Rewrite in simplest radical form

The two statements that justifies step three and four in the congruency proof are;

Reason 3: SSS Congruency Postulate

Reason 4: CPCTC (Corresponding Parts of Congruent Triangles are Congruent)

The two column proof is as follows;

Statement 1: AB ≅ AD, BC ≅ DC

Reason 1: Given

Statement 2: AC ≅ AC

Reason 2: Reflexive Property of Congruence

Statement 3: ΔABC ≅ ΔADC

Reason 3: SSS Congruency Postulate

Statement 4: ∠ABC ≅ ∠ADC

Reason 4: CPCTC (Corresponding Parts of Congruent Triangles are Congruent)

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The area and circumference of each circle are 78.5cm², 31.4cm, 113.04cm², 37.68cm, 28.26cm², 18.84cm and 153.86cm², 43.96cm respectively

Using the formula of area of a circle and circumference of a circle, we can solve for each circle as

a.

The area is given as;

A = πr²

A = 3.14 * 5²

A = 78.5cm²

The circumference = 2πr

C = 2 * 3.14 * 5 = 31.4cm

b

A = πr²

A = 3.14 * 6²

A = 113.04cm²

C = 2πr

C = 2 * 3.14 * 6

C = 37.68cm

c.

A = πr²

A = 3.14 * 3²

A = 28.26cm²

C = 2 * 3.14 * 3

C = 18.84cm

d.

A = πr²

A = 3.14 * 7²

A = 153.86cm²

C = 2πr

C = 2 * 3.14 * 7

C = 43.96cm

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The exact value of sin V in simplest radical form is 0.813.

For any triangle ABC, with side measures |BC| = a. |AC| = b. |AB| = c,

we have, by law of sines,

[tex]\dfrac{sin\angle A}{a} = \dfrac{sin\angle B}{b} = \dfrac{sin\angle C}{c}[/tex]

Remember that we took

[tex]\dfrac{\sin(angle)}{\text{length of the side opposite to that angle}}[/tex]

Given;

Sin ratio √74:7

Now,

AB/sinA=BC/sinB

√74/sinA = 7/sinB

√74/sin90 = 7/sinB

sinB=7/√74

sinB=0.813

Therefore, the answer of sin V will be 0.813.

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Answer: y = 2/3x

Step-by-step explanation:

This is pretty easy too

the equation for a line is: y = mx + b, where m is the slope and b is the y intercept

y = 2/3x + b, where we need to find b

substituting the point we are given:

-2 = 2/3(-3) + b

-2 = -2 + b

0 = b

so our line is simply:

y = 2/3x

Answer:

Step-by-step explanation:

4 x 6= 24

24+2=26

Answer:

27, 36

Explanation:

To find the possible two-digit numbers that meet the criteria, we can use algebra. Let x be the original two-digit number, and let y be the reverse of x. Then, we have:

x - y = 18

We can also write y in terms of x:

y = x % 10 * 10 + x / 10

Substituting the expression for y into the equation x - y = 18, we get:

x - (x % 10 * 10 + x / 10) = 18

Expanding and simplifying the right side of the equation, we get:

9x = 180 + 10

Dividing both sides of the equation by 9, we get:

x = 20

Since x must be a two-digit number, 20 is not a valid solution. However, we can check the two numbers that are close to 20, which are 18 and 21.

For x = 18, we have y = 81, which is a two-digit number, so 18 is a valid solution.

For x = 21, we have y = 12, which is a two-digit number, so 21 is also a valid solution.

Therefore, the possible two-digit numbers that meet the criteria are 27 and 36.

Using the two tangent exterior angle theorem:

x = 6

m(NK) = 153°

According to the two tangent exterior angle theorem, when you draw two tangent lines from a point outside a circle, the angle formed between them is equal to half the difference between the measures of the arcs they intercept inside the circle.

Therefore, using the above theorem, we have:

7x + 6 = 1/2[(25x + 3) - (9x + 3)]

Solve for x:

2(7x + 6) = 25x + 3 - 9x - 3

14x + 12 = 16x

14x - 16x = -12

-2x = -12

x = -12/-2

x = 6

m(NK) = 25x + 3 = 25(6) + 3

m(NK) = 153°

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Luke received a total of 640 marbles from the total of 1400 marbles that Luke, Andre and Shema had combined.

Luke, Shemai and Andre combined has 1400 marbles. Andre has 200 fewer than Luke and twice as many as Shemia.

Now, let us say that Luke had X marbles then Andre will have X-200 marble and Shemai will have X/2 marbles.

Now, all the marbles combined will be equal to 1400, so, the simple algebraic relation will be,

X + X-200 +X/2 = 1400

X+X+X/2 = 1600

5X/ = 3200

X = 640

So, Luke will have a total of 640 marble while Andre and Shemai will have 440 and 320 marbles each.

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Rounding this to the nearest cent, the total amount that was wanted to be saved is $64.29.

To solve this problem, we can set up a proportion using the given information. Let x be the total amount that was wanted to be saved.

We know that the amount saved ($45) is 70% of the total amount that was wanted to be saved. Therefore, we can write:

45 = 0.7x

To solve for x, we can divide both sides by 0.7:

x = 45 ÷ 0.7

x = 64.28571429

The answer to the problem is $64.29, rounded to the nearest cent. This means that the total amount that was wanted to be saved was $64.29, and 70% of this amount is equal to the amount that was actually saved ($45). To check our work, we can multiply 64.29 by 0.7 to see if it equals 45. When we do this, we get:

64.29 x 0.7 = 45.003, which rounds to $45, so our answer is correct.

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The correct decision in a hypothesis test when the data produces a t-statistic that is in the critical region is to reject the null hypothesis.

This is because a t-statics in the critical region indicates that the differences between the sample mean and the population mean are statistically significant. This means that the data indicates that the null hypothesis is wrong and that the alternative hypothesis is true. In a hypothesis test, the null hypothesis is what the researcher is trying to disprove. It is the general statement that suggests that there is no difference between the sample mean and the population mean. The alternative hypothesis is what the researcher is attempting to prove. It suggests that there is a difference between the sample mean and the population mean. Therefore, when the data produces a t-statistic that is in the critical region, it indicates that the alternative hypothesis is true. When a t-statistic is in the critical region, it means that the result is statistically significant. This means that the differences between the sample mean and the population mean are unlikely to have occurred by chance and that the alternative hypothesis is likely to be true. Therefore, when the data produces a t-statistic that is in the critical region, the correct decision is to reject the null hypothesis and accept the alternative hypothesis.

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The polynomial expression cannot be divided

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

(x + 1) /x³ − 3x² + 6x +11.

The degree of the numerator is 1

While the degree of the denominator is 3

For a polynomial quotient to be evaluated, the degree of the numerator must be greater than the degree of the denominator

Because 1 is less than 3, then the polynomial expression cannot be divided

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The amount paid to social security when Dr. Grumman earned $141,340 in 2020 is $8763.08.

A % in mathematics is a quantity or ratio that is stated as a fraction of 100 (from the Latin per centum, "by a hundred"). Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it.

We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100.

Formula for percentages: (Value/Total value) * 100

Dr. Grumman earned $141,340 in 2020.

The social security he paid is:

(141340)(6.2/100) = 8763.08

Hence, the amount paid to social security when Dr. Grumman earned $141,340 in 2020 is $8763.08.

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The missing sides of the two right triangles are B ≈ 75.5, b ≈ 10.7 and a ≈ 6.9.

In this problem we find two similar right triangles. Two triangles are similar when they have congruent angles and sides that are not congruent but proportional. Sides in right triangles are related each other by means of Pythagorean theorem:

r² = x² + y²

Where:

According to the statement, we need to use the following relationships:

B = √(C² - A²)

a / A = b / B = c / C

If we know that A = 49, C = 90 and c = 12.7, then the lengths of missing sides are:

B = √(90² - 49²)

B = √5699  (approx. 75.5)

b = B × (c / C)

b = √5699 × (12.7 / 90)

b = 127√5699 / 900 (approx. 10.7)

a = A × (c / C)

a = 49 × (12.7 / 90)

a = 6233 / 900 (approx. 6.9)

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The value of x is approximately 0.8 cm when rounded to the nearest tenth.

A triangle is a two-dimensional geometric shape that has three sides and three angles. It is the simplest polygon and is a fundamental building block in many areas of mathematics and science.

The three sides of a triangle can have different lengths and can be of different types, such as equilateral, isosceles, or scalene. An equilateral triangle has three sides of equal length, while an isosceles triangle has two sides of equal length and a third side of a different length. A scalene triangle has all three sides of different lengths.

In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. Thus, we have:

sin(IHJ) = IJ/IH

Taking the sine of both sides and substituting the given values, we get:

sin(23°) = x/2

Multiplying both sides by 2, we have:

x = 2*sin(23°)

Using a calculator, we get:

x ≈ 0.83

Therefore, the value of x is approximately 0.8 cm when rounded to the nearest tenth.

