Write the linear equation given slope and point.
(-4,-7); slope = 3

Yes , the integer k is divisible by 4 and statement (1) alone is sufficient to determine that k is divisible by 4.

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

To determine if the integer k is divisible by 4, let's analyze the given statements:

Statement (1): 8k is divisible by 16.

This means that 8k is a multiple of 16. Since 16 is divisible by 4, we can conclude that k must be divisible by 4 as well. Therefore, statement (1) alone is sufficient to determine that k is divisible by 4.

8k = 16

k = 2

b)

This statement does not provide direct information about the divisibility of k by 4. While 12 is divisible by 4, the fact that 9k is divisible by 12 does not guarantee that k itself is divisible by 4.

9k = 12

k = 12/9

k = 4/3

So , it is not an integer

In conclusion, statement (1) alone is sufficient to determine that k is divisible by 4. Statement (2) is not sufficient on its own.

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Step-by-step explanation:

Convert all into decimals:

0.14, 4/8=0.5,0.33

Answer:

0.14, 0.33, 0.5

      or

0.14, 3/9, 4/8

The statement that shows a discrepancy between the check register and bank statement is: C. Gavin: The balance in his check register is $500 and the balance in his bank statement is $510.

The check register shows a balance of $500, while the bank statement shows a balance of $510.

In the case of Gavin, where the balance in his check register is $500 and the balance in his bank statement is $510, there is a $10 discrepancy between the two.

A possible explanation for this discrepancy could be outstanding checks or deposits that have not yet cleared or been recorded in either the check register or the bank statement.

For example, Gavin might have written a check for $20 that has not been cashed or processed by the bank yet. Therefore, the check register still reflects the $20 in his balance, while the bank statement does not show the deduction. Similarly, Gavin may have made a deposit of $10 that has not yet been credited to his account in the bank statement.

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The missing Value, x, that when multiplied by 5/3^4 gives the result of 5^4 is 13125.

The missing value that, when multiplied by 5/3^4, gives the result of 5^4, we can set up the equation:

(5/3^4) * x = 5^4

To solve for x, we can simplify both sides of the equation. First, let's simplify the right side:

5^4 = 5 * 5 * 5 * 5 = 625

Now, let's simplify the left side:

5/3^4 = 5/(3 * 3 * 3 * 3) = 5/81

Now we have:

(5/81) * x = 625

To solve for x, we can multiply both sides of the equation by the reciprocal of 5/81, which is 81/5:

(81/5) * (5/81) * x = (81/5) * 625

On the left side, the fraction (81/5) * (5/81) simplifies to 1, leaving us with:

1 * x = (81/5) * 625

Simplifying the right side:

(81/5) * 625 = 13125

Therefore, the missing value, x, that when multiplied by 5/3^4 gives the result of 5^4 is 13125.

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Answer:

(x + 5)² + (y + 2)² = 120

Step-by-step explanation:

You need two pieces of information to write the equation of a circle, the center and the radius. This was given in the question so you can just use the following fill-in-the-blank formula to write the equation.

If the center is (h, k) and the radius is r, fill them in here:

(x - h)² + (y - k)² = r²

For your question the center is (-5, -2) and r is√120.

You do need to already know that "minus-a-negative" IS the same as "plus-a-positive" (that's why the final answer has + inside the parentheses) ALSO, you need to know that square and squareroot un-do each other. So if you square sqrt120, you just get "plain" 120. That is, (sqrt120)² is 120.

Fill in the center and radius:

(x - h)² + (y - k)² = r²

(x - -5)² + (y - -2)² = (√120)²

Simplify.

(x + 5)² + (y + 2)² = 120

Taaa-daaa! that's it! Don't you think more people would hate formulas less if they were sold as "fill-in-the-blank" and "shortcuts" !?!  I think so!

Step-by-step explanation:

#1 equals 1 1/4

The common denominator for 1/6, 2/3, and 5/12 would be 12. So I made the denominators 12 which means 1/6 would turn into 2/12, 2/3 turns into 8/12, and 5/12 stays the same. When I add them all up I get 15/12. I can turn that into a mixed number which would be 1 3/12. I can simplify that down to 1 1/4.

#2 equals 3/4

The first thing you have to do is turn 2 2/3 and 1 3/4 into improper fractions. Which would turn 2 2/3 into 24/3 and 1 3/4 into 21/12. The next thing is you have to find a common denominator which would be 12. Next you have to turn the denominators into a 12 and change the numerator. Which makes the fractions: 24/12, 6/12, and 21/12. When you add 24/12 and 6/12 together you get 30/12 minus 21/12 you get 9/12. You can then simplify that to 3/4.

#3 equals -1 17/36

The first thing you do is turn 3 5/18 into an improper fraction which would be 59/18. then you find a common denominator which would be 36 and make the denominators of those numbers into 36 which would be 11/36, 54/36, and 118/36. When you add up 11/36 and 54/36 you get 65. but when you - 65 by 118 you get -53 / 36. you can lend turn that into -1 17/36.

I'm not sure about number 4 and I don't want to give you the wrong answer. Hopefully what I did show you helped!

Answer:

6

Step-by-step explanation:

Constants are any numbers that don't change.

2x + 3y + 6

Since "6" is the only number here, that is the only constant.

Best of Luck!

Answer:

6

Step-by-step explanation:

Answer:

x = 5

Step-by-step explanation:

Also in this case we can use the Pythagorean theorem in this way

x^2 + (5√3)^2 = 10^2

x^2 + 75 = 100

x^2 = 25

x = +/- 5

we take only the positive value because a lenght can’t be negative

x = 5

Answer:

60%

Step-by-step explanation:

48 + 12 = 60

There is a 60% chance you randomly choose a medium out of 100 customers.

Answer:

gkekwjrjwitkciviewjfjic

Answer:

$23.99

Step-by-step explanation:

The sequence \(\(a_n = n + 3n^2\) for \(n \geq 1\)\) is increasing (option a).

To determine the monotonicity of the sequence \(\(a_n = n + 3n^2\) for \(n \geq 1\)\), we can compare consecutive terms of the sequence.

Let's consider \(\(a_n\) and \(a_{n+1}\):\\\)

\(\(a_n = n + 3n^2\)\\\\\(a_{n+1} = (n+1) + 3(n+1)^2 = n + 1 + 3n^2 + 6n + 3\)\)

To determine the relationship between \(\(a_n\) and \(a_{n+1}\)\), we can subtract \(\(a_n\) from \(a_{n+1}\):\)

\(\(a_{n+1} - a_n = (n + 1 + 3n^2 + 6n + 3) - (n + 3n^2) = 1 + 6n + 3 = 6n + 4\)\)

Since \(\(6n + 4\)\) is always positive for \(\(n \geq 1\)\), we can conclude that \(\(a_{n+1} > a_n\) for all \(n \geq 1\\)).

Therefore, the sequence \(\(a_n = n + 3n^2\)\) is increasing.

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Answer:

(a) m<3 = 103 degrees

(b) m<4 = 77 degrees.

Step-by-step explanation:

A: The sum of the measures of all three interior angles in a triangle always is 180 degrees. Knowing this, we add the two known interior angles, 20 and 57, then subtract that from 180 to get 103 degrees.

B: The measure of an exterior angle is the sum of the two opposite interior angles. So, we add 57 and 20 to get the m<4 = 77 degrees.

The probability that a random sample of 12 students will have a mean reading rate of more than 95 wpm is 0.0418.

There are several sorts of mean in arithmetic, in particular in statistics. each implies serves to summarize a given institution of information, often to better recognize the general fee of a given record set.

They imply (aka the mathematics mean, extraordinary from the geometric imply) of a dataset is the sum of all values divided with the aid of the entire variety of values. it is the maximum commonly used a degree of crucial tendency and is regularly referred to as the “average.”

Common can truely be described as the sum of all of the numbers divided by means of the entire quantity of values. An average is described as the mathematical common of the set of or more statistics values. common is commonly described as implying or arithmetic mean. mean is really a method of describing the average of the sample.

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Hey there!

5÷9v ≤ 45

5/9v ≤ 45

MUTLPLY 9/5 to BOTH SIDES
5/9v * 9/5 ≤ 45 * 9/5

CANCEL out: 5/9 * 9/5 because it give you 1

KEEP: 45 * 9/5 because it help solve for what is being compared to the v-value

NEW EQUATION: v ≤ 45 * 9/5

SIMPLIFY IT!
v ≤ 81

It is a CLOSED circle shaded to the LEFT

Therefore, your answer is: v ≤ 81

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

Step-by-step explanation:

if u is an irrational number added to a rational number (sqrt 15) to yield 2, then that would mean u would = root -1.78.....

which means you wouldn't have a real solution. if you want a complex answer, it would be sqrt(1.78)i

Building an solving an equation, it is found that the number is x = -1.87298334621 ...

------------------

Thus:

\(x + \sqrt{15} = 2\)

\(x = 2 - \sqrt{15}\)

\(x = -1.87298334621 ...\)

Which is a non-terminating decimal, thus it is irrational.

