LESSON 19 SESSION 5
✪ Which solutions, if any, do the inequalities -2(c-4) ≤-4 and d-6>-4
have in common? Show your work.

Answer: a

Step-by-step explanation:

The length of the arc with a central angle of 285 degrees and radius 16 inches is 79.6 inches

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

central angle = 285 degrees

Radius = 16 inches

Using the above as a guide, we have the following:

Length of arc = central angle/360 * 2 * 3.14 * Radius

Substitute the known values in the above equation, so, we have the following representation

Length of arc = 285/360 * 2 * 3.14 * 16

Evaluate

Length of arc = 79.6

Hence, the length of the arc is 79.6 inches

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There are 1820 different orders possible for selecting any 4 toppings out of a list of 16 toppings.

To calculate the number of different orders possible for selecting any 4 toppings out of a list of 16 toppings,

we can use the combination formula:

nCr = n! / r!(n-r)!

where n is the total number of items, r is the number of items to be selected, and ! represents the factorial operation.

Substituting the given values, we get:

16C4 = 16! / 4!(16-4)!

16C4 = (16 × 15 × 14 × 13) / (4 × 3 × 2 × 1)

16C4 = 1820

Therefore, there are 1820 different orders possible.

Option D. 1,820 is the correct option.

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The length of an American football field including end zones is 21600 inches.

To convert yards to inches, we multiply by 36, since there are 36 inches in one yard.

Therefore, a football field that is 120 yards long is equivalent to 120 x 36: = 4320 feet. To convert feet to inches, we multiply by 12, since there are 12 inches in one foot.

Therefore, a 120-yard football field is equivalent to 4320 x 12 = 51,840 inches. However, we must also take into account the two end zones, which are each 10 yards long, or 360 inches. Thus, the total length of an American football field including the end zones is 120 x 36 x 12 + 2 x 360 = 21,600 inches.

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Answer:

Step-by-step explanation:

the answer is D

Answer:

D. 5¹⁵ is the correct answer.

6 inches will be the length of the patio.

According to the scale, 1 inch on the plan corresponds to 3.5 feet in real life.

We must convert the patio's real length of 21 feet to inches using the scale in order to determine how long it would look on the blueprint:

3.5 feet to one inch

21 feet in x inches

If we cross-multiply, we obtain:

1 inch/3.5 feet * 21 feet

= x inches

= 6 inches.

As a result, the length of the patio will be indicated on the blueprint as 6 inches.

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Answer:

176

Step-by-step explanation:

To do this question, we can simplify it even further.

If x=25 when y=110, it is in the ratio 25:110.

If we divide by five on both sides, the ratio becomes:

5:22.

Then, if we multiply by eight on both sides,

it becomes 40:22x8 which means y is equal to 176.

The best response to Raina's comment will be that technology is good but handouts still serve the useful purpose of being a hard copy that speakers can use in case technology fails.

To respond to Raina, the best thing to do will be to acknowledge the fact that technology is good but handouts are still important because, unlike technology that can trip off by some sudden technical faults, handouts can be depended upon.

So, while responding to Raina, we will not discard her point but will let her know that technology is good but handouts still have their benefits.

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An equation which is true include the following: A. 4 × n × n × n × n = 4n⁴.

In Mathematics, an exponent is a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.

This ultimately implies that, an exponent is represented by the following mathematical expression;

bⁿ

Where:

By applying the multiplication law of exponents for powers to each of the expressions, we have the following:

4 × n × n × n × n = 4n⁴

4 × n⁴ = 4n⁴

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Hannon's maximum allowable production cost for the All-Body swimsuit is $80 if it wants to make a profit of $20 per unit.

Given data ,

a)

Using cost-plus pricing, the selling price is set 20% above the costs.

Selling price=Costs+(Costs x Markup)

Selling price=$100 + ($100x0.20)

Selling price=$100+$20

On simplifying the equation , we get

Selling price=$120

The price charged for the All-Body swimsuit would be$120.

