find three different vectors that are a linear combination of the given vectors. u = 3 −2 , v = −1 −5

Using the concept of ratio in the similar triangles, the length scale factor is 1:25

Similar triangles are triangles that have the same shape but may be scaled differently. Two triangles are considered similar if and only if their corresponding angles are congruent (equal in measure) and the ratio of their corresponding sides is the same. This property is known as the "AA Similarity Postulate" or "Angle-Angle Similarity".

In other words, similar triangles have the same shape and proportional sides. This means that if two triangles are similar, corresponding sides are in proportion and corresponding angles are equal in measure.

In the given figures, the two triangles have areas of 3m² and 75m²

The formula of area of a triangle is given as ;

A = 1/2 (b * h)

Assuming the side lengths are equal, we can apply heron's formula which is given as;

S = [a + b + c / 2]

A = √s(s - a)(s - b)(s - c)

But a = b = c

Using the two triangles to find the ratio between the ratios;

Q : R = 3 : 75 = 1 : 25

The length will be given as;

Area = 1/2 b * h

b = h

75 = 1/2 * a * a

a² = 75 * 2

a² = 150

a = √150

In the second triangle;

3 = 1/2(b²)

6 = b²

b = √6

The ratio between Q to R = √6 : √150 = 1 : 25

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Answer:

see below

Step-by-step explanation:

let n = x-5

so 3n+8n = 22

n = 22/11 =2

so x-5=2

x=7

IfIf this truss bridge shows two triangles ABC and DEF with ABC=DEF if mB=60 degrees, mE is 60 °.

ΔABC = ΔDEF

M∠E = M∠B

M∠B =60°

By equation 1 and 2

M∠B =60°

Since triangle ABC is congruent to triangle DEF, the corresponding angles are equal

so,

mB = mE

Hence, mE = 60 degrees

Therefore mE is 60 degree.

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Answer:

Step-by-step explanation:

After his football game malik drinks 1/2 Liter of water and the 1/3 liter of juice did malik drink more juice draw an estimate to partition explain your answer

After his football game, Malik drank 1/2 liter of water and 1/3 liter of juice. To compare the amounts, we can draw an estimate by partitioning the 1 liter unit into equal parts. For example, we can divide 1 liter into 6 parts, each representing 1/6 of a liter.

If 1/2 liter of water is represented by 3 parts, then 1/3 liter of juice is represented by 2 parts. We can see that Malik drank more water than juice. This is because the partition representing 1/2 liter of water is longer than the partition representing 1/3 liter of juice.

Therefore, the answer is that Malik drank more water than juice.

If angle A and angle B have the same measurement then m∠A = m∠B and ∠A ≅ ∠B. So, the correct option is B: II and IV only.

What is an angle?

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.

It is given that ∠A and ∠B have the same measurement.

This represents that ∠A and ∠B must be equal and congruent also.

This can be written in expression form as -

∠A ≅ ∠B

For example if ∠A = 90° then ∠B = 90°.

This can be written in expression form as -

m∠A = m∠B

The measure of angle A is equal to measure of angle B.

Therefore, option II and option IV are correct.

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True, when students are asked to list their age and the percentage of their college expenses that they pay for themselves, the type of data being collected is quantitative.

The data being collected is quantitative because both age and the percentage of college expenses paid for oneself are numerical values that can be quantified and measured. Age can be expressed in years and the percentage of college expenses can be expressed as a decimal or a percentage (e.g. 50%). This type of data can be analyzed using mathematical operations and statistical methods.

Hence, when students are asked to list their age and the percentage of their college expenses that they pay for themselves, the type of data being collected is quantitative.

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Matrix for reflection in line y=-x is [0 -1; -1 0].

What is matrix ?

A matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.

A reflection in the line y = -x can be represented as a linear transformation in 2D space. A linear transformation can be represented using a 2x2 matrix.

The matrix for the reflection in the line y = -x is given by:

a = [0 -1; -1 0]

This matrix represents a reflection about the line y = -x in the 2D plane. The first column of the matrix represents the image of the unit vector (1, 0) and the second column represents the image of the unit vector (0, 1).

The reflection is performed by multiplying the matrix a with the vector (x, y) representing the point in the 2D plane. The result is the reflection of the point across the line y = -x.

Matrix for reflection in line y=-x is [0 -1; -1 0].

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Answer:

2007 and beyond.

Step-by-step explanation:

y = 34  ==> y doesn't equal 34 billion as y is already measured in billions

Since y=10.5x:

34 = 10.5x  ==> solve for x

x = 34 / 10.5   ==> divide both sides by 10.5

x = 3.2  ==> x is approximately 3.2 years

2004 + 3.2 = 2007.2

2007.2 rounded to the nearest year is 2007

Hence, businesses will spend more than $34 billion in the year 2007 and beyond.

