Which set of side measures forms a Pythagorean triple

Answer:

Step-by-step explanation:

0.99

Answer:

i belive 6.3

Step-by-step explanation:

Answr: C

Step-by-step explanation:

...

Answer:

see explanation

Step-by-step explanation:

1

since Δ ABT is a 45- 45- 90 then it is isosceles with ∠ A = ∠ T and

legs are congruent, that is

BT = AB = x = 8

using the sine ratio and the exact value

sin45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then

sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{AB}{AT}[/tex] = [tex]\frac{8}{y}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )

y = 8[tex]\sqrt{2}[/tex]

so x = 8 and y = 8[tex]\sqrt{2}[/tex]

2

using the tangent ratio in the right triangle and the exact value

tan60° = [tex]\sqrt{3}[/tex] , then

tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{a}{8}[/tex] = [tex]\sqrt{3}[/tex] ( multiply both sides by 8 )

a = 8[tex]\sqrt{3}[/tex]

using the sine ratio in the right triangle and the exact value

sin30° = [tex]\frac{1}{2}[/tex] , then

sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{8}{b}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

b = 8 × 2 = 16

so a = 8[tex]\sqrt{3}[/tex] and b = 16

Answer:

1.  x = 8,  y = 8√2

2.  a = 8√3,  b = 16

Step-by-step explanation:

The interior angles of a triangle sum to 180°.

From inspection of triangle ABT, angle B is 90° and angle T is 45°. Therefore, angle A is also 45°. This means that this triangle is a special 45-45-90 triangle.

The measures of the sides of a 45-45-90 triangle are in the ratio 1 : 1 : √2.

Therefore, the formula for the ratio of the sides is b : b : b√2 where:

From inspection of triangle ABT, sides AB and BT are the legs of the triangle, and side AT is the hypotenuse. Therefore, as leg AB measures 8 units, then b = 8.

The side labelled "x" is the other leg of the triangle (side opposite the 45° angle). Therefore:

[tex]\rm \implies x = b=8[/tex]

The side labelled "y" is the hypotenuse of the triangle (side opposite the right angle). Therefore:

[tex]\implies \rm y=b\sqrt{2}=8\sqrt{2}[/tex]

[tex]\hrulefill[/tex]

From inspection of the interior angles of the given triangle, it is a special 30-60-90 triangle.

The measures of the sides of a 30-60-90 triangle are in the ratio 1 : √3 : 2.

Therefore, the formula for the ratio of the sides is c: c√3 : 2c where:

The side opposite the 30° angle is 8 units. Therefore, c = 8.

The side labelled "a" is the side opposite the 60° angle. Therefore:

[tex]\rm \implies a = c\sqrt{3} = 8\sqrt{3}[/tex]

The side labelled "b" is the side opposite the 90° angle. Therefore:

[tex]\implies \rm b = 2c = 2 \cdot 8 = 16[/tex]

Answer:

[tex]b=\frac{r}{9} +a[/tex]

Step-by-step explanation:

To solve this problem, we have to isolate b. The steps are shown below:

Given - [tex]9(b-a)=r[/tex]

Divide both sides by 9 - [tex]\frac{9(b-a)}{9}=\frac{r}{9}[/tex]  → [tex](b-a)=\frac{r}{9}[/tex]

Add a to both sides - [tex](b-a+a)=\frac{r}{9}+a[/tex]  → [tex]b=\frac{r}{9} +a[/tex]

So after doing these steps, we are left with our answer of  [tex]b=\frac{r}{9} +a[/tex].

[tex]b=\dfrac{r}{9}+a[/tex]

Main Concepts:

Concept 1. Solving for a variable

Concept 2. Undoing a multi-step equation

Concept 1. Solving for a variable

To solve any equation ever in mathematics, there are two main steps:

In this case, the variable already appears exactly once, so we can skip ahead to Step 2.

Concept 2. Undoing a multi-step equation

To "Isolate the variable", one must undo the things that are done to it.

To undo something, things must be undone in the reverse order in which they are done.

Looking at the equation, "b" appears on the left side of the equation.  Focusing on the left side, if everything were a number and we were trying to simplify it, Order of Operations would require us to take the "b" and do the following:

1. subtract  by "a" in the parentheses

2. then multiply by 9

To undo these things, we'll need to use the opposite operation of what would have been done in the first place.

To undo the steps above, we undo them in reverse order, so

1. Undo multiplication by 9

2. Then undo the subtraction by "a".

[tex]9(b-a)=r[/tex]

To undo the multiplication, divide both sides by 9

[tex]\dfrac{9(b-a)}{9}=\dfrac{r}{9}[/tex]

simplifying the left side gives

[tex]b-a=\dfrac{r}{9}[/tex]

To undo the subtraction by "a", add "a" to both sides

[tex]b-a+a=\dfrac{r}{9}+a[/tex]

simplifying the left side gives

[tex]b=\dfrac{r}{9}+a[/tex]

The coefficient of determination for a linear regression model fitting with bivariate dataset ( scatterpot present in above figure) is equals to the 90.097.

When we study about linear regressions, usually analyze two coefficients that help us to know about the quality of the regression model and strength of linear relationship between the variables. One is called the coefficient of determination, denoted by R². Consequently, by observing a scatter plot, we can estimate the value of these coefficients. We have a scatterpot for a linear model fitting of the bivariate dataset is present in above figure. Coefficient of determination is always positive. When data are very closely arranged along a approximate line, then coefficient of determination is more near to 1 (In percentage it is 100). Here points are almost closely arranged . So percentage should be near to 100. So possible answer is 90.097. Hence, the answer is 90.097.

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Complete question :

The above figure complete the question.

What is the coefficient of determination for a linear model fitting the following bivariate dataset?

Answer:

Step-by-step explanation:

Answer:

The surface area of a cube is given by the formula:

SA = 6s^2

where SA is the surface area and s is the length of one side.

In this case, we know that the surface area is 96 square meters, so we can set up an equation:

96 = 6s^2

Solving for s, we get:

s^2 = 16

s = 4

So the length of one side of the cube is 4 meters.

The volume of a cube is given by the formula:

V = s^3

where V is the volume and s is the length of one side.

Plugging in s = 4, we get:

V = 4^3 = 64 cubic meters

So the volume of the cube is 64 cubic meters.

Step-by-step explanation:

gg

Answer: 3

Step-by-step explanation:

The 2 parts of 1 seg multiplied = 2 parts of other seg multiplied

3(x+5)=4(2x)

3x+15=8x

15=5x

x=3

The variables x and y vary directly will be "y = one-third x".

Option (b)  is the correct answer.

The relationship between two variables that vary directly can be expressed mathematically using an equation.

In this case, we are given the values of x and y, and we need to write an equation that relates them.

To determine the correct equation, The definition of direct variation. When two variables vary directly, it means that if one variable increases by a certain factor, the other variable also increases by the same factor. In other words, their ratio remains constant.

Let's apply this concept to the given values of x and y. We know that x = 18 and y = 6. If we divide x by y, we get:

x / y = 18 / 6 = 3

Since this ratio is constant, we can write an equation that expresses this relationship as y = kx

where k is the constant of proportionality. To find the value of k, we can substitute the given values of x and y:

6 = k(18)

k = 1/3

Therefore, the equation that relates x and y in this case is:

y = (1/3)x

Option (b) "y = one-third x" is the correct answer.

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Answer:

The answer is 60

Step-by-step explanation:

Solution:

Complete the ratio

[tex] \frac{4}{?} = \frac{1}{15} \\ [/tex]

Hope you understand

Answer:The y-intercept is (0,10)

Step-by-step explanation:

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

x-intercept(s): (ln(11),0)

y-intercept(s): (0,10)

The step that is included in the graph of the ceiling function is given as follows:

y = -2 for -2 ≤ x ≤ -1.

The ceiling function is represented by the symbol ⌈x⌉ used in this problem, and represents the least integer greater than or equal to x,

For example, we have that:

⌈0 ≤ x < 1⌉ = 1.

In this problem, we have that the function is translated one unit right, hence the correct step is given as follows:

⌈x - 1⌉ = -2 for -2 ≤ x ≤ -1.

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Answer:

c

Step-by-step explanation:

174 of the 300 students in school chose pizza or hamburgers as their favorite meal.

We know that from the definition of Probability that,

Probability of an Event = (The favorable number of incidents under that Event)/(Total number of incident)

Here given that the total number of classmates in first = 50

Number of students whose favorite meal is pizza = 12

Number of students whose favorite meal is hamburgers = 17

So the probability of a student has pizza or hamburger as his favorite meal is = (12 + 17)/50 = 29/50

So for 300 such students, the number of students choose pizza or hamburger as their favorite meal is = 300*(29/50) = 6*29 = 174.

