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.

After simplifying each expression, we get (2+5a - 10 b), (8a² - 15ca +2c),

(11- 2a+b) and (a+ b) respectively.

The word simplify means to write an expression, equation or problems

in the simplest form so as to easy to evaluate it. we simplify an expression by removing the parenthesis and collecting like terms.

exercise 1.

given, A = 7 - 4a + 7a - 3b -5 -7b +2a

We collect the like term and get

A= 7 - 5 -4a +7a +2a -3b- 7b

A = 2 + 5a -10b

next, given B = 4a × 2a -5c - c +8c -3c × 5a

             B = 8a² -6c +8c - 15ca

        B = 8a² -15ca +2c

exercise 2.

given, A = 7 + [(2- a) -( 2+a) +9] + (b-5)

at first, we remove the parenthesis and get

A= 7 + [2-a - 2 -a+ 9] +b- 5

A = 7 + 9- 2a +b- 5

after collecting the like term

A = 11- 2a + b

given, B = 15 - [(7-b) - 9- (a-17)]

  B = 15 - [7- b- 9 - a+17]

 B = 15 - [15 - b -a]

after removing the parenthesis

B = b +a

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Answer: X^2y + 3xy + 2y -3x^2 -9x -6
explanation

1. Foil (x+2)(x+1)

X^2 +2x + x + 2

2. Simplify

X^2 + 3x + 2

3. Distribute x^2 + 3x +2 (y-3)

X^2y + 3xy + 2y -3x^2 -9x -6

Using simple unitary method and with the total and per unit value provided, The answer is 8 boxes maximum can be bought.

The unitary method is a method used in mathematics to solve problems involving units of measurement. It involves expressing the units of measurement as a fraction or multiple of a single unit and then using this fraction or multiple to solve the problem. The method is particularly useful in solving problems involving conversions between different units of measurement. The unitary method is particularly useful in solving word problems where the conversion of units is required. It involves expressing the given information in terms of a single unit and then using that information to find the unknown quantity.

The unitary method is a useful tool for solving problems involving units of measurement, it simplifies the problem and improves understanding of conversions. It also helps to develop critical thinking skills and is a useful tool for problem-solving in a variety of subjects.

each box costs  = 2.5

total money =20

maximum that can be bought = 20/2.5 =8

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After 156.25 miles will the cost be the same to rent a car. This can be solved by the concept of cross-multiplication.

Fractions are multiplied by multiplying the numerator of the first fraction by the denominator of the second fraction, and the numerator of the second fraction by the denominator of the first fraction.

In order to get the second fraction's numerator, multiply the first fraction's denominator by it. Cross multiply is another name for the butterfly technique of multiplication. The cross-multiply technique is used to find one or more variables in a fraction.

Let, assume miles be m.

and, Let the total cost be x.

According to the question,

0.25m + 50 = x ........(i)

0.41m + 25 = x ........ (ii)

By solving equation (ii) by (i) we get -

0.16 m - 25 = 0

or, 0.16m = 25

or, m = 25 /0.16

or, m = 156.25

Thus, number of miles = 156.25 miles.

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Answer: 9 2/3

Step-by-step explanation:

you take 29 and divide by 13 to get 2.23076923077 and you then take that times the 4 1/3 to get 9 2/3

Answer:

Step-by-step explanation:

13(X-4 1/3)=29

13X-56.3=29

     +56.3 = +56.3

13X=85.3

X=6.56

Answer:

x² + 7x + 5

Step-by-step explanation:

(- 3x² + 2x - 4) + (4x² + 5x + 9)

since both parenthesis are being multiplies by 1 , remove parenthesis

= - 3x² + 2x - 4 + 4x² + 5x + 9 ← collect like terms

= (- 3x² + 4x²) + (2x + 5x) + (- 4 + 9)

= x² + 7x + 5

if n is a positive integer: 1²+ 2² + 3² + ... +n² = 1/6n(n+1)(2n+1)​ IS 1

P(n) :

1²+ 2² + 3² + … +n² = 1/6n(n+1)(2n+1)​

P(1) :

[tex]1^2=\frac{1(1+1)(2(1)+1)}{6}[/tex]

[tex]1=\frac{6}{6}=1[/tex]

∴ LHS = RHS

Assume P(k) is true

P(k):

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Answer:

x = - 1 or x = - [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

to find the zeros let f(x) = 0 , that is

3x² + 5x + 2 = 0 ← in standard form

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 3 × 2 = 6 and sum = + 5

the factors are 3 and 2

use these factors to split the x- term

3x² + 3x + 2x + 2 = 0 ( factor the first/second and third/fourth terms )

3x(x + 1) + 2(x + 1) = 0 ← factor out (x + 1) from each term

(x + 1)(3x + 2) = 0 ← in factored form

equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

3x + 2 = 0 ⇒ 3x = - 2 ⇒ x = - [tex]\frac{2}{3}[/tex]

Answer:

triangle GHK

Step-by-step explanation:

angles add up to 180

angle N + angle M + angle O = 180

79 + 22 + angle N = 180

180 - 79 -22 = angle N = 79

triangle GHK has 2 of the same angles (79 and 79), so that is our answer

The measure of the central tendency is 67 as the data in the set are integers.

A single number that seeks to characterize a set of data by pinpointing the center position within that set of data is referred to as a measure of central tendency.

As a result, measures of central location are occasionally used to refer to measures of central tendency. They also fit within the category of summary statistics. You are probably most familiar with the mean (sometimes known as the average), but there are additional central tendency measures, including the median and the mode.

Given, A data set 70, 67, 75, 60, 67, 65.

Arranging the data set in ascending order,

60, 65, 67, 67, 70, 75.

Now, The mean of the set is (60 + 65 + 67 + 67 + 70 + 75)/6.

= 67.33.

Mode of the data set 67.

So, The central tendency of the data set is 67 as the data in the set are all integers.

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Field goal stats include number of made/attempted, percentage made, average points scored per made, total points scored/attempted, and possibly rebounds, assists, turnovers.

FG (field goal) stats are a way of measuring an individual or team's performance in the sport of basketball. Generally, the stats will include the number of field goals made, the number of field goals attempted, the percentage of field goals made, the average number of points scored per field goal made, the total number of points scored, and the total number of points attempted. This data can be used to compare different players or teams, or to track a player or team's performance over time. Depending on the context, other stats such as rebounds, assists, and turnovers may also be included. This data can help coaches, scouts, and analysts make decisions and evaluate performance. Ultimately, it is important to use field goal stats in combination with other data and context to create an accurate picture of a player or team's performance.

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When Python constructs a function, it also generates a temporary variable with the same name, and only the function can access the value of that variable.

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Using sine and cosine rule, the length of d in the triangle is equal to 4.5cm

The sine rule is a mathematical formula used to calculate the lengths of the sides and angles of any triangle when given two angles and one side or two sides and one angle. It is also known as the law of sines.

To find the length of d, we have to find the length of E.

Using sine rule;

f / sin F = e / sin E

5 / sin 75 = e / sin 79

e = 5sin79 / sin 75

e = 5.7cm

To find the length of d, we have to find the angle D by using the sum of angle theorem.

m∠ E + m∠ F + m∠ D = 180°

79 + 75 + m∠ D = 180

m∠ D = 180 - 154

m∠ D = 26°

Using cosine rule

d² = e² + f² - 2efCosD

d² = 5.7² + 5² - 2(5.7)(5)cos26

d² = 20.615598

d = √20.615598

d = 4.5cm

The length of side d is 4.5cm

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10 equally sized slices of the spinner's 250 results. 25 times were made by Diane's dial. 12 spins are for 208.33333333333334 .

12 spins are for 208.33333333333334, 5 spins are worth 500, and 8 spins are worth 312.5. There are eight possibilities each time you spin the spinner (1-8). One of these eight options is for you to land on the number 8. In this case, the probability is 18.

If you spin three times and fall on red (or any other colour), the likelihood is 3/30. The likelihood that the spinner will land on an even number is 5/10. The ratio of the number of "1s" to all the other numbers on the spinner determines this probability. The spinner has a total of 8 numbers on it. The spinner has three ones on it.

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In this equation, n represents the original price of the television before the sale.

Equation is a mathematical statement that expresses the equality of two expressions by using numbers, symbols, and operations. It is used to describe the relationship between different variables in a problem. Equations are usually written as a statement of equality, such as 2 + 2 = 4, where the left side of the equation (2 + 2) is equal to the right side (4). Equations can be used to solve for a single unknown value, or to determine the relationship between multiple variables.

In this equation, n represents the original price of the television before the sale.

This means that the original price of the television was $375.

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Answer:

by using sine rule and cosine rule.

An expression that describes the team’s total points will be 2w + t.

It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator

In this case, the soccer team earns 2 points for a win and 1 point for a tie.

Let w represent the number of wins and t represent the number of ties.

The expression that describes the team’s total points will be:

= 2(w) + t

= 2w + t

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The value of R² is 3/2

What are solids ?

A three-dimensional object that is closed (which may, according to some terminology conventions, be self-intersecting). A solid is any constrained area of space that is bounded by surfaces, according to Kern and Bland (1948, p. 18). The sphere, cube, cone, and cylinder, as well as the polyhedra more broadly, are some of the most basic solids.

We can see that EJCI is a rhombus and

Area of rhombus is given by

Area of rhombus  = Lenth of one diagonal * length of another dialonal / 2

Thus,

EC = (a^2 + a^2 + a^2)^0.5

=> EC = a * (3)^0.5

JI = (a^2 + a^2 )^0.5

=> JI = a * (2)^0.5

So,  the area of EJCI = EC * JI / 2

=> Area = (1/2) * (a^2)  * (6)^0.5

Area of face = a^2

R = [ (1/2) * (a^2)  * (6)^0.5] / a^2

=> R = 1/2 * 6^0.5

So, the required R² is

R^2 = (1/4) * 6

=> R^2 = 3/2

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With standard deviation of 2 pounds, the range of weight 99.7% of dogs have will be approximately 24–36 pounds.

The term "standard deviation" (or "σ") refers to a measurement of the data's dispersion from the mean. A low standard deviation indicates that the data are grouped around the mean, whereas a high standard deviation shows that the data are more dispersed.

We have given,

Mean weight of Eskimo dogs is μ = 30 pound

Standard deviation of Eskimo dogs is σ = 2 pound

The range of weights would 99.7% of the dogs have,

R =  μ ± 3σ

R = 30 ± 3*2

R = 30 ± 6

R = (30 - 6) , (30 + 6 )

R = 24, 36

With standard deviation of 2 pounds, the range of weight 99.7% of dogs have will be approximately 24–36 pounds.

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Answer:

( - 7, - 1, 1, 4 )

Step-by-step explanation:

( x, y )

where,

x is Domain

y is Range

Hence,

Domain is ( - 7, - 1, 1, 4 )

Answer:

17.3 miles / gallon

Step-by-step explanation:

Rates can be represented in different forms, such as speed (meters per second) or water flow rate (liters per minute or second)

Given information from the question,

2 gallons = 34.6 miles

1 gallon = 34.6 ÷ 2 = 17.3 miles / gallon

The real world situation that can be modelled with the given  expression can be modelled as shown below.

Given is the expression as -

D/3

A real world situation that can be modelled with this expression can be written as follows -

Amanda has a total of {D} bananas. She divides the bananas into 3 of her childrens equally. Write an expression that would represent the amount of bananas recieved by each of her child.

Therefore, the real world situation that can be modelled with the given  expression can be modelled as shown above.

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It is proven that ΔABD ≅ ΔDCA by RHS congruency criteria.

Triangles must have equal corresponding sides and equal corresponding angles in order to be congruent.

According to the RHS congruence theorem, two right-angled triangles are congruent if their respective hypotenuses and sides are the same as those of another right-angled triangle.

Here we have

AOC and BOD are diameters of a circle and have a center O.

It is given that AOC and BOD are diameters of a circle.

From the triangles Δ AOC and ΔBOD

⇒ BD = CA  [ Diameters of the circle i.e Hypotenuse of triangles ]    

⇒ ∠BAD = ∠CDA [ Right angles in a semicircle is 90°]

⇒ AD = AD [ Common in both triangles i.e sides of triangles ]

Thus, Using RHS congruence criteria

⇒ ΔABD ≅ ΔDCA

Hence,

It is proven that ΔABD ≅ ΔDCA by RHS congruency criteria.

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Answer:

the percentage is 62%

Step-by-step explanation:

Answer:

Step-by-step explanation:

3(23-2b) + 3b = 48

1. Use the distributive property and distribute the 3 before the parenthesis

             3(23-2b)   (make sure you read the (-) as part of the 2b so it's -2b

              69 - 6b

2. 69 - 6b +3b = 48   (combine like terms...the bs: -6b + 3b)

    69 -3b=48

3. 69 - 3b = 48         (subtract 69 from both sides)

   -69           -69

4. -3b = -21      (divide both sides by negative three...we want the b to be +

   /-3    /-3

Answer: b = 7

So, C is your answer

AE is congruent to CE.We can prove by assuming two triangle in the given diagram and by using SAS rule.

If all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle then the two triangles are said to be congruent by SSS rule. In the above-given figure, AB= PQ, BC = QR and AC=PR, hence Δ ABC ≅ Δ PQR.

Alternate angles are angles that occur on opposite sides of the transversal line. If two parallel lines are cut by a transversal then the alternate angles are equal.The pair of angles formed on the inner side of the parallel lines but on the opposite sides of the transversal are called alternate interior angles.

Now we have

Given a triangle ABC.Where E is the midpoint of AC. We have to prove that AE is congruent to CE.

In ΔAED and ΔCED

ED=ED              (∵Common side are equal)

∠AED=∠CED       (∵Alternate angles)

∠A=∠C        (∵Alternate angles)

By ASA rule, ΔAED≅ΔCED

By Corresponding Parts of Congruent triangles

AE=EC

Hence, AE is conruent to CE.

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Answer:

They are parallel line.

The temperature at midnight as required to ve determined in the task content is; 14°C.

According to the task content; the temperature was 11.2°C at 2 : 00am.

However, since the temperature dropped 1.4 °c each hour; we have that;

In the two hours between midnight and 2:00am, the total temperature drop is; 2 × 1.4°C = 2.8°C.

On this note, the temperature at midnight can be evaluated as; 11.2°C + 2.8°C = 14°C.

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An inverse does not exist for a parabola.

A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics.

It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves.

An inverse does not exist for a parabola.

One definition of a parabola includes a line and a point (the focus) (the directrix).

The directrix is not the main focus.

The locus of points in that plane that are equally spaced apart from the directrix and the focus is known as the parabola.

A right circular conical surface and a plane parallel to another plane that is tangential to the conical surface intersect to form a parabola, which is also known as a conic section.

Therefore, an inverse does not exist for a parabola.

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In the spring of 2012, 2300 student athletes participated in a sport.

The value must be divided by the entire value, and the resulting number must then be multiplied by 100 to get the percentage.

In 2014, there were 2277 student athletes participating in spring sports.

Suppose there were x contestants in 2013.

The answer was 2277, which was 110 percent more pupils competing in 2014 than in 2013. So,

[tex]$110 \%$ of $\mathrm{x}=2277$$\frac{110}{100} \times \mathrm{x}=2277$$\mathrm{x}=\frac{2277 \times 100}{110}$$\mathrm{x}=2070$[/tex]

2070 pupils therefore competed in 2013.

Let y be the student who will be vying in 2012.

Now, the number of pupils competing in 2070 was 90% that of the year 2012's.

So,

[tex]$90 \%$ of $y=2070$$$\begin{aligned}& \frac{90}{100} \times y=2070 \\& y=\frac{2070 \times 100}{90} \\& y=2300\end{aligned}$$[/tex]

As a result, 2300 students competed in the 2012 competition.

Therefore, the answer is 2300.

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