What coordinate do we plot first on the coordinate plane?.

No, the tan inverse is not equal to tan

A right triangle's opposing side to its adjacent side is calculated using the trigonometric function known as the tangent function (tan). It is described as tan(x) = adjacent/opposite. The opposite of the tangent function is called the inverse tangent function (tan-1). The angle whose tangent has the specified value is revealed. The formula for it is tan-1(y) = x, where tan(x) = y. An angle between -90 and 90 degrees is what is returned.

In other words, tan-1 undoes the tangent function because it is the inverse of the tangent function. In other words, the input of the tangent function is the output of the inverse tangent function. In conclusion, tan-1 and tan are inverse functions; they are not equal.

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When we say "0" or "infinity," what we're really saying is that the number has no end.

The original value of zero corresponds to the logarithm, and the original value of infinity to the logarithm +. We consider the initial values 0 and infinity similarly when we treat both of the conceivable values and + as a single infinity. Georg Cantor, a mathematician, developed the concept of infinity into The Absolute Infinite. You can think of it as a number that is greater than any other possible or inconceivable amount, whether it be transfinite or finite. Infinity is the unfathomable end of the number line, according to mathematics. No actual number is bigger than infinity since it cannot be believed to exist beyond it.

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Answer:

∠ J = 32°

Step-by-step explanation:

the secant- secant angle J is half the difference of the measure of the intercepted arcs, that is

∠ J = [tex]\frac{1}{2}[/tex] (EF - GH) = [tex]\frac{1}{2}[/tex] (123 - 59)° = [tex]\frac{1}{2}[/tex] × 64° = 32°

The value of x in the supplementary angle pair is obtained as x = 14°.

What is a supplementary angle?

The definition of "supplementary" in mathematics relates to angles that combine to form a straight angle. It indicates that when two angles sum up to 180 degrees, they are said to be supplementary angles.

Two angles are supplementary, if -

One of its angles is an acute angle and another angle is an obtuse angle.

Both of the angles are right angles.

The given angles are -

Angle 1, ∠1 = 156°

Angle 2, ∠2 = (x + 10)°

Since, both angles lie on same plane which a straight line it forms a supplementary angle.

The equation for supplementary angle pair is -

∠1 + ∠2 = 180°

Substituting the values in the equation -

∠1 + ∠2 = 180°

156° + (x + 10)° = 180°

166° + x = 180°

x = 180° - 166°

x = 14°

Therefore, the value of x = 14°.

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Answer:

9

Step-by-step explanation:

[tex] | \sqrt{130 \: } | { \: }^{2} \: = |7| {}^{2} + |x| { \\ }^{2} \\ [/tex]

= 130=49+x²

=130-49=x²

=81=x²

[tex] \sqrt{81 \: } = x \\ x = 9[/tex]

Therefore the third side is 9

The height of this hill is given as :  51.88 feet.

How to solve for the height of the hill

We can use trigonometry to find the height of the hill. Let's call the height of the hill "h".

From the information given, we know that:

tan(27°) = h / (103/2)

h = (103/2) * tan(27°)

Using a calculator, we would have to go ahead to get the value of the variable h or height.

So  that h ≈ 51.88 feet.

So, the height of the hill is approximately 51.88 feet.

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When a number is multiplied by itself, the result is the perfect square. The same two binomials are multiplied to produce the perfect square trinomial, which is an algebraic expression. This is the first condition to know that a given trinomial is a perfect trinomial.

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The solution of the integral are:

(a) ∫tanx secx dx = sec(x) + C,

(b) [tex]\int\limits{ \frac{y^3}{(1 - 2y^4)^5} \, dy = -\frac{1}{32(1 - 2y^4)^4}[/tex]

What is integral?

Integrals are used to evaluate such quantities as area, volume, work, and, in general, any quantity that can be interpreted as the area under a curve.

We have given,

∫tanx *secx dx = ?

∫y³/(1-2y⁴)⁵ dy = ?

∫tan(x)sec(x)dx

Rewrite the expression

∫ sin(x)/cos²(x) dx

Use the substitution dx = − 1/sin(x) dt to transform the integral

∫ sin(x)/cos²(x) ×(− 1/sin(x))dt

Simplify

∫− 1/cos²(x)dt

Use the substitution t=cos(x) to transform the integral

∫−t⁻²dt

= −(−t⁻¹)

Calculate

t⁻¹

Substitute back

1/cos(x)

Rewrite the expression

1 × sec(x)

Multiply the terms

sec(x)

Solution

sec(x) + C,  C ∈ R

∫y³/(1-2y⁴)⁵ dy =

[tex]= \int\limits {-\frac{1}{8u^5} } \, du[/tex]

[tex]= \frac{1}{8} \int\limits {-\frac{1}{u^5} } \, du[/tex]

[tex]= \frac{1}{8} (-\frac{1}{4u^4} )[/tex]

by substituting u = (1 - 2y⁴)⁴

[tex]= \frac{1}{8} (-\frac{1}{4(1-2y^4)^4} )[/tex]

[tex]= -\frac{1}{32(1 - 2y^4)^4}[/tex]

Hence, the solution of the integral are:

(a) ∫tanx secx dx = sec(x) + C,

(b) [tex]\int\limits{ \frac{y^3}{(1 - 2y^4)^5} \, dy = -\frac{1}{32(1 - 2y^4)^4}[/tex]

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The range in statistics for a given data set is the difference between the highest and lowest values.

As a result, the range can also be defined as the difference between the highest and lowest observations. The range of observation is the name given to the outcome. In statistics, the range indicates the dispersion of observations.

To find the range in statistics, we need to arrange the given values or set of data or set of observations in ascending order.

For example, if the given data set is {2,5,8,10,3}, then the range will be 10 – 2 = 8.

Thus, The range in statistics for a given data set is the difference between the highest and lowest values.

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Answer:[tex]\frac{8!}{2!*2!*2!}[/tex] = 5040.

Step-by-step explanation:

Since CALCULUS has 8 letters with 2 indistinguishable C's,

2 indisnguishable L's and 2 indistinguishable U's, the answer is

[tex]\frac{8!}{2!*2!*2!}[/tex] = 5040.

The component form of the vector u and v are < -60.11, 9.89 >

To find the component form of the sum of u and v, we first need to express each vector in terms of its components in the x and y directions. To do this, we use the trigonometric relationships between the magnitude and direction angle of a vector and its x and y components.

The x and y components of u can be found using the following formulas:

x_u = u * cos(u)

y_u = u * sin(u)

where u is the magnitude of u and u is the direction angle of u measured in radians.

So, x_u = 14 * cos(45°) = 9.89

and y_u = 14 * sin(45°) = 9.89

The x and y components of v can be found using the following formulas:

x_v = v * cos(v)

y_v = v * sin(v)

where v is the magnitude of v and v is the direction angle of v measured in radians.

So, x_v = 70 * cos(180°) = -70

and y_v = 70 * sin(180°) = 0

Now, we can find the x and y components of the vector sum by adding the corresponding components of u and v.

x_sum = x_u + x_v = 9.89 + (-70) = -60.11

y_sum = y_u + y_v = 9.89 + 0 = 9.89

Therefore, the component form of the sum of u and v is given by the vector < -60.11, 9.89 >

Note: the direction angle is measured in radians and the angle given in the question was in degrees, so it's important to convert the angle from degrees to radians before use it.

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Answer:

C. y=x-6

Step-by-step explanation:

x is input

y is output

difference is subtraction

Answer:

C.y=x-6

Step-by-step explanation:

x is input

y is output

output = input - 6

y = x - 6

Answer: $9.50 per hour

Hope this helps :)

Step-by-step explanation:

Find the rate of change

76/8 = 9.5

8.50 cents per hour because 8.50 x 9 is close to 76

The solution to the system of equations y = 1.5x - 4 and y = -x  is (1.6,-1.6)

The coordinates of the ordered pair (s) that satisfy all of the system's equations make up the solution set to an equational system. This means that the equations will be true for those x and y values. The intersection of all of the graphs, when a system of equations is graphed, is the solution.

These are the equations:

y = 1.5x - 4

y = -x

Put y = -x in place of y in the first equation.

-x = 1.5x - 4

Assemble similar terms

-1.5x - x = -4

This results

-2.5x = -4

Add -2.5 to both sides.

x = 1.6

Change y = -x to x = 1.6.

y = -1.6

As a result, the system of equations solution is (1.6,-1.6).

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The slope and the y intercept of the equation 3x + 2y = 5 is -3/2 and 5/2 respectively.

The term equation of the straight line is y = mx + c here m refers the slope and c refers the value where the line cuts the y-axis that is y intercept.

Here we have given that the equation 3x + 2y = 5.

In order to find the slope and the y intercept we have to rewrite the given equation as follows,

Here we need to find the value of y so we have to move the other terms to the next side then we get,

=> 2y = 5 - 3x

Then it can be rewritten as,

=> y = (5 - 3x)/2

Therefore, the resulting equation is written as,

=> y = -3x/2 + 5/2

So, the slope of the equation is -3/2 and the y intercept is 5/2.

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Answer: 11

Step-by-step explanation:

Answer:

uh. 11

Explanation:

7 + 4 = 11

An increase of 106.63 % in gold price is observed in that particular year.

The original value multiplied by 100 is used to get the percentage change, which is the difference between the original and final values. It is expressed as a percentage and can be used to demonstrate an increase or decrease over time. A higher proportion indicates growth, whereas a lower percentage indicates a decline.

initial price of gold per ounce is $513

final price of gold per ounce is $1060

change in rate = final price of gold - inital price of gold

=> 1060 -513

=> 547

so the change in rate = $547

percentange change =  (change in rate) / (inital rate of gold) *100

=> [tex]\frac{547}{513}[/tex] *100

=> 106.63 %

so the percentage change is 106.63%

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Yes, 7×5×3×2 + 3 is a composite number.

A composite number is a positive integer that has at least one positive divisor other than 1 and itself. In other words, a composite number is a positive integer that can be written as a product of at least two positive integers.

In the number expressed by 7×5×3×2 + 3, we can take 3 as a common factor

7×5×3×2 + 3 = 3(7×5×2 + 1)

So the number has 3 as a factor other than 1 and itself, so it is a composite number.

Also 7×5×3×2 + 3 = 213 = 3×71. So it is not a prime number.

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The Law of Cosines states that for a triangle with sides a, b, and c and with angle C opposite side c, the relationship between the sides and the cosine of the angle is:

c^2 = a^2 + b^2 - 2ab * cos(C)

Since the triangle is a right triangle, we can use the Pythagorean theorem to find the value of the angle.

For ∠A:

c^2 = a^2 + b^2 - 2ab * cos(A)

9^2 = 5^2 + 7^2 - 257 * cos(A)

81 = 25 + 49 - 70 * cos(A)

81 = 74 - 70 * cos(A)

81 - 74 = -70 * cos(A)

7 = -70 * cos(A)

cos(A) = -7/70

A = arccos(-7/70)

For ∠B:

a^2 = b^2 + c^2 - 2bc * cos(B)

5^2 = 7^2 + 9^2 - 279 * cos(B)

25 = 49 + 81 - 98 * cos(B)

25 = 130 - 98 * cos(B)

130 - 25 = 98 * cos(B)

105 = 98 * cos(B)

cos(B) = 105/98

B = arccos(105/98)

For ∠C:

b^2 = a^2 + c^2 - 2ac * cos(C)

7^2 = 5^2 + 9^2 - 259 * cos(C)

49 = 25 + 81 - 90 * cos(C)

49 = 106 - 90 * cos(C)

106 - 49 = 90 * cos(C)

57 = 90 * cos(C)

cos(C) = 57/90

C = arccos(57/90)

Keep in mind that the values of the angle are in radians.

