Patrick has just finished building a pen for his new dog. The pen is 3 feet wider than it is long. He also built a doghouse to put in the pen which has a perimeter that is equal to the area of its base. After putting the doghouse in the pen, he calculates that the dog will have 178 square feet of space to run around inside the pen. He also finds that the perimeter of the pen is 3 times greater than the perimeter of the doghouse.

If x represents the length of the pen and y represents the area of the doghouse, then which of the following systems of equations can be used to determine the length and width of the pen and the area of the doghouse?

Answer:

Step-by-step explanation:

Given that in the  town of Clover, 3 out of 5 citizens who are eligible to bit did so in the fall election.

A) No of citizens =400

Assume the same proportion as given holds good here

the number of citizens that voted in the fall election=[tex]\frac{3}{5} (400) \\= 240[/tex]

B) Assume the same proportion as given holds good here

No of citizens that voted in the fall election=180

Total no of citizens = [tex]\frac{5}{3} (180)\\=300[/tex]

g(x) = ax²

We have a point (1, 16)

Substitute

x = 1, g(x) = 16

a(1²) = 16

a = 16

g(x) = 16x² = 4²x² = (4x)²

Answer: A. g(x) = (4x)²

Answer:

Standard Form

Step-by-step explanation:

we know that

A quadratic function written in standard form is

[tex]y=ax^{2} +bx+c[/tex]

in this problem we have

[tex]y=2x^{2} +5x-1[/tex]  

so

[tex]a=2\\b=5\\c=-1[/tex]

Final answer:

The function y = -2x² + 5x - 1 is written in standard form, which for a quadratic function is ax² + bx + c.

Explanation:

The function given is y = -2x² + 5x - 1. This function is written in standard form, which is characterized by the quadratic term, followed by the linear term, and then the constant term. The general form of a quadratic function is ax² + bx + c, where a, b, and c are constants, and in this case, a is -2, b is 5, and c is -1.

Answer:

[tex]a^0=1[/tex]

Step-by-step explanation:

[tex]a^2\cdota^{-3}\cdota=a^{2+(-3)+1}=a^0=1\ for\ a\neq0[/tex]

Used:

[tex]a^n\cdot a^m=a^{n+m}[/tex]

Answer:

x=1/5

Step-by-step explanation:

-5x-(7-4x)=-2(3x-4)

-5x+7+4x=6x-8

-5x+6x+4x=5x    =     8-7=1

5x = 1

1/5 = x

x = 1/5

Hi!

Median:

0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6,

Answer - D. 3

The answer could be 2.64e+20

the slope is 1/4

and the y intercept is -4

Hope this helps

Answer:

y = -1/4x +4

Step-by-step explanation:

Slope intercept form of a line will have y on the left and mx+c on the right.

y = mx+c

Here m is the slope and c is the intercept

Any form of line can be brought to slope intercept form

Given that 2x+8y =32

We have to keep y along on left side

Hence subtract 2x first

8y =-2x+32

Now divide by 8

y = -1/4x +4 is the equation in slope intercept form

Remember that: "Platinum Gym charges a one-time registration fee of $60, and membership is $20 a month."

We are solving for a membership that will make Edward's statement untrue, that the gym membership fee will NOT have a month where the cost is the same.

For example, I can say that:

" Bob's Gym charges a one-time registration fee of $50, and membership is $10 a month ".

In this case, the pricing is much lower than Platinum Gym's and would not have a chance of getting the same cost in the same month.

Another example can be:

" SuperSneaker's charges a one-time registration fee of $100, and membership is $30. "

Again, the cost is much more higher than Platinum Gym's and would not have a chance of getting the same cost in the same month.

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hope this helps

The answer is 1 7/8. I got this by first looking at the two negatives. Negative times a negative is always a positive.So if you would write this expression again it would look like: -3 1/4 + 5 1/8

Now you find the common denominator which is 8. Convert -3 1/4 to have a denominator of 8: -3 2/8

Now you can convert both of those fractions into improper fractions: -26/8+41/8

Compute: 15/8

You can either leave your answer like that or you can change it into a mixed fraction :

1 7/8

Answer:

The correct answer here for [tex]\frac{f(x)}{g(x)}[/tex] is A [tex]\frac{x^8}{3}[/tex]

Step-by-step explanation:

[tex]\frac{f(x)}{g(x)} =\frac{5x^6}{15x^-2}[/tex]

By simplifying,

[tex]\frac{f(x)}{g(x)} =\frac{x^6}{3x^-2}[/tex]

Simplifying the exponents of [tex]x[/tex]

[tex]\frac{f(x)}{g(x)} =\frac{x^8}{3}[/tex]

Therefor the correct answer is [tex]\frac{x^8}{3}[/tex]

I did the work, and the quiz.

Your answer is A.

Answer: the equation has no solution.

I really hope this helps :)

-Izzie

Final answer:

To find the possible coordinates of point A with a known x-coordinate of -7 and a distance of 13 units from point B (5, 2), we used the distance formula and found two possible y-coordinates for point A, which are -3 and 7. Hence, the possible coordinates for point A are (-7, -3) and (-7, 7).

Explanation:

The question asks for the possible coordinates of point A given that point B has coordinates (5, 2), the x-coordinate of point A is -7, and the distance between points A and B is 13 units. To find the y-coordinate of point A, we can use the distance formula d = √((x2 - x1)^2 + (y2 - y1)^2). Substituting the known values, we have:

13 = √((5 - (-7))^2 + (2 - y1)^2)

Squaring both sides of the equation, we get:

169 = (12)^2 + (2 - y1)^2

This simplifies to:

169 = 144 + (2 - y1)^2

Subtract 144 from both sides:

25 = (2 - y1)^2

Now, taking the square root of both sides, we get two possible solutions for the y-coordinate:

y1 = 2 ± 5

Thus, the possible y-coordinates of point A are -3 and 7. Therefore, the possible coordinates for point A are (-7, -3) and (-7, 7).

The Mean is the value of all the numbers in a data set added together and divided by the amount of numbers there are for example the mean of the set 2,5,8,9 is 6.

The median is the middle values of all the numbers. If there are 2 medians, you usually have to add them both and divide by 2 to get the actual median

The mode is the number(s) that show up the most in the data set. for example, the mode of the data set 2,2,3,4,4,4,6,9 is 4, because it is repeated 3 times.

hope this helped!

  Your answer will be 1/55 or A because, at the beginning of the problem it states "you are one of 55 people" ((:

The probability that your name will be drawn first out of 55 people is 1/55.

The probability that your name will be drawn first out of 55 people can be calculated using the formula:

Probability = 1/Total number of people

Therefore, the probability that your name is drawn first is:

Probability = 1/55

So the correct option is A - 1/55.

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Answer:

179/180

Step-by-step explanation:

Step One

Find the prime factors of 18 and 20

18:3*3*2

20: 2 * 2 * 5

Step Two

You need two 2s two 3s and one 5 for the common denominator

The common denominator is 2 * 2 * 3 * 3 * 5 = 180

Step Three

Put the two fractions over 180

[tex]\dfrac{17*10}{10*18} + \dfrac{1*9}{10*18}[/tex]

[tex]\dfrac{170}{180} + \dfrac{9}{180}[/tex]

179/180

The equation of the perpendicular line is y= 4/3x

The equation is given as:

y = -3/4x + 1

The slope of the above equation is;

m = -3/4

Let the slope of the perpendicular line be n.

So, we have:

n = -1/m

This gives

n = -1/(-3/4)

Evaluate

n = 4/3

The equation of the line is then calculated as:

y = n(x - x1)  + y1

This gives

y = 4/3(x - 9) + 12

Evaluate

y= 4/3x - 12 + 12

Evaluate the like terms

y= 4/3x

Hence, the equation of the perpendicular line is y= 4/3x

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The equation of the line that is perpendicular to the line y=-3/4x+1 and passes through the point (9,12) is y = 4/3x + 1.

To solve your question, we first need to identify the slope of the given line. The equation y=-3/4x+1 is in the form y=mx+b, where m represents slope. So, the slope of the given line is -3/4.

But we require an equation that's perpendicular to this line, so its slope will be the negative reciprocal of -3/4, which is 4/3. Now, we have the slope of the new line, and we know it passes through point (9,12).

With that information, we use the point-slope formula, y - y1 = m (x - x1), where m is the slope and (x1, y1) is the point through which the line passes. Here, x1=9, y1=12 and m=4/3. Substituting these values in gives us y - 12 = 4/3 (x - 9). Simplifying yields the equation y = 4/3x + 1, which is the equation of the line that is perpendicular to the given line and passes through the point (9,12).

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By non example of division, it means that example for the situation where division is not possible.

Let x be any real number. We can divide x by any number except 0.

Hence, division by zero is a perfect non example for division.

The answer is 216 because we will compute 6^3 = 6*6*6 = 36*6 = 216

If we had 2 dice rolled out, then it would be 6^2 = 6*6 = 36. For each die added, we multiply another 6 because the die has 6 sides.

Visually, 2 dice form a 2D table of 36 possible outcomes. Three dice form a 3D cube of possible outcomes (a 6 by 6 by 6 cube with volume 216). You can think of it like a rubix cube. Each sub-block would house a possible combo such as {2,1,7} meaning that you rolled a '2' on the first die, a '1' on the second die, and a '7' on the third die.

Note: rolling a single die 3 times will produce the same sample space as rolling three separate dice 1 time.

216 is the answer to it

Initial amount in Elaine's account = m dollars ---- (1)

On December 8, total money deposited by Elaine = 1200 + r + 568.9

= r + 1768.9 ----- (2)

Total money on her account now = m + r + 1768.9

Total money she cashed by cheques = t + 73.7.

Therefore, her current balance in her account = (m + r + 1768.9) - (t + 73.7)

= (m + r - t) + 1695.2.

Hence, the algebraic expression that represents the amount of money in her account after the transactions is (m + r - t) + 1695.2.

Final answer:

Elaine's checking account balance after her transactions is represented by the algebraic expression m + 1200 + r + 568.90 - t - 73.70, with m being her initial balance, r the amount deposited, and t the amount from the check that was cashed.

Explanation:

Elaine had m dollars in her checking account. After various transactions, we can represent the amount of money in her account with an algebraic expression. The transactions include deposits and cashed checks. The deposits add money to her account, while cashing checks subtract money from her account.

To calculate the new balance, the following expression can be used:

New Balance = original balance + sum of deposits - sum of cashed checks

In Elaine's case, her initial balance is m dollars. She deposited $1,200, r dollars, and $568.90, which are added to her account. She also cashed checks for t dollars and for $73.70, which are subtracted from her account. Therefore, the algebraic expression representing the new account balance after these transactions would be:

m + 1200 + r + 568.90 - t - 73.70

1/2 because 3 divided by 6 equals 0.5 or 1/2

The integer n can take any value between -45 and 45, satisfying the given inequality |−n| < 46 and leaving a remainder of 4 when divided by 7.

An integer n leaves a remainder of 4 when divided by 7 if it satisfies the given inequality |−n| < 46.

To find the possible values of n, we can solve the inequality.

|-n| < 46 → -n < 46 and -n > -46 → 46 > n > -46.

Therefore, n can take any integer value between -45 and 45, with the condition that it leaves a remainder of 4 when divided by 7.

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Answer:

Step-by-step explanation:

Solution is given in attachment

Answer-

The total number of the 80 students responded to the poll.

Solution-

The percentage of student who responded that football was their favorite sport = 27.5%

The percentage of student who responded that basketball was their favorite sport = 17.5%

As the remaining students opted for others, so the percentage of student who opted other sport = 100-(27.5+17.5) = 100-45 = 55%

The number of student who chose others, was found to be 44. If total number of student participated in the opinion poll was x, then

[tex]\Rightarrow x \times\frac{55}{100} =44[/tex]

[tex]\Rightarrow x=44 \times\frac{100}{55}=80[/tex]

∴ The total number of the people who responded to the poll was 80.

2 squared X= 550

x = 550 square root

x=23.45

The solution to the equation [tex]2^x[/tex] = 550 is x ≈ 9.0959.

To solve the equation [tex]2^x[/tex] = 550, we need to isolate the variable 'x'. Here's the step-by-step process:

1. Take the logarithm (base 2) of both sides of the equation:

log2([tex]2^x[/tex]) = log2(550)

Using the property of logarithms, logb([tex]b^x[/tex]) = x, we have:

x = log2(550)

2. In this case, since we want to find x, we can use the logarithm function with base 2:

x ≈ log2(550) ≈ 9.0959

Therefore, the solution to the equation [tex]2^x[/tex] = 550 is x ≈ 9.0959.

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