Each graph shows a relation. The first and second numbers of each ordered pair in the relation are members of the set of real numbers. In each case, find the domain and the range of the relation and determine whether the relation is a function.

Midpoint formula : -

Midpoint calculation

The midpoint formula is a method used to locate the midway point between two coordinates on a graph. The midpoint of a line segment with endpoints A and B is the point that is precisely between A and B, that is, it is placed at the same distance from A and B, as shown in the illustration below.

The midpoint formula can be utilized when two points on a graph in the coordinate plane are known. The midpoint M of two points (x1, y1) and (x2, y2) is:

Notice that the midpoint formula includes calculating an average of the x- and y-values of two coordinates. The midway formula may be simpler to recall as a result. The sum of two number is equal to multiplying a number by 2. In a coordinate system, a line segment's midpoint is defined as the point midway between two points in the vertical and horizontal directions. This value is equivalent to the line segment's average x- and y-coordinates. It should be rather simple to recall the midway formula if you keep this in mind.

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Answer: 4/17

0.2353

0.24

Step-by-step explanation:

4 blue jelly beans. 17 total jelly beans.

4/17=0.235294

0.235294=0.2353

0.2353=0.24

Answer:

0

Step-by-step explanation:

[tex]n(S \cup T)=n(S)+n(T)-n(S \cap T) \\ \\ 15=15-n(S \cap T) \\ \\ n(S \cap T)=0[/tex]

Step-by-step explanation:

(1)

FP = FN

makes the triangle FNP an isoceles triangle (both legs have the same length). and that means both angles of these equal legs with the third side (PN) must be equal.

therefore, the angle N = P2 = 56°.

and we know that the angle P = P1 + P2 = 68 + 56 = 124°.

LE = LM

makes the triangle ELM an isoceles triangle. because of that, both angles of these 2 legs with the third side (ME) are equal.

therefore, M1 = E1 = 62°.

the fact that the sum of all angles in a triangle is always 180° gives us the angle L

180 = 62 + 62 + angle L = 124 + angle L

56° = angle L

because angles L and P are supplementary (that means together they have 180°, which is true as 124 + 56 = 180), it means that LM || PN. as this pair of supplementary angles means that their connecting line LP is intersecting the lines LM and PN at the same angles, which makes LM parallel to PN.

and as angle N = angle L (56°), this also proves that MN is parallel to LP (as now the line PN intersects LP and MN at the same angles and N and P are supplementary angles).

(2)

with the proof in (1) that we have 2 sets of parallel sidelines (LP || MN, LM || PN), this makes LMNP per basic definition a parallelogram.

Step-by-step explanation:

5.|12 - r| > 15

|12 - r| > 15/5

|12 - r| > 3

12 - r < -3 or 12 - r > 3

-r < -3 - 12 or -r > 3 - 12

-r < -15 or -r > -9

r > 15 or r < 9

Step-by-step explanation:

if there is no typo the expression is :

7 + 5c + 4d - 8c + d

to simplify combine all terms with the same variable and exponent of that variable.

so, this is

7 + (5c - 8c) + (4d + d) = 7 - 3c + 5d

Answer:

-3c+5d+7

Step-by-step explanation:

Step-by-step explanation:

let the number of wholewheat bread batches be x

let the number of muffin batches be y

prep condition: 4x + (1/2)y ≤ 16 or 8x + y ≤ 32

baking condition : 1x + (1/2)y ≤ 10 or 2x + y ≤ 20

graph each of those in the first quadrant shading in the region below each one.

Final shading is the region satisfying both conditions.

profit = 35x + 10y

allow this line to "slide" away from the origin as far as you can.

