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2 years ago

50 points!

Mathematics

1 answer:

jekas [21]2 years ago

3 0

Answer:

Attaching answer for 1 below!!

2. C. -- y=2x+9

3. B. -- y=5/3x+3

Step-by-step explanation:

1. First screenshot below

2. To convert standard equations (Ax+By=C) to slope intercept (y=mx+b), what you do is preform inverse operations on A to both sides (modeled below). Then, the equation will look like this; By= -Ax+C. The last thing you need to do to cancel out B from the y is divide both sides by B, and you'll have your answer. So, I did that exact process with the equation and that's how I got C. Now, when you have no number next to the y, you don't need to divide, so it's a very simple process that way.

-2x+y=9

+2 +2

3. Same process for 2, except this time we divided by 3.

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There are 276 students.

Lynna [10]

Step-by-step explanation:

Number of males is

276 - 158 = 118

Number of males not enrolled

118 - 82 = 36

Number of females not enrolled

158 - 102 = 56

(a)

The table based on data is

<u> Enrolled Not enrolled Total </u>

<u>Female 102 56 158 </u>

Total 184 92 276

(b)

Percentage of students were males that went to magic college

enrolled male / total students = (use table above)
82/276*100% = 29.71% (rounded)

(c)

Percentage of females went to magic college

enrolled female / total female = (use table above)
102/158*100% = 64.56% (rounded)

7 0

1 year ago

Selina didn't use the distributive property correctly. Where did she go wrong? Explain your thinking.

GarryVolchara [31]

Answer:

PEMDAS

Step-by-step explanation:

Well, I don't know if there should be a picture of the problem that should go with the question. But a trick for solving distributive property is to use the trick PEMDAS In order.

For Example:

P-Paraenthese

E-Exponent

M-Multiply

D-Divide

A-Add

S-Subtract

NOTE!

Remember to always Multiply and divide BEFORE adding and subtracting.

Hoped this helped!

6 0

3 years ago

There are 6 Programmers and 8 Analysts working on a team at CIA. What is the unsimplified ratio of Programmers to Analysts?

Rzqust [24]

Answer: $\dfrac{6}{8}$

Step-by-step explanation:

Given

There are 6 Programmers and 8 Analysts working on a team at CIA.

Ratio of Programmers to analysts is

$\Rightarrow \dfrac{6}{8}$

Un-simplified ratio is $\dfrac{6}{8}$

Simplified ratio is $\dfrac{3}{4}$

6 0

2 years ago

What is the derivative of x times squaareo rot of x+ 6?

Dafna1 [17]

Hey there, hope I can help!

$\mathrm{Apply\:the\:Product\:Rule}: \left(f\cdot g\right)^'=f^'\cdot g+f\cdot g^'$
$f=x,\:g=\sqrt{x+6} \ \textgreater \ \frac{d}{dx}\left(x\right)\sqrt{x+6}+\frac{d}{dx}\left(\sqrt{x+6}\right)x \ \textgreater \ \frac{d}{dx}\left(x\right) \ \textgreater \ 1$

$\frac{d}{dx}\left(\sqrt{x+6}\right) \ \textgreater \ \mathrm{Apply\:the\:chain\:rule}: \frac{df\left(u\right)}{dx}=\frac{df}{du}\cdot \frac{du}{dx} \ \textgreater \ =\sqrt{u},\:\:u=x+6$
$\frac{d}{du}\left(\sqrt{u}\right)\frac{d}{dx}\left(x+6\right)$

$\frac{d}{du}\left(\sqrt{u}\right) \ \textgreater \ \mathrm{Apply\:radical\:rule}: \sqrt{a}=a^{\frac{1}{2}} \ \textgreater \ \frac{d}{du}\left(u^{\frac{1}{2}}\right)$
$\mathrm{Apply\:the\:Power\:Rule}: \frac{d}{dx}\left(x^a\right)=a\cdot x^{a-1} \ \textgreater \ \frac{1}{2}u^{\frac{1}{2}-1} \ \textgreater \ Simplify \ \textgreater \ \frac{1}{2\sqrt{u}}$

$\frac{d}{dx}\left(x+6\right) \ \textgreater \ \mathrm{Apply\:the\:Sum/Difference\:Rule}: \left(f\pm g\right)^'=f^'\pm g^'$
$\frac{d}{dx}\left(x\right)+\frac{d}{dx}\left(6\right)$

$\frac{d}{dx}\left(x\right) \ \textgreater \ 1$
$\frac{d}{dx}\left(6\right) \ \textgreater \ 0$

$\frac{1}{2\sqrt{u}}\cdot \:1 \ \textgreater \ \mathrm{Substitute\:back}\:u=x+6 \ \textgreater \ \frac{1}{2\sqrt{x+6}}\cdot \:1 \ \textgreater \ Simplify \ \textgreater \ \frac{1}{2\sqrt{x+6}}$

$1\cdot \sqrt{x+6}+\frac{1}{2\sqrt{x+6}}x \ \textgreater \ Simplify$

$1\cdot \sqrt{x+6} \ \textgreater \ \sqrt{x+6}$
$\frac{1}{2\sqrt{x+6}}x \ \textgreater \ \frac{x}{2\sqrt{x+6}}$
$\sqrt{x+6}+\frac{x}{2\sqrt{x+6}}$

$\mathrm{Convert\:element\:to\:fraction}: \sqrt{x+6}=\frac{\sqrt{x+6}}{1} \ \textgreater \ \frac{x}{2\sqrt{x+6}}+\frac{\sqrt{x+6}}{1}$

Find the LCD
$2\sqrt{x+6} \ \textgreater \ \mathrm{Adjust\:Fractions\:based\:on\:the\:LCD} \ \textgreater \ \frac{x}{2\sqrt{x+6}}+\frac{\sqrt{x+6}\cdot \:2\sqrt{x+6}}{2\sqrt{x+6}}$

$Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions$
$\frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c} \ \textgreater \ \frac{x+2\sqrt{x+6}\sqrt{x+6}}{2\sqrt{x+6}}$

$x+2\sqrt{x+6}\sqrt{x+6} \ \textgreater \ \mathrm{Apply\:exponent\:rule}: \:a^b\cdot \:a^c=a^{b+c}$
$\sqrt{x+6}\sqrt{x+6}=\:\left(x+6\right)^{\frac{1}{2}+\frac{1}{2}}=\:\left(x+6\right)^1=\:x+6 \ \textgreater \ x+2\left(x+6\right)$
$\frac{x+2\left(x+6\right)}{2\sqrt{x+6}}$

$x+2\left(x+6\right) \ \textgreater \ 2\left(x+6\right) \ \textgreater \ 2\cdot \:x+2\cdot \:6 \ \textgreater \ 2x+12 \ \textgreater \ x+2x+12$
$3x+12$

Therefore the derivative of the given equation is
$\frac{3x+12}{2\sqrt{x+6}}$

Hope this helps!

8 0

2 years ago

What is the equation in slope-intercept form of a line that is perpendicular to y=2x+2 and passes through the point (4, 3)?

Ostrovityanka [42]

<h2>Answer: y = - ¹/₂ x + 5 </h2>

<h3>Step-by-step explanation: </h3>

<u>Find the slope of the perpendicular line</u>

When two lines are perpendicular, the product of their slopes is -1. This means that the slopes are negative-reciprocals of each other.

⇒ if the slope of this line = 2 (y = 2x + 2)

then the slope of the perpendicular line (m) = - ¹/₂

<u>Determine the equation</u>

We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line:

⇒ y - 3 = - ¹/₂ (x - 4)

We can also write the equation in the slope-intercept form by making y the subject of the equation and expanding the bracket to simplify:

since y - 3 = - ¹/₂ (x - 4)

y = - ¹/₂ x + 5 (in slope-intercept form)

8 0

2 years ago