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Write an equation that represents the line.
Use exact numbers.

Answer:

Sure. Here are the steps on how to solve for the sides and angles of triangle ABC using the law of cosines:

Draw a sketch of triangle ABC.

Label the sides and angles of triangle ABC.

Label the known and unknown values.

Use the law of cosines to solve for the unknown side or angle.

In this case, we know the following:

Side b = 60

Side c = 30

Angle A = 70°

We need to solve for side a and angles B and C.

The law of cosines states that

a^2 = b^2 + c^2 - 2bc cos A

where a, b, and c are the sides of the triangle and A is the angle opposite side a.

Plugging in the known values, we get

a^2 = 60^2 + 30^2 - 2(60)(30) cos 70°

a^2 = 900 + 900 - 3600 cos 70°

a^2 = 1800 - 3600 cos 70°

a = sqrt(1800 - 3600 cos 70°)

a = 57

Therefore, side a is 57.

To solve for angle B, we can use the law of sines. The law of sines states that

\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}

Plugging in the known values, we get

\frac{57}{\sin 70°} = \frac{60}{\sin B}

\sin B = \frac{57 \sin 70°}{60}

\sin B = 0.774

B = \sin^{-1}(0.774)

B = 81°

Therefore, angle B is 81°.

To solve for angle C, we can use the fact that the sum of the angles of a triangle is 180°.

A + B + C = 180°

70° + 81° + C = 180°

C = 29°

Therefore, angle C is 29°.

Therefore, the sides and angles of triangle ABC are a = 57, b = 60, c = 30, A = 70°, B = 81°, and C = 29°.

Step-by-step explanation:

The probability of drawing one paisley tie is 0.43

Three paisley ties and four solid ties are in a dresser. Therefore, the probability if drawing out one paisley tie without looking can be calculated as follows:

The total number of ties is the sum of the paisley ties and solid ties, which is 3 + 4 = 7.

Therefore, the probability of drawing out 1 paisley tie without looking is as follows:

probability of drawing out 1 paisley tie without looking = 3 / 7

probability of drawing out 1 paisley tie without looking = 0.42857142857

Hence , the probability of drawing out one paisley tie without looking is 0.43

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Line 4 of Raya's solution is the B. Distributive property of equality.

Line 4 of Raya's solution to 2.5(6.25x + 0.5) = 11 is shown as follows:

2.5(6.25x + 0.5) = 11

15.625x + 1.25 = 11

The correct reason for line 4 of Raya's solution is the Distributive property of equality. This property states that for any real numbers a, b, and c, a(b + c) = ab + ac. In line 4 of Raya's solution, the Distributive property is applied to distribute 2.5 to the terms inside the parentheses (6.25x and 0.5).

To see why the Distributive property is used, let's consider the expression 2.5(6.25x + 0.5). To simplify this expression, we can use the Distributive property as follows:

2.5(6.25x + 0.5) = 2.5(6.25x) + 2.5(0.5)

Now, we can use the Multiplication property of equality to simplify the expression further:

15.625x + 1.25 = 11

This means that 15.625x + 1.25 is equal to 11, and we can continue solving for x.

In summary, the Distributive property of equality is used to simplify expressions by distributing a factor to the terms inside parentheses. In Raya's solution to 2.5(6.25x + 0.5) = 11, the Distributive property is applied to simplify the expression before solving for x. Therefore, Option B is correct.

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The view factor from the 2 cm side to the 4 cm side of the infinitely long three-sided triangular enclosure is approximately 0.5.

The view factor (F) from Surface A to Surface B can be calculated using the formula:

F = A / (A + B)

where A and B are the areas of Surface A and Surface B, respectively.

The area of a triangle can be calculated using Heron's formula:

Area = sqrt(s * (s - a) * (s - b) * (s - c))

where s is the semi-perimeter of the triangle and a, b, and c are the side lengths of the triangle.

For Surface A:

a = 2 cm

b = 3 cm

c = 4 cm

s = (a + b + c) / 2 = (2 + 3 + 4) / 2 = 4.5 cm

Area_A = sqrt(4.5 * (4.5 - 2) * (4.5 - 3) * (4.5 - 4))

= √(4.5 * 2.5 * 1.5 * 0.5)

=√(5.625) ≈ 2.37 cm²

For Surface B:

a = 2 cm

b = 4 cm

c = 3 cm

s = (a + b + c) / 2 = (2 + 4 + 3) / 2 = 4.5 cm

Area_B = √(4.5 * (4.5 - 2) * (4.5 - 4) * (4.5 - 3))

= √(4.5 * 2.5 * 0.5 * 1.5)

=√(5.625) ≈ 2.37 cm²

Now we can calculate the view factor (F):

F = Area_A / (Area_A + Area_B)

= 2.37 / (2.37 + 2.37)

≈ 0.5

Therefore, the view factor from the 2 cm side to the 4 cm side of the infinitely long three-sided triangular enclosure is approximately 0.5.

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Answer:

$123,809.52

Step-by-step explanation:

The total bill is equal to the purchase price of the fridge/freezer plus the sales tax.

Total = Price + Tax

We know the total is 130,000.

We don't know the price, so let's call it x.

The tax is 5% of the price, or ⁵/₁₀₀ x, or 0.05 x.

130,000 = x + 0.05 x

130,000 = 1.05 x

x = 123,809.52

Answer:

Use the quotient property of logarithms, logb(x)−logb(y)=logb(xy) log b ( x ) - log b ( y ) = log b ( x y ) . log3(4010) log 3 ( 40 10 ). Step 2.

The irrational number can be multiplied by -~ 41 to get a product that equals 1 is 1/[tex]-\sqrt{41}[/tex] the correct option is A.

We are given that;

The number= [tex]-\sqrt{41}[/tex]

Now,

To find the irrational number that can be multiplied by sqrt(41) to get a product that equals 1, we need to find the multiplicative inverse of sqrt(41). The multiplicative inverse of a number is the number that when multiplied by the original number gives 1 as the product. For example, the multiplicative inverse of 2 is 1/2, because 2 * 1/2 = 1.

To find the multiplicative inverse of sqrt(41), we can divide 1 by sqrt(41). We get:

[tex]1 / \sqrt{41} = \sqrt{41} / \sqrt{41} \times \sqrt{41}) = \sqrt{41} / 41[/tex]

To simplify the expression, we can rationalize the denominator by multiplying both the numerator and the denominator by sqrt(41). We get:

[tex]\sqrt{41} / 41 \times \sqrt{41} / \sqrt{41} = (\sqrt{41})^2 / (41 \times \sqrt{41}) = 41 / (41 \times\sqrt{41}) = 1 / \sqrt{41}[/tex]

Therefore, by the fraction the answer will be 1/[tex]-\sqrt{41}[/tex].

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The quadrilateral has a area of 10 square units.

Because the vertices of the quadrilateral are p(3, 4), m(8, 4), n(5, 0).

This quadrilateral can be divided into two triangles.

For the first triangle, we can say that p(5) is the base and m(4) is the height.

Area of the triangle=1/2x5x4

                                 =5x2

                                 =10

The bases of the second triangle are p(5) and n(0).

Area of ​​the second triangle = 1/2x5x0

=0

Now the area of ​​the quadrilateral is the sum of both triangles-

Area of the first triangle + Area of the second triangle

=10+0

=10

Thus, the area of quadrilateral is 10.

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The exponential function has a horizontal asymptote at y = –3 will be; f (x) = –3^x – 3.

We get a horizontal asymptote for a function;

Note that the x-axis (y=0) is the horizontal asymptote.

Since the question asked for a function with asymptotic behaviors of y = -3,

we can shift the function 3 units above by changing Q to +3.

The exponential function has a horizontal asymptote at y = –3 will be;

f (x) = –3^x – 3.

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The percentage of Mr. Reyes total compensation that was withheld for federal taxes is given as follows:

14.2%.

From the table, we have that the parameters for this problem are given as follows:

Hence the proportion of Mr. Reyes total compensation that was withheld for federal taxes is given as follows:

8802.26/61987.5 = 0.142.

Then the percentage is given as follows:

0.142 x 100% = 14.2%.

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The graph that correctly represents the data in the table for this problem is given as follows:

Top right graph.

On the definition of a function, the y-intercept is given by the value of y for which the input assumes a value of zero.

Hence, on the graph of a function, the y-intercept is the value of y for which the graph touches or crosses the y-axis.

From the table, we have that when x = 0, y = 4, hence the graph should cross the y-axis at y = 4, hence the top right graph is the correct option in the context of this problem.

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The pairs of simultaneous equations have their x and y values to be (a) x+y=5 and xy=x+3: (1, 4) and (2, 3) & (b) 2x+y=5 and x² + y² =10: (x, y) = (1, 3) and (3, -1)

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

The pairs of simultaneous equations can be solved using a graphical method

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

(a) x+y=5 and xy=x+3

x and y values:

(x, y) = (1, 4) and (2, 3)

(b) 2x+y=5 and x² + y² =10

x and y values:

(x, y) = (1, 3) and (3, -1)

See attachment for graphs

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The numbers that are elements of both the subset of odd numbers and the subset of multiples of 3 are 3 and 9.

The odd numbers in the set are {1, 3, 5, 7, 9} and the multiples of 3 in the set are {3, 6, 9}.

The elements that are in both subsets are the ones that appear in both sets, which are only 3 and 9.

Therefore, the numbers 3 and 9 are the elements that are in both the subset of odd numbers and the subset of multiples of 3.

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Answer:

6 cups

Step-by-step explanation:

When two things are directly proportional (e.g. y and x), we can model the relationship with the direct variation equation, which is

y = kx, where

Step 1:  To find k, we can allow y to represent Jackie's total revenue from selling lemonade ($9) and x to represent the quantity of cups of lemonade sold ($3):

9 = 3k

k = 3

Step 2:  Now that we've found the constant of proportionality, we can plug in 18 for y and 3 for k, allowing us to solve for x:

18 = 3x

6 = x

Thus, in order for Jackie to earn $18, she must sell 6 cups in all.

The angular velocity of the connecting rod is w = 1.939 rad/s

Given data ,

To determine the angular velocity of the connecting rod CD at the instant angle θ = 30 degrees, we need to consider the relationship between the angular velocities of different components in a mechanism. In this case, we can use the concept of relative velocity

The angular velocity of the connecting rod CD can be found using the following equation

ω_CD = ω_AB + ω_BC

angular velocity of CD = angular velocity of AB x (AB/CD) x sin(u) x (1/cos(u))

angular velocity of CD = 4 rad/s x (10/20) x sin(30) x (1/0.825)

Therefore , the angular velocity is CD = 1.939 rad/s

Hence , the angular velocity is w = 1.939 rad/s

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Answer:

Normally, to calculate 9.2 percent, you would multiply a number by 9.2 percent and then you would take the product of that and divide it by 100 to get the answer.

Instead, you can simply multiply a number by 9.2 as a decimal to get the answer.

9.2 percent means 9.2 per hundred. Therefore, to get 9.2 as a decimal, all you have to do is divide 9.2 by 100 like so:

9.2 ÷ 100 = 0.092

Shortcut: When you divide anything by 100, just move the decimal point two places to the left.

Step-by-step explanation:

The zeros in a function are where it passes through the x-axis and  to find the zeros, set the equation equal to zero, then solve for x.

The zeros of a function are the values of the input variable (usually denoted as x) that make the output of the function equal to zero.

In other words, if you graph the function, the zeros are the points where the graph crosses the x-axis.

To find the zeros of a function, you need to set the function equal to zero and solve for the input variable.

This means you're looking for the x-values that make the function equal to zero.

Once you've found the zeros, you can use them to graph the function and analyze its behavior.

Hence, the zeros in a function are where it passes through the x-axis and  to find the zeros, set the equation equal to zero, then solve for x.

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Answer:

20 water fountains can be made when the cost is 770.

Verbal statement: The cost equals 30 times the fountains for cats plus 170

Step-by-step explanation:

Lets review the defined variables.

f = fountains for cats

C = cost

We are given the value of the cost, but not the amount of fountains for cats. This means we will have to solve for f in the equation.

Substitute 770 for C

[tex]770=30f+170[/tex]

Subtract 170 on both sides

[tex]600=30f[/tex]

Divide by 30

[tex]20=f[/tex]

20 water fountains can be made when the cost is 770.

To prove this, plug our numbers into the expression.

[tex]30(20)+170[/tex]

[tex]600+170[/tex]

[tex]770[/tex]

So our answer is correct.

∠g and ∠h are complementary angles and ∠g and ∠h are acute angles are true statements from the given information

Two angles are given.

∠g = (2x-90)°

∠h = (180-2x)°

We have to find the statement which is true about the angles g and h.

If both angles are greater than zero.

Complementary angles add up to 90 degrees

i.e., ∠g and ∠h are complementary if ∠g + ∠h = 90°.

Substituting the given values:

∠g + ∠h

= (2x-90)° + (180-2x)° = 90°

Thus, ∠g and ∠h are complementary angles.

and both the angles are less than 90 degrees so we can tell that angles ∠g and ∠h  are acute.

So the statement ∠g and ∠h are acute angles is also true

Hence, ∠g and ∠h are complementary angles and ∠g and ∠h are acute angles are true statements

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Answer:

The tan of angle A is equal to a/b, where a and b are the lengths of the opposite and adjacent sides of the angle respectively. In this case, we have a = 15, b = 8, which gives us a tan of 15/8 or approximately 1.875.

The correct option for the demand requirement constraint in a production scheduling LP is option (c): beginning inventory + production - ending inventory = demand.

In a production scheduling LP, the demand requirement constraint represents the balance between the available inventory and the demand for the product. The constraint ensures that the production and inventory levels are sufficient to meet the specified demand.

Option (c) represents this relationship accurately by stating that the beginning inventory, production, and ending inventory, when subtracted from each other, should equal the demand. This equation reflects the concept of maintaining a balance between the production output and inventory changes to meet the demand

Option (a) is incorrect because it uses the greater than or equal to (≥) symbol, which does not accurately represent the constraint.

Option (b) is also incorrect because it uses the equality (=) symbol, which implies an exact balance between the inventory and demand, disregarding the changes in inventory.

Option (d) is incorrect because it uses the greater than or equal to (≥) symbol, which does not accurately represent the constraint.

Therefore, option (c) is the correct representation of the demand requirement constraint in a production scheduling LP.

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This is a translation of 2 units to the left and 5 units up, so the correct option is the first one.,

Remember that a vertical translation of N units is:

g(x) = f(x) + N

if N < 0 the translation is down.

if N > 0 the translation is up.

And a horizontal translation of N units is:

g(x) = f(x + N)

If N > 0 the translation is to the right.

if N < 0 the translation is to the left.

Here we have the transformation:

f(x) = x²

g(x) = (x + 2)² + 5

So this is a translation of 2 units to the left and 5 units up.

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Nakeisha sold 8 lollipops and 5 fruit snacks yesterday to earn a total of $18.25.

Let's use a system of equations to solve this problem. Let x be the number of lollipops sold and y be the number of fruit snacks sold. From the problem, we know that:
- The price of each lollipop is $1.50, so the total amount of money earned from selling x lollipops is 1.5x.
- The price of each fruit snack is $1.25, so the total amount of money earned from selling y fruit snacks is 1.25y.
- Yesterday, Nakeisha made $18.25 from selling a total of 13 lollipops and fruit snacks, so we can write the equation:
1.5x + 1.25y = 18.25
We also know that Nakeisha sold a total of 13 lollipops and fruit snacks, so we can write the equation:
x + y = 13
Now we have two equations with two variables, which we can solve using substitution or elimination. Let's use substitution:
- Rearrange the second equation to solve for one variable in terms of the other:
x + y = 13
y = 13 - x
- Substitute y = 13 - x into the first equation:
1.5x + 1.25y = 18.25
1.5x + 1.25(13 - x) = 18.25
- Simplify and solve for x:
1.5x + 16.25 - 1.25x = 18.25
0.25x = 2
x = 8
- Substitute x = 8 back into y = 13 - x to find y:
y = 13 - x
y = 13 - 8
y = 5
Therefore, Nakeisha sold 8 lollipops and 5 fruit snacks yesterday to earn a total of $18.25.

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Answer:

To find the perimeter of a scale drawing, we need to use the same scale factor that was used to create the drawing. In this case, the scale factor is 7 inches: 28 feet, or 1 inch: 4 feet. This means that every inch in the drawing represents 4 feet in the actual floor.

