If triangle ABC is congruent to triangle DEF, solve for x and y

Answer:

5, -2

Step-by-step explanation:

Answer: 36

Step-by-step explanation: The equation that represents circles that have a diameter of 12 units and a center that lies on the y-axis is x²+ (y-3)² = 36

The standard form for finding the equation of a circle is expressed as;

(x-a)^2 + (y-b)^2 = b=r^2

where;

(a, b) is the center of the circle

r is the radius of the circle

Given the following

diameter = 12 units

radius = 12/2 = 6 units

If the centre lies on the y-axis, the center will be at (0, 3)

Substituting into the formula, we will have (x-0)^2 + (y-3)^2 = 6^2 equivalent to x²+ (y-3)² = 36

The total budget for their student film is $1200

A number or ratio that is expressed as a fraction of 100 is known as a percentage in mathematics. There are also sporadic uses of the acronyms "pct.," "pct," and "pc." However, the percent sign "%" is widely used to signify it; There are no dimensions to the percentage amount. Percentages are essentially fractions because they have a numerator of 100. Put the percent sign (%) next to a number to indicate that it is a percentage. For instance, you would score a 75% if you answered 75 out of 100 questions on a test correctly (75/100). Divide the money by the total to get percentages, then multiply the result by 100. The formula (value/total) x 100% is used to determine the percentage;

Given;

On a student movie, some pals were engaged.

On props and equipment, they used the entire budget.

A total of $24% of the budget was spent on equipment, or $912, on props.

Let the movie's overall budget be x;

Spent on the equipment= $870

The props budget = 24% of x.

Equipment costs plus prop costs equal the total budget;

x = 912 + 24% of x

x = 912 + 0.24x

x - 0.24x = 912

0.76x = 912

x= 912/0.76

x = 1200

Therefore, the student film's overall budget with 68 percent of the total budget on equipment will be $1200;

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Upon solving the root, the answer for given expression is option D: 3√x / 3.

In this case, the radical symbol for the number's root is "√". By multiplying the positive integer by itself, the square of the number is represented. By taking the square root of the square of a positive number, the original number can be found. For instance, 32 also equals 9, as does the square of 3 and the square root of 9.

This is the given expression:√27x + √48.

We will first simplify the square roots before simplifying the statement. √27 = 3 and √48 = 6.

Thus, the formula becomes 3√x + 6.

None of the suggested alternatives are equivalent to this statement. However, we can rephrase the expression in a way that is comparable to options A and D.

Let's multiply the expression's two sides by three.

The formula is now:√x + 2

Option D is represented by the formula  3√x/3 = √x + 2.

The solution is therefore option D: 3√x/3.

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Answer:

Each of them will get 42/3 = $14.00

Cami saves half of her money which is 14/2 = $7.00

Cami has 14 - 7 = $7.00 to spend.

The discriminant of the given equation is -195 and the number of real solutions is 0.

Quadratic expressions are polynomial equations of second degree.

The general form of a quadratic equation is ax² + b x + c = 0.

(a) Discriminant of a quadratic equation of the form ax² + b x + c = 0 is b² - 4ac.

Given quadratic equation is 7k² + k + 7 = 0.

Discriminant = 1² - (4 × 7 × 7) = 1 - 196 = -195

(b) Discriminant is negative.

So there are no real solutions for the given quadratic equation.

There are two complex solutions.

Hence the value of the discriminant is negative and there are no solutions.

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Answer:

30 x^2

Step-by-step explanation:

(5x)(7x)-5x^2=30x^2

Simplify the following:

5×7 x x - 5 x^2

5 x×7 x = 5 x^2×7:

5×7 x^2 - 5 x^2

5×7 = 35:

35 x^2 - 5 x^2

35 x^2 - 5 x^2 = 30 x^2:

Answer: 30 x^2

The approximation of 341.12 to 1 decimal place is 341.1.

To approximate 341.12 to 1 decimal place, you can follow these steps:

For example, if you want to approximate the number 341.12 to 1 decimal place, follow these steps:

341.12 * 10 = 3411.2

Round 3411.2 to the nearest whole number, which is 3411.

3411 / 10 = 341.1

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Answer:

341.1

Step-by-step explanation:

When you round to the first decimal place, or to the nearest tenth, the number in the hundredth point place will determine whether you round up or down. If the hundredths digit is a number between 5 and 9, round up to the nearest whole number. If it's a number between 0 and 4, you would "round down" by keeping the tenths place the same.

341.12

The number in the hundredths place is 2, which means that we would round down the first decimal place by keeping it the same:

341.1

Therefore , the solution of the given problem of interest comes out to be

$4,962.93 money more made by Alexander.

Simple interest is calculated by dividing the principal by the borrowing cost, the remaining time, and other elements. The simple return formula in marketing is principal + interest plus hours. Utilizing this method is the simplest way to calculate interest. As a percentage of the principle sum is the most frequent way to calculate income. For instance, he will only pay his portion of the 100% cost if he borrows $100 from a friend and agrees to pay the loan back with 5% interest.. You have to pay interest on money you borrow, and you have to charge interest on money you lend.

Here,

Given :

Luke :

Principal amount = $86,000

and rate of interest =  5 ⅛ % or 41/8% or 5.125%

Alexander :

Principal amount = $86,000

rate of interest = 5 ⅝ % or 45/8% or 5.625%

To find the amount of money after time =8 years.

So ,

using compound formula :

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

For luke = P=86000[tex](1 + 41/8*1)^{1*8}[/tex] = $42,276.33

For  Alexander =   P=86000[tex](1 + 45/8*1)^{1*8}[/tex] = $47,239.26

The amount made by Alexander by luke

=> 47,239.26 - 42,276.33 = 4,962.93

Therefore , the solution of the given problem of interest comes out to be

$4,962.93 money more made by Alexander.

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Answer:

About 95% used

Step-by-step explanation:

78÷82=95.12200

Therefor, 78 is 95.12200% of 82

The value of expression for x = 8 and y = 6 is,

⇒ 25

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 expression is,

⇒ (x² + y²) / 4

Here, We have;

⇒ x = 8 and y = 6

Substitute the value of x and y in above expression, we get;

⇒ (x² + y²) / 4

⇒ (8² + 6²) / 4

⇒ (64 + 36) / 4

⇒ (100) / 4

⇒ 25

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By using Percentage , Profit distributed to Charity A is £ 624 and Charity B is £ 336

A figure or ratio stated as a fraction of 100 is called a percentage. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.

The Latin phrase "per centum," which meaning "by the hundred," was the source of the English word "percentage." Fractions having a denominator of 100 are called percentages. In other words, it is a relationship where the value of the entire is always assumed to be 100.

Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. A percentage can be found in one of two ways:

Total ticket sold = 800

Cost of each ticket is £ 2

Total fund raised (raw) = 2 * 800 = £1600

4% of the ticket won a prize of £20 each

so total number of tickets winning a prize = 4 % of 800 = 32

Total prize money distributed = 32 * 20 = £ 640

Total amount to distribute to charity = 1600 - 640 = £ 960

Total profit that goes to Charity A is = 65 % of 960 = £624

And rest to charity B is = £ 336

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The statements that are true for line 'n' are

a) The slope of line n is equal to BC/AC    

d) The slope of line n is equal to DE/AE.  

A line's slope is defined as the ratio of the change in the y-coordinates to the change in the x-coordinate. And the formula for slope is given by  

Here we have

A line 'n' passing diagonally through a coordinate plane

From the given figure,

The points that the line passes are (4, 3) and (-2, 0)    

The slope of the line, 'm' = [-0 -3]/[-2 - 4] = 3/6 = 1/2    

From the given figure,

BC = 1 unit and AC = 2 units  

DE = 4 units and AE = 8 units

a) The slope of line n is equal to BC/AC = 1/2          

d) The slope of line n is equal to DE/AE = 4/8 = 1/2  

Therefore,

The statements that are true for line 'n' are

a) The slope of line n is equal to BC/AC    

d) The slope of line n is equal to DE/AE.  

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Complete Question:

Use the graph below to answer the question. Which statements about line n are true? n, Select all that apply.

Answer choices:

a) The slope of line n is equal to BC/AC.

b) The slope of line n is equal to AC/BC.

C) The slope of line n is equal to BC/DE.

d) The slope of line n is equal to DE/AE.

e) The slope of line n is equal to AE/DE.

f) The slope of line n is equal to AC/AE.

The expression to show the total number of songs on Iris's playlist after {w} weeks is → y = 120 + 4w.

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 Iris has 120 songs on her playlist. Each week, she downloads 4 new songs.

We can write the expression to show the total number of songs on Iris's playlist after {w} weeks as -

y = 120 + 4w

Therefore, the expression to show the total number of songs on Iris's playlist after {w} weeks is → y = 120 + 4w.

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Bryn is wrong as he says that the journey will definitely take less than an hour and a quarter

time = 1.17 hours = 1 hour 42 minutes

What is speed?

The definition of speed is. a measurement of how quickly an object's location changes in any direction. Speed is defined as the ratio of distance to the amount of time it took to cover that distance.

Average speed= distance / time

time= distance /Average speed = 80/68  hours

time = 1.17 hours = 1 hour 42 minutes

So, Bryn is wrong as he says that the journey will definitely take less than an hour and a quarter.

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Answer:

the answer is in the picture

Using standard normal distribution table, the hip breadth for men that separates the smallest 95% from the largest 5% is approximately 16.055 inches. This means that seats that are designed to be at least 16 inches wide will fit 95% of all males.

Normal distribution, also known as Gaussian distribution or bell curve, is a probability distribution that describes a continuous variable, such as a measurement or a test score, that is symmetric about the mean, with most of the observations clustering around the mean and fewer observations as we move away from the mean.

In the given question, to find the hip breadth that separates the smallest 95% from the largest 5% of men, we need to find the P95 value, which is also known as the 95th percentile.

Since the hip breadths of men are normally distributed with a mean of 14.8 inches and a standard deviation of 0.9 inches, we can use the standard normal distribution table (or a calculator with the inverse cumulative distribution function) to find the P95 value.

Using a standard normal distribution table or calculator, we find that P95 corresponds to a z-score of 1.65.

To find the P95 hip breadth, we can use the following formula:

P(95) = mean + (z-score * standard deviation)

P(95)= 14.8 + (1.65 * 0.9)

P(95) = 16.285 inches

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Answer: You need to exercise for 7 3/4 more hours

You need to do more exercise for  [tex]7\frac{3}{4}[/tex] hours.

A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

Given that, Your goal is to exercise for 15 hours this month. You exercise for [tex]3\frac{1}{2}[/tex] hours the first week and [tex]3\frac{3}{4}[/tex] hours the next week.

To find how much exercise is left, we will add both the hours and subtract it from 15 hours,

Therefore,

Exercise done = [tex]3\frac{1}{2} + 3\frac{3}{4}[/tex]

= 7/2 + 15/4

= (14 + 15) / 4

= 29/4

Exercise left = 15 - 29/4

= 31/4

= [tex]7\frac{3}{4}[/tex]

Hence, you need to do more exercise for  [tex]7\frac{3}{4}[/tex] hours.

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The length of a form represents its perimeter. The provided parallelogram's perimeter will therefore be 38 units.

Quadrilateral's perimeter.The measurement of a shape's perimeter is its length.It takes adding the lengths of all four sides to determine a rectangle's or square's perimeter.

Knowing that the quadrilateral's perimeter equals the sum of its sides (AB + BC + CD + DA), we can write it as ABCD.

The quadrilateral's perimeter is equal to the sum of its four side lengths.

From the accompanying photo,

The supplied parallelogram's perimeter is equal to

AB + BC + CD + DA.= 9 + 10 + 9 + 10

= 38 units

ABCD's circumference is 38 units.

The provided parallelogram's perimeter will therefore be 38 units.

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The car needs 59.5 gallons of gas for 714 ​a mile trip.

What is an integer?

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers.

Here, we have

Given: A particular hybrid car travels approximately 168 miles on 4 gals of gas.

We have to find the amount of gas required for the 714 ​-mile trip.

168 × d = 14 × g

168/14d = 1 g

12d = 1 g

1 gallon will take you 12 miles.

If you are given gallons, use the first one. If you are given miles, use the second one. You are given miles, so

= 714 miles ×(1 gallon/  12 miles)

= 59.5 gallons.

Hence, The car needs 59.5 gallons of gas for 714 ​a mile trip.

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Answer: Formulas for Solving Composite Figures

Step-by-step explanation:

The formula for finding the area of a rectangle is length x width.

The formula for finding the area of a square is side x side.

The formula for finding the area of a triangle is base x height/2.

The formula for finding the area of a circle is π x radius x radius

Hope this helps! :)

Answer:

System: A system of two equations that can be written in the form of y = mx + b where m is the slope and b is the y-intercept.

Graph: The graph of these two equations would be two straight lines in a coordinate plane.

Solution: The solution of the system would be the point where the two lines intersect on the coordinate plane, which represents the values of x and y that satisfy both equations.

Slope and y-intercept of 4x = y - 6:

Slope: 4 (m)

y-intercept: -6 (b)

Slope and y-intercept of 4y = 3x -5:

Slope: 3/4 (m)

y-intercept: -5/4 (b)

Note that the slope is the coefficient of x in the equation, and the y-intercept is the constant term in the equation. The solution can be found by equating the two equations and solving for x and y.

The equation that describes the diagram could be; 5 + 9 = 14

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

Since Adding a negative number is the same as subtracting a positive number just as subtracting a negative number is the same as adding a positive.

The equation becomes as

5 + 9 = 14

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Answer:

Step-by-step explanation: Hello! I can help you if you include the graph!

the triangle are congruent by AAA

What is congruent by AAA?

It can also be stated as the AAA (angle-angle-angle) similarity theorem, which states that two triangles have identical corresponding angles if and only if their corresponding sides are proportionate.given, ABC and XYZ, are congruent according to the AAA rule by looking at the image provided below. According to the AAA congruence rule, two triangles are said to be congruent if two of their respective sides and angles are equal to those of two other triangles and their respective sides and angles, respectively.

In the given two triangles,

The ratio of the sides are similar

And hence the angles are similar.

Hence the triangle are congruent by AAA

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The denominator for the final answer for fraction in question 2 is 75 and the numerator for the final answer for the fraction in question 3 is 25.

We shall simplify the fractions to get the final answer for the denominators and numerators as follows:

5/9 + 1/3 = (15 + 1)/9 {simplifying to a single denominator}

5/9 + 1/3 = 16/9

(5/9 + 1/3) ÷ 25/3x = 16/9 × 3x/25 {changing division to multiplication}

(5/9 + 1/3) ÷ 25/3x = 16 × x/75

(5/9 + 1/3) ÷ 25/3x = 16x/75 {denominator 75}

4/5 - 16/(x + 2) = [4(x + 2) - 16(5)]/5(x + 2) {simplifying to a single denominator}

4/5 - 16/(x + 2) = (4x + 8 - 80)/5(x + 2)

4/5 - 16/(x + 2) = (4x -72)/5(x + 2)

[20/(x + 2)] ÷ [4/5 - 16/(x + 2)] = 20/(x + 2) ÷ (4x -72)/5(x + 2)

[20/(x + 2)] ÷ [4/5 - 16/(x + 2)] = 20/(x + 2) × 5(x + 2)/(4x -72) {changing division to multiplication}

(x + 2) will cancel out and 4 is factored out from (4x -72)

[20/(x + 2)] ÷ [4/5 - 16/(x + 2)] = 20 × 5/4(x -16)

[20/(x + 2)] ÷ [4/5 - 16/(x + 2)] = 5 × 5/(x - 16)

[20/(x + 2)] ÷ [4/5 - 16/(x + 2)] = 25/(x - 16) {numerator 25}

Therefore, the first fraction have 75 as its denominator and the second fraction have 25 as its numerator.

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999999999999999999..j

The first question have the unknown sides a = 12.29 and b = 275. 84 approximately to 2 decimal place using the trigonometric ratio of cosine the the angles 35° and 25° for the respective right triangles.

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. The basic trigonometric ratios are: sine cosine and tangent.

cos 35° = a/15 {adjacent/hypotenuse}

a = 15 × cos 35° {cross multiplication}

a = 12.2873

cos 25° = 250/b {adjacent/hypotenuse}

b = 250/cos 25° {cross multiplication}

b= 274.8445

Therefore, the unknown lengths a is equal to 12.29 and b is equal to 275.84 approximately to 2 decimal place for the respective right triangles using the trigonometric ratio of cosine for angles 35° and 25°.

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We do not obtain a triangle, but rather a straight line with a single side. Contrary to the triangle, which is a closed figure with two sides, the straight line is not closed.

Two points A and B are here collinear. Points that are parallel to or within a single line are referred to as collinear points. In Euclidean geometry, two or more points are said to be collinear if they are situated on a line that is either close to or far from another.

As opposed to non-collinear points, which do not lie on a single straight line, collinear points are two or more points that are located along a straight line. Collinear points are three or more points on the same line. A, B, and C are on the line m, for instance. The two are parallel. Two lines will coincide if their slopes are the same and they cross at the same location.

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