select the most appropriate measurement for each of the following​

Answer:

[tex]IK = IJ\sqrt{2}[/tex]

Step-by-step explanation:

First, it's an isosceles right triangle, which means there is a 90 degree angle and the two other angles are equal.

To find what the two other angles are, you can set up a quick equation:

let x be angle

90 + 2x = 180, since the sum of the interior angles in a triangle is always 180.

then,

[tex]2x = 90\\x = 45[/tex]

Therefore, the triangle is a 45-45-90 triangle.

You have the measure of IJ, which is one of the legs of the triangle. The way you can find the length of the hypotenuse of a 45-45-90 triangle is by multiplying the length of one of the legs by [tex]\sqrt{2}[/tex].

This means the equation is [tex]IK = IJ\sqrt{2}[/tex]

Answer:

[tex]\sf IK=IJ\sqrt{2}[/tex]

Step-by-step explanation:

The interior angles of a triangle sum to 180°.  Therefore, if ΔIJK is an isosceles right triangle where m∠J = 90°:

To calculate the base angles:

⇒ m∠K + m∠I + m∠J = 180°

⇒ m∠K + m∠I + 90° = 180°

⇒ m∠K + m∠I = 90°

⇒ m∠K = m∠I = 45°

Therefore, IJ and JK are the legs of the right triangle and IK is the hypotenuse.

To find the length of the hypotenuse, use Pythagoras' Theorem.

Pythagoras’ Theorem:  [tex]\sf a^2+b^2=c^2[/tex]

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

Given:

Substitute the given values into the formula and solve for IK:

[tex]\sf \implies IJ^2+JK^2=IK^2[/tex]

[tex]\sf \implies 4^2+4^2=IK^2[/tex]

[tex]\sf \implies IK^2=32[/tex]

[tex]\implies \sf IK=\sqrt{32}[/tex]

[tex]\implies \sf IK=\sqrt{16 \cdot 2}[/tex]

[tex]\implies \sf IK=\sqrt{16}\sqrt{2}[/tex]

[tex]\implies \sf IK=4\sqrt{2}[/tex]

As IJ = 4 then:

[tex]\implies \sf IK=IJ\sqrt{2}[/tex]

Answer:

x=24, y=4

Step-by-step explanation:

x=6y

1/x+1/y=7/24,

1/6y+1/y=7/24

1/6y+6/6y=7/24

(1+6)/6y=7/24

7/6y=7/24, then

6y=24

y=24/6

y=4

x=6y=6*4=24

The differentiation of the function y = sin(2 sin⁻¹x) is; dy/dx = d√(1 - y²)]/(√1 - x²)

1) We want to differentiate the function;

[tex]\frac{\sqrt{x + 1} + \sqrt{x - 1}}{\sqrt{x + 1} - \sqrt{x - 1} }[/tex]

Differentiating this gives;

dy/dx = [tex]\frac{[(\frac{1}{2\sqrt{x + 1}} - \frac{1}{2\sqrt{x - 1}}) * \sqrt{x + 1} + \sqrt{x - 1}]}{(\sqrt{x + 1} - \sqrt{x - 1})^{2} }[/tex]

That can be simplified to get;

dy/dx = [tex]\frac{\sqrt{x + 1} + \sqrt{x - 1} }{(x - 1)\sqrt{x + 1} + (-x - 1) \sqrt{x - 1}}[/tex]

2) We want to differentiate the function;

y = sin(2 sin⁻¹x)

Differentiating the function gives;

dy/dx = [2cos(2 sin⁻¹x)]/√(1 - x²)

We know from trigonometric identity that;

cos²x = 1 - sin²x

Thus;

1 - sin²(2 sin⁻¹x) = cos²(2 sin⁻¹x)

But sin²(2 sin⁻¹x) = y²cos²(2 sin⁻¹x)

Thus; √(1 - y²) = cos(2 sin⁻¹x)

dy/dx = d√(1 - y²)]/(√1 - x²)

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Answer:

the answer is D

Step-by-step explanation:

the answer is D because the

Answer: d

Step-by-step explanation:

Step-by-step explanation:

5 because you have to round

Answer:

5

Step-by-step explanation:

because you have to round

Source: trust me bro

Answer:

24

Step-by-step explanation:

7 hours = 420 mins (7×60)

420-60=360 (time taken for lunch)

15mins=one ride

360÷15=24 rides

Answer:

D 18

Step-by-step explanation:

100% = 50 (all students)

1% = 100%/100 = 50/100 = 1/2 = 0.5

we get any percentage for any number by dividing the number by 1% (0.5) to see how often it fits in.

there are 9 votes for green.

9/ 0.5 = 18%

Answer:

(2,-3)

Step-by-step explanation:

Thats where the parabola is the lowest at

The expression obtained is 2g³-5g² +6 , Option C is the correct answer.

An expression is a mathematical statement that consists of constant , variable and mathematical operators.

The expression given is

[tex]\rm \dfrac{(5g^4 +5g^3 -17g^2 +6g) -(3g^4 +6g^3-7g^2 -12)}{g+2}[/tex]

On subtracting the numerator

2g⁴-g³-10g²+6g+12

Now dividing the numerator by denominator

The expression obtained is 2g³-5g² +6

Therefore Option C is the correct answer.

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The final expression will be given as  [tex][\dfrac{1}{243}][/tex] , where the numerator is 1 and the denominator is 243.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given expression:-

E = [tex][\dfrac{3^3}{3^4}]^5[/tex]

The ratio will be solved by elimination three times 3 with the denominator having four times three.

E = [tex][\dfrac{1}{3}]^5[/tex]

We will calculate the three to the power five now which is 243.

E = [tex]\dfrac{1}{243}[/tex]

Therefore the final expression will be given as  [tex][\dfrac{1}{243}][/tex] , where the numerator is 1 and the denominator is 243.

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Answer: 50m

Step-by-step explanation:

        The perimeter of the shape can be found by adding together all the lengths of the sides. See attached for my work.

[tex]\huge\textbf{Hey there!}[/tex]

[tex]\large\textbf{The missing number inside of the irregular figure is: \boxed{\bf9}}\\\large\textbf{because we had to do, 14 - 4, which gives you \underline{10}, then}\\\large\textbf{subtract 10 from another \underline{1}, \& that gives you you 9.}\\\large\textbf{The other missing number at the bottom: \boxed{\bf 7} because it measures}\\\large\textbf{the SAME length as the top number\large\textbf{Lastly, the last missing}}\\\large\textbf{number is \boxed{\bf4}.}[/tex]

[tex]\large\textbf{Now, let's solve for your perimeter of this irregular figure, }\\\large\textbf{shall we?}[/tex]

[tex]\large\textbf{14m + 9m + 7m + 7m + 4m +4m + 4m + 1m}[/tex]

[tex]\large\textbf{= 23m + 7m + 7m + 4m + 4m + 4m + 1m}[/tex]

[tex]\large\textbf{= 30m + 7m + 4m + 4m + 4m + 1m}[/tex]

[tex]\large\textbf{= 37m + 4m + 4m + 4m + 1m}[/tex]

[tex]\large\textbf{= 41m + 4m + 4m + 1m}[/tex]

[tex]\large\textbf{= 45m + 4m + 1m}[/tex]

[tex]\large\textbf{= 49m + 1m}[/tex]

[tex]\large\textbf{= 50m}[/tex]

[tex]\huge\textbf{Therefore, your answer is: \boxed{\mathsf{\mathsf{50m}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Pythagoras' theorem is a basic relationship between the three sides of a right triangle in Euclidean geometry. The correct option is D.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between the three sides of a right triangle in Euclidean geometry. The size of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides, according to this rule.

A triangle has points to monkeys, giraffes, and lions. The distance between lions and monkeys is 11 feet and between monkeys and giraffes is 16 feet. The distance between lions and giraffes is the hypotenuse of x feet. The equation that will find the distance between the lions and giraffes is,

c² = 11² + 16²

c² = 121 + 256

c² = 377

Hence, the correct option is D.

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Answer:

D on edge) 121+ 256...

The mean is 20.7

Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

Class     Frequency{f}      Midpoint of frequency{x}                fx    

1-7                    13                              4                                             72

8-10                  14                             9                                              126

11-15                  18                            13                                            234

16-20                6                           18                                              108

21-35                 13                           28                                           364

36-50                19                            43                                          817

Sum                   83                                                                          1721

So,

Mean = 1721/83 = 20.7

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[tex] - 7mn(4 {m}^{3} {n}^{2} + {m}^{2} ) \\ - 28 {m}^{4} {n}^{3} - 7 {m}^{3} n[/tex]

PLEASE GIVE BRAINLIEST

Using translation concepts, the values of k are given as follows:

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem:

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Answer:

(a) = 13

(b) = 8

(c) = 5

Step-by-step explanation:

Addition theorems on sets are

Theorem 1 :

n(AuB) = n(A) + n(B) - n(AnB)

Theorem 2 :

n(AuBuC) : = n(A) + n(B) + n(C) - n(AnB) - n(BnC) - n(AnC) + n(AnBnC)

Total number of students in the school is not given

so let there are 60 students in the school

using theorem 2

n(AuBuC) : = n(A) + n(B) + n(C) - n(AnB) - n(BnC) - n(AnC) + n(AnBnC)

let n(A) = Mathematics, n(B) =Physics and n(C) = Chemistry

so putting values,

   60             =    40 + 42 + 38 - 20 - 28 - 25 + n(AnBnC)

60 +73 -120 = n(AnBnC)

         13         = n(AnBnC)

therefore, there are total 13 students who take all three subjects

Number of students who had taken only Mathematics  =
n(A) - n(AnB) - n(AnC) + n(AnBnC)

40 - 20 - 25 + 13

53 - 45 = 8 students

Number of students who had taken only Physics  =

n(B) - n(BnA) - n(BnC) + n(AnBnC)

42 - 20 - 28 + 13

53 - 48 = 5 students

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Answer: $625

Step-by-step explanation:

Total beverage sales = $2,500

Beverage cost = 25%

So, $2,500 x 25% = $2,500 x 0.25 = $625

Answer:

i think the answer would be 53?

Step-by-step explanation:

i could be wrong

Step-by-step explanation:

the answer is d= -46/-7

or in simplest form

d= 6.57

hope this is correct...

A slope is also known as the gradient of a line. Slope of a line or straight object is the ratio of how much amount of rise occurs in correspondence to the increment in the run.

A slope is also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.

Slope of a line or straight object is the ratio of how much amount of rise occurs in correspondence to the increment in the run.

Thus, we get:

Slope = rise/ run

The slope of any line can found by finding the ratio of the vertical distance to horizontal distance between two ends. Therefore, the blanks can be filled as shown below.

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Answer:

x = 4

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

Beacuse the equation is 4+2>5 with equals 7

Answer:

x = 4 ...In the equation, substitute 4

4 + 2 > 5

6 > 5

(This sign > means greater than)

(This sign < means less than)

In this case of the equation, 6 > 5, it's True

Based on the calculations, the length of side AB is equal to 13.93 units.

Since the points of tangency are at A and B, we would determine the side length of the point lying between side A and D as follows:

AM = AD - BC

AM = 7 - 2

AM = 5 units.

Now, we can determine the length of side AB by applying Pythagorean's Theorem:

AB² = BM² + AM²

AB² = 13² + 5²

AB² = 169 + 25

AB = √194

AB = 13.93 units.

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Answer:

It should pass the horizontal and vertical line test.

hope it helps!

The slant height of the pyramid will be 5 inches.

Given Information and Formula Used

Volume of the clay = 48 cubic inches

Edge of the square base of the pyramid, a= 6 inches

Volume of the pyramid = (1/3) × Base Area × Height

Pythagoras Theorem, l² = x² + h²

Here, l is the hypotenuse, x is the base and [tex]h[/tex] is the height in a right angle triangle.

Calculating the Height, h of the Pyramid

Volume of the pyramid = Volume of the clay

Volume of the pyramid, V= 48 cubic inches

Base Area of the pyramid, B = a²

⇒ B = 6² square inches

⇒ B = 36 square inches

∵ V = (1/3)×B×H

[tex]\frac{1}{3}*36*h = 48[/tex]

∴ [tex]h = \frac{48*3}{36}[/tex]

⇒ h = 4 inches

Calculating the Slant Height, l of the Pyramid

Applying Pythagoras Theorem to determine the slant height,

l² = x² + h²

Here, we have x=a/2

[tex]l^{2} = \frac{a^{2} }{4} + b^{2}[/tex]      

[tex]l^{2} = \frac{6^{2} }{4} + 4^{2}[/tex]

[tex]l = \sqrt{9+16}[/tex]

[tex]l=\sqrt{25}[/tex]

l =5 inches

Thus, the slant height of the solid right pyramid with a square base made by Helen is 5 inches.

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Answer:

A or 0.31 per bar

Step-by-step explanation:

To solve this problem we want to find the price of the singular bar and find the cheapest one. So we will divide the amount of bars by the total price, so option A will equal 0.31, option B will equal 0.34, option C will equal 0.33, and option D will equal 0.32. The cheapest per bar price would be a or 3 pack of granola bars for 0.93 cents.

Answer:

x = 95°

y = 40°

z = 95°

Step-by-step explanation:

Answer: [tex]133^{\circ}[/tex]

Step-by-step explanation:

Opposite angles of a cyclic quadrilateral are supplementary, so:

[tex]4x+5+x+15=180\\\\5x+20=180\\\\5x=160\\\\x=32[/tex]

This means that [tex]m\angle A=4(32)+5=\boxed{133^{\circ}}[/tex]

The range of the function given the domain x > -2 is; Range; y < -8.

The range of a function is the set of all possible outcomes of the function. In this scenario, since the domain of the function is given as X > -2. It follows from the function that at all times, the range of the function is given by; y < -8 from; y < 5(-2) +2; y< -8.

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Answer:

a)(0,k)

b)(0,-k)

Step-by-step explanation:

Given:

[tex] \begin{cases} y = a {x}^{2} + k \\ y = a {x}^{2} - k \end{cases}[/tex]

Taking the derivative of y's yields

[tex] \begin{cases} y '= \dfrac{d}{dx} a {x}^{2} + k \\ \\ y '= \dfrac{d}{dx} a {x}^{2} - k \end{cases} \\ \implies\begin{cases} y '= 2a x\\ \\ y '=2ax\end{cases} [/tex]

Now set y' to 0 and solve for x:

[tex] \implies\begin{cases} 2a x = 0\\ \\ 2ax = 0\end{cases} \\ \implies\begin{cases} x= 0\\ \\ x= 0\end{cases} [/tex]

plug in the value of x into the original equation thus

[tex] \begin{cases} y = a ({0}^{2}) + k \\ y = a ({0}^{2} )- k \end{cases}\\ \implies \begin{cases} y = k \\ y= - k \end{cases} [/tex]

Hence,