What are three consecutive odd integers that have a sum of 39?

Group terms that contain the same variable, and move the constant to the opposite side of the equation

(x²−3x)=10

Complete the square. Remember to balance the equation by adding the same constants to each side.

(x²−3x+2.25)=10+2.25

Rewrite as perfect squares

(x-1.5)²=12.25----------> (+/-)[x-1.5]=3.5

Answer:

5 and -2 :)

explanation:

Answer:

[tex]2x^3+12x^2+10x-8[/tex]

Step-by-step explanation:

The product is found using the distributive property.

[tex](x+3)(2x^2+6x-8)\\x*2x^2 + x*6x+x*(-8)=2x^3+6x^2-8x\\\\and\\\\3*2x^2+3*6x+3*(-8)=6x^2+18x-8[/tex]

Now combine the two products by adding like terms together.

[tex]2x^3+6x^2-8x + 6x^2+18x-8\\2x^3+12x^2+10x-8[/tex]

Answer:

Area of the regular pyramid = 16.64 square units.

Step-by-step explanation:

Given  : Regular pyramid .

To find: Find the total area of the regular pyramid.

Solution : We have  given that regular pyramid.

Area = 4 ( area of triangle ) + area of base .

Area of the regular pyramid = 4 ( [tex]\frac{1}{2} * base * height + side * side[/tex].

Area of the regular pyramid =  [tex]4(\frac{1}{2}* 2* \sqrt{10}  + 2*2[/tex]

Area of the regular pyramid =   [tex]4( \sqrt{10} ) + 4[/tex]

Area of the regular pyramid =  (4 [tex]( \sqrt{10} ) \+\ 1[/tex].

Area of the regular pyramid = 16.64 square units.

Therefore, Area of the regular pyramid = 16.64 square units.

The one possible ordered pair that satisfies all conditions is (x, y) = (150, 134).

The ordered pair (x, y) that satisfies the following conditions:

1. The total revenue from selling x cups of lemonade and y lemon bars is at least $500. This gives us the inequality:

[tex]\[ 2x + 1.50y \geq 500 \][/tex]

2. The total expenses for preparing x cups of lemonade and y lemon bars is no more than $100. This gives us the inequality:

[tex]\[ 0.25x + 0.20y \leq 100 \][/tex]

3. At least 150 cups of lemonade were sold, which gives us the inequality:

[tex]\[ x \geq 150 \][/tex]

To find a combination of x and y that satisfies all these conditions, we can start by considering the minimum number of lemonade cups sold, which is 150. We can then calculate the revenue and expenses for this minimum number and see how many lemon bars would be needed to meet the revenue requirement while keeping the expenses within the limit.

Let's start with the minimum number of lemonade cups:

[tex]\[ x = 150 \][/tex]

The revenue from lemonade alone would be:

[tex]\[ 2 \times 150 = \$300 \][/tex]

The expenses for lemonade alone would be:

[tex]\[ 0.25 \times 150 = \$37.50 \][/tex]

Now, we need to find out how many lemon bars (y) would be needed to make up the remaining revenue to at least $500 while keeping the total expenses at or below $100.

Let's denote the remaining revenue needed as R and calculate it:

[tex]\[ R = 500 - 300 = \$200 \][/tex]

The revenue from selling y lemon bars is $1.50y, so we have:

[tex]\[ 1.50y \geq 200 \][/tex]

[tex]\[ y \geq \frac{200}{1.50} \][/tex]

[tex]\[ y \geq 133.33 \][/tex]

Since we cannot sell a fraction of a lemon bar, we round up to the nearest whole number, so at least 134 lemon bars must be sold.

Now let's check the expenses for the lemon bars. We have $100 - $37.50 = $62.50 left for expenses. The cost to prepare each lemon bar is $0.20, so we calculate the maximum number of lemon bars (y) that can be prepared with the remaining expenses:

[tex]\[ 0.20y \leq 62.50 \][/tex]

[tex]\[ y \leq \frac{62.50}{0.20} \][/tex]

[tex]\[ y \leq 312.5 \][/tex]

Combining the two conditions for y, we find that y must be at least 134 but no more than 312.

Therefore, one possible ordered pair that satisfies all conditions is (x, y) = (150, 134). This means that at least 150 cups of lemonade and at least 134 lemon bars were sold last Monday to meet the revenue and expense conditions.

Answer:

None

Step-by-step explanation:

There are no solutions to this equation.

Answer:

Measure of angle O is 56 degrees.

Step-by-step explanation:

We can see from diagram that NQ is minor arc and NRQ is major arc. Our angle R (inscribed angle) and O (central angle) are corresponding to minor arc NQ. We will use inscribed angle theorem which states that measure of inscribed angle is one-half the measure of central angle.

We are given that measure of inscribed angle R is 28 degrees. To find measure of our central angle O we will multiply 28 by 2.

[tex]28*2=56[/tex]

Therefore, measure of angle O will be 56 degrees.

Answer: B

Step-by-step explanation:

To simplify the given expressions into one fraction, we find a common denominator for each set of fractions, adjust the numerators accordingly, and then combine the numerators over the common denominator.

To simplify the given expressions into one fraction, we need to find a common denominator and combine the fractions accordingly. Let's go through each expression step by step.

For the expression 7/x-3 + 3/x-5, the common denominator would be (x-3)(x-5). We need to multiply each fraction by the denominator that it's missing to get common denominators, and then sum the numerators over the common denominator.

The expression -5/x-3 - (-4)/(x+2) involves subtracting fractions. To simplify, we again find a common denominator, which is (x-3)(x+2), and proceed similarly to the first expression.

For 6/x+7 - 3/x-2, the common denominator is (x+7)(x-2). We perform the same process of equating denominators and combining.

To illustrate with the first expression:
(7(x-5))/((x-3)(x-5)) + (3(x-3))/((x-3)(x-5)) = (7x - 35 + 3x - 9)/((x-3)(x-5))

Combine the numerators to get a single fraction:

(10x - 44)/((x-3)(x-5))

Apply the same approach to the other two expressions to get them into a single fraction form.

Answer:

[tex]x=1\pm\sqrt{47}[/tex]

Step-by-step explanation:

We have been given an equation [tex]2x^2+3x-7=x^2+5x+39[/tex]. We are asked to find the solution for our given equation.

[tex]2x^2+3x-7=x^2+5x+39[/tex]

[tex]2x^2-x^2+3x-7=x^2-x^2+5x+39[/tex]

[tex]x^2+3x-7=5x+39[/tex]

[tex]x^2+3x-5x-7-39=5x-5x+39-39[/tex]

[tex]x^2-2x-46=0[/tex]

Using quadratic formula, we will get:

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

[tex]x=\frac{-(-2)\pm\sqrt{(-2)^2-4(1)(-46)}}{2(1)}[/tex]

[tex]x=\frac{2\pm\sqrt{4+184}}{2}[/tex]

[tex]x=\frac{2\pm\sqrt{188}}{2}[/tex]

[tex]x=\frac{2\pm2\sqrt{47}}{2}[/tex]

[tex]x=1\pm\sqrt{47}[/tex]

Therefore, the solutions for our given equation are [tex]x=1\pm\sqrt{47}[/tex].

4.5872 > [tex]\sqrt{14}[/tex]

We have two numbers.

We have to compare these two numbers.

The square root of a number is always less then the number itself.

According to the question, we have -

A = 4.5872

B = [tex]\sqrt{14}[/tex]

Now -

The value of B = 3.472.

Clearly, A > B

Hence, 4.5872 > [tex]\sqrt{14}[/tex].

To solve more questions on comparing numbers, visit the link below-

https://brainly.com/question/15451569

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Final answer:

The ±3 percent represents the margin of error in the Gallup poll, indicating the potential variation in the poll results due to sampling. The percentage of people who jog regularly could be as low as 15% or as high as 21%.

Explanation:

The ±3 percent represents the margin of error in the Gallup poll. The margin of error is a measure of the uncertainty or potential variation in the poll results due to the sampling process. In this case, it means that the percentage of people who say they jog regularly could be as low as 15% or as high as 21%.

The missing number using Euler's formula is: Option A. 17

The maximum volume of a square pyramid is: Option B. 4,608

"It is a geometrical formula. V − E + F = 2, where V represents number of vertices, E represents number of edges and F represents number of faces."

"Square pyramid is a three dimensional geometrical figure where four triangular sides are associated to square base."

"A cube is a three-dimensional geometric structure with six congruent square face."

