Lesson 25: Geometric interpretation of the solutions of a linear system

Answer:y

=

93

−

q

a

q

−

67

Step-by-step explanation:

The value of the rationalization is 5√2

Surds are described as the nth root of a number, say x and a  number r which, when raised to the power n

Given that;

n is a positive integer or  the degree of the root.

It is also seen as an expression that includes a square root, a cube root or other roots.

They are used to write irrational numbers only.

Given the surds;

10/√2 × √2/ √2

Multiply the values

10√2/2

Divide the values

5√2

Hence, the value is 5√2

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Suppose that 90% of  batteries that are supplied from the certain supplier have acceptable voltages, probability that among all the batteries supplied least nine will work is 26 and 0.3076 .

M: Math

P: Physics

S: Statistic

n(Math) = 24

n(Physics) = 29

Formula:

Putting the values, we get,

Thus, 26 students took statistic.

Probability is basically  based on the possible chances or the chances of happening of something. The theoretical probability is a type of probability that is  mainly based on the reason behind that probability. For example, if a coin is tossed, the theoretical probability or the outcome of getting a head will be ½.

Probability is the branch of mathematics that basically concern about  the occurrence of a random event or the chances of favorable outcome and  there are mainly four  types of probability exist: classical, empirical, subjective and axiomatic.

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Answer:

(x^2 + 4x) + (y^2 - 18 y) - 5, complete the square on on x by adding to both sides.

Step-by-step explanation:

Answer:

The 4th answer: ((x1+x2)/2 , (y1+y2)/2)

Step-by-step explanation:

To find the midpoint of a segment, you get the average of the x intercepts and y intercepts. So for the x-intercept, add the x-intercepts and divide by 2 and for the y-intercept, add the y-intercepts and divide by two.

((x1+x2)/2 , (y1+y2)/2)

The coordinates of another point with the same y-value are (10, 10).

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

f(x) = |x|

For (-10, 10)

i.e,

x = -10

f(-10) = |-10| = 10

So,

(-10, 10) is on the graph.

Now,

For x = 10,

f(10) = |10| = 10

This means,

(10, 10) is also on the graph.

We see that,

(-10, 10) and (10, 10) has the same y-value.

Thus,

The coordinates of another point are (10, 10).

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The length PR is given as follows:

PR = 337.75 ft.

Similar triangles share these two features:

The similar triangles for this problem are given as follows:

PRE and POC.

Hence the equivalent side lengths are given as follows:

Then the proportional relationship among the equivalent side lengths is given as follows:

x/165 = (x + 125)/255.

Applying cross multiplication, the length PR, represented by x, is obtained as follows:

255x = 165(x + 125).

225x = 165x + 20625

60x = 20265

x = 20265/60

x = 337.75 ft.

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The volume of the given cylinder would be = 4300 in³

The formula that can be used to calculate the volume of a cylinder = V= πr²h

where,

π = 3.14

r = 14

h = 7

volume = 3.14× 14² × 7

= 3.14× 196× 7

= 4308.08

= 4300 in³

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The radius of the sphere is 42 feet.

The correct option is D.

Space occupied by an object in three dimensional space is called as volume of an object. In simple words space is taken by object.

Given:

A sphere has a volume of 2304π cubic feet.

The volume of sphere = 4/3 π r³

4/3 π r³ = 2304π

r³ = 1728

r = 41.6

r ≈ 42 feet.

Thererfore, the radius is 42 feet.

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Step-by-step explanation:

To find the value of x, we need to solve the equation:

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

Expanding the right-side expression:

5x - (x + 3) = 6 - 6x + x

Combining like terms on both sides:

6x - 3 = 6 - 5x

Adding 5x and 3 to both sides:

11x = 9

Dividing both sides by 11:

x = 9/11

So the value of x is approximately 0.818181818.

Answer:

[tex]\frac{1}{9}[/tex] or 11.11%

Step-by-step explanation:

P(A) = probability of an event

f = favored outcomes

N = number of total outcomes

[tex]P(A)=\frac{f}{N}[/tex]

In this equation there is one favored income, when the first counter is blue and the second one is green. There are also nine total outcomes. This means that the equation necessary is:

[tex]P(A)=\frac{1}{9}[/tex]

The probability that Mike takes a blue counter and then Ellie takes a green counter is [tex]\frac{1}{9}[/tex] or around 11.11%

Let's call the number of hours spent on a job as "h". Then, the fee charged to the client can be represented as a function of "h" as follows:

f(h) = 30h + 40

This means that for any value of "h" (representing the number of hours spent on a job), the function f(h) gives the corresponding fee charged to the client.

Function notation is a mathematical notation used to express a mathematical function, which assigns a unique output to each input of a set. The function is represented by a symbol, usually a letter (such as f or g), followed by a variable in parentheses.

For example, the function f(x) = x^2 assigns the value x^2 to the input x. The input is usually referred to as the argument of the function. The function notation is commonly used in calculus, algebra, and other branches of mathematics.

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The bearing of the airport from the plane is calculated as; 245 degrees

The parameter given is that the bearing from the airport to the plane is 65 degrees.

From the the diagram I have attached, since the bearing from airport to plane is 65 degrees, we see that the bearing is calculated from North.

Thus, the 360° covering the North to the south in the clockwise direction is 180°

When the bearing required is from plane to bearing , the angle will be;

180 + 65 = 245 degrees

So the bearing from plane to airport will be = 245 degrees

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Answer:

7.66

Step-by-step explanation:

Properties of triangle

Answer:16

Step-by-step explanation:

Answer:

128

Step-by-step explanation:

When dealing with those types of problems, that's just another way of saying it's multiplication.

(64)2=64×2

which in this case, if you multiply to those numbers

64×2

youll get 128

64×2=128

The number of permutations for the remaining hours is 6 hours.

Permutation is a mathematical concept that refers to the arrangement of objects or elements in a specific order. It is used to find the number of possible combinations of a given set of elements.

Let's assume that she takes exactly three hours of classes on Monday, two on Thursday, and one on Friday. Now, we have three hours left for Tuesday, Wednesday, and the rest of the week.

To find the number of permutations for the remaining hours, we can use the permutation formula, which is:

P(n, r) = n! / (n-r)!

Where n is the total number of items and r is the number of items being selected. In this case, n = 3 (hours left for Tuesday, Wednesday, and the rest of the week) and r = 3 (hours being selected).

So, the number of permutations for the remaining hours is:

P(3, 3) = 3! / (3-3)! = 6

Now, we have found the number of permutations for the remaining hours.

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Above 700: 5%, Above 550: 34%, Between 400 and 550: 26%, Below 400: 16%, Below 550: 55%.

To calculate the fraction of students who scored above 700, we can use the z-score formula, which is (x - μ) / σ, where x is the score, μ is the mean, and σ is the standard deviation. In this case, μ = 500 and σ = 100. Plugging in 700 for x, we get (700 - 500) / 100 = 2. This corresponds to a z-score of 2, which is .9772, meaning that 97.72% of the scores are below 700. This means that 5% are above 700. To calculate the fraction of students who scored above 550, we can use the same formula, but with 550 for x. This gives us (550 - 500) / 100 = .5, which corresponds to a z-score of .5, meaning that 84% of the scores are below 550. This means that 34% are above 550. To calculate the fraction of students who scored between 400 and 550, we can subtract the z-score of 400 from that of 550. This gives us .84 - .2 = .64, meaning that 64% of the scores are below 550. This means that 26% are between 400 and 550.

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The mean height of the four boys is 157657.75 centimeters.

The three main methods for identifying the average value of a set of integers are mean, median, and mode.

Adding the numbers together and dividing the result by the total number of numbers in the list yields the arithmetic mean.

The middle value in a list that is arranged from smallest to greatest is called the median.

The value that appears the most frequently on the list is the mode.

Given, Four boys have heights of 155155cm, 156156cm, 158158cm, and 162162cm.

Therefore, The mean height of the boys is the sum of the heights of boys divided by the total number of boys which is,

= (155155 + 156156 + 158158 + 162162)/4.

= 630631/4.

= 157657.75 cm.

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Part 1:

Domain = (-2, -1, 0, 2)

Range = (-4, -2, 2)

Part 2:

Domain = (-4, -2, 1, 4)

Range = (-2, 1, 4)

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Part 1:

From the function figure:

All the x values are domain and all the y values are codomain.

All the y values that are an image of an x value are called the range.

So,

Domain = (-2, -1, 0, 2)

Range = (-4, -2, 2)

Part 2:

From the table:

All the x values are domain and all the y values are range.

So,

Domain = (-4, -2, 1, 4)

Range = (-2, 1, 4)

Thus,

The domain and range are given above.

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If they want to make a profit of $1,725 or more, then they need to sell at least 101 tickets.

We know that each ticket costs $25, then if they sell t tickets the revenue is:

R(t) = 25t

We know that the band has a cost of $800, and they want to make a profit of at least $1,725, then we can write the inequality below:

25t - 800 ≥ 1,725

(remember that the profit is the difference between the revenue and the cost).

Now we can solve that for t.

25t  ≥ 1,725 + 800

25t  ≥ 2,525

t  ≥ 2,525/25

t  ≥ 101

They need to sell at least 101 tickets.

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The area of triangle NOP is given as follows:

1416 cm².

The area of a triangle, given two side lengths and the angle between them, is given by the multiplication of the side lengths and the sine of the angle between them.

