what is 14/25 as a decimal and as a percent?
​

The function rule for g(x) is h(x) = (x - 0)² - 7.

In Mathematics, the vertex form of a quadratic function is represented by the following mathematical equation:

f(x) = a(x - h)² + k

Where:

Based on the information provided about the vertex (0, -7) and other points (-3, 2), we can determine the value of a as follows:

f(x) = a(x - h)² + k

2 = a(-3 - 0)² - 7

2 + 7 = 9a

9 = 9a

a = 1

Therefore, the required quadratic function in vertex form is given by:

h(x) = a(x - h)² + k

h(x) = (x - 0)² - 7

h(x) = x² - 7

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Answer:

y = 3x + 3

Step-by-step explanation:

y = -x² + 4x + 5

→ Find the vertex

- ( x - 2 )² + 4 + 5 ∴ vertex = ( 2 , 9 )

→ Find the intersection with the x axis

- ( x - 5 ) ( x + 1 ) ∴ ( - 1 , 0 )

→ Find the gradient of the 2 point

( 0 - 9 ) ÷ ( -1 - 2 ) = 3

→ Write into y = mx + c format

y = 3x + c

→ Substitute in a coordinate pair

0 = -3 + c ∴ c = 3

→ Rewrite into y = mx + c

y = 3x + 3

Answer:

A) x = 0 and x = 3π∕4

Step-by-step explanation:

cot 0° = oo (infinite)

4/3 x = 0

=> x = 0

cot 180° = oo (infinite)

4/3 x= 180

x = 3/4 × 180

= 135°

= ¾π

The order of the given fractions will be 5/3>3/2>5/6.

What exactly is a fraction?

A fraction is a mathematical term that represents a portion or part of a whole. It represents the equal parts of the whole. A fraction has two components: the numerator and the denominator. The top number is referred to as the numerator, while the bottom number is referred to as the denominator. The denominator describes the total number of equal parts in a whole, whereas the numerator defines the number of equal parts taken.

5/10, for example, is a fraction.

In this case, 5 is the numerator and 10 is the denominator.

Now,

Given fractions are 5/6 ,5/3,  3/2

lets make the denominator same

Divide and multiply fraction 2 and 3 by 2 and 3 respectively

then fractions are 5/6, 10/6, 9/6

so, the order will be 10/6>9/6>5/6 i.e. 5/3>3/2>5/6

hence,

           The order of the given  fractions will be 5/3>3/2>5/6.

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The length of the arc CD is 14.13 centimeters.

Remember that for an arc defined by an angle a in a circle of radius R, the length of the arc is given by:

L  = (a/360°)*2*pi*R

Where pi = 3.14

Here the angle is a = 45°

And R = 18cm, so we can replace that in the formula above to find the length.

L = (45°/360°)*2*3.14*18cm = 14.13cm

That is the length of the arc CD.

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We see here that new thousand is actually liken to be the result in thousand that is gotten after carrying out an operation.

A thousand is a number that denotes the sum of 1,000 units or ten hundreds.

The word "thousand" is frequently used in daily speech to denote a significant but limited amount, such as a thousand money, a thousand individuals, or a thousand pages. Alternatively, it can be used as a round number to denote an approximation, as in "a thousand times" or "a thousand and one nights."

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We can simplify cosec(t)tant(t) to sec(t). A trigonometric function is a mathematical function that relates the angles of a triangle to the ratios of its sides.

The most common trigonometric functions are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).

To simplify the expression cosec(t)tant(t), we need to use the trigonometric identity:

cosec(t) = 1/sin(t)

tant(t) = sin(t)/cos(t)

Substituting these expressions into the original expression, we get:

cosec(t)tant(t) = (1/sin(t))(sin(t)/cos(t))

The sin(t) term in the numerator and denominator cancel out, leaving:

cosec(t)tant(t) = 1/cos(t)

Recalling the definition of secant, sec(t) = 1/cos(t), we can express the simplified expression as:

cosec(t)tant(t) = 1/sec(t)

Therefore, we can simplify cosec(t)tant(t) to sec(t).