[tex]V=\frac{1}{3}a^{2}h[/tex]

where [tex]a[/tex] represents the length of square base and [tex]h[/tex] represents the height of the pyramid.

Consider the first question,

number of vertices (V) = 13

number of edges (E) = 28

So, using Euler's formula:

[tex]13-28+F=2[/tex]

⇒ [tex]-15+F=2[/tex]

⇒ [tex]F=2+15[/tex]

⇒ [tex]F=17[/tex]

So, the number of faces are 17.

Hence, the correct answer is option A. 17

Consider last question,

the side length of a cube = 24 cm

As the square pyramid fit inside a cube.

⇒ the length of the square base of a pyramid [tex]b[/tex] = 24 cm

and the height of a square pyramid [tex]h[/tex] = 24 cm

So, the volume of a square pyramid is,

[tex]V=\frac{1}{3} a^{2} h[/tex]

⇒ [tex]V=\frac{1}{3}[/tex] × [tex]24^{2}[/tex] × [tex]24[/tex]

⇒ [tex]V= 4608[/tex] [tex]cm^{3}[/tex]

Therefore, the maximum volume of a square pyramid that can fit inside a cube with a side length of 24 cm is [tex]4608[/tex] [tex]cm^{3}[/tex].

And the correct answer is option B. 4,608

Learn more about Euler's formula here,

https://brainly.com/question/22069428

Learn more about volume of a square pyramid here:

https://brainly.com/question/2501401

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Answer: The center of this data is 2.

Step-by-step explanation:

Since we have given that

The data shows the number of Taylor's basketball team:

[tex]2, 0, 1, 2, 4, 1, 4, 0, 3, 2[/tex]

We need to find the center of this data.

As we know that "Median" gives the middle value of the data, So, it is known as "Center of this data".

1) First we write it in ascending order:

[tex]0,0,1,1,2,2,2,3,4,4[/tex]

2) Count the number of terms :

n=10

Since n is even.

3) As we know the formula for even number of data:

[tex]Me=\frac{\frac{n}{2}+({\frac{n}{2}+1)}}{2}\\\\Me=\frac{\frac{10}{2}+({\frac{10}{2}+)}}{2}\\\\Me=\frac{5^{th}+6^{th}}{2}\\\\Me=\frac{2+2}{2}\\\\Me=\frac{4}{2}\\\\Me=2[/tex]

Hence, The center of this data is 2.

Answer:

2

Step-by-step explanation:

2 is correct on plato

Answer:

Factorization of 2x²+5x+3 is:

A. (2x + 3)(x + 1)

Step-by-step explanation:

We have to factorize the expression:

2x²+5x+3

We will solve this expression by splitting the middle term method

2x²+5x+3

=2x²+2x+3x+3

=2x(x+1)+3(x+1)

=(2x+3)(x+1)

Hence, factorization of 2x²+5x+3 is:

A. (2x + 3)(x + 1)

57 chairs are needed if everyone is to have a seat

To calculate the number of additional chairs needed, we first need to determine the total number of seats required. This is the sum of the students, guests, and speaker. Then, we subtract the number of chairs already set up to find out the additional chairs needed.

Let's break it down step by step:

1. Total number of seats required:

  - Students: 856

  - Guests: 700

  - Speaker: 1 (assuming the speaker needs a seat)

  Total seats required = 856 (students) + 700 (guests) + 1 (speaker) = 1,557 seats

2. Number of chairs already set up: 1,500

3. Additional chairs needed:

  Total seats required - Chairs already set up = 1,557 - 1,500 = 57

So, Lincoln Technical College needs 57 more chairs to accommodate everyone if all students, guests, and the speaker are to have a seat.

Lincoln Technical College has 856 students and expects 700 guests for a special speaker, making the total number of attendees 1,557. The custodian has already set up 1,500 chairs. To find out how many more chairs are needed, we subtract the number of chairs already set up from the total seats required. This calculation reveals that 57 additional chairs are needed to ensure that everyone has a seat. It's essential to consider all attendees, including students, guests, and the speaker, to accurately determine the total seating requirements.

Complete question:

Lincoln Technical College has 856 students. They expect 700 guests for a special speaker. The custodian has set up 1,500 chairs. How many more chairs are needed if everyone is to have a seat?

Answer: 25.12 feet

Step by step explanation: