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Anna35 [415]
2 years ago
12

Work with your team to add parentheses to 1 + 3 · 2 + 8 + (−4) so that the resulting expression has the smallest possible value.

Then find a different way to add parentheses to the same expression so that it has the largest possible value. For each expression, draw a diagram of how Cecil would move.
Mathematics
1 answer:
Maurinko [17]2 years ago
5 0
Add them around 8 and -4 for smallest and around 1 + 3 and 2 + 8 for highest
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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
1 year ago
The rate at which energy is used is called <br> work, voltage, power, or amperage.
SSSSS [86.1K]

Answer:

The rate at which energy is used is called power.

Step-by-step explanation:

5 0
3 years ago
Solve the equation for x.
liq [111]

Answer:

x=55

Step-by-step explanation:

The given equation is \sqrt{x-6}+3=10

Group similar terms to get:

\sqrt{x-6}=10-3

\sqrt{x-6}=7

Square both sides to obtain:

x-6=7^2

x-6=49

Add 6 to both sides

x=49+6

Simplify the right hand side to obtain;

x=55

6 0
3 years ago
Each of the letters of the word ALABAMA are written on a piece of paper and then
Kruka [31]

Answer:

3/7

Step-by-step explanation:

There are 7 letters in ALABAMA. And there are 4 A's in ALABAMA. So if you're trying to not get an A then you would subtract 4 from 7. Which you would get 3/7 of the letters in ALABAMA are not A.

7 0
2 years ago
Box 1 measures 6cm in width, 12cm in length, and 4cm in height. The height is doubled to 8cm to produce a larger box, Box 2 Whic
arlik [135]

Step-by-step explanation:

i don't know but i think this is it

The height is doubled to 8cm to produce a larger box, Box 2 Which phrase accurately describes the volume of Box 2

6 0
3 years ago
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