describe the transformation of f(x)=cos x to g(x)=cos (x+pi/4)

m∠D = 40°, m∠F = 65°, and m∠E = 75°. Round to the nearest degree.

Angel is a geometric figure that can be described as the amount of rotation between two straight line or planes and angles is measured in degree with the full circle being 360°.

To determine the unknown angle measures of △DEF, we can use the fact that the sum of the angles of a triangle is 180°. Thus, if we know two angle measures in the triangle, we can use them to calculate the third.

Let's denote the two known angle measures as m∠D and m∠F. We can use the following equation to solve for the unknown angle measure:

m∠D + m∠F + m∠E = 180°

We can rearrange the equation to solve for m∠E:

m∠E = 180° - m∠D - m∠F

Therefore, once we know the measures of m∠D and m∠F, we can calculate the measure of m∠E.

For example, if m∠D = 40° and m∠F = 65°, then the measure of m∠E would be:

m∠E = 180° - 40° - 65° = 75°

Therefore, m∠D = 40°, m∠F = 65°, and m∠E = 75°. Round to the nearest degree.

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Answer: the answer is

m∠D = ✔ 46°

m∠F = ✔ 44°

Step-by-step explanation: I got it correct. it will be show below.

Answer:

Step 1: Given AD || BC and AB || CD.

Step 2: Angle A and Angle C are alternate interior angles, so they are congruent.

Step 3: Angle B and Angle D are alternate interior angles, so they are congruent.

Step 4: Angle B + Angle D = 180 degrees (because Angle A + Angle B + Angle C + Angle D = 360 degrees for a quadrilateral)

Step 5: Since Angle B and Angle D are congruent and their sum is 180 degrees, they must each be 90 degrees.

Step 6: Triangle ABZ and Triangle CDZ are both right triangles, since Angle B and Angle D are each 90 degrees.

Step 7: By the Angle-Angle Similarity Theorem, triangles ABZ and CDZ are similar.

Step 8: Since triangles ABZ and CDZ are similar, corresponding sides are proportional.

Step 9: Therefore, ZB/ZD = AB/CD, since ZB corresponds to AB and ZD corresponds to CD.

Step 10: Given that AB || CD, we know that AB/CD = AZ/CZ (the corresponding sides of similar triangles are proportional).

Step 11: Therefore, ZB/ZD = AB/CD = AZ/CZ.

Step 12: Since Angle A and Angle C are congruent (Step 2), we know that AZ = CZ (since they are opposite sides of an isosceles triangle).

Step 13: Therefore, ZB/ZD = AZ/CZ = 1, which means that ZB = ZD.

Thus, we have proved that ZB = ZD!

- Dante

Roberto spent 41 more minutes doing homework than he did reading and making his lunch.

What is the basic algebraic expression?

An algebraic expression is when we use numbers and words in solving a particular mathematical question.

First, let's convert all the times to minutes:

Now, we can calculate the difference:

90 - (40 + 9) = 41

Hence, Roberto spent 41 more minutes doing homework than he did reading and making his lunch.

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Answer:500

explanchion: 1000/50=500

Formula:

(A+B/2)H

A=base

B=Base

H=height

A. 100 cm (i think not to sure about this one)

B. 174 cm

C. 240cm

Answer:

Step-by-step explanation:Formula:

(A+B/2)H

A=base

B=Base

H=height

A. 100 cm (i think not to sure about this one)

B. 174 cm

C. 240cm

Line a could also be referred to as line EC.

In mathematics, a line can be named in a variety of ways depending on the context. One common way to name a line given a starting point and an ending point is to use the names of the two points.

For example, if the starting point is labeled A and the ending point is labeled B, we can refer to the line as "line AB" or "line BA" (the order doesn't matter, as the line extends in both directions).

In this case therefore, line a can be referred to as line EC which are the letters at the starting and ending points.

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The function family based on the information is a linear function.

A linear function is a type of mathematical function that has the form:

f(x) = ax + b

where a and b are constants, and x is a variable. The variable x is often called the independent variable, and the variable f(x) is called the dependent variable.

The value of a determines the slope of the line, while the value of b determines the intercept of the line with the y-axis. The slope of the line represents the rate of change of the dependent variable with respect to the independent variable, and the intercept represents the value of the dependent variable when the independent variable is zero.

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The equation of the osculating plane is (-1/3)(x-0) + (1/3)(y+1) + (2/3)(z-8 π) = 0.

