Which graph shows the correct solution to the
inequality below?
3(2x + 3) > 3(x + 12)
ANSWER QUICK PLEASE

Answer:

see explanation

Step-by-step explanation:

Using the product rule

Given

y = f(x)g(x) , then

[tex]\frac{dy}{dx}[/tex] = f(x).g'(x) + g(x).f'(x) ← product rule

(a)

let

f(x) = (3x - 1)³ , then using the chain rule

f'(x) = 3(3x - 1)² × [tex]\frac{d}{dx}[/tex](3x - 1) = 3(3x - 1)² × 3 = 9(3x - 1)²

let

g(x) = 2x + 5 ⇒ g'(x) = 2

Then

[tex]\frac{dy}{dx}[/tex] = (3x - 1)³ . 2 + (2x + 5) × 9(3x - 1)²

    = 2(3x - 1)³ +9(3x - 1)²(2x + 5) ← factor out (3x - 1)²

    = (3x - 1)²[ 2(3x - 1) + 9(2x + 5) ]

    = (3x - 1)² [ 6x - 2 + 18x + 45 ]

    = (3x - 1)²(24x + 43)

--------------------------------------------------------------

(b)

let

f(x) = 3x - 2 ⇒ f'(x) = 3

let

g(x) = 2x² + 3 ⇒ g'(x) = 4x

Then

[tex]\frac{dy}{dx}[/tex] = (3x - 2).4x + (2x² + 3). 3 ← distribute parenthesis

    = 12x² - 8x + 6x² + 9

    = 12x² - 8x + 9

Note

It is usual to simplify after differentiating the expressions

Answer:

[tex]h(0) = 10[/tex]

[tex]h(4) = NaN[/tex] (Not a number)

Step-by-step explanation:

According to the statement, we get the following piecewise function:

[tex]h(x) = \left\{ \begin{array}{ccc}3\cdot x -4,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x < 0\\2\cdot x^{2}-3\cdot x + 10,\,\,\,\,\, 0\le x < 4\\2^{x}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, x\ge 5\end{array}[/tex]

The value of the function when [tex]x = 0[/tex] is:

[tex]h(0) = 2\cdot (0)^{3}-3\cdot (0) +10[/tex]

[tex]h(0) = 10[/tex]

The value of the function when [tex]x = 4[/tex] is undefined, since 4 is out of any of the intervals covered by [tex]h(x)[/tex].

[tex]h(4) = NaN[/tex] (Not a number)

Answer: h(0)=10

h(4)=30

Step-by-step explanation:

Answer:

Step-by-step explanation:

It's C.

Answer:

A company provides commisssion to its agent at the following rate.

-0.5% in the sale upto Rs.15 lakh

-1% in the sale from 15 lakh to Rs.25 lakh

-1.5% in the sale from Rs.25 to Rs.40 lakh

-2% in the sale above Rs.40 lakh

calculate the amount of commission that can be obtained from the following sale amount by using the above rate of commission is 38 lakh

Answer:

2,200

Step-by-step explanation:

From the above, we were given that;

Total students in Christine's middle school = 900

Teachers in Christine's middle school = 45 teachers

Local high school = 110 teachers

Then, we can write an equation ratio and solve it.

900 students / X = 45 teachers / 110 teachers

If we cross multiply, we'll get

900 × 110 = 45 × X

45X = 99,000

Divide both sides by 45

45X/45 = 99,000/45

X = 2,200

Therefore, Christine would find 2,200 students when she gets to high school.

Answer:

b) similar by SSS theorem

Step-by-step explanation:

Answer:

i'm not sure what is it ?

Step-by-step explanation:

Answer:

The percent of interest is 12.3% per year

Step-by-step explanation:

According to the question Elwood invested 5000 $ in market account

The market account gives the compound interest annually

let p be the interest per year then

At the end of 1st year

amount =(1+0.p) x 5000  = 1.p x 5000

similarly at the end of 2nd year

amount =(1+0.p) x(1+0.p)x 5000  = [tex](1.p)^{2}[/tex] x 5000

similarly at the end of 3rd year

amount = 7100 $ = [tex](1.p)^3[/tex] x 5000

⇒ [tex]\frac{71}{50}[/tex] = [tex](1.p)^3[/tex]  

1.392 =  [tex](1.p)^3[/tex]

on further solving we get

1.p = [tex](1.42)^{1/3}[/tex] = 1.123

thus 1.p = 1 + 0.p = 1.123

thus p = 0.123

thus the percent of interest is 12.3% per year

Answer:

drop down 1 a slower rate per year

drop down 2 670

Step-by-step explanation:

as in three years you get $7100

you take that and subtract it by your starting amount (5000)

7100-5000= 2100

then divide 2100 by the number of years (3)

to get your annual rate of 700$

then you take the 8 year total and subtract it from your 3 year total

10350-7100= 3250

Then divide that by 5 because that how many years it has been

to get the annual rate of 650

making the 5 year rate slower.

The to find the average rate over all 8 year you take 10350 and subtract it from your starting number 5000

10350-5000= 5350

then take 5350 and divide it by the number of years (8)

you then get you average rate of 668.75

668.75=670

Hope this helps!

Answer:

f(3) = -14

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

f(x) = -2x² + x + 1

f(3) is x = 3

Step 2: Evaluate

Answer:

2 14/18

Step-by-step explanation:

because you just multiply the numerators and denomitors you must make an improper fraction first though

Answer:

32

Step-by-step explanation:

QC = 16 and CS = 16 so 16 + 16 = 32

Answer:

where is the question though

Step-by-step explanation:

Answer:

what

Step-by-step explanation:

Answer:

Answer is C...........................

Step-by-step explanation:

Answer:

C.) y = -2x

Step-by-step explanation:

To solve for y, u gotta divide both sides by -2 to get y by itself. When u do that, u get -2x.

Answer:

Question 4 is a statistical question aka answer D

Step-by-step explanation:

Correct on edge

Answer:

Your answer is D i guess

Step-by-step explanation:

Here you go mate

step 1

30 - 5(15- 10)  equation/question

step 2

30 - 5(15- 10)  simplify

30-(5)^2

30-25

answer

5

Answer:

D. 19.47

Step-by-step explanation:

91/113 = 80.53

100.00-80.53 = 19.47

Answer:

19.47% to the nearest hundredth.

Step-by-step explanation:

Value of the error = 113 - 91 = 22.

Percent error = (22/113) * 100

= 19.47.

Answer:

At least 15 weeks

Step-by-step explanation:

If Ella needs at least $360, she will have to save her $25 constantly for about 15 weeks.

25*15=375, which is more than 360, so she will have leftover money.

Answer:

2 weeks + 1day

Step-by-step explanation:

7 days a week. 7 + 7 = 14

25 x 14 = $350, missing another 10 dollars.

25 x 15(adding a extra day) = 275.

in change, you have 15 dollars left.

Answer:

d is false

Step-by-step explanation:

water = 14 and cola is 28

you are half as likely to select a water than cola

Answer:

92

Step-by-step explanation:

161 divided by 7 is 23. so you just multiply 4 by 23. And that gets you the answer. Hope this helps:)

Answer:

x=92

Solve for x by simplifying both sides of the equation, then isolating the variable. hopes this helps have a great day <3 :)

Answer:

X=-2

Step-by-step explanation:

Let's solve your equation step-by-step.

4(4x−4)+x+4=−46

Step 1: Simplify both sides of the equation.

4(4x−4)+x+4=−46

(4)(4x)+(4)(−4)+x+4=−46(Distribute)

16x+−16+x+4=−46

(16x+x)+(−16+4)=−46(Combine Like Terms)

17x+−12=−46

17x−12=−46

Step 2: Add 12 to both sides.

17x−12+12=−46+12

17x=−34

Step 3: Divide both sides by 17.

17x

17

=

−34

17

x=−2

Answer:

x=−2

Answer:

x=2

Step-by-step explanation:

Hope this helps!! If you need step by step I'll comment it in the comments.

Answer:

The person must leave the money for approximately 14.8 years.

Step-by-step explanation:

This can be calculated using the formula for calculating the future value as follows:

FV = PV * (1 + r)^n …………………………………. (1)

Where;

FV = Future value of the investment = 5600

PV = Present value of the investment = 3000

r = semiannual interest rate = 4.25% / 2 = 0.0425 / 2 = 0.02125

n = number of semiannuals = ?

Substitute the values into equation (1) and solve for n, we have:

5600 = 3000 * (1 + 0.02125)^n

5600 / 3000 = 1.02125^n

1.02125^n = 1.86666666666667

Loglinearizing both sides, we have:

nlog1.02125 = log1.86666666666667

n = log1.86666666666667 / log1.02125

n = 0.271066772286539 / 0.0091320695404719

n = 29.6829509548973

Since n is number of semiannuals, we divide the answer by 2 obtain the number of years as follows:

Number of years = 29.6829509548973 / 2 = 14.8414754774487

Rounding to the nearest tenth of year, we have:

Number of years = 14.8

Therefore, the person must leave the money for approximately 14.8 years.

Answer:

1/2 over 7/8

Step-by-step explanation:

becauseim smartt

Answer:

the bridge is 90ft long.

Step-by-step explanation:

3/18=15/x

solve for x

use reciprocals to get x as numerator for easier calculation

18/3=x/15

270/3=x

x=90ft

Answer:

-14

Step-by-step explanation:

Plug 3 in for x

-2 (3)² + 3 + 1

-2 (9) + 3 + 1

-18 + 3 + 1

-14

Answer:

f(3) = -14

Step-by-step explanation:

[tex]f(x)=-2x^{2} +x+1\\f(3)=-2(3)^2+3+1\\f(3) = -2(9)+4\\f(3) = -18+4\\f(3) = -14[/tex]

Answer:

1)

D. 3:2

2)

B. 40%

as, no. of girls=8

total no. of students =12+8=20

now,

percentage of girls=no.of girls/total no. of students ×100%

=8/20×100%

=40%

Answer:

13

Step-by-step explanation: If each glass can hold 1 liter than 13 glasses can hold 13 liters.

Answer:

perimeter of the following figure will be equal to 440 miles.

Step-by-step explanation:

perimeter refers to measure of total boundaries of a figure

hence perimeter will be the sum off all sides

so , P = 170 + 30 + 160 +80 = 440 miles

i hope u got it.

have a great day .