What is the measure of angle HEK in this figure?
a protractor, with segment DEF along the bottom, EH point to the 55 degree on the left, EJ to 90 degrees, EK to the 30 degrees on the right
85°
150°
95°
55°

The cosine value is given as follows:

[tex]\cos{\theta} = \frac{4\sqrt{23}}{23}[/tex]

The tangent value is given as follows:

[tex]\tan{\theta} = -\frac{\sqrt{7}}{4}[/tex]

First we must obtain the secant value, according to the identity presented as follows:

[tex]\sec^2{\theta} = 1 + \tan^{2}{\theta}[/tex]

Replacing the tangent into the expression, we have that:

[tex]\sec^2{\theta} = 1 + \frac{7}{16}[/tex]

[tex]\sec^2{\theta} = \frac{23}{16}[/tex]

[tex]\sec{\theta} = \frac{\sqrt{23}}{4}[/tex]

The secant is positive, as the angle is in the fourth quadrant, where the cosine is positive.

The cosine is then given as follows:

[tex]\cos{\theta} = \frac{1}{\sec{\theta}}[/tex]

[tex]\cos{\theta} = \frac{4}{\sqrt{23}} \times \frac{\sqrt{23}}{\sqrt{23}}[/tex]

[tex]\cos{\theta} = \frac{4\sqrt{23}}{23}[/tex]

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The given table represents a linear function with a constant rate of change of 2. Option D is the right answer.

To determine if the table represents a linear function and calculate the rate of change, let's examine the given values:

x   | y

-----------

1   | 3

2   | 5

3   | 7

4   | 9

By looking at the y-values, we can observe that for every increase of 1 in x, the corresponding y-value increases by 2. This indicates a constant rate of change, suggesting that the table represents a linear function.

To calculate the rate of change, we can use the formula:

[tex]\[\text{{Rate of Change}} = \frac{{\text{{Change in y}}}}{{\text{{Change in x}}}}\][/tex]

Taking any two points from the table, let's choose (1, 3) and (2, 5):

[tex]\[\text{{Rate of Change}} = \frac{{5 - 3}}{{2 - 1}} = \frac{2}{1} = 2\][/tex]

The table provided exhibits a linear function with a constant rate of change. As the x-values increase by 1 from [tex]1[/tex] to [tex]4[/tex], the corresponding y-values increase by [tex]2[/tex] from [tex]3[/tex] to [tex]9[/tex]. This consistent change in y for each unit change in x indicates a linear relationship between the variables.

The rate of change, also known as the slope of the function, is determined by the ratio of the change in y to the change in x. In this case, the rate of change is [tex]2[/tex], meaning that for every increase of [tex]1[/tex] in [tex]x[/tex], the y-value increases by 2.

Thus, the table represents a linear function with a rate of change of [tex]2[/tex].

Therefore, the correct answer is D) Yes; rate of change = [tex]2[/tex].

NOTE: The given question is incomplete. The complete question is:

Determine if the table below represents a linear function. If so, what's the rate of change?

options:

A)  Yes; rate of change = 4

B)  No; it's a non-linear function.

C)  Yes; rate of change = 3

D)  Yes; rate of change = 2​

Table:

x   | y

-----------

1   | 3

2   | 5

3   | 7

4   | 9

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Answer:

C) F(n) = 10n-1

Step-by-step explanation:

C) F(n) = 10n-1

Try a few points

F(n) = 10n-1

= 10(20) - 1

= 200-1

= 199 >>> which matches the table

F(n) = 10n-1

= 10(5) - 1

= 50-1

= 49 >>> which matches the table

F(n) = 10n-1

= 10(1) - 1

= 10-1

= 9 >>> which matches the table

The equation of line is y = -x - 9 which passes through the point Z(-4,-5)

Given data ,

To graph the line with a slope of -1 passing through the point (-4, -5), we can use the point-slope form of a linear equation:

Now , the value of A is

Let the line passes through the point P ( -4 , -5 )

The slope which is the rate of change is is m=-1

y-y₁ = m(x-x₁)

On simplifying , we get

y-(-5) = (-1)(x+4)

Expanding the brackets:

y + 5 = -x - 4

y = -x - 9

Now we have the equation in slope-intercept form. To graph the line, we can plot the given point (-4, -5) and use the slope to find additional points.

Hence , the equation of line is y = -x + 1

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The radius of the circle is [tex]\sqrt{59[/tex] and the coordinates are (6,8).

The given equation of the circle is:

[tex]x^2+Y^2-12x-16y+51=0[/tex]

To find the center and radius of the given circle, we need to rewrite the equation in the standard form [tex](x-a)^2 + (y-b)^2 = r^2[/tex],

where (a,b) is the center of the circle and r is the radius.

We can start by completing the square for the x and y terms. For the x terms, we add and subtract (12/2)² = 36 to get:

[tex]x^2 - 12x + 36 + y^2 - 16y = -51 + 36 + 0[/tex]

Similarly, for the y terms, we add and subtract (16/2)² = 64 to get:

[tex]x^2 - 12x + 36 + y^2 - 16y + 64 = -51 + 36 + 64[/tex]

Simplifying:

[tex](x - 6)^2 + (y - 8)^2 = 59[/tex]

Now we can see that the center of the circle is at (6, 8), and the radius is [tex]\sqrt{59[/tex].

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Answer:  A. 32

Step-by-step explanation:

Rule:  That if an angle is created on the end of circle The arc that it creates is 2 times the angle.

arc AX = 2 (<B)

arc AX = 2(56)

arc AX = 112

Rule:  The angle of 2 secants = 1/2 (outer arc - inner arc)

<C =  1/2 (arc AB - arc AX)

<C = 1/2 ( 176 - 112)

<C = 1/2 (64)

<C = 32     >A

Answer:

9a-2=7

Step-by-step explanation:

4a+ 5a-2=5+3-1

To simplify each side, combine like terms.

4a+5a = 9a

5+3-1 = 7

The equation becomes:

9a-2=7

The line of symmetry for the above figure is attached accordingly.

In mathematics, symmetry with regard to a reflection is known as reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry.

That is, a figure with reflectional symmetry does not alter when it is reflected. A line/axis of symmetry exists in 2D, while a plane of symmetry exists in 3D.

After inserting the symmetry lines, the above resulted in a kite.

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Answer: the answer  of mab is 72 degrees.

Answer:

146°

Step-by-step explanation:

The measure of an inscribed angle is half the measure of its intercepted arc.

73° = (1/2)m(arc)AB

Multiply both sides by 2.

2 × 73° = 2 × (1/2) × m(arc)AB

m(arc)AB = 146°

a. Materials price variance: U$990  and Materials quantity variance: F$198

b. Labor rate variance: F$248

Labor efficiency variance: U$752

a. Materials price and quantity variances:

Materials price variance:

The materials price variance measures the difference between the actual cost of materials purchased and the standard cost of materials.

Actual quantity purchased = 77,000 microns

Actual cost per micron = $0.30 per micron

Standard quantity allowed for production = (7 microns per toy) x (4,700 toys) = 32,900 microns

Standard cost per micron = $0.33 per micron

Materials price variance = (Actual quantity purchased x Actual cost per micron) - (Standard quantity allowed x Standard cost per micron)

Materials price variance = (77,000 x $0.30) - (32,900 x $0.33)

Materials quantity variance:

The materials quantity variance measures the difference between the actual quantity of materials used and the standard quantity allowed for production.

Actual quantity used = (77,000 microns purchased) - (35,875 microns in ending inventory)

Standard quantity allowed = (7 microns per toy) x (4,700 toys)

Materials quantity variance = (Actual quantity used - Standard quantity allowed) x Standard cost per micron

Materials quantity variance = ((77,000 - 35,875) - (7 x 4,700)) x $0.33

b. Labor rate and efficiency variances:

Labor rate variance:

The labor rate variance measures the difference between the actual labor rate paid and the standard labor rate.

Actual labor hours worked = 6,040 hours

Actual labor cost per hour = $45,904 / 6,040 hours

Standard labor hours allowed for production = (1.2 hours per toy) x (4,700 toys)

Standard labor cost per hour = $7.10 per hour

Labor rate variance = (Actual labor hours worked x Actual labor cost per hour) - (Standard labor hours allowed * Standard labor cost per hour)

Labor rate variance = (6,040 x Actual labor cost per hour) - (5,640 x $7.10)

Labor efficiency variance:

The labor efficiency variance measures the difference between the actual labor hours used and the standard labor hours allowed for production.

Labor efficiency variance = (Actual labor hours worked - Standard labor hours allowed) x Standard labor cost per hour

Labor efficiency variance = (6,040 - (1.2 x 4,700)) x $7.10

Please note that the actual labor cost per hour and the actual labor cost per micron need to be calculated before computing the variances.

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The product of [tex]2\frac{4}{5}[/tex] yards, 2 yards, and [tex]\frac{3}{5}[/tex] yards comes out to be [tex]16\frac{4}{5}[/tex] yards.

Firstly we have to convert the mixed fraction into the improper fraction.

1. We multiply the denominator and the whole number

2. To the product add the numerator to get the numerator of the fraction

3. The denominator remains the same.

[tex]2\frac{4}{5}[/tex] = 2 * 5 + 4 / 5 = 14/5

To multiply the fractions:

1. We multiply the numerators to get the numerator

2. Similarly the product of the denominator is the denominator

3. We simplify the resultant fraction

= 14/5 * 2 * 3/5 = 84/5

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Answer:

1 mile : 2 cm

Step-by-step explanation:

ratio is 4.5 miles : 9

Which, if you want simplified, 1:2

Answer:

2 cm is 1 mile

or 1 cm is 1/2 mile

Step-by-step explanation:

We are going  from 9 cm to 4.5 miles

9 cm * scale factor = 4.5 miles

scale factor = 4.5 miles / 9 cm

scale factor = 1/2 mile per cm

The scale is 2 cm is 1 mile

or 1 cm is 1/2 mile

The amount of paint needed to cover the walls of a room, you can use the area of the walls to estimate the amount of paint required.

The area of a two-dimensional shape is the amount of space inside its boundaries, while the perimeter is the length of its outer edge.

These concepts are often related, as the perimeter of a shape can be used to calculate its area.
For example, consider a square with sides of length 5cm.

The perimeter of the square would be 4 x 5cm = 20cm, while the area would be 5cm x 5cm = 25cm².

We can see that the area is greater than the perimeter, as there is more space inside the square than around its edges.
Another way that area and perimeter can be related is through similar shapes. Similar shapes have the same shape, but different sizes.

For example, a small square and a large square are similar shapes, but the large square has longer sides and therefore a larger area and perimeter.

The ratio of the areas of two similar shapes is equal to the square of the ratio of their corresponding side lengths.

Similarly, the ratio of their perimeters is equal to the ratio of their corresponding side lengths.
Understanding the relationship between area and perimeter can be helpful in a variety of situations.

For example, if you need to calculate the amount of fencing needed to enclose a rectangular garden, you can use the perimeter of the garden to determine the length of the fencing required.
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The variables for this problem are given as follows:

a = 16, [tex]b = 16\sqrt{2}[/tex] , c = 16, d = 16.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are obtained according to the rules presented as follows:

For side lengths a and c, we have a right triangle with angles of 45º, hence using the 45-45-90 Triangle Rule, with the hypotenuse of [tex]16\sqrt{2}[/tex], the lengths a and c are given as follows:

a = c = 16.

The length a is also the geometric mean of the lengths c and d, hence:

16² = 16d

d = 16.

Then the length b is obtained applying the Pythagorean Theorem as follows:

b² = 16² + 16²

[tex]b = \sqrt{2 \times 16^2}[/tex]

[tex]b = 16\sqrt{2}[/tex]

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Answer:

1?

Step-by-step explanation:

9 1/4 is the longest distance

2 times

According to the chart, the mile that she ran the fastest was [tex]9 \frac{1}{2}[/tex] miles. 1 dot equals 1 minute so her fastest mile was [tex]9 \frac{1}{2}[/tex].

I hoped this helped if not please tell me what I did wrong ૮ ˶ᵔ ᵕ ᵔ˶ ა

Answer:If the Diameter of a circle is 22 inches, the area will be 380.13in².

Step-by-step explanation:

These are the formulas you use:

Area=pi*Radius^2  or A=pi*Radius*Radius

Diameter=2*Radius

A=1

4*pi*Diameter*2=1 2

4*pi*222=380.13271in

380.13271in is approximately 380.13in².

The statement "When added, the sum of the y-intercepts must be 1" and "f(x) could have a rate of change equal to 1 and g(x) could have a rate of change of 2" can be used to describe the original functions f(x) and g(x).

Within mathematical study, we encounter various types of relations between objects – but none quite so distinctive as a function. These relations are essentially collections or sets composed solely from ordered pairs – pairings containing precisely two distinct elements each.

The defining trait for functions lies in how they operate with regards to these paired elements: specifically that every element comprising the domain – representing all potential inputs – correspond with absolute exclusivity to just one solitary member within the codomain – signifying all possible outputs.

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The graph of the inequality y ≤ (5/2)x - 5 is a downward-sloping line with shading below the line.

To graph the inequality 5x - 2y ≥ 10, we need to convert it to slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. Let's go step by step:

Step 1: Start with the original inequality:

5x - 2y ≥ 10

Step 2: Move the 5x term to the other side of the inequality by subtracting 5x from both sides:

-2y ≥ -5x + 10

Step 3: Divide the entire inequality by -2 (since we want to isolate y and have a positive coefficient for y):

y ≤ (5/2)x - 5

Now we have the inequality in the desired form. The graph of y ≤ (5/2)x - 5 represents all the points below or on the line y = (5/2)x - 5.

To graph this inequality, follow these steps:

Step 1: Plot the y-intercept, which is -5. This point is (0, -5).

Step 2: Find a second point by using the slope (5/2). The slope is the ratio of the change in y to the change in x. Starting from the y-intercept, move up 5 units (numerator of the slope) and move right 2 units (denominator of the slope). This gives us the point (2, 0).

Step 3: Draw a solid line passing through the two points (0, -5) and (2, 0). This line represents the equation y = (5/2)x - 5.

Step 4: Since the inequality is "y ≤ (5/2)x - 5," we need to shade the region below the line (including the line itself) to represent all the points that satisfy the inequality.

The graph should resemble a downward-sloping line passing through the points (0, -5) and (2, 0), with the shaded region below the line.

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Answer:

1. An ordered pair in polar coordinates (r, θ) represents a point in the plane with a distance of r from the origin and an angle of θ with respect to the positive x-axis. When r < 0, this means that the point is located on the opposite side of the origin from the positive x-axis. In other words, the angle θ is shifted by 180 degrees.

2. In polar coordinates, a point can be represented by infinitely many ordered pairs because the distance r and the angle θ are not unique. For example, the point (1, π/4) and the point (1, 9π/4) both represent the same point in the plane.

3. The component form of a vector (a, b) represents the horizontal and vertical displacement of the vector from its initial point to its terminal point. The graph of a vector in standard position is a line segment from the origin to its terminal point. The horizontal and vertical components of the vector correspond to the x- and y-coordinates of the terminal point, respectively.

4a. The velocity of the plane Vp relative to the air can be expressed as Vp = (450 cos(60°), 450 sin(60°)) - (30, 0) = (225 - 30, 389.71) = (195, 389.71) mph.

4b. The velocity of the wind V can be expressed as V = (-30, 0) mph.

4e. The true velocity of the plane vr can be expressed as vr = Vp + V = (195 - 30, 389.71) = (165, 389.71) mph. The true speed of the plane is the magnitude of the true velocity, which is approximately 414.7 mph.

Answer: (5, 3)

Step-by-step explanation:

this is just basic coordinate geometry. it tells you how far to go right and up.

Peter can have the electricity on for 18.5 hours if he wants to make a $49 profit.

We have,

Let's start by setting up an equation to represent the situation:

Profit = Revenue - Cost

We know that Peter's profit is $49, and we can find the revenue by multiplying the number of hours by the hourly rate:

Revenue = Hourly rate x Number of hours

The hourly rate is $4, and the cost includes the initial fee of $25 plus the hourly cost:

Cost = Initial fee + Hourly rate x Number of hours

Now we can substitute these equations into the profit equation and solve for the number of hours:

$49 = ($4 x Number of hours) - ($25 + $4 x Number of hours)

$49 = $4 x Number of hours - $25 - $4 x Number of hours

$49 + $25 = $4 x Number of hours - $4 x Number of hours

$74 = $4 x Number of hours

Number of hours = $74 / $4

Number of hours = 18.5

Thus,

Peter can have the electricity on for 18.5 hours if he wants to make a $49 profit.

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Answer:

  2a. maximum: (1, 8); minimum: (3, 0)

  2b. point of inflection: (2, 4)

  3.  a = 1/4

Step-by-step explanation:

You want the extrema and the point of inflection of f(x) = 2x³ -12x² +18x, and you want the value of 'a' that makes the end behavior a horizontal asymptote at y = 1.

The cubic function f(x) = 2x³ -12x² +18x has derivative ...

  f'(x) = 6x² -24x +18 = 6(x² -4x +3) = 6(x -1)(x -3)

The derivative will be zero at x = 1 and 3. These are the x-coordinates of the extrema of f(x).

The values of f(x) at those points are ...

  f(x) = 2x((x -6)x +9)

  f(1) = 2·1((1 -6)1 +9) = 2(-5 +9) = 8

  f(3) = 2·3(3 -6)·3 +9 = 6(-9 +9) = 0

The leading coefficient is positive, so the leftmost portion of the curve is increasing. The maximum will be at the leftmost turning point. The minimum is the other one (rightmost).

The maximum is (1, 8); the minimum is (3, 0).

The point of inflection is the midpoint between the extrema of a cubic:

  ((1, 8) +(3, 0))/2 = (2, 4) . . . . point of inflection

You want the limit as x → -∞ of ((x -2)(3x² +5) -4ax³)/(8ax³ +5x -1) to be 1.

The ratio of leading terms of the numerator and denominator is ...

  (3 -4a)x³/(8ax³) = 1

This requires ...

