Ask question

Ask question

All categories

2 years ago

9

3 Explain how the distributive property helps us multiply the following polynomials and why and how the final products differ: ●

(a + b)^2, ●(a – b)^2, and ●(a - b)(a + b).

1 answer:

Pavel [41]2 years ago

4 0

<span>●(a + b)^2 = (a +b) (a +b)

(a + b) (a + b) = a*a + a*b + b*a+ b*b = a^2 + 2ab + b^2

●(a – b)^2 (a - b) (a -b)

(a - b) (a -b) = a*a + -ab - ba + b*b = a^2 - 2ab + b^2

●(a - b)(a + b). =

= (a - b) (a + b) = a*a + ab - ba - b*b = a^2 - b^2
</span>

You might be interested in

Triangles Q R S and X Y Z are shown. Angles Q S R and X Z Y are right angles. Angles Q R S and X Y Z are congruent. The length o

kumpel [21]

Answer:

Three-fourths

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

∠QSR≅∠XZY ---> given problem

∠QRS≅∠XYZ ---> given problem

so

△QRS ~ △XYZ ----> by AA Similarity theorem

Remember that, if two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

That means

$\frac{QS}{XZ}=\frac{QR}{XY}=\frac{RS}{YZ}$

∠Q≅∠X

∠R≅∠Y

∠S≅∠Z

<em>In the right triangle XYZ</em>

Find the tangent of angle X

$tan(X)=\frac{YZ}{XZ}$ ---> opposite side angle X divided by adjacent side angle X

substitute the given values

$tan(X)=\frac{9}{12}$

Simplify

$tan(X)=\frac{3}{4}$

Remember that

∠Q≅∠X

so

$tan(Q)=tan(X)$

therefore

$tan(Q)=\frac{3}{4}$ ---->Three-fourths

7 0

1 year ago

Read 2 more answers

How much money do winners go home with from the television quiz show Jeopardy? To determine an answer, a random sample of winner

Liula [17]

Answer:

The 95% confidence interval would be given by (14444.04;33657.30)

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".

Data: $26,650 $6,060 $52,820 $8,490 $13,660$25,840 $49,840 $23,790 $51,480 $18,960$990 $11,450 $41,810 $21,060 $7,860

We can calculate the mean and the deviation from these data with the following formulas:

$\bar X= \frac{\sum_{i=1}^n x_i}{n}$

$s=\sqrt{\frac{\sum_{i=1}^n (x_i -\bar X)^2}{n-1}}$

$\bar X=24050.67$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=17386.13 represent the sample standard deviation

n=15 represent the sample size

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:

$df=n-1=15-1=14$

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 tabel to find the critical value. The excel command would be: "=-T.INV(0.025,14)".And we see that $t_{\alpha/2}=2.14$

Now we have everything in order to replace into formula (1):

$24050.67-2.14\frac{17386.13}{\sqrt{15}}=14444.04$

$24050.67+2.14\frac{17386.13}{\sqrt{15}}=33657.30$

So on this case the 95% confidence interval would be given by (14444.04;33657.30)

6 0

2 years ago

Eighty percent of one store's customers paid with credit cards. Forty customers came in that day. How many customers paid for th

mario62 [17]

80%=.8

40*.8=32

32 people made their purchases with credit cards.

6 0

2 years ago

Read 2 more answers

Find the output, yyy, when the input, xxx, is 555.<br><br> y = 5x-3y=5x−3

makkiz [27]

The output y is $y=22$

Explanation:

The expression is $y=5 x-3$

We need to determine the output y, when the value of input is x is 5.

That is, substituting $x=5$ in $y=5 x-3$ , we get,

$y=5(5)-3$

Multiplying the value within the bracket, we have,

$y=25-3$

Subtracting the terms, we get,

$y=22$

Thus, the value of output y is $y=22$

4 0

2 years ago

Read 2 more answers

Sarah loves farmers’ markets, but hates that they only accept cash. On one recent trip, she splurged on a $15.69 jar of honey. T

tamaranim1 [39]

Answer:

$29

Step-by-step explanation:

1) Write all of the prices in a single column:

$15.69

$3.45

$1.75

$0.98

$0.55

$6.15

2) Round all of the items to the nearest dollar:

$16

$3

$2

$1

$1

$6

3) Add all of the values:

$29

5 0

2 years ago

Read 2 more answers