Write a triangle congruence statement

The right-angled triangle have angle B = 40°, side c = 20.9 and b = 13.4 approximately to the nearest tenth.

We shall use the trigonometric ratios of sine and cosine of the angle 50° to get the length of the sides and apply the rule of the sum of interior angles of a triangle to get the angle B.

sin50° = opposite/hypotenuse

sin50° = 16/c

c = 16/(sin50°) {by cross multiplication}

c = 20.9

cos50° = adjacent/hypotenuse

cos50° = b/20.9 {by cross multiplication}

b = 20.9 × cos50°

b = 13.4

The sum of interior angles of a triangle is equal to 180° so;

angle B = 180° - (90° + 50°)

angle B = 180° - 140°

angle B = 40°

Therefore, by application of trigonometric ratios sine and cosine, we have the sides of the right-angled triangle b = 13.4, c = 20.9, and the angle B = 40°.

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Answer:

The slope of AB = slope of CD and slope of BC = slope of DA

Hope this helps!

Step-by-step explanation:

The total area of the card is 4+2π that is calculated as per the description.

Heart shaped ornament is made from a square and two semicircles each of whose diameter is the side of the square where one co-ordinate unit represents one in the coordinates of the six points are given.

The side of the square is 4 units or 4 inches as mentioned you can see from the cord this side of the square is 4 and these two are semicircles and the diameter of the semicircle is 4 and it is mentioned because these semicircles are built on the side of the square so diameter both semicircle equals to 4 inches or 4 units that implies radius would be diameter / to which equals to 2 inches . 2 π R by 2 that gives us to the second boundary as well as third boundary is semicircle to its perimeter aur length would be π R 25 + fire we are writing fire two times because there are two semicircles this one the fourth surface is also side of square this also equals to 4 inches so the overall aur total perimeter would be sum of all the total perimeter equals to 1 + 2 + 3 + 4 which gives a pool + 4 + 4 which will give you 4 + 4 is 8 + 45.

Thus, the total area of the card is 4+2π.

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Answer:

for the first question it would be 7.5

The second one would we 28

The third one would be A

Step-by-step explanation:

As per the divisibility rule, the number is 6552

In math, the divisibility rule states that one to check whether a number is divisible by another number without the actual method of division here if a number is completely divisible by another number then the quotient will be a whole number and the remainder will be zero.

Here we have given that 655Δ i a 4-digit number with one of it digit represented by Δ. 655Δ is divisible by 3.

Here we have to find the missing digit in the given number.

Here we have given that the number is 655Δ.

And we have also given that the given number is divisible y 3.

So, here we must know the divisibility rule of 3.

The divisibility rule of 3 states that a number is completely divisible by 3 if the sum of its digits is divisible by 3.

So, based on these rules let us consider that x be the missing digit.

Then it can be written as.

=> [6 + 5 + 5 + x]/3

=> 16 + x/3

Here we put the value of x as 2, then we get 18, that is divisible by 3.

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Answer:

-1 /3

Step-by-step explanation:

To get from one point to the next, go DOWN1 and OVER3.

DOWN1 and OVER3 is the slope -1/3

From B to C it looks like DOWN2 and OVER6. That is -2/6. But that can be reduced to -1/3. So its the same.



Answer:

Step-by-step explanation:

The given sequence is an arithmetic sequence with a common difference of 4. The 77th term of the sequence is the 77th term of the arithmetic sequence, which is given by the formula:

a_n = a_1 + (n - 1) * d

where a_n is the nth term of the sequence, a_1 is the first term of the sequence, and d is the common difference. Substituting the values for a_1, n, and d into this formula, we get:

a_77 = -8 + (77 - 1) * 4

= -8 + 76 * 4

= -8 + 304

= 296

Therefore, the 77th term of the sequence is 296.

189.55

...

.............

...

The value of x is 27 in the given figure.

An angle is formed when two straight lines or rays meet at a common endpoint.

We need to find the value of x.

The given two angles are (4x+7) and 5(x-4).

The two angles are opposite angles so the two angles are equal.

Let us equate 4(x+7) and 5(x-4).

4x+7=5(x-4).

Apply distributive property on RHS

4x+7=5x-20

4x-5x=-20-7

-x=-27

Multiply both sides by minus

x=27.

Hence, the value of x is 27.

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When a sample of size 25 is taken from a population with a mean of 120 and a standard deviation of 10,The expected distance between the sample mean and the population mean is 2.5.

