Using Pythagoras’ theorem or trigonometric ratios

Answer:

Step-by-step explanation:

0

Answer:

A and D

Step-by-step explanation:

its A and D, trust

Number of possible area codes = 144

The telephone area codes consist 3 digits.

The possible digits are 1, 2, 3,4,5,6,7,8,9,0. That is, a total of 10 digits.

The first digit was not 0 or 1. So the remaining are 2,3,4,5,6,7,8,9. There are 8 possibilities in first place.

The second digit is either 0 or 1. So there are only two possibilities for second place.

The third digit was anything except 0. So the third digit has 9 possibilities.

The total possibilities of the three digit number is the product of possibilities of digits in each place.

Hence, Number of possible area codes = 8 x 2 x 9 = 144

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Answer: The slope is 3.

Step-by-step explanation: Hope this helps :)

Answer:

The slope of the line represented by the table value is -8/5

√ x/4 + 4 is the inverse of the function f(x)=4x^2-16

What is inverse function?

In mathematics, the inverse function of a function f (also called the inverse of f) is a function that undoes the operation of f

Given  f(x)=4x²-16

Let f(x) = y

So we can say y =4x²-16

We will then make x the subject:

Since y = 4x²-16

4x² = y + 16

x² = y + 16/4

x = √ y/4 + 4

since x = f⁻¹(y)  = √ y/4 + 4

Thus  f⁻¹(x)  = √ x/4 + 4

Therefore, the inverse of f(x)=4x^2-16 is √ x/4 + 4

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The distance between the points is 2: x2 - x1 = -6 + 8. So, the midpoint would be located on a point that is half of this distance from both points.

2/2 = 1

-6 - 1 = -7
-8 + 1 = -7

-7 has a distance of 1 from both -8 and -6, so this is the midpoint.

The linear equation that represents how much he spent is given as y = 1.25x + 9.55

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear function is given y = mx + c

To solve this problem, we can simply use the values given to write a linear equation.

Can be written as

[tex]30.75 = 1.25x + c\\x = 17\\30.75 = 1.25(17) + c\\c = 30.75 - 21.25\\c = 9.55\\[/tex]

The equation to represent this problem is y = 1.25x + 9.55

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If a stick of length 60 inches is measured to be 63 inches long the the percent error will be 5% .

The Percent Error can be calculated by the formula

Percent Error = (measured value - actual value)/(actual value)  ×100

In the question ,

it is given that

the original length of the stick is 60 inches .

the measured length of the stick is 63 inches .

So, the measured value = 63 inches ,

actual value = 60 inches .

Substituting the measured values and actual value in the percent error formula , we get

Percent Error = (63-60)/60 × 100

= 3/60 × 100

= 1/20 × 100

= 100/20

= 5 %

Therefore , if a stick of length 60 inches is measured to be 63 inches long the the percent error will be 5% .

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The equation of a line in point-slope form that passes through the point (20,19) with slope 55 is y = 55x -1091.

As given in the question,

Line passes through the point ( x₁ , y₁ ) = ( 20, 19)

Slope of the line that passes through (20 , 19) is 55

Equation of a line in point-slope form that passes through the point (20,19) with slope 55

y - y₁ = m ( x- x₁)

⇒ y - 19 = 55 (x - 20)

⇒ y -19 = 55x - 1100

⇒ y= 55x - 1091

Therefore, the equation of a line in point-slope form that passes through the point (20,19) with slope 55 is y = 55x -1091.

The complete question is:

Use point-slope form to write the equation of a line that passes through the point (20,19) with slope 55.

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Answer:

(- 3, - 1 )

Step-by-step explanation:

1 down means subtract 1 from the y- coordinate

2 units right means add 2 to the x- coordinate

(- 5, 0 ) → (- 5 + 2, 0 - 1 ) → (- 3, - 1 )

a=1×10, b=2×2×5, c=5×5 and d=2×5. Option a, b and d are the prime factorization of 10 but option c is not a prime factorization of 10.

Given that,

a=1×10, b=2×2×5, c=5×5 and d=2×5

We have to find the prime factorization of 10.

