100 °F and the desired​ temperature is 100°

T(t) = 100 ⇒ cake's temperature at t minute

Using the model above to find t

[tex]T(t)=69+(111)e^-^1^3^6^8^3^5^7^0^2^1^t\\\\100=69+(111)e^-^1^3^6^8^3^5^7^0^2^1^t[/tex]

Subtract 69 from both sides

[tex]39=(111)e^-^1^3^6^8^3^5^7^0^2^1^t[/tex]

Divide both sides by 111

[tex]\frac{39}{111} =e^-^1^3^6^8^3^5^7^0^2^1^t[/tex]

Applying ㏑ for both sides

[tex]ln(\frac{39}{111}) =e^-^1^3^6^8^3^5^7^0^2^1^t[/tex]

Dividing both sides by - 0.136835702

t=9.321711938

t ≅ 9.32 minutes

It takes the cake 9.32 minutes to cool to the desired​ temperature.

To know more about an exponential model:

https://brainly.com/question/14938119

#SPJ4

The equation of line m passing through the points (-2,-8) and (1,1) is y = 3x - 2

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

The slope intercept form of a linear equation is:

y = mx + b

Where m is the rate of change and b is the y intercept.

Line M goes through the points (-2,-8) and (1,1). Hence:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\substituting:\\\\y-(-8)=\frac{1-(-8)}{1-(-2)} (x-(-2))\\\\y=3x-2[/tex]

The equation of line m is y = 3x - 2

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Step-by-step explanation:

The expression can be simplified as follows:

-12 + |-3| - |-14| = -12 + 3 - 14 = -23

So, the answer is -23.

Answer: -23

Step-by-step explanation: The absolute value symbols turn the numbers inside to positive. The subtraction symbols outside dont change. When doing this conversion the simplified version will be -12+3-14 which equals -23.

Answer:

5^-18

Step-by-step explanation:

here is the answer please mark me as the brainliest