rectangle pqrs will be translated to the point Q will be located at 8,3 .

what will be the.coordinates of point R​

Given parameters:

  Equation:

          (x-4)²=9

Problem, solve the equation by factoring and extracting the root

Solution:

    Given equation:

                  (x-4)²=9

         subtract 9 from both sides to equate to zero;

                (x-4)² - 9 = 0

                (x -4)² - 3² = 0

  Now, this is similar to the concept of difference of two squares;

          x² - y² = (x + y)(x-y)

Here x  = x-4 and y = -3

  So input and solve;

              (x - 4 -3)(x - 4 -(-3)) = 0

              (x - 7)(x - 4+3) = 0

              (x -7)(x -1) = 0

S0,

             x - 7 = 0 or x-1 = 0

             x = 7 or 1

If we extract the square roots;

          (x-4)² = 9

         √(x-4)² = √9

              x - 4 = 3

              x  = 4 + 3 = 7; this is not the only solution to the problem

So we cannot solve it by extracting the square root.

The solutions by checking are incorrect for the second solution, hence the expression cannot be solved by extracting the square root. The equation can only be solved by factoring

Given the expression;

(x-4)²=9

This expression can be solved by factoring

Factoring the expression on the left hand side

(x-4)(x-4)=9

x²-4x-4x+16 = 9

x² - 8x + 16 - 9 = 0

x² - 8x + 7 = 0

x² -x - 7x + 7 = 0

x(x-1) -7(x-1) = 0

x-7 = 0 and x - 1 = 0

x = 7 and 1

This shows that the expression can be solved by factoring

The other way is by squaring both sides

(√x-4)² = ±√9

x - 4 =±√9

x = -9+4 and x = 9 + 4

x = -5 and 13

Since the solutions by checking are incorrect for the second solution, hence the expression cannot be solved by extracting the square root

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The prοbability that mοre than twο machines need cοrrecting is apprοximately 0.0826 οr 8.26%.

Binοmial distributiοn is a prοbability distributiοn that describes the number οf successes in a fixed number οf independent trials, where each trial can οnly have twο οutcοmes: success οr failure.

Accοrding tο questiοn:

Let X be the number οf machines that need cοrrecting adjustments during a day's prοductiοn run, and let p = 0.2 be the prοbability that any οne machine needs cοrrecting.

Then, X fοllοws a binοmial distributiοn with parameters n = 6 (the number οf machines) and p = 0.2 (the prοbability οf a machine needing cοrrecting).

The prοbability οf X is:

P(X > 2) = 1 - P(X <= 2)

Tο calculate P(X <= 2), we can sum the prοbabilities οf X taking οn the values 0, 1, and 2:

P(X <= 2) = P(X = 0) + P(X = 1) + P(X = 2)

P(X = 0) = (6 chοοse 0) * 0.2⁰ * 0.8⁶ = 0.2621

P(X = 1) = (6 chοοse 1) * 0.2¹ * 0.8⁵ = 0.3932

P(X = 2) = (6 chοοse 2) * 0.2²* 0.8⁴ = 0.2621

Therefοre,

P(X <= 2)

= 0.9174

And

P(X > 2)

= 1 - P(X <= 2)

= 1 - 0.9174

= 0.0826

Sο the prοbability that mοre than twο machines need cοrrecting is apprοximately 0.0826 οr 8.26%.

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The value of cos(45°) is √2/2. The correct answer choice is D. √2.

In the given diagram, the angle labeled as 45° is part of a right triangle. To find the value of cos(45°), we need to determine the ratio of the adjacent side to the hypotenuse.

Since the angle is 45°, we can assume that the triangle is an isosceles right triangle, meaning the two legs are congruent. Let's assume the length of one leg is x. Then, by the Pythagorean theorem, the length of the hypotenuse would be x√2.

Now, using the definition of cosine, which is adjacent/hypotenuse, we can substitute the values:

cos(45°) = x/(x√2) = 1/√2

Simplifying further, we rationalize the denominator:

cos(45°) = 1/√2 * √2/√2 = √2/2

Therefore, the value of cos(45°) is √2/2.

The correct answer choice is D. √2.

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Answer:

A. The ordered pair (1,2) is a solution to the system of linear equations.

B. When (1,2) is substituted into the second equation, the equation is true

C. When (1,2) is substituted into the first equation, the equation is true

Step-by-step explanation:

X and Y coordinates is an address, which helps to locate a point in two-dimensional space. Any point in the coordinate plane is referred by a point (x, y), where the x value is the position of the point with reference to the x-axis, and the y value is the position of the point with reference to the y-axis. The x and y coordinates of a point have positive or negative values, based on the location of the point in the different quadrants.

so know that we know that the point (1,2) is the same as saying (x,y)

so now we just substitute both of the equation with the x and y values

x = 1

y = 2

y = -2x + 4, changes to 2 = -2(1) + 4

and

7x - 2y = 3, changes to 7(1) - 2(2) = 3

now lets solve them

Let's solve the first equation

2=(−2)(1)+4

Step 1: Multiply -2 by 1

2 = -2 + 4

Step 2: Add 4 to -2

2 = 2

Since 2 = 2, we know that (1,2) is true for this equation

Now lets solve the other, to see if it's true too

7(1) - 2(2) = 3

Step 1: Multiply 7 times 1, and -2 times 2

7 - 4 = 3

Step 2: Subtract

3 = 3

We know that (1,2) is true for this equation too

If you want to solve by substitution or elimination, you can do that too

So the answers are A, B, and C or option 1, 2, 3

The value of x will be 18.67 for the given data of the triangle.

We have,

Thale's theorem:

When a line parallel to one side of a triangle intersects the other two sides in distinct points, the other two sides are divided in the same ratio.

Given that the sides of the triangle are divided into two parts,

For the left part the parts will be x and x + 7 for the right side the parts will be 16 and 22.

The ratio will be the same according to Thale's theorem. The value of x will be calculated as:-

x / ( x + 7 ) = 16 / 22

22x = 16x + 112

6x = 112

x = 112 / 6

x = 18.67

Therefore, the value of x will be 18.67.

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complete question;

Find the values of x and y. Find value of x.

Answer:

x=10

Step-by-step explanation:

2x-10=10

2x=20

x=10

Answer:

x=10

Step-by-step explanation:

2(x - 5) = 10

You would first multiply 2 by x and 5

2x-10 = 10

then you would add ten to both sides

2= 20

then you would divide 2 by 20

x=10

Answer:

I believe it's option 3

explanation: you times inside by 3

Answer:

option 1.

Step-by-step explanation:

(4a⁵b)³ = 4³ * (a⁵)³ * b³

           \(= 64 *a^{5*3} * b^{3}\\\\= 64a^{15}b^{3}\)

Answer:

32°

Step-by-step explanation:

Angles 2 and 4 are vertical angles, so they are congruent. That means that their measures are equal.

First, we set their measures equal to each other.

Then we solve the equation for x.

Then, we use the value of x to find the angle measure.

m<2 = 6x + 5

m<4 = 4x + 14

Set the measures equal.

6x + 5 = 4x + 14

Subtract 4x from both sides.

2x + 5 = 14

Subtract 5 from both sides.

2x = 9

Divide both sides by 2.

x = 4.5

m<2 = 6x + 5

m<2 = 6 × 4.5 + 5

m<2 = 27 + 5

m<2 = 32

Answer: 32°

x = (12 ± √(-16)) / 4,The solutions would be complex numbers.

To solve quadratic equations of the form ax2 + bx + c = 0, use the quadratic formula. For this situation, your condition is as of now as a quadratic condition, with a = 2, b = - 12, and c = 20.

The quadratic formula is:

x = (-b ± √\((b^2 - 4ac)\)) / 2a

Plugging in the values for a, b, and c, we get:

x = (-(-12) ± √\(((-12)^2 - 4(2)(20)))\) / 2(2)

Simplifying the expression inside the square root:

x = (12 ± √\((144 - 160)\)) / 4

x = (12 ± √(-16)) / 4

Since the square foundation of a negative number is definitely not a genuine number, this condition has no genuine arrangements. Complex numbers would provide the answers.

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this is tough, if you explain the question better I can help!

Answer:

Step-by-step explanation:

1       super sorry im to lazy to do the work but its 1

Answer: ninety point one hundred and twenty five?

Step-by-step explanation:

Answer:

ninty point one two five

Step-by-step explanation:

Answer:

The answer is A

Step-by-step explanation:

Since the number that you are finding the multiple of is 2, it has to be an even number. Another way is if 2 by another whole number equals the answer choice then you got your answer.

The formula for slope is (y2 - y1)/ (x2 - x1)

Let's use (2,6) and (4,12)

12 - 6 = 6

4 - 2 = 2

6/2 = 3

The slope is 3.

Answer:

the probability is 1/4

The required amount of the space available is 0.045 cubic meter.

We need to determine Space inside the steps.

The Volume is defined as the mass of object per unit density.

The required space = 0.3*0.4*0.5 - 0.15*0.5*0.2

                                 =  0.06 - 0.015

                                 =    0.045 cubic meter

Hence, the required amount of the space available will be 0.045 cubic meter.

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The expression |-4| has a value of 4 when evaluated

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

|-4|

The above expression is an absolute expression

So, the solution is the positive value of the expression in bracket

Evaluate the expressions in the brackets

So, we have the following representation

|-4| = 4

Hence, the expression has a value of 4

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2(2a-3)

2 and 2a-3 are the two factors

Check the picture below.

Answer:

.4

Step-by-step explanation:

Answer: 128178718

That should be answer

Answer:

a

Step-by-step explanation:

Suppose that quiz scores in a beginning statistics class have a mean of 7.1 with a standard deviation of 0.4, the range in which at least 75% of the data will reside is from 6.3 to 7.9.

Chebyshev's Theorem is a statistical tool that provides a range for how much data is likely to fall within a certain number of standard deviations from the mean.

Specifically, it tells us that, for any set of data, no matter how it is distributed, at least 1 - (1/k^2) of the data will fall within k standard deviations from the mean, where k is any positive number greater than 1.

In this case, we want to find the range in which at least 75% of the data will reside. We can use Chebyshev's Theorem to determine the minimum value of k that will give us this range. We know that at least 75% of the data should fall within two standard deviations from the mean, so we can set k = 2.

Using Chebyshev's Theorem, we can say that at least 1 - (1/2^2) = 75% of the data will fall within 2 standard deviations from the mean. The standard deviation is 0.4, so two standard deviations would be 2 * 0.4 = 0.8.

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The probability of winning the jackpot on one try is 1/30 or 0.0333 (rounded to four decimal places).

To calculate the probability of winning the jackpot on one try, we need to determine the number of favorable outcomes (winning combinations) and the total number of possible outcomes.

The number of favorable outcomes can be calculated by selecting 4 different numbers from 1 to 45 (without considering the order) and one number from 1 to 30. This can be represented as:

C(45, 4) * C(30, 1)

where C(n, r) represents the number of combinations of n items taken r at a time.

The total number of possible outcomes is the total number of ways to select 4 numbers from 1 to 45 (without considering order) multiplied by the number of ways to select one number from 1 to 30. This can be represented as:

C(45, 4) * 30

To calculate the probability, we divide the number of favorable outcomes by the total number of possible outcomes:

Probability = (C(45, 4) * C(30, 1)) / (C(45, 4) * 30)

Simplifying the expression:

Probability = C(30, 1) / 30

Probability = 1 / 30

Therefore, the probability of winning the jackpot on one try is 1/30 or 0.0333 (rounded to four decimal places).

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Answer:

2/7

Step-by-step explanation:

There are 6 each of 7 different colored cards.

Therefore, total number of cards = 7 × 6 = 42

So the probability of each color card being chosen = 6/42 = 1/7

⇒ P(purple) = 1/7

⇒ P(green) = 1/7

So P(purple or green) = P(purple) + P(green)

                                     = 1/7 + 1/7

                                     = 2/7

The probability that the chosen card is either purple or green

Total number of cards ⇢42 cards

Total number of required card ⇢ 12 cards

probability of getting a purple or green card↷

\(⇢probability = \frac{favourable \: outcomes} {possible \: outcomes}\\ \)

\(⇢ \frac{12}{42} \\ \)

\(⇢ \frac{2}{7} \\ \)

Hence , option 3 ⇢ 2/7 is correct ✓

The amount of substance present determines the extent of the properties. Extensive properties include volume, size, mass, length, and weight.

An extensive property is one that is influenced by the quantity of matter in a test.  The vastness of a system is determined by its scale or the volume of materials contained within it. Extensive properties are those in which the value of a system's property equals the sum of the importance of its constituents.

The extent of a system is determined by its size or the amount of matter in it. The value of a system's property is said to be extensive if it equals the sum of the values of the system's parts.

There are properties of matter that are affected by the quantity or size of the matter, such as length, mass, volume, weight, and so on; these are known as extensive properties of matter, and their value changes as the size or quantity of matter changes.

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Answer:

0.2 = 20% probability that a student takes Spanish and engineering

Step-by-step explanation:

We solve this question treating the probabilities as Venn sets.

I am going to say that:

Event A: Student takes Spanish

Event B: Student takes Engineering.

35% of students take spainsh or engineering.

This means that \(P(A \cup B) = 0.35\)

30% of students take Spanish.

This means that \(P(A) = 0.3\)

25% of students take engineering.

This means that \(P(B) = 0.25\)

What is the probability that a student takes Spanish and engineering?

This is \(P(A \cap B)\).

These probabilities are related by the following formula:

\(P(A \cup B) = P(A) + P(B) - P(A \cap B)\)

So

\(P(A \cap B) = P(A) + P(B) - P(A \cup B)\)

Replacing the values

\(P(A \cap B) = 0.3 + 0.25 - 0.35 = 0.2\)

0.2 = 20% probability that a student takes Spanish and engineering

Answer:

37

Step-by-step explanation:

If the current temp is -37, than you would need to increases the temp by 37 to get back to 0 degrees f