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An isosceles right triangle has two sides that are equal in length; this means that the angles opposite the sides must also be equal. Since the triangle is a right triangle and the sum of angles of a triangle is 180 degrees, the angles must each be 45 degrees.

The acute angles of an isosceles right triangle are always 45 because of the Pythagorean Theorem. This theorem states that in a right triangle the sum of the squares of the two sides adjacent to the right angle (the legs) is equal to the square of the hypotenuse. Since an isosceles right triangle has two equal legs, and the hypotenuse is the longest side, the two legs must both have the same length, and the angles opposite from these sides must also be the same. This means that the two acute angles in an isosceles right triangle must both be 45 degrees.

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Answer:

m=4

Step-by-step explanation:

look at the traingle formed with line with points (6,5) and (4, -3)

look at change in y (how tall the triangle is) and change in x (the base of triangle)

change in y=8

change in x=2

m=rise/run also known as change in y/change in x

=8/2

=4

note that this is a positive gradeint line

A system of linear equations: y + 2x = -5 and 8x + 4y = -20  has infinitely many solutions.

The 3 possible solutions of a linear system are:

- Unique or one solution

- Infinite solutions

- No solution

If the linear equations are exactly (or can be transformed to exactly) the same equations, the solution is infinite.

The given linear system is:

y + 2x = -5           ....... (equation 1)

8x + 4y = -20     ..........(equation 2)

Rearrange equation 1 to:

2x + y = -5

Multiply both sides by 4:

8x + y4 = -20

Hence, equation 1 is equivalent to equation 2. Hence, the given linear system has infinitely many solutions.

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The Filling time is After 25 minutes, both Aquariums will contain same amount of water.

you've fully prepared the aquarium, all you need to do is follow these quick and easy steps and safely fill your aquarium with water.

Calculate the Filling Time of the aquarium Explanation

Given,

Water in Aquarium A = 4.6 gallons

Water in Aquarium B = 54.6 gallons

Filling rate = 1.2 gallons per minute.

Draining rate = 0.8 gallons per minute.

Let,

x represents the minutes.

A(x) = 4.6 + 1.2x

(Because Luis is adding water in the tank.)

B(x) = 54.6 - 0.8x

(Isacc is draining water from the tank.)

For same amount of water;

A(x) = B(x)

4.6+1.2x=54.6-0.8x

1.2x+0.8x=54.6-4.6

2x=50

Dividing both sides by 2

2x/2=50/2

x=25

Therefore, After 25 minutes, both Aquariums will contain same amount of water.

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Subtract the smaller of the two numbers from the larger of the two numbers to discover the difference between them.

Subtract the smaller of the two numbers from the larger of the two numbers to discover the difference between them. The difference between the two numbers is the sum's product.

Subtracting two integers from each other is a type of subtraction.

The process for determining the difference between two decimals and two whole numbers is the same.

We only add a new step.

Finding the difference between 8.967 and 7.2, for instance, could appear more difficult.

To give them all the same amount of decimal places, we must first convert each decimal.

7.2 becomes 7.200 as a result.

The computation may now be done as before:

8.967 - 7.200 = 1.767

Therefore, there is a 1.767 discrepancy between these figures.

In order to find the difference between two fractions, simplify and find the lowest common denominator of each fraction.

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The best answer is t = 7. Option C

A quadratic equation is simply defined as an equation that could be rearranged in standard form.

It is also described as an algebraic equation having the highest exponent of as 2.

It is so arranged such that;

It is important to note that the three methods of solving quadratic equation are;

From the information given, we have that the form is;

x² = c

Given  t squared minus 49 = 0

First, represent mathematically

t² - 49 = 0

Now, collect like terms, we have;

t² = 49

Take square root of both sides

t = √49

t = 7

Hence, the equation is  t = 7

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Answers:

Rose: y=500

$500

Summer: y=15x+200

$575

Poppy: y=30x

$750

Daisy: y=12.50x+350

$662.5

Violet: y=6x+450

$600

*Make sure you plug the 25 hours in yourself to double check my answers.*

Step-by-step explanation:

I just wrote the equation in number form and plugged the 25 hours in.

Angle ADC = 120 degrees.

A certain portion of a circle that is created based on two radius of the same circle and one arc. Area of sector for a circle with radius r is given by π r²Ф/ 360°

Given, two circles of radius 1 unit and 2 unit which have same center D.

We know area of a circle = π r²

Area of larger circle = π 2² = 4π

it is said that the total area of the shaded region that means area of a particular sector is 1/12 of the area of the larger circle.

area of sector, ACD = 1/12 ×4π

as per the question, the ACD sector is located in the smaller circle that has radius 1 unit.

formula for area of sector ACD = π r² ×Ф/360°

where,Фis the central angle of ACD sector

and Ф = ADC

from the above statement, 4π/12 = π r² ADC/360

                        ADC = 1/3×360°

ADC = 120 degrees

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Answer:

1240.4 mm²

Step-by-step explanation:

SA of Pentagonal pyramid:

(as)(5/2) + (sl)(5/2)

↑ ↑

base area lateral area

_____________________

a: apothem (in-radius) length, s: side length.

l: slant height.

______________________

Since we are already given the base area which is 440.4 mm². All we need to do is find the lateral area and add both areas together.

Given that the triangular face of the lateral part has a side/base length of 16mm, and a 20mm slant height.

A triangle has an area of ½bh and since there are 5 of these faces total, (5)(½bh) = (5/2)(bh). In a three dimensional perspective, b will be s and h will be l so (sl)(5/2).

With this information the surface area is:

(16)(20)(5/2)mm + (440.4 mm²) →

800 mm² + 440.4 mm² =

1240.4 mm²

An equation is formed of two equal expressions. The number of solutions that the given system of equation will give is 3. Thus, the correct option is D.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The number of solutions that the system of equations will have can be found by plotting both the equation on the graph.