It should be clear that the farthest we can go is the intersection of

8x+y = 32 and

2x + y = 20 or the x and y intercepts of our two boundary lines.

subtract them as they are:

6x = 12

x = 2

then in our head , y = 16

max profit = 2(35) + 10(16) = 230

Just to make sure, I will test the intercepts of our intersecting region, namely (4,0) and (0,20)

for (4,0) profit = 4(35)+1 = 140

for (0,32) profit = 0 + 10(20) = 200

so max profit is 230 when x=2 and y=16

(notice all the prep time and baking time is utelized)

The solution to the given equation are -2/5 and 1

Linear equation are equation that has a linear degree of 1. The standard linear equation is expressed as y - mx + b

Given the equation below:

(5v +2)(1 - v) = 0

Equate both expressions to zero to have:

5v+2 = 0 and 1 -v = 0

For the expression 5v+2 = 0

5v = -2

v = -2/5

Similarly

1 - v = 0

v = 1 + 0

v = 1

Hence the solution to the given equation are -2/5 and 1

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The possible values of the length of the garden is 151 ft to 450 ft. The length of the rectangle garden can vary from 151 ft to 450 ft

Given that A rectangle garden is to be constructed so that the width is 150 ft and atmost fencing can be used is 1200ft and asked to find the possible values of length of the rectangle garden.

It mean maximum value of perimeter = 1200ft

The minimum perimeter can be 2(150+151)=602ft as the length of rectangle must be greater than the bredth of rectangle

Therefore the minimum value of length of rectangle is 151 feet

The maximum perimeter is 1200ft

1200=2(150+length of rectangle)

Maximum value of the length of the rectangle=450ft

Therefore,The possible values of the length of the garden is 151 ft to 450 ft. The length of the rectangle garden can vary from 151 ft to 450 ft

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Answer:

answer should be A. 2⅖

Step-by-step explanation:

you can find out by turning it into an improper fraction: =5×2+2/5

=10+2/5

=12/5

Answer:

[tex]=4620000x[/tex]

Step-by-step explanation:

[tex]=1000000\cdot \:4.62x[/tex]
[tex]=4620000x[/tex]

Answer:

4620000

Step-by-step explanation:

4.62x10^6

1000000x4.62

Answer is  f(x)= [tex]\frac{x^{2}+ 2x - 8 }{x - 5}[/tex]

vertical asymptote, the denominator must be contained (x−5)

and for zeros the numerator must be contained (x−2)

then we get,

So far f(x)= f(x)= [tex]\frac{ (x - 2)}{x - 5}[/tex]

​

For slant asymptote, quotient of numerator divided by denominator must be (x+4)

Therefore:

f(x)= [tex]\frac{(x + 4) (x - 2)}{x - 5}[/tex]

after solving this equation we get,

So f(x)= [tex]\frac{x^{2}+ 2x - 8 }{x - 5}[/tex]

​A vertical asymptote is a vertical line that guides the graph of the function but is not part of it. It can never be crossed by the graph because it occurs at the x-value that is not in the domain of the function. A function may have more than one vertical asymptote.

In Mathematics, a slant asymptote, also known as an oblique asymptote, occurs when the degree of the numerator polynomial is greater than the degree of the denominator polynomial. The slant asymptote gives the linear function which is neither parallel to x-axis nor parallel to the y-axis.

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101011 in base 2 is equal to 43 in base 10

Answer:

Exact Distance = [tex]\boldsymbol{\sqrt{73}}[/tex] units

Approximate Distance = 8.544 units

====================================================

Explanation:

I'll relabel the points as A and B, and I'll be using the distance formula.

[tex]A = (x_1,y_1) = (-2,4) \text{ and } B = (x_2, y_2) = (6,1)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-2-6)^2 + (4-1)^2}\\\\d = \sqrt{(-8)^2 + (3)^2}\\\\d = \sqrt{64 + 9}\\\\d = \sqrt{73}\\\\d \approx 8.544\\\\[/tex]

The exact distance is [tex]\sqrt{73}[/tex] units.

The approximate distance is roughly 8.544 units.

Round the approximate value however your teacher instructs.

Answer:...