  3 -4a = 8a   ⇒   3 = 12a   ⇒   a = 1/4

The value of 'a' that makes the limit be 1 is 1/4.

__

Additional comments

A cubic is symmetrical about its point of inflection, so the point of inflection will be equidistant from the extrema, their midpoint. When the leading coefficient is positive, the function is increasing everywhere except between the local extrema. (The first attachment has a graph of the derivative, for reference.)

The end behavior of a rational function of equal numerator and denominator degree is the ratio of the leading coefficients.

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From the calculation and based on the Least common multiples, , we can tell that Maria del Carmen has a total of 36 stickers

The least common multiple is of a set of numbers is the least multiple that they have in common and is obtained by decomposing each number into prime factors and taking common and uncommon factors with their greatest exponent.

Then we break down each number to know how much is the minimum that Maria del Carmen has:

2 = 2

4 = 2*2 = 2²

6 = 2*3

9 = 3*3 = 3²

12 = 2*2*3 = 2²*3

18 = 2*3*3 = 2*3²

LCM = 2²*3² = 4*9 = 36

Now this number is between 30 and 50: so Maria del Carmen has 36 stickers

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Full Qustion:

Maria del carmen colecciona cromos de animales;tiene mas de 30 y menos de 50.los quiere organizar en un album de manera q en cada pagina guarde el mismo numero de cromos.si puede ubicar 2,4,6,9,12 o 18 cromos en cada pagina ¿cuantos cromos tiene maria del carmen?

Translation:
Maria del Carmen collects animal stickers; she has more than 30 and less than 50. She wants to organize them in an album so that on each page she keeps the same number of stickers. If she can locate 2,4,6,9,12 or 18 Stickers on each page. How many stickers does Maria del Carmen have?

Answer:

Area of circle = pi×r²

Where, pi =22/7 or 3.142

r = 8cm

Area =22/7 × 8²

=201.142

Approximately 201 to the nearest whole number

You're welcome

For the area to increase by 1. 2 square feet, the base would need to increase by 0. 4 ft.

The area of a triangle is given by the formula:

Area =  ( 1 / 2) x base x height

= 1 / 2 x 14 x 6

= 42 square feet

The new area after the increase would be :

= 42 + 1. 2

= 43. 2 square feet

The base for this to happen is:

43. 2 = 1 / 2 x base x 6

base = 14. 4 ft

The increase in base is:

= 14. 4 - 14.

= 0. 4 ft

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There are 35 different committees that can be formed, each consisting of one man and one woman.

To form the committee consisting of one man and one woman, we need to choose one man from the available seven men and one woman from the available five women.

Number of choices for selecting one man = 7

Number of choices for selecting one woman = 5

To find the total number of different committees that can be formed, we multiply these numbers together:

Total number of committees = 7 × 5

Total number of committees = 35

Therefore, there are 35 different committees that can be formed, each consisting of one man and one woman.

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Answer:

The answer is down below

Step-by-step explanation:

G={2,3,4}

W={1,5}

Total cards=1,2,3,4,5

let P(x) be G

Probability of X=G/Total

P(x)=3/5

P(not x)=2/5

X={2,3,4}

not X={1,5}

The value of the principal is $10,000.

The equation A = P(1 + 0.043t) represents the amount of money earned on a savings account with 4.3% annual simple interest A is the account balance after t years P is the principal amount, and 0.043 is the interest rate per year.

The account balance is $15,160 after 12 years.

Substituting these values into the equation, we get:

15,160 = P(1 + 0.043(12))

Simplifying the right-hand side, we get:

15,160 = P(1 + 0.516)

15,160 = P(1.516)

Dividing both sides by 1.516, we get:

P = 10,000

This means that the account was initially opened with a principal of $10,000 and it earned simple interest of 4.3% per year for 12 years resulting in an account balance of $15,160.

The principal and it does not take into account the interest that is earned on the interest itself.

In contrast compound interest takes into account the interest that is earned on both the principal and the previously earned interest.

The account in question had been earning compound interest instead of simple interest the final account balance after 12 years would have been higher than $15,160.

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If 0 < θ < [tex]360^0[/tex] and sin θ = 0.3097, then θ is approximately [tex]24^0[/tex].

In order to find the value of θ given sin(θ) = 0.3907, we can use the inverse sine function, also known as arcsine or [tex]sin^{(-1)[/tex].

Using a scientific calculator or trigonometric tables, we can find the inverse sine of 0.3907:

θ= sin^(-1)(0.3907)

θ ≈ 23.576 degrees

Since 0 < θ < 360 degrees, we can conclude that θ is approximately 24 degrees.

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