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son4ous [18]
3 years ago
10

Which value of h would horizontally translate a parabola to the right 4 units?

Mathematics
1 answer:
bonufazy [111]3 years ago
6 0
The answer is -4 for it to be translated right.
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Which of the following is the product of the rational expression shown below
wolverine [178]

Option C: \frac{x^{2}-9}{x^{2}-4} is the product of the rational expression.

Explanation:

The given rational expression is \frac{x+3}{x+2} \cdot \frac{x-3}{x-2}

We need to determine the product of the rational expression.

<u>Product of the rational expression:</u>

Let us multiply the rational expression to determine the product of the rational expression.

Thus, we have;

\frac{(x+3)(x-3)}{(x+2)(x-2)}

Let us use the identity (a+b)(a-b)=a^2-b^2 in the above expression.

Thus, we get;

\frac{x^{2} -3^2}{x^{2} -2^2}

Simplifying the terms, we get;

\frac{x^{2}-9}{x^{2}-4}

Thus, the product of the rational expression is \frac{x^{2}-9}{x^{2}-4}

Hence, Option C is the correct answer.

6 0
3 years ago
Tammy deposited $520 in the bank account that earns simple interest every year after 5 years she had earned $156 and interest if
aleksley [76]

Answer:

6%.

Step-by-step explanation:

We have been given that Tammy deposited $520 in the bank account that earns simple interest every year after 5 years she had earned $156.

To find the interest rate we will use simple interest formula.

I=P*r*T

I= Interest.

P= Principal amount.

r=Annual interest rate (in decimal form).

T= Time in years.

We have been given that I=156, T=5, P=520

Upon substituting our values in above formula we will get,

156=520*r*5

156=2600r

r=\frac{156}{2600}

r=0.06

Let us multiply 0.06 by 100 to convert annual interest rate in percentage.

0.06*100=6 \text{ percent}

Therefore, the annual interest rate was 6%.

6 0
3 years ago
National Ave gas prices
Musya8 [376]
Question: What equation models the data?
For this question I used a software to calculate the equation. When plotted, we can notice that the points form a parabolic function therefore we needed quadratic regression for this one. The quadratic equation is in the form of y=A+Bx+Cx^{2} where y represents the gas prices, x is the year, and A, B, and C are coefficients. I have found A, B, and C using the software and the equation for the data is:

y=-0.092+0.587x-0.026x^{2}

Question: What are the domain and range of the equation?
To find the range of the equation, we just transform the quadratic equation into the form y=a(x-h)^{2}+k. The value for k would be the maximum element in our range, and for the sake of the problem, let's assume that we don't have negative prices.

y=-0.092+0.587x-0.026x^{2}
y+0.092=0.587x-0.026x^{2}
y+0.092=-0.026(x^{2}-22.577x)
y+0.092-0.026(127.442)=-0.026(x^{2}-22.577x+127.442)
y-3.221=-0.026(x-11.289)^{2}
y=-0.026(x-11.289)^{2}+3.221

We can see that 3.221 is the maximum value of the range while zero is the minimum. Thus, we can express the range as {y|0 \leq y \leq 3.221}

For the domain, the number of years can extend infinitely but it will also depend if we want to consider the years where the price will be negative. Thus, let's just find the year when the price would be zero.

0=-0.026(x-11.289)^{2}+3.221
-3.221=-0.026(x-11.289)^{2}
123.885=(x-11.289)^{2}
+-11.130=x-11.289

x=0.159
x=22.419

Anywhere before and after the range of the x values above would result to a negative price therefore we can restrict the domain to those values. However, since x represents the year, we would need to round up the first value and round down the larger value.

Domain: {x|01 \leq x \leq 22}

Question: Do you think your equation is a good fit for the data?
To know whether our equation is a good fit or not, we just look at the value of the correlation coefficient r. We can calculate this manually but in this case I just used a software. According to the software, the value for r is 0.661. This is almost close to a strong correlation which is 0.7 thus we can say that this equation is a good fit.

Question: Is there a trend in the data?
There might be a trend, but it won't be a simple linear one. Since the data initially rose before continuously decreasing, our data would best be described by a quadratic trend. The quadratic trend would be the parabolic equation we just used to model the data.

Question: Does there seem to be a positive correlation, a negative correlation, or neither?
Neither. A positive or negative correlation only applies when we are talking about linear trends, where it's either one variable increases as the other one also increases or the variable decreases as the other one increases. In our case, the price rose and fall as the years increase so there is neither a positive nor a negative correlation.

Question: How much do you expect gas to cost in 2020?
We can answer this question by using the equation that we used to model the data. For this question, we would just need to substitute 20 for x since we want to know the price in 2020 (we have only used the last two digits of the year for the equation) while the answer to this would be the expected price.

y=-0.092+0.587(20)-0.026(20)^{2}
y=-0.092+11.740-10.400
y=1.248

The expected price in 2020 would be 1.248 units.
4 0
3 years ago
Take Meenu’s present age to be n years
Otrada [13]

Answer:what’s the initial age

Step-by-step explanation:

6 0
3 years ago
marge saved 350$ toward the cost of here vacation. the vacation will cost 1750$ what percent of the cost does margehave saved
katovenus [111]
So, 350 out of 1750

350/1750=
.1828/1

percent  is  parts out of 100 so x%=x/100

make bottom number 100


0.1828/1 times  100/100 =18.28/100=18.28%


about 18% saved
5 0
3 years ago
Read 2 more answers
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