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notka56 [123]
3 years ago
6

A photograph is reduced by a scale factor of 2/3. If the original length of the photograph was 6 inches, what is the length of t

he reduced photo?
A. 2 inches
B. 3 inches
C. 4 inches
D. 5 1/3 inches
Mathematics
1 answer:
AlladinOne [14]3 years ago
3 0
The answer is c, 4 inches
6 x (2/3) = 4
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Please explain with working!!! Find the set of values of x that satisfy the inequality 9x^2-15x<6
Oksi-84 [34.3K]

Answer:

-1/3

Step-by-step explanation:

When solving a quadratic inequality, first solve it normally like you would for a normal quadratic equation. We have:

9x^2-15x

Ignore the less than sign and replace it with an equal sign and solve the quadratic for its zeros:

9x^2-15x=6

Subtract 6 from both sides:

9x^2-15x-6=0

Divide everything by 3:

3x^2-5x-2=0

Factor. Find two numbers that equal (3)(-2)=-6 that add up to -5.

-6 and 1 works. Thus:

3x^2-6x+x-2=0\\3x(x-2)+1(x-2)=0\\(3x+1)(x-2)=0

Find the x using the Zero Product Property:

3x+1=0 \text{ or }x-2=0\\x=-1/3\text{ or }x=2

Now, we need to replace the equal signs with symbols again. To do so, we need to test which symbol to place. Let's do the first zero first.

So, the first zero is:

x=-1/3

Assume that the correct symbol is >. Thus,

x>-1/3

Now, pick any number that is greater than -1/3. I'll pick 0 since it's the easiest. Now, plug 0 back into the very original inequality. If it works, then the sign is correct, if it doesn't, then simply use the opposite one. Therefore:

9x^2-15x

0 is indeed less than six, so our first correct solution is:

x>-1/3

For the second one, do the same thing. We have:

x=2

Assume that the correct symbol is <. Thus:

x

Again, pick any number less than 2. I'm going to use 0. Plug 0 back into the original equation

9x^2-15x

Again, this is correct. Therefore, x<2 is also the correct inequality.

So together, we have:

x>-1/3 \text{ and } x

Together, we can write them as:

-1/3

(Note that we don't need to worry about the "or equal to" part since the original inequality didn't have it.)

6 0
3 years ago
The candle factory made 498 red candles and 204 white candles each day. About how many candles did the factory make in a day alt
stiv31 [10]

Answer:

about 700

Step-by-step explanation:

you add 204 + 498=

4 0
2 years ago
Read 2 more answers
PLZ HELP ASAP AREA OF A SECTOR
const2013 [10]
The fraction of a circle represented by the shaded region is:
 S '/ S = ((8/5) * pi * r) / (2 * pi * r)
 Rewriting we have:
 S '/ S = ((8/5)) / (2)
 S '/ S = 8/10
 S '/ S = 4/5
 Then, we can make the following rule of three:
 (64/5) pi -------> 4/5
 x ----------------> 1
 Clearing x we have:
 x = ((1) / (4/5)) * ((64/5) pi)
 Rewriting:
 x = (5/4) * ((64/5) pi)
 x = (5/4) * ((64/5) pi)
 x = 50.24
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The area of the complete circle is:
 
x = 50.24
4 0
3 years ago
How would you write a phrase that represents the expression 7(n - 12)?
NemiM [27]
7n-84 would be your correct answer, 7 times n is 7n. 12 times 7 is 84 so therefore your answer would be 7n-84
7 0
3 years ago
A study dealing with health care issues plans to take a sample survey of 1500 Americans to estimate the mean dollar amount that
frutty [35]

Answer:

The population parameter of this study is the population mean.

Step-by-step explanation:

A population parameter is a numerical measure representing a certain characteristic of the population. For example, population mean, population variance, population proportion, and so on.

The population parameter is computed using all the values of the population.

The population parameter can be estimated using the sample statistic. If the value of the population parameter is not known, then a random sample of large size, say <em>n</em> ≥ 30 can be selected from the population and the statistic value can be computed. This statistic value is considered as the point estimate of the parameter. It is also known as the unbiased estimator of the parameter.

In this case the survey involved sampling of 1500 Americans to estimate the mean dollar amount that Americans spent on health care in the past year.

The sample selected is used to compute the sample mean dollar amount that Americans spent on health care.

So, the population parameter of this study is the population mean.

7 0
2 years ago
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