First, we find the point on the curve at

[tex]t = 2\pi[/tex]

[tex]x = sin(2(2\pi)) = 0 \\

y = -cos(2(2\pi)) = -1 \\

z = 4(2\pi) = 8\pi[/tex]

So the point on the curve is

[tex] (0, -1, 8\pi)[/tex]

To find the normal plane, we take the cross product of the partial derivatives:

[tex]r_t = (2cos(2t), 2sin(2t), 4) \\

r_t(2\pi) = (2cos(4\pi), 2sin(4\pi), 4) = (2, 0, 4) \\

r_tt = (-4sin(2t), 4cos(2t), 0) \\

r_tt(2\pi) = (0, -4, 0) \\

n = r_t × r_tt = (-16, -8, -8)[/tex]

So the equation of the normal plane is

[tex]-16(x-0) - 8(y+1) - 8(z-8\pi) = 0.[/tex]

To find the osculating plane, we first find the unit tangent and unit normal vectors:

[tex]T = r_t / ||r_t|| = ( \frac{1}{2})cos(2t)i + ( \frac{1}{2}) sin(2t)j + ( \frac{1}{4})k \\

N = n / ||n|| = ( \frac{2}{3})cos(2t)i + ( \frac{1}{3})sin(2t)j + ( \frac{1}{3})k[/tex]

Then the binormal vector is B = T × N, which is

[tex]( \frac{ - 1}{3})sin(2t)i + ( \frac{1}{3} )cos(2t)j + ( \frac{2}{3} )k[/tex]

Finally, the equation of the osculating plane is

[tex]( \frac{ - 1}{3})(x-0) + ( \frac{1}{3})(y+1) + ( \frac{2}{3})(z-8\pi) = 0[/tex]

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In general, if the sample size is large, adding an extremely large outlier to a data set will not substantially affect the mean (average) of the data set.

This is because the mean is calculated by summing all the values in the data set and dividing by the total number of values. As the sample size increases, the influence of any individual value on the mean becomes smaller. An extremely large outlier may have a significant impact on the sum of the data set, but if the sample size is large enough, the impact on the mean will be relatively small.

However, adding an extremely large outlier to a data set can substantially affect other measures of central tendency and dispersion, such as the median and standard deviation. These measures are based on the order and spread of the data, rather than the sum of the data, and may be more sensitive to extreme values.

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Does the graph represent a function: B. No.

In Mathematics, a function can be defined as a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.

This ultimately implies that, a function is typically used in mathematics for uniquely mapping an input variable to an output variable.

Based on the ordered pairs (-5, 7) and (-2, 7), we can reasonably infer and logically deduce that the relation represented by this graph does not represent a function because the are not uniquely mapped.

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As per the information provided, a = 4√3/3 + 4, b = 4 - 4√3/3 the answer can be calculated with optimization method. it will be as follows:

Sum of a and b is 8, we get

a+b=8

b=8−a

Now, let x=a−b

Then we get,

[tex]x=a−(8−a) \\ x=2a−8 \\ x+8=2 \\ 1 \div 2x+4=a

[/tex]

we use this to answer to solve for b

[tex]b=8−a \\ =8−(1 \div 2x+4) \\ =4−1 \div 2x

[/tex]

Now we use the product of two numbers and its difference. This can be expressed as:

[tex]a⋅b⋅x=(1 \div 2x+4)(4−1 \div 2x) \\ x=2 {x}^{2} − \frac{1}{4} {x}^{3} +16x−2x^{2} \\ =−14x^{3} +16x

[/tex]

Thus, this expression that we need to maximize. Take the derivative, set it equal to zero, and solve for x

[tex]−3 \div 4x ^{2} +16=0 \\ 16 =3 \div 4 x ^{2} \\ 643=x \\ 28√3 \div 3=x[/tex]

Now for us to check that this is a maximum, we have to note that the second derivative is

[tex]−3 \div 2x

\\ At \\

x=8√3 \div 3

[/tex]

the second derivative is −4√3. Since this number is negative, the point is a maximum.

Now we must find the values of a and b for this x. We have to use the relationship

[tex]a=1 \div 2x+4[/tex]

[tex]a=1 \div 2 \times 8√3 \div 3+4 \\ =4√3 \div 3+4[/tex]

now we use the relationship b=8−a

[tex]b=8−(4√3 \div 3+4) \\ =4−4√3 \div 3[/tex]

The first step in determining a function's maximum or minimum value is differentiating it. Then, set this derivative to zero and conduct the computation.

x. This will reveal the location of a function's maximum or minimum, but it won't reveal which.

Take the second derivative to get more details. A local maximum occurs when both the first and second derivatives are negative. You have a local minimum when both the first derivative and the second derivative are zero.