Please note that the triangle does not have to be a right triangle, the Law of Cosines works for any triangle.

The y-intercept is 1 at the position (0,1) when x is 0 and y is 1.

When the line to be examined's slope is known, and the provided point also serves as the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b).

B stands in for the y value of the y-intercept point in the formula.

The y-intercept of a graph is the place where it crosses (or contacts) the y-axis, according to the definition of y-intercept.

The x-coordinate is known to be zero on the y-axis.

Therefore, the equation for determining the y-intercept of a function y = f(x) just requires the substitution of x = 0 and y-solving.

The slope is the ratio of Y change to x change:

Slope = (0-1) / 4-0) = -1/4

Slope = -1/4

When x equals 0, the Y value is known as the Y intercept.

The y-intercept is 1 at the position (0,1) when x is 0 and y is 1.

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The sum of all Payments made during the billing cycle is $975.00

What is the subtractions?

A subtraction is a mathematical operation that is used to find the difference between two numbers. It is represented by the symbol "-" or the word "minus". Subtraction is the inverse operation of addition, meaning that if you add two numbers and then subtract one of those numbers, you should end up with the original value of the other number.

In the FlashCard statement provided, the "DEBITS/CREDITS" section lists all the transactions made during the billing cycle, including payments, purchases, and credits. The payments are listed as negative numbers, indicating that they are subtractions from the balance. The sum of all the payments is calculated by adding up all the negative numbers listed in this section. In this case, it is $975.00.

It's also important to note that this section of the statement lists the transaction made on different days, in the case provided from 4 May to 21 May.

In summary, the sum of all Payments made during the billing cycle is $975.00 which is the total of payments made during that period.

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Answer: a)False

              b)False

              c)True

              d)True

Step-by-step explanation:

a) the are more crosses marked in the less than  1 mile side (false)

b) the most common one in this is 1/2 mile (false)

c) 5/8 mile is actually empty so it is (true)

d)  this is (true) as the shortest one is 1 therefore 1 x 5 is 5 so it is true

Answer: 33

Step-by-step explanation:

66 - 33

Answer:

x is 33...........................

Step-by-step explanation:

33 +x =66

66-33=x

According to the given quadratic equation  the sum of their pieces:

A. = 8x² + 2x + 10

B. 7x²- 7x -17

C.  incomplete information.

A quadratic equation is a third polynomial equation in one variable using the formula x = ax2 + bx + c = 0 and a 0. The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem. Real or complex solutions are also possible.

In mathematics, the quadratic issue is any problem that involves multiplying a variable by itself, often known as "squaring." This terminology comes from the fact that a square's area is equal to its side length divided by itself. The Latin term quadrature, which means square, is where the word "quadratic" derives.

A. Lisha

= 3x² + 2x + 8

Makulata = 5x² + 2

Sum of the given equation:

=  (3x² + 2x + 8) + ( 5x² + 2)

=(3x² + 5x² +2x + 10)

= 8x² + 2x + 10

B.

= 4x + 6x² - 11x + 2 + x² - 19

= (6x² + x²) + (4x - 11x) + 2 -19

= 7x²- 7x -17

C. incomplete information.

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The equation g(x) by translating the following function 4 units to the right would be g(x) = (x+4)² - 3(x+4) - 10.

What is a function?

A function is a mathematical relationship between a set of inputs and a set of outputs. More formally, a function is a rule that assigns to each input exactly one output. In mathematical notation, a function is typically represented by an equation of form f(x) = y, where x is the input and y is the output. The symbol f(x) is called the function notation, and x is called the independent variable, and y is called the dependent variable.