This equation is balanced, meaning that there is an equal number of atoms on both sides of the equation.

Since there are no gases on either side of the equation, the value of δngas (the change in the number of moles of gas) is 0.

The balanced equation 2pbo (s) o2 (g) ⇌ 2pbo2 (s) states that two moles of lead (II) borate (s) react with one mole of oxygen gas (g) to form two moles of lead (II) borate (s). Since the reaction does not involve any gases, the value of δngas (the change in the number of moles of gas) is 0.

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Answer:

$70.00

Step-by-step explanation:

Please find the attachment for detail

The minimum of y = f(x) occurs at (x,y) = (3,1). Hence y= f(x) >=1 for all other x in its domain of definition.

What is Quadratic equation ?

Quadratic equation can be defined as equation in which it is in the form of ax^2 + bx + c = 0

where c is a constant.

y = f(x) + 3 merely increases the value y by 3 for any x, or just raises its graph up 3. The x-value for its minimum remains at x=3 and y = f(3) + 3 = 1 + 3 = 4.  Hence, new minimum = (3,4)

y = f(x-2) just shifts or translates the graph of f to the right by 2.  So what occurred at x=3 (the minimum y) now occurs at x=5  without changing y = 1.  Hence, new minimum = (5,1).

y = f(1.5x) compresses the x-scale without changing y.  So what happened at x=3 before now happens at x'=2 on the new scale.

Therefore, the minimum point now becomes  (2,1).

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If the dot indicates the center of the circle, the equation that must be true is (c) A + B = 180

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

The circle

The angle in a semi-circle is 90 degrees

This means that

A = 90 and B = 90

When these angles are added, we have

A + B = 90 + 90

Evaluate

A + B = 180

Hence, the equation is (c) A + B = 180

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Using the quadratic formula we will see that the solutions are:

u₊  = 2

u₋ = -1/3

Here we have the quadratic equation:

3u² -2 = 5u

We can rewrite that in the general form so we get:

3u² -2 - 5u = 0

Now we can use the quadratic formula to find the solutions, we will get:

[tex]u = \frac{5 \pm \sqrt{(-5)^2 - 4*-2*3} }{2*3} \\\\u = \frac{5 \pm 7 }{6}[/tex]

Then the two solutions are:

u₊ = (5 + 7)/6 = 2

u₋ = (5 - 7)/6 = -2/6 = -1/3

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Theo used 2250 milliliters of water to water the garden.

Theo filled a watering can with 3 liters of water to water the garden. After using some of the water, he has 750 milliliters left in the can.

The amount of water used by Theo can be calculated by subtracting the remaining water from the total amount of water filled in the watering can.

For this, we first need to equate the unit of water present in the can initially with the amount of water left in the can.

We know, 1 liter = 1000 milliliters

Therefore, 3 liters = 3000 milliliters

This means that he used a total of 3000 milliliters - 750 milliliters = 2250 milliliters of water to water the garden.

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The equivalent expressions from the list will be 8 + 32y and 8•1+8•4y. Then the correct options are B and C.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expression is given below.

⇒ 8(1 + 4y)

Simplify the expression, then we have

⇒ 8(1 + 4y)

⇒ 8 + 32y

The equivalent expressions from the list will be 8 + 32y and 8•1+8•4y. Then the correct options are B and C.

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We will have 0.44 or 44% of original money after 8 quarters. The solution has been obtained by using arithmetic operations.

What are arithmetic operations?

Four fundamental mathematical operations can be used to represent any real number, and they are as follows:

1. The sum of the numbers is calculated using the addition operator ('+').

2. Subtraction with the "-" sign, which results in the difference between the numbers.

3. Multiply ('×') the result when it is the product of the numbers.

4. Division ('÷'), which yields the numbers' quotient.

We are given that we started the company with $5,000,000 and we lose 7% of that start up cash every quarter.

So,

Amount lost every quarter = $5,000,000 * 7% = $350,000

Now,

Amount lost in 8 quarters = $350,000 * 8 = $2,800,000

Therefore,

Money left = $5,000,000 - $2,800,000 = $2,200,000

Thus,

Percentage left of original money = $2,200,000/$5,000,000 * 100 = 44%

Hence, we will have 0.44 or 44% of original money after 8 quarters.

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Answer:Let's call the distance of the boat trip "d".

Since the whole trip took 5 hours, and Maxwell was driving for part of it, we know that:

d/40 + x/60 = 5

where x is the number of hours Maxwell spent driving.

We also know that the distance he drove is equal to the total distance minus the boat trip:

275 - d = x * 60

So we can substitute this into the first equation:

d/40 + (275 - d)/60 = 5

Expanding and simplifying this equation gives us:

6d = 1800

Finally, dividing both sides by 6 gives us:

d = 300

So the boat trip was 300 miles long.

Step-by-step explanation:

Let's call the distance of the boat trip "d".

Since the whole trip took 5 hours, and Maxwell was driving for part of it, we know that:

d/40 + x/60 = 5

where x is the number of hours Maxwell spent driving.

We also know that the distance he drove is equal to the total distance minus the boat trip:

275 - d = x * 60

So we can substitute this into the first equation:

d/40 + (275 - d)/60 = 5

Expanding and simplifying this equation gives us:

6d = 1800

Finally, dividing both sides by 6 gives us:

d = 300

So the boat trip was 300 miles long.

Answer:

Step-by-step explanation:

Although certain functions have discontinuities, it is feasible to redefine the function so that it becomes continuous at that point.

A continuous function in mathematics is a function without discontinuities, or any sudden changes in value. If we can guarantee arbitrarily small changes in the input of a function by limiting small enough changes, then the function is continuous.

We only need to change the function's value at this point to make f(x) continuous at x=0. To satisfy the concept of continuous functions and resolve the example issue, make the necessary adjustment to make the one-sided limits equal. We therefore set f(0)=4 f(0) = 4

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Answer: 900 peaches

Step-by-step explanation:

cuz please thank

First-principle differentiation of sec x results in ten times sec x.

Regarding the variable x, y = f(x). Wherever the limit occurs is defined to be the derivative of f at x if this limit exists and is finite. The first principle of derivative is another name for this definition.

Sec x tan x is, as far as we are aware, the derivative of sec x. Determining that sec x equals the integral of sec x tan x. Specifically, sec x tan x dx = sec x + C

On a graph, the first derivative shows the slope of the function at a particular position, while the second derivative shows how the slope changes as the independent variable is changed. The second derivative accounts for the curve in the above graph for a function with a variable slope.

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Percentage of sandwiches out of all lunch orders = 61%

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Order of sandwich = 61%

Total lunch order = 100%

Percentage of sandwiches = 61%

Hence, There are 61% of sandwiches out of all lunch orders.

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R500 is available for Savings.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Zekele earns = R 6500

His bills in one month are:

Rent R1 650,

Electricity R300,

Car payment R1 200,

Insurance R750,

Petrol R400,

Account repayments R500

and Groceries R1 200.

So, after spending on expenses he would save

= 6500 - ( 1650 + 300+ 1200+ 750 +400+ 500+ 1200)

= 6500- 6000

= R 500

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For the probability values - P(A) = 0.5, P(B) = 0.6, and P(A∩B) = 0.4, the values are -

a) P(A∪B) = 0.7

b) P(A∩B') = 0.2

c) P(A'∪B') = 0.6

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

The given probability values are -

P(A) = 0.5

P(B) = 0.6

P(A∩B) = 0.4

a) The formula for finding P(A∪B) is -

P(A∪B) = P(A) + P(B) - P(A∩B)

Substitute the values into the equation -

P(A∪B) = 0.5 + 0.6 - 0.4

P(A∪B) = 0.11 - 0.4

P(A∪B) = 0.7

b) To find P(A∩B') use the formula -

P(A∩B') = P(B) - P(A∩B)

Substitute the values into the equation -

P(A∩B') = 0.6 - 0.4

P(A∩B') = 0.2

c) To find P(A'∪B') first find P(A'), P(B') and P(A'∩B').

P(A') = 1 - P(A)

Substitute the value -

P(A') = 1 - 0.5

P(A') = 0.5

Now, find P(B') -

P(B') = 1 - P(B)

Substitute the value -

P(B') = 1 - 0.6

P(B') = 0.4

Now, find P(A'∩B')

P(A'∩B') = 1 - P(A∩B)

Substitute the value -

P(A'∩B') = 1 - 0.7

P(A'∩B') = 0.3

The formula for finding P(A'∪B') is -

P(A'∪B') = P(A') + P(B') - P(A'∩B')

Substitute the values into the equation -

P(A'∪B') = 0.5 + 0.4 - 0.3

P(A'∪B') = 0.9 - 0.3

P(A'∪B') = 0.6

Therefore, the values are P(A∪B) = 0.7, P(A∩B') = 0.2 and P(A'∪B') = 0.6.

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If P(A) = 0.5, P(B) = 0.6, and P(A∩B) = 0.4, find (a) P(AUB), (b) P(A∩B'), and (c) P(A'U B').

The value of b is 4.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

We can make the ordered pairs (x, y).

Where x is the number of quarters and y is the number of playable characters.

Now,

A video game was released with 4 playable characters.

This means,

(0, 4)

Now,

The video game company has a plan to add 6 new characters every quarter (every 3 months).

This means,

(1, 10)

(2, 16)

(3, 22)

Now,

y = mx + b

Now,

Take any two ordered pairs:

(1, 10)

(2, 16)

m = (16 - 10) / (2 - 1)

m = 6

Now,

(0, 4) = (x, y)

4 = 6 x 0 + b

b = 4

Thus,

4 is the value of b.

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The number of pints of ice cream used for each sundae is 0.8 pints.

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,

4 pints of icecream = 5 sundaes

Divide both sides by 5.

4/5 pints of icecream = 1 sundaes

0.8 pints of icecream = 1 sundaes

Thus,

0.8 pints of ice cream is used for each sundae.

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If the cyclist rode for 1 hour at the same average speed, she would have ridden 17.4 miles.

To find the average speed of a cyclist, you can divide the total distance covered by the total time taken. In this case, the cyclist rode for 3.5 hours and completed a distance of 60.9 miles, giving an average speed of 60.9 miles ÷ 3.5 hours = 17.4 miles per hour. This average speed is constant, meaning that the cyclist would have traveled the same distance in 1 hour as she did in 3.5 hours if she kept the same pace.

Therefore, if the cyclist rode for 1 hour at the same average speed, she would have ridden 17.4 miles. This calculation is important for cyclists and other athletes as it helps them to determine their speed and track their progress over time.

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The probability that exactly 10 of the 20 women have dark eyes is 0.2051.

The theory used in this question is the binomial probability formula, which is used to calculate the probability of a certain number of successes in a given number of trials.

The steps for this process are as follows

Step 1: Calculate the binomial formula: (n!)/(x!(n-x)!) * p^x * (1-p)^(n-x),

where n is the number of trials (in this case, 20), x is the number of successes (10), p is the probability of a success (0.40 in this case), and n-x is the number of failures (10).

Step 2: Plug the values into the formula: (20!)/(10!(20-10)!) * 0.40^10 * (1-0.40)^(20-10)

Step 3: Simplify the formula: (20*19*18*17*16*15*14*13*12*11) / (10*9*8*7*6*5*4*3*2*1) * 0.40^10 * 0.60^10

Step 4: Calculate the result: 0.2051

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Answer:

18.33 m/s

Step-by-step explanation:

Convert units.

1 km = 1000 m

1 h = 3600 s

66 km/h × (1000 m)/(1 h) × (1 h)/(3600 s) = 18.33 m/s

The probability of the second event is close to 1.

We can use the Central Limit Theorem to calculate the probability. According to the Central Limit Theorem, the distribution of the mean of a large number of independent random variables will be approximately normal, with mean equal to the mean of the individual variables and standard deviation equal to the standard deviation of the individual variables divided by the square root of the sample size.

In this case, the mean of 50 square yards is 50 * 1.6 = 80 flaws. The standard deviation of the mean is 1.2/sqrt(50) = 0.24.

So, we want to find the probability that the mean of 50 square yards is 2 or more, which is equivalent to finding the probability that a standard normal random variable is greater than or equal to (2 - 80)/0.24 = -333.33.

We can use a standard normal table to find this probability. The probability of a standard normal random variable being less than or equal to -333.33 is close to 0, so the probability of being greater than or equal to -333.33 is close to 1.

Therefore, the probability of the second event is close to 1.

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The probability of the second event is close to 1.

We can use the Central Limit Theorem to calculate the probability. According to the Central Limit Theorem, the distribution of the mean of a large number of independent random variables will be approximately normal, with mean equal to the mean of the individual variables and standard deviation equal to the standard deviation of the individual variables divided by the square root of the sample size.

In this case, the mean of 50 square yards is 50 * 1.6 = 80 flaws. The standard deviation of the mean is 1.2/sqrt(50) = 0.24.

So, we want to find the probability that the mean of 50 square yards is 2 or more, which is equivalent to finding the probability that a standard normal random variable is greater than or equal to (2 - 80)/0.24 = -333.33.

We can use a standard normal table to find this probability. The probability of a standard normal random variable being less than or equal to -333.33 is close to 0, so the probability of being greater than or equal to -333.33 is close to 1.

Therefore, the probability of the second event is close to 1.

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