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3 years ago

Help me answer and explain STEP BY STEP for #10 and #11

Mathematics

2 answers:

Reptile [31]3 years ago

4 0

these questions don't need steps

madam [21]3 years ago

4 0

Answer:

10. C, Quadratic trinomial

11. D, (6d - 1) (2d + 1)

Step-by-step explanation:

10. 7x² - 5x + 9 is a quadratic trinomial as there are 3 terms in the expression (trinomial)

11. to factor 12d² + 4d - 1 we can use the quadratic formula, factoring, or completing the square. when the first term is not equal to 1, it may be easier to use the quadratic formula or factoring by grouping. in this example, i will use factoring by grouping which is another way to factor. I will write the middle term (4d) as a subtraction using 2 numbers that when multiplied together give us 12. these 2 numbers are 6 and 2, as 6 x 2 = 12 and 6 - 2= 4

we have the following:

12d² + 6d - 2d - 1 < group 2 factors together

(12d² + 6d) (-2d - 1) < solve for each factor by factoring

to factor 12d² + 6d, we need to find a common factor between the 2 numbers. both have the number 6 in common and the letter d, so we can factor out 6d from the expression

6d(2d + 1)

now we will factor (-2d - 1). we want to get 2d + 1 as a result of the factorization we do, so we need to find a number that gives us that. both -2d and -1 have a -1 in common, so we can factor out a -1 from the expression

-1(2d + 1)

we now have the following:

6d(2d + 1) - 1(2d + 1) < since we have 2 (2d + 1), we only need to write one. we can combine 6d and -1 into one factor

(6d - 1) (2d + 1) is our answer. the answer choice would be D

You might be interested in

300 is what percent of 1200

Nadya [2.5K]

Two ways:

$\frac{300}{1200}$ = $\frac{1}{4}$ and 1/4 = 25%

Another way.

300 = n% of 1200
Problem - we can't move n% back two place to change it to a decimal since we don't know what n is. Solution - move the decimal back on the 1200 two places because since of means x, it doesn't matter. Sample .45 x 32 = 45 x .32 Notice that the decimal can be place on either number and it results in the same answer.

So 300 = 12n (1200 moved back 2 places)
now divide by 12
300 = 12n
12 12 and once again n=25(%)

4 0

3 years ago

Read 2 more answers

ASK YOUR TEACHER An article reported that for a sample of 42 kitchens with gas cooking appliances monitored during a one-week pe

xxMikexx [17]

Answer:

$654.16-2.02\frac{165.23}{\sqrt{42}}=602.66$

$654.16+2.02\frac{165.23}{\sqrt{42}}=705.66$

So on this case the 95% confidence interval would be given by (602.66;705.66)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=654.16$ represent the sample mean

$\mu$ population mean (variable of interest)

s=165.23 represent the sample standard deviation

n=42 represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=42-1=41$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,41)".And we see that $t_{\alpha/2}=2.02$