Which of the following is true regarding the solution to the logarithmic equation below?

Final answer:

The binomial factor of the trinomial 3x^2 + 18x + 24 is 'x + 4', which corresponds to Option A.

Explanation:

The student is asking which binomial is a factor of the trinomial 3x2 + 18x + 24. To find a factor, you can either factor the trinomial directly or use the zero product property, which states that if a product equals zero, then at least one of the factors must be zero. Since we're looking for a binomial factor and not solving for x, we'll factor the trinomial.

Factors of 3x2 are 3x and x, and factors of 24 that add up to 18 (when multiplied by 3 or 1 from the 3x2 term) are 6 and 4. Thus, the trinomial can be factored as (3x + 4)(x + 6). So, the binomial that is a factor of the trinomial is x + 4, which is Option A.

Answer:

y= -50x^2+1,150x+14,400

Step-by-step explanation:

fitness center currently has 320 members. Monthly membership fees are $45. The manager of the fitness center has determined that each time the membership fees increase by $5, approximately 10 members leave and go to a different gym.

LEt x be the number of price increases of $5

y is the revenue

Revenue= membership fee * members

for x number of increase in fee by 5  then member ship fee becomes 45+5x

approximately 10 members leave, so members becomes (320-10x)

y = (45+5x) (320-10x)

Multiply it using FOIL method

y=45 * 320 +45*(-10x) + 5x * 320 + 5x * (-10x)

y=14400 - 450x + 1600x - 50x^2

Combine like terms

y= -50x^2+1150x+14400

Answer:

→ The decimal expansion of rational number is either terminating or non terminating repeating.

→If the denominator of rational number is of the form [tex]2^a \text{or} 5^b \text{or} 2^a \times 5^b [/tex] , then the decimal terminates.

   [tex]\rightarrow -1 \frac{3}{4}=\frac{-7}{4}\\\\=-1.75[/tex]

The answer is C, 3d = 2d and 4n + 8 = 3d + 6

The required number would be x ≤ 2 which represents the number divided by three less two is at most two.

Inequality is defined as mathematical statements with at least two terms including non-equal variables or integers.

What is algebra?

Algebra is the study of mathematical symbols, whereas logic is the manipulation of those symbols.

The number divided by three less two equals the number specified in the question.

Let the required number would be x

As per the given condition, translate the phrase into an algebraic inequality as:

⇒ x/(3 - 2) ≤ 2

Apply the subtraction operation, and we get

⇒ x/1 ≤ 2

⇒ x ≤ 2

Therefore, the required number would be x ≤ 2.

To learn more about the inequalities click here:

brainly.com/question/20383699

#SPJ2

Industry which will have 25% more growth than health services over the period from 2000 to 2010 is Computer and data processing.

In computing, data is information that has been translated into a form that is efficient for movement or processing.

Given that, a graph titled top 10 Industries with Fastest Growth and Salary Employment 2000 to 2010.

Here,

Health services, 57;

Personnel supply services, 49;

Warehousing and storage, 45;

Water and sanitation, 45;

Computer and data processing, 86;

Management and public relations, 42;

Cable television services, 51;

Residential care, 64;

Business services, 43;

Equipment rental and leasing, 42.

So, according to the given data the highest record is given by computer and data processing.

Therefore, industry which will have 25% more growth than health services over the period from 2000 to 2010 is Computer and data processing.

Learn more about data here:

brainly.com/question/15403824

#SPJ3

"Your question is incomplete, probably the complete question/missing part is:"

A graph titled Top 10 Industries with Fastest Growth and Salary Employment 2000 to 2010 showing percent change for the following: health services, 57; personnel supply services, 49; warehousing and storage, 45; water and sanitation, 45; computer and data processing, 86; management and public relations, 42; cable television services, 51; residential care, 64; business services, 43; equipment rental and leasing, 42.

According to the above graph, which industry will have 25% more growth than health services over the period from 2000 to 2010?

