5. Open Response Consider triangles ABC and
JKL as shown. (Lesson 3)
(See photo)

We can express this interval using set-builder notation as: {x | x > 4}

What is expression?

An expression consists of one or more numbers or variables along with one more operation.

The monthly costs of each plan as functions of the number of movies watched:

A(x) = 22 + x

B(x) = 14 + 3x

To graph these functions, we can plot several points for each one, as shown in follow fig.

A(x) - B(x) < 0

(22 + x) - (14 + 3x) < 0

22 + x - 14 - 3x < 0

-2x + 8 < 0

-2x < -8

x > 4

Therefore, Plan A is cheaper than Plan B for any number of movies watched greater than 4. We can express this interval using set-builder notation as: {x | x > 4}

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Answer:

Large box = 50 pounds

Small box = 15 pounds

Step-by-step explanation:

Because there are 50 small boxes, the truck is carrying 50 combined large and small boxes. That means the area of those boxes are 50 * 65 = 3250 pounds. There are 10 large boxes left. 3750-3250 = 500. The weight of 10 large boxes is 500 pounds, which means 1 large box is 500/10 which is 50 pounds.

If a large box is 50 pounds, and the combined weight is 65 pounds, 65-50 = 15 pounds for a small box.

Using Pythagoras theorem, the value of c is √193.

What is Pythagoras' theorem?

A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Here, we have

Given:  the right triangle and given sides.

We have to find the value of c.

We apply here Pythagoras theorem and we get

a² + b² = c²

a = 7

b = 12

c = ?

(7)² + (12)² = c²

49 + 144 = c²

193 = c²

c = √193

Hence, the value of c is √193.

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So, each farmer pays the following amounts: The first farmer pays 738.40 euros. The second farmer pays 443.04 euros. The third farmer pays 418.56 euros

Proportion refers to the equality of two ratios. In other words, when two ratios are set equal to each other, they form a proportion. A proportion is typically written in the form of two fractions separated by an equals sign, such as a/b = c/d. Proportions are commonly used in mathematics to solve problems involving ratios and proportions, such as finding missing values or scaling up or down a given quantity.

Here,

To find out how much each farmer pays, we need to determine the proportion of the total rent that each farmer owes based on the number of sheep they have. First, we need to find the total number of sheep:

120 + 72 + 68 = 260

The first farmer has 120 sheep, which is 46.15% of the total number of sheep (120/260). Therefore, the first farmer owes 46.15% of the rent:

0.4615 x 1600 = 738.40 euros

Similarly, the second farmer has 72 sheep, which is 27.69% of the total number of sheep (72/260). Therefore, the second farmer owes 27.69% of the rent:

0.2769 x 1600 = 443.04 euros

The third farmer has 68 sheep, which is 26.15% of the total number of sheep (68/260). Therefore, the third farmer owes 26.15% of the rent:

0.2615 x 1600 = 418.56 euros

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Complete question:

The rent of 1600 euros for a piece of land is divided among three farmers who graze their sheep there. As they do not have the same number of sheep, they decide to pay proportionally according to the number of sheep each has. If the first one has 120 sheep, the second 72, and the third 68. How much does each one pay?

Answer:

-0.03334

Step-by-step explanation:

i just graphed it and looked at were y=4 and gave you the x value

:)

Answer:

x1 = -0.0333333, x2=0.7

The length of the missing leg of the triangle is 8 units. We have a right triangle ABC with angle BAC equal to 90 degrees. The length of one of the legs is 6 units, and the length of the hypotenuse is 10 units.

We are asked to find the length of the other leg of the triangle.

[tex]That is, a^2 + b^2 = c^2[/tex]

In this case, we know that the length of one leg is 6 units, and the length of the hypotenuse is 10 units. We can substitute these values into the Pythagorean theorem and solve for the missing leg:

[tex]a^2 + b^2 = c^2[/tex]

[tex]6^2 + b^2 = 10^2[/tex]

[tex]36 + b^2 = 100[/tex]

[tex]b^2 = 100 - 36[/tex]

[tex]b^2 = 64[/tex]

Taking the square root of both sides, we get:

b = 8

Therefore, the length of the missing leg of the triangle is 8 units.

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The number of National League players cards in the card collection in terms of the number of American League players cards can be expressed as 5x.

Let's start with the information given in the problem:

The baseball card collection contains five times as many National League players as American League players.

Let's use x to represent the number of American League players cards in the collection.

