In the diagram below of triangle MNOP, P is the midpoint of MO and Q is the midpoint of NO. If PQ=5x+62 and MN=6x-4, what is the measure of PQ

Answer: [tex]\triangle LAW \cong \triangle WKL[/tex] by ASA

Step-by-step explanation:

Therefore, [tex]\triangle LAW \cong \triangle WKL[/tex] by ASA.

Answer:

ans is= Rs.2925. . . . . . .

The vertex form of a quadratic equation is written as y = a(x-h)^2 + k, where (h,k) is the vertex of the parabola and a is the leading coefficient.

The vertex form can be converted from the standard form (y = ax^2 + bx + c) by completing the square and shifting the parabola horizontally and vertically.

The vertex form of a quadratic equation is y = a(x-h)^2 + k, where (h,k) is the vertex of the parabola, which is the lowest point for a parabola that opens upwards, and highest point for a parabola that opens downwards. The "a" coefficient is the leading coefficient which represents the direction of the parabola, whether it opens upwards or downwards. The vertex form is useful in identifying the vertex of the parabola and its symmetry axis, as well as its direction.

So, the vertex form of a quadratic equation is written as y = a(x-h)^2 + k, where (h,k) is the vertex of the parabola and a is the leading coefficient.

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The exact probability that would make the three marbles to be blue is  6/273,

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

Probability that exactly three marbles drawn would be blue = (number of blue marbles / total number of marbles) x [(number of blue marbles / total number of marbles) - 1] x [((number of blue marbles / total number of marbles) - 1]

Total number of marbles = 6 + 5 + 4 = 15

= (5/15) x (4/14) x (3/13) = 6/273

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The roots are hypothetical, meaning that they have two false roots. As a result, a quadratic equation has real, unequal, and irrational roots.

The quadratic equation with roots ax2 + bx + c = 0 has real and unequal roots when a, b, and c are real numbers, a 0, and the discriminant is positive.

5x 2 2x+3=0 a=5, b=2, c=3, D=b 2 4ac D=56 0

The equation's nature of roots indicates whether it contains rational, irrational, or fictitious roots. Imaginary roots and unreal roots are synonyms.

A degree two equation of the form ax2+bx+c = 0—where an is not equal to 0—is a quadratic equation. The quadratic equation's roots are the value of x in this equation. The only roots of a quadratic equation are two. These roots can have both real and made-up characteristics.

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Full Question = Write the nature of roots of the quadratic equation 5x2 - 2x + 3 = 0.

The trigonometric ratio sine compares the lengths of the right triangle's two sides. Sin, though commonly abbreviated to sin, is actually pronounced sine.

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Answer:

Step-by-step explanation:

ttt

The percentage of the students that do not like camping like travelling out of state is 33% and this can be determined by using the given data.

what is meant by camping?

To the complete questions is;

Likes Traveling Out of State Does Not Like Traveling Out of State Row totals Likes Camping 52 38 90

Does Not Like Camping 36 74 110

Column totals 88 112 200

a)32% b)34% c)38% d)42%

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The process to identify if the function is inverse is identified through the horizontal line test.

Function in math is known as a correspondence from one value x of the first set A to another value y of the second set B.

Here we need to identify the way to know that whether the given unction is inverse function or not.

By using the horizontal line test that is If any horizontal line intersects the graph of f more than once then the function f does not have an inverse.

Where as If no horizontal line intersects the graph of f more than once, then the function f does have an inverse.

Here we have also have the property of having an inverse is very important in mathematics, and it has a name.

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Answer:

Coordinates of C are (22, 20)

Step-by-step explanation:

We can see the squares are identical

The x-distance between A and B is 38 - 6 = 32

This covers 4 squares so each square side length = 32/4 = 8

Since point C is two squares away, the x-coordinate of C is 8 x 2 = 16 units away from the A x coordinate

x-coordinate of C = x-coordinate of A + 16 = 6 + 16 = 22

So x-coordinate of C is 22

To find the y-coordinate of C, because it is a square each vertical side of the square is also 8 units

If the third square were aligned with the top right of the second square, the y-coordinate of that square should be :
y-coordinate of A + 2 x 8 = 7 + 16 = 23

In this case, the y-coordinate of B should have been 23 + 2 x 8 = 23 + 16 = 39

However, because of the downward shift of the third square, the y-coordinate of B is only 36

39-36 = 3

So the third square has been shifted down by 3

Therefore y coordinate of C = 23 - 3 = 20

Coordinates of point C: (22, 20) which will result in the figure shown.

Just to verify

Since point B is 16 units to the right of C, its x-coordinate = 22 + 16 = 38
Point B

Point B y-coordinate is 16 units vertically up from y-coordinate of C.

So y-coordinate of B = 20 + 16 = 36

Hence verified

I hope that makes sense.

The attached figure shows exactly the figure in the question but with the coordinates marked. You can independently verify this

The form of function is a logarithmic function. either "y equals the log of x, base b" or "y equals the log, base b, of x."

What is logarithmic function?

An exponential function's inverse is a logarithmic function. An exponential function's basis is the same as that of a log function. Exponents include logarithms. f(x) = bx is the formula for the exponential function. f(x) = log base b of x is how the logarithmic function is expressed.

The expression "y equals the log of x, base b" or "y equals the log, base b, of x" is the definition of a logarithmic function. In both cases, b > 0, b 1, and x > 0. There are no limitations on y. logarithm, the exponent or power that a base must be increased to in order to get a specific number. If bx = n, then mathematically, x is the base-b logarithm of n.

Determine the logarithmic function of the provided graph by using the provided points in the following manner:

[tex]f(x) = log_a(x-h)[/tex]

Create two equations by substituting the provided points (3/2, 1) and (3, -1) into the formula:

[tex]log_a(\frac{3}{2}-h) = 1[/tex]

[tex]log_a({3}-h) = -1[/tex]

To isolate a, use the log law and rearrange each equation:

[tex]log_a(\frac{3}{2}-h) = 1[/tex]

⇒ [tex]a^1 = (\frac{3}{2}-h)[/tex]

⇒1/a = 3 - h

⇒ a = 1/ [tex]\frac{3}{2}[/tex] - h  ....................................(1)

[tex]log_a({3}-h) = -1[/tex]

⇒[tex]a^{-1} = ({3}-h)[/tex]

⇒ 1/a = 3-h

⇒ a = 1/3-h ..............................................(2)

Solve for h:

⇒ 3/2 - h = 1/3-h

⇒ 3-2h/2 = 1/3-h

⇒ 9 - 9h + 2h^2 = 2

⇒(2h-7)(h-1) = 0

⇒ h = 7/2, 1

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Answer:

1.77865216

Step-by-step explanation:

Answer: We know that sound travels about 343 meters per second. To convert the distance in meters to miles, we need to use the conversion factor that there are 3.28 feet in a meter and 5280 feet in a mile.

1 mile = 5280 feet = 5280/3.28 meters = 1600 meters

Therefore, the distance in miles from Alyssa to the lightning bolt can be calculated by dividing the distance in meters by the number of meters per mile:

distance in miles = distance in meters/1600

So, the distance in miles from Alyssa to the lightning bolt is 343 meters/1600 miles = 0.215 miles (approx)

Note that this calculation is based on the assumption that sound travels 343 meters per second and it's an approximation.

Step-by-step explanation:

Hence value of k does the system of equations k x +2y= 5 and 3x - 4y =10 have no solution[tex]\frac{-3}{2}[/tex]

The given system of equations:

k x + 2y = 5  

⇒ k x + 2y - 5 = 0 ….( i)  

3x - 4y = 10

⇒3x - 4y - 10 = 0 …(ii)

These equations are of the forms:

a1x + b1y + c1 = 0

a2x + b2y + c2 =0

where, a1 = k

            b1 = 2

             c1 = -5

            a2= 3

            b2 =-4

             c2 = -10

[tex]\frac{a1}{a2} \neq \frac{b1}{b2}[/tex]

[tex]\frac{k}{3} \neq \frac{2}{-4}[/tex]

[tex]k\neq \frac{-3}{2}[/tex]

Thus for all real values of k other than −3/2 ,

the given system of equations will have a unique solution.

(ii) For the given system of equations to have no solutions, we must have:

[tex]\frac{a1}{a2} = \frac{b1}{b2}\neq \frac{c1}{c2} \\\\ \frac{k}{3} = \frac{2}{-4}\neq \frac{-5}{-10} \\ \\ \frac{k}{3} = \frac{2}{-4}\\ \\ \frac{k}{3} \neq \frac{1}{2} \\ \\ \\k \neq \frac{3}{2} \\\\k =\frac{-3}{2} \\[/tex]

Hence value of k does the system of equations k x +2y= 5 and 3x - 4y =10 have no solution[tex]\frac{-3}{2}[/tex]

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The area of a triangle with a base of 4.8 cm and height of 3.6 cm is 8.64 cm².

Area of triangle = ½ × base × height

= ½ × 4.8 × 3.6

= 8.64 cm²

A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.

In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.

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An equation to model the data that India is witnessing is f(x) = 2757(0.95)^x.

A graph of this exponential equation is shown in the image attached below.

In Mathematics, an exponential function can be modeled by using this mathematical expression:

f(x) = ab^x

Where:

Since her colonies is dying at a rate of 5% per day, this ultimately implies that the relationship is geometric and the rate of change (decay rate) is given by:

Rate of change (decay rate) = 100 - 5 = 95% = 0.95.

Substituting the parameters into the exponential equation, we have the following;

f(x) = 2757(0.95)^x

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The minimum number of hikers that could have walked between 8 miles and 19 miles is given as follows:

7.

The maximum number of hikers that could have walked between 8 miles and 19 miles is given as follows:

17.

The frequency table gives the number of observations on each interval.

Then the minimum number of hikers that could have walked between 8 miles and 19 miles is obtained when:

Hence the minimum amount is of 7.

The maximum number of hikers that could have walked between 8 miles and 19 miles is obtained when:

Hence the maximum amount is of 4 + 7 + 6 = 17.

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We would expect about 16 people in a sample of 800 people to be redheads, give or take some random variation.

What is probability ?

Probability is the measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain. Probability can be expressed as a fraction, decimal, or percentage. For example, a probability of 0.5 is the same as a probability of 1/2 or 50%.

The probability of an event can be calculated by counting the number of favorable outcomes and dividing by the total number of possible outcomes.

If 2% of the population has red hair, we can expect 2 out of every 100 people in the population to be redheads. To find out how many redheads we would expect in a sample of 800 people, we can use this proportion and multiply it by the number of people in the sample.

2/100 * 800 = 16

So, we would expect about 16 people in a sample of 800 people to be redheads, give or take some random variation.

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Chance is a way to gauge how likely something is to happen. It is a number between 0 and 1, where 0 denotes the impossibility of an occurrence and 1 denotes its certainty. It is possible to represent probability as an integer, decimal, or percentage. A probability of 0.5, for instance, is equivalent to a possibility of 1/2 or 50%.

By counting the favorable outcomes and dividing by the total number of potential outcomes, one can determine the probability of an occurrence.

We can anticipate that 2 out of every 100 people in the community will have red hair if red hair makes up 2% of the population. We can calculate the proportion of redheads we would anticipate in an 800-person group by

Answer: 3:5

Step-by-step explanation:

total students: 12+18=30

ratio: 18 girls :30 students total

simplify: 18/6 : 30/6= 3:5

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Step-by-step explanation:

2*(-2)-4=

-4-4=

-8

There are total of 12 girls in the class.