A. Equipment rental and leasing

B. Residential care

C. Computer and data processing

D. None of these

The probability that he got at least 2 questions correct is 0.756

Lets assume, the event of getting a question correct is P

As, each question has 4 answer choices and only one choice is correct,

So, P = [tex] \frac{1}{4} [/tex]

When
the probability of getting 1 success in 1 trial is p, then the probability of getting exactly x successes out of n trials is given by the
formula :

(ⁿCₓ )(P)ˣ (1-P)ⁿ⁻ˣ

Here the total number of questions is 10. So, n= 10

Stan needs to get at least 2 questions correct, that means he can get 2, 3, 4, 5, 6, 7, 8, 9 or 10 questions correct.

Now according to the formula,

P(x=2) = ¹⁰C₂ ([tex] \frac{1}{4} [/tex])² ([tex] 1- \frac{1}{4} [/tex])¹⁰⁻²

= ¹⁰C₂ [tex] (\frac{1}{16})(\frac{3}{4})^8 [/tex]

= 0.281567573

P(x=3) = ¹⁰C₃ ([tex] \frac{1}{4} [/tex])³ [tex] (\frac{3}{4})^7 [/tex]

= (120) ([tex] \frac{1}{4} [/tex])³ [tex] (\frac{3}{4})^7 [/tex]

= 0.250282287

P(x=4) = ¹⁰C₄ ([tex] \frac{1}{4} [/tex])⁴ [tex] (\frac{3}{4})^6 [/tex]

= (210)([tex] \frac{1}{4} [/tex])⁴ [tex] (\frac{3}{4})^6 [/tex]

= 0.145998001

P(x=5) = ¹⁰C₅ ([tex] \frac{1}{4} [/tex])⁵ [tex] (\frac{3}{4})^5 [/tex]

= (252) ([tex] \frac{1}{4} [/tex])⁵ [tex] (\frac{3}{4})^5 [/tex]

= 0.058399200

P(x=6) = ¹⁰C₆ ([tex] \frac{1}{4} [/tex])⁶ [tex] (\frac{3}{4})^4 [/tex]

= (210) ([tex] \frac{1}{4} [/tex])⁶ [tex] (\frac{3}{4})^4 [/tex]

= 0.016222000

P(x=7) = ¹⁰C₇ ([tex] \frac{1}{4} [/tex])⁷ [tex] (\frac{3}{4})^3 [/tex]

= (120) ([tex] \frac{1}{4} [/tex])⁷ [tex] (\frac{3}{4})^3 [/tex]

= 0.003089904

P(x=8) = ¹⁰C₈ ([tex] \frac{1}{4} [/tex])⁸ [tex] (\frac{3}{4})^2 [/tex]

= (45) ([tex] \frac{1}{4} [/tex])⁸ [tex] (\frac{3}{4})^2 [/tex]

= 0.000386238

P(x=9) = ¹⁰C₉ ([tex] \frac{1}{4} [/tex])⁹ [tex] (\frac{3}{4})^1 [/tex]

= (10) ([tex] \frac{1}{4} [/tex])⁹ [tex] (\frac{3}{4})^1 [/tex]

= 0.000028610

P(x=10) = ¹⁰C₁₀ ([tex] \frac{1}{4} [/tex])¹⁰

= 0.000000953

Now we will just add all the probabilities and get:

0.281567573 + 0.250282287+ 0.145998001+ 0.058399200+ 0.016222000+0.003089904+0.000386238+ 0.000028610 +0.000000953

= 0.755974766

= 0.756 (rounding to the nearest thousandth)

So, the probability that he got at least 2 questions correct is 0.756

Answer:

Step-by-step explanation:

C on edge Test

Answer:

andy needs 80 carpet squares

Step-by-step explanation:

Final answer:

To cover the living room, multiply the room's length by its width to get the area in square feet (320 square feet), then divide by the area that one carpet square can cover (4 square feet), resulting in 80 carpet squares needed.