The mean of a population is the average value of all the data points, while the standard deviation is a measure of how spread out the data points are. When a sample of size 25 is taken from a population with a mean of 120 and a standard deviation of 10, the expected distance between the sample mean and the population mean is 2.5. This is because the standard deviation of the sample mean is equal to the population standard deviation divided by the square root of the sample size. In this case, the standard deviation of the sample mean would be 10/5 = 2, and the expected distance between the sample mean and the population mean would be 2 x 2.5 = 2.5.

Standard deviation of the sample mean = Population standard deviation / √ Sample size

= 10 / √25

= 10 / 5

= 2

Expected distance between the sample mean and the population mean = 2 x 2.5

= 2.5

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∇f(x, y) of the function  f(x, y) = 1 / squareroot (x^2 + y^2) is

Given function is f (x, y) = 1 / squareroot (x ^ 2 + y ^ 2)

∇f(x, y) that is the gradient of the function is ([tex]f_{x}[/tex], [tex]f_{y}[/tex])

[tex]f_{x}[/tex] = partial differentiation of the given function with respect to x

= - x / ( (x ^ 2 + y ^ 2) ^ 3/2)

[tex]f_{y}[/tex] = partial differentiation of the given function with respect to y

= - y / ( (x ^ 2 + y ^ 2) ^ 3/2)

Hence, the ∇f(x, y), the gradient of the function is:

(- x / ( (x ^ 2 + y ^ 2) ^ 3/2) , - y / ( (x ^ 2 + y ^ 2) ^ 3/2))

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Answer:

3

Step-by-step explanation:

The factorial of a number n is the product of all the positive integers from 1 to n. In other words, n! = 1 * 2 * 3 * ... * n. For example, the factorial of 5 is 5! = 1 * 2 * 3 * 4 * 5 = 120.

In this case, we are asked to find the value of the expression 10!/(4!7!). To do this, we first need to evaluate the factorials in the numerator and denominator of the expression. Since 10! = 1 * 2 * 3 * ... * 10, we have:

10! = 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10 = 3628800

Similarly, since 4! = 1 * 2 * 3 * 4 and 7! = 1 * 2 * 3 * 4 * 5 * 6 * 7, we have:

4! = 1 * 2 * 3 * 4 = 24

7! = 1 * 2 * 3 * 4 * 5 * 6 * 7 = 5040

Now that we have evaluated the factorials in the expression, we can plug these values into the expression and evaluate it:

10!/(4!7!) = 3628800 / (24 * 5040) = 3628800 / 120960 = 3

Therefore, the value of the expression 10!/(4!7!) is 3.

Note: It is important to remember that the factorial of 0 is defined to be 1, so 0! = 1. This means that any expression involving 0! can be simplified by replacing 0! with 1. For example, the expression 10!/(4!7!0!) can be simplified as follows:

10!/(4!7!0!) = 10!/(4!7!1) = 10!/(4!7) = 10!/(24 * 7) = 10!/168 = 3628800/168 = 3

This is the same result we obtained above using the factorials of 10, 4, and 7.

The value of the given expression is 30.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

The given expression is 10!/(4!7!).

Now, (10×9×8×7!)/(4!7!)

= (10×9×8)/(4×3×2×1)

= 5×3×2

= 30

Therefore, the value of the given expression is 30.

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Two two numbers whose difference is 88 and whose product is a minimum are -44 and 44.

Let the numbers be x and y where x is larger value and y is smaller number.

According to ques,

x - y =88

and we need to make product of numbers i.e 'xy' minimum.

So we can take x = 88 + y ------(2)

substituting value of x in xy, we get

(88 + y) (y) = y² + 88y ------(1) to make it minimum we need to equate its derivative equal to zero.

derivative of  (1) is 2y + 88

Equating it to zero, we get

2y + 88 = 0

subtracting 88 from both sides, we get

2y = -88

Dividing 2 from both sides, we get

y = -44 ------(3)

Substituting value of y from (3) in (2), we get

x = 88 - 44

x = 44

So, we get value of x as 44 and y as -44 to get their product as minimum.

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Answer:

a)y=x+6

b)y=42

c)

Step-by-step explanation:

if x=8 ,y=14that means that y=x +a thus y=14,x=8 14=8+a hence a=14-8. a=6 thus y=x+6

using the equation in a above y =x+6 ,x=36 thus y=36+6 hence y=42

Answer:

t = 39

Step-by-step explanation:

t - 52 = - 13 ( isolate t by adding 52 to both sides )

t = - 13 + 52 = 39

the integer from the solution set S that makes the equation true is 39

Answer:

[tex] \sf \: t = 39[/tex]

Step-by-step explanation:

Now we have to,

→ find the required value of t.

The equation is,

→ t - 52 = -13

Then the value of t will be,

→ t - 52 = -13

→ t = -13 + 52

→ [ t = 39 ]

Hence, the value of t is 39.

Answer: Exact Form: s = 5/4

Decimal Form: s = 1.25

Mixed Number Form: s = 1 1/4

Answer: $892.44

Step-by-step explanation:

Take 27 times 18.66 = $503.82

Then take 34 times 11.43 = $388.62

Then add them to find total

503.82 + 388.62 = $892.44

The owner only owe $892.44

Answer:

y= -5x

Step-by-step explanation:

The formula for direct variation is y=kx

The equation of the line n parallel to line m will be y = 3/2x - 9. The correct option is A.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

The equation of the lime m perpendicular to the line y = -2/3x + 6 will be,

y = 3/2x + c

The line n is parallel to n and passes through the point (4,-3),

y = 3/2x + c

-3 = (3/2 x 4)  + c

-3 = 6 + c

c = -9

The equation of line n will be written as,

y = 3/2x - 9

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Answer:

To solve this system, we need to find the values of x and y that make both equations true at the same time.

Let's start by solving the first equation for y:

|2х - бу = 1

2х - бу = 1

-2х + бу = -1

бу = 1 - 2х

y = (1 - 2х)/б

Now let's substitute this expression for y into the second equation:

x - (1 - 2х)/б = 1

x - 1 + 2х/б = 1

3х/б = 0

x = 0

Substituting this value for x back into the first equation, we get:

y = (1 - 2*0)/б = 1/б

So the solution to the system of equations is x = 0 and y = 1/б.

I hope this helps!

Answer: b=2/5

Step-by-step explanation:

Step 1: Cross-multiply.

2b−1/2 = b−1/6

(2b−1)*(6)=(b−1)*(2)

12b−6=2b−2

Step 2: Subtract 2b from both sides.

12b−6−2b=2b−2−2b

10b−6=−2

Step 3: Add 6 to both sides.

10b−6+6=−2+6

10b=4

Step 4: Divide both sides by 10.

10b/10 = 4/10

b = 2/5

Answer:

150 sequences

Step-by-step explanation:

Let's find the sets of 5 integers less than or equal to 6 that could multiply to 300 (where order doesn't matter for right now):

1, 2, 5, 5, 6

1, 3, 4, 5, 5

2, 2, 3, 5, 5

Now let's find the number of unique ways we could reorder these sets

There are [tex]\frac{5!}{2!} = 60[/tex] ways to order {1, 2, 5, 5, 6}

There are [tex]\frac{5!}{2!} = 60[/tex] ways to order {1, 3, 4, 5, 5}

There are [tex]\frac{5!}{2!2!} = 30[/tex] ways to order {2, 2, 3, 5, 5}

There could have, therefore, been 60 + 60 + 30 = 150 different sequences of rolls

The number of times that she has filled her 12-fluid-ounce will be 33.307.

Unit modification is the process of converting the measurement of a given amount between various units, often by multiplicative constants that alter the value of the calculated quantity without altering its impacts.

We know that in 1 gallon, there are 133.228 fluid ounces.

The amount of coffee in 3 gallons will be given as,

3 gallons = 3 x 133.228

3 gallons = 399.684 fluid ounces

The number of times that she has filled her 12-fluid-ounce will be given as,

⇒ 399.684 / 12

⇒ 33.307

The number of times that she has filled her 12-fluid-ounce will be 33.307.

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Answer: 16.16 in

Step-by-step explanation:

10^2 + x^2 = 19^2

100 + x^2 = 361

x^2 = 261

x = 16.16 in

Answer:

24

Step-by-step explanation:

If 4/6 of the items are jackets and the rest are gloves, this means 1 - 4/6 = 2/6 = 1/3 of the items are gloves in Saginaw Elementary School's lost and found.

We do 72 total items × 1/3 items are gloves = 24 items in the lost and found are gloves

Answer:

73,700

Step-by-step explanation:

You round up on the hundreds place. 73,653

Hope this helps! :)

73,653 rounded to the nearest hundred is: 73,700.

We can conclude that it is more likely that a child has side effects compared to an adult

What is probability ?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

The given information is expressed as

Side effect no side effect total

Adult 7 43 50

Children 22 28 50

Total 29 71 100

Probability is expressed as

Number of favorable outcomes/number of total outcomes

For the probability that an adult has side effects,

Total number of outcomes = 50

Number of favorable outcomes = 7

Probability that an adult has side effects = 7/50 = 0.14

For the probability that a child has side effects,

Total number of outcomes = 50

Number of favorable outcomes = 22

Probability that an adult has side effects = 22/50 = 0.44

Therefore, it is more likely that a child has side effects compared to an adult

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