A mathematical comparison of two or more values or quantities is called a ratio. It can be used to compare the relative sizes or amounts of various items since it expresses the relationship between the values in terms of a proportion or a fraction.

Let the number of girls in the class be x and the number of boys in the class be y

so total number of students in the class is x+y

ration of number of girls to the total number of students is x/(x+y)

given that total number of student is x+y which is 21

so x/21 = 4/7

=> x= (21*4)/7

=> x= 3*4

=> x=12

so the total number of girls in the class is 12.

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Complete question:

The ratio of girls to the total number of students in class is 4 to 7. How many students are girls if class has 21 students in all?

Standard form of the quadratic function is,

⇒ y = 4x² - 32x + 28

An algebraic equation with the second degree of the variable is called an Quadratic equation.

We have to given that;

The quadratic equation is,

⇒ y = 4 (x - 7) (x - 1)

Now, We can simplify the equation in standard from as;

⇒ y = 4 (x - 7) (x - 1)

⇒ y = 4 (x² - x - 7x + 7)

⇒ y = 4 (x² - 8x + 7)

⇒ y = 4x² - 32x + 28

Thus, The standard form is,

⇒ y = 4x² - 32x + 28

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By using the point-slope form, the equation of a line that passes through the point (-14, 6) with slope -7/4 is equal to y = -7x/4 + 30.5.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

From the information provided above, we have the following slope and data points on the line:

At data point (-14, 6), a linear equation of this line can be calculated in point-slope form as follows:

y - y₁ = m(x - x₁)

y - 6 = -7/4(x - (-14))

y - 6 = -7/4(x + 14)

y = -7x/4 + 24.5 + 6

y = -7x/4 + 30.5

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The formula of median is Med(x) = X [n=1/2].

The median of the data is the value of the middle observation found after sorting the data in ascending order. In many cases, it is challenging to consider the entire data set as a representation; in these cases, median is helpful. The median is a simple metric to calculate among statistical summary metrics. Since the data that is in the center of a sequence is used as the median, the median is also known as the Place Average.

Median Formula When n is Odd

Median = [(n + 1)/2] th term

Median Formula When n is Even

Median = [(n/2) th term + ((n/2) + 1) th term]/2

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Answer: In an equilateral triangle, the hypotenuse and its opposite side are equal

By the way, I am human. There is too many bot answers.

The values for sine and cosine are equal at 45 degrees because they are related to the right triangle formed by the angle.

In a right triangle, the sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse. The cosine of an angle is equal to the length of the adjacent side divided by the length of the hypotenuse.

When the angle is 45 degrees, the triangle formed is a 45-45-90 triangle, this is a special triangle in which all the angles are 45 degrees and all the sides are in the ratio of 1:1:√2.

In this triangle, the hypotenuse is √2 times the length of either leg. So, the sine of 45 degrees is opposite/hypotenuse = (1/√2) and the cosine of 45 degrees is adjacent/hypotenuse = (1/√2). Since the opposite and adjacent sides are of the same length in the 45-45-90 triangle, the sine and cosine of 45 degrees are equal.

So, sine 45 = cosine 45 = 1/√2.

Nelly's gross pay is $451.20 + $84.60 = $535.80.

Gross pay refers to the total amount of money an employee earns before any deductions or taxes are taken out. It is the total amount of money earned by an employee for the hours worked, including any overtime or bonuses.

First, we calculate her regular pay.

She worked 45 hours last week, and her regular hourly rate is $11.28 per hour. Therefore, her regular pay for the week is 40*$11.28 = $451.20. This is the pay she receives for the hours she worked up to 40 hours, which is considered the standard workweek.

Next, we calculate her overtime pay. Nelly worked 45 hours last week, and she is entitled to overtime pay for hours exceeding 40 hours. Therefore, she worked 45-40 = 5 hours of overtime.

Since she is paid time and a half for overtime, her overtime pay is calculated by multiplying her regular hourly rate by 1.5. Therefore, her overtime pay is 5*$11.28*1.5 = $84.60.

Finally, we add her regular pay and her overtime pay to get her gross pay. Her gross pay is the total amount she earns for the week, including both her regular pay and her overtime pay.

Therefore, her gross pay is $451.20 + $84.60 = $535.80.

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Answer:yes

Step-by-step explanation:

Answer:

correct

Step-by-step explanation:

The weight of the cashews plus the weight of the peanuts cannot be more than 192 ounces and the weight of the cashews must be at least one-fourth of the total weight of the mixture.

Step 1: Let c = weight of cashews

Step 2: Let p = weight of peanuts

Step 3: 0.25c + p ≤ 48

Step 4: Multiply both sides by 4

Step 5: 4(0.25c + p) ≤ 4(48)

Step 6: c + p ≤ 192

This system of inequalities models the situation of combining cashews and peanuts to make a nut mixture. The first inequality states that the weight of the cashews plus the weight of the peanuts cannot exceed 48 ounces, and the second inequality states that the weight of the cashews must be at least one-fourth of the total weight of the mixture. To model this situation, we let c equal the weight of the cashews and p equal the weight of the peanuts. We then multiplied both sides of the first inequality by four to get the second inequality, which states that the weight of the cashews plus the weight of the peanuts cannot exceed 192 ounces. This system of inequalities accurately models the situation of combining cashews and peanuts to make a nut mixture, and it ensures that the weight of the cashews is at least one-fourth of the total weight of the mixture.

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Answer:

  381 feet

Step-by-step explanation:

You are 220 ft from a tree whose top you see at a 60° angle of elevation. You want to know the height of the tree.

The tangent relation between sides of a right triangle is ...

  Tan = Opposite/Adjacent

where "opposite" and "adjacent" refer to the sides opposite and adjacent to the acute angle of interest.

Here, the 60° angle of elevation is adjacent to the 220 ft distance from the tree, and opposite the height of the tree. This means ...

  tan(60°) = height/(220 ft)

Multiplying by 220 ft, we find the height to be ...

  height = (220 ft)tan(60°) = 220√3 ft ≈ 381 ft

The tree is 381 feet tall.

__

Additional comment

The triangle that models this geometry is a 30°-60°-90° right triangle, one of the "special" right triangles that often shows up in geometry and trigonometry problems. Its side lengths have the ratio 1 : √3 : 2. Knowing this, you know the tree height is √3 times the distance from the tree:

  220√3 ft

Your calculator can tell you this is about 381 feet.

To find the height of the tree, we can use the tangent function, which relates the opposite side (the height of the tree) to the adjacent side (the distance from the tree) and the angle. The formula is:

Why is it referred to as a tangent function?

Tangent is derived from the Latin verb tangere, which means "to touch." A circle has one point where a line that is tangent to it intersects.

tangent(angle) = opposite / adjacent

In this case, the angle is 60 degrees, the opposite side is the height of the tree, and the adjacent side is the distance from the tree, which is 220 feet. So we can write:

tan(60) = height / 220

To find the height, we can divide both sides by the tangent of 60 degrees:

height = 220 * tan(60)

The exact value of the height of the tree is not possible to be obtained with the given information, the height of the tree is a number in the infinite set of real numbers.

We can use a calculator or a table of tangents to find an approximate value of the height.

It could be around 379.3 ft.

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Answer:

x = 3

Step-by-step explanation:

18/2 = 27/x

9/1 = 27/x

9x = 27 × 1

x = 3

Answer:

x = 3 because 18 divided by 2 equals nine, also meaning that 2 x 9 = 18. Now since we figured out that 9 is how many times more/less the number is between the polygons. (I'm so sorry if I can't explain clearly) Now we just get 27 and divide it by 9 which leaves us with our answer 3.