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The final inequality  that represents how many blankets Elle can make in her workshop would be:

3x ≤ 52 and x ≥ 16

In mathematics, an inequality is a statement that compares two values or expressions using an inequality symbol such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).

An inequality indicates that one value or expression is smaller, greater, or not equal to the other value or expression.

 The inequality "y <= 10" states that the value of "y" is less than or equal to 10.

Let "x" be the number of blankets Elle can make in her workshop.

Since each blanket requires 3 ft. of material, the total amount of fleece required for "x" blankets would be 3x ft.

We know that Elle has 52 ft. of fleece in her workshop, so we can set up the inequality:

3x ≤ 52

This inequality states that the amount of fleece required for "x" blankets must be less than or equal to the amount of fleece Elle has available.

To satisfy the condition of making at least 16 blankets, we can add the requirement that "x" must be greater than or equal to 16.

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Answer:

48

Step-by-step explanation:

3 x 16 = 48

OR

16 + 16 + 16 = 48

48

16 x 3 = 48.

Simple :)

The true statements are: The Chinese Remainder Theorem guarantees a unique solution to any system of modular equations.

Fermat's Little Theorem allows us to conclude that ap^−1≡1(mod p) for any integer a and any prime p.

The first formula given in the question for computing x using CRT is also true.

Statement 3, "If b≥p, then a^b−p+1≡a^b (mod p)", is not necessarily true. Fermat's Little Theorem states that if p is prime and a is not divisible by p, then a^(p-1) ≡ 1 (mod p). However, this does not extend to arbitrary exponents b.

Statement 4, "If b ≡ c (mod p), then a^b≡a^c (mod p)" is true by Fermat's Little Theorem, which implies that a^(p-1) ≡ 1 (mod p), we can write b = kp + c for some integer k, then

a^b = a^(kp+c) = (a^p)^k * a^c ≡ a^c (mod p)

since a^p ≡ a^(p-1) * a ≡ 1 * a ≡ a (mod p) by Fermat's Little Theorem.

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Answer: I am not understanding what you want us to help you with. In long form is says Area= 1/2 base x height

Step-by-step explanation:

The conversion of 3000 euros to dollars is 3,540 US dollars.

Please note that exchange rates can fluctuate over time, so the exact conversion may be different depending on the current exchange rate.

The conversion of 3000 euros to dollars depends on the current exchange rate between the two currencies. As of my knowledge cutoff date of September 2021, the exchange rate was approximately 1.18 US dollars per 1 euro.

Using this exchange rate, we can convert 3000 euros to US dollars as follows:

3000 euros * 1.18 dollars/euro = 3,540 US dollars

Therefore, 3000 euros is equivalent to approximately 3,540 US dollars using the exchange rate mentioned above.

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The tangent (tan) of an angle can be calculated using a calculator. The "tan" button on most scientific or graphing calculators can be used to calculate the tangent of an angle in degrees or radians.

Here's how to utilise a calculator's "tan" function:

To get the tangent of 45 degrees, for example, input "45" into the calculator and press the "tan" button. The calculator would then show the tangent value, which is around 1.00.

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The product of the fraction, 6 and 2/6 is greater.

A fraction is expressed as p/q, where q is equal to 0.

Proper fractions, in which the numerator is less than the denominator, and improper fractions, in which the numerator is higher than the denominator, are the two sorts of fractions.

Given, Are the product of two fractions, First one is 2 and 5/6 which is,

= (5/6)×2.

= 10/6.

= 5/3.

The second product is, 6 and 2/6 which is,

= 5×(2/6).

= 12/6.

= 2.

So, The product of 6 and 2/6 is greater.

Q. Which products are greater than 2 and 5\6 or 5 and 2/6?

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Answer:

Step-by-step explanation:

5/8

Answer: it equal 5 /8

This inequality is true, the given statement "The point (2,5) is inside the region defined by |a - 3| + |b - 4| < 5" is true. Therefore, the answer is True.

To determine whether the given statement is true or false, we need to substitute the values of a and b into the inequality and simplify:

|a - 3| + |b - 4| < 5

Substituting a = 2 and b = 5, we get:

|2 - 3| + |5 - 4| < 5

|-1| + |1| < 5

1 + 1 < 5

2 < 5

Since this inequality is true, the given statement "The point (2,5) is inside the region defined by |a - 3| + |b - 4| < 5" is true. Therefore, the answer is True.

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Check the picture below.

Answer: 16

Step-by-step explanation: Basic multiplication

4+4=8

4+4=8

8+8=16    [16!]

The conversion of 210 lbs to kg is 95.2544 kg.

Lbs and kg are units of weight or mass used to measure the amount of matter in an object.

Lbs is an abbreviation for pounds, which is an imperial unit of weight commonly used in the United States, United Kingdom, and a few other countries. It is defined as 0.45359237 kilograms, or approximately 16 ounces.

To convert pounds (lbs) to kilograms (kg), you can use the conversion factor of 1 lb = 0.45359237 kg.

So, to convert 210 lbs to kg, you can multiply 210 by 0.45359237:

210 lbs * 0.45359237 kg/lb = 95.2544 kg

Therefore, 210 pounds is approximately equal to 95.2544 kilograms.

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Answer:

boys-75,

Step-by-step explanation:

the ratio is 3:2 and the total ratio is 5, which stands for total learners in grade 8

boys;

3/5×125= 75

girls;

2/5×125= 50

Answer:

To prove that AD is a bisector of BC, we need to show that AD divides BC into two congruent segments.

Since AB ≅ AC, we have ∠BAC ≅ ∠CAB by the isosceles triangle theorem.

Since BD ≅ CD, we have ∠CBD ≅ ∠CDB by the same reasoning.

Now, we can use the angle bisector theorem, which states that if a ray bisects an angle of a triangle, it divides the opposite side into segments that are proportional to the adjacent sides.

Applying the angle bisector theorem to triangle BCD with angle ∠BCD, we get:

BD/DC = AB/AC

Since AB ≅ AC and BD ≅ CD, we can substitute and simplify to get:

BD/CD = 1

This implies that BD ≅ CD.

Therefore, AD divides BC into two congruent segments, and AD is a bisector of BC.

Hope this helps!

The areas of the compound figures are following;

1). The area of the compound figure,

= 121.12 square feet.

2). The area of the compound figure = 128 square meters.

3). The area of the compound figure = 69 square centimeters.

4). The area of the compound figure,

= 53.12 square feet.

5). The area of the compound figure,

= 63 square meters.

6). The area of the compound figure,

= 108 square yards.

The area is the amount of area occupied by an object's flat (2-D) surface or shape.

Given:

The area of the compound shapes can be calculated by the following process,

1). The area of the compound figure,

= (12 x 8) + (1/2 x 3.14 x 4 x 4)

= 121.12 square feet.

2). The area of the compound figure,

= (13 x 8) + (1/2 x 8 x 6)

= 128 square meters.

3). The area of the compound figure,

= (11 x 4) + (5 x 5)

= 69 square centimeters.

4). The area of the compound figure,

= (1/2 x 3.14 x 4 x 4) + (1/2 x 8 x 7)

= 53.12 square feet.

5). The area of the compound figure,

= (7 x 7) + (1/2 x 7 x 4)

= 63 square meters.

6). The area of the compound figure,

= (12 x 6) + (6 x 6)

= 108 square yards.

Therefore, all the areas are given above.

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The given inequality is x > (y – 2)2 – 4. To graph this inequality, we first need to plot the vertex of the parabola, which is (2, -4). This point is included in the shaded region because the inequality is "greater than" and not "greater than or equal to". Next, we need to determine whether the parabola opens upward or downward. Since the coefficient of the squared term is positive, the parabola opens upward.

Now, we need to decide which side of the parabola to shade. To do this, we can choose a test point that is not on the parabola and substitute its coordinates into the inequality. For example, the point (0,0) is a convenient test point. Substituting x=0 and y=0 into the inequality, we get:

0 > (0 – 2)2 – 4

0 > 0

Since 0 is not greater than 0, the point (0,0) is not in the shaded region. Therefore, we need to shade the side of the parabola that does not contain the point (0,0).

Among the given options, only the first one matches the graph described above. Therefore, the answer is: the graph that represents x > (y – 2)2 – 4 is the one where a parabola opens up and goes through (0, 0), has a vertex at (2, -4), and everything outside of the parabola is shaded.

89 centimeter is approximately equal to 35.0394 inches ( rounded to four decimal places )

To convert 89 cm to inches, we can use the following formula:

1 cm = 0.393701 inches

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

Therefore,

The length in inches = conversion factor × The length in centimeter

Substitute the values in the equation

89 cm = 89 x 0.393701

Multiply the numbers

= 35.0394 inches ( rounded to four decimal places )

Therefore, 89 centimeter is 35.0394 inches

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Answer:

7/12

Step-by-step explanation:

A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.

An equation you can use to solve for this is:

Therefore, the difference of 8/12 - 1/12 is 7/12.