The parameters for this problem are given as follows:

Hence the area of the triangle is given as follows:

A = 92 x 23 x sine of 138 degrees

A = 1416 cm².

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The area of the garden will be = 1512 square meters.

The formula for calculating the area of a rectangle.

Rectangle surface area. A = l × b.

Once the length and breadth of a rectangle are determined, the area is computed.

The area of a rectangle may be calculated by multiplying its length and width.

Let's assume the length of the garden is 6x meters and the width is 7x meters, where x is a positive value that we need to find.

From the given ratio, we have:

6x + 7x = 78

13x = 78

x = 6

So the length of the garden is 6 * 6 = 36 meters and the width is 7 * 6 = 42 meters.

The area of the garden can be calculated as: 36 * 42 = 1512 square meters.

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When considering buying a stock then the best time frame to use to analyze the price history depends on your investment goals but on average, 1 year to 5 years.

The time frame for analyzing a stock's price history depends on the investment horizon and the goals of the investor. If you are a short-term trader who seeks to make quick profits, you might use a 1-day or 5-day time frame to analyze the stock's price movements.

Medium-term investor with a horizon of a few months to a year, should use a 1-month or 3-month time frame. For long-term investors with a horizon of several years, use a 1-year or even longer time frame, such as 5 years or 10 years.

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Step-by-step explanation:

Rewrite the following equation in slope-intercept form. 8x + 13y = -9 Write your answer using integers, proper fractions, and improper fractions in simplest form.

Slope intercept form mean to solve for y:

8x + 13y = - 9

subtract 8x from both sides:

8x + 13y - 8x = - 9  - 8x

13y = - 9 - 8x

rearrange right side:

13y = - 9 - 8x becomes:

13y = - 8x - 9

divide both sides by 13:

13y/13 = (- 8x - 9)/13

Answer: y = [tex]\frac{-8}{13} x-\frac{9}{13}[/tex]

The probability of each team winning the tournament is A= 0,2 B= 0,2     C= 0,4 D=0,2

We know that only one team can win, so the sum of each probability of winning  is one

P(A)+P(B)+P(C)+P(D)=1

then we know that the probability of Team A and B are the same, so

P(A)=P(B)

And that the probability that either team A or team C wins the tournament is 0.6, so P(A)+Pc)= 0,6, then P(C)= 0.6-P(A)

Also, we know that team C is twice as likely to win the tournament as team D, so P(C)= 2 P(D) so P(D) = P(C)/2= (0.6-P(A))/2

Now if we use the first formula:

P(A)+P(B)+P(C)+P(D)=1

P(A)+P(A)+0.6-P(A)+(0.6-P(A))/2=1

0,5 P(A)+0.9=1

0,5 P(A)= 0,1

P(A)= 0,2

P(B)= 0,2

P(C)=0,4

P(D)=0,2

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There are a total of 10 different combinations for each of the four-letter words.

If reiteration is permitted

There are 10 possible combinations for each of the four letters, making a total of 104 four-letter words.

If reiteration is prohibited

The first letter has 10 potential outcomes, followed by 9 for the second, 8 for the third, and 8 for the fourth, for a total of 10 * 9 * 8 * 7 outcomes.

If the first letter must be A, there is only one alternative for that letter and ten possibilities for each of the following three letters, for a total of 103.

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Around 50% to 75% of the daffodils on the south side of the building are not between 46cm and 48cm.

Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty. A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.

Here,

This question asks for the probability that none of the three daffodils selected from the south side of the building are between 46cm and 48cm.

Since the median of the data is 46cm

the third quartile is 48cm,

this means that about 50% to 75% of the daffodils on the south side of the building are between 46cm and 48cm.

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Answer:

153.86

Explanation:

using 3.14 as pi and 7 as radius

type (3.14)7^2 into calculator

The ratio of the rainbow fish to guoramis to corydoras is 5:2:3

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.

Rainbow fish is half, this means that the percentage of rainbow fish is 100×1/2 = 50%

percentage of guoramis is 20%

therefore the percentage corydoras = 100-(20+50) = 30%

therefore the ratio of rainbow fish to guoramis to corydoras = 50:20:30

divide through by 10 = 5:2:3

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'One inch represents 2,000 feet' is a verbal type scale.

The link between a length unit on a map and its corresponding length on the ground is known as the map scale. It will be beneficial for you to carefully study this section because we will use map scale principles throughout the course.

We can use three distinct scales to relate a map to the ground:

'One inch represents 2,000 feet' is an example of a Verbal scale. The relationship between a map distance and a ground distance is expressed verbally using a verbal scale.

Here, it is inferred that one inch on the map corresponds to 2000 feet on the ground. Popular atlases and maps frequently use verbal scales.

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