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emmainna [20.7K]
3 years ago
14

Neil took his family of five out to dinner at HogTastic Pit BBQ. They all ordered the buffet and drink at $12.80 each. Neil left

a 15% gratuity for the waitress on the after-tax bill. Based on a tax rate of 7.5%, Neil ended up paying a total of $
for dinner.
Mathematics
1 answer:
adoni [48]3 years ago
6 0
The answer for your problem would be $64.225
there it is your answer
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Find the distance from the point (1,4) to the line y = 1/3x - 3
Troyanec [42]

Answer:

Step-by-step explanation:

If I'm not mistaken, and I very well could be, this is a calculus problem(?). In order to find the distance without calculus you'd need a point on the given line to use to find the distance in the distance formula. But you don't have a point on the given line, so we can find the shortest distance between the point (1, 4) and the given line using the derivative of the polynomial formed when using the distance formula.

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} and we have the x and y for x2 (or x1...it doesn't matter which you choose to fill in):

d=\sqrt{(1-x)^2+(4-y)^2}

but what we find is that we have too many unknowns here, namely, the distance, the x coordinate, and the y coordinate. So we can replace the y coordinate with what y is equal to in terms of the linear equation:

d=\sqrt{(1-x)^2+(4-\frac{1}{3}x-3)^2 } and simplify:

d=\sqrt{(1-x)^2+(7-\frac{1}{3}x)^2 }

. No we'll expand each binomial by squaring:

d=\sqrt{(1-2x+x^2)+(49-\frac{14}{3}x+\frac{1}{9}x^2)  }

.  Combining like terms gives us

d=\sqrt{\frac{10}{9}x^2-\frac{20}{3}x+50  }

The distance between the point (1, 4) and the given line will be at a minimum when the polynomial above is at a minimum. We find the value of x for which the polynomial is at a minimum by finding its derivative, setting the derivative equal to 0, and then solving for x. The derivative of the polynomial is

\frac{20}{9}x-\frac{20}{3}

Setting equal to 0 and getting rid of the denominators gives us

20x - 60 = 0

Solving for x gives us

20x = 60 and x = 3.

That's the value of x that gives us the shortest distance between (1, 4) and the line y = 1/3x - 3. Sub into the distance formula that x value to find the distance:

d=\sqrt{(\frac{10}{9})(3)^2-(\frac{20}{3})(3)+50   }

which simplifies down, finally, to

x ≈ 6.325 units

8 0
3 years ago
How to find lengths from hypotenuse
Phoenix [80]
Can you elaborate on the question??
3 0
3 years ago
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What is the area of a triangle with a base of 27 mm and a height of 10 mm?
nexus9112 [7]

Answer:

area of triangle = 135 mm²

Step-by-step explanation:

Area of a triangle = 1/2 × b × h

Area of a triangle = 1/2 × 27 × 10

Area of a triangle = 135 mm²

5 0
3 years ago
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Find the equation of the line using the point-slope formula. Write the final equation using the slope-intercept form. the x-inte
wariber [46]

Step-by-step explanation:

Given x intercept is 1, So (x,y) is (1,0)

When x intercept is 1 then y  value is 0

Another point on the line is (-2,3)

Two points are (1,0) and (-2,3)

Find out slope using the two given points

slope m=\frac{y_{2}-y_1}{x_2-x_1} =\frac{3-0}{-2-1} =-1\\m=-1

Use point slope formula

m=-1 and point(1,0)

y-y_{1}=m(x-x_{1})\\y-0=-1(x-1)\\y=-1x+1

Point slope equation is

y-0=-1(x-1)

Equation of the line in slope intercept form is

y=-1x+1

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3 years ago
PLEASE HELP ASAP !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! PLEASEEEEEEEEEE AND DO NOT LOOK IT UP ON ANY SOURCE THANK YOU AND ILY
AleksandrR [38]
I would go with Jesses survey.

Unlike everyone else’s survey Jesse chose 6th grade students in random, causing a more unbiased research.
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3 years ago
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