Since the collection contains five times as many National League players as American League players, we can express the number of National League players cards in terms of x as follows:

Number of National League players cards = 5 times the number of American League players cards

Number of National League players cards = 5x

So, if the number of American League players cards in the collection is x, then the number of National League players cards would be 5x, according to the problem statement.

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The height of the flagpole is approximately 68.53 feet.

Trigonometric equations are equations that involve trigonometric functions such as sine, cosine, tangent, and their reciprocals. These equations typically involve finding the values of the angles or sides of a right-angled triangle or periodic functions that repeat themselves after certain intervals.

This problem involves finding the height of a flagpole using trigonometry. The surveyor measures the angle of elevation from the tripod to the top of the pole and knows the distance from the base of the pole to the tripod. By using the tangent function and the given angle, we can set up an equation that relates the height of the pole to the distance and the angle. We simplify the equation and solve for the unknown height, which gives us an approximate value of 68.53 feet.

the height of the flagpole, we can use trigonometry. Let's call the height of the flagpole "h".

Using the tangent function, we can set up the following equation:

tan(26) = h / (150 + 3)

The 3 feet is added to the distance because the tripod is 3 feet tall.

Simplifying this equation, we get:

tan(26) = h / 153

To solve for "h", we can multiply both sides by 153:

h = tan(26) * 153

Using a calculator, we can evaluate the right side of the equation to get:

h ≈ 68.53

Therefore, the height of the flagpole is approximately 68.53 feet.

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The equation of the tangent line to the graph of y = xlnx at the point (2,2ln2) is y = (ln(2) + 1)x - 2ln2 - 2.

A tangent is a straight line or plane that touches a curve or curved surface at a single point, but does not intersect it at that point. The tangent line can be thought of as the instantaneous rate of change of the curve at that point. In calculus, the slope of the tangent line at a point on a curve is defined as the derivative of the curve at that point. The tangent line is often used to approximate the behavior of the curve near the point of tangency.

To find the equation of the tangent line to the graph of y = xlnx at the point (2,2ln2), we need to use the slope-point form of the equation of a line.

First, we find the slope of the tangent line by taking the derivative of the function y = xlnx:

y = xlnx

y' = ln(x) + 1

At x = 2, we have:

y' = ln(2) + 1

So the slope of the tangent line at (2,2ln2) is ln(2) + 1.

Next, we use the point-slope form of the equation of a line:

y - y1 = m(x - x1)

where (x1, y1) is the given point, and m is the slope we just found.

Substituting x1 = 2, y1 = 2ln2, and m = ln(2) + 1, we get:

y - 2ln2 = (ln(2) + 1)(x - 2)

Expanding and simplifying, we get the equation of the tangent line:

y = (ln(2) + 1)x - 2ln2 - 2

So the equation of the tangent line to the graph of y = xlnx at the point (2,2ln2) is y = (ln(2) + 1)x - 2ln2 - 2.

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Answer:

$47.7

Step-by-step explanation:

You first have to find how much of 53 is 10%:  53/10 = 5.3  53-5.3= 47.7

therefore , Kim earn Average is: $11.70(rounded) per hour

Total for two nights:$116.95

Friday, total earning:

(11 - 6)*$5.75 + $27.35

5×$5.75+$27.35

= $56.1

Saturday, total earning:

(11 - 6)*$5.75 + $32.10

5×$5.75+$32.10

= $60.85

Total for the two nights is:

$56.1 + $60.85 = $116.95

Define average per hour?

The term "hourly average" refers to the average result obtained from ongoing monitoring over each 60-minute interval. An arithmetic average of all entire 15-minute data blocks for a clock hour is referred to as the hourly average.

Average per hour is:

$116.95/(5 + 5)

= $116.95 / 10

= $11.70(rounded)

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On solving the provided question we can say that Based on Sandra's research, there is a 15% probability that a randomly picked bottle is appropriately put AND is a Plastic #4 bottle.

Probability is a measure of how likely an event is to occur. It is represented by a number between 0 and 1, with 0 representing a rare event and 1 representing an inescapable event. Switching a fair coin and coin flips has a chance of 0.5 or 50% since there are two equally likely outcomes. (Heads or tails). Probabilistic theory is an area of mathematics that studies random events rather than their attributes. It is applied in many disciplines, including statistics, economics, science, and engineering.

Therefore there are 15 bottles that match both requirements (well arranged and Plastic #4).

The sample has 100 bottles in total.

As a result, the likelihood that a randomly chosen bottle is appropriately put AND is a Plastic #4 bottle is:

P(properly positioned and Plastic #4) = the number of bottles that match both requirements. / The sample's total number of bottles

P(properly positioned and Plastic #4) = 15 / 100

P(properly positioned and Plastic #4) = 0.15 or 15%

Based on Sandra's research, there is a 15% probability that a randomly picked bottle is appropriately put AND is a Plastic #4 bottle.

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Step-by-step explanation:

The number line is GREATER than but does not INCLUDE -4 ( due to the hollow dot)  and is less than or EQUAL to 5  (solid dot)

-4 < n ≤ 5

The correct equation to find the measure of ∠CMD is C. 15° + 30° = a; 90° – a = m.

It is formed when two straight lines intersect at a single point, creating two equal and opposite angles.

This is because the angles in a triangle must add up to 180°.

In this case, ∠FMD and ∠BMC are the two angles of the triangle, and the third angle is a right angle.

Therefore, the measure of ∠CMD must be 90°.

To find the measure of ∠CMD, we must first find the sum of ∠FMD and ∠BMC.

This can be done by setting up the equation 15° + 30° = a.

We then subtract this sum from 90° to get the measure of ∠CMD, which gives us the equation 90° – a = m.

Therefore, the correct equation to find the measure of ∠CMD is

15° + 30° = a; 90° – a = m.

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Answer:

6.92 years

Step-by-step explanation:

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where:

A = the final amount (in this case, $8800)

P = the initial investment (in this case, $4500)

r = the annual interest rate (in decimal form, so 6.8% = 0.068)

n = the number of times the interest is compounded per year (in this case, daily, so n = 365)

t = the number of years

We want to solve for t, so we can rearrange the formula as follows:

t = (ln(A/P)) / (n ln(1 + r/n))

where ln is the natural logarithm.

Plugging in the given values, we get:

t = (ln(8800/4500)) / (365 ln(1 + 0.068/365))

t ≈ 6.92

Therefore, it would take about 6.92 years (or about 7 years) for the investment to grow to $8800 at an annual interest rate of 6.8% compounded daily.

The area of a parallelogram can be found by multiplying the base by the height

The formula for the area of a parallelogram is shown:

A = b × h

where A is the area, b is the base, and h is the height of the parallelogram.

Note that the base and the height must be perpendicular to each other.

1) A = 1/2bh

= 0.5 * 13/6 * 24

= 26 ft^2

1)A = bh

= 15/4 * 14/5

10.5 ft^2

3) 8/3 * x = 24

x = 24 * 3/8

x = 9 ft

4) x * 4/5 = 10

x = 10 * 5/4

= 12.5 ft

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The area of this triangle is equal to 26 yd².

The area of this parallelogram is equal to 21 ft² or 10 1/2 ft².

The base of this parallelogram as a fraction is 72/8 feet.

The base of this rectangle is 25/2 cm or 12 1/2 cm.

In Mathematics and Geometry, the area of a triangle can be calculated by using the following formula:

Area = 1/2 × base × height

Area = 1/2 × 24 × 2 1/6

Area = 12 × 13/6

Area = 156/6

Area = 26 yd²

In Mathematics and Geometry, the area of a parallelogram can be calculated by using the following formula:

Area of a parallelogram = base × height

Area of a parallelogram = 2 4/5 × 3 3/4

Area of a parallelogram = 14/5 × 15/4

Area of a parallelogram = 7 × 3/2

Area of a parallelogram = 21/2 = 10 1/2 ft²

24 = base × 2 2/3

24 = base × 8/3

Base = 72/8

Base = 9 feet.

For the base of the rectangle, we have:

Area of rectangle = length × breadth

10 = 4/5 × breadth

Breadth = 50/4

Breadth = 25/2 = 12 1/2 cm.

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147

$3 x 147 cookies = (approximately) $440

$440 x 2 = 880

Answer: The common difference of the arithmetic sequence 10, 8, 6, 4, 2,… is -2. Note: By considering the formula of arithmetic sequence we verify the common difference which we obtained.

Answer:

-2

Step-by-step explanation:

In the sequence we have three kinds of sequence namely, arithmetic sequence, geometric sequence and harmonic sequence. In arithmetic sequence we the common difference between the two terms, In geometric sequence we the common ratio between the two terms, In harmonic sequence it is a ratio of arithmetic sequence to geometric sequence.

Answer:

h ≈ 19 m

Step-by-step explanation:

using the tangent ratio in the right triangle

tan43° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{h}{20}[/tex] ( multiply both sides by 20 )

20 × tan43° = h , then

h ≈ 19 m ( to the nearest whole number )

To approximate the value of log(3)15309 using log(3)7 = 1.7712, we can use the following steps:

Express 15309 as a power of 3:

15309 = 3^x

Take the logarithm base 3 of both sides:

log(3)15309 = x

Use log rules to simplify the expression:

log(3)15309 = log(3)(3^x)

log(3)15309 = x * log(3)3

log(3)15309 = x * 1

log(3)15309 = x

Substitute the value of x by using log(3)7 = 1.7712:

log(3)15309 ≈ 1.7712 * log(3)81 (since 81 is the largest power of 3 that is less than 15309)

log(3)15309 ≈ 1.7712 * 4

log(3)15309 ≈ 7.0848

Therefore, log(3)15309 ≈ 7.0848.

To the nearest hundredths place: 29.03 kg

Answer:

3 km

Step-by-step explanation:

3000 m = x km

1000 m = 1 km

Form a proportion to represent the situtation based on a conversion.

[tex]\frac{3000}{x} = \frac{1000}{1}[/tex]

Cross multiply.

1000x = 3000

x = 3 km

To calculate 3000 Meters to the corresponding value in Kilometers, multiply the quantity in Meters by 0.001 (conversion factor). In this case we should multiply 3000 Meters by 0.001 to get the equivalent result in Kilometers:

3000 Meters x 0.001 = 3 Kilometers

Therefore, 3000 Meters is equivalent to 3 Kilometers.

Answer:

A' (0, 0 )

Step-by-step explanation:

a translation of 5 units right adds 5 to the x- coordinate

a translation of 2 units down subtracts 2 from the y- coordinate

A (- 5, 2 ) → A' (- 5 + 5, 2 - 2 ) → A' (0, 0 )

Answer:

[tex] {≈225.4 \: m}^{2} [/tex]

[tex] {≈248.2 \: m}^{2} [/tex]

Step-by-step explanation:

(My first few steps are in the photo I've added)

Now, we can find the area of the first cutout:

[tex]s(cutout1) = \frac{\pi \times {r}^{2} \times \alpha }{360°} = \frac{\pi \times {18}^{2} \times 114°}{360°} = \frac{36963\pi}{360°} = 102.6\pi[/tex]

We can also find the altitude of the first triangle using trigonometry:

[tex] \sin(∠obd) = \frac{od}{ob} [/tex]

We also need to find AB by using the Pythagorean theorem:

[tex] {ad}^{2} = {ao}^{2} - {od}^{2} = {18}^{2} - {5.56}^{2} = 293.0864[/tex]

[tex]ad > 0[/tex]

[tex]ad = \sqrt{293.0864} ≈ 17.12[/tex]

[tex]ab = 2 \times 17.12 = 34.24[/tex]

[tex]h1 = od = ob \times \sin(∠obd) = 18 \times \sin(18°)≈5.56[/tex]

Then, we can find the area of the 1st triangle:

[tex]s (1triangle)= \frac{1}{2} \times 5.56 \times 34.24 ≈95.19[/tex]

And we can also find the area 1:

[tex]area1 = s(cutout1) - s(triangle1) = 102.6\pi - 95.19≈225.25[/tex]

Now let's do the same thing with the second area:

[tex]s(cutout2) = \frac{\pi \times {r}^{2} \times \alpha }{360°} = \frac{\pi \times {18}^{2} \times 131°}{360°} = \frac{42444\pi}{360°} =117.9 \pi[/tex]

[tex] \sin(∠obe) = \frac{oe}{oc} [/tex]

[tex]h2 = oe = oc \times \sin(∠obe) = 18 \times \sin(24.5°)≈7.46[/tex]

[tex] {be}^{2} = {bo}^{2} - {oe}^{2} = {18}^{2} - {7.46}^{2} = 268.3484[/tex]

[tex]be > 0[/tex]

[tex]be = \sqrt{268.3484} ≈16.38[/tex]

[tex]bc = 2 \times 16.38 = 32.76[/tex]

[tex]s(triangle2) = \frac{1}{2} \times 7.46 \times 32.76 = 122.19[/tex]

[tex]area2 = s(cutout2) - s(triangle2) = 117.9\pi - 122.19≈248.2[/tex]

I don't know if I got this right, though...

The area of the shaded segments in the circle is 422.5 square meters

Given that

Radius = 18 meters

Angles = 114 degrees and 131 degrees

The area of the shaded segments is the sum of the area of the individual segments and this is calculated as

Segment area =  (½) × r² × [(π/180) θ – sin θ]

Using the above, we have

Shaded segments = (½) × 18² × [(114π/180) – sin (114)] + (½) × 18² × [(131π/180) – sin (131)]

Evaluate

Shaded segments = 422.5 square meters

Hence, the shaded segments is 422.5 square meters

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Andre makes green paint by mixing 5 cups οf yellοw paint with 2 cups οf blue paint.

Tο make the same shade οf green, Andre needs 20 cups yellοw paint if he uses 8 cups οf blue paint.

Andre needs 6 cups blue paint if she uses 15 cups οf yellοw paint.

Any cοlοred liquid, liquefiable, οr sοlid mastic substance that fοrms intο a film when applied tο a surface in a thin layer is referred tο as paint. It can be used tο give texture, cοlοr, οr prοtectiοn, amοng οther things. There are numerοus types and shades οf paint that can be prοduced. Mοst paint kinds eventually sοlidify, but they are nοrmally kept, purchased, and applied as liquids. The bulk οf paints are either οil- οr water-based, and each has unique characteristics.

Andre makes green paint by mixing 5 cups οf yellοw paint with 2 cups οf blue paint.

Suppοse tο make the same shade οf green, he uses 8 cups οf blue paint and x cups οf yellοw paint.

Then, yellοw/blue= 5/2= x/8

Or, 2x= 5*8

Or, x= 40/2

Or, x=20

Sο tο make the same shade οf green, Andre needs 20 cups yellοw paint if he uses 8 cups οf blue paint.

Suppοse Andre needs y cups blue paint if she uses 15 cups οf yellοw paint.

Yellοw/blue= 5/2= 15/y

Or, 5y= 15*2

Or, y= 30/5

Or, y=6

Sο Andre needs 6 cups blue paint if she uses 15 cups οf yellοw paint.

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Answer:

180 cubic centimeters

Step-by-step explanation:

We can find the volume of a box by multiplying the dimensions of the box together.
In other words

Volume = length × width × height

Given dimensions

By plugging these given dimensions into the formula we acquire

Volume = 6 × 10 × 3

==> multiply 10 and 6

Volume = 60 × 3

==> multiply 60 and 3

Volume = 180

The volume of the box is 180 cubic centimeters.

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Answer: The square root of 10 is 3.162

Answer:

3.5 seconds

Step-by-step explanation:

h(t) = 112t - 16t^2

we can re-write it: h(t) = -16t^2 + 112t

with a = -16 and b = 112

the formula -b/(2a) corresponds to x-coordinate of the maximum.

-112/(2 x -16) = 3.5

Answer:

1. 33 foot

2. 6.2 foot

Step-by-step explanation:

1.

Let's denote the height of the tree by "h". We can use the tangent function to solve the problem:

tangent of the angle of elevation = opposite / adjacent

In this case, the opposite side is the height of the tree, and the adjacent side is the distance from the tree to the point on the ground where the angle of elevation is measured. So we have:

tan(35) = h / 47

To solve for "h", we can multiply both sides by 47:

h = 47 tan(35)

Using a calculator, we get:

h ≈ 32.9 feet

So the height of the tree to the nearest foot is 33 feet.

2.

Let's call the distance we're trying to find "x". We can use trigonometry to relate the angle and the length of the guy wire to the distance "x". Specifically, we can use the sine function:

sine of the angle = opposite / hypotenuse

In this case, the opposite side is the distance "x", and the hypotenuse is the length of the guy wire, which is 8 feet. So we have:

sin(51) = x / 8

To solve for "x", we can multiply both sides by 8:

x = 8 sin(51)

Using a calculator, we get:

x ≈ 6.2 feet

So the stake is about 6.2 feet from the foot of the stop sign, to the nearest tenth of a foot.

The dimensions of the net will be the same as the dimensions of the rectangular prism, since the net is just a flattened version of the 3D shape.

What is Rectangular prism ?

A rectangular prism is a three-dimensional geometric shape that has six faces, all of which are rectangles.

To label the dimensions of the net for the current cereal box, you need to identify the six faces of the rectangular prism that makes up the cereal box.

Start by drawing a rectangular prism with the given dimensions (12 inches high, 8 inches wide, and 2 inches deep).

Then, label each face with its dimensions, as follows:

The top face (which will be the same size as the bottom face) has dimensions 8 inches by 2 inches.

The front and back faces have dimensions 12 inches by 8 inches.

The left and right faces have dimensions 12 inches by 2 inches.

Top face: 8 in. x 2 in.

Front and back faces: 12 in. x 8 in.

Left and right faces: 12 in. x 2 in.

Therefore, Note that the dimensions of the net will be the same as the dimensions of the rectangular prism, since the net is just a flattened version of the 3D shape.

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