witch equation is made true by the opposite angles theorem ​

The value of x is equal to 3.

The length of diagonal LN is equal to 18 units.

The length of diagonal MP is equal to 15 units.

In Mathematics, the diagonal of a rectangle can be defined as a line segment that connects any two (2) of its non-adjacent vertices together while dividing the rectangle into two (2) equal parts.

This ultimately implies that, the length of each diagonal of a rectangle is always equal to each other. Therefore, the diagonals of any rectangle is always equal to one other.

We would determine the value of x by equating the length of each diagonal as follows;

LN = MP

7x - 3 = 4x + 3.

7x - 4x = 3 + 3

3x = 6

x = 6/2

x = 3.

Next, we would calculate length of each diagonal as follows;

LN = 7x - 3

LN = 7(3) - 3

LN = 21 - 3

LN = 18 units.

MP = 4x + 3.

MP = 4(3) + 3.

MP = 12 + 3

MP = 15 units.

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Complete Question:

LMNP is a rectangle. Find the value of x and the length of each diagonal.

LN = 7x - 3 and MP = 4x + 3.

Suppose we want to choose 6 letters with out replacement from 13 distinct letters.

a. The number of  ways this be done if the order of the choices is not relevant is   1,235,520  ways.

b.  The number of  ways this be done if the order of the choices is relevant is 1716 ways.

a. Number of ways if choice are not relevant

[tex]^nP_r = n!/ (n-r)![/tex]

Where:

n =13

r = 6

So,

[tex]^1^3P_6[/tex] = 13! / (13 - 6)!

[tex]^1^3P_6[/tex] =6,227,020,800 /7!

[tex]^1^3P_6[/tex] =6,227,020,800/5,040

[tex]^1^3P_6[/tex] =  1,235,520 ways

b. Number of ways if choice are relevant

[tex]^nC_r =n!/ r! (n-r)![/tex]

[tex]^1^3C_6[/tex] = 13! / 6!(13-6)!

[tex]^1^3C_6[/tex] = 13! / 6! × 7!

[tex]^1^3C_6[/tex] =6,227,020,800 / 720×5040

[tex]^1^3C_6[/tex] =6,227,020,800 / 3,628,800

[tex]^1^3C_6[/tex] = 1,716 ways

Therefore the number of ways are 1,235,520 ways  and 1,716 ways.

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The measure of the angle (θ) is equivalent to sin⁻¹(6.3/14.5).

The Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. Mathematically, it can be written as -

(hypotenuse)² = (base)² + (perpendicular)²

Given is a right angle triangle with hypotenuse as 14.5 meters and

opposite side as 6.3 meters.

We can write sine of the angle (θ) as -

sin(θ) = P/H

sin(θ) = Opposite side/Hypotenuse

sin(θ) = 6.3/14.5

(θ) = sin⁻¹(6.3/14.5)

Therefore, the measure of the angle (θ) is equivalent to sin⁻¹(6.3/14.5).

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Answer: A

Step-by-step explanation: 2.5 inches = 63.5 millimeters

The correct answer is 571 quotient and 1 is remainder.We can solve easily by partial quotients.

Partial quotients division is a deviation from the standard method. The divisor is multiplied with a number and the multiple obtained is deducted from the dividend. This multiple of the divisor is as close as possible to the dividend, that is less than or equal to the dividend.

Partial quotient division provides natural differentiation because we can have students solve at a level they are comfortable with and then we can challenge them to find a more efficient way. And this means using fewer steps and solve easily.

Now we solve

first 9 multiply with 500 so we get 4500. 5140-4500=640

then 9 multiply with 70 so we get 630. 640-630=10

then 9 multiply with 1 so we get 9.   10-9=1

Hence       500+70+1=571

And our remainder is 1.

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The solution to the equation x³ + x - 4 = 0 is x = 1.38

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

x^3 + x - 4 = 0

Express the exponents as proper superscript

So, we have the following representation

x³ + x - 4 = 0

Next, we solve the equation using a graph

i.e. we plot the graph of x³ + x - 4 = 0

See attachment for the graph of x³ + x - 4 = 0

The points where the graph of x³ + x - 4 = 0 crosses the x-axis are the solution

In this case, the point is 1.38

Hence, the solution is x = 1.38

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Calculating the ratio between each pair of values in a table allows you to determine whether a proportional relationship is present. The table depicts a proportional relationship if all of those ratios are the same.

y = k x, where is the proportionality constant, is the equation that depicts a proportional relationship, or a line. Find k and create the equation by using k = y x from a table or graph. Tables, graphs, and equations can all be used to depict proportional relationships.

The equation y = kx represents a proportional relationship between two quantities y and x that have the same proportionality constant, k.

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If the amount of time in seconds, t, it takes for a bungee jumper to free fall is given by the function t equals the square root of the quantity d over 16. The distance the jumper fall is: A 400 feet.

Using this formula to find the distance by solving for d

t=√d/q

Where:

t = Time = 5 seconds

d = Distance = ?

q = Quantity = 16

So,

5 seconds=√d/16

d=16x5²

d=16 × 25

d= 400 feet

Therefore we can conclude that the correct option is A.

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Answer:

To solve this system of equations, you can use the method of elimination. To do this, you can add the two equations together:

4x + 5y - 5x - 3y = -7 - 1

-x + 2y = -8

Then, you can divide both sides of the equation by -1 to solve for y:

x - 2y = 8

y = (x - 8) / 2

Now that you have solved for y, you can substitute this expression back into either of the original equations to solve for x. For example, you can substitute y = (x - 8) / 2 into the first equation to get:

4x + 5((x - 8) / 2) = -7

4x + 5x - 40 = -7

9x = 33

x = 3.67

Now that you have solved for both x and y, you can find the solution to the system of equations:

x = 3.67

y = (3.67 - 8) / 2 = -2.17

So, the solution to the system of equations is x = 3.67 and y = -2.17.

Therefore the solution of the given question of equation comes out to be the object will hit the ground after 6 seconds.

Two variables that are equal—one on each side of a "equals" sign—are represented mathematically by an equation. Equations can be used to solve problems in daily life. To tackle challenges in real life, we frequently seek pre algebra assistance. The very foundation of mathematics is pre-algebra.

Here,

Given : -4.9t² + 2.94t + 25.48

Then,

To find the When does the object strike the ground :

We get :

=> -4.9t² + 2.94t + 25.48 = 0

Using discriminant formula

We find the value of t:

=> t = -19.6 ±[tex]\sqrt{19.6^{2} - 4 (-4.9)(25.48)}[/tex] /  2(-4.9)

=> t =-2 or 6

So we neglect -2

So solution for t = 6 seconds

Therefore the solution of the given question of equation comes out to be the object will hit the ground after 6 seconds.

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To find the sum or difference we must know what k is however you can simplify the expression by rewriting and removing the parenthesis furthermore collecting the like terms to get the solution.

Attached photo shows the steps to the solution :P

Divide 228/5 into 45, leaving a residue of 3, and divide 1,487 by 4 to get 371.75 . 2.28 divided by 5 using partial quotients = 40 + 5 = 45

The quotient is a whole number when a number is entirely divisible by another integer.For instance, 15 x 3 = 5. (whole number)The quotient is a decimal number when a number is not entirely divisible by another integer. For instance, 15 x 2 equals 7.5 (decimal number)

given

2.28 divided by 5 using partial quotients = 40 + 5 = 45

after all partial quotients are added up. 1.72 divided by 3 using sharing to divide = 1.72 / 3 = 0.58

Divide 228/5 into 45, leaving a residue of 3, and divide 1,487 by 4 to get 371.75 .

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The product of given equation is      [tex]6t^{4} + 6t^{2} bs-8bst^{2} -8b^{2} s^{2}[/tex] .

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

[tex]=(6t^{2} -8bs) (t^{2} + bs)[/tex]

[tex]=6t^{2} (t^{2} + bs) -8bs(t^{2} + bs)[/tex]

[tex]=6t^{4} +6t^{2}bs -8bst^{2} -8b^{2} s^{2}[/tex]

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Answer:

x=1252x^2

I'm not sure if I'm 100% correct

Sorry.

Answer:

84/60

Step-by-step explanation:

1 hour is 60 minutes so 84 minutes /60 gives how much it is in hours

Using the concept of proportion to find the value of x in the similar triangle, x is equal to 6.67

Similar triangle theorem states that if two triangles have corresponding angles that are equal, then the sides of the triangles are proportional to each other. This theorem can be used to solve problems involving triangles, such as finding the lengths of missing sides.

