Q 9-1 Pythagorean Theorem and Trig

A girl is 20 ft. east of her school and her bike is 21 ft. south of the school. How far is she from her bike? Round to the nearest hundredth.

Answer:

you would multiply 17% by  228,000

Step-by-step explanation:

you would get 177840

The solution to the system of equations is x = 4 and y = 5.

3x + 2y = 7

y = 3x - 11

Substitute 3x - 11 for y in the first equation:

3x + 2(3x - 11) = 7

Simplify:

3x + 6x - 22 = 7

Combine like terms:

9x - 22 = 7

Add 22 to both sides:

9x = 29

Divide both sides by 9:

x = 29/9

x = 4

Change x in the second equation to 4:

y = 3(4) - 11

Simplify:

y = 12 - 11

y = 1

The solution to the system of equations is x = 4 and y = 1.

The solution to the system of equations 3x + 2y = 7 and y = 3x - 11 is x = 4 and y = 1. To solve this system, we first substituted 3x - 11 for y in the first equation. We then simplified the equation and combined like terms to get 9x - 22 = 7. We then added 22 to both sides, divided both sides by 9, and got x = 29/9 which is x = 4. We then substituted 4 for x in the second equation, simplified, and got y = 1. Thus, the solution to the system of equations is x = 4 and y = 1.

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Answer:

Step-by-step explanation:

Since you already know that one of the angles is 21 degrees, this helps you A LOT. In total the line is 180 degrees so to find x you just do 180-21 which equals 159

x+ 159 degrees

The numerical coefficient of xy in the given expression -7xy is -7.

The numerical coefficient of an expression is a number that is multiplied by a variable or a product of variables. The coefficient is the number that appears in front of a variable or a product of variables. In the case of a constant term, the coefficient is the constant itself.

For example, in the expression 3[tex]x^2[/tex] + 4x - 5, the numerical coefficient of [tex]x^2[/tex] is 3, the numerical coefficient of x is 4, and the numerical coefficient of the constant term -5 is -5.

Here, in the expression -7xy, the numerical coefficient of xy is -7.

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The complete question is -

What is the coefficient of XY in the expression - 7xyz?

The provided expression can be simplified in the form 2y4/x4 option ( B) Using the integer exponent characteristics,  = [x[tex]^\frac{1}{8}[/tex] . y⁸]  is the right answer.

In mathematics, integer exponents are exponents that fall under the integer category. It's possible for the number to be either positive or undesirable. The positive integer exponents in this example dictate how many times that base number must be multiplied by itself.

It's possible for the number to be either positive or undesirable. The positive integer exponents in this example dictate how many instances the base number must be multiplied by itself.

= [x[tex]^\frac{1}{4}[/tex] . y¹⁶][tex]^\frac{1}{2}[/tex]

= [x[tex]^\frac{1}{8}[/tex] . y⁸]

The provided expression can be simplified in the form 2y4/x4 option ( B) Using the integer exponent characteristics,  = [x[tex]^\frac{1}{8}[/tex] . y⁸]  is the right answer.

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Hence proved that FG = IJ with CPCT theorem for ΔGHF ≅ ΔJHI by SAS Congruency rule.

Triangle congruence: Two triangles are deemed to be congruent if all three of their corresponding sides and angles have the same magnitude. Slides, rotations, flips, and turns can be used to make these triangles appear identical. They would be in alignment if they were moved. Congruence is represented by the letter "≅".

When two figures are similar to one another in terms of their size and shape, this is what mathematicians mean by congruence. It can be demonstrated that two triangles are congruent using four congruence rules in general. Finding all six dimensions is necessary, though.

Given that,

GH ≅ JH

FH ≅ HI

And,

∠GHF = ∠JHI

Therefore,

ΔGHF ≅ ΔJHI (SAS Congruency)

∴ FG = IJ (CPCT theorem)

Hence proved that FG = IJ with CPCT theorem for ΔGHF ≅ ΔJHI by SAS Congruency rule.

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The p-value of the test statistic is calculated as follows:

0.6386.

At the null hypothesis, it is tested if the mean is actually of 48.3 miles per gallon, that is:

[tex]H_0: \mu = 48.3[/tex]

At the alternative hypothesis, it is tested if the mean is different of that, hence:

[tex]H_1: \mu \neq 48.3[/tex]

The population standard deviation is known, hence the z-distribution is used to obtain the test statistic.

The equation is given as follows:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which:

The parameters for this problem are given as follows:

[tex]\overline{x} = 48.2, \mu = 48.3, \sigma = \sqrt{6.76} = 2.6, n = 150[/tex]

Hence the test statistic is obtained as follows:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{48.2 - 48.3}{\frac{2.6}{\sqrt{150}}}[/tex]

z = -0.47.

The p-value is found using a z-distribution calculator, with a two-tailed test, as we are testing if the mean is different of a value, with z = -0.47, hence it is of:

0.6386.

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In essence, a perfect square is produced when two equal integers are multiplied by one another.

Squaring an integer produces perfect squares. For instance, the number 81 is a perfect square since it can be calculated by squaring 9: 99=81. Due to the fact that 12 is squared to produce 144, 144 is a perfect square. Because 13 is squared to produce 169, 169 is a perfect square. Language of Mathematics. Informally: The result is known as a square number, a perfect square, or simply "a square" when an integer (a "whole" number), whether positive, negative, or zero, is multiplied by itself. So all square numbers are 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so forth.

given

In essence, a perfect square is produced when two equal integers are multiplied by one another.

Due to the fact that you are multiplying two equal integers (5 and 5) by one another, 25, it is a perfect square. The result of a number being multiplied by itself is referred to as the square of the number.

In the case when m and n are both natural numbers, m is a perfect square if m = n2. A perfect square is produced when two perfect squares are added together.

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The three combinations of pennies and quarters are:

A. 1,560 Pennies and 124 Quarters

B. 2,600 Pennies and 49 Quarters

C. 3,120 Pennies and 24 Quarters

The total value of the pennies and quarters is $62.00. This can be achieved with either 1,560 pennies and 124 quarters (1,560 x 0.01 + 124 x 0.25 = 62.00), 2,600 pennies and 49 quarters (2,600 x 0.01 + 49 x 0.25 = 62.00) or 3,120 pennies and 24 quarters (3,120 x 0.01 + 24 x 0.25 = 62.00).

To find the combinations of pennies and quarters that are worth $62.00, begin by finding the number of pennies that equal $

62.00. 62.00/0.01 = 6,200 pennies.

Next, subtract the value of the pennies from the total to find the value of the quarters.

62.00 - (6,200 x 0.01) = 24.00.

Divide the value of the quarters by 0.25 to find the number of quarters. 24.00/0.25 = 96 quarters.

To arrive at the three combinations

, 1,560 pennies and 124 quarters

(1,560 + 96 = 1,656, 1,656 x 0.01 + 124 x 0.25 = 62.00),

2,600 pennies and 49 quarters

(2,600 + 49 = 2,649, 2,649 x 0.01 + 49 x 0.25 = 62.00)

and

3,120 pennies and 24 quarters

(3,120 + 24 = 3,144, 3,144 x 0.01 + 24 x 0.25 = 62.00).

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Step-by-step explanation:

Regular decagons have two additional identifying properties: 10 exterior angles of 36° , summing to 360° 10 interior angles of 144° , summing to 1,440°

Each interior angle of a regular dodecagon is equal to 150°. Each exterior angle of a regular dodecagon is equal to 30°. 30×12= 360

The total surface area of a cone which has a base diameter of 7 cm and height of 8 cm is  126.5 cm ²

The total surface area of a cone can be found by the formula :

= (π x radius ²) + (π x radius x height )

Radius is half of diameter so :

= 7 / 2

= 3. 5 cm

The total surface area of the cone is;
= ( π x 3. 5 ²) + ( π x 3. 5 x  8)

= 38 . 5 + 88

= 126.5 cm ²

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Answer: 7

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let the costs of 1 t - shirt and 1 pair of pants be 'x' and 'y' respectively then:

Case 1 --> 8x + 5y = 220 ----------(1)

Case 2 --> 5x + y = 112 ----------(2)

Multiplying equation (2) by 5:

8x + 5y = 220

25x + 5y = 560 ------(3)

Subtracting equation (1) from equation (3) we get :

17x = 340

x = 20

Putting x in (2):

5 x 20 + y = 112

y = 12

therefore, cost of each t-shirt is 20 rupees and the cost of each pair of pants is 12 rupees

Answer:

The answer is 11

Step-by-step explanation:

The answer is 11 because you need to add the sides up that the points are on point P is 5 Point Q is 3 and point R is 3 5+3 is 8 8+3 is 11

Answer:

19.56

Step-by-step explanation:

PR = [tex]\sqrt{3^{2} + 3^{2} }[/tex] = [tex]\sqrt{18}[/tex] = 3[tex]\sqrt{2}[/tex]

RQ = [tex]\sqrt{5^{2} +5^{2} }[/tex] = [tex]\sqrt{50}[/tex] = 5[tex]\sqrt{2}[/tex]

QP = [tex]\sqrt{8^{2} +2^{2} }[/tex] = [tex]\sqrt{68}[/tex] = 2[tex]\sqrt{17}[/tex]

Perimeter = sum of the sides = 3[tex]\sqrt{2}[/tex] +  5[tex]\sqrt{2}[/tex] +  2[tex]\sqrt{17}[/tex] = 19.56

Break the triangle PQR into 3 right triangles, with each leg being a hypotenuse.  Then you can use the Pythagorean theorem to find the length of each leg.  Add them all together to get the perimeter.

The solution to the system of linear equations 3x + 2y = 14 and 5x + y = 32 is (x, y) = (6, 10).

3x + 2y = 14

5x + y = 32

Subtracting 3x from both sides of the first equation:

2y = 14 - 3x

Substituting this into the second equation:

5x + (14 - 3x) = 32

Simplifying:

8x = 18

x = 18/8

x = 2.25

This x value is substituted into the first equation.:

2y = 14 - 3(2.25)

2y = 14 - 6.75y

= 7.25

The solution is (x, y) = (2.25, 7.25)

The solution to the system of linear equations 3x + 2y = 14 and 5x + y = 32 is (x, y) = (2.25, 7.25). To solve the system, we first subtracted 3x from both sides of the first equation and then substituted this into the second equation. After simplifying, we obtained a value of x, which we then substituted into the first equation to obtain a value of y. This gave us the solution (x, y) = (2.25, 7.25).

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An expression that represents the total cost of an order of n number of tickets: 35n + 15

Let n be the number of tickets to a concert.

Let C be the cost for the tickets

Given that the tickets to a concert are $35 each.

So, by unitary method the cost of n number of tickets would be,

n × 35

And the cost for the tickets would be,

C = 35n

In addition to the cost for the tickets ordered, there is a $15 processing charge per order.

So, the cost for the tickets would be,

C = 35n + 15

This is the required expression.

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The complete question is:

Tickets to a concert are $35 each. In addition to the cost for the tickets ordered, there is a $15 processing charge per order.

Write an expression that represents the total cost of an order of n number of tickets.​

Answer:

They should sell the computer for $287.50

Step-by-step explanation:

Let's solve the 25% increase first

100% = $200

100% + 25% = 125% = 1.25

200 x 1.25 = $250

Then we find the 15% increase

100% = $250

100% + 15% = 115% = 1.15

250 x 1.15 = $287.50

So, they should sell the computer for $287.50

Answer:

y = [tex]\frac{1}{3}[/tex] x - 6

Step-by-step explanation:

9y - 3x = -54

We want in the form

y = mx + b

9y - 3x = -54  Add 3x to both sides

9y - 3x + 3x =  3x - 54

9y = 3x - 54   Divide all the way through by 9

[tex]\frac{9y}{9}[/tex] = [tex]\frac{3x}{9}[/tex] - [tex]\frac{54}{9}[/tex]

y = [tex]\frac{3}{9}[/tex] x - 6

We can simplify [tex]\frac{3}{9}[/tex] ÷ [tex]\frac{3}{3}[/tex] = [tex]\frac{1}{3}[/tex]

y = [tex]\frac{1}{3}[/tex] x - 6

If Isaac's father is four years older than three times of Isaac's age and the age of father is 49 years old. So, Isaac age will be 15 years old.

According to online myth, there is a mathematical equation that regulates the lower bound for a possible dating partner's socially acceptable age: half your age plus 7, or, in mathematical words, if x is your age, the bottom barrier is [tex]f(x) = x/2 + 7[/tex].

Consider Isaac is L

Let us suppose L is x years old.

3 times the age of L = 3x

3 times L’s age plus 4 years = 3x + 4

Furthermore, L’s father’s age is 49 years older than L’s age.

Therefore,

[tex](3x + 4) = (49) (49)\\(3x + 4) -4 = (49) – 4\\3x = 45\\3x/3 = 45/3\\X = 15[/tex]

L’s age is 15 years since we expected L’s age = x (and x=15).

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If the circle's center is in one of the foci, the inverse of the hyperbola is a Limaçon with an inner loop.

A hyperbola is a particular kind of smooth curve that lies in a plane and is classified by its geometric characteristics or by equations for which it is the solution set.

A hyperbola is made up of two mirror images of one another that resemble two infinite bows.

These two sections are known as connected components or branches.

The hyperbola's equation is expressed as (y−k)2b2−(x−h)2a2=1.

The transverse axis is defined by b, the conjugate axis by a, and the center is defined by (h,k).

The section of a line that a hyperbola's vertices form.

The inverse of the hyperbola is a Limaçon with an inner loop if the circle's center is in one of the foci.

Therefore, if the circle's center is in one of the foci, the inverse of the hyperbola is a Limaçon with an inner loop.

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Answer:

absolute deviation means distance between each data value and the mean of the data set.

Step-by-step explanation:

(MAD)

or

(Average)

Answer:

b:  5x-4y+31=0

Step-by-step explanation:

Let's look for an equation of the form y=mx+b, where m is the slope and b the y-intercept (the value of y when x=0).

We are given the slope, m, as (5/4), so we can write:  y = (5/4)x+b.

To find b, just enter the given point, (-3,4), into the above equation and solve for b:

 y=(5/4)x + b

 4=(5/4)(-3) + b   for (-3,4)

 4 = -(15/4)+b

 4 + (15/4) = b

 4 + (3 3/4) = b

b = 7 3/4

The equation becomes y = (5/4)x + 7 3/4

Also written as:  y = (5/4)x + (31/4)

To match this with one of the options, let's multiply by 4 to remove the two fractions:

   y = (5/4)x + (31/4)

   4y = (5)x + (31)

Rearrange so that the expression is = 0:

4y-5x-31 = 0

Now multiply by -1:   -4y+5x+31=0

Rearrange and this will match option b:  5x-4y+31=0

The linear function expressed by the table is y = -1x + 4.

What is a linear function?

A linear function is a type of mathematical function that represents a linear relationship between two variables, often represented by x and y. The general form of a linear function is y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis). Linear functions are also called lines.

To find the equation of the line from a table of values, you can use the slope-intercept form, y = mx + b

where m is the slope and b is the y-intercept

In order to find the slope 'm' we use the following formula:

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

Here,

m = (-2 - 2) / (2 - (-2)) = (-4)/4 = -1

The slope is -1, which means that for every one-unit increase in x there's a corresponding one-unit decrease in y.

To find the y-intercept, you can use one of the points from the table and substitute the x and y values into the equation

y = mx + b

So now we know that m = -1,

plugging the first point (x,y) = (-2,2) in the equation

2 = -2 - b

b = 4

So the equation of the line is y = -1x + 4

Hence, the linear function expressed by the table is y = -1x + 4.

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Answer:

[tex] \frac{7}{8} \times \frac{4}{5} = \frac{7 \times 1}{2 \times 5} \\ = \frac{7}{10} [/tex]

Answer: Based on the survey results, we can calculate the number of ice cream cones to sell for each flavor by multiplying the percentage of the flavor by the total number of ice cream cones to be sold.

Mint: 10% of 300 ice cream cones = 0.1 * 300 = 30 ice cream cones

Strawberry: 25% of 300 ice cream cones = 0.25 * 300 = 75 ice cream cones

Chocolate chip: 15% of 300 ice cream cones = 0.15 * 300 = 45 ice cream cones

Vanilla: 50% of 300 ice cream cones = 0.5 * 300 = 150 ice cream cones

So, based on the survey results, you should sell 30 ice cream cones of Mint flavor, 75 ice cream cones of Strawberry flavor, 45 ice cream cones of Chocolate chip flavor, and 150 ice cream cones of Vanilla flavor.

It's worth mentioning that the sum of the percentages provided, 10+25+15+50 = 100%. Which means that it is a proper survey and the total number of ice cream cones you expect to sell is equal to the survey results.

Step-by-step explanation:

Based on the survey results flavors sold at the sporting event are, 30 mint ice creams, 75 Strawberry icecreams, 45 Chocolate chip icecreams, and 150 Vanilla icecreams.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

The number of different types of ice creams can be obtained as follows,

10% - Mint.

= (10/100)×300.

= 30.

25% - Strawberry.

= (25/100)×300.

= 75.

15% - Chocolate chip.

= (15/100)×300.

= 45.

50% - Vanilla.

= (50/100)×300.

= 150.

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1287 combinations are a way to calculate the total outcomes of an event where order of the outcomes does not matter.

You win the jackpot if you match all six numbers. You receive a lesser fixed prize if you partially match some of the numbers.

Divide the number of winning lottery numbers by the total number of available lottery numbers to discover the probability of winning any lottery. Use the formula if the numbers are picked from a set and the order of the numbers is unimportant.

To find the winning combination we use the following formula

n !/ r!( n – r ) !

Where n = total number of to be drawn

r = the number which are drawn

In this question, n = 13, and r = 5

from the formula

13 !/5!( 13 – 5 ) !

= 13! / 5! 8!

= 13*12*11*10*9*8! / 5*4*3*2*1*8!

= 154,440 / 120

= 1287

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The duckweed increases by a percentage each day which is calculated by the equation

(1230.25t/16)/a - 1.

This equation can be further simplified to 1230.25t/16a - 1 and then multiplied by 100 to get a percentage.

So the percentage increase of duckweed each day is calculated by multiplying 1230.25t/16a - 1 by 100.

1230.25t/16a×100

This will give us the percentage of increase each day, rounded to the nearest whole number.

For example, if the initial number of fronds is 1000 and the number of days is 2, the percentage increase of duckweed will be (1230.25(2)/16(1000)) - 1 = 24.6%, rounded to the nearest whole number which is 25%.

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One side of the square has a length of 10 cm.

The triangle $ABC$ is a right triangle and it has one leg of length 6 cm and one leg of length 8 cm. Using the Pythagorean theorem, we can find the length of the hypotenuse:

c^2 = a^2 + b^2

c = √(a^2 + b^2)

c = √(6^2 + 8^2)

c = √(36 + 64)

c = √(100)

c = 10

So the hypotenuse of triangle $ABC$ has a length of 10 cm.

The square has one side on the hypotenuse of the triangle $ABC$ and a vertex on each of the two legs of the triangle $ABC$. Since the square is on the hypotenuse of the triangle, one side of the square has the same length as the hypotenuse of the triangle, which is 10 cm.

Therefore, one side of the square has a length of 10 cm.

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The residual of the given situation is 0.8

The residual for each observation is the difference between predicted values of y (dependent variable) and observed values of y.

Given that, The grade can be modelled by the equation y = 0.66x + 33.3, where y is the student's grade as a percentage and x is the number of days that the student attended class. We are asked to find residual if student who was in attendance for 75 days and has a grade of 82%,

Finding the actual value,

y = 0.66 × 75 + 33.3

y = 82.8

The predicted value = 82

Residual = actual y value − predicted y value

Therefore,

Residual = 82.8-82 = 0.8

Therefore, y = 0.8

Hence, the residual of the given situation is 0.8

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The rule for the given set of data is y = 3x - 1.

The relationship between dependent and independent variables, expressed as an equation, is referred to as a function rule. In order to calculate the value of the dependent variable, say y, in terms of the independent variable, say x, one must follow a specific function rule.

A function rule can be defined as the procedure that transforms an input value into an output in plain English.

Lets put two of the points in slope formula

y - y₁ = m(x - x₁)

29 - (-13) = m(10 - ( -4))

42 = m14

m = 42/14

m = 3

Now lets make the equation

y - 29 = m(x - 10)

y = 3x - 30 + 29

y = 3x - 1

Thus, the rule for the given set of data is y = 3x - 1.

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