What is the length of the hypotenuse of a 45 45 90 triangle with a leg of 12?

A)  13 meters

B)  2.3 centimeters

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Work Shown:

Part A

The ruler diagram shows the building on paper is 6.5 cm wide. The right side of the building lines up with the midpoint marker between 6 and 7.

1 cm = 2 m

6.5*(1 cm) = 6.5*(2 m)

6.5 cm = 13 m is the width of the building in real life

Or you can solve it like this

(1 cm)/(2 m) = (6.5 cm)/(x meters)

1/2 = 6.5/x

1*x = 2*6.5

x = 13

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Part B

(1 cm)/(2 m) = (x cm)/(4.6 m)

1/2 = x/4.6

1*4.6 = 2*x

4.6 = 2x

x = 4.6/2

x = 2.3 centimeters is the height of the building in the drawing

The options (a),(b) and (d) are true regarding the apothem of equilateral triangle.

What is an apothem of a polygon?

A line segment from a regular polygon's centre to one of its sides is known as the apothem.

The given options are the following:

a)The apothem can be found using the Pythagorean theorem.

b)The apothem can be found using the tangent ratio.

c)The perimeter of the equilateral triangle is 15 cm.

d)The length of the apothem is approximately 2. 5 cm.

e)The area of the equilateral triangle is approximately 65 cm².

Now we will see if each option is true or not

a) From below figure,

      b = 8.7 / 2 = 4.35 cm

      From right angled triangle ΔABD,

    Using Pythagorus Theorem,

       a² + b² = 5²

       a² + 4.35² = 5²

       a = [tex]\sqrt{5^{2} - 4.35^{2} }[/tex] = 2.5 cm

Apothem can be found using Pythagorus Theorem.

b) From the figure, the radius divide the angle 60° of equilateral triangle to two 30° angles.

So from ΔABD,

tan 30° = a / 4.35

0.577 = a / 4.35

a = 2.5 cm

The apothem can be found using tangent ratio.

c) Perimeter of given equilateral triangle = 3 × side length

                                                                    = 3 × 8.7 = 26.1 cm

   This option is false.

d) From options (a) and (b) we found that length of apothem a = 2.5 cm

Therefore this option is true.

e) The area of given equilateral triangle = [tex]\frac{\sqrt{3} }{4} } * side^{2}[/tex] = [tex]\frac{\sqrt{3} }{4} * 8.7^{2}[/tex]

                                                                       = 32.8 cm²

Therefore this option is false.

Therefore options (a),(b) and (d) are true regarding the apothem of equilateral triangle.

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In a reaction the amount f a substance which react with another substance is known as it's equivalent.

The definition of equivalent is "weight in grams of a substance that displaces or combines with one gram of hydrogen."

It is an important part of chemistry and comes under stoichiometry. In every reaction there is a reactant which forms the suitable product and the amount of that is calculated using stoichiometry.

The mole ratio is a typical sort of stoichiometric relationship that compares the amounts in moles of any two components in a chemical process.

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The capacity to complete complex tasks quickly enough to make them useful is the main benefit of choosing a parallel method over a sequential one.

Sequential Computing: One instruction is delivered at a specific time, and the subsequent instruction must wait for the first instruction to complete before it can be executed. This is known as sequential computing. Because all the instructions are carried out in order, it is often referred to as a conventional computing technique. It has a single CPU that performs poorly and has a heavy workload. The biggest drawback of employing this computing is that it requires more time because just one instruction is being processed at a time.

Parallel Computing: A computing method known as parallel computing involves running numerous calculations or processes simultaneously in parallel. Parallel computing is a kind of computing in which multiple processes can run at once.

Due to the simultaneous execution of the operations, time is saved. It resolves more complex issues. There are many processors with high performance and little work being put on each of them.

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The stripe's area in square feet is 240 square units.

The size of a region on a surface is measured in area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina. The total space occupied by a flat (2-D) surface or the form of an item is defined as its area. Draw a square on a sheet of paper using a pencil. It is a two-dimensional figure. The area of the form on the paper is referred to as its Area. Consider your square to be made up of smaller unit squares.

Here,

The cylinder can be "unwrapped" into a rectangle, and we see that the stripe is a parallelogram with base 3 and height 80.

area=3*80

=240 square units.

the area of the stripe in square feet is 240 square units.

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Answer: for A it is: 3 and 4 represent the number values for X and Y.

Step-by-step explanation:

Sorry, but you B and C you did not give enough information

Answer:

2 (21a−8)

Step-by-step explanation:

Answer:

2(21a - 8)

Step-by-step explanation:

42a - 16
The gcf of 42, 16 is 2
=> 2(21a-8)

Answer:

the equation of line parallel to y=-3x+2

is y=-3x+k---(1)

Since,line(1) passes through point (4,3).

3=-3(4)+k

or,3=-12+k

or,k=3+12

:.k=15

Putting value of k in line (1), we get

y=-3x+15,which is the required eqn.

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$1553.91

Step-by-step explanation:

839.95 ×.85 = 713.96

839.95 + 713.96 = 1553.91

Answer:

55 miles per hour

Step-by-step explanation:

The equation is:

R = d / s

We know

d = 495 miles

s = 9 hours

Let's solve

R = 495 / 9

R = 55 miles per hour

So, their driving rate is 55 miles per hour

The simplified form of 21b − 32 7b − 20b would be 8b - 32.

Reducing an equation is a technique for rewriting it in a more straightforward format. Although some mathematical equations are not in the form of linear equations, they can be converted into linear equations by applying certain mathematical operations to them. These equations can be easily solved after being reduced to linear form, and the value of the unknown can be determined.

21b – 32 + 7b – 20b

= 21b + 7b – 20b – 32

= 28b – 20b – 32 = 8b – 32

21b - 32 + 7b - 20b

= 21b + 7b - 20b -32

= 8b - 32

=8b - 32.

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Answer: I think it's 6816606.576

Step-by-step explanation: Hope this helps?

Answer:

9.75

Step-by-step explanation:

3/4 |1/3x+2| < 6

you can turn the < into a =

then subtract 3/4 from 6 which leaves you with 5.25. And since you know 2 will always be positive because it's in an absolute value bracket 5.25-2=3.25. Which leaves you with

|1/3x| = 3.25

then do 3.25/(1/3) which leaves you with 9.75

:)

Answer:

Step-by-step explanation:6

Answer:

Option 2

Step-by-step explanation:

Hello!

We can solve the equation for n by isolating the variable.

The answer would be the second option: "n = the quantity 3 times c minus 9 all over negative p."

The polynomial's zero is 2 since the value of k = -2 is  [tex]3x^{2}[/tex]  +4x+2k . A polynomial is an equation that combines variables, constants .

Using just the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables, a polynomial is an expression in mathematics made up of variables (also known as indeterminates) and coefficients. Using addition, subtraction, multiplication, and division of numbers, a polynomial is an equation that combines variables, constants, and exponents (No division operation by a variable).

given

−2 is a zero of f(x)=[tex]3x^{2}[/tex]+4x+2k

f(−2)=0

∴[tex]3(-2)^{2}[/tex] +4(−2)+2k=0

=>12−8+2k=0

=>2k=−4

=>k=−2

The polynomial's zero is 2 since the value of k = -2 is  [tex]3x^{2}[/tex]  +4x+2k .

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Answer:

Step-by-step explanation:

Answer:

6,532

Step-by-step explanation:

ixl

Answer:

do your own work don't ask any question

Answer:

Below

Step-by-step explanation:

How many times will the colony double ?    124 / 31 = 4 times

2^4   * 100 000 = 1 600 000

Answer:

The angle in the sector is 180°.

Because the area of circle is 36 pie cm². So the angle is the half of 360°.

[tex]\boxed{\begin{array}{l} \\ \sf\huge{ \quad \underline{Answer} } \\ \\ \underline{ \underline\textsf{ Area of sector is given by : }} \\ \\ \dashrightarrow \sf{ A = \dfrac{ \theta}{360 \degree} \times \pi {r}^{2} } \\ \\ \dashrightarrow\sf{18 \pi = \dfrac{ \theta}{360 \degree} \times \pi {(6)}^{2} } \\ \\ \dashrightarrow \dfrac{ \theta}{360 \degree} = \dfrac{18 \pi}{ \pi(36)} \\ \\ \dashrightarrow \theta = 360 \degree \times \dfrac{1}{2} \\ \\ \dashrightarrow\theta = 180 \degree \\ \\ \end{array} } [/tex]

Retail price of the product will be double its mean will have a prbability of 0.0401.

An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range while the remaining ones taper off symmetrically toward either extreme. The distribution's mean is another name for the center of the range.

A probability distribution that is symmetric around the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution appears as a "bell curve" on a graph.

The value of the product considering = $37*2 = $74(x)

Mean = $37

Standard Deviation (SD)= $20

here z= [tex]\frac{x - mean}{SD}[/tex] = [tex]\frac{74 - 37}{20} = \frac{37}{20} = 1.75[/tex]

P(z>1.75) = 1 - [tex]\phi(1.75)[/tex] = 1 - .9599 = 0.0401

Retail price of the product will be double its mean will have a prbability of 0.0401.

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The height of a triangle can be found using the triangle area formula, which states that the area of a triangle is equal to (1/2) * base * height. Therefore, the height of a triangle can be found by rearranging the formula to height = (2 * area) / base.

To find the height of a triangle when the base is given, first use the triangle area formula, which states that the area of a triangle is equal to (1/2) * base * height. Next, rearrange the formula to height = (2 * area) / base so that the height can be found by dividing the area by the given base. Once the area is known, the height can be found by plugging the area and base into the rearranged formula. For example, if the base of a triangle is 8 and the area is 12, then the height of the triangle can be found by dividing 12 by 8, which is equal to 1.5. Therefore, the height of the triangle is 1.5.

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Enchanted Rock State Natural Area is located at latitude 30.506130 and longitude -98.820064. The geographic coordinates of Enchanted Rock State Natural Area in Fredericksburg, United States, are 30° 30' 22.068" N and 98° 49' 12.2304" W. Enchanted Rock State Natural Area falls under the Mysterious Sites category.

The standard datum used by default for GPS devices used for commercial and recreational purposes is WGS84. GPS users are advised to always verify the datum of the maps they are utilising.

WGS 84, also known as the datum, is now in use by US forces.

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a)  The maximum mortgage amount they could afford to borrow from the bank, if all the other conditions were the same =  $369,181.93.

b)  The total amount that would be paid to the lender over 25 years = $540000

To find the maximum mortgage amount they could afford to borrow if they could only pay $1800.

Here, future value = 0

number of periods = 25 years

                                = 25 × 12 months per year

                                = 300

payment amount = -1800 dollars

interest rate = 4.25% per year

                    = 0.3542% per month

the maximum mortgage amount they could afford = $369,181.93.

And the total payments would be equal to 300 × 1800 = 540000

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The complete question is:

Aya and Harumi would like to buy a house and their dream house costs $500,000. They have $50,000 saved up for a down payment but would still need to take out a mortgage loan for the remaining $450,000 and they're not sure whether they could afford the monthly loan payments. The bank has offered them an interest rate of 4.25%, compounded monthly.

What if Aya and Harumi could only afford a monthly payment of $2,000?

What would be the maximum mortgage amount they could afford to borrow from the bank if all the other conditions were the same?

What is the total amount that would be paid to the lender over 25 years?

To solve for x, we need to get x by itself on one side of the equation. To do this, we can start by subtracting 1.4x from both sides of the equation. This gives us:

3 1/2 - 1.4x ≥ 0

Next, we can simplify the left side of the equation to get:

7/2 - 7/5x ≥ 0

Now we can divide both sides of the equation by -7/5 to get:

-5/2x ≤ -7/2

Finally, we can multiply both sides of the equation by -2/5 to get:

x ≥ 4 9/10

Therefore, the solution is x ≥ 4 9/10, which corresponds to answer choice C.

Answer:
x ≥ 4 9/10 C:)

Step-by-step explanation:

When solving the following system of equations,  the x in the first equation would be the easiest to solve for.

Systems of equations can be solved using one of three techniques: graphing, substitution, or elimination. Simply plot the provided equations on a graph and locate the point(s) where they all cross to solve a problem by graphing. You may find the values of the variables you are working for by finding the location of this point.

The result of the first equation is

x + 6y = 25

we can easily solve for x by subtracting 6y from both sides we have  

x + 6y - 6y = 25 - 6y

x - 25 - 6y

So, the first equation's x term can be simply solved.

When solving the following system of equations,  the x in the first equation would be the easiest to solve for.

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An equation that represents the relationship between x and y shown in the table is y = 1.5x.

In order to write an equation that represents the relationship between x and y shown in the table, we would have to find the slope from the table and then write the required equation based on the data points by using the point-slope form.

Mathematically, the point-slope form of a line is given by this mathematical equation:

y - y₁ = m(x - x₁)

Where:

By substituting the given parameters into the point-slope formula, an equation for the data points contained in this table is given by;

y - y₁ = m(x - x₁)

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 21 = (96 - 21)/(64 - 14)(x - 14)

y - 21 = 75/50(x - 14)

y - 21 = 1.5(x - 14)

y = 1.5x - 21 + 21

y = 1.5x

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The formula for vector direction is: Direction = arctan (y/x) , Where x is the x component of the vector and y is the y component of the vector.

1. Find the x and y components of the vector

2. Divide the y component by the x component

3. Calculate the arctan (inverse tangent) of the result

4. The result is the direction of the vector in radians (or degrees if you prefer).

If you want to convert the result from radians to degrees, you can use the following formula:

(in degrees) = arctan (y/x) * (180/π)

Where π (pi) is approximately equal to 3.14.

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The resultant output of  the given question is 7 by 2 is 14.

This is because 7 multiplied by 2 is equal to 14

When you multiply two numbers, the result is the product of the two numbers. In this case, 7 multiplied by 2 is equal to 14.

Mathematicians use the process of multiplication to calculate the product of two or more given numbers. It is a fundamental mathematical operation in maths that is frequently utilised in everyday life. When we need to combine groups of similar sizes or values , we utilise multiplication.

Hence the correct answer to the given question is 14 .

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