A natural number other than 1 is said to have a prime factor if its only factors are 1 and itself. The first few prime numbers are actually 2, 3, 5, 7, 11, and so on. So, let's take something like the number 20 as an example. That can be divided into two components. We can say, "Well, that's 4 times 5." Note that the number five is a prime.

Option a is 1×10

1×10=10

Option a is a prime factor of 10.

Option b is 2×2×5

2×2×5=10×2

Option b is a prime factor of 10.

Option c is 5×5

5×5=25

Option c is not a prime factor of 10.

Option d is 2×5

2×5=10

Option d is a prime factor of 10.

Therefore, Option a, b and d are the prime factorization of 10 but option c is not a prime factorization of 10.

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If the sample size were to increase, and all other numbers remaining stays the same, then the standard error would be less.

Standard error is defined as the measures of the preciseness of an estimate of a population mean. It can be calculated by dividing the sample standard deviation by the square root of the sample size.

SE = SD / √n

where SE = standard error

SD = sample standard deviation

n = sample size

Increasing the sample size, n, while the samples remain the same(hence, the standard deviation will be the same), will result to smaller standard error.

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The Ratios 5 : 3 and 17 : 12 does not form a proportion.

What is Proportion?

A Proportion, in mathematics, can be defined as when two ratios are set equal to each other.

Now, the given ratios are: 5 : 3 and 17 : 12

We can also write the ratios as: [tex]\frac{5}{3}[/tex] and [tex]\frac{17}{12}[/tex]

To determine, if they are a proportion, we can cross multiply and get the same answers on both the sides.

When we multiple, the numerator from the first by the denominator of the second, we get

5 * 12 = 60                             …(1)

Now, multiply the denominator from the first by the numerator of the second, we get

3 * 17 = 51                             …(2)

Since, (1) and (2) are not equal. Therefore the ratios does not form a proportion.                

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Answer:

4x + 9

Step-by-step explanation:

the product of 4 and x is 4x

then 9 more is addition, so 4x + 9

Answer:

-4/27

Step-by-step explanation:

The length of three sides will be 35 feet, 70 feet and 51 feet

Define Perimeter of triangle

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length.

Perimeter of Triangle = side1 + base + side2

Let, the shortest side of the triangle = x

The other side length is = 2x

and, the length of third side is = x + 16

given perimeter = 156 feet

We know, perimeter of triangle = a + b +c

where, 'a' and 'c' stands for sides of triangle

and, b stands for base

hence, the expression will be according to formula,

x + 2x + x + 16 = 156

solve for 'x'

4x + 16 = 156

4x = 156 - 16

x = 140/4

x = 35

2x = 2 * 35 = 70

x + 16 = 35 + 16 = 51

Therefore, the length of three sides will be 35 feet, 70 feet and 51 feet.

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The sequence's 61st term is -972.

The sequence is -12 , -28 , -44.

The following arithmetic sequence is: -12, -28, -44, ..

Find the common difference between the succeeding and preceding terms.

         c.d = first term - second term

-28 - (-12) = -28 + 12 = -16

-44 - (-28) = -44 + 28 = -16

As a result, the distinction between the terms remains constant.

This is a mathematical sequence.

The formula for the nth term of an arithmetic sequence is:

an = a1 + (n - 1 ) d

Where,

an is the sequence's nth term.

a1 is the sequence's first term.

The common difference between terms is denoted by d.

-12, -28, -44 are the numbers in the given sequence.

By changing the values in the formula,

a1 = -12

d = -16

Substituting values,

an = -12 + (n - 1 )(-16)

an = -12 - 16n + 16

an = 4 - 16n

Substitute n = 61 to find the 61st term.

a61 = 4 - 16 x 61

a61 = 4 - 976

a61 = -972

As a result, the sequence's 61st term is -972.

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Answer:

She will earn 18 dollars in interest.

Step-by-step explanation:

0.09*(100*2)

0.09*(200)

18

The area of the Caribbean Sea is 2.7182 × 10^6 km2, The area of the South Atlantic Ocean is 4.027 × 10^7 km2, then the total area of the Caribbean Sea and the South Atlantic Ocean is 4.29882 × 10⁷ km².

We are to determine the total area of the Caribbean Sea and the South Atlantic Ocean.

From the given information,

The area of the Caribbean Sea is 2.967 × 10⁶ km² and

The area of the South Atlantic Ocean is 4.149 × 10⁷ km²

To determine the total area, we will add the given areas together,

   2.7182 × 10⁶ km²

+  4.027 × 10⁷ km²

So, That is,

   2.7182 × 10⁶ km²

+  40.27 × 10⁶ km²

----------------------------

42.9882 × 10⁶ km²

So,

We can write,

= 4.29882 × 10⁷ km²

Therefore,

The total area of the Caribbean Sea and the South Atlantic Ocean is 4.29882 × 10⁷ km².

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The standard deviation for the number of seeds germinating in each batch is 1.3.

Given, the probability that a radish seed will germinate is 0.7.

In binomial distribution, standard deviation is given as:

σ = √np(1-p)

Where "n" is the number of observations

"p" is probability of getting success

We are given that:

Total batches of seed = 8

Probability that a radish seed will germinate is 0.7

Here success is getting radish seed germinated

Then, the standard deviation for the number of seeds germinating in each batch.

Plugging in values in formula, we get:

σ = √(8)(0.7)(1-0.7)

= √(8)(0.7)(0.3)

= √1.68

= 1.29614 ≈ 1.3

Therefore the standard deviation for the number of seeds germinating in each batch is 1.3

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The biggest number you can make from the numbers 12, 1, 4 and 7 is given by:

336 = 12 x 1 x 4 x 7.

The operation that leads to the bigger number is the power operation, however, as stated in the problem, you cannot use any powers in this problem.

After the power, the operation that leads to the highest numbers is the multiplication operations.

These are no constraints relating the symbols, only that each number cannot be used more than once, hence the biggest number is obtained multiplying all values, as follows:

12 x 1 x 4 x 7 = 336.

If one of the numbers had been a fraction with a greater denominator than numerator, the fraction should be divided, as dividing by a fraction is the same as multiplying by the inverse of the fraction.

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Answer: 2,3,4

Step-by-step explanation:

y=1/4x +2

x=0  y=2

x=4  y=3

x=8  y=4

The triangle's edges measure (3x - 4) feet, (x² - 1) feet, and (2x² - 15) feet, respectively. The perimeter of the triangle is 42 feet.

Given that,

Kat is using reflective orange paint to outline a triangle stage prop. The triangle's edges measure (3x - 4) feet, (x² - 1) feet, and (2x² - 15) feet, respectively.

We have to find if x = 4, what is the triangle's perimeter.

The perimeter of the triangle is equal to sum of the three sides of the triangle.

=3x - 4 + x² - 1 + 2x² - 15

=3x²+3x-20

Take the x value as 4

We get,

=3(4)²+3(4)-20

=3×16+3×4-20

=48+14-20

=62-20

=42

Therefore, The perimeter of the triangle is 42 feet.

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Marcy is a 5-ft-5 in. She took measurements of both her own shadow. h=520 is the building's height.

Given that,

Marcy is a 5-ft-5 in. She took measurements of both her own shadow and that of the structure in order to determine its height.

We have to find what is the building's height, h.

Use the fact that 1 feet is equivalent to 12 inches to convert all measures to a single unit, inches.

We convert

MN=26×12=312 inches.

QR=3×12+3=36+3=39 inches.

PQ=5×12+5=60+5=65inches.

Since the Sun's rays that generate LN and PR are parallel, they are also parallel. the angles they make with the earth as a result are consistent:

∠N≅∠R

The Right Angle Congruence Theorem illustrates ∠M≅∠Q.

As a result, according to the Angle-Angle Similarity △LMN~△PQR

Calculate a ratio using the known lengths of the sides and the unknown length (height of the building).

PQ/QR=LM/MN

65/39=h/312

h=65×312/39

h=20280/39

h=520

Therefore, h=520 is the building's height.

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1/4π is area of a circle when the radius is 6 cm.

What is the circumference of a circle?

 A = πr²

differentiate both sides with respect to 't'

dA/dt = πr² dr/dt

dA/dt = 2πr dr/dt

dA/dt = 3  ,     r = 6

3 = 2π * 6dr/dt

dr/dt = 1/4π

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