A parallelogram is transformed according to the rule (x, y) → (x, y). Which is another way to state the transformation?

As the teacher-to-student ratio is equivalent in all schools, the number of students in school B is 506, the number of teachers in school C is 25 and  the number of students in school D is 792 respectively.

What are ratio and proportion?

An equation known as proportion shows that the two ratios presented are equal to one another. A ratio is the comparative or condensed form of two quantities of the same type. The majority of the explanations for ratios and proportions use fractions. A ratio is a fraction that is expressed as a:b, but a proportion says that two ratios are equal. In this case, a and b can be any two integers. 

Given, the teacher-to-student ratio is equivalent for all schools.

For school A, ratio of teacher-to-student = 15/330 = 1:22

Then, for school B, the number of students = 23*22 = 506

For school C, the number of teachers = 550/22 = 25

For school D, the number of students = 36*22 = 792

Hence, these are the required number of students and teachers for the respective schools.

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1. The slope of Abha's climb is 2 (rise/run).

2. No, the line 54y=13x does not pass through the origin.

3. The y-intercept of the line is 5.

4. The equation of the line is y = -5x + 3.

A linear function is one that has one or two variables and no exponents, according to the definition given in mathematics. It is a graphing function that produces a straight line.

To finish the graph, use a straightedge to draw a line through the two points as two points decide a line. The formula for a linear function is f(x)=mx+b, where m and b are real values representing the slope. Set f(x)=0 and work out the value of x to determine the x-intercept, if one exists. We can use y and f(x) interchangeably because y=f(x).

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The equivalent expression by combining like terms is 1.10b and

If the cost increases by 10%, you can multiply the former cost by 110%

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

Expression of 10% raise = b + 0.10b

Evaluate the like terms in the above expression

So, we have the following representation

Expression of 10% raise = 1.10b

Hence, the expression is 1.10b

Recall that we have the mathematical statement to be

If the cost increases by 10%, you can multiply the former cost by %.

In this case, the factor is calculated as

factor = 1 + 10%

So, we have

Factor = 110%

So, the missing expression in the statement 110%

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Answer:

-38

Step-by-step explanation:

The sequence is decreasing by 7 everytime

-10 to -17 decrease of 7

-17 to -24 decrease of 7

-24 to -31 decrease of 7

Part a: Time taken to double the population of chipmunks is 5/2 months.

Part b: Population at population size; P = 200 is 50.

Part a: Time taken to double the population of chipmunks;

P(t) = 100[1 + (0.3)t + (0.04)t²].

P(0) = 100[1 + 0 + 0] = 100

P(t) = 200 = 100 + 30t + 4t²

4t² + 30t − 100 = 0

2t² + 15t − 50 = 0

(2t − 5)(t + 10) = 0

t = 5/2

It will take 5/2 months population to double its initial size P(0).

Part b: Population at population size; P=200

P'(t) = 0 + 30 + 8t

P = 200 when t = 5/2

P'(200) = 30 + 8(5/2)

P'(200) = 30 + 20

P'(200) = 50

Thus, the instantaneous rate of growth of the population when the population size is P=200 is 50.

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The inequality that is used to find the domain of the function would be B x - 3 ≥ 0

The domain of a function is defined as the set of all the possible input values that are valid for the given function.

The given function is f(x) = √x - 3

Here we have to find the inequality that is used to find the domain of the function.

Therefore, the function (x - 3) must be greater than or equal to 0

That is;

x - 3 ≥ 0

We will use the above inequality to find the domain of the function.

When we solve the above inequality, we get the domain of the function then;

x - 3≥0

Now add 3 on both sides, we get;

x - 3 + 3 ≥ 0 + 3

x ≥ 3

Therefore,  the answer is x - 3 ≥ 0

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Answer:

Bro you require a protector to measure angle

Answer:

A. 45 degrees

B.90 degrees

Step-by-step explanation:

Answer:

-4

Step-by-step explanation:

Take two points and plug into the distance formula  [tex]\frac{y_{2}- y_{1}}{x_{2}- x_{1}}[/tex]

We will use (-2, 17) for ([tex]x_{1} , y_{1}[/tex]) and (-1, 13) for ([tex]x_{2} , y_{2}[/tex])

[tex]\frac{13- 17}{-1- -2}[/tex] = [tex]\frac{-4}{1} = -4[/tex]

The required angles  ∠TBS and ∠TCV are 48° and 22° respectively.

A right-angled triangle is a kind of triangle that has one of its points equivalent to 90 degrees. The other two points summarize to 90 degrees. The sides that incorporate the right point are opposite and the foundation of the triangle. The third side is known as the hypotenuse, which is the longest side of each of the three sides

∠TBV = 24°

∠VBS = 24°

So, ∠TBS = (24° ) = 48°

And,

∠SAU = 92°,

So,

∠VAU = 46°

In ΔTAC

∠TAC + ∠TCA = 90°

∠TCA = 90° - 46° = 44°

This angle is bisect by CV

Then,

∠TCV = 44/2 = 22°

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∠TBS = 48°

SV = 17

∠TCV = 20°

What is a angle bisector?

In geometry, an angle bisector is a line that divides an angle into two equal angles. The term "bisector" refers to a device that divides an object or a shape into two equal halves. An angle bisector is a ray that divides an angle into two identical segments of the same length.

As given in question:

AV , BV and CV are the angle bisector of ΔABC

UV = 17, BV = 18

∠SAU =92° and ∠TBV = 24°

Now,

∠TBV = ∠SBV = 24° ( BV is angle bisector)

So, ∠TBS = ∠TBV + ∠SBV

      ∠TBS = 24° + 24° = 48°

SV = UV = 17 (V is the incenter of ΔABC.)

∠SAU + ∠TBS + ∠TCU = 180° (Sum of angles of a triangle)

92° + 48° + ∠TCU = 180°

∠TCU = 180° - 140°

∠TCU = 40°

So, [tex]\angle TCV = \frac{40\degree}{2}[/tex]

       ∠TCV = 20°

∴ ∠TBS = 48°

SV = 17

∠TCV = 20°

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The arithmetic sequence has a 2nd term of -2 and a 7th term of 18 has the following answers.

What is arithmetic progression?

An progression or arithmetic sequence may be a sequence of numbers specified the difference between the consecutive terms is constant.

Main body:

General formula for arithmetic sequence

a + (n-1)d = aₙ

arithmetic sequence has a 2nd term of -2  , which means

a+d = -2    

a = -(d+2)      ---------(1)

7th term of 18 , which means

a+ 6d = 18

substituting value from equation 1,

-(d+2) +6d = 18

-d -2 +6d = 18

5d = 20

d = 5

using d= 5 in equation 1,

a = -(5+2)

a =-7

A) 10th term

=a +9d

= -7+9*5

= 38

B)  recursive formula for the sequence = aₙ+1=aₙ+d  .

Hence for the given sequence , it is

a₃ = a₂ +d

a₃ = -2+5

a₃ = 3

C) sum of first 10 terms

Sₙ =  n/2{2a+ (n-1)d}

S₁₀ = 5 {2*-7 + 9*5}

S₁₀ = 5[ -14 +45]

S₁₀ = 5*31

     = 105

Hence the sum of the first 10 terms is 105.\

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The cartesian coordinates of the given polar coordinates are

(A) (2, π); (X, Y) = (-2, 0)

(B) (6, -2π/3); (X, Y) = (-3, -3√3)

The cartesian coordinates for the polar coordinates are calculated by the formulae,

x = rcosθ, and y = rsinθ

Where the polar coordinates are (r, θ).

The cartesian coordinates for the given polar coordinates are as follows:

(A) (r, θ) = (2, π)

Then,

x = r cosθ = 2 cos(π) = 2(-1) = -2

y =r sinθ = 2 sin(π) = 2(0) = 0

Therefore, the cartesian coordiantes are (X, Y) = (-2, 0).

(B) (r, θ) = (6, -2π/3)

Then,

x = r cosθ = 6 cos(-2π/3) = 6(-1/2) = -3

y =r sinθ = 6 sin(-2π/3) = 6(-√3/2) = -3√3

Therefore, the cartesian coordinates are (X, Y) = (-3, -3√3)

The plot for the given polar coordinates on a polar grid is shown below:

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In the given situation where Jack writes 5 * 216 as (5*200) + (5*16), he uses the distributive property.

The distributive property of binary operations in mathematics generalizes the distributive law, which states that in elementary algebra, equality is always true.

For instance, in basic mathematics, one has to According to one, addition is distributed more evenly than multiplication.

The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.

So, in this instance, the multiplication is as follows:

5 * 216

This multiplication can be rewritten as follows:

5*(200+16)

We then put the distributive property to use. So, we have:

(5*200) + (5*16)

Therefore, in the given situation where Jack writes 5 * 216 as (5*200) + (5*16), he uses the distributive property.

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Correct question:
Jack broke apart 5x216 as (5x200)+(5x16) to multiply mentally. What strategy did Jack use?

Twice a day for 20 minutes is the required time to realize that meditation practiced is beneficial for persons physical and mental health.

Meditation practiced helps person in different ways:

Twice a week is very less time and does not make consistency.

