Now you will attempt to copy your original triangle using one of its angles:
Draw a line segment, DE of any length anywhere on the coordinate plane, but not on top of ∆ABC.
Choose one of the angles on ∆ABC. From point D, create an angle of the same size as the angle you chose. Then draw a ray from D through the angle. You should now have an angle that is congruent to the angle you chose on ∆ABC.
Create a point anywhere outside the mouth, or opening, of the angle you created. The point will initially be named F by the tool, but you should rename it point G. Now draw a ray from E through G such that it intersects the first ray. Your creation should be a closed shape resembling a triangle.
Label the point of intersection of the two rays F, and draw ∆DEF by creating a polygon through points D, E, and F.
Click on point G, and move it around. By moving point G, you can change
DEF and EFD while keeping FDE fixed.
Take a screenshot of your results for one position of G, save it, and insert the image in the space below.

The length of chord BC is 3 cm

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

The angle in a semicircle is 90 degrees

This means that

B = 90 degrees

Using the pythagorean theorem, we have

AC^2 = AB^2 + BC^2

This gives

5^2 = 4^2 + BC^2

So, we have

BC^2 = 9

This gives

BC = 3

Hence, the length s 3 units

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This years tuition is $1900

Let us assume that the next year tuition fee be x dollars.

The next year's tuition will be $2000 which is $600 more than this year's tuition fee.

Chana will pay $2000 which is 80 percent of her college tuition.

Using percentage formula we get an equation,

x × (80/100) = 2000

we solve this equation for x.

x = (2000 × 100)/80

x = 2500

If the next year's tuition fee is $600 more than this year's tuition fee, then this year's tuition fee would be,

2500 - 600 = 1900 dollars

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The volume of the prism formed of two rectangles is 528 cm³

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.

Volume of the prism is the amount of space that it occupied. From the prism shown:

Volume of prism = area of L shaped base * height

Area of L shaped base = (2 cm * 6 cm) + (8 cm * 15 cm) = 132 cm²

Volume of prism = 132 cm² * 4 cm = 528 cm³

The volume of the prism is 528 cm³

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Answer:

The ratio of flies to all insects is 1:5

For every 1 bee, there are 10 insects

Step-by-step explanation:

give brainlist please

The ingredient you need to serve, round the amount of an ingredient instead of using an exact amount, is vanilla extract.

Rounding is a process to estimate a particular number in a context.

Given that, a recipe serving 10 persons, but you need to serve 30, we need to multiply the amount of each ingredient by to adjust the recipe

Here we have a recipe that works for 10 serves.

Then, if we want to make 30 servings, we need to use that recipe 3 times. (because x·10 = 30, then x = 30/10 = 3)

This would be equivalent to multiply each ingredient by 3.

for 30 cupcakes, we need:

3 cups of vegetable oil.

3 cups of all-purpose flour

(because for each one of these ingredients, we needed only 1 cup to make 10 cupcakes).

for 10 cupcakes, we need 1 teaspoon of vanilla.

for 30 cupcakes we need 3 teaspoons of vanilla, the difference is 3 - 1 = 2.

So the difference is 2 teaspoons.

About which quantities we should round are those where we may have mixed numbers or big numbers.

For example, we have 4 tablespoons of sour cream for 10 servings, then for 30 servings we should have:

3×4 = 12 tablespoons.

We could round this down to 10 tablespoons.

Hence, the ingredient you need to serve, round the amount of an ingredient instead of using an exact amount, is vanilla extract.

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Answer: 345 + n

For finding the total, we have to add 345 with n.

Answer:

1.77777777778

The linear inequalities in the given graph  is [tex]y\geq \frac{1}{2} -1[/tex] and  y< -1/2x -3.

Linear inequalities:

Linear inequalities are the expressions where any two values are compared by the inequality symbols such as, ‘<’, ‘>’, ‘≤’ or ‘≥’. These quantities may be numerical, algebraic, or a combination of the two.

The symbols "" and ">" signify tight inequalities, while "" and "" signify slack inequalities. A linear inequality has the same appearance as a linear equation, but uses a different symbol to link the two expressions.

In the given graph, the area above solid line,

points, (-2 , -2) , (0 , -1)

slope = [tex]\frac{-1-(-2)}{0-(-2)}[/tex]= [tex]\frac{1}{2}[/tex]

so,  [tex]y\geq \frac{1}{2} -1[/tex]

The area below dashed line ,

points, (-2 ,-2) , (0 ,-3)

slope= [tex]\frac{-3-(-2)}{0-(-2)}= \frac{-1}{2}[/tex]

so, y< -1/2x -3.

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Answer:?=-9

Step-by-step explanation:

9x+3x-4-5=12x-9

Answer: h=12  r=√12

Step-by-step explanation:

volume of cone=πr^2 h/3

πr^2 h/3=48π

πhr^2=144π

hr^2=144

h=12  r=√12

Answer:

△ABC ~ △MLN

Step-by-step explanation:

Because the sum of all the angles in a triangle equals 180, we can find the missing angle in both triangles

△ABC

c + 90 + 51 = 180

c = 39

△MLN

[tex]l[/tex] + 90 + 39 = 180

[tex]l[/tex] = 51

Because <C has the same angle degree as <N,  <B has the same angle degree as <L, and  <A has the same angle degree as <M, then △ABC must be similar to △MLN

Answer:

150.72 cubic inches

Step-by-step explanation:

The volume of a cylinder can be calculated using the formula:

V = π * r^2 * h

where V is the volume, π (pi) is approximately equal to 3.14, r is the radius, and h is the height.

For the cylinder with a radius of 4 inches and a height of 3 inches, the volume can be calculated as follows:

V = π * r^2 * h = π * 4^2 * 3 = 3.14 * 16 * 3 = 3.14 * 48 = 150.72 cubic inches.

So the volume of the cylinder is approximately 150.72 cubic inches.

The solution is Option A.

The inequality equation is -2 ≤ x < -11

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the first inequality equation be represented as A

Now , the value of A is

4x + 7  ≤ -37   be equation (1)

Let the second inequality equation be represented as B

5x + 3 > -7   be equation (2)

On simplifying the equation , we get

From equation (1) , Subtracting 7 on both sides of the equation , we get

4x ≤ -44

Divide by 4 on both sides of the equation , we get

x ≤ -11

And , from equation (2) , Subtracting 3 on both sides of the equation ,

5x > -10

Divide by 5 on both sides of the equation , we get

x > -2

Hence , the inequality equation is -2 ≤ x < -11

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Answer:

I wasn't sure if you had wanted decimals or remainder so here is both.

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Step:Start by setting it up with the divisor 93 on the left side and the dividend 478 on the right side .

The divisor (93) goes into the first digit of the dividend (4), 0 time(s). Therefore, put 0 on top:

Step 3:

Multiply the divisor by the result in the previous step (93 x 0 = 0) and write that answer below the dividend.

Step 4:

Subtract the result in the previous step from the first digit of the dividend

Move down the 2nd digit of the dividend (7) like this:

The divisor (93) goes into the bottom number (47), 0 time(s). Therefore, put 0 on top:

Step 7:

Multiply the divisor by the result in the previous step (93 x 0 = 0) and write that answer at the bottom:            

Factor of the expression are,

⇒ (x - 1) (x - 12) (x - 10)

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The equation is,

⇒ x³ - 23x² + 142x - 120 = 0

Now, Put x = 1;

⇒ x³ - 23x² + 142x - 120 = 0

⇒ 1 - 23 + 142 - 120 = 0

⇒ 0 = 0

Thus, One factor of the equation is,

⇒ (x - 1)

Now, After divide we get;

⇒ (x³ - 23x² + 142x - 120 ) ÷ (x - 1)

⇒ x² - 22x + 120

⇒ x² - (12 + 10)x + 120

⇒ x² - 12x - 10x + 120

⇒ x (x - 12) - 10 (x - 12)

⇒ (x - 12) (x - 10)

Thus, Factor of the expression are,

⇒ (x - 1) (x - 12) (x - 10)

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Answer:

(-3.1)^8

Step-by-step explanation:

(-3.1)^4•(-3.1)^4

Because they have the same base is -3.1, we can add the ^4 with ^4 and get

(-3.1)^8

So, the answer is (-3.1)^8

The perimeter of the figure composed of a semicircle and rectangle is 59.7 inches

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 perimeter of a figure is the total distance along the boundary of that figure.

From the image attached:

Perimeter of circle = π * radius = 3.14 * 5 = 15.7 inches.

Perimeter of rectangle = 2(length + breadth) = 2(12 + 10) = 44 inches

Perimeter of figure = Perimeter of circle + Perimeter of rectangle = 15.7 + 44 = 59.7 inches

The perimeter of the figure is 59.7 inches

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The Board of Trustees can choose a president and a provost in 1000 different ways because there are 1000 professors on the college's faculty. The concept used in this is permutations and combinations.

What are combinations?

A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant (unlike permutations). Three fruits, such as an apple, an orange, and a pear, for instance, can be combined into three different pairs: an apple and a pear, an apple and an orange, or a pear and an orange. A k-combination of a set S is officially defined as a subset of S's k unique elements. So, if and only if each combination contains the same elements, two combinations are said to be identical.

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Correct question:

Suppose that a college has 1000 professors.

a) In how many ways can the Board of Trustees pick a president? The president should be one of the 1000 professors.

Answer:

23°

Step-by-step explanation:

As We All Know Sum Of Angles In A Straight Line is 180° so,

157° + a = 180°

or, a = 180° - 157°

or, a = 23°

Answer: a) i) The width of the floor can be expressed in terms of c as: w = c - 2 cm.

ii) The area of the floor can be expressed in terms of c as: A = c * (c - 2) cm^2.

b) If the area of the room is 15 cm^2, then we can write the equation as:

c * (c - 2) = 15.

c) Solving for c, we get:

c^2 - 2c - 15 = 0.

Using the quadratic formula, we find that:

c = 5 or c = -3.

Since the length of the room cannot be negative, we choose c = 5.

Therefore, the length of the room is 5 cm and the width of the room is 3 cm.

Step-by-step explanation:

Answer: To divide 9x³ - 18x² - x + 2 by 3x + 1 using long division, we can follow the following steps:

Step 1: Divide the first term of the dividend 9x³ by the first term of the divisor 3x. The result is 3x².

Step 2: Multiply the divisor 3x + 1 by 3x². The result is 9x³ + 3x².

Step 3: Subtract 9x³ + 3x² from 9x³ - 18x² - x + 2. The result is -18x² - 4x + 2.

Step 4: Repeat the division and multiplication process by dividing the first term of the new dividend, -18x², by the first term of the divisor, 3x. The result is -6x.

Step 5: Multiply the divisor 3x + 1 by -6x. The result is -18x + 6.

Step 6: Subtract -18x + 6 from -18x² - 4x + 2. The result is -4x² + 10.

Step 7: Repeat the division and multiplication process by dividing the first term of the new dividend, -4x², by the first term of the divisor, 3x. The result is -4/3 x.

Step 8: Multiply the divisor 3x + 1 by -4/3 x. The result is -4/3 x + 4/3.

Step 9: Subtract -4/3 x + 4/3 from -4x² + 10. The result is 10 - 4/3.

Thus, the final answer is:

(9x³ - 18x² - x + 2) / (3x + 1) = 3x² - 6x - 4/3 x + 4/3 + 10

Step-by-step explanation:

Answer:

The formula for the future value of a single sum is:

F = P * (1 + r/n)^(nt)

Where:

F is the future value

P is the principal (the initial deposit)

r is the annual interest rate

n is the number of compounding periods per year

t is the number of years

For our calculation, we have:

P = £7000

r1 = 3% = 0.03

r2 = 1.5% = 0.015

n = 1 (annual compounding)

t1 = 1 (first year)

t2 = 1 (second year)

So, the future value of Ella's investment at the end of the first year is:

F1 = £7000 * (1 + 0.03/1)^(1 * 1) = £7000 * (1.03)^1 = £7,210

And the future value of Ella's investment at the end of the second year is:

F2 = £7,210 * (1 + 0.015/1)^(1 * 1) = £7,210 * (1.015)^1 = £7,333.15

So, at the end of 2 years, the value of Ella's investment is £7,333.15.

Step-by-step explanation:

For 5 batches, 65 cups of chocolate chips are needed.

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 Marie’s recipe for one batch of chocolate chip cookies calls for 13 cup of chocolate chips. If Marie is making 5 batches of cookies.

For 1 batch - 13 cups of chocolate chips are needed.

For 5 batches - (13 x 5) = 65 cups of chocolate chips are needed.

Therefore, for 5 batches, 65 cups of chocolate chips are needed.

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Answer:

-1/2 is the answer of this question

The oak tree is 35.5 feet tall.

A mathematical expression known as an algebraic expression can include variables, numbers, and operations (such as addition, subtraction, multiplication, and division). If the values of the variables are known, it indicates a value that can be calculated. Although an algebraic expression lacks an equal sign and cannot be solved like an equation, algebraic methods can be used to simplify or manipulate it. For example, the expression 2x + 3y is an algebraic expression, where x and y are variables.

a) To solve this problem, we can draw a diagram to represent the situation:

In this diagram, "A" represents Benjamin's position, "B" represents the mirror, and "C" represents the top of the oak tree. Let's call the height of the oak tree "h".

b) We can use Angle-Angle Similarity to solve for h. In this case, we have two similar right triangles: ABC and ABD. We can write an equation to relate their sides:

(AB)/(BC) = (AD)/(CD)

c) Plugging in the known values:

(5)/(40) = (5.75)/(h + 5.75)

Expanding and solving for h:

h = (40 * 5.75)/5 - 5.75

h = 35.5 feet

So, the oak tree is 35.5 feet tall.

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The corresponding side in the smaller triangle is 10 cm.

When two or more objects or figures appear the same or equal due to their shape, this property is known as a similarity.

Given that, the ratio of similitude in two similar triangles is 3:1. the side in the larger triangle measures 30 cm, we are asked to find the measure of the corresponding side in the smaller triangle.

Let the corresponding side in the smaller triangle be x,

Since, the ratio similitude is 3:1, therefore, the ratio of the corresponding sides of both the triangle will be in same ratio,

Therefore,

1 / 3 = x / 30

x = 30 / 3

x = 10

Hence, the corresponding side in the smaller triangle is 10 cm.

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The ratio of the areas of the two similar figures is 9 : 16.

We can use comparisons or ratios to compare the size of an object with other objects. The quantity of an object can be in the form of length, speed, mass, time, number of objects, and so on.

For example, penguins have 2 legs, while dogs have 4 legs. We say that the ratio of the number of legs above can be written in three ways, namely:

2 to 4, 2 to 4, or 2/4.

The writing above is read: a comparison of 2 to 4, a comparison between 2 and 4, or a comparison of 2 to 4.

The order of the numbers in the comparison is important and should receive special attention. The first number in the comparison must be written as a numerator, if the comparison is written in fractional form.

Example:

The ratio of the number of penguin and dog legs is 2: 4 or 2/4

The ratio of the number of dog and penguin legs is 4 : 2 or 4/2

According to the question above:

Side figure 1 : side figure 2

6 : (6+2)

6 : 8

3 : 4

The ratio of the areas of two similar figure is equal to the square of the ratio of the corresponding sides.

Squaring the ratio 3 : 4, gives us:

3² : 4² = 9 : 16

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A regular frequency distribution table provides more detailed and accurate information about the scores in a dataset than a grouped frequency distribution table.

In a regular frequency distribution table, individual scores and their corresponding frequencies are listed, whereas in a grouped frequency distribution table, the scores are grouped into intervals and the frequencies of the intervals are listed.

The following information can be obtained from a regular frequency distribution table but not from a grouped table:

Individual Scores: A regular frequency distribution table lists individual scores, providing a clear understanding of the exact values that make up the data.

Accuracy: A regular frequency distribution table provides a more accurate representation of the data as it doesn't involve grouping the scores into intervals, which can lead to loss of information.

Outliers: In a regular frequency distribution table, outliers (unusual or extreme values) can be easily identified as they stand out from the other scores.

Shape of Distribution: A regular frequency distribution table provides a more detailed representation of the distribution, allowing for easier evaluation of the shape of the distribution, such as whether it is symmetrical, skewed, etc.

Measures of Central Tendency: Measures of central tendency, such as the mean, median, and mode, can be more accurately calculated from a regular frequency distribution table as the exact values of the scores are available.

In conclusion, a regular frequency distribution table provides more detailed and accurate information about the scores in a dataset than a grouped frequency distribution table.

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Yes, it is appropriate to calculate the probability of a sample mean being more than $0.32 using an approximately normal model, under certain assumptions.

What is Probability?

Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.

Yes, it is appropriate to calculate the probability of a sample mean being more than $0.32 using an approximately normal model, under certain assumptions.

The central limit theorem states that the distribution of the sample means approaches a normal distribution, as the sample size increases, regardless of the shape of the population distribution. So, for large enough sample sizes, the sample mean is approximately normally distributed, even if the population distribution is not normal.

In this case, a sample size of 50 is considered large enough to use the normal approximation. Therefore, we can assume that the distribution of the sample mean is approximately normal, with mean equal to the population mean of $0.29, and standard deviation equal to the standard deviation of the sample mean, which can be calculated as the standard deviation of the population divided by the square root of the sample size.

The standard deviation of the sample mean is given by the formula:

[tex]$\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} = \frac{0.1164}{\sqrt{50}} \approx 0.039$[/tex]

Using this information, we can calculate the desired probability as the area under the normal curve to the right of $0.32$. This can be done using a standard normal table or a normal probability calculator.

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