Ella is playing hide and seek with Dante and Mary. Dante is hiding 9 meters south of Ella, and Mary is hiding due east of Dante. If Ella is 15 meters from Mary, how far apart are Dante and Mary?

The Cartesian equation of the curve is y = 0. This is a horizontal line at y = 0.

To find the Cartesian equation of the curve, we need to eliminate the parameter θ from the parametric equations.

First, let's rearrange the first equation to isolate θ:
2x = cotθ - cscθ
2x + cscθ = cotθ
cscθ - cotθ = -2x
1/(sinθ) - 1/(tanθ) = -2x
1/(sinθ) - (cosθ)/(sinθ) = -2x
(cosθ)/(sinθ) = 1/(sinθ) + 2x
cosθ = 1 + 2x*sinθ

Now, let's rearrange the second equation to isolate θ:
4y = 2cscθ - 2cotθ
2y = cscθ - cotθ
2y + cotθ = cscθ
cotθ - cscθ = -2y
1/(tanθ) - 1/(sinθ) = -2y
(cosθ)/(sinθ) - 1/(sinθ) = -2y
(cosθ)/(sinθ) = 1/(sinθ) - 2y
cosθ = 1 - 2y*sinθ

Now we can set the two equations equal to each other and solve for sinθ:
1 + 2x*sinθ = 1 - 2y*sinθ
4x*sinθ = -4y*sinθ
sinθ = -4y/4x
sinθ = -y/x

Finally, we can use the Pythagorean identity, sin^2θ + cos^2θ = 1, to find the Cartesian equation:
(-y/x)^2 + cos^2θ = 1
y^2/x^2 + cos^2θ = 1
cos^2θ = 1 - y^2/x^2
cosθ = √(1 - y^2/x^2)

Substituting this back into one of the original equations, we get:
1 + 2x*sinθ = 1 - 2y*sinθ
1 + 2x*(-y/x) = 1 - 2y*(-y/x)
1 - 2y^2/x = 1 + 2y^2/x
4y^2/x = 0
y^2 = 0
y = 0

So the Cartesian equation of the curve is y = 0. This is a horizontal line at y = 0.

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The given function, f(x)=-3x^(2)+4, has three types of symmetry: 1. Symmetry with respect to the y-axis (even symmetry).
2. Symmetry with respect to the x-axis (odd symmetry). 3. Symmetry with respect to the origin (rotational symmetry)

To check for symmetry with respect to the y-axis, we can substitute (-x) for x in the function and see if it is equal to the original function.

f(-x)=-3(-x)^(2)+4=-3x^(2)+4

Since f(-x)=f(x), the function is symmetric with respect to the y-axis.

To check for symmetry with respect to the x-axis, we can substitute (-y) for y in the function and see if it is equal to the original function.
-3x^(2)+4=-y
y=-3x^(2)-4

Since this is not equal to the original function, the function is not symmetric with respect to the x-axis.

To check for symmetry with respect to the origin, we can substitute (-x) for x and (-y) for y in the function and see if it is equal to the original function.
-3(-x)^(2)+4=-y
y=-3x^(2)-4

Since this is not equal to the original function, the function is not symmetric with respect to the origin.

Therefore, the given function f(x)=-3x^(2)+4 has symmetry with respect to the y-axis, but does not have symmetry with respect to the x-axis or the origin.

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Answer:

6969696969696969695969696966969696969696969699६9६9६9६959596869494982285959585868586868696959695968684828282828३8474747474848475757718१883757474839485747747474747474747474747484858384848485858587575757585848484848585857494857585958584858585858685969686(696066969686868696960

The probability of observing 2 heads is 1/4, the probability of observing 1 head is 2/4, and the probability of observing 0 heads is 1/4.

The question is asking what the probability of getting two heads (x=2) and one head (x=1) when tossing a coin.

The probability of getting two heads is P(x=2) = 1/4 and the probability of getting one head is P(x=1) = 2/4.

It is important to remember that the sum of all the probabilities in an experiment must equal 1.

In this case, P(x=2) + P(x=1) = 1/4 + 2/4 = 3/4. This means that the probability of observing 0 heads, represented as P(x=0), must be equal to 1/4 in order for the sum of all the probabilities to equal 1.

In conclusion, the variable x is used to represent the number of heads observed in a coin toss experiment, and the probabilities of observing different numbers of heads are given as fractions.

The probability of observing 2 heads is 1/4, the probability of observing 1 head is 2/4, and the probability of observing 0 heads is 1/4.

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7 / 15  is the probability that it will be orange. A marble drawing is a separate action. In other words, the results of drawing a marble will not be influenced by each other.

We must ascertain the sample space, the number of occurrences in the sample space, and the number of successful outcomes in order to calculate the necessary probability. The colour determines every consequence that can occur when drawing a marble. The total number of marbles is 15, including 7 orange and 8 blue. Hence, there are 7+5=15 elements in the sample space.

As we are interested in drawing an orange marble and returning the orange marble to the urn after each drawing, the number of favourable events, in this case, is 7. Due to their independence, past drawings won't have an impact on the most recent ones. The likelihood of an event P(A) = total outcomes / favourable outcomes can be used to define A as the ratio of the number of favourable outcomes to the number of total outcomes in the sample space.

Hence, the following is true for the event P(A₀)= total outcomes / favorable outcomes 7 / 15

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The factors which would be considered while constructing a road for a steep slope are the terrain of the area, the estimated daily traffic, minimum and maximum sight distance, and the design speed.

Constructing roads on a steep slope is a challenge for every civil engineer. It is because such slopes which are possibly found in hilly areas have less access to main land from where the resources/ material for construction are to be transported and also need specific calculations to estimate maximum durability of the roads and also prevent accidents which might occur due to steep slopes.

Hence, an engineer has to keep in mind several factors which can help to reduce the accident cases, provide road safety and better connectivity with major areas.  It is essential that roadway engineers design roads that allow drivers to travel at the right speed. Topography determines the terrain, the different gradient and the construction cost. Every roadway should be built with illuminated raised pavement markings for facilitating safe travel during the night.

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By applying synthetic division concept, it can be concluded that if f(v) = 8v⁴ + 34v³ - 26v² + 21v + 11, then, f(-5) = 6.

Synthetic division is a shorthand way of dividing polynomials where we can divide the coefficients of the polynomial by omitting variables and exponents. As a result, we get the coefficient of the quotient and the remainder.

Polynomial remainder theorem states that the value of p in argument b is equal to the remainder of the polynomial division p(x) / (x - b). Specifically, p(x) is divided by x - b with a remainder of zero if, and only if, b is a root of p.

We have the following polynomial:

f(v) = 8v⁴ + 34v³ - 26v² + 21v + 11

To find f(-5) using synthetic division, we will divide the polynomial f(v) by (z + 5). The steps are as follows:

1. Put the coefficients in a row and multiply the outside coefficient by the divisor: 8(-5)= -40.

2. Add the inside coefficient to the product from the previous step: -40 + 34 = -6.

3. Multiply the result from the previous step by the divisor: -6(-5) = 30.

4. Add the next coefficient to the product from the previous step: 30 - 26 = 4.

5. Multiply the result from the previous step by the divisor: 4(-5) = -20.

6. Add the next coefficient to the product from the previous step: -20 + 21 = 1.

7. Multiply the result from the previous step by the divisor: 1(-5) = -5.

8. Add the last coefficient to the product from the previous step: -5 + 11 = 6.

The final result of the synthetic division is 6, so the answer to the question is f(-5) = 6.

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Answer:

y = -43x - 175

Step-by-step explanation:

Slope-intercept form is y = mx + b

m = -43

x = -4

y = -3

-3 = -43(-4) + b

b + 172 = -3

b = -3 - 172 = -175

=> y = -43x - 175

Three points that are equivalent to the polar point (7,40°) are (7,400°), (7,-320°), and (7,760°). These points are equivalent because they all have the same magnitude of 7, but their angles differ by multiples of 360°.

In polar form, these points are written as:
- (7,400°) = 7cis(400°)
- (7,-320°) = 7cis(-320°)
- (7,760°) = 7cis(760°)

These points are equivalent because the angle in polar coordinates is measured modulo 360°. This means that any angle that differs by a multiple of 360° will be equivalent. For example, 40° is equivalent to 400° because 400° - 40° = 360°. Similarly, -320° is equivalent to 40° because -320° + 360° = 40°, and 760° is equivalent to 40° because 760° - 720° = 40°.

In conclusion, the three points that are equivalent to the polar point (7,40°) are (7,400°), (7,-320°), and (7,760°), and they are written in polar form as 7cis(400°), 7cis(-320°), and 7cis(760°).

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Answer:

410=50x+10

Step-by-step explanation:

your total is 410 so to get there you have to know the number of nights which is x. the 10 is a one time fee so you only need that once and not per night.

The value of p(3) is p(3)=12.

