State if the three numbers can be the measures of the sides of a triangle

  From the picture attached,

Coordinates of point A → (0, 0)

Coordinates of point M → [tex](\frac{a}{2}, \frac{b}{2} )[/tex]

Coordinates of point A → (0, b)

Coordinates of point A → (a, 0)

Since, we have to prove that midpoint (M) of the hypotenuse BC is equidistant from all three vertices A, B and C,

AM = BM = CM

Use the expression for the distance between two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].

Distance = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

AM = [tex]\sqrt{(\frac{a}{2}-0 )^2+(\frac{b}{2}-0)^2}[/tex]

      = [tex]\sqrt{(\frac{a}{2})^2+(\frac{b}{2} )^2}[/tex]

BM = [tex]\sqrt{(a-\frac{a}{2} )^2+(\frac{b}{2})^2}[/tex]

      = [tex]\sqrt{(\frac{a}{2})^2+(\frac{b}{2})^2}[/tex]

CM = [tex]\sqrt{(0-\frac{a}{2} )^2+(b-\frac{b}{2})^2}[/tex]

      = [tex]\sqrt{(\frac{a}{2})^2+(\frac{b}{2})^2}[/tex]

Therefore, AM = BM = CM = [tex]\sqrt{(\frac{a}{2})^2+(\frac{b}{2})^2}[/tex]

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YES, the midpoint of the hypotenuse of a right triangle is equidistant from three vertices -

AM = CM = BM.

We have a right - angled triangle → ΔABC.

We have to prove that midpoint of the hypotenuse of a right triangle is equidistant from three vertices.

A right angled triangle is a triangle with one of the angles as 90 degrees.

According to the question -

Consider the hypotenuse BC. The mid - point of BC has the coordinates as -

M([tex]\frac{a}{2} , \frac{b}{2}[/tex]).

Now -

Length AM →

AM = [tex]\sqrt{(\frac{a}{2}) ^{2} + (\frac{b}{2}) ^{2} }[/tex]

Length CM →

CM = [tex]\sqrt{(\frac{a}{2}) ^{2} + (\frac{b}{2} - b) ^{2} }=\sqrt{(\frac{a}{2}) ^{2} + (\frac{b}{2}) ^{2} }[/tex]

Length BM →  

BM = [tex]\sqrt{(\frac{a}{2} -a) ^{2} + (\frac{b}{2} ) ^{2} }=\sqrt{(\frac{a}{2}) ^{2} + (\frac{b}{2}) ^{2} }[/tex]

Therefore -

AM = CM = BM

Hence, the midpoint of the hypotenuse of a right triangle is equidistant from three vertices.

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The odds in favor of winning $5 or more at the carnival are 3 to 10.

To determine the odds in favor of winning $5 or more at the carnival, we need to consider the number of tickets that win $5 or more and the total number of tickets.

Identify the tickets that win $5 or more: Yellow tickets win $5 and Blue tickets win $10.

Count the number of these tickets:

Yellow tickets: 25

Blue tickets: 5

Total tickets that win $5 or more:

25 + 5  = 30

Total number of tickets:

100 + 25 + 5 = 130

Odds in favor of winning $5 or more is the ratio of favorable outcomes to unfavorable outcomes:

Winning tickets: 30

Non-winning tickets:

130 - 30 = 100

Simplified odds:

30 to 100 = 3 to 10

Therefore, the odds in favor of winning $5 or more are 3 to 10.

The odds in favor of winning $5 or more in a carnival drawing are 3 : 10. So, the correct option is (B).

To determine the odds in favor of winning $5 or more in a carnival drawing, observe the number of tickets for each prize and calculate the favorable outcomes.

Here are the ticket counts:

⇒ 100 (green) + 25 (yellow) + 5 (blue) = 130 tickets

⇒ 25 (yellow) + 5 (blue) = 30 tickets

⇒ 130 (total) - 30 = 100 tickets

Therefore, the odds in favor of winning $5 or more are 30:100, which simplifies to 3:10. This converts to the following odds as a ratio:

So, the correct option is (B) 3:10.

Complete question:

In a carnival drawing, a green ticket wins $1, a yellow ticket wins $5 and a blue ticket wins $10. There are 100 green tickets, 25 yellow tickets and 5 blue tickets. In simplest form, what are the odds in favor of winning $5 or more?

A. 1:1

B. 3:10

C. 2:1

D. 1:3

Answer:

abc

Step-by-step explanation:

A=4  B= 26 C= 4 and 2

Answer:

The answer is in the attachment.

Step-by-step explanation:

Coefficient in front of x^2 is 0.4. What that means is that for same increase of x now we will have less increse of y. If you picture that we can also say that graph would be wider. The graph will stay on positive side of y axis because x^2 is always positive and 0.4 times that is again always positive.

The answer is third graph (middle one)

y² + 15y + 56 = (y + 7)(y + a)

y² + 15y + 56 = y² + (7 + a)y + 7a

We can now compare the coefficient of the like terms, either the one with y or the one without y, and find the value of a.

15 = 7 + a; a = 8

OR

56 = 7a; a = 8

Second factor is (y + 8)

The largest perfect square less than or equal to 45 is 36, which is the square of 6. Squaring numbers less than 7 shows that 36 is the perfect square closest to, but not exceeding 45.

Answer:

True  

Step-by-step explanation:

Given : Statement - 'A degree is larger than 30 arc minutes'.

To find : True or False ?

Solution :

We know that,

1 degree is [tex]1^\circ=\frac{1}{360}[/tex] of a circle

1 arc minute is [tex]1^'=(\frac{1}{60})^\circ[/tex] of degree.

So, 30 arc minutes is [tex]30^'=(\frac{30}{60})^\circ[/tex] of degree.

30 arc minutes is [tex]30^'=(\frac{1}{2})^\circ[/tex] of degree.

Which clearly means,

[tex]1^\circ>(\frac{1}{2})^\circ[/tex]

[tex]1^\circ>30^'[/tex]

Therefore, The given statement is true.

'A degree is larger than 30 arc minutes'.

The required value will vary Between [1,∞)

It is the branch of science that studies the relation between right-angled triangles.

if sin u = x and u varies from 0 to [tex]\frac{\pi }{2}[/tex]

We know, Sec u = [tex]\frac{1}{cos u}[/tex]

Then, for sec u or sec u varying from 0 to [tex]\frac{\pi }{2}[/tex] value will be in between [1,∞)

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Use the chain rule of differentiation to calculate ∂z/∂s and ∂z/∂t. Start by differentiating the functions z with respect to x and y, then differentiate the functions x and y with respect to s and t. Finally, plug the derived values into the chain rule formula to get the expressions for ∂z/∂s and ∂z/∂t.

To solve the problem, we will need to apply the chain rule in order to calculate ∂z/∂s and ∂z/∂t. The chain rule is used in calculus to differentiate a function that has other functions inside of it.

We will differentiate z which is the function of x and y, and x and y themselves are functions of s and t.

The steps are as follows:

The chain rule formula is:

∂z/∂s = ∂z/∂x * ∂x/∂s + ∂z/∂y * ∂y/∂s

and

∂z/∂t = ∂z/∂x * ∂x/∂t + ∂z/∂y * ∂y/∂t.

This will give you the final expressions for ∂z/∂s and ∂z/∂t as functions of x, y, s, t.

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The correct answer is: Option (D) x = 72°

Explanation:

When two lines are crossed by another line, the angles in matching corners are called corresponding angles. When the two lines are parallel, the corresponding angles are equal.

Here in this case, the two lines are "AB" and "CD", and both are parallel and are crossed by the line; therefore, the corresponding angles will be the same.

Since the first corresponding angle is 72°, the second angle x will be 72° as well. The correct answer is: x = 72° Option (D).

In the diagram below, AB is parallel to CD. What is the value of x?

Answer: 72!

Answer:

3/4 sq. ft.

Step-by-step explanation:

Hope it helps.

1. D (4,5)                        

2. C

3. D

4. A

5. C

6. D

7. B

8. C

9. A

10. B

OR

1. B (2,6)

2. A

3. A

4. C

5. D

6. A

7. A

8. B

9. C

10. A

Don't deny it, you came here for the answers ;)

Final answer:

A half pepperoni pizza contains 660 calories and a ham-and-pineapple pizza contains 580 calories.

Explanation:

Let's represent the number of calories in half a pepperoni pizza as x, and the number of calories in a ham-and-pineapple pizza as y. We can set up a system of equations to represent the given information:

0.5x + 0.75y = 765 -- Equation (1)

0.25x + y = 745 -- Equation (2)

We can solve this system of equations using the method of substitution:

From Equation (2), y = 745 - 0.25x

Substitute this value of y into Equation (1):

0.5x + 0.75(745 - 0.25x) = 765

Simplify and solve for x:

0.5x + 558.75 - 0.1875x = 765

0.3125x = 206.25

x = 660

Now substitute the value of x back into Equation (2) to find y:

0.25(660) + y = 745

Simplify and solve for y:

165 + y = 745

y = 580

Therefore, there are 660 calories in a half pepperoni pizza, and 580 calories in a ham-and-pineapple pizza.

The given number 0.333333 is rational number and real number.