Explanation:

To calculate the number of carpet squares needed to cover Andy's living room, we start by finding the area of the room. The area is the product of the length and the width, so we multiply the room's dimensions: 20 feet (length) by 16 feet (width). This calculation gives us an area of 320 square feet. Next, we divide the total area by the area that each carpet square can cover. Since each square covers 4 square feet, we divide 320 square feet by 4 square feet per square to determine the number of squares needed:

320 square feet ÷ 4 square feet/square = 80 squares.

Therefore, Andy will need to purchase 80 carpet squares to cover the living room.

Final answer:

The pair of measurements that is not equivalent is 450 mm and 4.5 m.

Explanation:

When comparing pairs of measurements, it's important to convert them to the same unit before making a comparison. Let's examine the pairs to determine which one is not equivalent:

The non-equivalent pair is 450 mm and 4.5 m. All other pairs are equivalent after conversion.

The answer is 9cm

SA = r + r 2

452.16 m 2 = (3.14)(6 m)(x) + (3.14)(6 m) 2

452.16 m 2 = (3.14)(6 m)(x) + (3.14)(36 m 2)

452.16 m 2 = (18.84 m)x + 113.04 m 2

339.12 m 2 = (18.84 m)x

18 m = x

Answer:

Option D. 9 cm

Step-by-step explanation:

Surface area of the given figure is S = 243 cm² and we have to find the slant height.

We can see this figure comprises of 1 square and 4 triangles.

Let the slant height of the given triangles is L.

So area of one triangle = [tex]\frac{1}{2}(Slant height).(Base)[/tex]

and the area of square = side² = 9² = 81 cm²

Now surface area of total figure = Area of square + 4×(area of a triangle)

[tex]243=9^{2}+\frac{4}{2}(9.L)[/tex]

243 = 81 + 2×9L

18L = 243 - 81 = 162

[tex]L=\frac{162}{18}[/tex]

L = 9 cm

Therefore Option D. 9 cm is the correct answer.

  75p + 150(10) = 100(p + 10)

Mixture problems such as this can be solved by writing an equation that expresses the total cost of the mixture in terms of the costs of the constituents.

Here, the cost (in cents) of p pounds of cashews will be 75p. The cost (in cents) of the 10 pounds of pecans at $1.50 per pound will be 150(10). The total cost of p+10 pounds of the mixture is desired to be 100(p+10).

The equation of the 1st selection is appropriate. It tells that the prices of the contributing nuts add to give the price of the mixture, just as you want:

  75p + 150(10) = 100(p+10)

The correct equation to solve for the pounds of cashew nuts, denoted as p, that must be mixed with pecans to get a mixture worth $1.00 a pound is: 75p + 150(10) = 100(p + 10).

We are trying to determine how many pounds of cashew nuts that are worth 75 cents a pound must be mixed with 10 pounds of pecans worth $1.50 a pound to create a mixture worth $1.00 a pound. Let's denote the pounds of cashew nuts needed as p. The respective values of each type of nut are included in calculating the total value of the mix. Therefore, the value of the cashews (at 75 cents per pound) plus the value of the pecans (at $1.50 per pound) should equal the value of the desired mixture (at $1.00 per pound). The correct equation to use would be:

75p + 150(10) = 100(p + 10)

To solve for p, we multiply the cost per pound by the weight for each type of nut, then equate this to the cost per pound of the mixture multiplied by the total weight of the mixture. After solving this equation for p, we will know the required pounds of cashew nuts.

Answer:

Option C. 13

Step-by-step explanation:

Since f(x) is a linear function then we can rewrite the function in the form of an equation y = mx + c

where m is the slope of a line.

Since line passes through two points (3, 7), (9, 16)

Therefore m = (16 - 7)/(9 - 3) = 9/6 = 3/2

Now we know a point (16, 26.5) also lie on the line so by putting the values of m, x, and y in the equation.

y = 3x/2 + c

26.5 = 3×16/2 + c

c = 26.5 - 24 = 2.5

So the equation is y = 3x/2 + 5/2

y = 1/2(3x + 5)

If a point (7, n) lies on the line then

n = 1/2(3×7 + 5) = 1/2(21 + 5) = 26/2 = 13

Therefore n = 13 is the answer.