How to find the legs of a 45 45 90 triangle given the hypotenuse?

Answers

Answer 1

If the hypotenuse is given to the 45 45  90 triangles, the leg of the triangle is calculated after dividing the hypotenuse by [tex]\sqrt{2}[/tex].

The 45, 45, and 90 triangle is a type of isosceles triangle where the two legs are the same as each other and other non-right angles are both 45 degrees. Most of the time, Pythagoras' theorem is used for finding out the missing legs and hypotenuses of 45, 45, and 90 triangles.

If the leg of the triangle is equal to a, then:

The second leg is also equal to a;The hypotenuse is a√2;The area is equal to a²/2; andThe perimeter equals a(2 + √2).

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Related Questions

Is 4x² 3x 7 a polynomial?

Answers

As all the exponents of x are whole numbers, the expression 4x² – 3x + 7 is a polynomial in one variable.

What is exponents?

The exponent of a number shows how many times the original value of the number has been multiplied. For example, the number 34 indicates that we have multiplied three by four. 3 × 3 × 3 × 3 × 3 is its expanded form. Exponent is another term for a number's power. It might be a decimal, a fraction, a negative number, or a whole number.

Exponents are important because without them, writing the product when a number was repeated many times on its own would be very difficult. For example, it is much easier to write 57 than it is to write 5 × 5 × 5 × 5 × 5.

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The steepness of a ramp is graphed using the points (0,3) and (36,0). The steepness of a second ramp is represented by the function g(x)= -1/4x+2. What is the slope of the ramp?

Answers

The slope of a line is a measure of its steepness and can be calculated using the formula:

slope = (y2 - y1) / (x2 - x1)

In this case, the points (0,3) and (36,0) represent the coordinates of two points on the ramp. To find the slope of the ramp, we can plug these values into the formula:

slope = (0 - 3) / (36 - 0) = -3 / 36 = -1/12

The slope of the ramp is -1/12. This indicates that the ramp is relatively flat, as a negative slope means that the line is sloping downward.

To find the slope of the second ramp, represented by the function g(x) = -1/4x + 2, we can take the derivative of the function. The derivative of a function represents the slope of the function at any given point, and it is calculated using the formula:

derivative = f(x) = -1/4

The derivative of the function g(x) is a constant value of -1/4, which means that the slope of the second ramp is also -1/4. This is a steeper slope than the first ramp, as the value of the derivative is larger in magnitude.

Find values of a and b that make the following equality into identity:
(2x+5)/(x-8)(2x+1)=a/(x-8) + b/(2x+1)
Giving 30+ points!

Answers

The values of a and b in the fraction are 21/17 and -8/17

How to determine the values of a and b

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

(2x+5)/(x-8)(2x+1)=a/(x-8) + b/(2x+1)

Take the LCM

So, the expression can be expressed as

(2x+5)/(x-8)(2x+1)=a(2x+1) + b(x-8)/(x-8)(2x+1)

Multiply both sides by (x-8)(2x+1)

(2x+5) = a(2x+1) + b(x-8)

Open the brackets

2x + 5 = 2ax + a + bx - 8b

By comparison, we have

2a + b = 2

a - 8b = 5

Make a, the subject in a - 8b = 5

a = 5 + 8b

Substitute a = 5 + 8b in 2a + b = 2

10 + 16b + b = 2

Evaluate the like terms

17b = -8

Divide by 17

b = -8/17

Substitute b = -8/17 in a = 5 + 8b

a = 5 + 8 * -8/17

Evaluate

a = 5 - 64/17

So, we have

a = 21/17

Hence, the values are 21/17 and -8/17

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A company wanted to determine the health care costs of its employees. A sample of 25 employees were interviewed and their medical expenses for the previous year were determined. Later the company discovered that the highest medical expense in the sample was mistakenly recorded as 10 times the actual amount. However, after correcting the error, the corrected amount was still greater than or equal to any other medical expense in the sample. Which of the following sample statistics must have remained the same after the correction was made

Answers

After the modification, the maximum amount of medical costs in the sample must have stayed the same.

After the wrongly recorded medical expense was repaired, the adjusted amount remained more than or equal to every other medical expense in the sample. This suggests that the sample statistic linked to the highest value must have remained unchanged after the modification.

The highest value, also known as the maximum or largest value, of the medical expenses in the sample, had to have remained constant. Even though the real quantity was mistakenly recorded as being 10 times its value, the rectified amount still had the highest value in the sample.

