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Answer:

(9, -13.5)

Step-by-step explanation:

It's given in the question that a quadrilateral RSTV is dilated with a scale factor of 1.5 with respect to the origin to form R'S'T'V'.

Rule for dilation is,

(x, y) → (kx, ky)

where 'k' is the scale factor.

If vertex R of the quadrilateral is (6, -9),

By the given rule of dilation,

R(6, 9) → R'[(1.5 × 6), -(1.5 × 9)]

           → R'(9, -13.5)

Therefore, Option given in bottom right (9, -13.5) will be the answer.

The point (2,-4) satisfies y < 3x - 6

The consumer surplus is approximately $145.83.

To find the consumer surplus, we first need to find the demand function's inverse, which gives us the willingness to pay for each unit of the product. The demand function is:

D(x) = √(739 - 3x)

Setting D(x) equal to the equilibrium price of $25, we get:

25 = √(739 - 3x)

Squaring both sides, we get:

625 = 739 - 3x

Solving for x, we get:

So at a price of $25 per unit, the consumer is willing to buy 38 units per month.

Now we can calculate the consumer's surplus.

The consumer\(x = (739 - 625) / 3 = 38\) surplus is the difference between the total amount that consumers are willing to pay for a certain quantity of a good and the total amount they actually pay. In this case, the consumer's surplus can be calculated as:

\(CS = \int_0^{38} [D(x) - 25] dx\)

where D(x) is the demand function, and the integral is taken over the range of 0 to 38, which represents the quantity demanded at a price of $25 per unit.

Evaluating this integral, we get:

\(CS = \int_0^{38} [\sqrt{(739 - 3x)} - 25] dx\\\\= [1/6 (739 - 3x)^{(3/2)} - 25x]_0^{38}\\\\= \$ 145.83\)

Therefore, the consumer surplus is approximately $145.83.

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A, percentages

You would see percentages on a circle graph, because it's how many parts of the whole that they take up.

Happy to help, have a great day! :)

Answer:

$3040 profit made

Step-by-step explanation:

$13×95=$1235 cost to make all the shoes they sold

$45×95=$4275 money she made

$4275-$1235=$3040 profit

Answer:

Step-by-step explanation:

\(y=(\frac{1}{g} )x\)

Constant up a proportionally is  \(\frac{1}{g}\).

Answer:

24

Step-by-step explanation:

2b = b+24

2b-b = 24

b = 24

The simplified form of the expression -6g(3g+2) is option (D) \(-18g^2-12g\)

The expression is

-6g(3g+2)

The distributive property states that the multiplying the sum of two or more variables by a number will give the same answer as multiplying each variables individually by the number and then adding the products together.

The distributive property of addition is

A(B + C) = AB + AC

The distributive property of subtraction is

A(B - C) = AB - AC

Here the expression is

-6g(3g+2)

Apply the distributive property in the expression

-6g(3g+2) = (-6g) ×3g + (-6g)×2

Multiply it

= \(-18g^2-12g\)

Hence, the simplified form of the expression -6g(3g+2) is option (D) \(-18g^2-12g\)

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Answer:

−18g^2−12g

Step-by-step explanation:

got it right on the quiz

The given function y = sec⁻¹(x³) is differentiated as dy/dx = 3x/√(x² - 1).

The differentiation of a function is defined as rate of change of its value at a point. It can be written as f'(x) = Lim h --> 0 (f(x + h) - f(x)) /(x + h - x).

Its geometric meaning is the slope of tangent of the function at a given point.

The given function is as below,

y = sec⁻¹(x³)

The given function is a composite function of sec⁻¹x and x³.

In order to differentiate it, first differentiate x³ and then sec⁻¹x as follows,

dx³/dx = 3x²

And, dsec⁻¹x /dx = 1/x√(x² - 1)

Now, differentiation of sec⁻¹(x³) is given as,

d sec⁻¹(x³)/dx = 3x²/(x√(x² - 1))

                      = 3x/√(x² - 1)

Hence, the differentiation of the given function is 3x/√(x² - 1).

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Answer:

it is a

Step-by-step explanation:

Answer:

  3

Step-by-step explanation:

Those wearing a shirt of another color are ...

