Select the correct answer from each drop-down menu.
Points A, B, and C form a triangle. Complete the statements to prove that the sum of the interior angles of ΔABC is 180°.
Statement Reason
Points A, B, and C form a triangle. given
Let be a line passing through B and parallel to . definition of parallel lines
∠3 ≅ ∠5 and ∠1 ≅ ∠4
m∠1 = m∠4 and m∠3 = m∠5
m∠4 + m∠2 + m∠5 = 180° angle addition and definition of a straight line
m∠1 + m∠2 + m∠3 = 180° substitution

The combined area of the square and rectangle is 3x² + 3x - 3.

The expression 2x² + 6x - 4 represents the area of a square.  The area of a rectangle is represented by x² - 3x + 1.  The combined area of the square and the rectangle is the sum of the area of the square and the area of the rectangle.

Therefore,

area of the square = 2x² + 6x - 4

area of the rectangle = x² - 3x + 1

Let's find the combined area as follows:

combine area of the square and rectangle = 2x² + 6x - 4 + x² - 3x + 1

combine area of the square and rectangle = 2x² + x² + 6x - 3x - 4 + 1

combine area of the square and rectangle = 3x² + 3x - 3

Therefore,

the combined area = 3x² + 3x - 3

learn more on area here: https://brainly.com/question/29087271

#SPJ1

Step-by-step explanation:

this you solve via the determinant of the matrix.

for a matrix A

a b

c d

the determinant (A) = ad - bc

so, we have here

x² - 5×-4 = 24

x² + 20 = 24

x² = 4

x = ±2

so, as a simple quadratic equation, there are 2 solutions for x.

The value of the functions for the condition is,

1. f(x + h) = 3(x + h)² - (x + h) + 5,

2. (fog)(x) =  27x² -33x + 15,

3. f(g(h(-1))) = 16,060.

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.

Given f(x) = 3x² - x + 5

g(x) = -3x + 2

h(x) = -5x³

1. Find f(x + h),

so  f(x) = 3x² - x + 5

substitute x = x+ h

f(x + h) = 3(x + h)² - (x + h) + 5

2. (fog)(x),

f(g(x))

g(x) = -3x + 2

f(-3x + 2)  = 3(-3x + 2)² - (-3x + 2) + 5

f(g(x)) = 3(9x² + 4 - 12x) - 2 + 3x + 5

f(g(x)) = 27x² + 12 - 36x - 2 + 3x + 5

f(g(x)) = 27x² -33x + 15

3. Find f(g(h(-1)),

h(x) = -5x³

g(x) = -3x + 2

g(h(x)) = -3(-5x³)² + 2

g(h(x)) = -75x⁶ + 2

f(x) = 3x² - x + 5

f(g(h(x))) = 3(-75x⁶ + 2)² - (-75x⁶ + 2) + 5

f(g(h(x))) = 3(5625x¹² + 4 - 300x⁶) + 75x⁶ - 2 + 5

f(g(h(x))) = 16875x¹² + 12 - 900x⁶ + 75x⁶ -2 + 5

f(g(h(x))) = 16875x¹² - 825x⁶ + 10

substitute x = -1,

f(g(h(-1))) = 16875(-1)¹² - 825(-1)⁶ + 10

f(g(h(-1))) = 16,060

Hence  f(x + h) = 3(x + h)² - (x + h) + 5,

2.f(g(x)) = 27x² -33x + 15,

3. f(g(h(-1))) = 16,060.

Learn more about functions;

https://brainly.com/question/12431044

#SPJ1

Step-by-step explanation:

The equivalent expression in the form of a product is:

(8x) * (4x + 6)

The missing entries would be x = 4 and y = 2.

Equation is a physical and mathematical statement that describing physical phenomena and the relationship between different physical quantity typically consist of variable simple presenting physical quantity and then it personal variable may be pointed such as your energy.

In this equation, x and y are variables. To determine the values of the missing entries, we need to solve the equation. The equation is a quadratic equation of the form y2 = x. To solve it, we need to take the square root of both sides of the equation. This gives us the solution y = √x. So, the value of the missing entries is √x.

For example, if x = 4, then the value of y would be √4 = 2. Therefore, the missing entries would be x = 4 and y = 2.

To know more about Equation click-
https://brainly.com/question/26408808
#SPJ1

The correct inequality that represent the dogs could he have walked on Saturday is,

⇒ 100 + 12.50x > 210

A relation by which we can compare two or more mathematical expression is called an inequality.

We have to given that;

On Saturday, Dylan earned $100 for cleaning a local business.

And, He also walked dogs to earn money, charging $12.50 for each dog he walked.

Now, Let number of dogs = x

Then, We get;

The correct inequality that represent the dogs could he have walked on Saturday is,

⇒ 100 + 12.50x > 210

Learn more about the inequality visit:

https://brainly.com/question/25944814

#SPJ1

The statement that will not produce a triangle is side lengths of 5.5 ft, 11 ft, and 5.5 ft, the correct option is C.

Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side.

Suppose a, b and c are the three sides of a triangle. Thus according to this theorem,

[tex](a+b) > c\\(b+c) > a\\(c+a) > b[/tex]

Given;

A. angle measures of 47o, 58o, 75o

Here,47o+ 58o,+75o=180

B. angle measures of 61o, 61o, 58o

Here, 61o+61o+58o=180

C. side lengths of 5.5 ft, 11 ft, and 5.5 ft

5.5+5.5 is not equal to 11

D. side lengths of 5 in, 7 in, and 8 in

5+7 is greater than 8

Therefore, the triangle with side lengths of 5.5 ft, 11 ft, and 5.5 ft is not the triangle.

Learn more about triangle inequality theorem here:

https://brainly.com/question/342881

#SPJ1

The area of the circle is 78.5 ft^2.

Given that,

A segment is drawn from one point on the circle to another point on the circle through the center of the circle is 10 feet.

So, the diameter of the circle d = 10 feet

The formula for the area of the circle = Пr^2

where r is the radius of the circle and П is given as 3.14

Radius = diameter/2

r = 10 feet/2

= 5 feet

So, by applying the formula

Area of the circle = П × 5 × 5

= 3.14 × 5 × 5

= 78.5 ft^2

To learn more about circles,

https://brainly.com/question/29614115

Note that where Tom Harris is 24 years old and he wishes to purchase a $7,000 value 10-year term insurance, his annual premium will be:  $290.5.

Gross premiums written in the insurance sector are the sum of direct and assumed premiums written before subtracting ceded reinsurance. Direct premiums written are the premiums on all policies issued by the company's insurance subsidiaries throughout the fiscal year.

To compute Tom's insurance premium we must use the information given as well as the table above:

Given:

Tom's Age = 24 years

Value of Insurance Cover Requested = $7,000

Type of Insurance cover requested = 10-Year Term

The rate for the Type of Insurance Cover requested: Since he 24 and wants a 10-year term, the rate applicable from the table is; 4.15%

Thus, his annual premium  = 7000 * 4.15%
= 29050/ 100
= $290.5

Thus, Tom Harris' annual insurance premium is: $290.5

Learn more about Term Insurance:
https://brainly.com/question/27910991
#SPJ1

Answer: 67.1 cm

Step-by-step explanation:

Using the Law of Sines:

[tex]\frac{i}{\sin I}=\frac{h}{\sin H}\\\\\frac{i}{\sin 24^{\circ}}=\frac{97}{\sin 144^{\circ}}\\\\i=\frac{97 \sin 24^{\circ}}{\sin 144^{\circ}}\\\\i \approx 67.1 \text{ cm}[/tex]

Answer:  67.1

Step-by-step explanation:

Answer:

12.10 pm

Step-by-step explanation:

just take the 45 minutes she uses to bake and add to the time she starts

11.25 a.m+45

12.10 pm

The measure of angle 4 is 90 degrees

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

The rectangle

Also, we have

<5 = 12x -3

<6 = 10x + 9

Angles 5 and 6 add up to 90

So, we have

12x - 3 + 10x + 9 = 90

Evaluate the like terms

22x = 84

So, we have

x = 3.82

The angles in a triangle add up to 180

So, we have

<4 + 12 * 3.82 - 3 + 10 * 3.82 + 9 = 180

Evaluate

<4 = 90

Hence, the measure o this angle is 90 degrees

Read more about angle at

https://brainly.com/question/7620723

#SPJ1

To locate the fractions we must divide the unit in the number of the denominator (point A). According to the information, each shell symbol means 2 shells. Mark found 4 fewer shells than Tania. Mark and Carlos found 10 more shells than Mei Ling. Lastly, the numbers are rounded to the nearest number.

To locate the fractions we must divide the unit in the part number that says the denominator of the fraction and locate the fraction in the numerator position as shown in the graph. They all go in the first position.

Based on the information in the graph, it can be established that:

To approximate the numbers we must identify which of the numbers in the graph is closest:

Learn more about numbers in: https://brainly.com/question/17429689

#SPJ1

The correct equation for the graph include the following: C. y = 2x/3 - 4.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

From the information provided above, we have the following slope and data points on the line:

At point (0, -4), a linear equation of this line can be calculated in point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - (-4) = (0 + 4)/(6 - 0)(x - 0)

y + 4 = 2x/3

y = 2x/3 - 4

Read more on slope here: brainly.com/question/3493733

#SPJ1

Answer:

( 0,1)

Step-by-step explanation:

y-4x=1

We want to find the y-intercept ( where it crosses the y-axis).

Let x = 0

y-4*0=1

y = 1

The coordinates of the y-intercept are ( 0,1).

The function at its maximum value will be at point (9,2) and its value is 51 which can be derived keeping in mind the constraints that have been given.

The maximum value of any kind of a function is the place where the said function reaches its highest point, or vertex, on a graph. If your kind of quadratic equation has something as a negative of a term, it will also have a maximum value.

There are a bit of three ways to find that maximum, depending on which form of a quadratic function you have got.

here, we have,

Herein we can find the closed region ABC from the three equations or constraints given

and can mark the points as

A = (2,2)

B = (5, 2)

C = (9, 2)

if we put up the values of the points, we get

at (9, 2) ,

z=5x+3y

 =45+6

  =51 that is the maximum value amongst the three.

Thus, the maximum point of the function can be calculated as (9,2)

How do you extract out the maximum or minimum value of a function?

We will at first set out the first derivative of the function to absolute zero and then solve for x to get the exact critical point.

If we then take the second derivative or f’’(x), there in we can find out whether this point will be a maximum or minimum. If the second derivative is seen as positive, it will be a minimum value

What is the maximum value of a function called?

The maximum or minimum value that is calculated over the entire function is called an “Absolute” or “Global” maximum or minimum of the function.

There is presence of only one global maximum (and only one global minimum) but there can be several that is more than one local maximum or minimum

To know more about maximum value of a function visit:

brainly.com/question/14996337

#SPJ1

Answer:

To solve the expression [(4r²t)³]², you need to follow the order of operations (PEMDAS):

Calculate the expression inside the outermost parenthesis first: (4r²t)³ = (4 * r^2 * t)^3, where r and t are variables.

Raise the result to the power of 3: (4 * r^2 * t)^3 = 64 * r^6 * t^3.

Raise the result to the power of 2: (64 * r^6 * t^3)^2 = 4096 * r^12 * t^6.

So, [(4r²t)³]² = 4096 * r^12 * t^6.

Step-by-step explanation:

The larger television is Vehicle Viewing, explanation is mentioned below,

The diagonal of a television refers to the length of a line segment connecting two opposite corners of the screen. It is a way of measuring the size of the television screen, rather than its width or height. The diagonal measurement gives a good indication of the overall screen size and is commonly used as a specification for television screens.

Given that,

Two television,

Vehicle Viewing having diagonal 75 inches

Traveling TV Co having diagonal 8.5 inches

larger television =?

Vehicle Viewing, Inc. has the larger television with a diagonal of 75 inches compared to Traveling TV Co.'s diagonal of 8.5 inches.

This can be determined by simply comparing the two diagonal measurements given.

Hence, the larger television is Vehicle Viewing.

To know more about diagonal check:

https://brainly.com/question/12274248

#SPJ1

Answer:

In Fig. 12.35, if ATB = 82°, then the angles of ABC would be A = 82°, B = 98°, and C = 180°. This can be determined by using the fact that the sum of the angles in a triangle is 180°.

Step-by-step explanation:

The correct theorem with the correct pair of congruent triangles are given below:

Two triangles are congruent if all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent.

The theorems for the congruence of triangles is as follows:

Learn more about congruent theorems of triangles at: https://brainly.com/question/3168048

#SPJ1

Answer:1/6 can be represented as a fraction of a whole unit, where the whole unit is divided into 6 equal parts. Each of these parts represents 1/6 of the whole.

1/2, on the other hand, represents half of the whole unit, so it is twice as much as 1/6.

To visualize this, you can think of a ruler divided into 6 equal parts. 1/6 would represent 1 mark on the ruler, while 1/2 would represent 3 marks. To have the same length as 1/2, you need to add up 3 marks, or 3 copies of 1/6.

You can also think of this as converting 1/6 to a common denominator, which in this case is 6. 3 copies of 1/6 is equal to 3/6 or 1/2.

Step-by-step explanation:

1/6 can be represented as a fraction of a whole unit, where the whole unit is divided into 6 equal parts. Each of these parts represents 1/6 of the whole.

1/2, on the other hand, represents half of the whole unit, so it is twice as much as 1/6.

To visualize this, you can think of a ruler divided into 6 equal parts. 1/6 would represent 1 mark on the ruler, while 1/2 would represent 3 marks. To have the same length as 1/2, you need to add up 3 marks, or 3 copies of 1/6.

You can also think of this as converting 1/6 to a common denominator, which in this case is 6. 3 copies of 1/6 is equal to 3/6 or 1/2.

The time at which Miwa takes both medications together again will be 7:30 p.m. Then the correct option is D.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

She takes one medication every 6 hours. She takes the other medication every 4 hours.

The LCM of 4 and 6 will be 12. Then after 12 hours, she takes both medications.

Then the time is given as,

Time = 7: 30 a.m. + 12 hours

Time = 7: 30 p.m.

The time at which Miwa takes both medications together again will be 7:30 p.m. Then the correct option is D.

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ1

Answer: Undifined!

Step-by-step explanation: Division by zero is considered an invalid operation in mathematics because there is no number that can be multiplied by zero to produce the original number. In other words, there is no single valid answer to dividing by zero. Example: You have 0 cookies and you want to share them among 9 friends. There's no way to share, since you don't have cookies haha!

Answer:

Step-by-step explanation:

An expression without a value is referred to as being undefined; it has an indeterminant form. When a number is divided by zero, it usually has no specified meaning. Mathematically, we can't divide by zero because the result is an equation we can't compute.

Answer:

Below

Step-by-step explanation:

Points   (-3,5)   and   ( 3,1)

distance d can be found using the distance formula ( modified Pyhtagorean theorem)

d^2 = ( x1-x2)^2 + ( y1-y2)^2

d^2 = ( -3 -3)^2  + ( 5-1)^2

d^2 = 36 + 16

d^2 = 52

d = sqrt(52) = 2 sqrt(13)

Answer:

9.818 years after 2008

Step-by-step explanation:

Y_A = 0.35 * X + 9.6

Y_B = 0.9 * X + 6.5

Equal in year X = (Y_B - Y_A) / (0.35 - 0.9) = (6.5 - 9.6) / (-0.55) = 9.818 years after 2008

X = 9.818 + 2008 = 2018.818

Y_A = 0.35 * (2018 - 2008) + 9.6 = 14.3 billion

Y_B = 0.9 * (2018 - 2008) + 6.5 = 15.3 billion

1. [tex]m\angle BOC=45^{\circ}[/tex] since angles on a straight line add to [tex]180^{\circ}[/tex]

2. [tex]m\angle DOE=60^{\circ}[/tex] because vertical angles are congruent

3. [tex]m\angle AOE=120^{\circ}[/tex] because vertical angles are congruent

The size of the total economic surplus in this market is $32.

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

Welfare and Efficiency-End of Chapter Problem

Consider the national market for in-home childcare, depicted in the accompanying graph

The size of the total economic surplus in this market,

= (1/2)(18 - 10) 8

= 32

Therefore, the surplus is $32.

To learn more about the multiplication;

https://brainly.com/question/19634536

#SPJ1

The predicted interval for the given function is, f(x) ≥ 0 over the interval [-1,1]. So Option C is correct

Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).

Vertical line test:-

Whenever we want to check whether a given expression is a function or not we can apply a vertical line test, in this test we check for a single image of x , we are getting a single image or more.

If we get more images then it will not be a function.

For example, let us take, y² = 4ax

y = ±√4ax

For single value of x we get two values of y

Hence, it will not be a function.

Given that,

The ordered pairs of the given function

(-3,15), (-2,-5), (-1,0), (0,5), and (1,0).

It can be observed from the values of f(x) with respect to x, that the function reaches zero at x = -1, then then reach up to 5 at x = 0 and then again reaches zero at x = 1

Hence, the value of f(x) remains positive within the interval of [-1,1].

To know more about Functions check:

https://brainly.com/question/5975436

#SPJ1

The amount of compound remaining from a 84-ounce sample after seven weeks is 4.32 ounces.

Given a half-life of 5 days and a sample of 84 ounces, the exponential decay function can be represented as:

A(t) = 84 * (1/2)^(t/5)

Where A(t) represents the amount of the compound remaining after t days.

To find the amount of compound remaining after 7 weeks

7 weeks * 7 days/week = 49 days,

we can substitute t = 49 into the function:

A(49) = 84 * (1/2)^(49/5)

A(49) = 84 * (1/2)^9.8

A(49) ≈ 4.32 ounces

So, the amount of the compound remaining after 7 weeks would be approximately 4.32 ounces.

Learn more about half life here:

https://brainly.com/question/29580188

#SPJ1

22% of the population more than 25 years of age have bachelors degree.

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

Given that the total population is 298957

66722 cincinnati residents over the age of 25 have the bachelors degree.

We have to find the percent of the population more than 25 years of age have bachelors degree.

x/100×298657=66722

2986.6x=66722

Divide both sides by 2986.6

x=22.340

Hence, 22% of the population more than 25 years of age have bachelors degree.

To learn more on Percentage click:

https://brainly.com/question/28269290

#SPJ1