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3 years ago

It takes Bob 3 hours and 30 minutes to drive from Albuquerque to Las cruises which is 360 km away?

Mathematics

1 answer:

nata0808 [166]3 years ago

7 0

Answer:

it actually takes 3 hours and 11 min.

Step-by-step explanation:

in no sure what you are trying to ask

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Carl works at a garment factory and sews buttons on shirts. For each shirt he completes that passes inspection, he earns $2. How

Ratling [72]

do 2*52 which gives you 104 so 104 dollars

6 0

3 years ago

Complete the square and write in standard form. Show all work.What would be the conic section:CircleEllipseHyperbolaParabola

mote1985 [20]

ANSWER

This is an ellipse. The equation is:

$\frac{(x-1)^2}{3^2}+\frac{(y+4)^2}{4^2}=1$

EXPLANATION

We have to complete the square for each variable. To do so, we have to take the first two terms and compare them with the perfect binomial squared formula,

$(a+b)^2=a^2+2ab+b^2$

For x we have to take 16x² and -32x. Since the coefficient of x is not 1, first, we have to factor out the coefficient 16,

$16x^2-32x=16(x^2-2x)$

Now, the first term of the expanded binomial would be x and the second term -2x. Thus, the binomial is,

$(x-1)^2=x^2-2x+1$

To maintain the equation, we have to subtract 1,

$16(x^2-2x+1-1)=16((x-1)^2-1)=16(x-1)^2-16$

Now, we replace (16x² - 32x) from the given equation by this equivalent expression,

$16(x-1)^2-16+9y^2+72y+16=0$

The next step is to do the same for y. We have the terms 9y² + 72y. Again, since the coefficient of y² is not 1, we factor out the coefficient 9,

$9y^2+72y=9(y^2+8y)$

Following the same reasoning as before, we have that the perfect binomial squared is,

$(y+4)^2=y^2+8y+16$

Remember to subtract the independent term to maintain the equation,

$9(y^2+8y)=9(y^2+8y+16-16)=9((y+4)^2-16)=9(y+4)^2-144$

And now, as we did for x, replace the two terms (9y² + 72y) with this equivalent expression in the equation,

$16(x-1)^2-16+9(y+4)^2-144+16=0$

Add like terms,

$\begin{gathered} 16(x-1)^2+9(y+4)^2+(-16-144+16)=0 \\ 16(x-1)^2+9(y+4)^2-144=0 \end{gathered}$

Add 144 to both sides,

$\begin{gathered} 16(x-1)^2+9(y+4)^2-144+144=0+144 \\ 16(x-1)^2+9(y+4)^2=144 \end{gathered}$

As we can see, this is the equation of an ellipse. Its standard form is,

$\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$

So the next step is to divide both sides by 144 and also write the coefficients as fractions in the denominator,

$\begin{gathered} \frac{16(x-1)^2}{144}+\frac{9(y+4)^2}{144}=\frac{144}{144} \\ \\ \frac{(x-1)^2}{\frac{144}{16}}+\frac{(y+4)^2}{\frac{144}{9}}=1 \end{gathered}$

Finally, we have to write the denominators as perfect squares, so we identify the values of a and b. 144 is 12², 16 is 4² and 9 is 3²,

$\frac{(x-1)^2}{(\frac{12}{4})^2}+\frac{(y+4)^2}{(\frac{12}{3})^2}=1$

Note that we can simplify a and b,

$\frac{12}{4}=3\text{ and }\frac{12}{3}=4$

Hence, the equation of the ellipse is,

$\frac{(x-1)^2}{3^2}+\frac{(y+4)^2}{4^2}=1$

3 0

10 months ago

There were 178 old cars at the junkyard. Then a truck brought in some more cars. Now there are a total of 236 cars in the junkya

crimeas [40]

Answer:

<u>The correct answer is 58 cars.</u>

Step-by-step explanation:

Cars in the junkyard before the truck arrived with some = 178

Cars after the truck brought into the junkyard some more= 236

Cars brought in by the truck = 236 - 178

Cars brought into the junkyard by the truck = 58

<u>The number of cars brought by the truck is 58 cars.</u>

5 0

3 years ago

Andrea calls two truck rental companies to compare costs. Action trucks charges $80 for the day plus $0.22 per kilometer and tru

Amanda [17]

Answer:it will take 200 kilometers for the costs to be the same.

Step-by-step explanation:

Let x represent the number of kilometers that Andrea would have to drive for the total cost of renting from both companies to be the same.

Action trucks charges $80 for the day plus $0.22 per kilometer. It means that the total cost of x miles would be

80 + 0.22x - - - - - - - - - 1

Truck experts charges $100 for the day plus $0.12 per kilometer. It means that the total cost of x miles would be

100 + 0.12x - - - - - - - - - 2

Therefore, for the cost of renting from both companies to be the same,

80 + 0.22x = 100 + 0.12x

0.22x - 0.12x = 100 - 80

0.1x = 20

x = 20/0.1 = 200

4 0

3 years ago

if x and y are two overlapping subsets of a universal set U, write the relation between n(U),n(X U Y), and n(xūy).

Andrew [12]

Answer:

the relation between them are

n(U) = n(X U Y) + n(xūy).

4 0

2 years ago

It takes Bob 3 hours and 30 minutes to drive from Albuquerque to Las cruises which is 360 km away?​

It takes Bob 3 hours and 30 minutes to drive from Albuquerque to Las cruises which is 360 km away?