Hannon might consider manufacturing the All-Body swimsuit under the cost-plus pricing approach if the market demand is strong enough to justify the selling price of $120 and if Hannon can efficiently produce and sell the swimsuit to generate profits.

(b)

Using target costing, the price charged by Hannon to the retailer is determined by subtracting the desired profit per unit from the target selling price.

Target selling price=$100 (given)

Desired profit per unit=$20 (given)

Price charged to retailer=Target selling price - Desired profit per unit

Price charged to retailer=$100-$20

On simplifying the equation , we get

Price charged to retailer=$80

The price that Hannon would charge the retailer for the All-Body swimsuit under target costing is$80.

(c)

To determine the highest acceptable manufacturing cost for the All-Body swimsuit under target costing, we subtract the desired profit per unit from the target selling price.

Target selling price=$100 (given)

Desired profit per unit=$20 (given)

Highest acceptable manufacturing cost=Target selling price-Desired profit per unit

Highest acceptable manufacturing cost=$100-$20

Highest acceptable manufacturing cost=$80

Hannon would be ready to spend up to $80 in manufacturing costs to develop the All-Body swimsuit if it wanted to make $20 each unit.

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The vertical component of the particle's location, when its horizontal component is 2, is:

y = -1.25

To find the vertical component of the particle's location when its horizontal component is 2, we need to first find the value of t when x = 2.

Given the equation:

x = 3sin(t)

Substitute x with 2:

2 = 3sin(t)

Now, isolate t by dividing both sides by 3:

sin(t) = 2/3

Take the inverse sine (arcsin) of both sides:

t = arcsin(2/3)

Now, plug the value of t back into the y equation:

y = t - 4cos(t) + 1

y = arcsin(2/3) - 4cos(arcsin(2/3)) + 1

Using a calculator to find the approximate value of y, we get:

y ≈ -1.25

Therefore, the vertical component of the particle's location when its horizontal component is 2 is:

y = -1.25

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the object will fall a distance of 1024 feet in 8 seconds. So the answer is (C) 1024 ft.

what is distance  ?

Distance is a scalar quantity that refers to the total length traveled by an object or person, without considering the direction. It is a measure of the path length between two points, usually measured in units such as meters (m), feet (ft), or kilometers (km).

In the given question,

The formula t = √(d/16) relates the time t (in seconds) it takes an object to fall a distance d (in feet) to the acceleration due to gravity, which is approximately 32.2 feet per second squared.

To find how far the object will fall in 8 seconds, we can rearrange the formula to solve for d:

t = √(d/16)

t² = d/16 (Squaring both sides)

d = 16t² (Multiplying both sides by 16)

Substituting t = 8 into the formula, we get:

d = 16(8)² = 1024

Therefore, the object will fall a distance of 1024 feet in 8 seconds.

So the answer is (C) 1024 ft.

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As a result, the triangle formed by the vertices A(0,0), B(3,8), and C(9,0) has an area of 18 square units.

A triangular is a three-sided, tri-geometric shape. It is a double figure that is frequently represented by the character "." A triangle's angles can never add up to more than 180 degrees. Triangles can be categorized into equilateral, elliptic, and scalene varieties according to the length of their sides and the dimensions of their angles. Three equal edges and three equal, 60-degree angles make up an equilateral triangle. Equal size ends and equal size angles make up an isosceles triangle. The sides and angles of a scalene triangle are not equal.

Given a triangle's vertices in the coordinate plane, we can apply the following formula to get its area:

A is equal to [tex]|(x1(y_2 -y_3) + x_2(y_3 -y_1) + x3(y_1 -y_2)) / 2|.[/tex]

where the triangle's vertices' coordinates are [tex](x_1, y_1), (x_2, y_2), and (x_3, y_3).[/tex]

We obtain: by substituting the coordinates of the specified vertices.

[tex]A = |(0(8 - 0) + 3(0 - 0) + 9(0 - 8)) / 2| = |-36| / 2 = 18[/tex]

As a result, the triangle formed by the vertices A(0,0), B(3,8), and C(9,0) has an area of 18 square units.

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The ordered pair that represents the week before is given as follows:

A. (1,7).

The general format of an ordered pair is given as follows:

(x,y).

In which the coordinates are given as follows:

The meaning of each coordinate in this problem is given as follows:

For the current week, the ordered pair is given as follows:

(5,3).

For the previous week, the total number of hours was the same, that is, 5 + 3 = 8, however with x = 1 and y = 8 - 1 = 7, as only one hour was spent on chores.

Thus option A is correct.

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The set of numbers that can represent the sides of a triangle are:

{11, 14, 22} and {13, 20, 35}.

We can determine which set of numbers would represent the sides of a triangle by applying the triangle inequality theorem.

This theorem states that the sum of any two sides of a triangle must be greater than the length of the third side to make it a triangle.

Applying the theorem, we have:

A. (6,8,14)

6 + 8 > 14 (not true, since 6 + 8 = 14 and not greater than 14)

6 + 14 > 8 (true)

8 + 14 > 6 (true)

Therefore, (6,8,14) cannot represent the sides of a triangle.

B. {11, 14, 22}

11 + 14 > 22 (not true, since 11 + 14 = 25 and not less than 22)

11 + 22 > 14 (true)

14 + 22 > 11 (true)

Therefore, {11, 14, 22} does not represent the sides of a triangle.

C. {13, 20, 34}

13 + 20 > 34 (not true, since 13 + 20 = 33 and not greater than 34)

13 + 34 > 20 (true)

20 + 34 > 13 (true)

Thus, {13, 20, 34} cannot represent the sides of a triangle.

D. {13, 20, 35}

13 + 20 > 35 (not true, since 13 + 20 = 33 and not less than 35)

13 + 35 > 20 (true)

20 + 35 > 13 (true)

This means, {13, 20, 35} can represent the sides of a triangle.

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The features of function g if g(x) = -f(x)-1 include the following:

B. domain of (0, ∞).

C. vertical asymptote of x = 0.

D. x-intercept at (1/2, 0).

In Mathematics and Geometry, a domain is the set of all real numbers for which a particular function is defined.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following key features:

Domain = (0, ∞)

Range = (-∞, ∞).

vertical asymptote, x = 0.

x-intercept = (1/2, 0).

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A) The area of the walls is 700 ft²

B) The area of the doors, windows, and rectangular opening is 226ft²

C) The area that Kamrie will paint is 474 ft², and she will need to purchase 2 cans of paint.

Part A:

The area of each of the short walls is

10 ft x 15 ft

= 150 sq ft.

So, the total area of the four walls is:

2(200 sq ft) + 2(150 sq ft)

= 700 sq ft

Part B:

The area of the three windows along the long wall is

3 ft x 8 ft

= 24 sq ft each, so their total area is

3(24 sq ft)

= 72 sq ft

The area of the two windows along the short wall is also

3 ft x 8 ft = 24 sq ft each,

so their total area is

2(24 sq ft)

= 48 sq ft

The area of the rectangular opening along the other long wall =

7 ft x 8 ft = 56 sq ft.

So, the total area of the doors, windows, and rectangular opening is

72 sq ft + 48 sq ft + 56 sq ft

= 176 sq ft

Part C:

To determine the area that Kamrie will paint, we need to subtract the area of the doors, windows, and rectangular opening from the total area of the walls

700 sq ft - 176 sq ft

= 524 sq ft

To determine how many cans of paint Kamrie needs to buy, we divide the area to be painted by the coverage per can

524 sq ft ÷ 415 sq ft/can

≈ 1.26 cans

So Kamrie needs to buy at least 2 cans of paint to cover the entire living room.

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The probability of picking a jack and spinning an odd number is 2/9.

Let's first list the sample space in set notation for picking a card (jack, queen, or king) and spinning a 3-section spinner with the numbers 5, 8, and 9:

The sample space is {(jack-5, jack-8, jack-9, queen-5, queen-8, queen-9, king-5, king-8, king-9)}

Now, to find the probability of picking a jack and spinning an odd number, we need to count the outcomes that meet these conditions and divide it by the total number of outcomes in the sample space.

There are two outcomes that meet these conditions: jack-5 and jack-9.

So, the probability is the number of favorable outcomes divided by the total number of outcomes:

P(jack, odd number) = 2 (favorable outcomes) / 9 (total outcomes) = 2/9

Thus, the probability of picking a jack and spinning an odd number is 2/9.

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The dimensions of each book are 3 inches by 8 by 9 inches.  The dimensions of the crate cannot be determined from the information provided.

A) The dimensions of the crate are 36 inches by 96 inches by 108 inches.

No. The dimensions of the crate cannot be determined from the information provided.

B) The total volume of the books is 2,592 cubic inches.

Yes. The volume of each book is 3 x 8 x 9 = 216 cubic inches. Therefore, the total volume of 12 books would be 12 x 216 = 2,592 cubic inches.

C) The crate could also hold 24 books that are each 3 inches by 8 inches by 9 inches.

Thus, The crate could not hold 24 books of the given dimensions because each book has a height of 9 inches, and the height of the crate is only 12 inches.

Therefore, the crate can only hold 12 books of the given dimensions.

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1. n - 4 = 12

2. n - 13 = 20

3. n + 9 = 25

4. n + 5 = 75

5. x + 6 = 13

6. n - 6 = 5

For 1 n = 16

For 2 n = 33

For 3 n = 16

For 4 n = 70

For 5 x = 7

For 6 n = 11

Hope that helps, :).

Answer:

  (a) ±{1, 2, 5, 10}

  (b) attached

  (c) {-2, -1, 5}

  (d) P(x) = (x +2)(x +1)(x -5)

Step-by-step explanation:

You want the possible and actual rational zeros for P(x) = x^3-2x^2-13x-10, and the factored form of the polynomial.

The rational root theorem tells you the possible rational zeros of a polynomial will be of the form ...

  ±(divisor of the constant)/(divisor of the leading coefficient)

The leading coefficient is 1, and the divisors of the constant are {1, 2, 5, 10}, so the possible rational zeros are ...

  {±1, ±2, ±5, ±10}

The attached graph shows the actual zeros of P(x) to be {-2, -1, 5}.

Each zero q corresponds to a factor (x -q). The factored form of the polynomial is ...

  P(x) = (x +2)(x +1)(x -5)

The coordinates of the fourth vertex are (-2.2, 1.5).

To find the coordinates of the fourth vertex, we can use the fact that opposite sides of a rectangle have equal length and are parallel to each other.

First, we can find the length of one of the sides of the rectangle. Let's take the side connecting the points (-2.2, -2.3) and (-2.2, 1.5):

length = |1.5 - (-2.3)| = 3.8

Since this is a rectangle, the length of the side opposite to this one must also be 3.8. We can find this side by taking the points (-2.2, 1.5) and (1.5, 1.5):

width = |1.5 - (-2.2)| = 3.7

Now we know the length and width of the rectangle, so we can find the coordinates of the fourth vertex. Let's call this point (x, y).

Since the fourth vertex is opposite to the point (-2.2, -2.3), the x-coordinate of the fourth vertex must be the same as the x-coordinate of (-2.2, -2.3):

x = -2.2

Similarly, since the fourth vertex is opposite to the point (1.5, 1.5), the y-coordinate of the fourth vertex must be the same as the y-coordinate of (1.5, 1.5):

y = 1.5

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Thus, equation shows the connection between the quantity of weeks, w, and the quantity of books gathered, b: b = 10w.

Simply put, the slope-intercept form is the way to write a line's equation so that the y-intercept (at which line crosses a vertical y-axis) and slope (steepness) are instantly visible. This form is frequently known as the y = mx + b form.

The table shows an increase of 10 volumes every week in the total number of books acquired.

Weeks (w) Books Collected (b)

1                   10

2                  20

3                  30

4                   40

As a result, the quantity of books gathered and the number of weeks (w) have a linear relationship (b). The following equation can be used to illustrate this relationship:

b = mw + c

where w is the number of weeks, m denotes the slope (rate of change), and c denotes the number of books aquired at week 0.

The weekly shift in the amount of books gathered, which is 10, is the slope (m). By adding one of the points from table to the equation, we can now get the y-intercept (c). Use the first and tenth points:

10 = 10 * 1 + c

c = 0

Currently, the following equation reflects the relationship among the number of weeks (w) as well as the quantity of books gathered (b):

b = 10w + 0

b = 10w

Thus, equation shows the connection between the quantity of weeks, w, and the quantity of books gathered, b: b = 10w.

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Complete question:

The data in the form of a table, which shows the total number of books collected (b) for different number of weeks (w).

Weeks (w) Books Collected (b)

1                   10

2                  20

3                  30

4                   40

Trisha is collecting books to donate. The table below shows the total number of books collected, b, for different number of weeks, w. Which equation represents the relationship between the number of weeks, w, and the number of books collected, b?

second square

add up all the inches and youll see second had bigger number leading to the answer b

The work done in stretching the spring from 10 cm to 40 cm is 10,837.5 J.

The work done in stretching a spring is given by the formula:

W = (1/2)k[tex]x^{2}[/tex]

where W is the work done, k is the spring constant, and x is the displacement of the spring from its original position.

To find the spring constant k, we can use the given information:

F = kx

where F is the force applied to the spring. Rearranging this equation, we get:

k = F/x

Substituting the given values, we get:

k = 350 N / 30 cm = 11.67 N/cm

Now, we can find the work done in stretching the spring from 10 cm to 40 cm:

W = (1/2)k([tex](x_{2})^{2} -(x_{1} )^{2}[/tex])

where [tex]x_{1}[/tex] is the initial displacement of the spring (10 cm) and [tex]x_{2}[/tex] is the final displacement (40 cm).

Substituting the values, we get:

W = (1/2) * 11.67 N/cm * ([tex](40 cm)^{2} - (10 cm)^{2}[/tex])

W = (1/2) * 11.67 N/cm * (1600  [tex]cm^{2}[/tex] - 100  [tex]cm^{2}[/tex])

W = (1/2) * 11.67 N/cm * 1500 [tex]cm^{2}[/tex]

W = 10,837.5 joules (J)

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Answer:

2

Step-by-step explanation:

So there are 2 ways to do this, but the easy way is to do [tex]\frac{4}{1}[/tex] x [tex]\frac{4}{8\\}[/tex]

it becomes [tex]\frac{16}{8}[/tex] then divided 16 by 8 and it's 2.

Have a good day!

Answer:

-3x - 24 < -36

-3x < -12

x > 4

Answer:

8. mArc ED = 38°

9. mArc EA = 142°

10.mArc BDC = 308°

Step-by-step explanation:

The measure of an a central angle and it's intercepted arc are equal

So if the measure of the angle for the angle that intercepts Arc ED is 38° the arc is also 38°

Same thing with Arc EA, the central angle that intercepts it is 142° so the measure of Arc EA is 142°

Arc BDC is a major arc so it is greater than 180°. It goes around the circle from point B to point C and point D is one of the points on the arc.

We could find the value of the arc two ways. We could add all the angles  the that make up the central angle it is intercept by or we could simply subtract the 52° that isn'tt a part of the arc and subtract that from 360°

360 - 52 = 308

So the central angle intercepting Arc BDC is 308° so the arc also has a measure of 308°.

Answer:

C. 84.8 m

Step-by-step explanation:

Circumference of circle = D x 3.14

D = 27 m

Let's solve

27 x 3.14 = 84.78 m

So, the circumference of the circle is C. 84.8 m