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a) The median would be larger than the mean because the life expectancy of some countries may be much lower than the others, thus affecting the mean.

b) The median should be reported as it is a better measure of central tendency, as it is not affected by outliers.

a) The median is expected to be larger than the mean because the life expectancy of some countries may be much lower than the others, thus affecting the mean. The mean is calculated by adding all the values together and dividing by the number of values, and if there are any values that are much lower or higher than the rest, this will affect the mean significantly. The median, however, is the midpoint of the values, so outliers have less of an influence on it.

b) The median should be reported as it is a better measure of central tendency, as it is not affected by outliers. The median is the midpoint of the values, which means that if there are any values that are much lower or higher than the rest, it will not affect the median as much as it does the mean. This makes the median more accurate in representing the life expectancy of countries, as it is not skewed by outliers. Furthermore, the median is generally more reliable when dealing with skewed distributions, which is often the case with life expectancy data.

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The area of the trapezoid KELP is approximately 2285.47 square units.

What is a trapezoid?

A polygon with only one set of parallel sides is called a trapezoid. The parallel bases of a trapezoid are another name for these parallel sides. Trapezoids have two additional sides that are not parallel and are referred to as their legs.

The formula to find the area of a trapezoid is -

A = (1/2) × h × (b1 + b2)

where -

A is the area of the trapezoid.

h is the height of the trapezoid.

b1 and b2 are the lengths of the parallel bases of the trapezoid.

Using the given values, we can substitute them into the formula and solve for the area -

A = (1/2) × h × (b1 + b2)

A = (1/2) × 52.6 × (47.8 + 39.1)

A = 2285.47

Therefore, the area value is 2285.47 square units.

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The value of the expression is 5.

What is order of operations?

The order of operations is a rule that specifies the correct sequence of steps to be taken when evaluating a mathematical equation.

To simplify this expression, we need to follow the order of operations, which is:

Exponents (powers, roots)

Multiplication and Division (from left to right)

Addition and Subtraction (from left to right)

So, we start with the exponents:

[tex]3^0+4^{-1} \\= 1 + 1/4 \\= 5/4[/tex]

Now we substitute this value back into the original expression:

[tex](3^0+4^{-1} )*2^2\\ = (5/4) * 2^2 \\= (5/4) * 4 \\= 5[/tex]

Therefore, the value of the expression is 5.

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Answer:

Step-by-step explanation:

A graph shows Time in minutes along the x-axis and the Truck's distance from the factory in miles along the y-axis. The scales on the x- and y-axes are from 0 to 10 at increments of 1. There are three straight lines in the graph. The first line joins the ordered pair 0, 0 with 3, 3. The second straight line joins 3, 3, and 5, 3, and the third straight line joins ordered pairs 5, 3 with the ordered pair 10, 0.

Answer:

$115

Step-by-step explanation:

12 + 11 = 23

There are 23 students in the class.

Cost of supplies: $5 per student.

total cost = 23 × $5 = $115

The total cost to purchase the supplies is,

⇒ $115

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

Given that;

There are 12 girls and 11 boys registered for the class.

And, You need to purchase supplies that will cost $5 per student.

Here, Total students = 12 + 11 = 23

Hence, The total cost to purchase the supplies is,

⇒ 23 x $5

⇒ $115

Thus, The total cost to purchase the supplies is,

⇒ $115

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The probability that the number of dropouts next year will be exactly 305 is virtually zero, the probability of less than 305 is 68%, greater than 305 is 32%, and within one standard deviation of 305 is 95%.

Probability of dropouts next year being exactly 305: 0

Probability of dropouts next year being less than 305: 0.68

Probability of dropouts next year being greater than 305: 0.32

Probability of dropouts next year being within one standard deviation of 305: 0.95

The probability that the number of dropouts next year will be exactly 305 is virtually zero. This is because the standard deviation of 50 suggests that the number of dropouts is likely to be different from 305.

The probability that the number of dropouts next year will be less than 305 can be calculated using the normal distribution. The probability that the number of dropouts will be less than 305 is approximately 0.68, or 68%.The probability that the number of dropouts next year will be greater than 305 can be calculated using the normal distribution. The probability that the number of dropouts will be greater than 305 is approximately 0.32, or 32%.The probability that the number of dropouts next year will be within one standard deviation of 305 (i.e. between 255 and 355) can be calculated using the normal distribution. The probability that the number of dropouts will be within one standard deviation of 305 is approximately 0.95, or 95%.

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Answer:

y= -5/4x+

Step-by-step explanation:

find the gradient first ∆y/∆5x

-4-1/ 8-4

=-5/4

assume one of the points to be x, y

y-1/ x-4 =-5/4

cross multiply

4y-4=-5x+20

4y= -5x+20+4

divide both sides by 4

y= -5/4x+

[tex] \frac{9}{3} = \frac{x}{2} \\ [/tex]

Cross multiply...

[tex]3x = 18[/tex]

[tex]x = \frac{18}{3} \\ [/tex]

x = 6

Answer:

it's 6. 9 is divided by 3 and the answer is 3 .so 3=x÷2. and multiplie 2 in both side.so the answer is 6.

Answer:

Center is (10, 3)

Radius = 6

Step-by-step explanation:

The standard equation of a  circle is

(x - a)² + (y - b)² = r²

where
(a, b) is the center of the circle and

r is the radius

Comparing (x - 10)² + (y - 3)² = 36

it is easy to  see that a = 10, b = 3 and r =√36 = 6
So center is(10, 3) and radius is 6

The measure of each interior angle of a regular polygon having 15 sides is equal to option B: 156°.

A polygon is an enclosed figure composed of more than three straight lines. To find the measure of each interior angle of a regular polygon having n sides, we would first find the total sum of interior angles of this polygon. The formula is:

(n-2) × 180°

= (15-2) × 180°

= 13 × 180°

= 2340°

We, here, found that the sum of all interior angles of a regular polygon having 15 sides is equivalent to 2340°. Now, to find the measure of each angle, we can divide this sum by the number of sides as:

2340/15 = 156°.

Therefore, the measure of each angle of a regular polygon having 15 sides is equivalent to 156°.

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Complete question is:

Find the measures of each interior angles of a regular polygon having 15 sides.

A. 106°

B. 156°

C. 206°

D. 256°

The integers 6,21 from the set will make the inequality 3(j-5)>3(7-2j) true.

An inequality response is defined?

An expression in mathematics where the sides are not equal is referred to as being inequal. A comparison of any two values, known as an inequality, demonstrates that one value is less than, larger than, or equal to the value on the opposite side of the equation.

The given inequality is 3(j-5)>3(7-2j). The given set is S:{−4, 4, 6, 21}.

First, we will simplify the given inequality.

3(j-5)>3(7-2j)

⇒j-5>7-2j

⇒3j>12

⇒j>4

It means that numbers greater than 4 will satisfy the given inequality.

Numbers greater than 4 in the given set are 6,21.

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As per unitary method, Reeta's salary is 21,000 rupees.

The unitary method is a technique of solving problems by assuming a unit value and then finding out the required value in terms of that unit.

In this problem, we can assume Reeta's salary to be the unit value and then find out how much she spent on car repair work and how much money she has left using this unit value.

Let's assume Reeta's salary to be x rupees. Now, according to the problem, she has spent 2/7 of her salary on car repair work. So, the amount of money she spent on car repair work can be calculated as:

2/7 * x

Using the unitary method, we can now find out how much money she has left with her. We know that she has 15,000 rupees left. So, we can set up the following proportion:

2/7 * x = x - 15,000

Simplifying this equation, we get:

2x = 7(x - 15,000)

2x = 7x - 105,000

5x = 105,000

x = 21,000

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Answer:

3 times

Step-by-step explanation:

6 x 3 = 18

Answer:

3

Step-by-step explanation:

18/6 = 3

or

6 + 6 + 6 = 18

The rate at which lemons are being used in cups of lemonade per lemon is 0.83 cups of lemonade per lemon

To find the rate at which lemons are being used in cups of lemonade per lemon, we need to divide the number of cups of lemonade produced by the number of lemons used.

In this case, 5 cups of lemonade are produced from 6 lemons, so the rate at which lemons are being used in cups of lemonade per lemon is:

5 cups of lemonade ÷ 6 lemons = 0.83 cups of lemonade per lemon (rounded to two decimal places)

the rate at which lemons are being used in cups of lemonade per lemon is 0.83 cups of lemonade per lemon

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The probability of the coin being the weighted one given that it returned heads is 0.8.

P(Weighted | Heads) = ( P(Heads | Weighted) * P(Weighted) ) / P(Heads)

                   = ( 0.8 * 0.5 ) / 0.5

                   = 0.8

The probability of the coin being the weighted one given that it returned heads can be calculated using Baye's Theorem. This theorem states that the probability of an event given a condition is equal to the probability of the condition given the event multiplied by the probability of the event divided by the probability of the condition. In this case, the event is the coin being weighted, the condition is the coin returning heads. Therefore, the probability of the coin being the weighted one given that it returned heads is equal to the probability of the coin returning heads given that it is weighted multiplied by the probability of the coin being weighted divided by the probability of the coin returning heads. The probability of the coin returning heads given that it is weighted is 0.8, the probability of the coin being weighted is 0.5, and the probability of the coin returning heads is 0.5. Thus, the probability of the coin being the weighted one given that it returned heads is 0.8.

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