Since the point at which the graph intersects is the solution of the system of equations.

Hence, the number of solutions that the given system of equation will give is 3. Thus, the correct option is D.

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Answer:

6 meters

Step-by-step explanation:

^_^

Answer:

200 is your answer. (insert more text to be helpful here)

Answer: C= 30

Step-by-step explanation:

A^2+B^2=C^2

C= √(B²+A²)

C= √(18²+24²)

C=30

Step-by-step explanation:

a) (i) length = 2(pi)r = 2(3.14)(.5 m) = 3.14 m

(ii)3.14 m × ($4.70/m) = $14.76

b) A = (pi)r^2 = (3.14)(18 m)^2 = 1017.9 m^2

Answer:

2.5

Step-by-step explanation:

Taking eguation i

4x+y=13

x= 13-y/4

Taking equation ii

x-y = 2

Substituting the value of x in eq i from ii

x- y =2

13-y/4- y=2

13-y-y=2×4

13-2y =8

-2y=8-13

y=-5/-2

Therefore y=2.5

Answer:

30

Step-by-step explanation:

{x=-1/3-10/3y

5x+20y=5

5(-1/3-10/3y)+20y=5

solve the equation

.

.

Y=5

substitute the value of y into the equation

x=-1/3-10/3×2

.solve the equation

.

.x=-7

(x,y)=(-7,2)

{3×(-7)+10×2=-1

5x(-7)+28×2=5

simplify

{-1=-1

5=5

the ordered pair is asolution

(X,Y)=(-7,2)

That's all!!!!

Answer:

x = -7 y = 2

Step-by-step explanation:

Let's solve this using the elimination method:

3x + 10y = -1. #1

5x + 20y = 5. #2

Multiply Eqtn #1 by -2

-6x - 20y = 2

5x + 20y = 5

Add these two equations together and we will get

-x = 7 or x = -7

Use this value of x into either Eqtn #1 or #2

3(-7) + 10y = -1 ----> 10y = 20 or y = 2

Answer:

3/2

Step-by-step explanation:

5x-7=-11x-25

5x+11x=-25+7

16x=18

x=18/16

x=3/2

If George is trying to fence the garden with less fences possible between the two options given in the question, the first option of measurements i.e 20 feet long and 15 feet wide would take less fencing.

It is the entire distance encircled on all sides by the rectangle.One of the key equations for the rectangle might be regarded to be its perimeter.

The formula for calculating the perimeter of a rectangle is :

P = 2*l + 2 *b where , l and b are the length and breadth of the rectangle.

For the first option, where the garden is 20 feet long and 15 feet wide, the perimeter would be 20+20+15+15 = 70 feet.

For the second option, where the garden is 30 feet long and 10 feet wide, the perimeter would be 30+30+10+10 = 80 feet.

Therefore, the first option where the garden is 20 feet long and 15 feet wide would use less fencing, 70ft in this case, as the perimeter is lower than the other option which is 80 ft.

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Answer:

Step-by-step explanation:

48 * [tex]\pi[/tex] / 180 = 0.837758041

Answer:

(the last one) i think its B

Step-by-step explanation:

Answer:

Turning her body toward Carly.

Step-by-step explanation:

Since turning someone's body towards the speaker means that they are actively paying attention. If she would return text messages, it would make it look like Stephanie doesn't care at all, same thing for focusing on people in the background. If she were to stop Carly's story to ask off-topic questions, it would also make Stephanie seem ignorant.

answer:

my answer to the first one would be false

my answer to the second would be a

Answer:

x = 3[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

4 + 6 = 10

[tex]\frac{2}{6}[/tex] = [tex]\frac{x}{10}[/tex]

6x = 20

x = 3[tex]\frac{1}{3}[/tex]

Answer:

as a factor 2(x-1) this should help or be the correcr answer

Writing the whole number in the numerator and 1 in the denominator. Fraction in simplest form is 8

How to Find the Most Basic Form

Determine the GCF of the fraction’s numerator and denominator.

Divide the created GCF by the numerator and denominator.

Fill in the blanks with the simplified fraction of the supplied fraction.

The most basic form, If the top and bottom have no common components other than 1, the fraction is in its simplest form. In other words, the top and bottom cannot be divided any further and still remain full numbers. You may sometimes hear the phrase “lowest terms” when referring to the simplest form.

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Answer:

C

Step-by-step explanation:

edge 2020

C 12y^2+5y-6/(y-3)(6y)

Answer:

(0, -54)

Step-by-step explanation:

We find the y-intercept by plugging in 0 for x:

[tex]y=-2(x-3)(x-9)\\y=-2(0-3)(0-9)\\y=-2*-3*-9\\y=6*-9\\y=-54[/tex]

The mean, variance, and standard deviation for the probability distribution given are A. Mean = 5.5; B. Variance = 13.875; C. Standard Deviation = 3.722.

The mean, variance and standard deviation of the probability distribution can be calculated using the formula. The mean is calculated by summing up the product of all the values and their respective probabilities and then dividing it by the total probability. In this case, the mean is calculated as:

(1*0.587 + 3*0.115 + 9*0.21 + 12*0.088)/(0.587 + 0.115 + 0.21 + 0.088) = 5.5.

The variance is calculated by summing up the product of the squares of the values and their respective probabilities and then dividing it by the total probability. In this case, the variance is calculated as:

(1^2*0.587 + 3^2*0.115 + 9^2*0.21 + 12^2*0.088)/(0.587 + 0.115 + 0.21 + 0.088) = 13.875.

The standard deviation is the square root of the variance and it is calculated as √13.875 = 3.722.

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