The area of a rectangular barnyard is given by the trinomial 6x2 + 7x – 20. What are the possible dimensions of the barnyard? Use factoring. (1 point)

The given series is an arithmetic series with a common difference of 3. The sigma notation for this series is [tex]\[\sum_{n=1}^{5} (1 + 3 \cdot (n-1)).\][/tex]

The given series 1+4+7+10+13 is an arithmetic series, where the common difference between consecutive terms is 3. Sigma notation or summation notation is a way of expressing this long sum in a concise way. The rule for the nth term in your series is

[tex]\(a_n = 1 + 3 \cdot (n-1)\), where \(a_n\)[/tex]

stands for the nth term. So, the sigma notation for this series would be

[tex]\[\sum_{n=1}^{5} (1 + 3 \cdot (n-1)).\][/tex]

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The Main answer is the function value at [tex]x=12[/tex] is [tex]2[/tex], not [tex]12[/tex], so the point [tex](12,2)[/tex] is not a solution to the equation. Therefore, statement C is false.

The statement that is FALSE based on the lessons about the slope-intercept form of the equation of a line is:

C: The point [tex](12,2)[/tex] is a solution to the equation

To check if a point is a solution to the equation, we substitute the coordinates of the point into the equation and see if it satisfies it. For the given function

[tex]F(x)= (3/4 )x-7:[/tex]

Substituting x=12 into the equation:

[tex]F(12)= 3/4 (12)-7\\F(12)=9-7\\F(12)=2[/tex]

The function value at [tex]x=12[/tex] is [tex]2[/tex], not [tex]12[/tex], so the point [tex](12,2)[/tex] is not a solution to the equation. Therefore, statement C is false.

COMPLETE QUESTION:

Study the function: [tex]F(x)=(3/4)x-7[/tex] and select the statement that is FALSE based on the lessons you have learned about the slope-intercept form of the equation of a line.

A: The slope of the function is .[tex]75[/tex] and would increase from left to right if you were to graph the function on a coordinate plane

B: The y-intercept is [tex](0,-7)[/tex]

C:The point [tex](12,2)[/tex] is a solution to the equation

D:The x-intercept is [tex](10,0)[/tex]

To find who ran faster, we have to find the speed of Max and Molly

The formula for speed is given as Distance/Time

Max's speed

Distance Max ran  = 50 meters

Time = 30 seconds

Speed = 50 m/30s

= 1.67 meters/second

Molly's speed

Distance Molly ran = 30 meters

Time = 5  seconds

Speed = 30m/5s

= 6 meters/second

Therefore, Max ran faster than Molly with a speed of 1.67 meters/second.

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answer is 1

as Shelley has to live in Boston for only 2 years, she needs to consider that the owner is flexible enough to make 2 year rent agreement and the short term rent of the house.

Other choices are irrelevant. they may be applied while purchasing home with long term aim to stay in the place.

Answer:

C. J-Shaped graph

Step-by-step explanation:

A. T-Shaped graph

T- shaped graph can represents a rational function or quadratic function

B. S-Shaped graph

S shaped graph represents a cubic function. because it crosses x axis at two points.

C. J-Shaped graph

J shaped graph represents exponential function. the graph of J shape goes on increasing so its an exponential growth

D. Straight horizontal line

Straight line graph represents linear equation.

To calculate Jane's monthly car loan payments, we must determine the amount financed, total of the payments, and monthly payment. After deducting the down payment from the price of the SUV, we find the amount financed. To calculate the total of the payments, we multiply the amount financed by the monthly interest rate. Finally, we divide the total of the payments by the number of months to find the monthly payment.

To find the monthly payments for Jane Smart's car loan, we need to calculate the amount financed, the total of the payments, and the monthly payment.

So, Jane's monthly payment for the SUV is $345.08.

To determine how often ATM withdrawals must be made for the local savings account to be a better deal than the online savings account, we compare the interest earned and ATM fees. By solving the inequality, it is found that more than $14.06 ATM withdrawals must be made in a year.

To determine how often you must make ATM withdrawals for the local savings account to be a better deal than the online savings account, we need to compare the interest earned from each account and the fees associated with ATM withdrawals. Let's assume the time period is one year.

For the local savings account, you earn interest of 1.75% annually. So, if you deposit $3,750, you will earn ($3,750 * 1.75%) = $65.63 in interest.

For the online savings account, you earn interest of 3.25% annually. However, each ATM withdrawal incurs a fee of $4. Let's assume you make 'x' withdrawals in a year. So, the total interest earned would be ($3,750 * 3.25%) - ($4 * x).

We need to find the point where the interest earned from the online savings account is less than the interest earned from the local savings account. This can be calculated as:

($3,750 * 3.25%) - ($4 * x) < $65.63

Simplifying this inequality, we get:

0.0325 * $3,750 - $4 * x < $65.63

Adding $4 * x to both sides, we have:

0.0325 * $3,750 < $65.63 + $4 * x

Simplifying further, we get:

$121.87 < $65.63 + $4 * x

Subtracting $65.63 from both sides, we have:

$121.87 - $65.63 < $4 * x

Simplifying again, we get:

$56.24 < $4 * x

Dividing both sides by $4, we find:

$14.06 < x

So, you must make more than $14.06 ATM withdrawals in a year for the local savings account to be a better deal than the online savings account.

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The product of the numbers 0.04,-0.9,1.5 is -0.054 because the multiplication of negative and positive quantities is negative.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

As we know, we can apply the arithmetic operation to any real numbers

Also, the number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.

The numbers are:

0.04, -0.9, and 1.5

= 0.04x-0.9x1.5

First, multiply the first two numbers 0.04 and -0.9

= -0.036x1.5

(The multiplication of negative and positive quantity is negative)

= -0.054

Thus, the product of the numbers 0.04,-0.9,1.5 is -0.054 because the multiplication of negative and positive quantity is negative.

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Answer:

163.85 bucks,bix,backs,boks :P

Step-by-step explanation:

In order to find the retail price, we must first find the amount of markup. Remember that a markup rate is a percentage of the wholesale price that a store adds to get a selling or retail price. With this knowledge, we can figure out the following equation:

markup rate× wholesale price = amount of markup

Since the markup rate is a percentage, we have to convert it into a decimal first. Percent means "out of one hundred," so 45% is equivalent to 45/100  which is also equal to 45 \ 100 so 45/100 = 0.45. 0.45 * 113 = 50.85.

Since the markup rate is a percentage of the wholesale price that is added to get the retail price, we can find the retail price with the following equation:

amount of markup + wholesale price = retail price. 50.85 + 113 = 163.85

The probability of drawing the two of diamonds, the three of spades, the six of hearts, the ten of clubs, and the king of hearts in that order from a 52-card deck is approximately 1 in 380,204,032.

The subject of the question is the probability of drawing specific cards from a 52-card deck. This problem involves choosing five specific cards: the two of diamonds, the three of spades, the six of hearts, the ten of clubs, and the king of hearts.

To find the probability, we need to consider that the deck contains 52 distinct cards. Assuming that each card is equally likely to be drawn, the probability of drawing any specific card is 1 out of 52 (or 1/52). And because we want to draw these cards one after another, we multiply these probabilities together.

Thus, the probability of drawing these five specific cards from a 52-card deck in this order is (1/52) * (1/52) * (1/52) * (1/52) * (1/52), which is approximately 1 in 380,204,032. Please note that this probability is infinitesimally small because the event is highly specific. Also, the order of the cards matters in this calculation. If the order does not matter, the probability will be higher.

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replace x with y and y with x,

the answer is the option A.) Y=log 6x 

Answer:

A

Step-by-step explanation:

edge 2021

The mean of x is 1.35 and the variance of x is approximately 1.267.

To find the mean of x, we need to calculate the expected value. We can do this by multiplying each value of x by its corresponding probability and then summing up the results. In this case, using the given values and probabilities, we have 0(0.20) + 1(0.45) + 2(0.20) + 3(0.10) + 4(0.05) = 1.35. Therefore, the mean of x is 1.35.

To find the variance of x, we need to calculate the squared difference between each value of x and the mean, weighted by their respective probabilities. We then sum up these values. Using the formula for variance, we have (0-1.35)²(0.20) + (1-1.35)²(0.45) + (2-1.35)²(0.20) + (3-1.35)²(0.10) + (4-1.35)²(0.05). By simplifying this expression, we find that the variance of x is approximately 1.267.

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Answer: 2023

Step-by-step explanation:

Since, the initial population of the city is 55,210,

And, it is declining at a rate of 1.09%.

Thus, the function that shows the population after x years since 2010 is,

[tex]f(x) = 55210(1-\frac{1.09}{100} )^x[/tex]

[tex]f(x) = 55210(1-0.0109)^x[/tex]

[tex]f(x) = 55210(0.9891)^x[/tex]

If the population of town is 48000 in x years.

⇒ [tex] 55210(0.9891)^x= 48000[/tex]

⇒ [tex] (0.9891)^x= 0.869407715993[/tex]

⇒ [tex]x = 12.769[/tex]

Therefore, after 12.769 years the population of town will be equals to 48,000

⇒ After 12.770 years the population will first be below 48,000.

⇒ After approx 13 years the population will first below 48,000.

⇒ Around 2023 the population will be first below 48,000.

Answer:2022

Step-by-step explanation:

Answer:

13.5 years.

Step-by-step explanation:

We know that exponential growth function is in form [tex]y=a\cdot(1+r)^x[/tex], where, a is initial value and r is growth rate in decimal form.

Population of goldfish after x years would be [tex]y=20\cdot(1+0.20)^x[/tex].

We know that a linear function is in form [tex]y=mx+b[/tex], where, b is initial value and m is slope.

Population of minnow after x years would be [tex]y=100+10x[/tex].

Graphing both equations, we will get our required graph as shown in the attachment.

Since both graphs intersect at [tex]x=13.5[/tex], therefore, in the 13.5 years both populations will approximate the same.

Answer:

A

Step-by-step explanation:

A graph where y varies directly as x is a straight line that passes through the origin (0, 0). This is because when two variables vary directly, their ratio is constant, and in the case of y and x, this ratio is the slope of the line.

The equation for direct variation is y = kx, where k is the constant of variation. When we plot this equation on a graph with y on the vertical axis and x on the horizontal axis, we get a straight line that passes through the origin, with a slope of k.

For example, if we have a set of data points that vary directly, such as (1, 2), (2, 4), (3, 6), and so on, we can plot these points on a graph and draw a straight line that passes through the origin and all the points. This line represents the direct variation between y and x, and any other points that satisfy the equation y = kx will lie on this line.

In summary, a graph where y varies directly as x is a straight line that passes through the origin, with a constant slope representing the constant of variation.