To find the perimeter of the floor in the scale drawing, we need to add up the lengths of all the sides. Since the floor is rectangular, it has two pairs of equal sides. The length of the floor is 28 feet, so the length of the scale drawing is 28 / 4 = 7 inches. The width of the floor is 24 feet, so the width of the scale drawing is 24 / 4 = 6 inches.

The perimeter of the scale drawing is then:

7 + 6 + 7 + 6 = 26 inches

MARK AS BRAINLIEST!!! THIS TOOK A LOT OF TIME!!!

An office building of 21,000 f t squared would require 140 air vents according to the recommendation of 2 air vents for every 300 f t squared of floor space.

Based on the recommendation of 2 air vents for every 300 f t squared of floor space, we can calculate the number of air vents required for an office building of 21,000 f t squared by dividing the total floor space by 300 and multiplying the result by 2.

21,000 / 300 = 70
70 x 2 = 140

Therefore, an office building of 21,000 f t squared would require 140 air vents according to the recommendation of 2 air vents for every 300 f t squared of floor space.

It is important to note that this is just a recommendation and the actual number of air vents required may vary depending on factors such as ceiling height, insulation, and other building characteristics. It is always best to consult with an HVAC specialist to determine the appropriate number and placement of air vents for optimal air circulation and comfort in a building.

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Hello

2/3 = 8/12

3/4 = 9/12

                9/12

0 - - - - - - - - - - - - 1 - - - - - - - - - - - - 2

              8/12

Answer :

                3/4

0 - - - - - - - - - - - - 1 - - - - - - - - - - - - 2

              2/3

=> 2/3 = the 8th graduation

=> 3/4 = the 9th graduation

=> 1 unit = 12 graduations

To calculate the probability that at least one of the six lightbulbs selected from the shipment is defective, we need to first calculate the probability that all of them work and then subtract that from 1. Therefore, the probability that at least one of the six lightbulbs is defective is 0.2649 or 26.49%.

The probability that a single lightbulb is defective is 0.05 and the probability that it works is 0.95. Therefore, the probability that all six lightbulbs work is:
0.95 x 0.95 x 0.95 x 0.95 x 0.95 x 0.95 = 0.7351
To calculate the probability that at least one of the six lightbulbs is defective, we need to subtract this from 1:
1 - 0.7351 = 0.2649
Therefore, the probability that at least one of the six lightbulbs is defective is 0.2649 or 26.49%. In other words, there is a little over a one in four chance that at least one of the six lightbulbs selected is defective.

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Customers at the old store bought milkshakes about 20.46% of the time.

Customers at the new store bought milkshakes about 26.29% of the time.

Of all the milkshakes sold at Ezra's Ice Cream Shops, 59.29% were sold at the old store.

To calculate the percentages, we need to find the conditional probabilities based on the given information.

Let's calculate the percentages step by step:

Customers at the old store bought milkshakes about:

Milkshakes sold at the old store = 13,400

Total sales at the old store

= 52,100 (Ice Cream) + 13,400 (Milkshakes) = 65,500

Percentage

= (Milkshakes sold at the old store / Total sales at the old store) x 100

Percentage = (13,400 / 65,500) x 100 ≈ 20.46%

Customers at the new store bought milkshakes about:

Milkshakes sold at the new store = 9,200

Total sales at the new store = 25,800 (Ice Cream) + 9,200 (Milkshakes) = 35,000

Percentage = (Milkshakes sold at the new store / Total sales at the new store) x 100

Percentage = (9,200 / 35,000) * 100 ≈ 26.29%

Of all the milkshakes sold at Ezra's Ice Cream Shops, the percentage sold at the old store:

Total milkshakes sold at both stores = Milkshakes sold at the old store + Milkshakes sold at the new store = 13,400 + 9,200 = 22,600

Percentage = (Milkshakes sold at the old store / Total milkshakes sold) x 100

Percentage = (13,400 / 22,600) x 100 ≈ 59.29%

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Answer:

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

Use the slope equation:

Substitute given values for the slope and coordinates and and solve for h:

The value of h is - 6.