Jason's age is 1/2 of his brother's age. His brother's age can be represented by the expression 12a - 9. Write an expression that can be used to represent the sum of their ages.
A) 12a - 5.5
B) 18a - 13.5
C) 18a + 21
D) (12a-9)/2

Answer:

[tex]log_8(21)=\frac{log21}{log8}[/tex]

Step-by-step explanation:

Given : Log expression [tex]log_8(21)[/tex]

To find : Write the expression using the change of base formula.

Solution :

Logarithmic change of base rule formula is

[tex]log_ab=\frac{log_eb}{log_ea}[/tex]

Now, using logarithmic rule in [tex]log_8(21)[/tex]

where a=8 and b=21

[tex]log_8(21)=\frac{log_{10}21}{log_{10}8}[/tex]

[tex]log_8(21)=\frac{log21}{log8}[/tex]

Therefore, The expression Devonte use [tex]log_8(21)=\frac{log21}{log8}[/tex]

2a-9 +a = 90 degrees

3a -9 = 90

3a = 99

a = 33

angle GEF is 33 degrees

Answer:

Area of each slice of pizza is 28.27 square inches.

Step-by-step explanation:

The formula calculating the area of circle is

A = π[tex]r^{2}[/tex] where r is radius ( half of the diameter )

A = [tex](12)^{2}[/tex]

A = 452.38934 [tex]inches^{2}[/tex]

pizza cut into 16 equal slices

Therefore 452.38934 ÷ 16 = 28.27433 [tex]inches^{2}[/tex]

So the total area of the pizza is 452.39 square inches and the area of each slices are 28.27 square inches approximately.

Answer:

About 28 in ^2

Step-by-step explanation:

Answer:

8.95

Step-by-step explanation:

Because 1.79x5=8.95 You can look it up too

:)

Answer:

In PLATO the answer is B

Step-by-step explanation:

Notice that all of the values start high at 0 and gradually get lower until 8

Answer: took the test

Step-by-step explanation:

The value of p is [tex]\frac{67}{8}[/tex], which is approximately 8.375. Therefore, the correct option is D. 8

To solve for  p  in the equation 10p + 5 = 18p - 62, we first need to isolate p on one side of the equation.

First, we'll subtract 10p from both sides to move the variable terms to one side:

10p + 5 - 10p = 18p - 62 - 10p

This simplifies to:

5 = 8p - 62

Next, we'll add 62 to both sides to isolate the term with p on one side:

5 + 62 = 8p - 62 + 62

This simplifies to:

67 = 8p

Finally, we divide both sides by 8 to solve for p:

[tex]\frac{67}{8} = p[/tex]

In conclusion, the value of p is 8.

The total ticket cost for Mr. Delong's drama class to attend Mozart's opera Don Giovanni, with 23 students and 2 teachers at $39 per ticket, is $975.

To calculate the total ticket cost for Mr. Delong's drama class field trip to see Mozart's opera Don Giovanni, we need to combine the number of students and teachers going to find out how many tickets in total need to be purchased. There are 23 students and 2 teachers, so that's a total of 25 people needing tickets. The cost per ticket is $39.

The expression to find the total ticket cost is (Number of Students + Number of Teachers) x Cost per Ticket, which translates to (23 + 2) x $39.

Doing the math: (25) x $39 = $975.

Therefore, the group's total ticket cost for attending the opera will be $975.

The pattern 1,3,5,7... represents odd numbers, as each number cannot be evenly divided by 2.

The correct option is (A).

The pattern 1,3,5,7... represents odd numbers. These numbers are considered odd because they cannot be evenly divided by 2. Every number in the sequence is one greater than an even number, which means adding 1 to an even number gives you an odd number. For instance, the number 1 is odd because 0 (an even number) plus 1 equals 1. Similarly, 2 (which is even) plus 1 equals 3, and so on. This pattern of numbers is used to represent all numbers that, when divided by 2, have a remainder of 1.

complete question given below:

The pattern 1,3,5,7... represents numbers.

A.odd

B.even

C.whole

To solve the system of equations by substitution, substitute the value of y from the second equation into the first equation. The solution is x = 1/2 and y = 5/2 or 2.5.

To solve the system of equations by substitution, we substitute the value of y from the second equation into the first equation.

Given that y = 5x, we can substitute this value into the first equation:

4x + 2(5x) = 7

Simplifying the equation:

4x + 10x = 7

Combine like terms:

14x = 7

Divide both sides by 14:

x = 7/14

Simplify:

x = 1/2

Now substitute this value of x back into the second equation to find y:

y = 5(1/2)

Simplify:

y = 5/2 or y = 2.5

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Answer:

[tex]c=11.49[/tex]

Step-by-step explanation:

It is given that  a = 5, b = 12, and c = 72°, then using the cosine formula, we get

[tex]c^2=a^2+b^2-2abcosC[/tex]

[tex]c^2=(5)^2+(12)^2-2(5)(12)Cos72^{\circ}[/tex]

[tex]c^2=25+144-2(60)(0.309)[/tex]

[tex]c^2=169-37.08[/tex]

[tex]c^2=131.92[/tex]

[tex]c=\sqrt{131.92}[/tex]

[tex]c=11.49[/tex]

Therefore, the value of the length of the side c is 11.49.

If f(x)= 3x - 1 and g(x) = x+2, (f +g)(x) is 4x+1.

(3x-1)+(x+2)

=3x+x-1+2

=4x+1.

A function operation guidelines that are accompanied as a way to remedy functions. Learn the definition of a feature operation such as the guidelines for addition, subtraction, multiplication, and division.

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89/3 = 63

63-2 = 61

63 +2 = 65

61 +63 +65 = 189

This should help

Let's say Set A = {1,2,3}, Set A can have subsets of:

{1}, {2}, {3}, {1,2}, {1,3}, {2,3}

And so there is 6 subsets.

The radius of a circle in Euclidean geometry is the distance from its center to any point on the circumference, and it can be calculated by dividing the circumference by 2π. In physics, the radius is also the radius of curvature for an object's circular path, determined by position data and the Pythagorean theorem.

In mathematics, especially in Euclidean geometry, the radius of a circle is a fundamental concept that refers to the distance from the center of the circle to any point on its circumference.

Referring to the examples provided, one method to find the radius (r) is by understanding the relationship between the circumference of a circle (C) and its radius. In a flat, Euclidean space, the ratio C/r is a constant 2π, where π (pi) is approximately 3.14159. Therefore, if you know the circumference, you can calculate the radius by rearranging the formula to r = C/(2π).

In one of our more practical examples, the radius of curvature is used in the context of circular motion. When dealing with the path of an object in a circular trajectory, the radius of the circle also represents the radius of curvature. For instance, using position data where x = 3 m and y = 4 m, we can use the Pythagorean theorem to find the radius, r = √(3² + 4²) = 5 m.

Understanding these principles is crucial in fields such as physics, where the radius is directly related to calculating velocities and accelerations in circular motions as seen with centripetal acceleration.

x + y = 50 

Q = x * y 

Combining the two:
Q = x * (50 - x) 
Q = 50x - x^2 
Q = -x^2 + 50x 
Q = -(x^2 - 50x) 
Q = -(x^2 - 2 * 25x + 25^2 - 25^2) 
Q = 25^2 - (x - 25)^2 
Q = 625 - (x - 25)^2 

So what we got is an equation for parabola with a vertex at (25 , 625) and it opens downward. We know that parabolas only have one critical value, so if x and y are unrestricted, then there's no minimum product.

No, there cannot be a minimum product. The product of two numbers is maximized when the numbers are equal or close to each other.

The student is asking if there can be a minimum product when x and y are numbers whose sum is 50 and we are trying to maximize the product xy. The answer is no, there cannot be a minimum product. This is because the product of two numbers is maximized when the numbers are equal or close to each other. In this case, when x = 25 and y = 25, the product xy is maximized at 625. If x and y were further apart, the product would be smaller.

Thus,

Q = x * (50 - x)

Q = 50x - x^2

Q = -x^2 + 50x

Q = -(x^2 - 50x)

Q = -(x^2 - 2 * 25x + 25^2 - 25^2)

Q = 25^2 - (x - 25)^2

Q = 625 - (x - 25)^2

The value of the segment 'x' is 9° as ∠ABC is a right angle.

When the value of an angle is 90°, then it is called right angle.

Here, AB is perpendicular to CD.

Therefore, ∠ABC = 90°.

Again,  ∠ABC = (7x + 27)° = 90°.

Therefore, 7x + 27 = 90

⇒ 7x = 63

⇒x = 9

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