help me answer this 100 POINTS!!!!!

The area of the triangle is given by the product of 0.5 and the distances of the x and y intercepts from the origin.

Reasons:

The area of the triangle, A = 0.5·x·y

Where;

x and y are the values of the line at the intercepts

The equation of the line is; (y - 7) = m·(x - 8)

At the y-intercept, x = 0, therefore;

(y - 7) = m·(0 - 8) = -8·m

At the y-intercept, y = 7 - 8·m

At the x-intercept, y = 0, therefore;

(0 - 7) = m·(0 - 8) = -8·m

At the x-intercept, -7 = m·x - 8·m

8·m - 7 = m·x

[tex]\displaystyle x = \mathbf{8 - \frac{7}{m}}[/tex]

Therefore;

[tex]\displaystyle A = 0.5 \times \left(7 - 8 \cdot m\right) \times \left(8 - \frac{7}{m} \right) = \mathbf{\frac{-32 \cdot m^2 +56 \cdot m - 24.5}{m}}[/tex]

When the area is minimal, we have;

[tex]\displaystyle \frac{dA}{dm} =0 = \frac{d}{dm} \left(\frac{-32 \cdot m^2 +56 \cdot m - 24.5}{m}\right) = \mathbf{-\frac{32 \cdot m^2 - 24.5}{m^2}}[/tex]

m² × 0 = 24.5 - 32·m²

[tex]\displaystyle m^2 = \frac{24.5}{32} = \frac{49}{64}[/tex]

[tex]\displaystyle m = \sqrt{\frac{49}{64}} = \frac{7}{8}[/tex]

[tex]\displaystyle m = \pm \frac{7}{8}[/tex]

The equation of the line when [tex]\displaystyle m = + \frac{7}{8}[/tex] is therefore;

(y - 7) = m·(x - 8)

[tex]\displaystyle (y - 7) = \mathbf{\frac{7}{8} \cdot (x - 8)}[/tex]

[tex]\displaystyle (y - 7) = \frac{7}{8} \cdot (x - 8) = \frac{7}{8} \cdot x - \frac{7}{8} \times 8 = \frac{7}{8} \cdot x - 7[/tex]

[tex]\displaystyle y = \frac{7}{8} \cdot x - 7 + 7 = \frac{7}{8} \cdot x[/tex]

[tex]\displaystyle y = \mathbf{\frac{7}{8} \cdot x}[/tex]

The x and y intercept of the above line are 0

When [tex]\displaystyle m = - \frac{7}{8}[/tex], we have;

[tex]\displaystyle (y - 7) = -\frac{7}{8} \cdot (x - 8) = -\frac{7}{8} \cdot x + \frac{7}{8} \times 8 = -\frac{7}{8} \cdot x + 7[/tex]

Which gives;

[tex]\displaystyle y = \frac{7}{8} \cdot x + 7 + 7 = \frac{7}{8} \cdot x + 14[/tex]

[tex]\mathrm{The \ equation \ of \ the \ line \ is, }\displaystyle \ y = \mathbf{14 - \frac{7}{8} \cdot x}[/tex]

The equation of the line through P = (8, 7) such that the triangle bounded by the line and the axes in the first quadrant has minimal area is therefore;

[tex]\displaystyle \ \underline{ y = 14 - \frac{7}{8} \cdot x}[/tex]

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Answer:

Step-by-step explanation:

-3 (xy+2y)+5y-x

-3xy-6y+5y-x

-3xy-y-x

Answer:

Infinite, any number

Step-by-step explanation:

Simplify

30 - 3x = 30 - 3x

Answer:479001600

Step-by-step explanation:

12 factorial is 12 * 11 * 10 ..... all the way to one

A way to do it by hand is

12 * 1

11 * 2

10 * 3

9 * 4

8 * 5

7 * 6

stop here because 6 * 7 and 5 *8 are already listed

This gives you 6 products then multiply those 6 products by pairs which gives you three pairs which gives you three products then compute a pair then multiply by last product.

Easy math but a lot of written work

Answer:

x=7/10

Step-by-step explanation:

1/5=2/10

9/10-       =2/10

Substitute the blank with X

9/10-  X  =2/10

x=7/10

Answer:

7/10

Step-by-step explanation:

9/10 - _ = 1/5

Let's represent the unknown as x

Therefore,

9/10 - x = 1/5

9/10 - 1/5 = x

x = 9/10 - 1/5 = 7/10

Answer:

22 + 9 - S

Step-by-Step Explanation:

Amelia started with 22 seashells and found 9 more so you add that together then since she gave S amount of seashells away to her sister you minus it.

Answer: D

Step-by-step explanation:

Tim should expect to pay an extra $52.88 because he forgot to refuel the car. option D is correct.

Two or more expressions with an Equal sign is called as Equation.

The car that Tim rented needed 11.75 gallons of gas to refill to the same fuel level as indicated on the Check-Out sheet.

Since the rental agency charges $4.50 per gallon of gas plus a $5.00 refueling charge, the cost of refueling the car will be:

11.75 gallons x $4.50/gallon + $5.00

= $57.88

Therefore, Tim should expect to pay an extra $57.88 because he forgot to refuel the car. The correct answer is (d).

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Answer:

Step-by-step explanation:

100% - 1.1% = 98.9% = 0.989

79000(0.989)¹ = 78,131

or

1.1% = 0.011

79000(0.011) = 869

79000 - 869 = 78,131

Part A

The given angle is 4pi/3. Multiply it by the factor 180/pi to convert from radians to degree mode.

Note how the given angle has pi in the numerator, while the conversion factor has pi in the denominator. The two pi terms will cancel.

(4pi/3)*(180/pi)

(4/3)*(180/1)

(4*180)/(3*1)

720/3

240

The angle 4pi/3 radians is equivalent to 240 degrees. This 240 degree angle is in quadrant 3. Any angle in this quadrant is between 180 degrees and 270 degrees, excluding both endpoints. This is the bottom left quadrant, aka the southwest quadrant.

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

Part B

To find the reference angle, we'll subtract off pi. This only works for angles in quadrant 3. This is because the first pi radians, aka 180 degrees, is taken up by the first two upper quadrants. The remaining bit in the third quadrant is all we care about to find the reference angle.

reference angle = (given angle in quadrant 3) - pi

reference angle = (4pi/3) - pi

reference angle = (4pi/3) - (3pi/3)

reference angle = (4pi - 3pi)/3

reference angle = pi/3

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

Part C

Use a calculator or a reference table to find that

tan(4pi/3) = tan(pi/3) = sqrt(3)

Alternatively, you can compute the sine and cosine values first

Dividing the two items in the order mentioned will get us the tangent value

tan = sin/cos

tan(pi/3) = sin(pi/3) divide cos(pi/3)

tan(pi/3) = sqrt(3)/2 divide 1/2

tan(pi/3) = sqrt(3)

In the jump from the second to last step, to the last step, the denominators '2' cancel out when dividing.

Answer:

27g of sucrose

Step-by-step explanation:

You would need 3g of sucrose per ever 100ml and you have 900ml therefore 27g

Answer:

Step-by-step explanation:

Begin by finding a common denominator in the numerator of that rational expression. The common denominator is 3(x+2):

[tex]\frac{\frac{(3)1}{(3)x+2} -\frac{(x+2)1}{3(x+2)} }{x-1}[/tex] which simplifies to

[tex]\frac{\frac{3}{3x+6} -\frac{(x+2)}{3x+6} }{x-1}[/tex] which simplifies further to

[tex]\frac{\frac{3-x-2}{3x+6} }{x-1}[/tex] and

[tex]\frac{\frac{1-x}{3x+6} }{x-1}[/tex]  Bring up the lower fraction and flip it and multiply:

[tex]\frac{1-x}{3x+6}*\frac{1}{x-1}[/tex]  In order to make the 1-x into x-1, multiply the numerator of that fraction on the left by -1 to get:

[tex]-\frac{x-1}{(3x+6)(x-1)}[/tex] and now the x-1 terms cancel out, leaving us with:

[tex]-\frac{1}{3(1)+6}=-\frac{1}{9}=-.1111[/tex]

We need to find distance they travel as a function of time. This simply means that x is the function of time. The destination is 120 miles away, this is irrelevant for the question that is currently being asked. However, we know that they have already travelled 20 miles and are going 50 miles and hour. So lets plug in what we have.

50 is our rate of change, so we match that with the x.

20 is our constant, the distance already travelled.

This means our function is:

f(x) = 50x + 20

This means our answer is D) f(x) = 50x + 20

Lets also plug in 120 to solve how much further they need to travel before arriving.

120 is our f(x) as it is the final distance travelled.

120 = 50x + 20

120-20 = 50x

100 = 50x

100/50 = x

2 = x

This means that they need to travel 2 hours in addition to the 20 miles they have already gone.

I hope I've helped! :)

Answer:both involving 6 and 7. (-6,-7) would be in quadrant 3 while point (-6,7) would be on top of it in quadrant 2.

Step-by-step explanation:

Answer:

7/50

Step-by-step explanation:

Here is an easy way of converting a decimal number to fraction.

Step 1:

Write it down as 0.14/1

Step 2:

Multiply bottom and top by 10 for every number after the decimal, since there is 2 numbers after the decimal you do 10*10 = 100

[tex]\frac{0.14(100)}{1(100)}[/tex] = 14/100

Step 3:

You can simplify 14/100 to 7/50 and thats why 7/50 is the answer

Answer:

[tex]\frac{14}{100}[/tex] or [tex]\frac{7}{50}[/tex]

Step-by-step explanation:

To find 0.14 we have to see what place it's in, since it was in the hundredths place, we put 14 over 100, which is 14/100.

To simplify this fraction we have to find the GCM (Greatest Common Factor), the GCM of 14 and 100 is 2. Then we divide both the bottom and the top by 2 (whatever you do to the bottom, you do to the top), which gives us 7/50.

To conclude, 0.14 as a fraction is 14/100 or 7/50.

Answer:

M/140 = 50/60 or C

Step-by-step explanation:

Since the total is 200 it will be the denominator but we already have 60 gallons so we do 200-60=140

the ratio is 50 per 60

Answer:

x = 7

y = -5

Step-by-step explanation:

x + y = 2

x - y = 12

( x + y ) + ( x - y ) = 2 + 12

2x = 14

x = 7

7 + y = 2

y = -5

Check:

7 + -5 = 2

7 - (-5) = 12

Correct

-Chetan K

2 × 10 = 20

see Picture.

Variance is the exact average deviation of data values from the mean in squared units and the Standard deviation of data values from the mean in regular units.

Variance is a statistical measure of the dispersion of numbers in a data collection. Variance estimates how much more each number in the set deviates from the mean, and from each and every other number in the set.

The variance is a measure of the degree of variability. It is determined by averaging the squared deviations out of the mean.

The greater the spread of the data, the greater the variance in proportion to the mean.

The standard deviation is determined as the square root of variance by calculating the departure of each data point from the mean. The standard deviation represents the average level of variation in your dataset. It informs you how far each number deviates from the mean on average.

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Answer:

0.573

Hope that helps :)

Answer:

e

Step-by-step explanation:

chicken nuggets

A) 6/25

B) 13/15

C) 4/15

Explanation:

A) P(both will be alive) = (3/5)(2/5) = 6/25

B) P(at least one will be alive) = 1-P(both die) = 1-(2/5)(1/3) = 13/15

C) P(only the wife will be alive)=(2/5)(2/3) = 4/15

Answer:

416

Step-by-step explanation:

Plug in the variables

8(7) + (5*2 * 6*6)

56 + (10 * 36)

56 + 360

416

Answer:

Step-by-step explanation:

Slope is change in y over the change in x

(r - 3) / (6 - 5) = -1

(r - 3) / (1) = -1

r - 3 = -1

r = 2

Answer:

1.NO  2. Yes

Step-by-step explanation:

Answer:

The first and second one is no

Step-by-step explanation:

(1/5) to the second power is 1/25 and adding 25/25 gets 26/25 which is not equal to 24/25

1 to the second power is still one and (1/4) to the second power is 1/16. 16/16 plus 1/16 is 17/16 which is not equal to 25/26

Answer:

Step-by-step explanation:

1 yd(36 in/yd)(2.54 cm/in) / (100cm/m) = 0.9144 m

(4(0.9144)) x (3(0.9144)) = 10.03352832 = 10.03 m²

Answer:

£0.00 probably is the answer

Answer:

7158

Step-by-step explanation:

Answer:

B. P′ (−4, 0)

Step-by-step explanation:

You can look at the graph. The X-axis always goes first. SO -4 is first because it's on the x-axis. ANSWER= (-4, 0)

The rate of growth will she need to achieve her goal is 2.8%

The formula for finding the compound amount is expressed as:

[tex]A =P(1+\frac{r}{n} )^{nt}[/tex]

P is the amount invested = $25000

t is the time in years = 25 years

A is the amount = $125000

r is the rate in %

Substitute the given parameters into the formula to have:

[tex]125000 =25000(1+r )^{25}\\5 =(1+r)^{25}\\log5=25log(1+r)\\log(1+r)=\frac{log5}{25} \\log(1+r)=0.02796\\1+r = e^{0.02795}\\1+r=1.0283\\r = 1.0283 -1\\r = 0.0283\\[/tex]

Hence the rate of growth will she need to achieve her goal is 2.8%

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Answer:

3.34

Step-by-step explanation:

First step: 3x44=132, 132+15=147. Then use 147 as numerator and 44 as denominator.

Second step: Divide 147/44= 3.3409090909091, round and get 3.34.

Hope this helps.

Answer:

Volume is the amount of space taken up by an object