help pls Use the polygon tool to graph the image of the triangle with vertices (3, 1) , (3, 4) , and (1, 4) when reflected across the y-axis.
Keyboard Instructions
Initial graph state
The horizontal axis goes from -8 to 8 with ticks spaced every 1 unit(s).
The vertical axis goes from -8 to 8 with ticks spaced every 1 unit(s).
Polygon with coordinates: (3, 1), (3, 4), (1, 4), (3, 1).

Answer:

98

Step-by-step explanation:

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We have found the missing angle x = 60° using the angle sum property.

The triangle's angle sum property states that the sum of its angles can equal 180 degrees. Since a triangle has three sides, each of its vertices has an angle. Regardless of whether a triangle is acute, obtuse, or right-angled, its interior angles always sum to 180 degrees.

The triangle's angle sum property is one of the geometry's most frequently used properties. The main application of this property is in the calculation of the unknown angles. The angle sum property is used to calculate the measure of an unknown interior angle when the values of the other two angles are known.

Here,

Given that

Let the angles be y, z and x

y = 80°

z = 40°

x = ?

Using the angle sum property

Sum of the interior angle of a triangle = 180°

x + y + z = 180°

x + 80 + 40 = 180

x + 120 = 180

x = 180 - 120

x = 60°

Thus, we have found the missing angle x = 60° using the angle sum property

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You must discover the point at which the total cost of each process is equal in order to identify the crossover point between processes a and b. The sum of the fixed cost and the variable cost per unit, multiplied by the number of units, is the cost of process A as a whole. The sum of the fixed cost and the variable cost per unit, multiplied by the quantity of units, is the cost of process b as a whole.

 You can make the overall cost of each process equal to one another and solve for the number of units to determine the crossover point.

  When x is the number of units, the total cost of process an is equal to $1000 + (5 * x).

Process B has a total cost of $500 plus (7.50 * x), where x is the number of units.

When we equalize  these two expressions, we obtain:

$1000 + (5 * x) = $500 + (7.50 * x)

     2.5 *x=500

        x=200$

    So, 200$ is the crossover point between a and b.

   Therefore,200$ crossover point between process a and process  b.

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The production level that will maximize profit is 300 units

Given,

C(x) = 12000 + 400x − 3.8x^2 + 0.004x^3

P(x) = 4000-8x

First we need to find revenue function

R(x) = x.P(x) = x(4000-8x) = 4000x-8x^2

Now, we need to find marginal revenue

R'(x) = d/dx (4000x-8x^2) = 4000-16x

And now we'll find marginal cost

C'(x) = d/dx (12000+4000x-3.8x^2=0.004x^3) = 400-7.6x+0.012x^2

for maximum profit,

C'(x) = R'(x)

or, 4000-16x = 400-7.6x+0.012x^2

or, 0.012x^2+8.4x-3600 = 0

or, x^2+700x-300000=0

or, (x+1000) (x-300) = 0

so, x=-1000 or, x=300

Production level can not be negative.

So, the production level is 300 units

The production level that will maximize profit is 300 units

The production level that will maximize profit is 300 units

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The period of the function f(x) = cos 2x is π

A function is defined as a relation between a set of inputs having one output each.

Given is a function, f(x) = cos 2x

If we express the cosine function in the following way :

y = a cos(bx+c)+d

Then:

∣a∣ = the amplitude

2π/|b| = the period

-c/b = the phase shift

d = the vertical shift

For given function we have :

∣b∣=2

So period is :

2π/2 = π

Hence, The period is π

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Systematic Sampling is the probability sampling method involves selecting large, broad groups rather than individuals.

Systematic sampling is a type of probabilistic sampling technique that selects sample members from a larger population according to random starting points, but with regular periodic intervals. This interval, called the sampling interval, is calculated by dividing the population size by the desired sample size.

Systematic sampling is a type of probabilistic sampling technique that selects sample members from a larger population at regular periodic intervals according to random starting points. This interval, called the sampling interval, is calculated by dividing the population size by the desired sample size. Systematic sampling is considered random if the regular intervals are predetermined and the starting point is random, even though it preselects the sample population.

Systematic sampling, when performed correctly on large populations of a defined size, allows researchers, including marketing and sales professionals, to obtain representative results on large groups of people. without having to contact each individual. Example, if we select a random group of 1,000 people from a population of 50,000 by systematic sampling, we should list all potential participants and choose a starting point. When the list is created, every 50th of her on the list (starting counting from the starting point you chose) will be selected as participants because 50,000 ÷ 1,000 = 50.