Step-by-step explanation:

Answer:

Step-by-step explanation:

444

Answer: 1L = 1000 mL

Step-by-step explanation:

1.     1 milligram (mg) is equal to 0.001 gram (gm), so 10mg = 0.01. The first choice is incorrect

2.    1 liter (L) = 1000 milliliter (mL) so the second choice is correct

3.    1 microgram (mcg) is equal to 0.001 milligram (mg), so the third                                                                 choice is incorrect.

4.    1 liter (L) = 1000 milliliter (mL), so the fourth choice is evidently                                        incorrect. (1000 L would be 1,000,000 mL)

Answer:

120

Step-by-step explanation:

l = (w*3)+2

w = 6

area = ((6*3)+2) * 6

            ((18) + 2) * 6

               20        * 6

                     120

The friend doesn't have a fever when the temperature increases by 1°C.

To convert Celcius to Fahrenheit,we have to multiply by 1.8 and add 32°.

This will be:

37°C = (37 × 1.8) + 32

= 98.6

When we add 1°, we will get 99.6.

Therefore, the friend doesn't have a fever when the temperature increases by 1°C.

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Answer:

Answer:

A because of the way the pipe is designed

Answer: 60 rides

Step-by-step explanation:

18/30% = (as fraction) 180/3

= 60

Answer:

heheghgcfyhcggh I am a bit of a bit of a bit of a bit of a bit of a bit of a bit

The expression √4x  using rational exponents ( 4x )^{\frac{1}{2} } .

What is rational exponents?

What is Integer Exponents?

√4x  

use [tex]\sqrt[n]{a^{x} } = a^{x/n}[/tex]

to rewrite

√4x   = [tex]( 4x )^{\frac{1}{2} }[/tex]

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Answer:

formula for the derivative of x*lnx is equal to 1 + lnx.

Step-by-step explanation:

we need to find derivative of f(x) = x*lnx,

so we take the limiting value as x approaches x + h.

To simplify this, we set x = x + h,

and we want to take the limiting value as h approaches 0.

Now according to first derivative formula we have;

f'(x) = [tex]\lim_{h \to \zer0}[/tex]f(x+h) - f(x)]/[(x+h) - x]

[tex]\lim_{h \to \zer0}[/tex][ ln (1 + x) ] / x = 1

ln a - ln b = ln(a/b)

Using the above formulas, we have

d(xlnx)/dx = [tex]\lim_{h \to \zer0}[/tex][(x+h) ln(x+h) - xlnx]/[(x+h) - x]

= [tex]\lim_{h \to \zer0}[/tex][x ln(x+h) + h ln(x+h) - xlnx]/h

= [tex]\lim_{h \to \zer0}[/tex][x ln(x+h) - x lnx + h ln(x+h)]/h

= [tex]\lim_{h \to \zer0}\\[/tex][x(ln(x+h) - lnx) + h ln(x+h)]/h

=[tex]\lim_{h \to \zer0}[/tex][x ln [(x+h)/x] + h ln(x+h)]/h

=[tex]\lim_{h \to \zer0}[/tex][x ln (1+h/x) + h ln(x+h)]/h

=[tex]\lim_{h \to \zer0}[/tex] [x ln (1+h/x)]/h + limh→0 ln(x+h)

= [tex]\lim_{h \to \zer0}[/tex][ ln (1 + h/x) ] / (h/x) + limh→0 ln(x+h)

= 1 + lnx --- [Using limit formula [tex]\lim_{h \to \zer0}[/tex] [ ln (1 + x) ] / x = 1]

Hence, we have proved that the formula for the derivative of x*lnx is equal to 1 + lnx.

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Answer:

Step-by-step explanation:

In this section, we will determine the differentiate of xlnx using the first principle of derivatives, that is, the definition of limits. To derive the derivative of f(x) = xlnx, we take the limiting value as x approaches x + h. To simplify this, we set x = x + h, and we want to take the limiting value as h approaches 0. We will use the following formulas to prove the result:

f'(x) = limh→0[f(x+h) - f(x)]/[(x+h) - x]

limx→0 [ ln (1 + x) ] / x = 1

ln a - ln b = ln(a/b)

Using the above formulas, we have

d(xlnx)/dx = limh→0[(x+h) ln(x+h) - xlnx]/[(x+h) - x]

= limh→0[x ln(x+h) + h ln(x+h) - xlnx]/h

= limh→0[x ln(x+h) - x lnx + h ln(x+h)]/h

= limh→0[x(ln(x+h) - lnx) + h ln(x+h)]/h

= limh→0[x ln [(x+h)/x] + h ln(x+h)]/h

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Following the first term [tex]n[/tex], the [tex]k[/tex]-th term [tex]\left(k\in\{1,2,3,\ldots,n\}\right)[/tex] in [tex]f(n)[/tex] is given by

[tex]\dfrac{16k + (9-4k)n - 3n^2}{4kn + 3n^2}[/tex]

That is,

[tex]k=1 \implies \dfrac{16 + (9-4)n - 3n^2}{4n + 3n^2} = \dfrac{16 + 5n - 3n^2}{4n + 3n^2}[/tex]

[tex]k=2 \implies \dfrac{16\cdot2 + (9-8)n - 3n^2}{4\cdot2n + 3n^2} = \dfrac{32 + n - 3n^2}{8n + 3n^2}[/tex]

and so on, up to

[tex]k=n \implies \dfrac{16n + (9-4n)n - 3n^2}{4n^2 + 3n^2} = \dfrac{25n - 7n^2}{7n^2}[/tex]

We then have

[tex]\displaystyle f(n) = n + \sum_{k=1}^n \frac{16k + (9-4k)n - 3n^2}{4kn + 3n^2} \\\\ ~~~~~~~ = n + \frac1n \sum_{k=1}^n \frac{16\frac kn + 9}{4\frac kn + 3} - \frac1n \sum_{k=1}^n \frac{4kn + 3n^2}{4k + 3n} \\\\ ~~~~~~~ = n + \frac1n \sum_{k=1}^n \frac{16\frac kn + 9}{4\frac kn + 3}- \frac1n \sum_{k=1}^n n \\\\ ~~~~~~~ = \frac1n \sum_{k=1}^n \frac{16\frac kn + 9}{4\frac kn + 3}[/tex]

Now as [tex]n\to\infty[/tex], the right side converges to a definite integral.

[tex]\displaystyle \lim_{n\to\infty} f(n) = \lim_{n\to\infty} \frac1n \sum_{k=1}^n \frac{16\frac kn + 9}{4\frac kn + 3} \\\\ ~~~~~~~~~~~~~ \,= \int_0^1 \frac{16x + 9}{4x + 3} \, dx[/tex]

Wrap up by substituting [tex]x\mapsto\frac{x-3}4[/tex].

[tex]\displaystyle \lim_{n\to\infty} f(n) = \frac14 \int_0^1 \frac{16x + 9}{4x + 3} \, dx \\\\ ~~~~~~~~~~~~~\, = \frac14 \int_3^7 \frac{4x - 3}x \, dx \\\\ ~~~~~~~~~~~~~\, = \frac14 \int_3^7 \left(4 - \frac3x\right) \, dx \\\\ ~~~~~~~~~~~~~\, = \left. \frac14 (4x - 3\ln|x|) \right\vert_3^7\\\\ ~~~~~~~~~~~~~\, = \boxed{4 + \frac34 \ln\left(\frac37\right)}[/tex]

Answer:

x=4

Step-by-step explanation:

6+14=5x

Add 6 and 14 which is equal to 20.

You will get 20=5x which you will then divide by 5 inorder to solve for x.

X=4

Pull out like factors :

5x - 20 = 5 • (x - 4)

Solve : 5 = 0

This equation has no solution.

A a non-zero constant never equals zero

Solve : x-4 = 0

Add 4 to both sides of the equation :

x = 4

Answer:

175

Step-by-step explanation:

because 7/8 of 200 is 175