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Answer:

use desmos graphing and put (3,8) and y=5x-4 it help me

Answer:

88

Step-by-step explanation:

multiply 44 times 2 which gives you 88 as the diameter.

Hope this helps!!

The rate at which the area of the cloud is increasing is equal to the product of the rate of expansion and the square of the radius of the cloud.

Therefore, the rate at which the area of the cloud is increasing is equal to the product of the rate of expansion and the radius of the cloud. The rate of expansion can be calculated using the equation . Therefore, the rate at which the area of the cloud is increasing can be calculated as .

The area of a circle is determined by the square of its radius. Thus, when the radius of the cloud is expanding at a rate, the area of the cloud is increasing at a rate that is proportional to the square of its radius.

Therefore, in order to calculate the rate at which the area of the cloud is increasing, we must calculate the rate of expansion of the radius of the cloud and then multiply it by the square of the radius of the cloud. To calculate the rate of expansion of the radius of the cloud, we can use the equation .

After we have calculated the rate of expansion, we can then multiply it by the square of the radius of the cloud to calculate the rate at which the area of the cloud is increasing.

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The two cars will meet in 14.5 hours.

To find out how long it will take for the two cars to meet, we need to determine the time it takes for Car A and Car B to cover the remaining distance between them.

Let's calculate the distance Car A has to travel until they meet. The total distance between the two cars is 580 km, and Car A has already traveled 130 km. Therefore, Car A has to cover a distance of 580 km - 130 km = 450 km.

Now, we can calculate the time it will take for Car A to cover this distance. Car A's speed is 50 km/h, so the time it takes is:

Time = Distance / Speed = 450 km / 50 km/h = 9 hours.

Since Car B took off after Car A traveled 130 km, it means that Car B has to cover the entire distance of 580 km.

Now, we know that Car B's speed is 40 km/h. The time it will take for Car B to cover the distance is:

Time = Distance / Speed = 580 km / 40 km/h = 14.5 hours.

Therefore, the total time it will take for the two cars to meet is the maximum of the times for Car A and Car B, which is 14.5 hours.

Final answer: It will take the two cars 14.5 hours to meet.

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Answer:

a = 40 + root(7) , b = 5 root(7)

Step-by-step explanation:

\(49 + \sqrt{7} - \sqrt{81} + \sqrt{-175}\\ = 49+\sqrt{7}-9+5\sqrt{7}i\\ = 40+\sqrt{7} + 5\sqrt{7}i\)

Answer:

$699

Step-by-step explanation:

15825.8693-15126.9611

698.9082 (round to nearest dollar)

Answer: $699

After 7 years, the amount of money that Noah would have more than Samuel would be $698.91.

The formula for calculating future value:

FV = P (1 + r)^nm

Difference in amount = 9200x [(1.0059375^84) - (1.0002123287^2555)] =$698.91

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The probability that Victor selects a code that has four even digits is approximately 0.0238 or 1/42.

To solve this problem, we can use the permutation formula to determine the total number of possible codes that Victor can choose. Since he can only use each digit once, the number of permutations of 10 digits taken 4 at a time is:

P(10,4) = 10! / (10-4)! = 10 x 9 x 8 x 7 = 5,040

Next, we need to determine how many codes have four even digits. There are five even digits (0, 2, 4, 6, and 8), so we need to choose four of them and arrange them in all possible ways. The number of permutations of 5 even digits taken 4 at a time is:

P(5,4) = 5! / (5-4)! = 5 x 4 x 3 x 2 = 120

Therefore, the probability that Victor selects a code with four even digits is:

P = (number of codes with four even digits) / (total number of possible codes)

= P(5,4) / P(10,4)

= 120 / 5,040

= 1 / 42

≈ 0.0238

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Answer:

is 16.75

Step-by-step explanation:

Answer:

15%

Step-by-step explanation:

Answer:

1 and 2

Step-by-step explanation:

A denominator divides a number

to find the two common denominators of 14 and 16,

first we find the factors of 14 and 16.

Factors of 14 are: 1, 2, 7, 14.

Factors of 16 are: 1, 2, 4, 8, 16.

The two common factors between this numbers that will be able to divide these numbers without remainder are 1 and 2, therefore,

the two common denominators of 14 and 16 are 1 and 2

Answer:

Linear

Step-by-step explanation:

You can either graph the points or calculate the slope between them.  The slope will be Rise/Run:

(-7,10) to (-1,2.5):

Rise = (2.5 - 10) = -7.5

Run = (-1 - (-7)) = 6

Slope (Rise/Run) = -7.5/6 = -1.25

(-1,2.5) to (9,-10):

Rise = (-10 - 2.5) = -12.5

Run = (9 - (-1)) = 10

Slope = (-12.5/10) = -1.25

The slopes are the same, so it is a straight line.

The equation for the circle of area that is watered is (x - 0)^2 + (y - 20)^2 = 25, where (0, 20) represents the center of the circle and 5 represents the radius.

To find the equation for the circle of area that is watered by the sprinkler, we first need to determine the radius of the circle.

The diameter of the circular area is given as 10 feet, which means the radius is half of the diameter. So the radius (r) is 10 feet / 2 = 5 feet.

Since the house is located at the origin (0, 0), and the sprinkler is located 20 feet north of the house, we can say that the center of the circle is at (0, 20).

Therefore, the equation for the circle of area that is watered can be written in the form of the equation of a circle:

(x - h)^2 + (y - k)^2 = r^2

where (h, k) represents the center of the circle and r is the radius.

Plugging in the values, we have:

(x - 0)^2 + (y - 20)^2 = 5^2

Simplifying the equation gives:

x^2 + (y - 20)^2 = 25

So, the equation for the circle of the watered area is x^2 + (y - 20)^2 = 25.

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Answer:  the equation for the circle of area that is watered by the sprinkler is x^2 + (y - 20)^2 = 25.

The equation for the circle of area that is watered by the sprinkler can be determined using the formula for the equation of a circle.

First, we need to find the radius of the circle. The diameter of the circle is given as 10 feet, so the radius is half of that, which is 5 feet.

Next, we need to determine the coordinates of the center of the circle. The house is located at the origin, and the sprinkler is located 20 feet north of the house. Since the sprinkler is 20 feet north, the y-coordinate of the center is 20. The x-coordinate remains at 0 since the house is at the origin. Therefore, the coordinates of the center of the circle are (0, 20).

Using the formula for the equation of a circle, which is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius, we can substitute the values into the equation.

Plugging in the values, we have (x - 0)^2 + (y - 20)^2 = 5^2. Simplifying further, we have x^2 + (y - 20)^2 = 25.

Therefore, the equation for the circle of area that is watered by the sprinkler is x^2 + (y - 20)^2 = 25.

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Answer:

\(((6 + 8) \div 2) + 63 \div 21 \\ (14) \div 2) + 3 \\ 7 + 3 = 10 \\ we \: can \: use \: bodmas \: \\ thank \: you\)

Answer:

\( \boxed{a = \frac{w}{ 6} - \frac{b}{2} + \frac{2}{3} } \)

Step-by-step explanation:

\(Solve \: for \: a: \\

= > w=3(2a+b)-4 \\ \\

w=3(2a+b)4 \: is \: equivalent \: to \: 3(2a+b)-4= w: \\

= > 3(2a+b) - 4=w \\ \\

Expand \: out \: terms \: of \: the \: left \: hand \: side: \\ = > (3 \times 2a) + (3 \times b) - 4 = w \\

= > 6a+3b - 4=w \\ \\

Subtract \: 3b - 4 \: from \: both \: sides: \\ = > 6a + 3b - 4 - (3b - 4)=w - (3b - 4) \\ = > 6a = w - 3b + 4 \\ \\ Divide \: both \: sides \: by \: 6: \\ = > \frac{ \cancel{6}a}{ \cancel{6}} = \frac{w - 3b + 4}{6} \\ = > a = \frac{w}{6} - \frac{3b}{6} + \frac{4}{6} \\ = > a = \frac{w}{ 6} - \frac{b}{2} + \frac{2}{3} \)

The arc length of the polar curve r = e^5θ from 0 to 2π is √26 [(e^10π - 1) / 5].

To find the arc length of a polar curve, we use the formula:

L = ∫[a,b] √(r(θ)² + [dr(θ)/dθ]²) dθ

where r(θ) is the polar equation of the curve, and dr(θ)/dθ is its derivative with respect to θ.

In this case, we have r(θ) = e^5θ, so:

dr(θ)/dθ = 5e^5θ

Plugging these into the arc length formula, we get:

L = ∫[0,2π] √(e^10θ + (5e^5θ)²) dθ

Simplifying the integrand, we have:

L = ∫[0,2π] √(e^10θ + 25e^10θ) dθ

L = ∫[0,2π] √(26e^10θ) dθ

L = √26 ∫[0,2π] e^5θ dθ

Using the formula for the integral of e^x, we get:

L = √26 [e^5θ / 5] |_0^(2π)

L = √26 [(e^10π - 1) / 5]

So the arc length of the polar curve r = e^5θ from 0 to 2π is √26 [(e^10π - 1) / 5].

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