Shawna and her best friend Keisha go shopping.
The function p(x) = 3x^4 + 2x^3 − 4x^2 + 21 represents how much money each girl spent based on the number of hours they were shopping. If Shawna and Keisha each go shopping for 2 hours, how much money did they spend together?

$37
$69
$101
$138

Answer:

[tex]f'(x)=1+\ln x[/tex]

Step-by-step explanation:

[tex]f'(x)[/tex] is notation for the first derivative of [tex]f(x)[/tex].

Recall the product rule:

[tex](f\cdot g)'=f'\cdot g+g'\cdot f[/tex]

Therefore, we have:

[tex]\displaystyle \frac{d}{dx}(x\ln x)=\frac{d}{dx}(x)\cdot \ln(x)+\frac{d}{dx}(\ln x)\cdot x[/tex]

Note that:

[tex]\displaystyle \frac{d}{dx}(x)=1,\\\\\frac{d}{dx}(\ln x)=\frac{1}{x}[/tex]

Simplify:

[tex]\displaystyle \frac{d}{dx}(x\ln x)=1\cdot \ln x+\frac{1}{x}\cdot x, \\\\\frac{d}{dx}(x\ln x)= \ln x+1=\boxed{1+\ln x}[/tex]

The derivative is:

[tex] \bold{f(x) \: = \: x \: \times \: (In(x))}[/tex]

[tex] \bold{f'(x) \: = \: \frac{d}{dx} (x \: \times \: In(x))}[/tex]

[tex] \bold{f'(x) \: = \: \frac{d}{dx} (x) \: \times \: In(x) \: + \: x \: \times \: \frac{d}{dx} (In(x))}[/tex]

[tex] \bold{f'(x) \: = \: 1In(x) \: + \: x \: \times \frac{1}{x} }[/tex]

[tex] \bold{f'(x) \: = \: In(x) \: + \: x \: \times \: \frac{1}{x} }[/tex]

[tex] \boxed{ \bold{f'(x) \: = \: In(x) \: + \: 1}}[/tex]

Answer:

By adding

please mark me brainliest

Step-by-step explanation:

Find x-intercept (where line cuts the x axis) by substituting y=0.

Find y-intercept by substituting x=0.

Once you get those 2 intercepts, join them with a straight line.

Answer:

17

Step-by-step explanation:

You need to add 4 degrees to get to 0.

You need to add 13 degrees to get to 13

The total = 4 + 13 = 17                      

Answer:

Part A)

Approximately 318.1318 meters.

Part B)

Approximately 137.7551 meters.

Step-by-step explanation:

The path of a projectile is given by the equation:

[tex]\displaystyle y = \sqrt{3} x -\frac{49x^2}{9000}[/tex]

Part A)

The range of the projectile will be given by the difference between its starting point and landing point. In other words, its two zeros.

Let y = 0 and solve for x:

[tex]\displaystyle 0 = \sqrt{3}x - \frac{49x^2}{9000}[/tex]

Factor:

[tex]\displaystyle 0 = x\left(\sqrt{3} - \frac{49x}{9000}\right)[/tex]

Zero Product Property:

[tex]\displaystyle x = 0 \text{ or } \sqrt{3} - \frac{49x}{9000} = 0[/tex]

Solve for each case:

[tex]\displaystyle x = 0 \text{ or } x = \frac{9000\sqrt{3}}{49}\approx 318.1318[/tex]

Hence, the range of the projectile is approximately (318.1318 - 0) or 318.1318 meters.

Part B)

Since the equation is a quadratic, the maximum height is given by its vertex. Recall that the vertex of a quadratic is given by:

[tex]\displaystyle \text{Vertex} = \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]

In this case, a = -49/9000 and b = √3.

Find the x-coordinate of the vertex:

[tex]\displaystyle x = - \frac{(\sqrt{3})}{2\left(\dfrac{-49}{9000}\right)} = \frac{4500\sqrt{3}}{49}[/tex]

Then the maximum height will be:

[tex]\displaystyle \displaystyle \begin{aligned} y\left(\frac{4500\sqrt{3}}{49}\right) &=\sqrt{3} \left(\frac{4500\sqrt{3}}{49}\right) -\frac{49\left(\dfrac{4500\sqrt{3}}{49}\right)^2}{9000} \\ \\ &= \frac{13500}{49} -\frac{6750}{49}\\ \\ &=\frac{6750}{49}\\ \\ &\approx 137.7551\text{ meters}\end{aligned}[/tex]

The maximum height reached by the projectile will be 137.7551 meters.

Answer: 17

Step-by-step explanation:

since there are two minuses, you change them to a plus and add, ending up with 5+12 to get 17

Answer:

so

Step-by-step explanation:

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Step-by-step explanation:

3x²+1+8=27

3x²+9=2

3x²=27-9

3x²=19

x²=19/3

[tex]x = \frac{ \sqrt[]{19} }{ \sqrt{3} } [/tex]

Answer:

[tex]3^{2x} + 1 + 18 = 27\\ 3^{2x} = 18\\2x = log_{3} 18[/tex]

Step-by-step explanation:

Answer:

5.975

Step-by-step explanation:

Step-by-step explanation:

6x-2+9y-3y-3x

6x-3x-2+9y-3y

3x-2+6y

Therefore its 3x-2+6y.

Step-by-step explanation:

if I understand the typed information here, we have

(-4 + 8x) + 3 > -4

so, I am looking at that :

-4 + 8x + 3 > -4

let's first add 4 on both sides

8x + 3 > 0

then subtract -3 on both sides

8x > -3

and finally divide both sides by 8

x > -3/8

since we never multiplied or divided by a negative number, the inequality sign stays the same.

so, this inequality is true for all x > -3/8

Answer:

rational function is the correct answer

Answer:

No

Step-by-step explanation:

Any point that aligns on the line of y = 2 is a solution. But (8, -2) falls below that line since the point's y-coordinate is equal to -2, not 2. Hope this helps!

Answer:

the addition property of equality

.the multiplication property of equality

Step-by-step explanation:

1/3x - 6 =11

Add 6 to each side using the addition property of equality

1/3x-6+6 = 11+6

1/3x = 17

Multiply each side by 3, using the multiplication property of equality

1/3x *3 = 17*3

x = 54

Answer:

No

Step-by-step explanation:

[5+3x] is an expression that cannot be added because 5 is a natural interger but 3x is an unknown

and therefore it cannot be divided by 2 to get 4

Better example :

if the question will give 4x , then

it should be [5x+3x]/2 = 8x/2 = 4x

it's obvious from the example I gave that 8x can be divided by 2 to give 4x

Step-by-step explanation:

-5c+5c+2c–6c–16=c

-16c - 16=c

-16 = c + 16c

-16 = 17c

-16/17 = c

Answer:

f(m+n+p) = 9^(m+n+p)

while f(m) × f(n) × f(p) = 9^m+9^n+9^p = 9^(m+n+p)

so the second property explains why it's a + instead of ×

Answer:

B

Step-by-step explanation:

Answer:

Hope its help you...........

Answer:

It is (a + b)(b + c)

Step-by-step explanation:

[tex]ab + bc + {b}^{2} + ac[/tex]

arrange the function:

[tex] = (ab + ac) + ( {b}^{2} + bc)[/tex]

factorise out common terms [ a and b ]:

[tex] = a(b + c) + b(b + c)[/tex]

form a bracket of factors:

[tex] = (a + b)(b + c)[/tex]

Step-by-step explanation:

4(1-3x)+7x-8

4-12x+7x-8

-12x+7x+4-8

-5x-4

Answer:

30%

Step-by-step explanation:

14+ 18+ 28 = 60

18/60 × 100 = 30%

Answer:

[tex] \frac{18}{60} = \frac{3}{10} = 30\%[/tex]

Step-by-step explanation:

Total token sample = 14 + 18 + 28 = 60

Frequency of blue:

[tex] = \frac{18}{60} \: [/tex]

[tex] = \frac{18}{60} \times 100\%[/tex]

[tex] = 30\%[/tex]

Answer:

x=50°

Step-by-step explanation:

x+3°+x+20°+x+7°=180°

or,3x+30°=180°

or,3x=150°

or,x=50°

Answer:

50

Step-by-step explanation:

→ First add all the angles together as angles on a straight line add to 180°

x + 3 + x + 20 + x + 7 = 180

→ Simplify

3x + 30 = 180

→ Minus 30 from both sides

3x = 150

→ Divide both sides by 3

x = 50

Answer:

11703.7 metres

Step-by-step explanation:

* means multiply

/ means divide

plug in the values

T=26- h/500

-53 =  26- h/500

-53 -26 = h/500

-79 = h/500

-79 * 500 = h

-39500 = h

-39500 is in feet

3³/8 =

39500 / 3.375 =

11703.7037037 metres

Answer:

10

Step-by-step explanation:

By using intersecting chord theorem:

NH.HT=MH.HY

(x+20)*8=12*20

x+20=12*20/8

x+20=240/8

x+20=30

x=30-20

x=10

Step-by-step explanation:

18 2+6(4+1)-2

18 8(5)-2

18 40-2

18 38

18×38

multiply it to get your answer

Answer:

[tex]a. \: \: x = 3 \: \: and \: 5[/tex]

Step-by-step explanation:

[tex]a. \: \: \: x^2-8x+ 15 = 0 \\ {x}^{2} - 5x - 3x + 15 = 0 \\ x(x - 5) - 3(x - 5) = 0 \\ (x - 3)(x - 5) = 0 \\ x = 3 \: and \: 5[/tex]

[tex]b. \: \: 2x^2 - 5x - 6 =0 \\ x = \frac{5± \sqrt{73} }{4} [/tex]