A decimal number is said to be irrational if it never repeats. For instance, since there is no repetition, the decimal representation of pi is an estimate. All rational numbers have decimal expansions that either come to an end (in which case all subsequent values are zero) or follow a pattern.

The ratio is defined as a relationship between two quantities, it is expressed one divided by the other.

A rational number is defined as a number that can be represented as the ratio of two integers, where the denominator must not equal zero.

A rational number is any number that can be written as a ratio. Think of a ratio kind of like a fraction, functionally at least.  

Given number, 0.333333 is a repeating decimal that comes from the ratio of 1 to 3, or 1/3.  Thus, it is a rational number.

The number 0.333333 is also real number.

Hence, the number 0.333333 is rational number and real number.

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On a number line, closed circle on a point indicates that point is also included and the open circle indicates that point is not included.

Number lines are represented as straight lines drawn horizontally on which integers are written in equal intervals.

This line is extended to infinity on both sides.

Number line includes positive numbers, zero and negative numbers.

Closed circles and open circles are used in number line to represent linear inequalities in one variable.

Let 'n' be any number on the number line.

We use open circles on 'n' to denote inequalities like x < n and x > n.

We use closed circles on 'n' to denote inequalities like x ≤ n and x ≥ n.

Hence, open circles are used to numbers which are greater than or less than ( > or < ) and closed circles are used to numbers which are greater than or equal to and less than or equal to ( ≥ or ≤ ).

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All the bird seed bags Nellie is considering have the same cost per pound ($0.72). She should choose based on her weekly usage and storage preference. Any size will be cost-effective.

To determine the best deal on bird seed, Nellie needs to calculate the unit price for each option. The unit price is the price per pound of bird seed.

For the 3.5-pound bag:

[tex]\[ \text{Unit price} = \frac{\$2.52}{3.5 \text{ pounds}} \approx \$0.72/\text{pound} \]\\For the 7.5-pound bag:\[ \text{Unit price} = \frac{\$5.40}{7.5 \text{ pounds}} = \$0.72/\text{pound} \]For the 11-pound bag:\[ \text{Unit price} = \frac{\$7.92}{11 \text{ pounds}} \approx \$0.72/\text{pound} \][/tex]

Since all three options have the same unit price of approximately $0.72 per pound, Nellie should choose the size that offers her the most pounds of bird seed for the best value, as he has anyway room for storing extra purchase. Here, can choose to buy any of them.

Answer:

A) 5√22

Step-by-step explanation:

I took the K12 quiz and it was right

The simplification form of the √550 is 5√22 after factorization of 550 or 550 can be written as 5x5x2x11 option (A) 5√22 is correct.

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

It is given that:

The number in radical sign is 550 ie.

= √550

The factors of the 550 can be written as:

550 = 5x5x2x11

= √(5x5x2x11)

= 5√(2x11)

= 5√22

Thus, the simplification form of the √550 is 5√22 after factorization of 550 or 550 can be written as 5x5x2x11 option (A) 5√22 is correct.

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The first thing we are going to do to find the total cost of the meal before tax:

Total cost before tax = $8.99 + 2($14.99) + $12.99 + 3($1.99)

Total cost before tax = $8.99 + $29.98 + 12.99 + $5.97

Total cost before tax = $57.93

Regarding the 15% gratuity, remember that the unofficial rule for tipping at restaurants is to tip according to the actual value of the meal and not the tax, so we calculate the value of the tip first, and then we add it to the total at the end of our calculations.

Tip = 15%($57.93) = $8.69

Now, lets calculate the tax

Tax = 7.5%($57.93) = $4.34

Finally, we can calculate the total cost of the meal

Total cost = cost before tax + tip + tax

Total cost = $57.93 + $8.69 + $4.34 = $70.96

We can conclude that the correct answer is a. $70.96

Answer:

$70.96

Step-by-step explanation:

Cost of 1 appetizer = $8.99

Cost of 1 entrees= $14.99

Cost of 2 entrees= [tex]14.99 \times 2 = 29.98[/tex]

Cost of 1 entree: $12.99

Cost of 3 drinks = 1.99 \times 3 =5.97

Total cost before tax = $8.99 + $29.98 + 12.99 + $5.97

Total cost before tax = $57.93

there is 7.5% tax

So, tax =[tex]7.5 \% \times 57.93 = \frac{7.5}{100} \times 57.93 =4.34[/tex]

The customer leaves a 15% gratuity.

Gratuity=[tex]15 \% \times 57.93 = \frac{15}{100} \times 57.93 =8.69[/tex]

So, Total cost including tax and gratuity = $57.93 + $8.69 + $4.34 = $70.96

So, Option A is true