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4 years ago

-9m-8+4m combine like terms ?

Mathematics

1 answer:

KatRina [158]4 years ago

5 0

Answer:

-8-5m

Step-by-step explanation:

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Looking to recieve help on this practice question, thank you!

dimaraw [331]

In general, the standard form of an ellipse is

$\begin{gathered} \frac{(x-h){}^2}{a^2}+\frac{(y-k)^2}{b^2}=1 \\ a,b,h,k\rightarrow\text{ constants} \\ (h,k)\rightarrow\text{ center} \end{gathered}$

Thus, in our case, complete the squares for x and y, as shown below

$\begin{gathered} 3x^2-12x=3(x^2-4x) \\ and \\ x^2-4x+c^2=(x-c)^2 \end{gathered}$

Finding c,

$\begin{gathered} \Rightarrow x^2-4x+c^2=x^2-2cx+c^2 \\ \Rightarrow-4x=-2cx \\ \Rightarrow c=2 \\ \Rightarrow3x^2-12x+3*4=3(x^2-4x+4)=3(x-2)^2 \end{gathered}$

Therefore, after adding +12 to both sides of the initial equation, we get,

$\begin{gathered} 3x^2+5y^2-12x+30y+42+12=12 \\ \Rightarrow3(x-2)^2+5y^2+30y+42=12 \end{gathered}$

Similarly, completing the square for the variable y,

$\begin{gathered} 5y^2+30y=5(y^2+6y) \\ \Rightarrow y^2+6y+c^2=(y-c)^2 \\ \Rightarrow y^2+6y+c^2=y^2-2cy+c^2 \\ \Rightarrow6=-2c \\ \Rightarrow c=-3 \end{gathered}$

Thus,

$\begin{gathered} \Rightarrow5y^2+30y+5*(-3)^2=5(y+3)^2 \\ \Rightarrow5y^2+30y+45=5(y+3)^2 \end{gathered}$

Therefore, after adding +45 to the initial expression

$\begin{gathered} \Rightarrow3(x-2)^2+5y^2+30y+42+45=12+45 \\ \Rightarrow3(x-2)^2+5(y+3)^2+42=57 \end{gathered}$

Then,

$\begin{gathered} \Rightarrow3(x-2)^2+5(y+3)^2=15 \\ \Rightarrow\frac{3(x-2)^2}{15}+\frac{5(y+3)^2}{15}=1 \\ \Rightarrow\frac{(x-2)^2}{5}+\frac{(y+3)^2}{3}=1 \end{gathered}$ <h2>The answer is the expression immediately above this line.</h2>

The center of the ellipse, its minor axis, and major axis are

$\begin{gathered} center\rightarrow(h,k)=(2,-3) \\ semi-minor\text{ axis}\rightarrow\sqrt{3} \\ semi-major\text{ axis}\rightarrow\sqrt{5} \end{gathered}$

7 0

1 year ago

Need help with these 3 ! Please help me

Slav-nsk [51]

21. The number who responded is 600 -150 = 450. Expressed as a fraction of the total, that is
450/600 = (150*3)/(150*4) = 3/4

22. Total fabric used is
6*(3 1/6) +8*(2 3/4) = 19 +22 = 41 . . . . yards
Fabric unused is . . .
50 yd -41 yd = 9 yd

23. The problem statement is ambiguous. We suppose it is intended to say that the stock increased by 1/4 of its original value. In that case, the present value is
$2000 +$2000*(1/4) = $2500
_____
An alternate interpretation of the statement is that the amount of increase was 1/4. In that case, the present value is
$2000 + 0.25 = $2000.25

5 0

3 years ago

28% of consumers read the ingredients listed on a product's label.

kotegsom [21]

Answer:

The probability that between 64 and 90 of them read the ingredients listed on a product's label is 0.82.

Step-by-step explanation:

We know the proportion of the population, that is π=0.28.

The standard deviation for this sampling distribution is

$\sigma=\sqrt{\frac{\pi(1-\pi)}{N} } =\sqrt{\frac{0.28*0.72}{256} }= 0.028$

The value 64 represents a proportion of p=64/256=0.25, and the value 90 represents p=90/256=0.35.

With these values, we can calculate the z-values.

$z_1=\frac{p_1-\pi}{\sigma} =\frac{0.25-0.28}{0.028} =\frac{-0.03}{0.028} =-1.07\\\\z_2=\frac{p_2-\pi}{\sigma} =\frac{0.35-0.28}{0.028} =\frac{0.07}{0.028} =2.5$