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If a linear function is increasing, the reciprocal function must be decreasing, mathematically because the reciprocal function is the inverse of the linear function

The reciprocal function of a linear function is given by the formula:

f(x) = 1/x

If a linear function is increasing, then its slope (m) is positive. This means that the slope of the reciprocal function must be negative. The slope of the inverse of a linear function is the negative reciprocal of the slope of the linear function, meaning that the slope of the reciprocal function must be negative for the linear function to be increasing.

To illustrate this, we can consider a simple example of a linear function, f(x) = 2x. This linear function has a positive slope (2), so its reciprocal function, f(x) = 1/x, must have a negative slope (-1). This means that the reciprocal function is decreasing.

In general, if a linear function is increasing, then its reciprocal function must be decreasing, as the slope of the reciprocal function must be the negative reciprocal of the slope of the linear function.

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Answer:

x = 49

Step-by-step explanation:

The sum of angles is 360

(x + 84) + 80 + 3x = 360

x + 3x = 360 - 84 - 80

4x = 196

x = 196/4 = 49

Answer:

sin(–45°) = –sin(45°)

cos(–45°) = cos(45°)

Step-by-step explanation:

The statements which involving cosine and sine are true are sin(–45°) = –sin(45°) and cos(–45°) = cos(45°).

Trigonometric ratios are the ratios which is described for two sides of a right angled triangle.

The main three trigonometric ratios are sine, cosine and tangent functions.

Trigonometric functions are also called as Circular functions.

There are five statements given.

We have the identities that,

sin (-x) = - sin(x) and

cos (-x) = cos x

Using this for each of the statement,

sin(–45°) = –sin(45°) is true.

sin(–45°) = sin(45°) is false

cos(–45°) = –cos(45°) is false

cos(–45°) = cos(45°) is true

For the last one,

cos(–45°) = cos (45°) = sin (45°) ≠ sin(–45°)

So this is false.

Hence the true statements are sin(–45°) = –sin(45°) and cos(–45°) = cos(45°).

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Answer:

Explanation:

Here, we want to select the appropriate logarithmic relationship

We have the general rule as:

This is the rule we are going to use. Since there are 4 tiles, we shall be selecting the 4 logarithmic expressions and use their number equivalent on the right side

a)

b)

c)

d)

5 and 8 do not take part in any Pythagorean triple at the same time; therefore, we would identify the Pythagorean triple among the options.

In general, a Pythagorean triple is an arrangement of numbers (a,b,c), such that

Where a,b, and c are positive integers

Then, in our case,

a)

b)

c)

d)

Options b) and c) are Pythagorean triples.

Due to the lack of information about the 'Pythagorean identity' one is supposed to use, we cannot determine which of the two options is the correct one.

However, notice that

Therefore, option c) might be a more suitable answer to the question.

There can be multiple outputs (monthly charges) for a given input (number of credit cards), violating the definition of a function. hence, Situation 3 does not represent a function.

Situation 3: the total amount of money charged monthly on credit cards to the number of credit cards owned does not represent a function.

In a function, each input (or x-value) should have a unique output (or y-value). However, in this situation, the total amount of money charged monthly on credit cards depends on the number of credit cards owned. It is possible to have different credit card numbers but still have the same total amount of money charged monthly.

For example, two people could own different numbers of credit cards but have the same monthly charges.

As a result, the definition of a function can be violated by having many outputs (monthly charges) for a single input (number of credit cards).

Because of this, case 3 does not represent a function.

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The calculated length of the segment MN in the triangle is 20

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

The triangle

The third angle in the triangle is calculated as

Third angle = 180 - 50 - 50

Evaluate

Third angle = 80

The length of the segment MN is then calculated as

MN/sin(50) = 20/sin(50)

This gives

MN = sin(50) * 20/sin(50)

Evaluate

MN = 20

Hence, the length of the segment MN in the triangle is 20

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Answer:

true

Step-by-step explanation:

Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

Answer:

320units²

Step-by-step explanation:

one half triangle

area =1/2bh

area of the triangle= 1/2*5*8

= 20units²

area of the octagon= 16*20

=320units²

16 semi triangle will make up the octagon full

I hope it work for you

Using the distributive property, 3(50.15) can be simplified to 150.45 by multiplying 3 with each term inside the parentheses.

The distributive property is a fundamental concept in mathematics, explains how multiplication distributes over addition or subtraction. It says that you can distribute or apply the multiplication to each term inside the parentheses separately when you multiply a number by a sum or difference enclosed in parentheses.

expression: 3(50.15)

apply the distributive property, which states that a number outside parentheses can be multiplied by each term inside the parentheses.

Multiply 3 by 50.15.

3 × 50.15 = 150.45

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The image of the graph is missing, so i have attached it.

Answer:

g(x) = 5/3 * f(x)

Step-by-step explanation:

We want to find the equation represents g(x) as a translation of f(x).

From the graph, the y = f(x) function curve has the following observations,

- At x = 0, y = f(0) = 30

- At x = 10, y = f(10) = 36

Similarly, from the graph, the y = g(x) function curve has the following observations,

- At x = 0, y = g(0) = 50

- At x = 10, y = g(10) = 60

From those coordinates on the graph, we can see that;

f(0) = 30 and g(0) = 50

It means that for us to make g(x) as a translation of f(x), g(0) = fraction * f(0)

Fraction = g(0)/f(0) = 50/30 = 5/3

Thus;

g(x) = 5/3 * f(x)

Let's confirm with the second coordinate;

Thus;

g(10) = 5/3 * f(10)

g(10) = 5/3 * 36

g(10) = 60

This value is same as what is on graph, thus we can conclude that;

The equation represents g(x) as a translation of f(x) is; g(x) = 5/3 * f(x)

Based on the information, there are 25 cars with good brakes and good tires.

Total cars = 50

Cars with faulty brakes = 10

Cars with faulty tires = 15

Cars with faulty brakes and good tires = 2

Let's calculate the number of cars with good brakes and good tires:

Cars with faulty brakes or faulty tires = Cars with faulty brakes + Cars with faulty tires - Cars with faulty brakes and good tires

= 10 + 15 - 2

= 25

Cars with good brakes and good tires = Total cars - Cars with faulty brakes or faulty tires

= 50 - 25

= 25

Therefore, there are 25 cars with good brakes and good tires.

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The approximate distance around the outside of the circular field is the circumference = 172.7 feet and the correct option is B.

To calculate the circumference of a circle, multiply the diameter of the circle with π (pi). The circumference can also be calculated by multiplying 2×radius with pi (π = 3.14).

We shall derive the approximate distance around the outside of the circular field by calculating for the circumference as follows:

Radius of the circular feild = 27.5

circumference of the circular feild = 2 × 27.5 feet × 3.14

circumference of the circular feild = 55 feet × 3.14

circumference of the circular feild = 172.7 feet.

Therefore, the approximate distance around the outside of the circular field is derived as the circumference which is equal to 172.7 feet.

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Answer:

288

Step-by-step explanation:

Hope it helps :>

Answer:

288

Step-by-step explanation:

The value of one-sixth times quantity x plus 24 end quantity equals negative 6 is -180.

The expression simply refers to the mathematical statements which have at least two terms that are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

In this case, the expression given will be illustrated as:

1/6x + 24 = -6

Collect like terms

x / 6 = -6 - 24

x/6 = -30

Cross multiply

x = -30 × 6

x = -180

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The solution is, the simplification of the equation is :

4x^2 - 4 = (2x -2 ) (2x+2)

Here, we have,

given that,

the expression is:

4x^2 - 4

now, we have to simplify this.

we know that ,

The a^2 - b^2 formula is also known as "the difference of squares formula". The a square minus b square is used to find the difference between the two squares without actually calculating the squares.

It is one of the algebraic identities.

It is used to factorize the binomials of squares.

The a^2 - b^2 formula is given as:

a^2 - b^2 = (a - b) (a + b).

so, we have,

4x^2 - 4

= (2x)^2 - 2^2

= (2x -2 ) (2x+2)

Hence, The solution is, the simplification of the equation is :

4x^2 - 4 = (2x -2 ) (2x+2)

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Answer:

7: 63

8: 73

arithmetic sequence

y = 10x - 7

or f(n) = 10x -7

or

\(a_{n}\) = 3 + (n-1)10

Step-by-step explanation:

the output increases by 10 every time that the input increases by 1.  That gives us our common difference or slope.  The y intercept is -7. That is the value is you worked backwards until you get to n = 0.  The initial value  is 3.  That is when n is 1.

When n is 3, f(n) is 23

When n is 2, f(n) is 13

When n is 1, f(n) is 3

When n is 0, f(n) is -7

I am not sure if this is clear.  I am assuming that you have a lot of knowledge of linear equations and how to write arithmetic sequence.  If my explanation is confusing it is me and not you.

Answer:

a. 63,73

b. Arithmetic sequence

c.t(n)=10n-7

Explanation:

a. Here is the completed table:

n | t(n)

4 | 33

5 | 43

6 | 53

7 | 63

8 | 73

b.

The type of sequence is arithmetic.

An arithmetic sequence is a sequence of numbers where the difference between any two consecutive terms is constant.

In this case, the difference between any two consecutive terms is 10.

c.

The equation for the arithmetic sequence is:

t(n)=a+(n-1)d

where:

For Question:

Now

equation becomes:

t(4) = a+(4-1)10

33=a+30

a=33-30

a=3

Now, the Equation becomes

t(n) = 3+(n-1)10

t(n) = 3+10n-10

t(n)=10n-7

Answer:

8.15

Step-by-step explanation:

Answer: 40 dollars

Step-by-step explanation:

i hope the explanation is right:)

If he invites 5 friends for 40 bucks each then one friend that he knows will go is 40 dollars. So the only thing you have to do for this problem is multiply 40 by the number of friends which in this case i believe is 1.

Answer:

90720ways

Step-by-step explanation:

Permutation has to do with arrangement

First we need to find the number of ways 6 people can be arranged in a row from a group of 10people using the formula

(10-1)P(6-1) = 9P5

9P5= 9!/(9-5)!

9P5 = 9×8×7×6×5×4!/4!

9P5 = 9×8×7×6×5

9P5 = 15,120

Since there is restriction that the bride must be in the picture (the bride is just a person and cam be placed at any point along the row). Hence the number of different ways the bride can be placed is 6 different ways

Hence, the number of ways a photographer at a wedding arrange 6 people in a row from a group of 10 people if the bride must be in the picture is 6×15120 = 90,720

Hence the correct answer is 90720 ways

Answer:

\(\frac{2}{3}\)

Step by Step Explanation:

Convert any mixed numbers to fractions.

Reduce fractions where possible.

Then your initial equation becomes:

\(\frac{143}{120}\) - \(\frac{21}{40}\)

Applying the fractions formula for subtraction,

= (140 × 40) - (21 × 120)

          120 × 40

= \(\frac{5720 - 2520}{4800}\)

= \(\frac{3200}{4800}\)

Simplifying \(\frac{3200}{4800}\), the answer is \(\frac{2}{3}\).

Answer:

. C. The graph of g(x) is the graph of f(x) stretched horizontally by a factor of 2.

g(x)=x² is the function of g(x).

A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

Graph of g(x) is the graph of f(x) compressed vertically by a factor of 1/4

Graph of g(x) is the graph of f(x) shifted down 4 units

Graph of g(x) is a graph of f(x) shifted up 4 units

Graph of g(x) is a graph of f(x) stretched vertically by a factor of 4

g(x) = 4·f(x) = 4x²

Graph of g(x) is a graph of f(x) stretched vertically by a factor of 4

Graph of g(x) is a graph of f(x) compressed vertically by a factor of 1/4

=> g(x) = (1/4)f(x)  = x²/4

Graph of g(x) is a graph of f(x) shifted down 4 units

=> g(x) = f(x) - 4

Graph of g(x) is the graph of f(x) shifted up 4 units

=> g(x) = f(x) + 4

Graph of g(x) is a graph of f(x) stretched vertically by a factor of 4

=>  g(x) = 4·f(x) = 4x²

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