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What are the solutions of the equation 9x4 minus 2x2 7 0?

Answers

The solution of the equations are x = √1 = ± 1

Now, According to the question:

The given equation is [tex]9x^4 - 2x^2 - 7 = 0[/tex]

Using the substitution rule we put [tex]x^{2}[/tex] = u .

The given equation now changes to

[tex]9u^2 - 2u - 7 = 0[/tex]--- (1)

Equation(1) is a simple quadratic equation which can be solved by factorization as follows:

[tex]9u^2 - 2u - 7 = 0[/tex]

(9u + 7)(u - 1) = 0

Therefore

9u + 7 = 0 → u = -7/9

u -1 = 0→ u = 1

Since u = [tex]x^{2}[/tex] implies

x = √-7/9 = ± i√7/9

x = √1 = ± 1

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The complete question is this:

What are the solutions of the equation [tex]9x^4 - 2x^2 - 7 = 0[/tex]? use u-substitution to solve.

What is the formula of polynomial?

Answers

The general formula of a polynomial is:

P(x) = a_nx^n + a_(n-1)x^(n-1) + ... + a_2x^2 + a_1x + a_0

A polynomial is a mathematical expression consisting of variables (such as x), coefficients, and exponents. The general formula of a polynomial is P(x) = a_nx^n + a_(n-1)x^(n-1) + ... + a_2x^2 + a_1x + a_0. Here, a_n, a_(n-1), ... , a_2, a_1, and a_0 are coefficients, and n is the degree of the polynomial. The highest exponent in the polynomial is the degree of the polynomial. For example, in the polynomial 3x^2 + 5x – 8, x^2 is the highest exponent, so the degree of the polynomial is 2. The coefficient of the highest exponent is known as the leading coefficient. In the example above, 3 is the leading coefficient. Polynomials can be used to represent a variety of functions, from simple linear equations to complex curves.

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Find y for 0.5y-2 2/5=1/2y+2.4

Answers

To solve this equation for y, you can follow these steps:

First, get all the terms with y on one side of the equation and all the other terms on the other side. To do this, you can add 2/5 to both sides to get rid of the 2/5 on the left side:

0.5y - 2 2/5 + 2/5 = 1/2y + 2.4 + 2/5

Simplify the left side of the equation:

0.5y - 2 + 2/5 = 1/2y + 2.4 + 2/5

0.5y - 2 + 2/5 + 2/5 = 1/2y + 2.4 + 2/5 + 2/5

0.5y - 2 + 4/5 = 1/2y + 2.4 + 4/5

Combine like terms on each side:

(0.5y + 4/5) - 2 = (1/2y + 2.4) + 4/5

Simplify:

0.5y + 4/5 - 2 = 1/2y + 2.4 + 4/5

0.5y - 2 + 4/5 = 1/2y + 2.4 + 4/5

Combine like terms on each side:

(0.5y + 4/5) = (1/2y + 2.4) + 4/5

Simplify:

0.5y + 4/5 = 1/2y + 2.4 + 4/5

Combine like terms on each side:

0.5y = 1/2y + 2.4

Subtract 1/2y from both sides:

0.5y - 1/2y = 1/2y - 1/2y + 2.4

0 = 2.4

Solve for y:

0 = 2.4

This equation has no solution, so there is no value of y that satisfies the given equation.

Answer:

Step-by-step explanation:nosoulution

Find the missing angle. 60° 75° 75° ?​

Answers

Answer:

65?

Step-by-step explanation:

im not to sure but maybe 65

A
70°
B
E
30
What angle relationship describes angles CBE and DEB?

Answers

[tex]\angle CBE[/tex] and [tex]\angle DEB[/tex] are same-side interior angles.

4 Siobhan and Ralph shared £700 in the
ratio 2:3.
Siobhan gave a quarter of her share to Karen.
Ralph gave a fifth of his share to Karen.
What fraction of the £700 did Karen receive?

Answers

Therefore ,the solution to the given problem of proportion comes out to be karen got  £70.

What is a proportion?

The rule of three is used to link the measures because a proportion is a fraction of a total amount. It is possible to construct equation or relations between variables that are either direct (when both rise or decrease) or inverse proportional (when one increases and the other declines, or vice versa) in order to determine the necessary measures in the situation.

Here,

Given :

Siobhan and Ralph shared £700 in the

ratio 2:3.

Thus,

280 / 420 = 2/3

Thus,

Siobhan and Ralph has  £280 and £420  respectively.

and Siobhan gave a share of quarter to karen :

So,

280/4 =70

Therefore ,the solution to the given problem of proportion comes out to be karen got  £70.

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Pls answer asap I’m literally stumped it’s not that hard tho

Answers

Answer:

[tex]d=11.3125[/tex]

Step-by-step explanation:

Given

[tex]\frac{-4(-8.625+2d)}{-8} +3=10[/tex]

Lets solve for [tex]d.[/tex]

Start on the left side with the fraction.

Factor -4 out of -8.

[tex]\frac{-4(-8.625+2d)}{-4(2)} +3=10[/tex]

Cancel the common factor of -4.

[tex]\frac{-8.625+2d}{2} +3=10[/tex]

Subtract 3 from both sides.

[tex]\frac{-8.625+2d}{2} =7[/tex]

Multiply both sides by 2.

[tex]\frac{-8.625+2d}{2} *2=14[/tex]

Cancel the common factor of 2.

[tex]-8.625+2d=14[/tex]

[tex]2d-8.625=14[/tex]

Add 8.625 to both sides.

[tex]2d=22.625[/tex]

Divide both sides by 2.

[tex]d=11.3125[/tex]

Work out the value of (6.31 x 10^5)+(2.6 x 10^4)
Give your answer in standard form

Answers

The answer in standard form is given by 65.7 ×10⁴

What is the Standard Form of a Number?

A standard form of a number in Maths is basically mentioned for the representation of large numbers or small numbers. We use exponents to represent such numbers in standard form.

Given here:  (6.31 x 10⁵)+(2.6 x 10⁴)

Simplifying the equation further we get

(6.31 x 10⁵)+(2.6 x 10⁴)= 63.1×10⁴+2.6×10⁴

                                    =65.7×10⁴

Hence, The answer in standard form is given by 65.7 ×10⁴

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Find the volume of the pyramid.
7 m
12 m
The volume is
16 m
cubic meters.

Answers

The value of volume of pyramids is 448 cubic meter.

How to calculate volume of pyramid?

A triangular pyramid's volume can be calculated using the formula Volume= 1/3 Base area Height. The side, height, and slant height of a triangular pyramid are the three parameters needed to calculate its surface area.

The basic formula for volume is length, breadth, and height, as opposed to length, width, and height for the area of a rectangular shape. The calculation is unaffected by how you refer to the various dimensions; for instance, you can use "depth" instead of "height."

Given,

Length=12m

Width=7m

height=16m

volume =l * w * h / 3

= 12*7*16/3

= 448 cubic meter

Therefore volume of pyramid is 448 cubic meter .

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If a temperature at 9pm i one third the temperature at midnight then what i the anwer ?

Answers

-4°F is equal to -20°C, or 253°K, which is the temperature above absolute zero. Thus, the temperature at midnight was 759°K, or almost 1400°F.

What is temperature ?

The physical concept of temperature indicates in numerical form how hot or cold something is.

A thermometer is used to determine temperature.

Thermometers are calibrated using a variety of temperature scales, which historically defined distinct reference points and thermometric substances.

The most popular scales are the Celsius scale, sometimes known as centigrade, with the unit symbol °C, the Fahrenheit scale (°F), and the Kelvin scale (K), with the latter being mostly used for scientific purposes. One of the seven base units in the International System of Units is the kelvin (SI).

The lowest point on the thermodynamic temperature scale is absolute zero, or zero kelvin, or 273.15 °C. It can be very closely approximated experimentally but never actually reached, as stated in the third rule of thermodynamics.

Hence, -4°F is equal to -20°C, or 253°K, which is the temperature above absolute zero. Thus, the temperature at midnight was 759°K, or almost 1400°F.

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YG and h are parallel. what is the value of n​

Answers

Answer:

139⁰

Step-by-step explanation:

since g and h are parallel

then n= 139⁰ (corresponding angles)

How do you find out if a triangle is acute obtuse or right?

Answers

a right angle has a 90 degree angle, an obtuse angle has an angle greater than 90 degrees, and an acute angle has an angle less than 90 degrees

What are the worst and best time complexity and the best and worst time input given to sort a set of elements using bubble sort?

Answers

With a temporal complexity of O(n2) in the average and worst circumstances, and O(n) in the best case, Bubble Sort is a simple, reliable sorting algorithm.

what is algorithm ?

A mathematical algorithm is a process that describes a series of steps that can be used to accomplish a mathematical computation. A typical illustration of a mathematical algorithm would be the step-by-step process used in long division. Integral calculus and differential calculus are the two varieties of calculus. These fields work together to let you calculate rate of change, a crucial component of many algorithms and programs. Particularly crucial are differential equations.

given

With a temporal complexity of O(n2) in the average and worst circumstances, and O(n) in the best case, Bubble Sort is a simple, reliable sorting algorithm.

The outer loop, in the worst case, executes O(n) times.

Therefore, bubble sort's worst-case time complexity is O(n x n) = O(n x n) (n2).

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Which shape has atleast one pair of perpenicular sides

Answers

The fourth shape which is a square has at least one pair of perpendicular sides.

What is a quadrilateral?

A quadrilateral is a closed object in geometry that is created by connecting four points, any three of which are not collinear. There are 4 sides, 4 angles, and 4 vertices in a quadrilateral.

In the third figure, it is a parallelogram,

In a parallelogram, the opposing or confronting sides are of equal length, and the opposing angles are of equal size.

The sum of adjacent angles is 180° but individuals are not right angles.

The fourth figure is a square and by the properties of a square, all the interior angles are right angles.

Therefore, It has two pairs of perpendicular sides.

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The average sale price of new one-family houses in the United States for a recent year was . Find the range of values in which at least of the sale prices will lie if the standard deviation is . Round your to the nearest whole number

Answers

The price range for 75% of sales will be between $149,300 and $343,300.

What is meant by Chebyshev's Theorem?

The minimum percentage of observations falling within a given range of standard deviations from the mean is calculated using Chebyshev's Theorem. Numerous probability distributions can use this theorem. Also known as Chebyshev's Inequality, Chebyshev's Theorem.

Between $149,300 and $343,300 is where 75% of transactions are priced. Only 75% of the distribution's numbers must fall within two standard deviations for Chebyshev's theorem to hold, which makes it weaker than the proportion of numbers that are within two standard deviations of the mean.

Since the standard deviation given exists 48500, 2 standard deviations will be 2 × 48500 = 97000.

The lower limit will be 246300 - 97000 and the upper limit will be 246300 + 97000.

Lower limit = 246300 - 97000 = 149300

Upper limit = 246300 + 97000 = 343300

So 75% of the sales prices will be between $149,300 and $343,300

The complete question is:

The average sale price of new one-family houses in the United States for 2003 was $246,300. Using Chebyshev's theorem, find the range of values in which at least 75% of the sale prices will lie if the standard deviation is $48,500. Hint: You should memorize that when k is 2, it is 75% and when k is 3 it is 88.89%. Please answer with whole numbers: ex. 55,232 to 65,450 with commas

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Please help- thank you!!

Answers

Answer: u = -3

Step-by-step explanation:

   To solve the equation, we will isolate the u variable by simplifying and using inverse operations.

Given:

   4(3u + 5) = 2(2u - 2)

Distribute the 4 and the 2:

   12y + 20 = 4u - 4

Subtract 20 from both sides of the equation:

   12y = 4u - 24

Subtract 4u from both sides of the equation:

   8u = -24

Divide both sides of the equation by 8:

   u = -3

What does log2 mean on a calculator?

Answers

The log base 2 calculator quickly computes the value of the logarithm function with base two, i.e., log₂(x) for arbitrary (positive) x

What do we mean by an expression?

An expression or mathematical expression is a finite combination of symbols that is well-formed according to context-dependent rules.

To help determine the order of operations and other aspects of logical syntax, mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping.

To find which expression is equivalent to log₅32:

Law of logarithms:

The law of logarithms states that: log(a) b = log(10)b/log(10)a

Given the log function, which is written as log₅32

a = 5

b = 32

Substitute as: log₅32 = log32/log5

Therefore, the given expression log₅32 is equivalent to the expression log32/log5.

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The function f open argument x close argument varies inversely with x and f open argument x close argument equals 0.5 when x

Answers

The value of function f(x), when x=2.4 is f(x)=0.00625.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

If the function f(x) varies inversely with x, then this function is of the form -

f(x)=a/x

where a is unknown number.

Since  f(x)=0.5 when x =0.3, then -

0.5 = a/0.3

a = 0.5 × 0.3

a = 0.15

So, the function now becomes -

f(x) = 0.15/x

Substituting for x = 2.4 -

f(2.4) = 0.15 / 2.4

= 15/240

= 1/16

= 0.00625

Therefore, f(x) value is obtained as 0.00625.

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The function f(x) varies inversely with x and f(x)=0.5 when x =0.3. what is f(x) when x=2.4?

A commuter wants to determine the average price of gas in the area. Which is the best method of collecting a population sample so that the commuter can answer this question? Responses: A. Check gas prices at several gas stations near the commuter’s house. B. Find the gas prices over the past several years at a single particular gas station in the area. C. Look up a number of randomly selected gas stations in the area to find out gas prices. D. Survey friends on social media to see how much people are paying for gas.

Answers

The best method of collecting a population sample so that the commuter can answer this question is C. Look up a number of randomly selected gas stations in the area to find out gas prices.

What is the population?

The entire group about which you want to draw conclusions is referred to as a population. The particular group from which you will gather data is known as a sample. The sample size is always smaller than the total population size.

A sample is characterized as a more manageable and compact version of a larger group. a smaller population that possesses the traits of a larger population. When the population size is too large to include all participants or observations in the test, a sample is used in statistical analysis.

This method would be the most representative of the entire population of gas stations in the area, and therefore the most likely to produce an accurate average price.

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What is the first step for solving 2x 3 7?

Answers

the question is of set of equations and the solution is as follows,

the equation is 2x -3 = 7,

First, add 3 to each side to get

2x - 3 + 3 = 7 +3

2x = 10

x = 10/2

x =5.

equations

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For Example, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

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Find the values of x and y in parallelogram PQRS.


PT =y. TR = 3x + 1, QT = 3y. TS = 5x + 11



x=


y=



PLEASE HELPPP!!!!

Answers

In the parallelogram PQRS, x = 2 and  y=7

Parallelogram:

A parallelogram is a quadrilateral with two pairs of parallel sides. A parallelogram has opposite sides of equal length and opposite angles of equal length. Also, the interior angles on the same side of the horizontal line are supplementary angles. The sum of all interior angles is 360 degrees. A three-dimensional shape whose faces are parallelograms is called a parallelepiped. The area of ​​a parallelogram depends on its base (one of its parallel sides) and its height (height drawn from top to bottom). The perimeter of a parallelogram depends on the length of its four sides.

Given that

PT=​y, TR=3x+​1, QT=3​y, TS=5x+11

The diagonals of a parallelogram bisect each other

PT = TR    and  QT = TS

y = 3x+1     and 3y = 5x+11

Now,

We have a system of equations

Multiply the first equation by 3

3y = 9x+3  and 3y = 5x+11

Set them equal

   9x + 3 = 5x + 11

⇒ 9x - 5x = 11 -3

⇒ 4x = 8

⇒ x =2

Now,

Putting the value of x =2 in equation :

y = 3x+1

  =3(2)+1

  =7

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Estimate the difference by rounding each number to the nearest whole number and then subtracting.

10.04 − 6.3

Answers

Answer:

Estimate of difference is 4.

Step-by-step explanation:

10.04 = 10 to nearest whole number

6.3 = 6 to nearest whole number.

10 - 6 = 4.

103M) solve on the interval 0 ≤ x < 2pi
sin ( 4x ) = √3 / 2

Answers

solving sin ( 4x ) = √3 / 2 , the value of x is 15°

What is trigonometry?

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

For angle of 30° and 60°

sin 30° = 1/2

cos 60° = √3/2

tan60° = √3

for angle 60 °

sin60° = √3/2

cos 60° = 1/2

tan60° = 1/√3

since sin(4x) = √3/2

and sin 60° = √3/2

sin60° = sin(4x)

this means 60° = 4x

divide both sides 4

x = 60/4

x = 15°

therefore the value of x is 15°

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Maria finished with 160 percent of her original amount. If she finished with 7200, what was Maria's original amount

Answers

On solving the provided question, we can say that the equation will be 1.8x=7200 => x=4000

What is equation?

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

here,

the equation will be

1.8x=7200

x=7200/1.8

x=4000

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Triangle ABC is shown below

Answers

Answer:180 degrees

Step-by-step explanation: add the angles

Please graph the question in the image.

Answers

Answer:

I used desmos to make the graph

Step-by-step explanation:

Hopefully this helps!

Other Questions
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