To translate a function 4 units to the right, we can add 4 to the input variable (x) inside the function. Therefore, the equation for g(x) would be:

g(x) = (x+4)^2 - 3(x+4) - 10

Hence, the equation g(x) by translating the following function 4 units to the right would be g(x) = (x+4)² - 3(x+4) - 10.

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The function f(x) is [tex]-32(x - 2)(x + 2)^2.[/tex].

A linear function has the equation f(x) = mx + b, where m is the slope and b is the y-intercept. In this case, g(x) is a linear function with an x-intercept of 2 (meaning it passes through the point (2,0)) and a slope of 4. So the equation for g(x) would be:

g(x) = 4(x - 2)

A quadratic function has the equation f(x) = [tex]a(x - h)^2[/tex] + k, where (h, k) is the vertex of the parabola. In this case, h(x) is a quadratic function with vertex (-2, -8) and passing through the origin (0, 0) so the equation for h(x) would be:

h(x) = [tex]-8(x + 2)^2[/tex]

Now since f(x) = g(x) ⋅ h(x), we can substitute the equation of g(x) and h(x) in the equation of f(x) to get the equation for f(x) :

f(x) = [tex]g(x) *h(x) = (4(x - 2)) * (-8(x + 2)^2)[/tex]

f(x) =[tex]-32(x - 2)(x + 2)^2[/tex]

So the function f(x) is [tex]-32(x - 2)(x + 2)^2[/tex].

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The subtraction equation the inequality solve is

-9 + -4 = -13

A number line is a horizontal line with uniformly spaced numerical increments.

The number on the line can are represented depending on the numbers that are provided. A number is used to plot a point depending on the question that goes with it and the number type.

For the problem one unit represent a digit number with intervals of 1.

The shorter line is as -4 and the longer is at +9

adding bot together will be

= -9 + -4

= -9 - 4

= -13

hence the subtraction equation is -9 - 4 = -13

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The track rises 31.88 feet over a horizontal distance.

One of the six fundamental functions in trigonometry is the tangent function. As stated, Tan A = Opposite Side/Adjacent Side is the Tangent Formula. Tangent may be modeled using sine and cosine as follows: Tan A = Sin A / Cos A.

Given:

A train track slopes upward at an angle of 12°.

The track rise over a horizontal distance of 150 feet.

From the attached image:

tan(12)° = AB/OA

AB = 150 x tan12°

AB = 31.88 feet.

Therefore, the required distance is 31.88 feet.

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We have proved that BC² ×AD = AC² ×BD using AAA congruence rule.

Triangles that are identical in size and shape are said to be congruent. This implies that the corresponding sides and angles are equal.

Without comparing each of the triangles' sides and angles, we can determine whether two triangles are congruent. The four rules that demonstrate triangle congruence will be discussed in this lesson. They are referred to as the SSS rule, SAS rule, ASA rule, and AAS rule.

We'll discuss the Hypotenuse Leg rule, a right triangle proof, in a later lesson. It is sufficient to demonstrate that the two triangles are congruent if only one of the rules is accurate.

Consider △ACD&△ABC

∠CAD=∠CAB

∠CDA=∠ACB

∴△ACD∼△ABC,{ By AA similarity criterion}

⟹ AC/AB = AD/AC

∴ AC ² =AB×AD  

Similarly, △BCD∼△BAC { by AA similarity criterion}

⟹ BC/BA =BD​/BC

∴BC² =BA×BD

∴ BC²/AC² = AB×BD/AB×AD

∴BC² ×AD = AC² ×BD

Thus, We have proved that BC² × AD = AC² × BD using AAA congruence rule.

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Complete question:

Triangle ABC is right angled at C and CD is perpendicular to AB. Prove that BC² ×AD = AC² ×BD

y=x-1 is the equation of the line in slope intercept form.

The slope of the line is the ratio of the rise to the run, or rise divided by the run.

It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The two points from the graph are (1, 0) and (0, -1).

Slope= -1/-1

=1

Now let us find the y intercept.

0=1(1)+b

b=-1

The slope intercept form is y=x-1.

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