We can use the concept of ratio to find the value of x.

12 / 5 = 16 / x

Cross multiply both sides and solve for x

12 × x = 16 × 5

12x = 80

x = 80 / 12

x = 6.67

The value of x is 6.67

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The value of angle of elevation (x) is 67°

The angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.

Angle of elevation can be found by using trigonometry ratio

The height of the house is the opposite and the height of the ladder is the hypotenuse.

Therefore from trigonometry ratio;

sin x = 11/12

sin x = 0.92

x = sin^-1 (0.92)

x= 66.93°

x = 67° ( nearest degree)

Therefore the value of angle of elevation is 67°

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J''(-6, 3) , K''(-10, 2) , and L''(-5, 1) those exists the vertices after the transformations.

[tex](x_1,y_1), (x_2,y_2),[/tex] and [tex](x_3,y_3)[/tex] are the coordinates of a triangle's vertices [tex](x_3,y_3)[/tex]. The line connecting the first two is divided in the proportion l:k, and the line connecting this point of division to the opposing angular point is divided in the proportion m:k+l.

When you write coordinates as (x, y), it means to write the x-axis point first and then the y-axis point. Some kids might be instructed to remember this by saying "along the corridor, up the stairs," which means they should follow the x axis first and then the y axis.

First do the first transformation, the translation.

J (6, -1 + 4), K (10, -2 + 4), and L (5, -3 + 4).

After adding, we get J'(6, 3) , K'(10, 2) , and L'(5, 1).

We Utilize those new coordinates to do the reflection in the y axis.

J''(6(-1), 3) , K''(10(-1), 2) , and L''(5(-1), 1).

After multiplying, we get J''(-6, 3) , K''(-10, 2) , and L''(-5, 1).

Those exists the vertices after the transformations.

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J''(-6, 3) , K''(-10, 2) , and L''(-5, 1) those exists the vertices after the transformations.

[tex](x_{1}, y_{1}), (x_{2}, y_{2}) and (x_{3}, y_{3})[/tex]  are the coordinates of a triangle's vertices . The line connecting the first two is divided in the proportion l:k, and the line connecting this point of division to the opposing angular point is divided in the proportion m:k+l.

When you write coordinates as (x, y), it means to write the x-axis point first and then the y-axis point. Some kids might be instructed to remember this by saying "along the corridor, up the stairs," which means they should follow the x axis first and then the y axis.

First do the first transformation, the translation.

J (6, -1 + 4), K (10, -2 + 4), and L (5, -3 + 4).

After adding, we get J'(6, 3) , K'(10, 2) , and L'(5, 1).

We Utilize those new coordinates to do the reflection in the y axis.

J''(6(-1), 3) , K''(10(-1), 2) , and L''(5(-1), 1).

After multiplying, we get J''(-6, 3) , K''(-10, 2) , and L''(-5, 1).

Those exists the vertices after the transformations.

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The answer to the stated domain range puzzle is 0.

both domain and range. The range of values that can be plugged into a function is known as its domain. In a function like f, this set represents the x values (x).  The values that the function outputs when we enter an x value are in this set.

The collection of all possible inputs and outputs constitutes a function's domain and range, respectively. Important features of a function are the domain and range.

(f(g)(x) = (√x)² - 1

(f(g)(x) = x - 1

(f(g)(x)(1)  = 1 - 1 = 0

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Answer:

6√2

Step-by-step explanation:

-√2×2×2 -√2×3×3×3 + 2√3×3

-2√2 - 3✓6 + 2×3

-2√2 - 3√2×2 +2 + 6

6√2

The scale of measurement most reasonably applies to Confidence in Science is ordinal.

The basic  four scales used in measurements are continuous, discreet, ordinal and nominal. The continuous measurement scale is used to take the values in between a permitted range. For example weight, height, sales, rate etc.

In discreet measurements only take the whole numbers within a permitted range. For example, count of people, number of objects etc. Ordinary, logically ordered categorical values. For example, the size of clothes,

Nominal measurements include not logically ordered categorical values. For example, nationality, language etc.  The scale of measurements most reasonably applies to Confidence in Science is ordinal.

