course 3 chapter 5 triangles and the pythagorean theorem answer key

Since line C has a slope of -8/3 and line D is parallel to line C, the slope of line C is equal to -8/3.

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

y - y₁ = m(x - x₁)

Where:

In Geometry, two (2) lines are parallel under the following conditions:

m₁ = m₂

This ultimately implies that, the slope of the two lines are equal and the same:

Slope of line C = Slope of line D

-8/3 = -8/3.

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When added to 2 PM, this gives us a time of 2:17 PM. Thus, Ron returned home at 2:17 PM.

Ron left his home at 7:00 AM. To determine what time he returned home, we need to add 7 hours and 35 minutes to the time he left. This can be done by adding 7 hours to the hours portion of the time and 35 minutes to the minutes portion of the time. In this case, 7 hours added to 7 AM is 2 PM, and 35 minutes added to 0 minutes is 35 minutes, so Ron returned home at 2:35 PM. To be more precise, we can convert the minutes portion of the time to a fraction of an hour, which would give us 2 hours and 35/60 of an hour or 2 hours and 0.5833 hours. When added to 2 PM, this gives us a time of 2:17 PM. Thus, Ron returned home at 2:17 PM.

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The square root function contains a variable under the square root sign. The cube root function contains a variable under the cube root sign.

What is a function?

A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between varying quantities and other variables.

A variable under the square root sign is present in a square root function, and a variable under the cube root sign is present in a cube root function.

Zero has a square root of zero, and one has a square root of one. Keep in mind that the graph only contains points where x and y are positive. For instance, using the imaginary number i is necessary when taking the square root of a negative number.

The square root function is f(x) = √x

For positive values, the graph resembles the square root graph, but cube roots can also be negative, making this equation infinite for all real numbers. Recall that a negative number will result from being multiplied an odd number of times.

The cube root function is f(x) = ³√x

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The slant height,

x = 5 meters.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.

Given:

A right circular cone is 4 meters tall and have a radius 6/2 = 3 meters.

Applying the Pythagoras' theorem,

The slant height = √{(3)² + (4)²}.

The slant height = √25

The slant height = 5 meters.

Therefore, the slant height = 5 meters.

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Subtracting mixed numbers with the same denominators

Follow the steps to subtract mixed numbers with the same denominators:

Step 1– Subtract the wholes.                

Step 2– Converting the fractions into improper fractions.

Step 3– Subtract the fraction.

Step 4– Swap the improper fraction into a mixed number.

Step 5– Write down the mixed number with wholes and the fraction.

Example- [tex]5\frac{7}{3} - 3\frac{2}{3}[/tex]

Subtract 3 from 5.

                    5 – 3 =2

Subtract the fractions:

             [tex]\frac{7}{3} - \frac{2}{3}[/tex]

Write the fraction with the whole.

[tex]5\frac{7}{3} - 3\frac{2}{3} = 2\frac{5}{3}[/tex]

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To convert 162 pounds to kilograms, you can use the following conversion factor 1 pound = 0.453592 kilograms

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"15 + r" is the expression that represents the total number of rows knitted by Christine. Thus, option B is correct.

To find the total number of rows Christine has knit, we need to add the number of rows she knit over the weekend (represented by the variable "r") to the number of rows she had already knit (15).

This can be done by using the expression:

This expression states that the total number of rows is equal to the initial number of rows (15) plus the additional rows knit over the weekend (represented by the variable "r"). The value of "r" could be any number, so the expression "15 + r" could represent any total number of rows.

For example, if Christine knit 5 more rows over the weekend, the expression "15 + 5" would equal 20, so Christine has knit a total of 20 rows.

This question should be provided as:

Christine had already knit 15 rows of a scarf. She knitted r more row over the weekend. Choose the expression that shows the number of rows Christine has knitted in all.

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The adult male foot length of 24.2 cm is significantly low as it falls outside of the range of 26.10 cm to 28.72 cm.

The range is just the difference between the greatest and smallest data points in a set.

The square root of the variance is the standard deviation.

The standard deviation measures how far apart the data is from the mean.

The range is a less useful measure of variance than the standard deviation.

The range of data is a measure of variance that indicates the difference between the dataset's maximum and least observation.

It is based only on two observations, the maximum and minimum.

The range rule of thumb states that approximately 68% of the data falls within one standard deviation of the mean, and approximately 95% of the data falls within two standard deviations of the mean.

So, the lower limit separating significantly low values will be:

27.41 - 1.31 = 26.10 cm

And the upper limit separating significantly high values will be:

27.41 + 1.31 = 28.72 cm.

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Avery write an explicit equation is  t(n)=19+(n-1)*(-2)=21-2n and a  Collin write a recursive equation is t(n+1)=t(n)/6-10/3.

What is explicit equation & recursive equation?

A closed-form expression or a mathematical expression expressed in terms of a limited set of well-known functions are examples of explicit formulas. the mathematical formula expressed analytically, using a limited or infinite number of well-known functions.

A recursive function is one that generates a series of phrases by repeating or using its own prior term as input. The arithmetic-geometric sequence, which has words with a common difference between them, is typically the basis on which we learn about this function.

To write an explicit equation, we can use the given recursive equation and find the value of the first term, t(1).

Substituting n=1 into t(n+1)=t(n)−2

gives t(2)=t(1)−2.

We know that t(2)=19, so t(1)=19+2=21.

Thus, the explicit equation for the sequence is t(n)=19+(n-1)*(-2)=21-2n. This is an arithmetic sequence.

To write a recursive equation, we can use the explicit equation that Avery wrote, t(n)=6n+8.

Rearranging this equation gives n=(t(n)-8)/6.

Substituting this expression into the recursive equation t(n+1)=t(n)−2 gives t(n+1)=(t(n)-8)/6−2.

Expanding t(n) on the right-hand side and simplifying gives t(n+1)=t(n)/6-10/3.

A explicit equation is  t(n)=19+(n-1)*(-2)=21-2n and a recursive equation is t(n+1)=t(n)/6-10/3.

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The candy I want to buy will cost $2.53

They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

According to the data problem,

Total cost = $5.27/ pound * 0.48 pound

Total cost = $2.5296

Rounding to the nearest whole number value of a cent.

Hundredth value = 2,

Since the digit after the hundredth value is ≥5 ; we round to 1 and add to the hundredth value to give 3

Total cost = $2.53

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Correctly written question:

A candy store sells chocolates for $5. 27 per pound. The piece you want to buy weigh 0. 48 pound. How much will it cost, to the nearest cent?

Answer:

22 quarters

Step-by-step explanation:

$3.00 + $2.50 = $5.50

1 quarter = $0.25

$5.50 divided by $0.25 = 22

The line of the  best fit for the data points plotted in the scatter plot is y = -0.88x + 8

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

The graph

Using the line of the best fit, we have"

(x, y) = (8, 1) and (0, 8)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx + 8

Using the points, we have

1 = 8m + 8

This gives

m = -0.88

So, we have

y = -0.88x + 8

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The ratio of smiley face to triangle is 5/2. The ratio of smiley face to square is 5/4. The ratio of triangle to smiley face is 2/5. The ratio of triangle to square is 2/4. The ratio of square to smiley face is 4/5.

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorise ratios. Part to whole ratio is one, and part to part ratio is the other. The part-to-part ratio shows the relationship between two separate entities or groupings. For instance, a class has a 12:15 boy-to-girl ratio, whereas the part-to-whole ratio refers to the relationship between a particular group and the entire.

The ratio of smiley face to triangle is 5/2.

The ratio of smiley face to square is 5/4.

The ratio of triangle to smiley face is 2/5.

The ratio of triangle to square is 2/4.

The ratio of square to smiley face is 4/5.

The ratio of square to triangle is 4/2.

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Answer:

A linear yard is equal to 3 linear feet, so Marnie's hallway runners cost $28.56 per linear yard ($9.52 x 3 = $28.56).

The probability of the coin landing on tail and a 4 on die is 1/12 or 0.08 or 8%

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%

Probability = sample space / total outcome

when a coin is tossed, the probability of the tail landing = 1/2

when a die is rolled, the probability of getting a 4 = 1/6

therefore the probability of the coin to land on its tail and a 4 is on the die = 1/2×1/6 = 1/12

1/12 = 0.083

to percentage we multiply the decimal by 100 = 8.3 %

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If you multiply 256 by 10 powered by k, then the number of zeros in the product is k

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The multiplication of the given expression gives the value 144.

Radicals are defined as the nth root of a number using the symbol [tex]^n\sqrt{x}[/tex].

This is the opposite form of the exponential functions.

Given expression is (4 √9) × (4 √9).

We can write this as (4 √9) × (4 √9) = (4 × 4) × (√9 × √9).

Multiplying the radicals together and whole numbers together,

(4 √9) × (4 √9) = 16 × (3 × 3) = 144

Hence the multiplication of the radicals gives the value 144.

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The density of the cube is 11341 kg/m3 and changed density if one of the sides were doubled is 5670.5 kg/m3.

Cube is a three dimensional object bounded by 6 square faces or sides and it is the only regular hexahedron . Number of edges in the cube are 12, Number of vertices in the cube are 8, Number of faces in the cube are 6.

Let side of the cube be x.

The density is the ratio between mass and the volume.

Density = x^3 = 11341

If one of the side of the cube is doubled, then density will become half of the original density.

original density = x^3 = 11341

If side is doubled, 2x*x*x=11341

Density = x^3 = 11341/2 = 5670.5 kg/m3.

Therefore, the changed density if one of the sides were doubled is 5670.5 kg/m3.

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Answer: B, It would quadruple

Step-by-step explanation: I just did it

To travel downstream, a boat needs 2 hours while to travel back upstream, it needs 4 hours. The river flows at speed of 3.58  3.58 km/hour

The relation between distance and speed is given by:

distance = speed x travelled time

In the problem, let:

vb = boat speed

v = river speed

Then, when the boat travels downstream:

28.62 = (vb + v) x 2

2vb + 2v = 28.62   ... (Equation 1)

When the boat travels upstream:

28.62 = (vb - v) x 4

Divide both sides by 2:

14.31 = (vb - v) x 2

2vb - 2v = 14.31  ... (Equation 2)

Substract equation 1 by equation 2

2vb + 2v = 28.62

2vb  - 2v = 14.31 _

       4v  = 14.31

          v = 3.58

Hence, the speed of water = 3.58 km/hour

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Dana ordered a box of fresh-baked gingerbread cookies and sugar cookies, the percentage of the cookies were gingerbread are 70%.

She got 70 gingerbread cookies and 30 sugar cookies

So total number of cookies she ordered are 100

Percentage of gingerbread cookies are

= 70 / 100

= 70 %

The Latin word "per centum," which meaning "by the hundred," was the source of the English word "percentage." Fractions with a denominator of 100 are called percentages. In other words, it is a relationship where the value of the entire is always assumed to be 100.

A percentage is a ratio or fraction where the full value is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his arithmetic test. In ratio form, it is expressed as 30:100 and in fraction form as 30/100.

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The party cost for 19 guests is 95 dollars.

We assume there is a proportional relation between the number of guests and the cost.

y is the cost and x the number of guests, then we can write:

y = k*x

k is the unit rate.

We know that it costs $20 to invite 4 people, then:

20 = k*4

20/4 = k

5 = k

Then the relation is:

y = 5*x

So, if x = 19 we will have:

y = 5*19 = 95

The cost for 19 guests is $95.

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1) Technically speaking, the equation has no real solution. This is because the square of a real number cannot be negative.

2) To correctly solve for the time taken for the load of dirt to fall, Russel would need to use a different method that takes into account the velocity and acceleration of the object.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign.

A complicated number, symbolized by ± is the square root of a negative number. This indicates that there is no true number for t that will fulfill the equation, thus the solution to the issue is impossible to find.

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The required difference of the polynomial functions is -9s^2 + 4s - 2

Given the following difference of polynomial expressed as:

(–6s2 + 12s – 8) – (3s2 + 8s – 6)

We are to find the difference

(–6s2 + 12s – 8) – (3s2 + 8s – 6)

Expand

–6s^2 + 12s – 8 - 3s^2 - 8s + 6

Collect the like terms

–6s^2- 3s^2 + 12s - 8s - 8 + 6

-9s^2 + 4s - 2

Hence the required difference of the polynomial functions is -9s^2 + 4s - 2

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complete question

Find each difference.

(–6s2 + 12s – 8) – (3s2 + 8s – 6) =

–9s2 + 4s – 14

–9s2 + 4s – 2

–9s2 + 20s – 14

–9s2 + 20s – 2

Settings to convert Text to table is Click Insert > Table > Convert Text to Table, then set the desired parameters.

What is settings in computer?

Microsoft Windows has a feature called Windows Settings, formerly known as PC Settings. Users may manage their connected devices, customise their operating system, and change their user settings. Microsoft initially intended for Settings to replace the Windows Control Panel, which has not happened 10 years after it was first released with Windows Server 2012 and Windows 8.

Start by selecting the Show/Hide paragraph mark on the Home tab so you can see how text is separated in your document before converting text to a table or a table to text.

Text to a table conversion in Microsoft Word -

When dividing the text into table columns, use separator characters like commas or tabs.

To indicate where to start a new table row, use paragraph markers.

Click Insert > Table > Convert Text to Table after selecting the text you wish to convert.

Make your selections in the Convert Text to Table box.

Make sure the figures under "Table size" correspond to the amount of columns and rows you desire.

Select the desired appearance for your table under AutoFit behaviour.

Word chooses a width for the table column automatically.

Select the separator character you used in the text under Separate text at.

Select OK.

Therefore, the procedure to convert text to table is explained.

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The least number of terms required to compute pi as 3.14 is approx 400.

The series is π = 4 - 4/3 + 4/5 - 4/7 + .................

We have to determine the least number of terms required to compute pi as 3.14.

We can write the series as

π = 4(1 - 1/3 + 1/5 - 1/7 + .................)

The general equation of this series is

π = 4[tex]\Sigma_{k=0}^{\infty}(-1)^k(2k+1)^{-1}[/tex]

Now let S = π. So

S = 4[tex]\Sigma_{k=0}^{\infty}(-1)^k(2k+1)^{-1}[/tex]

From the Alternating series theorem

|S - S(n)| ≤ 4/(2n+1)

Hence, the accuracy should be

4/(2n+1) ≤ 1/2 × 10^{-2}

Multiply by 2 on both side, we get

8/(2n+1) ≤ 10^{-2}

We can write 10^{-2} as 1/100. Now the expression is

8/(2n+1) ≤ 1/100

Multiply by 100 on both side, we get

800/(2n+1) ≤ 1

Multiply by 2n+1 on both side, we get

800 ≤ 2n+1

Subtract 1 on both side, we get

2n ≥ 799

Divide by 2 on both side, we get

n ≥ 399.5

Hence, approx 400 terms need to compute pi as 3.14.

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The complete question is:

What is the least number of terms required to compute pi as 3.14 using the series:

π = 4 - 4/3 + 4/5 - 4/7 + .................

Answer:

21 miles

Step-by-step explanation:

we should also use pythagoras theorem to find out how far they are from each other.

[tex] {c}^{2} = {a}^{2} + {b}^{2} \: \: \: \: \: \: \\ = {20}^{2} + {5}^{2} \\ {c}^{2} = 425 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ c = \sqrt{425} \: \: \: \: \: \: \: \: \\ = 20.61 \: \: \: \: \: [/tex]

The Spearman-Brown formula is used to adjust the reliability estimate of a test when concerns arise about the shortness of the test, i.e., the limited number of test items. Thus, B is correct.

The formula takes into account the number of items in the test and calculates the expected increase in reliability if the test were to be made longer. The formula is based on the assumption that adding more items to a test would increase its reliability, and thus provides a way to estimate the theoretical minimum length of a test required to achieve a desired level of reliability.

The formula is widely used in psychological testing and educational measurement to evaluate the reliability of test scores and to make decisions about the number of items needed in a test to achieve a desired level of reliability.

This question should be provided as:

The Spearman-Brown formula is for which purpose?

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The volume inside the kite is equal to 540 cm³.

Given is that Oliver is building a box kite. The frame of the kite has the dimensions shown. He covered the sides of the kite (but not the top and bottom) with 7200 centimeters square of lightweight fabric.

We can write the total area covered as -

4 x 30 x h = 7200

120h = 7200

h = 7200/120

{h} = 60 cm                                              .... Eq { 1 }

Volume enclosed inside the kite -

V = {l} x {b} x {h}

V = 30 x 30 x 60

V = 540 cm³                                                 .... Eq { 2 }

Therefore, the volume inside the kite is equal to 540 cm³.

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Answer:

D.  4x - 3y = 15

Step-by-step explanation:

The slope of a line is defined as the "change in y" over the "change in x".  

This is also commonly referred to as "rise over run".

From inspection of the graphed line, we can see that the "rise" between the two points is 4 units up, and the "run" between to the two points is 3 units right.  "Up" and "right" are positive directions, therefore the slope of the line is ⁴/₃.

The given answer options are all in standard form.

The standard form of a linear equation is Ax + By = C, where A, B and C are constants and A is positive.

The slope of a linear equation in standard form is -A/B.

If two lines are parallel, they have the same slope.

Therefore:

[tex]\implies \sf \dfrac{4}{3}=-\dfrac{A}{B}[/tex]

Remember that the constant A is positive, so this means that A=4 and B=-3. Therefore, we are looking for an answer option that includes "4x - 3y" on the left side of the equation.

Therefore, the line that is parallel to the graphed line is:

Answer: Your answer will be D. [tex]4x-3y=15[/tex]

Answer:

Point H is at 4.75 on the number line.

Step-by-step explanation: