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3 years ago

HELP IM GONNA FAIL!!!

Mathematics

2 answers:

disa [49]3 years ago

7 0

Answer:

Hope this helped don't know when this question was submitted though lol.

Nina [5.8K]3 years ago

5 0

I think that the answer is B

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Determine whether each scale factor produces an expansion or a contraction under a dilation of the original image

blondinia [14]

Answer:

see the explanation

Step-by-step explanation:

we know that

If the absolute value of the scale factor is less than 1, then the dilation produces a contraction of the original image

If the absolute value of the scale factor is greater than 1, then the dilation produces an expansion of the original image

<u><em>Verify each value</em></u>

1) -4

$\left|-4\right|=4$

$4> 1$

therefore

The dilation produces an expansion of the original image

2) 0.25

$\left|0.25\right|=0.25$

$0.25 < 1$

therefore

The dilation produces a contraction of the original image

3) -2/3

$\left|-2/3\right|=2/3$

$2/3 < 1$

therefore

The dilation produces a contraction of the original image

4) 2.3

$\left|2.3\right|=2.3$

$2.3 > 1$

therefore

The dilation produces an expansion of the original image

4 0

2 years ago

Theodore and Sarah have a small business selling custom-made T-shirts. They currently sell 205 shirts per month and charge $15 p

solong [7]

Answer:

(205-9x) times15

Step-by-step explanation:

7 0

3 years ago

Question 9- Graph the standard form equation (only need a 5 by 5 grid to make this)

kramer

The correct answer is 57

4 0

3 years ago

A fish is 5 feet below the surface of a lake. If its position can be recorded as -5 feet what would the position of 0 represent

eduard

The surface of the lake.
6
5
4
3
2
1
0 Here is the surface of the lake
-1
-2
-3
-4
-5 Here is the fish
-6

5 0

2 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

1 year ago