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3 years ago

Determine whether the polynomial is a difference of squares and if it is, factor it.

1 answer:

8 0

Remember these three formulas (really, learn these by heart):

${(a + b)}^{2} = a^{2} + 2ab + b^{2}$

${(a - b)}^{2} = a^{2} - 2ab + b^{2}$

$(a + b)(a - b) = a^{2} - b^{2}$

The stated formula is a manifestation of the last of these three. So indeed,

$(y + 15)(y - 15) = y^{2} - 225$

You might be interested in

A number is added to 9. The result is then multiplied by 4 to give a new result of

Ivanshal [37]

Answer:

the number is 21

Step-by-step explanation:

(9+x)(4)=120

9+x=30

x=21

7 0

3 years ago

Read 2 more answers

a veterinarian purchases some medication for $19.50 and wants to make a $2 profit. what is the percent markup on this medication

uysha [10]

So he has to sell it at 19.5+2=21.5 dollars

so assume19.5=100%
the markup is 2 dollars
2=x%
find x if 19.5=100%

so since they are proportionite
19.5:100 and 2:x
if we make them fractions and flip one of them then multiply we will get 1 since
2/4=1/2
2/4 times 2/1=4/4=1 so

19.5/100 times x/2=19.5x/200=1
19.5x/200=1
multiply both sides by 200
19.5x=200
divide both sdies by 19.5
x=10.256 aprox
x=10.3% markup

6 0

4 years ago

mark wants to fence 4 rectangular gardens with a length of 9 1/4 amd a width of 4 1/2 what is the total length of fenceing mark

Otrada [13]

Step-by-step explanation:

length of each rectangle= 9 1/14=127/14

breadth of each rectangle=5=4 1/2= 9/2

so perimeter of 1 rectangle= 2(l+r)

=2(127/14+ 9/2)

=2(127+63)/14

=2×190/14

=190/7

=27.14 feet

so total length of fencing= 4×27.14

=108.57 feet

hope you understand the solution and good luck!!

5 0

3 years ago

Assume the blood pressures of 10 people were measured before and after sleeping for the night. What is the corresponding critica

NeX [460]

Answer:

For the critical value we need to calculate the degrees of freedom given by:

$df = n-1= 10-1=9$

And since we have a one tailed test we need to look in the t distribution with 9 degrees of freedom a quantile who accumulates 0.05 of the area on a tail and we got:

$|t_{crit}| =1.833$

Step-by-step explanation:

Previous concepts

A paired t-test is used to compare two population means where you have two samples in which observations in one sample can be paired with observations in the other sample. For example if we have Before-and-after observations (This problem) we can use it.

Let put some notation

x=test value with right arm , y = test value with left arm

The system of hypothesis for this case are:

Null hypothesis: $\mu_y- \mu_x = 0$

Alternative hypothesis: $\mu_y -\mu_x \neq 0$

The first step is calculate the difference $d_i=y_i-x_i$

The second step is calculate the mean difference

$\bar d= \frac{\sum_{i=1}^n d_i}{n}= \frac{361}{5}$

The third step would be calculate the standard deviation for the differences, and we got:

$s_d =\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1}$

The 4 step is calculate the statistic given by :

$t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}$

For the critical value we need to calculate the degrees of freedom given by:

$df = n-1= 10-1=9$

And since we have a one tailed test we need to look in the t distribution with 9 degrees of freedom a quantile who accumulates 0.05 of the area on a tail and we got:

$|t_{crit}| =1.833$

5 0

3 years ago

The money spent on gym classes is proportional to the number of gym classes taken. Max spent $\$45.90$ to take $6$ gym classes.

gladu [14]

Answer:

7.65 dollars is spent per gym class

Step-by-step explanation:

The remaining part of Question

What is the amount of money, in dollars, spent per gym class

Given -

Total money spent on Gym $= 45.90$ dollars

Number of gym classes taken $= 6$

The amount spend per gym class is equal to the total money spent on gym divided by total number of gym classes.

i.e

$\frac{45.90}{6} \\7.65$ dollars

7.65 dollars is spent per gym class

3 0

3 years ago