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The values of angles for the intervals given are obtained as 135°,  405° and -135° respectively.

The trigonometric ratios are defined for a right angled triangle.

The example of these ratios are sin, cos, tan, cosec, sec and cot.

The trigonometric ratios are useful in determining the heights and distances of the large objects.

The given trigonometric equation is sin(θ) = √2/2.

It can be written as,

sin(θ) = √2/2

⇒ sin(θ) = 1/√2

⇒ θ = 45°

(a) The value of the angle in interval 90° < θ < 270° is given as,

⇒ 180°- θ = 180° - 45° = 135°

(b)  The value of the angle in interval 270° < θ < 450° is given as,

⇒ 360°+ θ = 360°+ 45° = 405°

(c) The value of the angle in interval -270° < θ < -90° is given as,

⇒ -180° + θ = -180° + 45° = -135°

Hence, the required values of angles for the given interval are 135°,  405° and -135° respectively.

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Yes, the point (5, 6) a vertex of the triangle.

A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle. The sum of all three angles of the triangle is equal to 180 degrees.

Given that, the sides of a triangle are formed by the x-axis, the line 3x-2y=3, and the line 5y+6x=60.

Here, 3x-2y=3 -------(I) and 6x+5y=60 -------(II)

Multiply equation (I) by 2, we get

6x-4y=6 -------(III)

Subtract equation (III) from equation (II), we get

6x+5y-6x+4y=60-6

9y=54

y=6

Substitute y=6 in equation (I), we get

3x-2(6)=3

3x=15

x=5

So, the vertex is (5, 6)

Yes, the point (5, 6) a vertex of the triangle.

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The value of (x + 4)² will be x² + 8x + 16

The value of (7x + 5y)² will be 49x² + 70xy + 25y²

The value of (4x + 5y)² will be 16x² + 40xy + 25y²

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number.

The value of (x + 4)² will be:

(x + 4)²

= (x + 4)(x + 4)

= x² + 4x + 4x + 16

= x² + 8x + 16

(7x + 5y)² will be:

= (7x + 5y)(7x + 5y)

= 49x² + 35xy + 35xy + 25y²

= 49x² + 70xy + 25y²

(4x + 5y)² will be:

= (4x + 5y)(4x + 5y)

= 16x² + 20xy + 20xy + 25y²

= 16x² + 40xy + 25y²

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A SSS (side-side-side) theorem is kind of Congruence rule where two triangles with three congruent sides. So, we can solve it by showing the congruency between two triangles.

Statement: Side-Side-Side (SSS) ,the congruence theorem states that two triangles are congruent if three of their sides are equal to the corresponding sides of the other triangle.

Proof: Given, AB = DE, BC = EF, AC = DF.

To prove: ΔABC ≅ ΔDEF.

We know that the three sides of both triangles are equal in size and length. With both triangles superimposed, DE is placed on AB, EF is placed on BC, and DF is placed on AC. That is, AB = DE, BC = EF, AC = DF. Therefore, we can say that ΔABC ≅ ΔDEF.

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=========================================================

Explanation:

Method 1

The exterior angles of any polygon always add to 360 degrees.

3x+8x+9x = 360

20x = 360

x = 360/20

x = 18

Then,

which represent the exterior angles of this triangle.

As a check: 54+144+162 = 360 which confirms we have the correct values.

The smallest exterior angle is therefore 54 degrees

---------------------

Method 2

The exterior angles 3x, 8x, and 9x have the corresponding interior angles of 180-3x, 180-8x, and 180-9x in that order.

For any triangle, the interior angles always add to 180 degrees.

angle1+angle2+angle3 = 180

(180-3x)+(180-8x)+(180-9x) = 180

540-20x = 180

-20x = 180-540

-20x = -360

x = -360/(-20)

x = 18

This then leads to 3x = 3*18 = 54 degrees as the final answer.

The number of weeks (x) when you both donate the same number of items (y) is equal to 3 weeks.

In order to write and solve a system of linear equations to describe this situation, we would assign variables to the number of weeks and number of items respectively, and then translate the word problem into algebraic equation as follows:

Since you have already donated 14 items and plan to donate 3 more each week, a linear equation which represents this situation is given by;

D = 3x + 14         ........equation 1.

Since you have already donated 8 items and plan to donate 5 more each week, a linear equation which represents this situation is given by;

D = 5x + 8         ........equation 2.

Equating equation 1 and equation 2, we have:

3x + 14 = 5x + 8

5x - 3x = 14 - 8

2x = 6

x = 6/2

x = 3 weeks.

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Extra people required is 50.

Each of the five workers should increase their efficiency to a rate of 15 sandwiches per 10 hour shift.

Proportions are defined as the concept where two or more ratios are set to be equal to each other.

Question 1 :

Number of associates = 30

Number of direct workers = 30 - 2 = 28

You work 8 hours a day and 5 days a week with two 15 minutes break or 30 minutes break per day.

Direct rate = 150 units per hour

Number of working hours in a week with break = 8 × 5 = 40 hours per week Number of working hours in a week = 7.5 hours per day × 5 days a week

                                                            = 37.5 hours per week

Units that department produce in a 40 hour week = 37.5 × 150 = 5625 units

28 people produce 5625 units in a week

Let x people produce 10,000 + 5625 = 15,625 units in a week

Using proportion,

28 : 5625 = x : 15,625

28 / 5625 = x / 15,625

x = (28 × 15,625) / 5625 = 77.78 ≈ 78

Extra people required = 78 - 28 = 50

Question 2 :

Number of sandwiches made in 10 minutes = 1

Number of sandwiches made in 10 hours = 60

5 workers are there. one worker makes 60/5 = 12 sandwiches

But Deli want number of sandwiches in 10 hours = 75

One worker should make 75/5 = 15 sandwiches instead of 12.

Number of sandwiches made in 8 minutes should be 1.

So the working efficiency on each worker should be increased and produce each one should produce 15 sandwiches in a 10 hour shift.

Hence extra people required in question 1 is 50 and efficiency of each worker in question 2 should be increased to 15 sandwiches in 10 hours shift.

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After the rotation of 270° counter-clockwise about the origin, the coordinates become A'(6, - 9).

Given is the coordinate of point as (6, 9). It is rotated by 270° counter clockwise about the origin.

After the rotation of 270° counterclockwise about the origin, the coordinates will become -

A(x, y) → A'(y, - x)

So, the coordinates will become -

A(6, 9) → A'(6, - 9)

Therefore, after the rotation of 270° counter-clockwise about the origin, the coordinates become A'(6, - 9).

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The first special case of the chain rule for the composition f o c states that the derivative of f(c(t)) is equal to f'(c(t))c'(t).

For case (a):

(f o c) (t) = f(c(t)) = f(e cos(t)) = e cos(t) sin(t)

Therefore, (f o c)' (t) = f'(c(t))c'(t) = [e cos(t) sin(t)]' (e cos(t))' = e sin(t) cos(t) (e cos(t))' = e cos(t) (-sin(t)) = -e cos2(t)

For case (d):

(f o c) (t) = f(c(t)) = f(t, -t) = t exp(-t)

Therefore,

(f o c)' (t) = f'(c(t))c'(t) = [t exp(-t)]' (t, -t)' = exp(-t) (t, -t)' = exp(-t) (1, -1) = t exp(-t) (-1) = -t exp(-t)

The first special case of the chain rule for the composition f o c states that the derivative of f(c(t)) is equal to the product of f'(c(t)) and c'(t). This means that the derivative of the composition of two functions, f and c, is equal to the product of the derivative of the outermost function and the derivative of the innermost function. To verify this for each case, we need to calculate the derivatives of both f and c, then substitute them into the equation for the derivative of the composition. For example, in case (a), we have (f o c) (t) = f(c(t)) = e cos(t) sin(t). Therefore, (f o c)' (t) = f'(c(t))c'(t) = e sin(t) cos(t) (e cos(t))' = -e cos2(t). Similarly, for case (d), we have (f o c) (t) = f(c(t)) = t exp(-t). Therefore, (f o c)' (t) = f'(c(t))c'(t) = exp(-t) (t, -t)' = -t exp(-t).

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The complete question is

Verify the first special case of the chain rule for the composition f o c in each of the cases. (a) f(x, y) .xy, c(t) (e cos(t)) (f o c) (t) '(cos (t) sin t (f o c) (t) (e e Y 2t 2t (f o (c) (t) n e (d) f(x, y) x exp(x y c (t) (t, -t) (f o c) (t) 4t 1 exp(-t ) (f o c) (t) t exp(-t )

It will take 5 months for Eduardo and Peta to weigh the same.

Eduardo weighs 120 pounds and is gaining 5 pounds each month, so after 1 month he will weigh 120 + 5 = 125 pounds.

After 2 months he will weigh 125 + 5 = 130 pounds.

This pattern continues, so after n months he will weigh 120 + 5n pounds.

Peta weighs 160 pounds and is losing 3 pounds each month, so after 1 month she will weigh 160 - 3 = 157 pounds.

After 2 months she will weigh 157 - 3 = 154 pounds.

This pattern continues, so after n months she will weigh 160 - 3n pounds.

We want to find the number of months it will take for Eduardo and Peta to weigh the same, so we set the expressions for their weights equal to each other and solve for n:

120 + 5n = 160 - 3n

8n = 40

n = 5

It will take 5 months for Eduardo and Peta to weigh the same.

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Answer:
-5, -4, 0, 6.009, 6.3

If this help please set brainliest.

The curvature of the curve is k = [tex]\sqrt{\frac{5}{(1 \:+\: 5t^2)^3}}[/tex].

The complete question is in the attachment. The parameterized curve

r(t) = t i + t² j + t²/2 k

The curvature of the curve

k = |v(t) × a(t)| ÷ |v(t)|³

k = |v(t) × a(t)| ÷ |v(t)|³

[tex]k \:=\: \frac{\sqrt{5}}{(\sqrt{1 \:+\: 5t^2})^3}[/tex]

[tex]k \:=\: \sqrt{\frac{5}{(1 \:+\: 5t^2)^3}}[/tex]

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9 f(x) dx of f(x) = 5 for x < 5 x for x ≥ 5 is  53 when x is between 0 and 9.

What is integration ?

Integration is a fundamental concept in calculus, which is used to find the area under a curve and the total change of a function. It is the reverse process of differentiation and can be used to find the original function, given its derivative.

For f(x) = 5 for x < 5, we have

∫(5dx) from 0 to 5 = 5*(5-0) = 25

For f(x) = x for x ≥ 5, we have

∫(x dx) from 5 to 9 = (1/2)x^2 from 5 to 9 = (1/2)(9^2 - 5^2) = (1/2)(81 - 25) = (1/2)(56) = 28

So the definite integral of the piecewise function is

∫(9 f(x) dx) from 0 to 9 = ∫(5dx) from 0 to 5 + ∫(x dx) from 5 to 9 = 25 + 28 = 53,

Therefore , 9 f(x) dx of f(x) = 5 for x < 5 x for x ≥ 5 is  53 when x is between 0 and 9.

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The probability of getting a 3 on the first roll and a 4 on the second roll when a the probability of getting a 3 on the first roll and a 4 on the second roll is 1/36.

Therefore the answer is 1/36.

The probability of rolling a 3 on the first roll and a 4 on the second roll is the product of the probabilities of rolling each number separately.

Since the number cube is fair, the probability of rolling any number on a single roll is 1/6. Therefore, the probability of rolling a 3 on the first roll and a 4 on the second roll is

(1/6) × (1/6) = 1/36.

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The probability of rolling a 3 on the first roll and a 4 on the second roll is 1/36, or approximately 0.028.

This is because the probability of rolling any particular number on a 6-sided number cube is 1/6. Therefore, the probability of rolling a 3 on the first roll is 1/6, and the probability of rolling a 4 on the second roll is also 1/6. Since these events are independent (rolling a 3 on the first roll does not affect the probability of rolling a 4 on the second roll), you can multiply the probabilities of each event to find the probability of both events occurring.

Therefore, the probability of rolling a 3 on the first roll and a 4 on the second roll is (1/6) * (1/6) = 1/36. This can also be written as a decimal as 0.028.

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Answer:angles of 720˚ has 1+5=6 sides.

Step-by-step explanation:

7 dollar because I don't know

Part 1: A = 0, B = 2, C = 3, D = 0, E = -2

Part 2: The derivative f'(3) is 6.

Part 3: The equation of the tangent line to the curve y = f(x) at x = 3 is y = 6x – 15.

This equation of the tangent line can be found by substituting x = 3 into the simplified difference quotient expression C + Dh + Eh2 , and then taking the limit as h approaches 0.

This expression can then be rearranged to give the equation of the line, which is y = 6x – 15. The equation of the tangent line gives the slope of the line at the given point, in this case x = 3. The slope of the line is 6, which is the same as the derivative of the function at the given point.

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Since Larry needs 3 bags of mulch and each bag costs $3.25, the total cost of the mulch will be 3 × $3.25 = 9.75$

Larry is only ready to put mulch on 3/4 of his rose garden, so he will need 3/4 × $9.75 = 7.31$

answer: 7.31$

Answer:

To find the inverse of a function, you need to switch the roles of the x and y variables. So the inverse of ƒ(x) = 4x² for x ≤ 0 is written as ƒ^(-1)(y) = ?.

To find the inverse function, we can solve for x in terms of y:

4x² = y

x² = y/4

x = √(y/4)

So the inverse of ƒ(x) = 4x² for x ≤ 0 is ƒ^(-1)(y) = √(y/4). Note that this inverse function is only defined for y ≤ 0, since the original function is only defined for x ≤ 0.

On solving the provided question, we can say that -- the value of the  function will be f(x) = [tex]x^{-2}[/tex]

The topic of numbers, formulae and associated structures, forms and the areas where they exist, quantities and their variations, and spaces where they exist are all included in the field of mathematics. An association between a collection of inputs, each of which has an output, is known as a function. A function is, to put it simply, a relationship between inputs and outputs, where each input has a single, specific outcome. A domain and a codomain, or scope, are assigned to each function. Typically, f is used to represent functions (x). input is x. Four different sorts of functions are available. Based on the following items: One-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions.

here,

we have the function

x^2 + 37xy + y^5

the answer is =  [tex]x^{-2}[/tex]

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SSS - Side - Side - Side

SAS - Side - Angle - Side

ASA - Angle - Side - Angle

AAS - Angle - Angle - Side

The above theorems can be used to compare two triangles.

SSS, which stands for "side, side, side," represents two triangles having identical angles on each of their three sides. Two triangles are said to be congruent if their third sides coincide with those of another triangle.

That is what the SAS regulation says. The triangles are congruent if the two sides and included angle of one triangle match the two sides and included angle of the other triangle. Any angle that may be made by two particular sides is regarded as an included angle.

A triangle is comparable to another if its two matching angles are congruent, according to the AAA postulate of Euclidean geometry. The AAA postulate is derived from the observation that the total internal angle of a triangle is always equal to 180°.

While in case of ASA the angle - side and another angle of first triangle is equal to the corresponding angle - side - angle of other triangle.

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SSS, SAS, ASA, and AAS are four types of triangle congruence.

SSS (Side-Side-Side) is the congruence of three sides of a triangle. This means that all three sides of the triangle have the same length. To prove SSS congruence, you need to show that the corresponding sides of the two triangles have the same length. This can be done by calculating the length of each side and comparing them.

SAS (Side-Angle-Side) is the congruence of two sides and the included angle of a triangle. This means that the two sides of the triangles must have the same length, and the angles between those two sides must also be the same. To prove SAS congruence, you need to show that the corresponding sides of the two triangles have the same length, and that the angles between those two sides are also the same.

ASA (Angle-Side-Angle) is the congruence of two angles and the included side of a triangle. This means that the two angles of the triangles must have the same measure, and the side between those two angles must also be the same length. To prove ASA congruence, you need to show that the corresponding angles of the two triangles have the same measure and that the side between those two angles is also the same length.

AAS (Angle-Angle-Side) is the congruence of two angles and a non-included side of a triangle. This means that two angles of the triangles must have the same measure, and the side not included between those two angles must also be the same length. To prove AAS congruence, you need to show that the corresponding angles of the two triangles have the same measure, and that the side not included between those two angles is also the same length.

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By using properties for quotients we will see that:

a^v = 1

Only if v = 0.

We need to remember two properties.

First, the quotient of two equal numbers is always equal to 1. So for any real number a different than zero, we can write:

a/a = 1

The second property is for the quotient of powers with the same base, we can write:

a^n/a^m = a^{n - m}

Now, notice that if we take the quotient of two numbers with the same exponent, we will get:

(a^n)/(a^n) = a^{n - n} = a^0

And that is the quotient between two equal numbers, then that is equal to 1, so:

a^0 = 1

For any real number a different than zero.

Then the value of v such that:

a^v = 1

must be v = 0.

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The equation of the parabola shown with its focus on this graph is D. y = [tex]-\frac{1}{12} \text x^2[/tex] + 1.

A parabola is a mirror-symmetrical, roughly U-shaped plane curve that is used in mathematics. It corresponds to a number of mathematical explanations that appear to differ on the surface but which all define the same curves.

A line and a point (the focus) are two ways to describe a parabola (the directrix). Not the directrix is the main focus. The location of points in that plane that are equally spaced apart from the directrix and the focus is known as the parabola.

Conic sections, which are formed when a right circular conical surface and a plane perpendicular to another plane that is tangential to the conical surface intersect, are another way to describe parabolas.

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