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Thus,  the smallest value of k that satisfies the condition is: k = ceil(mn / (r + n + 1)).

To find the smallest value of k such that the rank-k approximation uses the same or more amount of data as the original picture, we need to compare the sizes of the original picture and the rank-k approximation. The rank-k approximation of a matrix A can be obtained by performing singular value decomposition (SVD) on A and keeping only the k largest singular values.

Let m and n be the dimensions of the original picture (assuming it is a grayscale image) and let r be the rank of the image. The number of data points (i.e., pixels) in the original picture is mn, and the number of data points in the rank-k approximation is kr + k + kn. The first term kr corresponds to the k singular values, the second term k corresponds to the k left singular vectors, and the third term kn corresponds to the k right singular vectors.

We want to find the smallest value of k such that kr + k + kn is greater than or equal to mn. Using the values above, we can write this as:

kr + k + kn >= mn

Simplifying, we get:

k(r + n + 1) >= mn

Dividing both sides by (r + n + 1), we get:

k >= mn / (r + n + 1)

Therefore, the smallest value of k that satisfies the condition is:

k = ceil(mn / (r + n + 1))

where ceil is the ceiling function (i.e., rounding up to the nearest integer).

To obtain this result, we first calculated the number of data points in the original picture and the rank-k approximation, and then set them equal to each other. We simplified the resulting inequality to get an expression for k in terms of the other variables, and then used the ceiling function to round up to the nearest integer.

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Results:

(i)The amount Willow would lose in profit per mug if she uses the printing company = $12.50.

(iii) the total profit she would lose after selling all 65 mugs at $22 per mug = $812.50

To calculate the profit Willow would lose per mug, we use the formula:

Profit (P) lost per mug = Selling price (SP) per mug - Cost Price (CP) per mug:

$22 - $9.50 = $12.50

Thus, Willow will lose $12.50 in profit per mug if she uses the printing company.

To calculate the total profit, she would lose after selling all 65 mugs, we  multiply the profit lost per mug by the number of mugs:

$12.50 x 65 = $812.50

Therefore, Willow would lose $812.50 in profit after selling all 65 mugs at $22 per mug using the printing company instead of her own printing press.

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The temperature indoors and outdoors the same after 16 minutes

The function is given as

f(x) = -5log4 (x-15)

When the temperatures are equal, we have

f(x) = 0

So, the equation becomes

-5log4 (x-15) = 0

Divide by -5

So, we have

log4 (x-15) = 0

Take the exponent of both sides

x - 15 = 4^0

So, we have

x - 15 = 1

Evaluate

x = 16

Hence, the time is 16 minutes

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Answer:

20,000 mL

Step-by-step explanation:

Liter = 1000 mL

She bought 10 two liter bottles, so in total:

10 * 2 = 20 liters

20 L * 1000 mL/L = 20,000 mL

Answer:

7

Step-by-step explanation:

if 4 people equals 24 then 7 is your answer

The number of text messages teenagers in the United States send each month is,

⇒ =3.24 × 10¹⁰

Given that:

Total teenagers = 27 million

Number of text messages per month = 1200

Total messages sent by teenagers per month = 27 million × 1200

= 32,400,000,000

Decimal point should be after the first significant value from the left.

Count the number of digits remaining after the decimal point

= 3.24 × 10¹⁰

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The third root of 20 would give a result of

Radical numbers, are also called roots or surds.

These are mathematical expressions that represent the inverse operation of exponentiation.

They are used to find the value that, when raised to a certain power, results in a given number.

The most common types of radical numbers are

The cube root of 20 also written as ∛20 is solved using calculator to give 2.714417617 and to four decimal place will give 2.7144

This means that 2.714417617 x 2.714417617 x 2.714417617 is approximately equal to 20

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To represent the value of the collection after 3 years if it appreciates at a rate of 3% per year, we can use the following equation:

V = P(1 + r)^t

Where:

V = the value of the collection after 3 years

P = the initial value of the collection, which is $390 in this case

r = the annual appreciation rate, which is 3% or 0.03 as a decimal

t = the number of years, which is 3 in this case

Substituting the given values, we get:

V = $390(1 + 0.03)^3

Simplifying the equation, we get:

V = $390(1.03)^3

V = $390(1.0927)

V = $426.99 (rounded to the nearest cent)

Therefore, the equation that represents the value of the collection after 3 years if it appreciates at a rate of 3% per year is:

V = $390(1.03)^3

V = $426.99

Answer:

32

Step-by-step explanation:

20% of 40 = 8

40 - 8 = 32

32 students are not taking part of the club.

Answer:

Step-by-step explanation:

To find a quadratic equation with only two points, we need to use the general form of a quadratic equation, which is:

y = ax² + bx + c

where "a", "b", and "c" are constants and "x" and "y" are the variables.

Let's say the two points we have are (x₁, y₁) and (x₂, y₂). We can use these points to form two equations:

y₁ = ax₁² + bx₁ + c

y₂ = ax₂² + bx₂ + c

We can then solve these equations simultaneously to find the values of "a", "b", and "c".

Here's an example:

Suppose we have two points, (2, 3) and (4, 7), and we want to find the quadratic equation that passes through these two points.

We start by plugging in the coordinates of the first point into the equation:

3 = a(2²) + b(2) + c

Next, we plug in the coordinates of the second point:

7 = a(4²) + b(4) + c

We now have two equations with three variables. To solve for the variables, we can use either substitution or elimination. Here, we will use substitution:

From the first equation, we can solve for "c":

c = 3 - 4a - 2b

We can now substitute this expression for "c" into the second equation:

7 = a(4²) + b(4) + 3 - 4a - 2b

Simplifying the equation, we get:

7 = 16a - 2b + 3

4a - b = 2

We can now use the first equation to solve for "b" in terms of "a" and substitute this expression into the second equation:

b = (3 - 4a - c) / 2

b = (3 - 4a - (3 - 4a - 2b)) / 2

b = -2a + 3

Substituting this expression for "b" into the equation 4a - b = 2, we get:

4a - (-2a + 3) = 2

6a = -1

a = -1/6

Now that we know "a", we can use one of the earlier equations to solve for "c":

3 = (-1/6)(2²) + b(2) + c

c = 3 + (1/3) - b

Substituting this expression for "c" into the equation c = 3 - 4a - 2b, we get:

3 + (1/3) - b = 3 + (2/3) + 2(-2a + 3)

b = -2a + (8/3) = 1/3

Therefore, the quadratic equation that passes through the points (2, 3) and (4, 7) is:

y = (-1/6)x² + (1/3)x + 1

Note that this is a quadratic equation in standard form. If we want to write it in vertex form, we can complete the square.

Answer:

B. [tex]y = -\frac{11}{3}x - \frac{2}{3}[/tex]

Step-by-step explanation:

The equation of a line is

y = mx + b

Since they gave us two points we could use it to find the slope(m) of the equation. The formula to find the slope of the line is:

[tex]m=\frac{y_{2} - y_{1} }{x_{2}-x_{1} }[/tex]

They gave us the coordinate of the first point: (-2, 6), and the coordinate of the second point: (1, -4)

so, we plug in the x and y values into the slope formula:

[tex]m=\frac{-4-6}{1-(-2)}[/tex]

[tex]m=\frac{-11}{3}[/tex]

Since the answer choices all have different slope, we just have to look for the equation with the right slope which is [tex]\frac{-11}{3}[/tex], so the answer is C.

Step-by-step explanation:

For RIGHT trianges

sin Φ = opposite leg / hypotenuse

for THIS triangle

sin m =  6 sqrt(2) / 9   = 2/3  sqrt (2)    <=======exact value

                                   = .9428    <======four decimal value

The weight of Bill's pack is a quantitative variable, so the weight can take on any numerical value within a certain range (in this case, likely between 0 and 100 lbs or so).

The type of variable for the weight of Bill's pack is a continuous variable, and the corresponding level of measurement is the ratio level of measurement.

Continuous variable: A continuous variable is a variable that can take on any value within a given range. In this case, the weight of Bill's pack can take on any value within a certain range (e.g., from 0 lb to 100 lb or more), making it a continuous variable.
Ratio level of measurement: The ratio level of measurement has a true zero point and allows for meaningful comparisons and calculations, such as multiplication and division. Since the weight of Bill's pack has a true zero point (0 lb) and allows for meaningful comparisons (e.g., one pack can be twice as heavy as another), it falls under the ratio level of measurement.

Hence,  The weight of Bill's pack (48.3 lb) is a continuous variable, and its corresponding level of measurement is the ratio level of measurement.

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