  1 - 5/8 -1/4 = 8/8 -5/8 -2/8 = 1/8

of the total number of students in the classroom

  (1/8)×(24 students) = 3 students . . . . wearing another color

_____

Alternate solution

With the given information, you know ...

  (5/8)(24) = 15 . . . students wear blue

  (1/4)(24) = 6 . . . . students wear white

  24 -15 -6 = 3 . . . students wear another color

The percentage change in GDP is 2.04%

Percentage Change is the difference coming after subtracting the old value from the new value and then divide by the old value and the final answer will be multiplied by 100 to show it as a percentage. Generally, to convert a fraction into a percent, we multiply it by 100.

The formula of percentage change is given as

Percentage change =[ (New increase - old value) / old value] * 100

Percentage change = [(14.72 - 14.42) / 14.72] * 100

Percentage change = 2.04%

In this case, there is a percentage decrease of 2.04%

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Using compound interest, it is found that she will earn $23 in interest during the 18-month period.

The amount of money earned, in compound interest, after t years, is given by:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

In which:

The parameters in this problem are given as follows:

\(P = 1200, r = 0.0125, n = 12, t = 1.5\).

The amount of money at the end of the 18 months will be of:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

\(A(t) = 1200\left(1 + \frac{0.0125}{12}\right)^{12(1.5)}\)

A(t) = $1,223.

The amount of interest earned is:

I = $1,223 - $1,200 = $23.

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The rewritten  statement : "It is not the case that there exists an x for which P(x) and Q(x) are true, and for all y, if R(y) is true, then P(y) is true."

The symbolic logic statement: ¬(∃x)(P(x) ∧ Q(x)) ∧ (∀y)(R(y) → P(y)).

The statement can be translated as: "There does not exist an x such that P(x) and Q(x) hold true, and for all y, if R(y) is true, then P(y) is true."

Potential ambiguities in this statement can arise from the unclear precedence of logical operators, specifically the negation operator "¬" in relation to the existential quantifier "∃".

To eliminate ambiguities while maintaining the original meaning, we can add parentheses to make the precedence explicit: (¬(∃x)(P(x) ∧ Q(x))) ∧ (∀y)(R(y) → P(y)).

This ensures that the negation applies only to the existential quantifier, not to the entire conjunction.

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Answer:

B. The second graph

Step-by-step explanation:

got the answer from edge

Proved that, sin⁴x-cos⁴x/ sin²x-cos²x = 1​.

Here, we have,

given that,

the LHS is:

sin⁴x-cos⁴x/ sin²x-cos²x

now, we know that,

sin²x+cos²x = 1

and, we know that,

a² - b² = (a+b) (a-b)

so, we get,

sin⁴x-cos⁴x/ sin²x-cos²x

= (sin²x+cos²x) (sin²x-cos²x ) / sin²x-cos²x

=(sin²x+cos²x)

=1

= RHS

Hence, Proved that, sin⁴x-cos⁴x/ sin²x-cos²x = 1​

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gbaijwghwugaggaufgwhhsuhwkhsiw

Answer: Triangle D'E'F' is larger than triangle DEF, because the scale factor is greater than 1.

Step-by-step explanation:

The dilation rule (x, y) → (2.5x, 2.5y) means that the x-coordinates and y-coordinates of each point in triangle DEF are multiplied by 2.5. This means that the distance between any two points in triangle D'E'F' will be 2.5 times the distance between the corresponding two points in triangle DEF.

Since 2.5 is greater than 1, the scale factor is greater than 1. Therefore, triangle D'E'F' is larger than triangle DEF.

Option (c) correctly states that triangle D'E'F' is larger than triangle DEF and is the correct answer.

Triangle D'E'F is smaller than triangle DEF, because the scale factor is less than 1 which is true. The correct option is A.

Three coordinates—x, y, and R—make up this system. It's simply a binary 0 or 1 because the x, y, and R coordinates identify the rhombus you're in and the R coordinate indicates whether you're in the lower-left triangular half of the rhombus or the upper-right one.

The given dilation rule (0.25x, 0.25y) indicates that each coordinate of triangle DEF is multiplied by 0.25, resulting in triangle D'E'F. Since the scale factor is less than 1, the resulting image will be smaller than the original triangle. Therefore, we can conclude that triangle D'E'F is a smaller image of triangle DEF.

Thus, the ideal selection is option A.