Incorrect option.

Several hours at a stretch is not possible for all individual and it is not practical .

Incorrect option.

Twice a day for 20 minutes is the best time and helps individual to practice  meditation.

Therefore, Option C. twice a day for 20 minutes is the best time for mediation.

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Answer: 12.5%

Step-by-step explanation:

Take 1750 divided by 1999, then time 100% = 87.5%

100% - 87.5% = 12.5%

The rate of discount is 12.5%

The real and complex solutions of the polynomial equation [tex]x^{3} - 8[/tex] = 0 is 2,  -1 + [tex]\sqrt{3}[/tex]i  and  -1 - [tex]\sqrt{3}[/tex]i. option 2 is correct.

Polynomial equations are those created using exponents, coefficients, and variables. The greater of its possible exponents is referred to as the equation's degree. By factoring polynomials according to their degree and the variables in the equation, we may find their solutions.

Our equation is [tex]x^{3} - 8[/tex]

and we know that:  [tex]x^{3} = 8[/tex]

then we can write our equation as: [tex]x^{3} - 2^{3}[/tex]

And using the identity: [tex]a^{3} - b^{3} = (a-b) *(a^{2} +ab+b^{2} )[/tex]

where a = x and b = 2, then our equation is:

them, if x = 2 the first part is zero, so x = 2 is a solution, and now we need to see the second part in order to find the complex solutions.

[tex]x^{2} + 2x +2^{2}[/tex] = 0

Here we need to use.

a[tex]x^{2}[/tex] + bx + c = 0 if  for a, b and c constants, then:

x = [tex]-b +-\sqrt{b^{2} - 4ac } /2a[/tex]

in our problem we have:

x = -2 +-[tex]\sqrt{4 - 16}[/tex] /2

x = -1 +-[tex]\sqrt{-3}[/tex]

x =  -1 +-[tex]\sqrt{3}[/tex] i

So here we have two complex solutions:  -1 + [tex]\sqrt{3}[/tex]i  and  -1 - [tex]\sqrt{3}[/tex]i

So the value of x are 2,  -1 + [tex]\sqrt{3}[/tex]i  and  -1 - [tex]\sqrt{3}[/tex]i

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I think you mean

What are the real and complex solutions of the polynomial equation? (1 point)

[tex]x^{3} - 8[/tex] = 0

( the equation is [tex]x^{3} - 8[/tex] = 0 and not x-8 =0)

In linear equation,   20x + 45y = 440 ,     y = 2x  Where x is the number of small boxes sent and y  is the number of large boxes sent.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                                  Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Let be x the number of small boxes sent and y the number of large boxes sent.

Since each small box can hold 20 books (20x), each large box can hold 45 books (45y)and altogether can hold a total of 440 books, we can write the following equation to represent this

                 20x + 45y = 440

According to the information provided in the exercise, there were 4 times as many large boxes sent as small boxes. This can be represented with this equation

              y = 2x

Therefore, the system of equation that be used to determine the number of small boxes sent and the number of large boxes sent, is

                20x + 45y = 440

                      y = 2x

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Answer:

I think it's repeating pattern

Probability sampling is not "wrong," and convenience sampling allows allowing generalizations to a wider group.

Convenience sampling is any non sampling technique where units are chosen for the sample based on their accessibility to the researcher.

Thus, probability sampling is not "wrong," and convenience sampling allows allowing generalizations to a wider group.

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There are 990 ways to select 6 starters from a possible 14 using precisely two of the three triplets.

= C(3,2) = 3! / ( 2! x 1! ) = 3

To select the final 4 starters out of the 11 players ,

= C(11,4) = 11! / (4!7!)

= 330

There are a total of 6 ways to select starters.

= 3*330 = 990

Contrary to permutations, the order of selection is irrelevant when choosing elements from a collection using the combination method.

The number of combinations can be counted in simpler situations. Combination is the taking together of n items, k at a time, without repetition.

The terms k-selection or k-combination with repetition are frequently used to describe combinations where repetition is permitted.

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Answer:

83

Step-by-step explanation:

(78+72+87+90+x)/5=82

327+x=82*5

327+x=410

x=410-327

x=83

The domain of the function (g·f)(x) is {x∈ℝ|x ≠ -1}. Therefore, option B is the correct answer.

Given that, f(x)=x²+2x-4 and g(x) =[tex]\frac{1}{(x+1)}[/tex].

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Here, (g·f)(x) can be determined as follows

(g·f)(x)=g(x)×f(x)

= [tex]\frac{1}{(x+1)} \times x^2+2x-4[/tex]

Find the domain by finding where the expression is defined.

Interval Notation:

(-∞,-1)∪(-1,∞)

Set-Builder Notation:

{x∈ℝ|x ≠ -1}

The domain of the function (g·f)(x) is {x∈ℝ|x ≠ -1}. Therefore, option B is the correct answer.

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Answer:

m=-12/5

Step-by-step explanation:

yes

The value of measure of ''angle f'' in the figure will be 46°.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to given that;

In the figure,

The value of angle a and e are;

⇒ a = 115°

⇒ e = 69°

Now,

Since, There are two parallel lines shown in figure.

Hence, We know by the definition of alternate angles of parallel lines,

⇒ ∠a = ∠f + ∠e

Here, We have to given that;

The angles are,

⇒ a = 115°

⇒ e = 69°

So, We get by substitute the value of angle a and e;

⇒ ∠a = ∠f + ∠e

⇒ 115° = ∠f + 69°

Subtract 69° both side, we get;

⇒ ∠f = 115° - 69°

⇒ ∠f = 46°

Thus, The value of measure of angle f;

⇒ ∠f = 46°

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The linear model representing the information is y = 600x + 1500.

To produce 12 solar heaters it cost $8,700.

The domain of the linear model is [1, 80].

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,

10 solar heaters = $7500

20 solar heaters = $13,500

The linear model can be in the form of y = mx + c

m = (13,500 - 7500)/(20 - 10)

m = 6000/10

m = 600

Now,

(10, 7500) = (x, y)

7500 = 600 x 10 + c

c = 7500 - 6000

c = 1500

Now,

The linear model is y = 600x + 1500.

Where y is the cost of x solar heaters.

Now,

x = 12,

y = 600 x 12 + 1500

y = 7200 + 1500

y = 8700

Now,

y ≤ 50,000

We see that,

x = 81

y = 600 x 81 + 1500 = 48600 + 1500 = 50,100

x = 80

y = 600 x 80 + 1500 = 48000 + 1500 = 49,500

The domain is from x = 1 to x = 80.

Thus,

The linear model is y = 600x + 1500.

$8,700 is the cost to produce 12 solar heaters.

The domain is [1, 80].

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Answer: The common ratio of the geometric sequence is 1/2, the first term is -72, and the 4th term is -9.

Step-by-step explanation: The common ratio r of a geometric sequence is found by dividing the second term by the first term, and the nth term of the geometric sequence is given by a1 * r^(n-1), where a1 is the first term.

To find the common ratio r of this geometric sequence, we can use the fact that the 3rd term is -18 and the 6th term is 9216:

-18 = a1 * r^2

9216 = a1 * r^5

Dividing these two equations, we get:

-18/9216 = (a1 * r^2) / (a1 * r^5)

-18/9216 = r^-3

r = (-18/9216)^(-1/3)

Since r is the common ratio, it must be positive. Since (-18/9216)^(-1/3) is negative, we must take the positive root:

r = ((-18/9216)^(-1/3))^(1/3)

r = ((-18/9216)^(1/9))

r = (9216/-18)^(1/9)

r = (-512)^(1/9)

r = (-8)^(1/9)

r = (-2)^(2/9)

r = (-2)^(2/3)

r = (1/4)^(2/3)

r = 1/2

To find the first term a1, we can use the fact that the 3rd term is -18 and the common ratio is 1/2:

-18 = a1 * (1/2)^2

-18 = a1/4

a1 = -72

To find the 4th term a4, we can use the fact that the first term is -72 and the common ratio is 1/2:

a4 = (-72) * (1/2)^3

a4 = -9

Therefore, the common ratio of the geometric sequence is 1/2, the first term is -72, and the 4th term is -9.

Answer:

Window view rooms is 50, no window view rooms is 150.

Step-by-step explanation:

I just multiplied the prices times random number of rooms until they added together to 8,500$. It was purely by chance that I discovered the answer ngl to you lol

Answer:

-1.8x^2

Step-by-step explanation:

Zero is the slope of a line parallel to this line.

-1/9 is the slope of a line perpendicular to this line.

According to linguists, the Middle English adverb aslope, which meaning "at an angle," is where the term slope is said to have originated. A steep hill or the ramp in a parking garage are examples of things that are at an angle or on a slope and may be described using the word's noun form.

The ratio of the vertical change between two places is referred to as the slope. A line's slope is another indicator of how steep it is. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

The line becomes: y = 9x - 3

line is in the Slope-Intercept form : y = mx + c

Now comparing this two and we get slope, (m) = 9

So, The line perpendicular will have slope (m') = -1/m

or, m' = -1/9

The line parallel to this line will have slope (m'') = 0

because here the two lines are parallel, so they have no slope.

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