Mathmatical proofs. please help

The length of KI is 10 cms.

The skill of measuring the lengths of objects and understanding the units of length is very crucial as it helps us to interact with our environment in a more organized manner.

Here, ΔRJS ≈ Δ IJK

then JR / JI = SR/KI

         1/2   =5 /ki

         kI = 5 X 2

        kI = 10 units.

Thus, The length of KI is 10 cms.

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Answer:

Answer is 71.95°

Step-by-step explanation:

Cosine formula is

a^2=b^2+c^2-2bc(cosA)

cos A =b^2+c^2-a^2/2bc

if a= 119,b=94,c=173

cos A=94^2+173^2-119^2/2(94*173)

=8836+29,929-14,161/2(16,262)

=38765-14,161/32,524

=24604/32,524

=0.7564

cos A=0.7564

cos^-1=40.85°.that's for angle A.

Using the same formula

B=31.1°

C=180-(40.85+31.1)

C=180-71.95

C=108.05

Since angle on a straight line is 180

therefore x is 71.95

Also the sum of angles A and B

Answer:

the red parallelogram had x=6

for the blue one, other sides values must be known which is not in the picture

Step-by-step explanation:

Reason:

The line is going uphill as it moves to the right.

Answer:

Option C is correct

Correlation coefficient of the following data is 0.37

Step-by-step explanation:

Correlation coefficient formula :

r = Σ [([tex]x - x_{m}[/tex]) × ([tex]y - y_{m}[/tex])] ÷ √ [Σ [tex](x - x_{m})^{2}[/tex] × Σ [tex](y - y_{m}) ^{2}[/tex]]

x =  Data points in Data set x

y =  Data points in Data set y

[tex]x_{m}[/tex]= Mean of Data set x

[tex]y_{m}[/tex]= Mean of Data set y

Now put all the values and sumation it as of given in the formula

Mean of Data set x = (1+4+8+6+2)÷5 = 21÷5 = 4.2

Mean of Data set y = (16+20+15+22+9)÷5 = 82÷5 = 16.4

Now put the values in the equation

r = Σ [(x - 4.2) × (y - 16.4)] ÷ √ [Σ [tex](x - 4.2)^{2}[/tex] × Σ [tex](y - 16.4) ^{2}[/tex]]

Now put every single value of x and y and after we will get the required Correlation coefficient.

And that is Correlation coefficient of the following data is 0.37

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The measure of the angle θ is 30 degrees, or the magnitude of theta is 30 degrees.

When two lines or rays converge at the same point, the measurement between them is called a "Angle."

We have a diagram shown in the picture.

The measure of an angle is 30 degrees shown.

The triangle is a right-angled triangle

30-60-90

Two parallel lines are shown which are intersected by a transversal.

The adjacent angle is 60 degrees.

The measure of angle θ:

θ = 90 - 60

θ = 30 degrees

Thus, the measure of the angle θ is 30 degrees, or the magnitude of theta is 30 degrees.

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Using proportion, the equivalent units of the following units are as follows:

Using proportion,

1.60934 km = 1 miles

6 km = ?

cross multiply

distance(m) = 6 / 1.60934 = 3.7282364199 = 3.73 miles

1 litre = 0.264172 gallons

2.5 litres = ?

volume(gallons) = 2.5 × 0.264172 = 0.66 gallons

1 pounds = 0.453592 kg

90 pounds  = ?

weight(kg) = 40.82328 = 40.82 kg

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Answer:

5

Step-by-step explanation:

As seen in the figure, we know that because ΔABC is isosceles, ∠B = ∠C, so we know that 75 = 3x, x = 15. Next, following the rule that all angles in a triangle sum to 180°, we can set up this equation and solve it:

  4y + 10 + 75 + 75 = 180

                          4y = 180 - 160

                            y = 20

                         ∴ y = 5

The function that models the horizontal displacement as a function of time in seconds is y = 5cos(2π/3 x)

The given parameters are:

Start by calculating the amplitude, A using:

A = h/2

This gives

A = 10/2

A = 5

Next, we calculate the period using:

B = π/t

This gives

B = π/1.5

Evaluate

B = 2π/3

The pendulum is at the middle.

So, it has no vertical displacement

The function is then represented as:

y = Acos(Bx)

This gives

y = 5cos(2π/3 x)

Hence, the function that models the horizontal displacement as a function of time in seconds is y = 5cos(2π/3 x)

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Answer:

1/2, -1/8, 1/32

Step-by-step explanation:

[tex] - 2( - \frac{1}{4} ) = \frac{1}{2} [/tex]

[tex] \frac{1}{2} ( - \frac{1}{4} ) = - \frac{1}{8} [/tex]

[tex] - \frac{1}{8} ( - \frac{1}{4}) = \frac{1}{32} [/tex]

Answer:

w = 3 or 6

Step-by-step explanation:

[tex]w {}^{2} - 9w + 18 = 0 \\ w {}^{2} - 6w - 3w + 18 = 0 \\w(w - 6) - 3(w - 6) = 0 \\ w - 3 = 0 \\ w - 6 = 0 \\ w = 3 \: or \: 6[/tex]

Answer:

If you're asking for the interest:

a) 960

b) 80

c)2.63 approx.

Step-by-step explanation:

interest = principal x rate x time OR [tex]I = prt[/tex]

TIME IS IN YEARS.

Thus, the first would be [tex]I = 4000 *4 *6%[/tex]% = 960

Second: 4 months = [tex]\frac{1}{3}[/tex] year

I = 4000x[tex]\frac{1}{3}[/tex]x6% = 80

Third: t = 4 days =[tex]\frac{4}{365}[/tex]year

I = 4000x6%x[tex]\frac{4}{365}[/tex] ≈ 2.63

Answer:

Step-by-step explanation:

[tex]log_{b}a=c = > b^c=a\\ln(a) = > log_{e}a=c = > e^c=a\\log(a) = > log_{10}a=c = > 10^c=a[/tex]

[tex]log(1000) = 3 = > =10^3 =1000\\ log_{5}(25)=2 = > 5^2=25\\log_{12}144=x = > 12^x=144\\ln(12) =x = > e^x=12[/tex]

Step-by-step explanation:

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Answer:

Subtraction is a mathematical operation that reflects the removal of things from a collection. The number of bags that zips on them is 78.

Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.

Given the number of bags that the company makes is 140. 39 of the bags have buttons but no zips. 21 of the bags have zips but no buttons. 23 of the bags have neither zips nor buttons.

Bags that have both zip and button

= Total number of bags - Number of bags with zips but no buttons - Number of bags with buttons but no zips - Number of bags with nor zips nor the buttons

= 140 - 21 - 39 - 23

= 57

Now, the number of bags that has zips will be the bags that only have zips and the number of bags that has zips and buttons. Therefore, the number of bags with zips is,

n = Bags that have both zip and button + Number of bags with zips but no buttons

   = 37 + 21

   = 78

Hence, the number of bags that zips on them is 78.

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Answer:

Bags with zip = (bag with button and zip) + (bag with no button but only zip)

i.e.,

Rotal bags – (bags with neither of two + bags with only buttons)

=> 140-(39+23)

=> 140-62

=> 78

So, 78 bags have zips on them.

Answer:

Step-by-step explanation:

Answer:

98

Step-by-step explanation:

There are 180 degrees in a triangle.

180 - 53 - 29 = 98

Answer:

Archimedes

Step-by-step explanation:

Archimedes is known as the Father Of Mathematics.

Answer:

Archimedes

Archimedes is known as the Father Of Mathematics

Step-by-step explanation:

Tony's coins in ascending order of value will be 5p, 10p, and 15p.

Based on the information given, the values of the coins will be 5p, 5p, 10p, 15p, and 15p.

In this case, 5p + 10p + 15p = 30p

10p + 15p + 15p = 40p

5p + 5p + 10p + 15p + 15p = 50p

Therefore, Tony's coins in ascending order of value will be 5p, 10p, and 15p.

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Answer:

5p, 5p, 10p, 10p, 20p

Step-by-step explanation:

5p, 5p, 10p, 10p, 20p,

[ ISN} and {TSW} so the answer is D

The volume of the cylinder shown below is 252πcm³

The formula for calculating the volume of a cylinder is expressed as:

V = πr²h

where:

r is the radius

h is the height

Given the following

radius = 6 units

height = 7 units

Substitute

V = πr²h

V = π(6)²(7)

V = 252πcm³

Hence the volume of the cylinder shown below is 252πcm³

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Answer:

09 l

Step-by-step explanation:

p0-9

The equivalent exponential expression for the given radical expression √(3 + 7) is √10.

To convert the given radical expression √(3 + 7) into its equivalent exponential expression. This process involves using exponentiation to represent the radical form.

The given radical expression is √(3 + 7). To find its equivalent exponential expression, we need to express the radical in terms of an exponent.

Recall that a radical expression of the form √(a) is equivalent to raising 'a' to the power of 1/2. In this case, 'a' is the quantity inside the radical, which is 3 + 7. So, we can write:

√(3 + 7) = (3 + 7)^(1/2).

Next, we simplify the expression inside the parentheses:

3 + 7 = 10.

Now, the expression becomes:

(10)^(1/2).

To further simplify, we raise 10 to the power of 1/2. Recall that raising a number to the power of 1/2 is the same as finding the square root of that number. So:

(10)^(1/2) = √10.

Therefore, the equivalent exponential expression for the given radical expression √(3 + 7) is √10.

To summarize, we transformed the radical expression √(3 + 7) into its equivalent exponential expression √10 by using the rule that √(a) is equal to a^(1/2). By raising the expression inside the radical to the power of 1/2, we simplified it and found the square root of 10 as the final result.

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Answer:

the algebraic expression is; x+15

Answer:

x^3y^2

Step-by-step explanation:

[tex]\sqrt{x^9y^4}\\ =\sqrt{x^9}\sqrt{y^4}\\ = x^3y^2[/tex]

The period of the y=1/2 sin (2x)-3 is 2.

We have given that,

y=1/2 sin (2x)-3

We have to determine the period

A period is the part of the menstrual cycle when a woman bleeds from her vagina for a few days.

Normally the period of sin(2x) is 2x, but the pi inside the sin(2x) is a horizontal compression by a factor of 1/pi.

 So 2pi·1/pi = 2

The 1/2 and -3 do not impact the period. Those just impact the amplitude (vertical aspect) of the graph.

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Answer:

It's actually D. Pi.

Step-by-step explanation:

I have no clue what the other guy was saying. The period of this graph is Pi or π.

Answer:

18

Step-by-step explanation:

30/5=6

6*3=18

An expression is defined as a set of numbers, variables, and mathematical operations. The simplified version of the given expression is (3√2-2)√x³.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given expression [tex]\sqrt{32x^3} - \sqrt{16x^3} + \sqrt{4x^3} -\sqrt{2x^3}[/tex] can be simplified as shown below.

[tex]\sqrt{32x^3} - \sqrt{16x^3} + \sqrt{4x^3} -\sqrt{2x^3}\\\\=\sqrt{x^3}(\sqrt{32}-\sqrt{16}+\sqrt{4}-\sqrt{2}})\\\\= \sqrt{x^3} (4\sqrt{2}-4+2-\sqrt2)\\\\= \sqrt{x^3} (3\sqrt{2}-2)[/tex]

Hence, The simplified version of the given expression is (3√2-2)√x³.

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Answer:

-64

Step-by-step explanation:

use PEMDAS order : Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)

-9(5 - 2) - 111÷3 =

-9(3) - 111÷3 =

-27 - 111÷3 =

-27 - 37 =

-64