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Answer:

35/100

Step-by-step explanation:

You have 12% of horses (10÷84=0.1190 and 0.1190 = 12%)

You have 54% of sheep (54÷84=0.535 and 0.535=54%)

Subtract the amount of Sheep and Horses for the total amount of animals

84-(10+54)

You have 35% of cows (29÷84=0.345 and 0.345=35%)

35% to a fraction is 35/100 (simplified version 7/20)

I hope this helps (:

Answer:

29/84

There is 84 animals in total. That is the bottom half.

Ten you add 10 and 45 which equals to 55.

Subtract 55 from 84 which equals to 29.

So the answer is 29/84.

Answer:

1. b_ 2. a_ 3. c_ 4. d

Step-by-step explanation:

1 is b mainly because it is marked that way. Your picture doesn't show all of d so not really sure about it, but I used the process of elimination. Picture c is side angle side b/c of the vertical angles.

Approximately 37.5% of the data are greater than 28, 33.3% of the data are less than 23, 91.7% of the data are greater than 17.5, and 62.5% of the data are between 17.5 and 28.

To answer the questions, we can analyze the given data set.

First, let's count the number of data points that satisfy each condition:

Greater than 28:

There are 9 data points greater than 28 (29, 29, 29, 30, 29, 29, 28, 28, 28).

Less than 23:

There are 8 data points less than 23 (20, 18, 15, 17, 17, 15, 17, 19).

Greater than 17.5:

There are 22 data points greater than 17.5.

Between 17.5 and 28:

There are 15 data points between 17.5 and 28.

Now, let's calculate the approximate percentage for each condition:

Percent greater than 28:

The total number of data points is 24. Approximately, 9 out of 24 data points are greater than 28.

Percentage =\((9 / 24) \times 100 = 37.5\)%.

Percent less than 23:

Approximately, 8 out of 24 data points are less than 23.

Percentage = \((8 / 24) \times 100 = 33.3\)%.

Percent greater than 17.5:

Approximately, 22 out of 24 data points are greater than 17.5.

Percentage = \((22 / 24) \times 100 = 91.7\)%.

Percent between 17.5 and 28:

Approximately, 15 out of 24 data points are between 17.5 and 28.

Percentage = \((15 / 24) \times 100 = 62.5\)%.

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Answer: question

Step-by-step explanation: answer

a) \(\frac{(x+1)^{2}}{3^{2}}-\frac{(y+2)^{2}}{2^{2}} = 1\).

b) (h, k) = (-1, -2).

c) F₁ (x, y) = (-1 - √13, -2), F₂ (x, y) = (-1 + √13, -2).

d) y = ±2 · (x + 1) / 3 - 2.

e) See the image attached below.

In this question we must analyze the general equation of a hyperbola  and derive all the required information by algebraic and graphic means. All this information is derived from the standard equation of the hyperbola, which is presented below:

\(\frac{(x-h)^{2}}{a^{2}}-\frac{(y-k)^{2}}{b^{2}} = 1\)   (1)

Where:

The foci are located at the following two points: \(F_{1} (x, y) = (h - c, k)\), \(F_{2} (x,y) = (h + c, k)\).

Where \(c = \sqrt{a^{2}+b^{2}}\).

And the asymptotes of the hyperbola are described by the following formulas:

y₁ = b · (x - h)  / a + k   (2)

y₂ = - b · (x - h) / a + k   (3)

a) We transform the general equation into its standard form:

The standard equation of the hiperbola is \(\frac{(x+1)^{2}}{3^{2}}-\frac{(y+2)^{2}}{2^{2}} = 1\). \(\blacksquare\)

b) From the result found in a) we conclude that the center of the hyperbola is (h, k) = (-1, -2).

c) The foci of the hyperbola are located at the following two points:

\(c = \sqrt{3^{2}+2^{2}}\)  

\(c = \sqrt{13}\)

F₁ (x, y) = (-1 - √13, -2), F₂ (x, y) = (-1 + √13, -2)

The foci of the hyperbola are F₁ (x, y) = (-1 - √13, -2) and F₂ (x, y) = (-1 + √13, -2). \(\blacksquare\)

d) And the asymptotes of the hyperbola are presented below:

y₁ = 2 · x / 3   (2)

y₂ = - 2 · x / 3   (3)

The asymptotes of the hyperbola are y₁ = 2 · (x + 1) / 3 - 2 and y₂ = - 2 · (x + 1) / 3 - 2. \(\blacksquare\)

e) The graph of the hyperbola and all its characteristics are presented by means of graphing tool. The result is presented in the image attached below.

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Answer:

The equation of the hyperbola = (x + 1)^2/3^2 - (y + 2)^2/2^2 = 1

The center of the hyperbola = (-1, -2) (h, k)

The vertices of the hyperbola (my assingment asked me for vertices) = (2, -2) and (-4, 2)

The asymptotes = one at y = (2x+2/3) - 2 and the other is at

y = -((2x+2/3) -2)).

Step-by-step explanation:

For the graphing part plug the equation into desm0s and the asymptote equation. For the guiding box part, you use the B variable. Since b = 2 in this problem, you count up two spaces from the center (-1,-2) and then down two spaces. These will be the top and bottom of your guiding box. Then use your vertices as the sides and make a box that connects.

Good luck!

Answer:

7.21+4.2

for 4.2 we can write it as 4.20 because 0 has no value after decimal point

then 7.21+4.20

by adding both we get 11.41

hope it helps you mate

please mark me as brainliast

Answer:

11.41

Step-by-step explanation:

7.21

+4.2

= 11.41

Answer:

y = 7

Step-by-step explanation:

3y + (y+1) + (4y-3) = 54

3y + y + 4y + 1 - 3 = 54

8y - 2 = 54

8y = 54 + 2

8y = 56

y = 56/8

y = 7

Check:

3*7 + (7+1) + ((4*7)-3) = 54

21 + 8 + 28-3 = 54

29 + 25 = 54

9514 1404 393

Answer:

  100 ft

Step-by-step explanation:

The centroid divides each median into parts in the ratio 2 : 1. The longest part is 2/(2+1) = 2/3 of the whole length of the median.

That is, AG = 2/3AC = (2/3)(150 ft) = 100 ft.

The correct answer is John's weekly salary is $240 based on his hourly pay rate and the number of hours worked.

Let's choose the function "Weekly salary is a function of the hourly pay rate and the number of hours worked."Example: John works as a part-time employee at a grocery store. His hourly pay rate is $12, and he worked for 20 hours in a week. We can evaluate the function to find his weekly salary.

Weekly salary = Hourly pay rate * Number of hours worked

Weekly salary = $12/hour * 20 hours

Weekly salary = $240

So, John's weekly salary is $240 based on his hourly pay rate and the number of hours worked.

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The equations give values of 1/2 and -11/8

you should be aware that two equations are solved simultaneously if they are solved together

The given equations are

-8x+10y=16 .............................1

-4x-5y=13 ..................................2

Multiply equation 2 by 2 to have

-8x -10y=26

Subtract equation 1 from equation 2

-8x+10y=16

-(-8x-10y=26)  To get

The we have 20y = 10

Make y the subject of the relation

y=1/2

Put y = 1/2 in equation 1

-8x +10(1/2) = 16

-8x +5 = 16

-8x = 16-5

-8x = 11

Making x the subject of the formula we have

x=-11/8

In conclusion the values of x and y are -11/8 and 1/2 respectively

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The area of the shaded region is 3915 units².

We have,

Area of the sector.

= 13.08 units²

Now,

To find the area of an isosceles triangle with side lengths 5, 5, and 4 units, we can use Heron's formula.

Area = √[s(s - a)(s - b)(s - c)]

where s is the semi-perimeter of the triangle, calculated as:

s = (a + b + c) / 2

In this case,

The side lengths are a = 5, b = 5, and c = 4. Let's calculate the area step by step:

Calculate the semi-perimeter:

s = (5 + 5 + 4) / 2 = 14 / 2 = 7 units

Use Heron's formula to find the area:

Area = √[7(7 - 5)(7 - 5)(7 - 4)]

= √[7(2)(2)(3)]

= √[84]

≈ 9.165 units (rounded to three decimal places)

Now,

Area of the shaded region.

= Area of the sector - Area of the isosceles triangle

= 13.08 - 9.165

= 3.915 units²

Thus,

The area of the shaded region is 3915 units².

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Answer:1 and 4

Step-by-step explanation: