find the distance between the points (5, 7) and (5, -3)

Answer:

The equation of the parabola with a focus at (2,4) and a directrix of y=8 is,

48-8y=(x-2)²

Answer:

the original price = $800

Step-by-step explanation:

To find the fraction of the original price, subtract 0.17 from 1.00, obtaining 0.83.  Then 0.83n = $664 yields n = the original price = $800

The number of bacteria after 8 hours is approximately 2,713.

Let's apply the exponential growth formula:

N = N0 * e(rt),

N is the number of bacteria at a particular period. N0 is the initial bacterial population, e is the mathematical constant (about equal to 2.71828), r is the growth rate, and t is the amount of time that has passed.

The information provided in the problem can be used to determine the growth rate:

N1 = N0 * e(r*2)

N2 = N0 * e(r*4)

To get eliminate N0, divide the second equation by the first equation:

N2/N1 = e(r4) / e(r2)

385/135 = e(r4) / e(r2)

If we condense this expression, we get:

e(r*2) = 385/135

e(r*2) = 2.8519

When we take the natural logarithm of both sides, we get:

r*2 = ln(2.8519)

r = ln(2.8519)/2

r = 0.5457 (rounded to 4 decimal places)

The number of bacteria after 8 hours can now be determined using the exponential growth algorithm once more:

N = N0 * e(rt)

N = 135 * e(0.5457*8)

N = 2,713 (rounded to the nearest whole number)

Therefore, the number of bacteria after 8 hours is approximately 2,713.

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Step-by-step explanation:

First, find the vector.

= (4,2) - (-3,5)

= (4-(-3),2-5)

= (7,-3)

And then, find the distance.

= √(7² + (-3)²)

= √(49 + 9)

= √58 ✓

Answer:

4

Step-by-step explanation:

A mode is the number having the highest frequency, that is, the number which occurs the most times. (The number which occurs the most here is 4, there are two 4s. You only have one of the rest of the numbers.)

m = n+ x/p

m (*p) = n (*p) + x/p (*p)

mp = np + x

x= mp - np

x= p ( m - n)

Answer:

0.45 miles per minute

Step-by-step explanation:

Answer:

Step-by-step explanation:

You know two sides and the angle between them. Use the Law of Cosines to find the third side.

q = √(p²+r²-2pr·cosQ) ≅ 8.533 units

Use Heron's formula to find area

semi-perimeter s = (p+q+r)/2 ≅ 10.317 units

area = √(s(s-p)(s-q)(s-r)) ≅ 16.3 units²

Answer:

A.

monthly earnings

Step-by-step explanation:

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hope it helps.

The values of {m} that is greater than 4.6 represent the solution of the given inequality.

An inequality is used to compare two or more expressions or numbers.

For example -

2x > 4y + 3

x + y > 3

x - y < 6

The given inequality is -

5m - 7 > 16

Adding 7 on both sides, we get -

5m - 7 + 7 > 16 + 7

5m > 23

m > 23/5

m > 4.6

Therefore, the values of {m} that is greater than 4.6 represent the solution of the given inequality.

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1. The x - intercepts of the parabola are

2. The meaning of the x-intercepts are the plane takes of at x = 2.5 s and lands at x = 7.5 s

3. The vertex of the parabola is at (5, 80).

A parabola is a curved shape

1. Given the parabola above, to find the x - intercepts, we proceed as follows.

The x-intercepts are the points at which the graph cuts the x-axis.

They are

2. The meaning of the x-intercepts in this problem are the points where the plane takes off and lands on the ground.

The plane takes of at x = 2.5 s and lands at x = 7.5 s

3. The vertex is the maximum point on the graph.

So, we see that the vertex is at x = 5 s and y = 80 ft

So, the vertex is at (5, 80).

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Answer:

X is 70 degrees

Step-by-step explanation:

In a triangle, all the angles add up to 180.

We can set up an equation:

48+62+x=180

x=180-(48+62)

x=70

The minimum profit occurs at L = 0, where Q = 0.

To find the value of L that maximizes the profit Q = L²\(e^{(0.01L)\).

We need to differentiate Q with respect to L and find the critical points where the derivative equals zero.

Then we can determine whether each critical point is a maximum or a minimum by examining the second derivative.

Testing for critical points:Q = L²\(e^{(0.01L)\)

Q' = \(2Le^{(0.01L)\) + \(0.01 L^2e^{(0.01L)\)

= 0(2L + 0.01L²) \(e^{(0.01L)\)

= 0L (critical point) or 200 \(e^{(0.01L)\)

= 0 (extraneous, ignore)

2L + 0.01L² = 0L(2 + 0.01L) = 0L = 0 or L = -200 (extraneous, ignore)

The only critical point is at L = 0.

Testing for maximum or minimum:Q'' = \(2e^{(0.01L)\) + 0.02Le^(0.01L) + 0.0001L²\(e^{(0.01L)Q''(0)\)

= \(2e^{(0)\) = 2Since Q''(0) > 0,

The critical point at L = 0 is a minimum.

Therefore, there is no value of L that maximizes the profit.

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The values of L that will maximize the profit are 0 and -200

From the question, we have the following parameters that can be used in our computation:

\(Q = L\²e^{0.01L\)

Differentiate the function

So, we have

\(Q' = \frac{L \cdot (L + 200) \cdot e^{0.01L}}{100}\)

Set the equation to 0

\(\frac{L \cdot (L + 200) \cdot e^{0.01L}}{100} = 0\)

Cross multiply

\(L \cdot (L + 200) \cdot e^{0.01L} =0\)

When expanded, we have

L = 0, L + 200 = 0 and \(e^{0.01L} =0\)

When solved for L, we have

L = 0 and L = -200

Hence, the values of L are 0 and -200

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Answer:

sin Φ/(sin Φ + cos Φ) = 12/17

Step-by-step explanation:

sin Φ = 12/13

then sin Φ + cos Φ = 12/13 + 5/13

= 17/13

So , sin Φ/(sin Φ + cos Φ) = 12/13 ÷ 17/13

= 12/13 × 13/17

= 12/17

Answer:

n + 8 ÷ 7

Step-by-step explanation:

I think that's the answer, but I could be wrong- lol.

The addition of the given fraction expression is 7/8.

In mathematics, an expression is a combination of numbers, symbols, and/or operators that represents a mathematical quantity or relationship. It can be a simple combination of numbers or a more complex combination involving variables, functions, or other mathematical constructs.

When adding fractions with the same denominator, you simply add the numerators and keep the denominator the same.

In this case, both fractions have a denominator of 8, so we can add their numerators:

5/8 + 2/8 = (5 + 2)/8 = 7/8

Thus, the sum of 5/8 and 2/8 is 7/8.

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Answer:

Area of circle is equal A = πr²

Here r =  7.5 and π = 3.142

so,

A = 3.142(7.5)²

A = 176.17 after rounding off.

The volume of the solid thus formed is \(\frac{26}{27} \pi\) .

Let us think of any region that is enclosed by a function g(x) and the x-axis between x=a and x=b. If this region is rotated about the x-axis, the solid of rotation that results can be thought of as consisting of thin cylindrical discs with a width of dx and a radius of g (x). Therefore, by integrating the volume of this disc, the whole volume of the solid will be revealed.

Volume=\(\int^{a}_{b}\pi [g(x)]^2dx\)

The given function is g(x)=(1/3)x+2 ranging from x=1 to x=3

Therefore volume of the solid formed is:

\(\int^{3}_{1}\pi [\frac{1}{3}x]^2dx\\=\int^{3}_{1}\pi [\frac{1}{9}x^2]dx\\=\pi \int^{3}_{1} [\frac{1}{9}x^2]dx\\\\=\pi [\frac{1}{27}x^3 ]^3_1\\= \frac{26}{27} \pi\)

The volume of the solid thus formed is \(\frac{26}{27} \pi\) .

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Answer:he would be able to jump all tall as the  C H I C K E N

Step-by-step explanation:

Two triangles are congruent if they meet one of the following criteria. : All three pairs of corresponding sides are equal. : Two pairs of corresponding sides and the corresponding angles between them are equal. : Two pairs of corresponding angles and the corresponding sides between them are equal.

x^2 + y^2 + 2x – 10y + 10 = 0

x^2 + 2x + y^2 - 10y = 0

We must complete the square in x and y.

(x^2 + 2x + 1) + (y^2 -10y + 25) = 4 + 25

(x + 1)^2 + (y - 5)^2 = 29

The radius r is found solving r^2 = 29 for y.

(x + 1)^2 + (y - 5)^2 = sqrt{29}

See picture for the center and radius.

Answer: 128 ounces

Step-by-step explanation:

One ounce has a mass of 16 and 16 x 8 is 128

Answer:

Craig's height= 78

Step-by-step explanation:

You did not give me a question to answer, so I assumed you were asking for Craig's height, and answered accordingly.  When it says "difference" it usually refers to subtraction.  However, the subtraction has already been done.  This means that Craig's height-66=12.  So to find Craig's height, you add 66 and 12 to get 78.

Explanation:

A = set of odd numbers = {1,3,5}

B = set of factors of 12 = {1,2,3,4,6}

A U B = union of set A and set B

A U B = {1,3,5} union {1,2,3,4,6}

A U B = {1,3,5,       1,2,3,4,6}

A U B = {1,2,3,4,5,6}

The set union operation combines two sets into one bigger set. Duplicates are tossed out.

There are 6 elements in the set A U B = {1,2,3,4,5,6} out of 6 faces of the number cube.

Therefore, the probability event  A U B happens is 6/6 = 1 = 100%; i.e. it is guaranteed to happen. Each face of the number cube is either odd, a factor of 12, or both.

Side notes:

Answer:

3/36 or 8.333

Step-by-step explanation:

the way you get it is write all the possibilities and that how you get 3/36

Answer: choice (B)

Step-by-step explanation:

(-4,4)

(0,5)

slope=  \(\frac{5-4}{0-(-4)}= \frac{1}{4}\)

Answer:

F' : (-5,5)

G' : (0,5)

H' : (0,9)

Step-by-step explanation:

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Answer:

F = (-10,0)

G= (-5,0)

H= (-5,40

my explanation: We want to translate it to the left 5 units so if we move over the whole triangle 5 units to the left, this is your answer! Hope I could help. <3