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a) The patient weight in pounds is 234 lbs.

b) The patient weight in kilograms is 106.36 Kg.

The same attribute is expressed using a unit conversion, but in a different unit of measurement. For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.

Given:

The patient’s weight is 245 lbs.

Each week patient loses = 1 Kg

So, In 5 week patient loses = 5 Kg

As, 1 kg = 2.2 lbs

In 5 week patient loses = 11 lbs

a) The weight of the patient after 5 weeks = 245 lbs. - 11 lbs.

                                                                      = 234 lbs.

b) The weight of the patient after 5 weeks =  234 lbs.

The weight of the patient after 5 weeks in Kg

= 234 lbs x 1 kg per 2.2 lbs.

= 106.36 kg

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Answer:

sorry needed points so sorry

Step-by-step explanation:

An area surrounding a measurement that indicates how accurate it is called a confidence interval.

Let X = The proportion of n randomly selected consumers who receive the discount. So, X = B(n, p), where p is the likelihood that a consumer will receive the discount.

Back-up Theory 100(1 - α) % Confidence Interval for the population proportion, p is:

p ± Zα/2[√{P(1 –p)/n}] ……(1)

where

Zα/2 is the upper (α/2)% point of N(0, 1),

pcap = sample proportion, and

n = sample size.

One can conclude with 100(1 - )% confidence that the population proportion, p, is p if a 100(1 - )% Confidence Interval for p holds a specific hypothesized value of p…………. (2)

Now to work out the solution,

The given confidence interval is: 0.12 ± 0.05 i.e., [0.07, 0.17] or [7%, 17%]……………………. (3)

for Part (a)

equation (2) and (3), [7%, 17%] holds 15%. Hence the statement is NOT valid.

for Part (b)

equation(2) and (3), [7%, 17%] holds 15%. Hence the statement is valid.

For Part (c)

Margin of error is: Zα/2[√{P(1 –P)/n}]

If the sample sizes under Part (c) and (a) are respectively, n2 and n1, the ratio of respective margin of errors would be

[Zα/2.√t{P(1 –P)/n2}]/[Zα/2√{P(1 –P)/n1}]

= √(n1/n2)

= 1/√6 [given the second sample size is 6 times the first sample size]

= 0.4082

= > the margin of error under Part (c) = the margin of error under Part (c) x 0.4082

= 0.05 x 0.4082

= 0.020.

Thus, the margin of error when the sample size if 6-fold is 0.020.

For Part (d)

The revised Confidence Interval from Part (c) is 0.12 ± 0.02 or [0.10, 0.14], which does not hold 0.15 as a result, according to (2), the program is NOT operating as anticipated.

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Therefore , the solution to the given problem of interest comes out to be $272.

Simple interest is calculated by dividing initial capital by the interest rate, the duration, and other variables. The formula employed in marketing is simple return = principle + interest plus hours. This approach is the simplest way to calculate interest. Calculating interest as a percentage of the principle sum is the most common approach. For instance, he may only pay his portion of the interest if he borrowed $100 from a friend and agreed to pay it back with 5% interest. $100 (0.05) = $5. You should pay interest when you make loans, and you also must pay interest when you lend it. Usually, interest is calculated as a portion of a loan.

Here,

Given: $250 in principal

a 2.2% interest rate

and a 4-year term

To discover the basic interest:

Using this formula

Simple interest is equal to

=>P*R*T/100,

=> 250*2.2*4/100

=> 22.

Total amount after 4 years = 250 + 22 =272

Therefore , the solution to the given problem of simple interest comes out to be $272.

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Answer:

Basically, LON would be 8z + 112 + 6z - 17

So, our equation will look like this

8z + 112 + 6z - 17 = -1z + 65

Subtract the 6z from the 8z

2z + 112 - 17 = -1z + 65

112 - 17 = 95

2z + 95 = -1z + 65

add the 1z

3z + 95 = 65

subtract the 95

-30

3z = -30

The answer is -10 :)

Step-by-step explanation:

Answer:

LON=75

Step-by-step explanation:

LON= LOM=NOM

-1z+65=8z+112-6z-17

-1z+65=2z+95

3z=-30

z=-10

LON= -1z+65

       = -1(-10)+65

       = 10+65

LON= 75

Answer:

The ratio given cannot be used to find the answer