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3 years ago

14

Serena is writing an expression that is equivalent to 12ab - 6b, but she has not completed it. ? (2a - 1) What is missing from t

he expression?

1 answer:

zysi [14]3 years ago

3 0

12ab - 6b = (2a-1)(6b)

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Which polynomial function has a leading coefficient of 1 and roots /7 and - /3 with multiplicity 1?

VladimirAG [237]

Answer:

A. f(x) = (x - √2)(x + √3)

Step-by-step explanation:

Leading coefficient is 1, multiplicity is 1, roots are √2 and -√3. It means the function is the product of two binomials.

<u>The function with the roots of a and b is:</u>

f(x) = (x - a)(x - b)

<u>Substitute and and b:</u>

f(x) = (x - √2)(x - (-√3)) ⇒
f(x) = (x - √2)(x + √3)

Correct choice is A

4 0

3 years ago

Read 2 more answers

A piece of wire 19 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral tria

mr Goodwill [35]

Answer: 8.26 m

Step-by-step explanation:

$Let s be the length of the wire used for the square. \\Let $t$ be the length of the wire used for the triangle. \\Let $A_{S}$ be the area of the square. \\Let ${A}_{T}}$ be the area of the triangle. \\One side of the square is $\frac{s}{4}$ \\Therefore,we know that,$$A_{S}=\left(\frac{s}{4}\right)^{2}=\frac{s^{2}}{16}$

$The formula for the area of an equilateral triangle is, $A=\frac{\sqrt{3}}{4} a^{2}$ where $a$ is the length of one side,And one side of our triangle is $\frac{t}{3}$So,We know that,$$A_{T}=\frac{\sqrt{3}}{4}\left(\frac{t}{3}\right)^{2}$$We have to find the value of "s" such that,$\mathrm{s}+\mathrm{t}=19$ hence, $\mathrm{t}=19-\mathrm{s}$And$$A_{S}+A_{T}=A_{S+T}$

$$$Therefore,$$\begin{aligned}&A_{T}=\frac{\sqrt{3}}{4}\left(\frac{(19-s)}{3}\right)^{2}=\frac{\sqrt{3}(19-s)^{2}}{36} \\&A_{T+S}=\frac{s^{2}}{16}+\frac{\sqrt{3}(19-s)^{2}}{36}\end{aligned}$

$Differentiating the above equation with respect to s we get,$$A^{\prime}{ }_{T+S}=\frac{s}{8}-\frac{\sqrt{3}(19-s)}{18}$$Now we solve $A_{S+T}^{\prime}=0$$$\begin{aligned}&\Rightarrow \frac{s}{8}-\frac{\sqrt{3}(19-s)}{18}=0 \\&\Rightarrow \frac{s}{8}=\frac{\sqrt{3}(19-s)}{18}\end{aligned}$$Cross multiply,$$\begin{aligned}&18 s=8 \sqrt{3}(19-s) \\&18 s=152 \sqrt{3}-8 \sqrt{3} s \\&(18+8 \sqrt{3}) s=152 \sqrt{3} \\&s=\frac{152 \sqrt{3}}{(18+8 \sqrt{3})} \approx 8.26\end{aligned}$

$The domain of $s$ is $[0,19]$.So the endpoints are 0 and 19$$\begin{aligned}&A_{T+S}(0)=\frac{0^{2}}{16}+\frac{\sqrt{3}(19-0)^{2}}{36} \approx 17.36 \\&A_{T+S}(8.26)=\frac{8.26^{2}}{16}+\frac{\sqrt{3}(19-8.26)^{2}}{36} \approx 9.81 \\&A_{T+S}(19)=\frac{19^{2}}{16}+\frac{\sqrt{3}(19-19)^{2}}{36}=22.56\end{aligned}$

$$$Therefore, for the minimum area, $8.26 \mathrm{~m}$ should be used for the square$

8 0

2 years ago

ZOHK is a straight angle. Find mZLAK.

Kazeer [188]

Answer:

LHK = 101

Step-by-step explanation:

LGK + LHK = 180

79 + LHK = 180

LHK = 180 -79

LHK = 101

3 0

4 years ago

Read 2 more answers

100 points and brainiest answer this right if there is already brainiest u get a thank you 7x multiply by 19 get x by itslef

zloy xaker [14]

Answer:

Step-by-step explanation:

7x × 19

= 133x

4 0

3 years ago

Richard practice each of three piano solos for 5/12 hour how long did he practice in all

Nonamiya [84]

3 * 5/12 = 15/12 = 1 1/4 hrs total

6 0

3 years ago