What is the difference of 85.23 and 2.676

The angle between the 3D vectors a = (3, -1, 2) and b = (1, -1, -2) is 2.23 radians. The angle between a = (0, -1, -3) and b = (2, 3, -1) is 2.43 radians.

The angle between two vectors a and b in three-dimensional space can be found using the dot product formula:

cos(θ) = (a * b) / (||a|| * ||b||)

Where ||a|| and ||b|| represent the magnitude (length) of vectors a and b, respectively, and "*" represents the dot product of the two vectors. The dot product is given by:

a * b = a1 * b1 + a2 * b2 + a3 * b3

Where a1, a2, and a3 are the components of vector a, and b1, b2, and b3 are the components of vector b. The angle θ is then calculated using the inverse cosine function:

θ = arccos(cos(θ))

Finally, the angle θ is expressed in radians.

For the first problem, we have:

a = (3, -1, 2)

b = (1, -1, -2)

So, we have:

a * b = 3 * 1 + (-1) * (-1) + 2 * (-2) = 3 - 1 - 4 = -2

||a|| = [tex]\sqrt{(3^2 + (-1)^2 + 2^2)} = \sqrt{(14)}[/tex]

||b|| = [tex]\sqrt{(1^2 + (-1)^2 + (-2)^2) }= \sqrt{(6)}[/tex]

cos(θ) = [tex](-2) / (\sqrt{(14)} * \sqrt{(6)} ) = -\sqrt{(2)} / \sqrt{(21)[/tex]

θ = arccos[tex](-\sqrt{(2)} / \sqrt{(21)})[/tex] = 2.23 radians (rounded to two decimal places)

For the second problem, we have:

a = (0, -1, -3)

b = (2, 3, -1)

So, we have:

a * b = 0 * 2 + (-1) * 3 + (-3) * (-1) = -3

||a|| = [tex]\sqrt{(0^2 + (-1)^2 + (-3)^2)} = \sqrt{(10)}[/tex]

||b|| = [tex]\sqrt{(2^2 + 3^2 + (-1)^2)} = \sqrt{(14)}[/tex]

cos(θ) = [tex]-3 / (\sqrt{(10)} * \sqrt{(14)}) = -3 / \sqrt{(140)}[/tex]

θ = arccos[tex](-3 / \sqrt{(140)})[/tex] = 2.43 radians (rounded to two decimal places)

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Answer:

Step-by-step explanation:

The parent function of the function f(x) = 3√(-8x - 4) will be h(x) = √x.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The function is given below.

f(x) = 3√(-8x - 4)

Simplify the function, then we have

f(x) = 3√(-8x - 4)

f(x) = 6√- (2x + 1)

Divide the equation by 6, then we have

g(x) = √(-2x - 1)

Replace -(2x + 1) with x, then we have

h(x) = √x

The parent function of the function f(x) = 3√(-8x - 4) will be h(x) = √x.

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Answer:

Rewrite the equation by factoring –8 from the radicand and taking the cube root to get –2 in front of the radical symbol.

The graph is reflected over the x-axis.

The graph is also reflected over the y-axis.

The graph is vertically stretched by a factor of 2.

The graph is translated ½ unit to the left.

Step-by-step explanation: All possible answers for edge

Angles in a triangle add to 180 degrees

make a little equation for that

58 + 42 + x = 180

simplify

100 + x = 180

x = 180 - 100

x = 80

Hope this helps,

- Jeron :- )

Answer:

a.) (1,4), (-2,3), (0,4)

b.) (4,1), (3,-2), (4,0)

Step-by-step explanation:

a. When we want to find the reflection over the Y axis, that means the X coordinate signs reflect. For A, it says (-1,4). To reflect it, we reflect the X coordinate, so now it's (1,4) instead. You'll do that to the other two.

b. When rotating, you would switch the numbers of the coordinates and switch the sign of X. For the first one (-1,4), we'll switch it to (1,4). Not we'll switch the numbers around to make it (4,1). You'll do that for the other two

The coordinates of the point H of the parallelogram is H ( 2 , 0 )

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

The four types are parallelograms, squares, rectangles, and rhombuses

Properties of Parallelogram

Opposite sides are parallel

Opposite sides are congruent

Opposite angles are congruent.

Same-Side interior angles (consecutive angles) are supplementary

Each diagonal of a parallelogram separates it into two congruent triangles

The diagonals of a parallelogram bisect each other

Given data ,

Let the parallelogram be represented as EFGH

Now , the coordinates of the parallelogram is given by

Substituting the values in the equation , we get

The coordinate of E = E ( 1 , 3 )

The coordinate of F = F ( 3 , 5 )

The coordinate of G = G ( 4 , 2 )

The coordinate of H = H ( x , y )

Now , the difference in the x coordinates of F and G = ( 4 - 3 ) = 1

The difference in the y coordinates of F and G = ( 2 - 5 ) = -3

So , the coordinates of the point H = x coordinate of E + 1 and y coordinate of E - 3

On simplifying the equation , we get

The coordinate of H = H ( 2 , 0 )

Hence , the coordinates of the parallelogram is H ( 2 , 0 )

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The simplification of the algebraic expression results in 7m^5 - 3m^3 - 3.

Algebraic expressions are mathematical expressions that consist of integers, variables, and arithmetic operations. To simplify algebraic expressions, some mathematical properties are being used such as distributive property in opening the brackets and additional property in adding like terms together.

Given that:

= (6m^5+3-m^3-4m)-(-m^5+2m^3-4m+6)

Apply distributive property

= 6m^5 + m^5 - m^3 -2m^3 - 4m + 4m + 3 - 6

Add like terms

= 7m^5 - 3m^3 - 3

Therefore, we can conclude that the simplification of the algebraic expression results in 7m^5 - 3m^3 - 3.

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Answer:

"18", "54", and "108"

Step-by-step explanation:

A straight line has an angle of 180 degrees. It can be seen as "half a circle", which has an angle of... 360 degrees, and since it's half, it's just 180 degrees.

Now we're also given the angles that compose the straight line (x, 3x, and 6x), and by adding these angles together, we should get the angle of the straight line. So that means that: [tex]x+3x+6x=180[/tex]

Now from here we can just combine them all into one term:

[tex]10x=180[/tex]

Now divide both sides by 10:

[tex]x=18[/tex]

Our angles are equal to "x", "3x", "6x", and to calculate their value, we just plug in "18" as x giving us: "18", "3(18)", "6(18)" which simplifies to the angles: "18", "54", "108"

Answer: $51,000

Step-by-step explanation:

At first, I multiplied 8,500 times 3 then the outcome I got was 25,500 so now I'm going to try multiplying 8,500 times 6 which equals 51,000 but I'm sorry if I got the answer wrong

1. store A sells at cheaper rate.

2. Runner B tun at faster rate.

3. Submarine 2 will reach at depth of -1056 feet at faster rate.

4.  Kira collected 18.33 points in one hour.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

1. Store A: y= 0.40 x

so, the unit rate is 0.40.

Store B:

the cots of 3 pound carrot= 20.16

and, the cost of 48 ounce carrot = 20.16

and, cost per ounce= 20.16 /48= 0.42

so, the unit rate is 0.42.

Thus, store A sells at cheaper rate.

2. The unit rate rate of runner A

= 54/4.5

= 12

and, the unit rate of runner B

= 275/20
= 13.75

Thus, Runner B tun at faster rate.

3. Submarine 1 descends at rate of 22 feet.

and Submarine 2 descends at rate of = 480/20 = 24 feet.

Thus, Submarine 2 will reach at depth of -1056 feet at faster rate.

4. Jess collected 18 points in one hour.

and, Kira collected 18.33 points in one hour.

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Answer: The Zeros Are(in order) -3,-2,-1,1, 1.5 ALL have a multiplicity of 1.

Step-by-step explanation: Since the 0's cross the graph and don't "bounce" on the x-axis, they're all for a multiplicity of 1.

The following information can be extracted from the system of triangles ABC and DEF:

Case A: 3 / 5 = y / z

Case D: m ∠ C = m ∠ F

Case E: Δ ABC ~ Δ DEF

In this problem we find a representation of a system with two similar triangles, that is, two triangles with two congruent internal angles and proportional sides. Then, the following relationships are derived below:

m ∠ A = m ∠ D

m ∠ B = m ∠ E

m ∠ C = m ∠ F

AB / DE = BC / EF = AC / DF

6 / 10 = y / z = x / w

3 / 5 = y / z = x / w

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Answer:

C.

Step-by-step explanation:

Its more likely to happen

Answer:

3 trombones

Step-by-step explanation:

9 divided by three is 3.

An equation of a line using slope-intercept format goes through the point (4, 2) and is parallel to y = 1/2x - 3 is y = x/2.

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:

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

m₁ = m₂ ⇒ 1/2 = 1/2

At data point (4, 2), a linear equation of this line can be calculated in point-slope form as follows:

y - 2 = 1/2(x - 4)

y - 2 = x/2 - 2

y = x/2 - 2 + 2

y = x/2

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Expressions using words: 2/5 as the sum of 4 and 8.

Expression with using numbers: 2/5 x(8+4)

Value = 12 2/5.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given:

First, the Expressions using words

2/5 of the product of 8 and 4.

4 times as mush as 2/5 of 8.

2/5 as the sum of 4 and 8.

Now, Expression with using numbers

2/5 + (8+4)

2/5 x (8 x 4)

4 x (2/5 x 8)

2/5 x(8+4)

Values are: 2 2/5, 4 2/5, 32 2/5, 12 2/5.

Now, the Answers is

Expressions using words: 2/5 as the sum of 4 and 8.

Expression with using numbers: 2/5 x(8+4)

Value = 12 2/5.

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The class width for a frequency distribution with 9 classes is 35.

The difference between the highest and lowest values for a given data collection is the range in statistics. In statistics, we must put the given values, set of data, or set of observations in ascending order in order to determine the range. That indicates that you should start by writing the observations from lowest to highest value. The formula must now be used to determine the range of observations.

The range of the data is given as:

Range = highest value - lowest value

Range =  389 - 77

Range = 312

The class width for a frequency distribution with 9 classes is:

Class width = 312 / 9 = approx. 35.

Hence, the class width for a frequency distribution with 9 classes is 35.

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Answer:

Below

Step-by-step explanation:

y= mx + b     is the slope intercept form of a line  

                           m = slope     and       b = y-axis intercept

Plug in the given values

y = -4/5 x -3

Answer:

1:3

Step-by-step explanation:

the greatest common factor is 3 so to simplify divide both sides by 3.

Answer:

15.1

Step-by-step explanation:

15.0782 is between 15.0 and 15.1.  It is closer to 15.1

Quadrile 1: 70 Quartile 3: 90 Median: 83.5 Lowest: 58 The average of the five summaries is maximum: 102.

The mean of even a dataset, often described as the mean and median, is the sum including all values divided by the overall number of values (as opposed to the geometric mean). This represents the most often used indicator of central tendency and is constantly referred to as the "mean." This is obtained by dividing the number of values contained within the dataset by the sum of all the values. Calculations can be conducted using either raw data or data that has been integrated into frequency tables. A number's average is called to as its average. Simple statistics can be used to determine: After adding up all the digits, divide by the number of digits total. the sum divided by the number.

given

The first quartile, median, third quartile, and maximum are the five summaries that make up the distribution of the ordered observation.

Five-number formula overview

Minimum: The first piece of the set

(n+1)/4 is the first quartile.

Average: (n+1)/2

Quartile three: 3(n+1)/4

Maximum: The set's final component

The five-digit grade summary (90, 85, 97, 76, 89, 58, 82, 102, 70, 67)

58 minimum

70 in the top quartile

Average: 83.5

90th percentile:

The most: 102

Quadrile 1: 70 Quartile 3: 90 Median: 83.5 Lowest: 58 The average of the five summaries is maximum: 102.

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Answer:

Step-by-step explanation:

To find the percent change, we can use the formula:

percent change = (final value - initial value) / initial value * 100

In this case, the initial value is 8 and the final value is 120. Plugging in the values, we get:

percent change = (120 - 8) / 8 * 100 = 1,400%

So, the percent change in the number of Crayola crayon colors is 1,400%. This represents a significant increase from the initial 8 colors in 1903.

The population is 900 gasoline stations. The sample is 800. The parameter is price of gasoline. The statistics is for 900 stations and not all stations.

The ratio of the sum of the values in a particular set to all the values in the set is the mean value, which is the definition of the average. The average formula has numerous practical uses. If we were asked to determine the average male height in India or the average age of the men and women in a group, we would add up all the data and divide it by the total number of data points.

The population is 900 gasoline stations.

The sample is 800.

The parameter is price of gasoline.

The statistics is for 900 stations and not all stations.

The sample selected is a good sample as it covers most of the gas stations.

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The probability of not ordering nonalcoholic beverages is 66.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favourable outcomes / Number of samples

Given that at a Noodles & Company restaurant, the probability that a customer will order a nonalcoholic beverage is 44%.

The probability of not ordering the beverages will be:-

P = 100% - 44%

P = 66%

Therefore, the probability of not ordering nonalcoholic beverages is 66.

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Step-by-step explanation:

Is some of the problem missing? impossible to answer unless we know how much they make an hour

1080 quarts can be made in 36 hours.

The rate per day is 30 quarts.

It is the quantity of an amount of something at a rate of one of another quantity.

In 2 hours, a man can walk for 6 miles

In 1 hour, a man will walk for 3 miles.

We have,

150 quarts of icecream = 5 hours

This can be written as,

5 hours = 150 quarts

Divide both sides by 5.

1 hour = 30 quarts

Multiplying 36 on both sides.

36 hours = 36 x 30 quarts

36 hours = 1080 quarts

Thus,

1080 quarts can be made in 36 hours.

30 quarts per day.

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The amount of the down payment for the house, given the market value and the amount your bank requires is $ 36, 000

The bank that you work for requires that for mortgage loans, the applicants ( in this case Mr. and Mrs. Brady) , should be able to pay 1 / 5 of the market value of the property as down payment.

The down payment is therefore :

= Market value of house x Requirement of bank

= 180, 000 x 1 / 5

= 180, 000 / 5

= $ 36, 000

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The rest of the question is:

Your bank requires 1/5 of the market value as a down payment.

What is the amount (in $) of the down payment?

Answer:

Four thousand two hundred and

Step-by-step explanation: