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

The required value of z is "i√6" to the given expression√(6/2 - 9) = z.

A complex number is a combination of real values and imaginary values. It is denoted by z = a + ib, where a, and b are real numbers and i is an imaginary number.

The expression is given in the question, as follows:

√(6/2 - 9) = z

We have to determine the value of z to the given expression.

As per the question, we have

⇒ √(6/2 - 9) = z

⇒ √(3 - 9) = z

⇒ √(- 6) = z

⇒ √(6 × -1 ) = z

⇒ (√6 × √-1 ) = z    [∵ imaginary number i = √-1 ]

⇒ (√6 × i ) = z

⇒ z = i√6

Therefore, the required value of z is "i√6" to the given expression.

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Answer:

A letter A

Step-by-step explanation:

Segment CE only

mypoints!

The perpendicular line AB is segment CE only. The correct option is A.

The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle termed trigonometry.

Two geometric objects are perpendicular in simple geometry if they intersect at a right angle. If two lines cross at a right angle, they are said to be perpendicular to one another.

The line CE is making an angle of 90 degrees with the line AB, then the line CE will be perpendicular to the line AB.

Therefore, the perpendicular line AB is segment CE only. The correct option is A.

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Answer:

15

Step-by-step explanation:

There is a formula for this it is,

B1+B2/2

B1= Base one or TA in this case

B2= Base two or NK in this case

You replace the values with the variable:

B1=12

B2=18

12+18/2 = 30/2= 15

OB=15

The midsegment of the trapezium OB is 15

The midsegment of a trapezoid is parallel to each base, and its length is one-half the sum of the lengths of the bases.

OB = mid segment

Therefore, mathematically,

OB = 1 / 2 (AT + KN)

where

AT = 12

KN = 18

Therefore,

OB = 1 / 2(12 + 18)

OB = 30 / 2

OB = 15

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Given:

A figure of a robotics project.

To find:

The volume of the finished object assuming it is empty inside.

Solution:

The given figure contains a triangular prism and a cuboid.

The dimensions of the cuboid are 6 cm, 8 cm and 5 cm. So, the volume of the cuboid is:

[tex]V_1=length\times width\times height[/tex]

[tex]V_1=6\times 8\times 5[/tex]

[tex]V_1=240[/tex]

So, the volume of the cuboid is 240 cubic cm.

The area of a triangle is:

[tex]Area=\dfrac{1}{2}\times base\times height[/tex]

So, the area of the base of the triangular prism whose base is 8 cm and height 4 cm, is:

[tex]B=\dfrac{1}{2}\times 8\times 4[/tex]

[tex]B=16[/tex]

The volume of a triangular prism is:

[tex]V_2=Bh[/tex]

Where, B is the base area and h is the height of the prism.

The base area of the triangular prism is 16 square cm and the height is 5 cm. So, the volume of a triangular prism is:

[tex]V_2=16(5)[/tex]

[tex]V_2=80[/tex]

Now, the volume of the given figure is:

[tex]V=V_1+V_2[/tex]

[tex]V=240+80[/tex]

[tex]V=320[/tex]

Therefore, the volume of the finished object is 320 cubic cm.

Answer:

[tex]t=75[/tex]

Step-by-step explanation:

Given

[tex]\frac{1}{5} t+2-2=17-2[/tex]

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

Subtract 2 from 2.

[tex]\frac{1}{5} t=17-2[/tex]

Subtract 2 from 17.

[tex]\frac{1}{5} t=15[/tex]

Combine [tex]\frac{1}{5}[/tex] and [tex]t[/tex].

[tex]\frac{t}{5} =15[/tex]

Multiply both sides of the equation by 5.

[tex]\frac{t}{5}*5 =15*5[/tex]

[tex]t=75[/tex]

Answer:

easy just think thoroughly

Step-by-step explanation:

1 is A

2 is C

3 is B

4 is D

Answer:

Part A: Two types of transformations: translation and reflection.

Part B: g(x)=f(x)+k

-1= -1+ k

k= -1+1=0

g(x)=f(x)+k

-1= 5+k

k= -1-5=-6

g(x)=f(x)+k

14= 14+k

k= 0

k= -6,0,-6,0

Part C: For horizontal translation, g(x)=f(x+2)

In case of vertical translation, g(x)=f(x)+10

Therefore, the equation of transformation can be written as g(x)=f(x+2)+10.

Step-by-step explanation:

I thought. :') Ever since yesterday, and today. Hope this helps!

Answer:

Step-by-step explanation:

a.50%=[tex]\frac{1}{2}[/tex]

b.so 50% of 188 means 188·[tex]\frac{1}{2}[/tex]=94

answer is 94

Answer: length of EF is 18 units.

Step-by-step explanation:

similar triangles (as displayed in the photo) have the same angle measures, but can have different side lengths. however, these side lengths are proportional to each other, meaning that with similar triangles, there will ALWAYS be a number you can multiply the first triangle by to get its similar triangle.

you can find this number by dividing one side length of whichever triangle is bigger with its corresponding side on the other triangle (for example, sides DF and AC correspond, so you'd divide whichever value's bigger by the smaller one. in this case you'd divide 21 by 14.) this gives you 1.5, which tells you that triangle DEF is 1.5 times larger than triangle ABC. so to get EF, just multiply BC (which is 12) by 1.5. this gives you 18. so, EF equals 18. hope this helped :3

Answer:

CH = 22°

Step-by-step explanation:

We know that Arc AC and Arc CH both equal to 180°, therefore we can say;

AC + CH = 180°

158 + CH = 180°

CH = 180 - 158

CH = 22°

Hope this helps!

The value of x is 0

Now, According to the question:

Let's know:

How to find the value of 'x'

Generally, the algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.

The given equation is:

9x - 7 = -7

To solve the value of 'x'

9x - 7 = -7

Add 7 on both sides:

9x - 7 + 7 = -7 + 7

9x = 0

x = 0/9

x = 0

Hence, The value of x = 0

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The complete question is this:

How do you solve 9x - 7 = -7

both Square and Rectangle

because all squares are rectangles, but not all rectangles are squares. Hope this helps. :)

Consequently, it would take polynomials roughly 690,64 years for the disintegrations to disappear.

A polynomial is a mathematical statement made up of coefficients and uncertainty that exclusively uses additions, subtractions, multiplications, and positive integer powers of variables. A single indeterminate x polynomial is represented by the expression x2 4x + 7. A polynomial is an expression in mathematics that consists of variables (sometimes referred to as indeterminates) and coefficients that may be added, subtracted, multiplied, and raised to negative integer powers of non-variables. A polynomial is an algebraic expression made up of coefficients and variables. The only operations that an expression can contain are addition, subtraction, multiplication, and non-negative integer exponents. These expressions are known as polynomials.

The formula for this is Activity = decay constant x atoms.

1238 = 2.64 x 1010 times the decay constant

decay constant is equal to 4.76 x 10-8 min-1.

Currently, the disintegrations are being slowed to 809 disintegrations per minute.

Ln(809) = Ln(2.64 x 1010) - Ln(4.76 x 10-8 x t)

t=3.63x108min = 690.64y

Consequently, it would take roughly 690,64 years for the disintegrations to disappear.

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The relationship between xzw and wzv on the vertical angle is as follows:

∠ xzw + ∠ wzv = 180

Vertically opposite angles are angles that are opposite one another at a specific vertex and are created by two straight intersecting lines. Vertically opposite angles share the same vertex and they are congruent to each other.

Therefore,

∠vzy ≅ ∠wzx(vertical angles)

Hence, the relationships between angles xzw and wzv  is as follows:

∠ xzw + ∠ wzv = 180 (sum of angles on a straight line)

3x + 17 + x - 9 = 180

4x + 8 = 180

4x = 180 - 8

4x = 172

x = 172 / 4

x = 43

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Answer:

y=-28

Step-by-step explanation:

-17-y=11

-y=11+17

-y=28

y=-28

Answer:

61.74%

Step-by-step explanation

Find the vol of container one: Volume = Pi(r^2)(height) = 3.14159*81*10 = 2544.69 cu.ft.

Find the vol of container two: Pi(r^2)(height) = 1570.79 cu.ft.

Now the % of container A that is empty is

(1 - ((Volume A - Volume B)/Volume A))*100% = 61.73%

Step-by-step explanation:

use Pythagoras theorem

[tex]b = \sqrt{h ^{2} - p ^{2} } [/tex]

Answer:

x+x+x=3x

2-1=1

3x+1

this is ansver

Answer:

[tex] \displaystyle A _{XYZ - \text{triangle}} = 24 {cm}^{2} [/tex]

Step-by-step explanation:

we have two right angle triangles

we want to figure out the area of XYZ triangle

we are given the base not the altitude (height) so we need to figure the height of XYZ to figure out the area of XYZ

in that case we can use Pythagoras theorem given by

[tex] \displaystyle {a}^{2} + {b}^{2} = {c}^{2} [/tex]

given that, c=5 and b=3 thus

substitute:

[tex] \displaystyle {3}^{2} + {a}^{2} = {5}^{2} [/tex]

simplify squares:

[tex] \displaystyle 9 + {a}^{2} = 25[/tex]

cancel 9 from both sides:

[tex] \displaystyle {a}^{2} = 16[/tex]

square root both sides:

[tex] \displaystyle {a}^{} = 4[/tex]

we have figured out the height of XYZ triangle

remember that,

[tex] \displaystyle A _{ \text{triangle}} = \frac{1}{2} bh[/tex]

we have h=4 and b=9+3=12

substitute:

[tex] \displaystyle A _{ \text{triangle}} = \frac{1}{2} \times 12\times 4[/tex]

reduce fraction:

[tex] \displaystyle A _{ \text{triangle}} = 12\times 2[/tex]

simplify multiplication:

[tex] \displaystyle A _{ \text{triangle}} = 24[/tex]

hence,

the area of triangle XYZ is 24 cm²

Answer:

Answer:

I think it's either 1/2 or 1/3.

Step-by-step explanation:

number of men =12

time taken = 10 days

time taken to complete the work by 15 men = 12÷10=1.2

= 1.2 ×15 = 18

therefore, 18 days is taken to complete the work by 15 men

Answer:

2nd

Step-by-step explanation:

Answer: They are not proportional.

Step-by-step explanation: The numerator is multiplied my 0.5 but the denominator is not.

Answer:

3(x+5)x(x-6)

Just fyi download photo math and it literally answers the question for you so you dont waste any more points

Step-by-step explanation:

Answer:

5 ( or ) - 5

Step-by-step explanation:

12/3 = 4

240/4 = 60

m² + 35 = 60

m² = 60 - 35

m² = 25

m = - 5 ( or ) 5

Because,

( - 5 )² = - 5 * - 5 = 25

5² = 5 * 5 = 25

the middle value in a data set when the values are put in order

For example, the set {3,1,2} sorts to {1,2,3} where the median is 2.

Another example: The set {1,2,3,4} has 2 and 3 tied for the middle most position. The midpoint is (2+3)/2 = 5/2 = 2.5 which is the median.

On solving the provided question we can say that - the prime factors of 32 are 2 × 2 x 2 x 2 x 2 and of 64 are - 2 x 2 × 2 x 2 x 2 x 2

Any natural number other than 1 with just itself and the number 1 as its divisors is considered a prime factor. Actually, 2, 3, 5, 7, 11, and so on are some of the first prime numbers. an amount that has been multiplied to produce another amount. By dividing 15 by 3 and 5, for instance, we get 3 5 = 15. main elements: Prime factors include all factors that are prime but are not composite. A few prime factors of 30 are 2, 3, and 5. Only 2 and 3 are prime factors of 12, so listing 2 twice as 2 2 3 (or 22 3) is necessary to factorize 12. The sum of 2 + 3 is not 12.

the prime factors of

32 are 2 × 2 x 2 x 2 x 2

64 are - 2 x 2 × 2 x 2 x 2 x 2

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