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3 years ago

After how many hours does he break even?

Mathematics

1 answer:

finlep [7]3 years ago

5 0

25+30x=5x²-10
5x²-30x-35=0
x²-6x-7=0 -7=-7*1, -6=-7+1
(x-7)(x+1)=0
x-7=0, x=7 hours.
x+1=0, x=-1 (we cannot take negative for hours)
So, answer is 7

Check
y=25+30*7=235
y=5x²-10= 5*7²-10=245-10 =235

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Caroline's coffee shop sells a refill mug for $8.95. Each refill cost $1.50. Last month Sean spent $26.95 on a mug and refills.

Talja [164]

Alright! First you'd have to subtract the flat fee of the mug which is $8.95, then you'd have to divide by the rate which is $1.50. Your equation would be:
(26.95 - 8.95) ÷ 1.50 = r

Then you solve using your head.. lol.
(26.95 - 8.95) = 18.
(18 ÷ 1.50) = 12.
R = 12.

Hope this helps :).

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3 years ago

Create truth table to determine whether or not the following statements are logically equivalent

otez555 [7]

The statement is totally false.

$\neg P\lor\neg Q \equiv \neg(P \land Q) \not\equiv P\land Q$

because (P and ¬P) is a contradiction.

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2 years ago

the length of diagonal of a rectangular field is 23.7 m and one of its sides is 18.8 m. find the perimeter of the field.

katen-ka-za [31]

Answer:

Approximately 66.4 Meters

Step-by-step explanation:

So we have a rectangle with a width of 18.8 meters and a diagonal with 23.7 meters. To find the perimeter, we need to find the length first. Since a rectangle has four right angles, we can use the Pythagorean Theorem, where the diagonal is the hypotenuse.

$a^2+b^2=c^2$

Plug in 18.8 for either a or b. Plug in the diagonal 23.7 for c.

$(18.8)^2+b^2=23.7^2\\b^2=23.7^2-18.8^2\\b=\sqrt{23.7^2-18.8^2} \\b\approx14.4 \text{ meters}$

Therefore, the length is 14.4 meters. Now, find the perimeter:

$P=2l+2w\\P=2(14.4)+2(18.8)\\P=66.4\text{ meters}$

7 0

3 years ago

25 POINTS AVAILABLE

myrzilka [38]

Answer:

$\large\boxed{1.\ (-3, 0),\ r = 3}\\\boxed{2.\ (x+4)^2+(y-3)^2=36}\\\boxed{3.\ (x-2)^2+(y-1)^2=(\sqrt{34})^2}$

Step-by-step explanation:

The equation of a circle in standard form:

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

(h, k) - center

r - radius

1. We have the equation:

$(x+3)^2+y^2=9\\\\(x-(-3))^2+(y-0)^2=3^2$

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2. We have the center (-4, 3) and the radius r = 6. Substitute:

$(x-(-4))^2+(y-3)^2=6^2\\\\(x+4)^2+(y-3)^2=36$

3. We have the endpoints of the diameter: (-1, 6) and (5, -4).

Midpoint of diameter is a center of a circle.

The formula of a midpoint:

$\left(\dfrac{x_1+x_2}{2};\ \dfrac{y_1+y_2}{2}\right)$

Substitute:

$h=\dfrac{-1+5}{2}=\dfrac{4}{2}=2\\\\k=\dfrac{6+(-4)}{2}=\dfrac{2}{2}=1$

The center is in (2, 1).

The radius length is equal to the distance between the center of the circle and the endpoint of the diameter.

The formula of a distance between two points:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Substitute the coordinates of the points (2, 1) and (5, -4):

$r=\sqrt{(5-2)^2+(-4-1)^2}=\sqrt{3^2+(-5)^2}=\sqrt{9+25}=\sqrt{34}$

Finally we have:

$(x-2)^2+(y-1)^2=(\sqrt{34})^2$

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3 years ago

How to calculate down payment on a house

Scrat [10]

Answer:

Steps below:)

Step-by-step explanation:

1. Find the mortgage amount.

2. Choose a interest rate on your mortgage.

3. Choose a mortgage term that is the median for your financial needs.

4. Calculate the monthly principal and interest payment using a financial calculator, a spreadsheet program such as Excel or an online mortgage calculator.

5. Determine the monthly amount you will pay into escrow each for payment of your property taxes.

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3 years ago