Here, we have,

Synthetic division :

It is a shorthand method of dividing polynomials for the special case of dividing by a linear factor whose leading coefficient is 1.

The given function is,

p(z)=8z⁴-17z³-20z²-4z+15                  

We have to find  p(3)  

Substitute z= 3 in above function.

p(3)=8×3⁴-17×3³-20×3²-4×3+15                

     =12      

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The value of function h(x)=5 at x tends to [tex]2^{+}[/tex] will be 5.

In mathematics, a functional equation is, in the broadest sense, an equation in which one or more functions appear as variable. A functional equation, however, is frequently used in a more narrow sense, where it refers to an equation that connects many values of the same function. For instance, the logarithmic functional equation effectively describes the logarithm functions.

log⁡(x×y)=log⁡(x)+log⁡(y).

lim h(x)=5 at x tends to [tex]2^{+}[/tex]

Given function is constant.

Value of function at x tends to [tex]2^{+}[/tex]will be 5

Hence, the value of h(x)=5 at x tends to [tex]2^{+}[/tex] will be 5

Graph of the given function is attached below;

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The correct statement regarding the domain and the range of the quadratic function are given as follows:

D. The domain is all real numbers, the range is y ≥ -4.

Hence, on a graph, the values are given as follows:

Meaning that option D is correct.

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Answer:

E(2,-4), F(8,0), and G(5,3).

Step-by-step explanation:

Reflection in the y-axis means the signs of the x-coordinates should be flipped.

Answer:

Answer A

Step-by-step explanation:

I know that you already have the answer, but I wanted to show you a picture.

The domain of a function is the set of all possible input values (x) for which the function is defined.

The range of a function is the set of all possible output values (f(x)) that the function can produce.

For the given function f(x) = 2^(x+1), the domain includes all real numbers because we can substitute any real number for x and obtain a valid output.

To find the range, we can examine the behavior of the function as x approaches positive and negative infinity. As x approaches negative infinity, the exponent (x+1) becomes very large negative number, and 2^(x+1) approaches zero. As x approaches positive infinity, the exponent (x+1) becomes very large positive number, and 2^(x+1) approaches infinity. Therefore, the range of the function is (0, infinity).

So, the domain is (-infinity, infinity) and the range is (0, infinity).

For the given square, m∠OKL=45° and m∠MOL=90°.

A square is a regular quadrilateral in Euclidean mathematics because it has four equal sides and four equal angles (right angles, 90-degree angles). It can also be explained as a rectangle with two adjacent sides that are of identical length. It is the only regular polygon whose diagonals are all the same length and whose internal, central, and exterior angles are all equal (90°).

In mathematics, 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 sections. An angle bisector is a beam that divides an angle into two identical segments of the same length.

Angle bisector points are equally spaced from both angle lines.

Any angle, including acute, obtuse, and right angles, can have an angle bisector traced to it.

In the given square,

The diagonals NL and KM are angle bisectors of ∠K, ∠L, ∠M and ∠N.

Therefore, ∠OKL= 90/2

                  ∠OKL=45°

We know that, in a square, diagonals are equal and bisect each other at right angles.

Therefore, ∠MOL=90°

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Answer:

acute

Step-by-step explanation:

9 is bigger than 6

12 is bigger than 9

therefore all the angles will be smaller than a right angle

this makes the triangle acute

[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{20})\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{22}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{22}-\stackrel{y1}{20}}}{\underset{\textit{\large run}} {\underset{x_2}{-1}-\underset{x_1}{(-2)}}} \implies \cfrac{2}{-1 +2} \implies \cfrac{ 2 }{ 1 } \implies 2[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{20}=\stackrel{m}{ 2}(x-\stackrel{x_1}{(-2)}) \implies y -20 = 2 ( x +2) \\\\\\ y-2=2x+4\implies {\Large \begin{array}{llll} \end{array}} y=2x+6\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

The mode of the set {2, 5, 6, 8, 9, 11, 15} is the number that appears most frequently in the set. In this case, all of the numbers appear only once, so there is no mode.

The mode of a set of numbers is the value that appears most frequently in the set. To find the mode of the set {2, 5, 6, 8, 9, 11, 15}, we need to count how many times each number appears and then determine which number appears most frequently.

From the set, we can see that no number appears more than once. Therefore, there is no single number that appears most frequently and we cannot determine a mode for this set.

In some cases, a set of numbers may have multiple modes if two or more numbers appear with the same frequency. For example, the set {1, 2, 2, 3, 3, 3, 4, 5, 5} has two modes, 2 and 3, since both of these numbers appear three times in the set.

However, in the case of the set {2, 5, 6, 8, 9, 11, 15}, there are no repeating numbers, so there is no mode.

In conclusion, the mode of the set {2, 5, 6, 8, 9, 11, 15} is undefined as there are no repeating numbers in the set.

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The symbols, in accordance with the provided assertion, are 27 ÷ 3 + 5 × 2 = 19

A object must imply a meaning that is distinct from its true definition in order to be referred to as a symbol; a symbol is a thing that transcends class or type. A emblem might signify several different things.

The triple bar, also known as the tribar, or, is a sign that denotes the equality of two distinct objects and has a variety of context-dependent meanings. Logic and arithmetic are its two primary applications. It looks like a third line attached to an equals symbol (=).

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The solutions to the given polynomial equation are x = (1 + √5)/(3) and x = (1 - √5)/(3).

To solve the given polynomial equation using the quadratic formula, we need to first identify the values of a, b, and c. In this case, a = -9, b = 6, and c = 4. The quadratic formula is given by:

x = (-b ± √(b^(2) - 4ac))/(2a)

Plugging in the values of a, b, and c into the formula, we get:

x = (-(6) ± √((6)^(2) - 4(-9)(4)))/(2(-9))

Simplifying the equation, we get:

x = (-6 ± √(36 + 144))/(-18)

x = (-6 ± √180)/(-18)

x = (-6 ± 6√5)/(-18)

x = (1 ± √5)/(3)

Therefore, the solutions to the given polynomial equation are x = (1 + √5)/(3) and x = (1 - √5)/(3).

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The equation with a solution of -7 is x^2 = 49

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

The list of options and x = -7

To check which equation has a solution of x = -7, we can simply substitute -7 for x in each equation and see which one is true.

Hence, the equation x^2 = 49 has x = -7 as a solution.

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1. HP price for Susie is R 282600 and David is R 179300

2. The difference between the total price paid by Susie and David  is R 103300

3. The interest that Susie and David have to pay as a percentage of the cash price​ is 117.38% and 37.92%

The HP price, also known as the hire purchase price, is the total amount that a buyer pays for a product when purchasing it through a hire purchase agreement.

It includes the cash price of the product plus any interest and fees charged by the lender.

Here we have

3.1.1, For Susie:

The cash price of the car is R 130000.

She pays a 10% deposit, which is:

= [10/100] × 130000 = R 13000

=> HP price =  the cash price - the deposit

=>  130000 -  13000 = R 117000

She will pay monthly installments of R 4600 for 3 years,

which is 36 months.

Therefore, the total amount she will pay is:

36 x 4600 = R 165600

Therefore, the total amount she will pay is R 165600

The HP price for Susie is,  

117000 + 165600 = R 282600

For David:

The cash price of the car is R 130000. He pays a 35% deposit, which is:

=> [ 35/100] × 130000 = R 45500

The HP price = 130000 - 45500 = 84500

He will pay monthly installments of R 3950 for 2 years, which is 24 months. Therefore, the total amount he will pay is:

24 × 3950 = 94800

The HP price for David is, therefore:

=> 84500 + 94800 = R 179300

3.1.2, The difference between the total price paid by Susie and by David  

=  282600 - 179300 = R 103300

3.1.3

For Susie:

The total interest she has to pay is the difference between the HP price and the cash price, which is:

=> 282600 - 130000 = R 152600

The interest rate as a percentage of the cash price is:

=> (152600/130000) × 100% = 117.38%

For David:

The total interest he has to pay is the difference between the HP price and the cash price, which is:

=> 179 300 - 130 000 = R 49 300

The interest rate as a percentage of the cash price is:

=> (49 300/130000) × 100% = 37.92%

Therefore,

1. HP price for Susie is R 282600 and David is R 179300

2. The difference between the total price paid by Susie and David  is R 103300

3. The interest that Susie and David have to pay as a percentage of the cash price​ is 117.38% and 37.92%

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The measure of width of the computer is 75.89 inches.

Ratio is defined as the relationship between two quantities where it tells how much one quantity is contained in the other.

The ratio of a and b is denoted as a : b.

Given that,

Ratio of diagonal to length of a rectangular computer = 13 : 7

This means that,

If diagonal = 13k and length = 7k for some constant k.

Given Actual length = 18 inches.

3k = 18

k = 18/3 = 6

So Diagonal length = 13 × 6 = 78 inches

We know that, the length, width and diagonal of a rectangle form a right angled triangle.

Let width of the rectangular computer be x.

Using Pythagorean Theorem,

(Length)² + (Width)² = (Diagonal)²

18² + x² = 78²

x² = 78² - 18²

x² = 5760

x = 75.89 inches.

Hence the measure of width is 75.89 inches.

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The mark down rate for the dress originally tagged at Php 5,220 but now being sold at Php 4,900 is 6.13%.

To calculate the mark down rate, use the formula:

Mark down rate = (Original Price - Discounted Price) / Original Price

Plugging in the numbers:

Mark down rate = (5,220 - 4,900) / 5,220 = 0.0613

To convert to a percentage, multiply 0.062 by 100 and you will get 6.13%.

Therefore, the mark down rate for the dress is 6.13%.

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The formula for the exponential function passing through the points (-2,768) and (2, 3) is:

[tex]y = 48 \times ((3/768)^{1/4})^x[/tex]

We have,

To find a formula for the exponential function passing through the points (-2, 768) and (2, 3), we can use the general form of an exponential function: y = a x [tex]b^x[/tex], where "a" is the initial value or y-intercept, and "b" is the base of the exponential function.

Let's start with the first point (-2, 768).

Plugging in the values, we have:

768 = a x [tex]b^{-2}[/tex]

Next, let's consider the second point (2, 3).

Plugging in the values, we have:

3 = a x b²

Now we have a system of equations:

768 = a x [tex]b^{-2}[/tex]

3 = a x b²

To solve this system, we can divide the second equation by the first equation:

3/768 = (a x b²) / (a x [tex]b^{-2}[/tex])

Simplifying further:

3/768 = [tex]b^4[/tex]

Taking the fourth root of both sides:

[tex](b^4)^{1/4} = (3/768)^{1/4}\\b = (3/768)^{1/4}[/tex]

Now we can substitute the value of b back into either of the original equations to solve for a.

Let's use the first equation:

[tex]768 = a \times b^{-2}[/tex]

Substituting [tex]b = (3/768)^{1/4}:[/tex]

[tex]768 = a \times ((3/768)^{1/4})^{-2}[/tex]

Simplifying:

[tex]768 = a \times (3/768)^{-1/2}[/tex]

Now, we can simplify the right-hand side:

[tex]768 = a \tmes (768/3)^{1/2}[/tex]

Simplifying further:

[tex]768 = a \times (256)^{1/2}[/tex]

Taking the square root of 256:

768 = a x 16

Solving for a:

a = 768 / 16 = 48

Therefore,

The formula for the exponential function passing through the points (-2,768) and (2, 3) is:

[tex]y = 48 \times ((3/768)^{1/4})^x[/tex]

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The simplified expression is  [tex]8x^4y^4[/tex].

Simplifying an expression is just another way to say solving a math problem. When you simplify an expression, you're basically trying to write it in the simplest way possible. At the end, there shouldn't be any more adding, subtracting, multiplying, or dividing left to do. For example, take this expression: 4 + 6 + 5.

Here the given expression is

=> [tex](4x^3y^3)(2x.2y)[/tex]

=> [tex]4\times x^3\times y^3\times2x\times2y[/tex]

=> [tex]4\times2\times2\times x^3\times x \times y^3\times y[/tex]

=> 8[tex]\times x^{3+1}\times y^{3+1}[/tex]

=> [tex]8x^4y^4[/tex]

Hence the simplified expression is  [tex]8x^4y^4[/tex].

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Answer:

Trust me I guarantee you it's correct.

Step-by-step explanation:

D. 8x^5y^4

The solution to the system of equations is [tex]x = -3/4 $ and $ y = -3^{1/2}.[/tex] The solution has been obtained by using substitution method.

What is substitution method?

The substitution approach is one approach of solving equation problems. To use the substitution method, obtain an expression for one variable in terms of the second variable using one equation. Replace that variable with that expression in the second equation after that.

We are given system of equations as:

y = -2x - 5

y = 2x - 2

Now, by using the substitution method, we get

⇒-2x - 5 = 2x - 2

⇒-4x = 3

⇒x = -3 / 4

On substituting the value of x in y = 2x - 2, we get

⇒y = 2(-3/4) - 2

⇒y = (-3/2) - 2

⇒y = -7/2

Hence, the solution to the system of equations is[tex]x = -3/4 $ and $ y = -3^{1/2}.[/tex]

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Answer: why do u need help again? this is easy boy

Step-by-step explanation: