Find the scale factor of the figures. Then list all pairs of congruent angles.

Answer:

Step-by-step explanation:

they are expecting you to know a few things.

first,  that ∠x   is asking for the interior angle of the labeled angle, here they call it  1 , so find that angle and look at the inside of the triangle,  it's also referred to as the minor angle.

second, they are expecting you to know how many degrees it is around the interior or a triangle... do you know?

then , just take that number and subtract the two given numbers to find the final number ,  or the  ∠1

got it?

We want to find a prime number greater than 10 and less than 19.

* What is a prime number?

Prime number is a number that cannot be divided by any number other than 1 and itself

There are so many possibilities:

Ellie's street address could be 11, 13 or 17

Hope it helps!

The art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper for proper distribution.

To determine the largest number of identical kits the art teacher can make using all the crayons and drawing paper, we need to find the greatest common divisor (GCD) of the quantities.

The GCD represents the largest number that can divide all the quantities without leaving a remainder.

The GCD of the quantities of crayons can be found by considering the prime factorization:

72 = 2³ × 3²

48 = 2⁴ × 3

48 = 2⁴ × 3

48 = 2⁴ × 3

The GCD of the crayons is 2³ × 3 , which is 24.

Now, we need to find the GCD of the quantity of drawing paper:

120 = 2³ × 3 × 5

The GCD of the drawing paper is also 2³ × 3 , which is 24.

Since the GCD of both the crayons and drawing paper is 24, the art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper.

Each kit would contain an equal distribution of crayons and drawing paper.

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Answer:

zero

Step-by-step explanation:

The given measurements are:

   A= 61º, a = 23, b = 24

In a triangle, the sum of the angles therein is 180°.  A triangle is a figure with three sides.

With internal angles summing up to 180°

To know if the given angles are of a triangle, the must add up to 180°;

  So;

 Summation  = 61 + 23 + 24  = 108°

This is not a triangle.

Therefore, from the summation of the angles given, we can see that they do not add up to the sum of angles within a triangle.

Answer: These measurements determine two triangles.

Step-by-step explanation:

Given: A=61º, a=23, b=24

sinA/a=sinB/b

sin61º/23=sinB/24

24sin61º=23sinB

(/23)24sin61º=23sinB(/23)

sin^-1(24sin61º/23)=sin^-1(sinB)

B=65.8737º

***

61º+65.8737º+C=180

C=53.1263º

***

sinA/a=sinC/c

sin61º/23=sin53.1263º/c

csin61º=23sin53.1263º

(/sin61º)csin61º=23sin53.1263º(/sin61º)

c=23sin53.1263º/sin61º

c=21.03667

***

A=61º

B=65.8737º

C=53.1263º

a=23

b=24

c=21.03667

Therefore, the distance across the river is approximately 283 feet (rounded to the nearest foot).

An equation is a mathematical statement that uses symbols, such as letters and numbers, to show that two expressions are equal. It typically consists of two sides separated by an equals sign. The expressions on both sides can contain variables, constants, functions, and operators, and the goal is often to solve for the value(s) of the variable(s) that make the equation true. Equations are used extensively in mathematics, science, engineering, and many other fields to model real-world phenomena, make predictions, and solve problems.

Here,

Without a diagram, it is difficult to determine the exact location and orientation of the points and lines. However, based on the information provided, we can use the Law of Sines to find the length of PR.

In triangle ROC, we have:

sin(CEO) = RO/OC

sin(CEO) = 165/330

sin(CEO) = 0.5

CEO = sin⁻¹(0.5)

CEO = 30 degrees

In triangle REO, we have:

sin(ERO) = RO/RE

sin(ERO) = 165/210

sin(ERO) = 0.7857

ERO = sin⁻¹(0.7857)

ERO = 51.06 degrees

Now, in triangle PER, we have:

sin(PER) / 210 = sin(ERO) / PR

Therefore, we can solve for PR:

PR = 210 * sin(ERO) / sin(PER)

PR = 210 * sin(51.06) / sin(180 - CEO - ERO)

Plugging in the values, we get:

PR = 210 * sin(51.06) / sin(99.94)

PR ≈ 283.2 feet

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Answer:

The amount spent on taxes is $7650

Explanation:

The annual income of the family is $30,600

1/4 of this income is spent on taxes

That is 1/4 of $30,600.

Let us find what this amount is

The amount is $7650

This is the amount spent on taxes

Answer:

a. Possible outcomes for this chance experiment are:

(Here, D means a defective battery, and N means a nondefective battery.)

b. The number of outcomes in the sample space is infinite, as the experiment could potentially continue indefinitely. However, in practice, we can define a maximum number of batteries that could be examined before the experiment is stopped.

c. The event E, that the number of batteries examined is a number, would include outcomes where the experiment stopped at a particular number of batteries. For example, if the experiment stopped after examining three batteries (i.e., the fourth battery was nondefective), then the outcome would be DDDN, and it would be included in event E. However, outcomes where the experiment continued indefinitely (e.g., DDDDD...) would not be included in event E.

Answer: $5,150

Step-by-step explanation:

5000x0.03=150+5000=5,150

The scaled triangle will be larger than the initial size by a factor 2.

The scaled square will be smaller than the initial side by a factor 4.

Dilation refers to a transformation that changes the size of a geometric figure without altering its shape.

Dilation involves scaling an object by a certain factor, that might result in  enlarging or reducing its dimensions uniformly in all directions.

Based on the given diagram, the new length and size of the object is calculated as follows;

For the triangle, (measure the length with ruler)

For the square; (measure the length with ruler)

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The given integral is:

∫ ∫ ( x) ×(8 × (√ x)) dx dy

By changing the order in which we integrate with respect to the variables x and y, we can rewrite this integral as an iterative integral of the other five orders. The other five commands are:

a. ∫ ∫ (√ x) ×(8 × (√t x)) dy dx

b. ∫ ∫ (8 × (√ x)) × (√ x) dx dy

c. ∫ ∫ (8 × (√ x)) × (√ x) dy dx

d. ∫ ∫ (√ x) × (√x) dx (8 × y)

e. ∫ ∫ (√ x) × (√ x) (8 * y) dx

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An expression that can be used to find the cost of an n-minute long distance call, where n is at least 5 minutes is (0.55 + (n - 5) x 0.07) dollars.

Given:

Long Distance Rates Time (minutes) Cost5 $0.556 $0.627 $0.698 $0.769 $0.8310 $0.90We need to find an expression that can be used to find the cost of an n-minute long-distance call, where n is at least 5 minutes.

The cost of making a long-distance call is given for 5 minutes, 6 minutes, 7 minutes, 8 minutes, 9 minutes, and 10 minutes.

We can observe from the above table that for every increase of 1 minute, the cost increases by $0.07.

We can conclude that the cost of n minutes long-distance call is given by: (0.55 + (n - 5) x 0.07) dollars when n is at least 5 minutes.

Therefore, the required expression is: (0.55 + (n - 5) x 0.07) dollars when n is at least 5 minutes. The above expression is based on the pattern in the table provided for long-distance call rates. We can use this expression for values of n greater than or equal to 5.

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Answer:

pppppppppppppppppppppppppppppppppppppppppp

Answer:

25

100

55

Step-by-step explanation:

Givens

Let the first angle = x

Let the second angle = 4x

Let the third angle = 2x + 5

All triangles have 180

Equation

x + 4x + 2x + 5 = 180

Solution

Begin by combining like terms

7x + 5 = 180

7x = 180 - 5

7x = 175

7x/7 = 175/7

x = 25

Answer

First angle = x    =          25

Second angle = 4x =    100

Third angle = 2x + 5 =    55

Total                               180

The complete diagram map is given as,
1 - 3
2 - 5,
3 - 7,
8 - 17,
10 - 21
100 - 201

Given that,
To complete the map diagram,

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

here,
The given map diagram follows the general term as nth term = 2n + 1
So for n = 3
= 2 [3] + 1
= 7
Similarly,

10th = 21
100th = 2001

For the value 17

17 = 2n + 1
n = 8
So the 8th term is 17 in the map diagram,

Thus, The complete diagram map has been shown.

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Answer

43.59

Step-by-step explanation:

Answer:

3:7

Step-by-step explanation:

Let x = pounds of the $10 rice in the mixture

Let y = pounds of the $30 rice in the mixture

Total cost of the $10 rice = 10x

Total cost of the $30 rice = 30y

(10x + 30y) / (x + y) = 24

Solve this equation for y/x:

10x + 30y = 24(x + y)

10x + 30y = 24x + 24y

30y - 24y = 24x - 10x

6y = 14x

y/x = 6/14  simplify the fraction

y/x = 3/7

So, the ratio of the two different types of rice (y:x) is 3:7, meaning a pound of the rice mixture has 3 parts of the $30 rice to 7 parts of the $10 rice.

Answer:

The growth model that represents the population of this city is not linear--it is exponential:

\(f(t) = 10000( {1.025}^{t} )\)

\(t = 0 \: represents \: 2010\)

Answer:

27%

Step-by-step explanation:

100% (total population) - 73% (people who will approve) = 27% (no opinion or disapprove)

-> We can take our whole, 100%, and subtract the portion that will approve to find the percentage (%) of people that will not approve or that will have no opinion

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

A personal example of a measurement I use routinely is converting weight from U.S. customary units to metric units. Let's convert pounds to kilograms.

To convert pounds to kilograms, we use the conversion factor of 1 pound = 0.453592 kilograms.

For example, if I have a weight of 150 pounds, I can calculate the equivalent weight in kilograms as follows:

150 pounds * 0.453592 kilograms/pound = 68.0388 kilograms

Therefore, 150 pounds is approximately equal to 68.0388 kilograms.

In this conversion, we multiply the weight in pounds by the conversion factor to obtain the weight in kilograms. By using the appropriate conversion factor, we can accurately convert weights from U.S. customary units to metric units.

It's important to note that conversion factors may vary slightly depending on the rounding used and the exact value of the conversion factor.

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The number of pounds in  \(1\frac{1}{2}\) pounds and and 8 ounces is 2 pounds.

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

We know that 1 pound = 16 ounces.

As there are \(1\frac{1}{2}\) pounds=1.5×16= 24 ounces.

The total number of ounces in   \(1\frac{1}{2}\) pounds and 8 ounces is

24+8

32 ounces.

Now let us convert Ounces to pounds.

we divide the number of ounces by 16.

Therefore, 32 ounces is equal to 32/16 = 2 pounds.

Hence, 2 pounds will be there in  \(1\frac{1}{2}\)  pounds and 8 ounces

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Answer:

0.025

Step-by-step explanation:

Rounded to the nearest thousandth

We are given the expression

We must recall a property of exponents:

In this case, x=7 and y=1 (the exponent is hidden but it's 1)

Thus, applying the above property:

Answer: The radius of the circle is 5 3/8 inches.

Step-by-step explanation:

The radius of the circle is half of the diameter. We can start by converting the mixed number diameter to an improper fraction:

10 3/4 = (10 × 4 + 3)/4 = 43/4

So, the diameter of the circle is 43/4 inches. The radius is half of this, which we can find by dividing by 2:

r = (43/4) ÷ 2 = 43/8

To simplify the fraction, we can divide the numerator and denominator by their greatest common factor (GCF), which is 1:

r = 43/8 = 5 3/8

Therefore, the radius of the circle is 5 3/8 inches.

Answer:5 3/4

Step-by-step explanation:

10 3/4 * 1/2

1/2 * 43/4 = 43/8

8/43=5 3/4

Answer:

(4.75, 2.5), (-0.35, -7.7), (0.4, -6.2)

Step-by-step explanation:

Given the line

\(y = 2x- 7\)

Given the missing coordinates:

(4.75, )

(, –7.7)

(0.4, )

We know that every coordinate is of the form \((x,y)\).

So, we can easily solve the for other variable if one variable is given from the given line using the graph or the given equation.

For the first coordinate:

(4.75, )

From graph it can be found that y = 2.5

Verifying using the equation.

Putting the value of x = 4.75 in the equation we get:

y = 2\(\times\) 4.75 - 7

y = 9.5 - 7 = 2.5

So, the coordinate is  (4.75, 2.5)

For the second coordinate:

(, -7.7 )

From graph it can be found that x = -0.35

Verifying using the equation:

Putting the value of y = -7.7 in the equation we get:

-7.7 = 2x - 7

2x = -7.7 + 7 = -0.7

x = -0.35

So, the coordinate is  (-0.35, -7.7).

For the third coordinate:

(0.4, )

From graph it can be found that y = -6.2

Verifying using the equation.

Putting the value of x = 0.4 in the equation we get:

y = 2\(\times\) 0.4 - 7

y = 0.8 - 7 = -6.2

So, the coordinate is  (0.4, -6.2)

Also, please refer to the attached graph.

So, the answer is:

(4.75, 2.5), (-0.35, -7.7), (0.4, -6.2)

Answer: its 2.5, -0.35, -6.2

Step-by-step explanation: in easier words

Answer: Equilateral

Step-by-step explanation:

It's equilateral because it says that each side of the triangle is 4cm. In simple words, all the sides of triangle are equal. Such a triangle is called an equilateral triangle.

Hope you understood.

Answer: The U.S. Weather Bureau has a station on Mauna Loa in Hawaii that has measured carbon dioxide levels since 1959. At that time, there were 313 parts per million of carbon dioxide in the atmosphere. In 2005, the figure was 383 parts per million.

Step-by-step explanation:

Answer:

Jean is 9 years old and Tom is 15 years old.

Step-by-step explanation:

let t = Tom's present age

let j = Jean's age

Three years ago, Tom was twice as old as Jean,

t-3 = 2(j-3)

t - 3 = 2j - 6

t = 2j - 6 + 3

t = 2j - 3

In two years the sum of their ages will be 28 years.

(t+2) + (j+2) = 28

t + j + 4 = 28

t + j = 28 - 4

t + j = 24

For their present ages, replace t with (2j-3) from the 1st statement

2j - 3 + j = 24

2j + j = 24 + 3

3j = 27

j = 27/3

j = 9 yrs is Jean's age

Find Tom's age

t = 2(9) - 3

t = 15 yrs is Tom's age

An equation is formed of two equal expressions. The age of Tom is 15 years and the age of Jean is 9 years.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the present age of Tom and Jean be represented by x and y, respectively. Therefore, the given statement three years ago Tom was twice as old as Jean in the form of an equation can be written as,

(x-3) = 2(y-3)

Solving the equation for x,

x - 3 = 2y - 6

x = 2y - 3

Also, it is given that in two years the sum of their ages will be 28 years.

(x+2) + (y+2) = 28

(2y - 3 + 2) + (y + 2) = 28

2y -3 + 2 + y + 2 = 28

3y + 1 = 28

3y = 27

y = 9

Substitute the value of y in the equation of x formed above,

x = 2y - 3

x = 2(9) - 3

x = 15

Hence, the age of Tom is 15 years and the age of Jean is 9 years.

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Answer:

m = -3 ; c = 1

Step-by-step explanation:

y = -3x + 1

y = mx + c

m = -3

c = 1