I just need the answer to the first question (16) plz thx

A)Evaluate g(0)
B)Find x if g(x)=0
C) domain and range

The slope of the tangent line to the polar curve r = 2 - sin(θ) at the point specified by θ = π/3 is -1/2.

To find the slope of the tangent line to the polar curve r = 2 - sin(θ) at the point specified by θ = π/3, we need to first find the derivative of r with respect to θ, and then evaluate it at θ = π/3.

Differentiating both sides of the polar equation with respect to θ, we get:

dr/dθ = d/dθ(2 - sinθ)

dr/dθ = -cosθ

So, the derivative of r with respect to θ is -cosθ.

Evaluating this derivative at θ = π/3, we get:

dr/dθ|θ=π/3 = -cos(π/3) = -1/2

Therefore, the slope of the tangent line to the polar curve r = 2 - sin(θ) at the point specified by θ = π/3 is -1/2.

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We have to apply the rule of three to solve this.

We will use the equivalencies of the first row to complete the others.

The cups of flour needed are 3 cups/loaf.

The water needed is 12 tablespoons/loaf.

The salt needed 1 teaspoon/loaf.

With these equivalencies we can calculate the ingredients needed for any number of loaves:

Answer:

x=11

Step-by-step explanation:

Answer:

x=11

Step-by-step explanation:

10x-4+5x+19=180

Combine like terms

15x+15=180

      -15    -15

15x=165

divide by 15

x=11

Answer:

(d). 1/14

(e). -2 11/14

(f). -6.315

Step-by-step explanation:

Answer:

d). 1/14  e). -59/24  f). -6.315

Step-by-step explanation:

d). 1/14

e). -59/24

f). -6.315

Answer:

Can you give me the choices for each of these, I'm not sure how they might phrase it.

The logical expression that represents the statement "Despite the fact that it is sunny today, I will bring my umbrella" is (B) s∧m.

The logical expression that represents the statement "Despite the fact that it is sunny today, I will bring my umbrella" is (B) s∧m. This is because the conjunction "and" (∧) is used to connect two statements that must both be true in order for the overall statement to be true. In this case, both s (It is sunny today) and m (I will bring my umbrella) must be true in order for the statement to be true.

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(B) s∧m, which represents the logical expression for "Despite the fact that it is sunny today, I will bring my umbrella."


The logical operator ∧ (conjunction) connects two propositions and represents the idea of "and." Therefore, s∧m means "It is sunny today and I will bring my umbrella." This is the logical expression that represents the statement given in the question.


To summarize, the correct answer is (B) s∧m, which represents the logical expression for "Despite the fact that it is sunny today, I will bring my umbrella."
Main Answer: The correct logical expression is (B) s∧m.

In the given statement, "Despite the fact that it is sunny today, I will bring my umbrella," both propositions s (It is sunny today) and m (I will bring my umbrella) are true at the same time. The logical expression that represents this is s∧m, which means "s AND m" are both true.

The statement "Despite the fact that it is sunny today, I will bring my umbrella" is best represented by the logical expression (B) s∧m, as it shows that both s and m are true.

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Answer:

108 degrees

Step-by-step explanation:

3x+x+6x=10x, 180/10=18 and 18x6 is 108

The amount of material needed by Marta to make the flag is;

\(\rm Area =\sqrt{50(50-d_1)(50-d_2)(50-d_3)}\) square inch.

The total cost of making the flag is;

\(\rm 0.15 \times\rm \sqrt{50(50-d_1)(50-d_2)(50-d_3)}\) dollar.

Given

Marta is making a flag with the given dimensions.

The perimeter of the flag is 100 inches.

Let us consider that the flag has a triangular shape.

According to the Hero's formula;

The area of the triangle is given by;

\(\rm Area =\sqrt{s(s-a)(s-b)(s-c)}\)

Where, s is the semi perimeter and a, b, and c are the sides of the triangle.

Semi perimeter s = P/2,

Since the perimeter of the flag is 100 inches.

\(\rm S=\dfrac{100}{2}\\\\S=50\)

The dimensions of triangular shape are \(\rm d_1, d_2 \ and \ d_3\).

Then,

The area of the triangular flag becomes;

\(\rm Area =\sqrt{s(s-a)(s-b)(s-c)}\\\\\rm Area =\sqrt{50(50-d_1)(50-d_2)(50-d_3)}\)

So the amount of material needed to make the flag is;

\(\rm Area =\sqrt{50(50-d_1)(50-d_2)(50-d_3)}\)

Therefore,

The cost of material = C = $0.15 per square inch

So the total cost in making the flag will be;

\(\rm C\times A=0.15 \times A\\\\=0.15 \times\rm \sqrt{50(50-d_1)(50-d_2)(50-d_3)}\).

Hence, The amount of material needed by Marta to make the flag is \(\rm Area =\sqrt{50(50-d_1)(50-d_2)(50-d_3)}\).

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Answer:

1

Step-by-step explanation:

If the length of the rectangle is represented by "x," then the width is (x - 58), and the area can be calculated as x² - 58x.

Let's go through the problem step by step to find the area of the rectangle.

Let's assume that the length of the rectangle is represented by the variable "x" (as stated in the question). According to the given information, the width of the rectangle is 58 units less than its length.

If the width is 58 units less than the length, we can represent the width as (x - 58). This means that the length minus 58 gives us the width.

Now, to find the area of the rectangle, we use the formula:

Area = Length × Width

Substituting the values we have:

Area = x × (x - 58)

Expanding the equation:

Area = x² - 58x

So, the area of the rectangle is given by the expression x² - 58x.

To summarize, if the length of the rectangle is represented by "x," then the width is (x - 58), and the area can be calculated as x² - 58x.

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Answer:

2/35

Step-by-step explanation:

original equation:q+1/7=1/5

subtract both sides by 1/7

q=1/5-1/7

q=2/35

(give me brainly pls)

Answer:

Is there supposed to be a picture?

Step-by-step explanation:

Where the above is given, the required angle m∠BAC = 45°.

In triangle ABC. AC represents the foreman’s line of sight to the top of the landfill. Landfill height is BC

The triangle is geometric shape which includes 3 sides and sum of interior angle should not grater than 180°

According to conditions angle b = 90°

The sum of angles of a triangle= 180°

That is a + b + c = 180

Therefore, c = a

       a = (180 - b)/2

          = (180 - 90) / 2

          = 90 / 2

          = 45°

Hence, the required angle m∠BAC = 45°

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Full Question:

Although part of your question is missing, you might be referring to this full question:

Question 1 Create Triangle ABC by drawing AC. Segment AC represents the foreman’s line of sight to the top of the landfill. What is Angle m BAC?

If abcde is a regular pentagon, the smallest rotation about e which maps a to d is 144 degrees.

Using the fact that a regular pentagon has rotational symmetry of order 5. This means that if we rotate the pentagon by 72 degrees around its center, it will appear the same as it did before the rotation.

To map a to d, we need to rotate the pentagon by some angle around point e. Since e is the center of rotation, we need to find an angle that is a multiple of 72 degrees.

To determine the smallest angle of rotation, we need to find the number of 72 degree rotations that take us from a to d.

Starting from a, we can count the number of 72 degree rotations we need to make to reach d. We see that we need to make two 72 degree rotations in a counterclockwise direction.

Therefore, smallest rotation about e that maps a to d is a 144 degree counterclockwise rotation.

We can visualize this by drawing a regular pentagon and marking the point a and d on it. Then, we draw a line segment from a to d and a line segment from e to the midpoint of segment ad.

The angle between these two line segments is 144 degrees.

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Answer:

1/49

Step-by-step explanation:

Answer:

5040

Step-by-step explanation:

This problem is about indistinguishable permutation. We have indistinguishable objects, in this case, these are the letter of the word ELLIPSES. The permutations for the word ELLIPSES is the same when you swap the places of the Ls. We need to not count them to avoid double counting.

We first count how many letters we have on the word, and then count the repeating letters.

ELLIPSES has 8 letters, 2 Es, 2Ls, and 2S.

The formula for indistinguishable permutation is

where n is the total number of objects and  are the number of indistinguishable objects.

We have 2Es, 2Ls, and 2S; the formula then becomes:

Simplifying gives us

There are 5,040 distinguishable permutations of the word ELLIPSES.

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The total 5040 distinguishable permutations are possible with all the letters of the word ELLIPSES.

The given word is ELLIPSES.

It is required to find total distinguishable permutations that are possible with the above word.

A permutation can be defined as the number of ways a set can be arranged.

Permutation formula as below:

\(P=\frac{n!}{p!q!r!...}\)

Where n = Total number of objects.

     p,q,r...= the number of indistinguishable objects.

Here total number of letters in the word n = 8

and ELLIPSES have 2Es, 2Ls, and 2S; the formula then becomes:

\(=\frac{8!}{2!2!2!}\)

\(=\frac{8*7*6*5*4*3*2*1}{2*1*2*1*2*1}\)

\(=5040\)

Thus, the total 5040 distinguishable permutations are possible with all the letters of the word ELLIPSES.

