If sin 0= -3/5 in quadrant 3, what is cos 0?

Answer: [tex](x-5)^2 +(y+4)^2 =25[/tex]

Step-by-step explanation:

The equation of a circle with center [tex](h, k)[/tex] and radius [tex]r[/tex] is [tex](x-h)^2 +(y-k)^2 =r^2[/tex].

So, the equation is [tex](x-5)^2 +(y+4)^2 =25[/tex].

The equation of the circle in the figure is (x-5)²+(y+4)²=25

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

From the figure the circle has a center at (5, -4) and radius 5

The standard form equation of the circle is (x-h)²+(y-k)²=r²

(h, k) is the center of the circle and r is the radius of circle

Plug in the values of center and r

(x-5)²+(y-(-4))²=5²

(x-5)²+(y+4)²=25

Hence, the equation of the circle in the figure is (x-5)²+(y+4)²=25

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In a parallelogram, opposite angles are congruent, this means that,

Similarly, in a parallelogram, we have that angles in green are congruent because they are alternate interior angles:

This implies that

On the other hand, opposite sides are congruent, this implies that

Then, by moving 3 to the right hand side, we get

Therefore, the answers are

The distance between point (6,-3) and (4,3) is 3.162 units using the point formula for distance that is √((x2-x1)²+(y2-y1)²) units.

Since it only represents a dot, a point is a dimensionless shape, whereas a line is one dimension. Both points are lines that can be used to depict various sizes and shapes in a plane.

Coordinates are numerical distances or angles that uniquely identify points on two-dimensional (2D) surfaces or in three-dimensional (3D) space ( 3D ). Mathematicians, scientists, and engineers frequently use a variety of coordinate systems.

Here,

distance between point (6,-3) and (4,3)

=√((x2-x1)²+(y2-y1)²)

=√((4-6)²+(3+3)²)

=√((-2)²+(6)²)

=√(4+36)

=√(40)

=2√(10)

=3.162

According to the point formula for distance, which is √((x2-x1)²+(y2-y1)²) units, the distance between point (6,-3) and point (4,3) is 3.162 units.

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Answer: -20%

Step-by-step explanation:

new-old divided by old

68-85=-17

-17/85=-0.2

-0.2x100=-20

-20%

The Radius is 15.27 cm and the the Diameter is 30.55 cm

Given

Circumference = 96cm

Circumference is the total arc length of a circle or it is simply the perimeter of a circle.

The formula for circumference is 2πr

where π = Ratio of circumference to the diameter of a circle

π = 3.14

r = Radius of the circle

Substituting the value in the formula we get

2πr = 96 cm

πr = 48 cm

r = 15.27 cm

Diameter (d)  = 2 × r

hence        d = 2 × 15.27 cm

                 d = 30.55 cm

Hence the radius = 15.7cm

Diameter = 30.55 cm

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The function that gives f(x) = 2x² - 7

The core concept of mathematics' calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

f (14) = 2(14)²−7

Now, here the changing value is 14 according to which the resultant values changes.

so, every time it depends on the function value which can be any number.

Then, let us consider that number is x.

Thus, the function that gives f(x) = 2x² - 7

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Given that Angelo's kayak travels 10km/h in still water, and the river's current flows at a rate of 4km/h.

Travelling downstream means Angelo is travelling with the current, that is the current of the water will add to Angelo's speed.

Their combined speed will be;

To travel 35 km downstream;

Recall that;

substituting the given values;

Therefore, it'll take 2.5 hours

The image of point (-3,-1) under a reflection in the origin( 3 , 1 )

Point (x, y) is reflected over the line y = x, and the reflection is (y, x)

Find the point of a reflection on a point by what method?

The x-coordinate and y-coordinate of a point change positions when it is reflected across the line y = x. The x- and y-coordinates shift positions and are negated when a point is mirrored across the line y = -x. Therefore, Point (x, y) is reflected over the line y = x, and the reflection is (y, x)

following a reflection, a 3-1 picture Reason: A(3,1) becomes A'(3,3+3(1)), or A', when it is reflected over y=3 (3,7)

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Given data:

First find f( -1 ) and g( -1 ),

Therefore, we have

Answer:

112

Step-by-step explanation:

448/4=112

The angle relationships which are correct are:

∠4 and ∠6 are same side interior angles.

∠3 and ∠6 are alternate interior angles.

Side interior angles

Two angles that are on the same side of the transversal and written the same side of the transversal when two lines are intersected by a third line are called side angles.

Alternate interior angles

Alternate interior angles are the angles formed on the opposite sides of the transversal.

Hence the correct relationship are ∠4 and ∠6 are same side interior angles and ∠3 and ∠6 are alternate interior angles.

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The sum of the first four terms of the arithmetic sequence is 24.

From the information illustrated, the arithmetic sequence is given by 2n + 1.

The first term will be:

= 2n + 1

= 2(1) + 1 = 3

The second term will be:

= 2n + 1

= 2(2) + 1 = 5

The third term will be:

= 2n + 1

= 2(3) + 1

= 7

The fourth term will be:

= 2n + 1

= 2(4) + 1

= 9

The sum of the first four terms will be:

= 3 + 5 + 7 + 9

= 24

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An arithmetic sequence is given by 2n + 1. What is the sum of the first 4 terms of that arithmetic sequence?

Consider the upper triangle

if we want to find b side, consider the following trigonometric identity:

in this case, we have:

solve for b:

then, we can conclude that

Now, for a-side, consider the following trigonometric identity:

in this case, we have:

solve for a:

then, we can conclude that

Now, for the c-side, consider the greater triangle :

if we denote the hypotenuse by h, then by Pythagorean theorem we have:

but h = a + c, then, replacing this in the previous equation we have

but, we know that a is

then we have:

now, taking the square root of both sides of the equation we obtain:

solve for c:

then we can conclude that :

and

In a proportional relationship, the ratio between the two variables are equaivalent.

We can also say that one variable is a constant times the second variable in a proportional relationship.

Therefore, the situation that does not represent a proportional relationship from the given choices is:

C. The weight in x weeks of a puppy that gains 2 pounds per week it is starting weight is 5 pounds.

This is because there is an initial value of 5 pounds here

So:

f(x) = 2x + 10

To solve for x, we are going to subtract 10 on both sides of the equation:

f(x) - 10 = 2x + 10 - 10

f(x) - 10 = 2x

Then, dividing by 2, we get:

Answer:

Answer:

a/c

Step-by-step explanation:

Sine is always the side opposite the angle and the hypotenuse

Answer:

[tex]\large \text{Second Choice: $\dfrac{a}{c}$}[/tex]

Step-by-step explanation:

For any given triangle, the Law Of Sines states that the ratio of each side to the sine of the angle opposite that side is the same

So we have
[tex]\dfrac{a}{\sin \angle F} = \dfrac{c}{\sin \angle 90} = \dfrac{b}{\sin \angle G} \\\\[/tex]

[tex]\sin \angle 90 = 1[/tex]

So we get from the first two ratio equality,
[tex]\dfrac{a}{\sin \angle F} = \dfrac{c}{1} \\\\\\\dfrac{a}{\sin \angle F} = c\\\\\\\dfrac{a}{c} = sin \angle F\\\\[/tex]

Or, in other words,

[tex]\sin \angle F = \dfrac{a}{c}[/tex]

If a test requires that you answer either part A or part B. Part A consists of 6 true-false questions, and part B consists of 6 multiple-choice questions with one correct answer out of six. 46720 different completed answer sheets are possible.

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items.

A test requires that you answer either part A or part B.

Part A consists of 6 true-false questions.

i.e.  there are 2 choices to answer each question

Now, the number of ways to answer Part A :  2⁶=64   (1)

Part B consists of 6 multiple-choice questions with one correct answer out of five.

i.e.  there are 6 choices to answer each question.

Now, the number of ways to answer Part B : 6⁶=46656

Now, the number of  different ways to completed answer sheets are possible= 46656+64

=46720

Hence 46720 different completed answer sheets are possible.

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Answer:

C    x = 5

Step-by-step explanation:

4x - 3 = 12 + x

Add 3 on both sides:
4x - 3 + 3 = 12 + 3 + x

4x = 15 + x

Subtract x from both sides:
4x - x = 15 + x - x

3x = 15

x = 15/3

or

x = 5

Answer:

[tex]4x - 3 = 12 + x \\ \\ ➪4x - x = 12 + 3 \\ \\ ➪3x = 15 \\ \\ ➪x = \frac{15}{3} = 5[/tex]

C] x = 5 Is ᴛʜᴇ ʀɪɢʜᴛ ᴀɴsᴡᴇʀ.

By using 3 factors 2, 3, and 7, if we create a product game board with the numbers 4 6 9 14 49 then the missing product is 21.

To solve this problem we have to follow a few steps. First, we should know about factors.

What are the factors?

Factors of a number are such numbers as they can divide the whole number without remaining.

Example: The factors of 24 are 1, 2, 3, 4, 6, 8, and 12.

Now we have to analyze the given numbers,

4 = 2× 2

6 = 2× 3

9 = 3× 3

14 = 2× 7

49 = 7× 7

The factors are 2, 3, and 7. Therefore, the missing product is, 3× 7= 21

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To find the greatest common factor (GCM) for monomials, as you have in this case, you can write the complete factorization of each monomial and find the common factors. Then:

As you can see, all of these terms have x*x*x*x in common, and this is equal to x^4.

Thus, the GCF for this list of terms is:

The probability that the student scores an 85 or better and he receive an A in the score is 0.45.

In the question it is given that the professor tells that the student has 90% chance of getting A, if he gets 85 or better in mid term exam.

The student is 50% sure that he will get 85 or better in the examination.

To get the probability of the student scores an 85 or better and he receives an A grade, we use multiplication rule.

P( student getting A grade and 85 or better)= P(getting A) x P(getting 85 or better)

P(getting A)=0.9

P(getting 85 or better)=0.5

= 0.9x0.5

P( student getting A grade and 85 or better)=0.45

Therefore, probability that the student scores an 85 or better and getting A is 0.45.

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Answer:

84

Step-by-step explanation:

5*6=30

14*6=84

If you need further explanation just tell me!

Work Shown:

(14 children)/(5 teachers) = (x children)/(30 teachers)

14/5 = x/30

14*30 = 5*x

420 = 5x

5x = 420

x = 420/5

x = 84

The solution to the questions are

The given parameters are:

Every item is on sales for half the original price, plus 3 dollars.

In this case, the function g(x) is half the original price

Let the original price be x

So, we have the following equation

Price = 1/2x

Express as a function

g(x) = 1/2x

The given parameters are:

Every item is on sales for half the original price, plus 3 dollars.

In this case, the function f(x) is the 3 dollars added

Let the original price be x

So, we have the following equation

Price = x + 3

Express as a function

f(x) = x + 3

In (A) and (B), we have

g(x) = 1/2x

f(x) = x + 3

The function (f o g)(x) is calculated as

(f o g)(x) = f(g(x))

So, we have

(f o g)(x) = g(x) + 3

Substitute g(x) = 1/2x

(f o g)(x) = 1/2x + 3

Here, we have

(f o g)(x) = 1/2x + 3

This means that x = 60

So, we have

(f o g)(60) = 1/2 x 60 + 3

Evaluate

(f o g)(60) = 33

Hence, the value of the shirt is $33

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The equation of this line is y =4.

From the given graph we can infer that line A is a horizontal line

It can be expressed in the form y = constant

Hence the equation of this line is y = 4

Similarly, from the given graph we can infer that line B is a vertical line

It can be expressed in the form x = constant

Hence the equation of this line is x = 8

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To make 4 batches of lemon cookie, Ronald will need 13.3 cups of sugar.

Firstly converting mixed fraction to fraction, thus getting the amount of cups of sugar required for 1 batch.

Number of cups of sugar required for 1 batch = (3×3 + 1)/3

Performing multiplication and addition in numerator

Number of cups of sugar required for 1 batch = 10/3

Number of cups of sugar required for 4 batches = 10/3 × 4

Performing multiplication to find the number of cups of sugar required

Number of cups of sugar required for 4 batches = 40/3

Performing division to find the number of cups in decimal

Number of cups of sugar required for 4 batches = 13.3

Thus, 13.3 cups of sugar will be needed by Ronald.

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Answer: nonlinear function

Step-by-step explanation:

The rate at which y increases is not constant with respect to x.

The horizontal component of the provided vector is 100cos35 or 8.19 after reducing.

It is defined as the quantity that has magnitude as well as direction also the vector always follows the sum triangle law.

It is given that:

The vector is shown in the picture.

Let's draw an imaginary line from the tail of the vector and it makes the angle between the imaginary line and the vector 35 degrees.

The horizontal component of the vector:

H = 100cos35

The value of the cos35 is 0.819

H = 10(0.819)

H = 8.19

Thus, the horizontal component of the provided vector is 100cos35 or 8.19 after reducing.

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Distributing and combining similar terms

Subtracting 4/3x at both sides

Adding 25 at both sides:

Multiplying by 3/8 at both sides

Answer:

x=10 am not sure

Step-by-step explanation: