explaination with steps

The diameter of the circle is 30 feet

To compute the diameter of the circle, we can use the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the hypotenuse is the diameter of the circle, and the other two sides are the radius and the distance between the chord and the center of the circle.

So, we can write the equation:

diameter^2 = radius^2 + (distance between chord and center)^2

We know the radius is half the diameter, so we can substitute that in:

diameter^2 = (diameter/2)^2 + (15)^2

And we can solve for the diameter:

diameter^2 = diameter^2/4 + 225

diameter^2 = diameter^2/4 + 225

4diameter^2 = diameter^2 + 900

3diameter^2 = 900

diameter^2 = 900/3

diameter = sqrt(900/3)

So the diameter of the circle is 30 feet.

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Answer: HL

Step-by-step explanation:

HL because the hypotenuse leg theorem shows how a given set of right triangles are congruent if the corresponding lengths of their hypotenuse and one leg are equal.

The solution of the equation 3(2m - 1) ≤ 4m + 7 is option A m ≤ 5.

A mathematical statement known as an inequality in algebra uses the inequality symbol to show the relationship between two expressions. An inequality symbol denotes that the expressions on each side are not equal.

The given inequality is 3(2m - 1) ≤ 4m + 7

Remove the brackets by multiplying 3 with each term inside it:

6m - 3 ≤ 4m + 7

Subtract 4m from both sides of the equation.

6m - 3 - 4m ≤ 4m + 7 - 4m

2m -3 ≤ 7

Add 3 to both sides of the equation.

2m - 3 + 3 ≤ 7 + 3

2m ≤ 10

Divide both sides of the equation with 2.

2m/2 ≤ 10/2

m ≤ 5

Hence the solution of the equation is m ≤ 5, that is option A.

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Answer:

The answer is (4x² - 36x + 81)

Step-by-step explanation:

So,

(2x - 9)² = (2x)² - 2(2x)(9) + (9)²

(2x - 9)² = 4x² - 36x + 81

Thus, The product of (2x - 9)² is (4x² - 36x + 81)

If Conan borrows $3,000 at a yearly simple interest rate of 1.6% for 2 years then he has to pay 3009.6 back.

percentage, a relative value indicating hundredth parts of any quantity.

Given that Conan borrows $3,000 at a yearly simple interest rate of 1.6% for 2 years.

A=P(1+rt)

Where, A is final amount, P is principal amount, r is rate of interest, t is time period.

P=3000, r=0.16%=0.16/100=0.0016, t=2

A=3000(1+(0.0016)2)

=3000(1+0.0032)

=3000(1.0032)

=3009.6

Hence, Canon needs to pay back 3009.6

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The ratio 5:73 represents the ratio of 8th grade baseball players to total athletes.

In mathematics, a ratio is a comparison of two or more numbers that demonstrates how large one number is relative to the other. The divisor or number that is dividing is known as the consequent, while the dividend or number being divided is known as the antecedent. A ratio divides two numbers to compare them.

Given that the Total number of athletes are 2+4+7+1+6+5+7+4+4+8+15+10

= 73

Ratio of 5:73 represent the athletes in a particular grade with specific games to total number of athletes in the school.

There are on one event is where 5 athletes are, that is 8th grade baseball players.

So the correct answer is The ratio 5:73 represents the ratio of 8th grade baseball players to total athletes.

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Answer:

Step-by-step explanation:

y=2x-5+2

then you do minus 2 on both sides

Hope this helped!

The point at a graph where the graph cuts the x-axis is known as the x-intercept. Therefore, the x-intercept is a point.

A graph is made up of four quadrants in which two are positive and two are negative quadrant.

There are two types of axis which are x-axis and y-axis two negative and two positive.

The y-intercept is the point where the graph cuts the y-axis .Graph Theory is the study of graphs which comes under discrete mathematics.

It is defined as a mathematical structure that connects a group of points to express a specific function.

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No, It is not possible to have a complex number in the form of a + bi when b = 0.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Complex number.

It is in the form of a + ib.

Where a and b are real numbers.

Now,

If b = 0 then we can not have a complex number.

Example:

a + bi

a = 1 and b = 0

1 + 0i = 1 which is not a complex number.

In order to have a complex number a can be any real number and 0 but b  can not be a zero.

Thus,

It is not possible to have a complex number in the form of a + bi when

b = 0.

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The equation 5x + 5 = 5x - 5 has no solution because the left side of the equation (10) cannot equal the right side of the equation (-5).

No solution equation:

5x + 5 = 5x - 5

To solve this equation, we must first isolate the variable. To do this, we can subtract 5x from both sides of the equation.

5x + 5 = 5x - 5

Subtract 5x from both sides:

5 + 5 = - 5

Simplify:

10 = -5

At this point, we can see that this equation has no solution because the left side of the equation (10) cannot equal the right side of the equation (-5).

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Answer:

hhhhhhhhhhhhhhhh hhhhhhhhhhh

Step-by-step explanation:

hhhhhhhhh hhhhhhhhh hhhhhhh hhhhhh

Answer:

7.0

Step-by-step explanation:

from the first figure which is not a 0

7.3-7.0(1 significant figure)

The radius of a sphere whose surface area is  324*pi cm² is:

R = 9 cm.

We know that the surface of a sphere of radius R is given by:

S = 4*pi*R^2

Where pi = 3.14

Here we know that a sphere has a surface of 324*pi cm², then we can write the equation:

S =  324*pi cm² = 4*pi*R^2

We can divide both sides by pi, so we get:

324 cm^2 = 4*R^2

Now we can solve that equation for R, we will get:

R^2=  (324 cm^2)/4 = 81cm^2

R = √(81 cm^2)

R = 9cm

The radius of the sphere is 9cm.

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Answer:

Step-by-step explanation: 2.922

Answer: 2.922

Step-by-step explanation: (Look at the attachment for the best experience, or idea) So, as you can see in the attachment below, we first need to line up the decimal points with one another. They subtract in line with the other decimals and borrow. As we know, our answer is 2.922.

Answer:

24 students are in the class

Step-by-step explanation:

Let x represent the total number of students in the class. We have the equation:

(2/3)x = 16

x = 24 students

So, there are 24 students in the class.

Answer:

24 students

Step-by-step explanation:

16/2=8

8*3=24

Step-by-step explanation:

6(8x+5)

Use the distributive property to multiply 6 by 8x+5.

48x+30

Hope it Helps!

On solving the provided question, we can say that - by the prime factors we have x^2 + 1 +2x = X= -1, -1

Any natural number other than 1 with just itself and the number 1 as its divisors is considered a prime factor. Actually, 2, 3, 5, 7, 11, and so on are some of the first prime numbers. an amount that has been multiplied to produce another amount. By dividing 15 by 3 and 5, for instance, we get 3 5 = 15. main elements: Prime factors include all factors that are prime but are not composite. A few prime factors of 30 are 2, 3, and 5. Only 2 and 3 are prime factors of 12, so listing 2 twice as 2 2 3 (or 22 3) is necessary to factorize 12. The sum of 2 + 3 is not 12.

here we have the equation,

[tex]x^2 + 1 + 2x\\[/tex]

(x+1)(x+1)

x = -1, -1

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Answer:

perpendicular

Step-by-step explanation:

The length of the hypotenuse of a 45 90 45 triangle whose leg measures 9 in is 12.73 in.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the square of the length of the other two sides (a and b).

In this case, a = b = 9 in, so:

c2 = 92 + 92

c2 = 81 + 81

c2 = 162

c = √162

c = 12.73 in

The length of the hypotenuse of a 45 90 45 triangle whose leg measures 9 in is 12.73 in, calculated using the Pythagorean theorem.The length of the hypotenuse of a 45 90 45 triangle whose leg measures 9 in is 12.73 in.

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Answer:

B

Step-by-step explanation:

14.50 / 1.75 = 8.3

26.25 / 2.5 = 10.5

3/8 * 2 = 0.75 .... 5.5 * 2 = 11 (no need to continue)

Answer:

see explanation

Step-by-step explanation:

there is a common ratio between consecutive terms, that is

12 ÷ 6 = 24 ÷ 12 = 48 ÷ 24 = 96 ÷ 48 = 2

this indicates the sequence is geometric

the nth term of a geometric sequence is

f(n) = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

here a₁ = 6 and r = 2 , then

f(n) = 6 [tex](2)^{n-1}[/tex]

Answer:14

Step-by-step explanation:You can use distance formula to find the length of each side, and then add them together to approximate the perimeter.

Answer:

D

Step-by-step explanation:

Because the account that gets debited depends on the specific transaction

The probability of each of your three friends having an ace is 32%.

The probability of each of your three friends having an ace is calculated using the Binomial Probability Formula. The formula is P(x) = nCr * p^x * (1-p)^(n-x). Here, n = 13 (number of cards dealt to each person) , r = 1 (number of aces you want to calculate the probability of), p = 4/52 (probability of getting an ace from a deck of 52 cards) and x = 1 (number of aces each of your three friends have).

Therefore, the probability of each of your three friends having an ace is P(x) = 13C1 * (4/52)^1 * (48/52)^(13-1) = 0.32.

This means that the probability of each of your three friends having an ace is 32%.

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5 half-dozens he should buy to make enough cookies.

What is an average?

Average, mean, median, and norm all refer to something that sits in the middle. The average is the ratio created by dividing the total number of figures in a set by the total number of figures. scored 85 on tests on average. The term "mean" can refer to the simple average or a figure that lies halfway between two extremes.

Here, we have

If 108 students eat 2 cookies on average, there will need to be 108× 2 = 216 cookies.

There are 15 cookies per pan, meaning there need to be {216}/{15} = 14.4 pans.

However, since half-recipes are forbidden, we need to round up and make{216}/{15} = 15 pans.

1 pan requires 2 eggs, so 15 pans require 2×15 = 30 eggs.

Since there are 6 eggs in a half dozen,

we need 30/6 = 5 half-dozens of eggs.

Hence, 5 half-dozens he should buy to make enough cookies.

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Answer:

C

Step-by-step explanation:

Answer:

- 7√10

Step-by-step explanation:

Step 1 : Take √10 common

2√10 - 5√10 - 4√10

= √10 ( 2 - 5 - 4 )

Step 2 : Subtract the numbers separately.

2 - 5 - 4

= 2 - 9

= - 7

Step 3 : Multiply √10 and - 7

√10 * - 7 = - 7√10

Answer:

y = [tex]\frac{2}{3}[/tex] x + 2

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 2 ) and (x₂, y₂ ) = (3, 4 )

m = [tex]\frac{4-2}{3-0}[/tex] = [tex]\frac{2}{3}[/tex]

the line crosses the y- axis at (0, 2 ) ⇒ c = 2

y = [tex]\frac{2}{3}[/tex] x + 2 ← equation of line

Answer:

f(3) = 2

Step-by-step explanation:

See the attached graph.  f(3) = ____ is asking us to find the value of the function, f, at the point x = 3.  At x = 3, the value of y is 2.