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Answer:

6 laps

Step-by-step explanation:

Each lap Jeffrey needs to run is one tenth of a mile he wants to run threee fifths of a mile how many laps does he need to run

One tenth of a mile = 1/0

Three fifths of a mile = 3/5

From the question:

1/10 mile = 1 lap

3/5 mile = x

Cross Multiply

1/10 mile × x = 3/5 mile × 1 lap

x = 3/5 mile × 1 lap/ 1/10 mile

x = 3/5 ÷ 1/10

x = 3/5 × 10/1

x = 6 laps

Therefore, for there fifths of a mile(3/5) he needs to run 6 laps

The approximate volume of sand in the container is about 0.2 gallons. To find the volume of the sand, we need to find the volume of the cylinder container. We can use the formula for the volume of a cylinder: V=πr²h.

First, we need to find the radius by dividing the diameter by 2: r = 12/2 = 6. So, the volume of the cylinder is: V = 3.14 x 6² x 10 = 1,128 cubic inches. To convert cubic inches to gallons, we divide by 231 (the number of cubic inches in a gallon): 1,128/231 ≈ 4.9 gallons. Rounding this to the nearest gallon gives us 5 gallons.

However, the child completely filled the container with sand, which means that some sand may have spilled over the top. So, it's safe to assume that the actual volume of sand in the container is slightly less than 5 gallons. We can estimate the volume to be about 0.2 gallons.

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Answer:

hypergeometric

Step-by-step explanation:

For each winning ticket, there are only two possible outcomes. Either it is held by a men, or it is not.

There is a set number of X, and as the number of winning tickets decrease, the probability of a winning ticket being held by a men can decrease or increase. This is a characteristic of the hypergeometric distribution.

To calculate the interest owed after 93 days, we use the formula for simple interest: Interest = Principal x Rate x Time. Substituting the given values, the interest amounts to $624.49.

This is the total interest that Melissa will owe to the bank after 93 days.Melissa took out a loan of $15,400 from a bank for home renovations. The bank charges a simple interest rate of 16% per year If Melissa doesn't make any payments towards the loan, the total amount owed after 93 days is obtained by adding the principal and the interest together.

Therefore, the total amount owed would be $16,024.49. This means that if Melissa does not make any payments during the 93-day period, her loan balance will increase to approximately $16,024.49, including both the original principal amount and the accrued interest.

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The expression √180 * 2√30 is equivalent to the expression 60√6

An equation is an expression that shows the relationship between two numbers and variables.

The square root is a factor of a number that, when multiplied by itself, gives the original number.

Given the expression √180 * 2√30

Collecting like terms give:

= 2√(180 * 30)

Simplifying:

= 60√6

The expression √180 * 2√30 is equivalent to the expression 60√6

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The equation of the line that passes through the point (−11,−14) is y = x - 3.

What is the slope of the line?

A line's steepness can be determined by looking at its slope. The slope is calculated mathematically as "rise over run" (change in y divided by change in x).

We have,

The line that passes through the point (−11,−14)

With Slope (m) = 1,

The general equation of a straight line is

y = mx + c,

where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

so here,

y = mx + c,

(-14) = 1(-11) + c

c = -14 + 11

c = -3

The equation becomes:

y = x - 3.

Hence, the equation of the line that passes through the point (−11,−14) is

y = x - 3.

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Question 1

The angles 52 degrees match up. So if the sides are in proportion, then the triangles are similar.

Notice how 8/12 = 18/27 is a true equation. So the sides are in proportion to one another.

Therefore, the triangles are similar. I used the SAS similarity theorem.

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

Question 2

Let's find the missing angle of the triangle on the right. For now, make that missing angle to be x.

Rule: For any triangle, the three angles always add up to 180

x+70+32 = 180

x+102 = 180

x = 180-102

x = 78

The missing angle of the triangle on the left is 78 degrees

Repeat for the other triangle as well

y+78+32 = 180

y+110 = 180

y = 180-110

y = 70

Both triangles have the angles 32, 70, 78 in whatever order you wish.

Since the angles match up like this, the triangles are similar because of the AA Similarity theorem

Technically, we only need 2 pairs of congruent angles at minimum. But having 3 congruent pairs doesn't hurt either.

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

Question 3

We have a pair of congruent 54 degree angles shown. There's another pair of angles at the very top that overlap (aka shared angles).

Since we have two pairs of congruent angles, the two triangles are similar.

This time we use the AA Similarity theorem

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

Question 4

Let's divide the longest side of the bottom triangle by the longest side of the triangle on top

48/32 = 1.5

Now let's divide the shortest sides of each triangle in the same order

36/24 = 1.5

Repeat for the middle-most sides

45/30 = 1.5

We get the same linear scale factor 1.5 each time. Therefore, the triangles are similar due to the SSS Similarity theorem

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

Question 5

Any angle is equal to itself due to the reflexive property. So that will go for reason number 2.

Reason 3 is SAS similarity because we have the sides in proportion (statement 1) and the angles are congruent (statement 2).

The integral for the volume generated is V = ∫[0, π] 2π(x + 2) [sin(x)] dx

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

y = 0 and y = sin(x)

Also, we have

The line u = -2

Set the equations to each other

So, we have

sin(x) = 0

When evaluated, we have

x = 0 and x = π

For the volume generated from the rotation around the region bounded by the curves, we have

V = ∫[a, b] 2π(x + 2) [g(x) - f(x)] dx

This gives

V = ∫[0, π] 2π(x + 2) [sin(x) - 0] dx

So, we have

V = ∫[0, π] 2π(x + 2) [sin(x)] dx

Hence, the integral for the volume generated is V = ∫[0, π] 2π(x + 2) [sin(x)] dx

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The student needs a minimum score of 84.5 on the fourth test to ensure a grade of B.

To find the minimum score the student needs on the fourth test, we can use the formula for the average of four numbers:

Average = (sum of the numbers) / 4

We know that the student needs an average of at least 80 to earn a grade of B, and we also have the scores for the first three tests: 77, 77.25, and 81.25. So, we can set up the equation:

80 = (77 + 77.25 + 81.25 + x) / 4

where x is the score the student needs on the fourth test. Solving for x:

80 = (235.5 + x) / 4

320 = 235.5 + x

x = 320 - 235.5

x = 84.5

So, the student needs a minimum score of 84.5 on the fourth test to ensure a grade of B.

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We can simplify the expression by combining like terms: 4AA - CTBTCTBT. Finally, the simplified expression is 4AA - CTBTCTBT.

To simplify the given expression (2AT - BC)T 2A + CTBT, let's break it down step by step:

Step 1: Transpose (2AT - BC)

The first step is to transpose the matrix 2AT - BC. Transposing a matrix means flipping it over its main diagonal. In this case, we have:

(2AT - BC)T = (2AT)T - (BC)T

The transpose of a scalar multiple of a matrix is the same as the scalar multiple of the transpose of the matrix, so we have:

(2AT)T = 2A and (BC)T = CTBT

Substituting these values back into the expression, we get:

(2AT - BC)T = 2A - CTBT

Step 2: Multiply by 2A + CTBT

Next, we multiply the result from step 1 by 2A + CTBT:

(2A - CTBT)(2A + CTBT)

To simplify this expression, we can use the distributive property of matrix multiplication. When multiplying two matrices, we distribute each term of the first matrix to every term of the second matrix. Applying this property, we get:

(2A)(2A) + (2A)(CTBT) - (CTBT)(2A) - (CTBT)(CTBT)

Note that the order of multiplication matters in matrix multiplication, so we need to be careful with the order of terms.

Simplifying further, we have:

4AA + 2ACTBT - 2ACTBT - CTBTCTBT

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The distance traveled by Jasmine and Chelsea is given by the equations of speed and J = 20.4 km and C = 39 km , where T is the time taken and T = 0.6 hours

Speed is defined as the rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude

Speed = Distance / Time

Given data ,

Let the speed of Jasmine be represented as S₁ = 34 km/h

Let the speed of Chelsea be represented as S₂ = 65 km/h

Now , the distance traveled by Jasmine = J

And , the distance traveled by Chelsea = C

The measure of J = measure of C

So , the distances are the same

Let the time taken by both Jasmine and Chelsea be T

Now , Speed = Distance / Time

Substituting the values in the equation , we get

Distance D = 34T

And , distance D = 65T

Now , the total distance D = 59.4 km

So , 34T + 65T = 59.4

On simplifying the equation , we get

99T = 59.4

T = 0.6 hours

Hence ,

The distance traveled by Jasmine and Chelsea are 20.4 km and 39 km respectively

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The unit of measurement used is A. Standard deviation is the unit of measurement used to describe how far a set of values are from the mean.

The degree of variation of data from the average, or mean, is gauged by the standard deviation. It provides us with information on the average amount by which each data point diverges from the mean.

A lesser standard deviation suggests that the data points gather closely around the mean, whereas a greater standard deviation signifies that the data points are further dispersed. To standardize a value, we subtract the mean from the value and then divide by the standard deviation.

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keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the PQ line

\(P(\stackrel{x_1}{-3}~,~\stackrel{y_1}{9})\qquad Q(\stackrel{x_2}{8}~,~\stackrel{y_2}{-2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{9}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{(-3)}}} \implies \cfrac{-11}{8 +3}\implies -1\)

if indeed RS || PQ, then their slopes are exactly the same, thus

\(R(\stackrel{x_1}{-8}~,~\stackrel{y_1}{8})\qquad S(\stackrel{x_2}{0}~,~\stackrel{y_2}{y}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{y}-\stackrel{y1}{8}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{(-8)}}} \implies \cfrac{y -8}{0 +8}~~ = ~~\stackrel{\stackrel{slope}{\downarrow }}{-1} \\\\\\ \cfrac{y-8}{8}=-1\implies y-8=-8\implies \boxed{y=0}\)