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motikmotik
3 years ago
13

Use a special-product rule to factor the perfect-square trinomial. 81y^2+ 126y + 49

Mathematics
1 answer:
Ivahew [28]3 years ago
7 0

Answer:

The perfect -square trinomial

                  (9y+7)²

Step-by-step explanation:

<u><em>Explanation:-</em></u>

Given polynomial equation

                        81 y² + 126 y +49

               ⇒     9² y² + 2(9)(7)y + 7²

                ⇒   (9y)² + 2(9)(7)y +7²

we will use formula

   (a+b)² = a² + 2ab +b²

             ⇒ (9y+7)²

<u><em>Final answer:-</em></u>

The perfect -square trinomial

                  (9y+7)²

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3 years ago
Which number line shows the solution set for |a|=6?
ivann1987 [24]

Answer:

the third one

Step-by-step explanation:

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3 0
3 years ago
Extreme cold and hot temperatures are known to affect the operation of electronic components. Winter is approaching and you are
Musya8 [376]

Answer:

A 95% confidence interval for the true mean minimum temperature that will damage an iPod is between 2.55°F and 7.45°F

Test statistic(Z) = 2.31

P-value = 0.0104

Step-by-step explanation:

Step 1

Null hypothesis: The average damaging temperature of nine iPods is 5°F

Alternate hypothesis: The average damaging temperature of nine iPods differs from 5°F

Step 2

Mean=5°F, Sd=3, df=n-1=9-1=8

The t-value corresponding to 8 degrees of freedom and 95% confidence level (5% significance level) is 2.306

Confidence Interval(CI) = (mean + or - t×sd/√n)

CI = (5 + 2.306×3/√8) = 5 + 6.918/2.828= 5+2.45=7.45°F

CI = (5 - 2.306×3/√8) = 5-2.45 = 2.55°F

Z = (sample mean - population mean)/(sd÷√n) = (5-2.55)/(3÷√8) = 2.45/1.061 = 2.31

Step 3

Using the standard distribution table, the cumulative area to the left of Z = 2.31 is 0.9896

P-value = 1 - 0.9896 = 0.0104

Step 4

Conclusion: A 95% confidence interval for the true mean minimum temperature that will damage an iPod is between 2.55°F and 7.45°F

7 0
4 years ago
1. Write a survey question for which you would expect to collect numerical
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Answer:

How many siblings do you have?

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5 0
3 years ago
You have D dollars to buy fence to enclose a rectangular plot of land (see figure at right). The fence for the top and bottom co
alex41 [277]

The perimeter of the rectangular plot of land is given by the expression below

P=2x+2y

On the other hand, since the available money to buy fence is D dollars,

\begin{gathered} D=4(2x)+3(2y) \\ \Rightarrow D=8x+6y \\ D\rightarrow\text{ constant} \end{gathered}

Furthermore, the area of the enclosed land is given by

A=xy

Solving the second equation for x,

\begin{gathered} D=8x+6y \\ \Rightarrow x=\frac{D-6y}{8} \end{gathered}

Substituting into the equation for the area,

\begin{gathered} A=(\frac{D-6y}{8})y \\ \Rightarrow A=\frac{D}{8}y-\frac{3}{4}y^2 \end{gathered}

To find the maximum possible area, solve A'(y)=0, as shown below

\begin{gathered} A^{\prime}(y)=0 \\ \Rightarrow\frac{D}{8}-\frac{3}{2}y=0 \\ \Rightarrow\frac{3}{2}y=\frac{D}{8} \\ \Rightarrow y=\frac{D}{12} \end{gathered}

Therefore, the corresponding value of x is

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7 0
1 year ago
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