Ray estimates that it will cost $400,000 to send his daughter to a private college in 18 years. He currently has $90,000 to deposit in an account. What simple interest rate must his account have to reach a balance of $400,000 in 18 years?

Answer:

[tex]\displaystyle \frac{d}{dx} \Big [ \frac{3}{x^2} \Big ]=-\frac{6}{x^3}[/tex]

Step-by-step explanation:

We can use either the Power Rule or the Quotient Rule to find the derivative of 3/x².

Rewrite [tex]\displaystyle \frac{3}{x^2}[/tex] as [tex]\displaystyle 3\cdot \frac{1}{x^2}[/tex] which is equivalent to [tex]3\cdot x^-^2[/tex].

Now we can apply the power rule to 3x⁻². Subtract 1 from the exponent and multiply the coefficient by -2.

This can be rewritten as [tex]\displaystyle -\frac{6}{x^3}[/tex].

Substituting 3 for f(x) and x² for g(x), we get:

Simplify.

Using exponent rules, we can rewrite this as:

This can be rewritten as [tex]\displaystyle -\frac{6}{x^3}[/tex], which is the same as what we got using the product rule.

Answer:

[tex]\displaystyle \frac{d}{d x}\left[\frac{3}{x^2}\right] = -\frac{6}{x^{3}}[/tex].

Step-by-step explanation:

Let [tex]f(x)[/tex] and [tex]g(x)[/tex] denote two functions of [tex]x[/tex]. Assume that [tex]g(x) \ne 0[/tex]. The quotient rule states that:

[tex]\displaystyle \frac{d}{d x}\left[\frac{f(x)}{g(x)}\right] = \frac{{f}^\prime(x) \cdot g(x) - f(x) \cdot g^{\prime}(x)}{{(g(x))}^2}[/tex].

In this question:

Find [tex]{f}^{\prime}(x)[/tex] and [tex]{g}^{\prime}(x)[/tex].

Notice that the value of [tex]f(x)[/tex] is constantly [tex]3[/tex] regardless of the value of [tex]x[/tex]. By the constant rule, [tex]{f}^{\prime}(x) = 0[/tex].

For [tex]{g}^{\prime}(x)[/tex], consider the power rule:

if [tex]m[/tex] represents a rational number (such as [tex]2[/tex],) then by the power rule, [tex]\displaystyle \frac{d}{d x}\left[{x}^{m}\right] = m\, {x}^{m-1}[/tex].

Apply this rule to find [tex]{g}^{\prime}(x)[/tex].

[tex]\begin{aligned}{g}^{\prime}(x) &= \frac{d}{d x} \left[x^{2}\right] \\ &= 2\, x^{2 - 1} \\ &= 2\, x\end{aligned}[/tex].

Substitute [tex]f(x) = 3[/tex], [tex]{f}^{\prime}(x) = 0[/tex], [tex]g(x) = x^{2}[/tex], and [tex]{g}^{\prime}(x) = 2\, x[/tex] into the quotient rule expression to find [tex]\displaystyle \frac{d}{d x}\left[\frac{3}{{x}^{2}}\right][/tex]:

[tex]\begin{aligned}&\; \frac{d}{d x}\left[\frac{3}{{x}^{2}}\right] \quad \genfrac{}{}{0em}{}{\leftarrow f(x) = 3}{\leftarrow g(x) = {x}^{2}} \\ =&\; \frac{d}{d x}\left[\frac{f(x)}{g(x)}\right]\\ =&\; \frac{{f}^\prime(x) \cdot g(x) - f(x) \cdot g^{\prime}(x)}{{(g(x))}^2} \\ =& \; \frac{0 \, x^2 - 3\, (2\, x)}{\left({x}^{2}\right)} \\ =&\; -\frac{6}{x^{3}}\end{aligned}[/tex].

Therefore, [tex]\displaystyle \frac{d}{d x}\left[\frac{3}{{x}^{2}}\right] = -\frac{6}{x^{3}}[/tex].

Answer:

Step-by-step explanation:

4x3 is the max of 12

Answer:

4 more students

Step-by-step explanation:

10% of 40 is 4, since the membership went up by 10% it is clear that there are 4 more students that joined the chess club.

Answer:

10/100*40

=4 more students joined the club

Step-by-step explanation:

Answer:

13 in

Step-by-step explanation:

just add all the numbers lol

Answer:

the perimeter of the triangle is 13[tex]in^{2}[/tex]

Step-by-step explanation:

All you have to do is add up all the sides together, but first we need to find a common denominator, and it can be 12

[tex]3\frac{1}{3}[/tex] = [tex]\frac{10}{3} = \frac{40}{12}[/tex] ( i multiplied them by 4 (numerator and denominator))

[tex]4\frac{1}{6} = \frac{25}{6} = \frac{50}{12}[/tex] ( i multiplied them by 2 (numerator and denominator))

[tex]5\frac{1}{2} = \frac{11}{2} = \frac{66}{12}[/tex] ( i multiplied them by 6 (numerator and denominator))

Now that you have a common denominator for all 3 fractions, you can now add them all up

[tex]\frac{40}{12} + \frac{50}{12} + \frac{66}{12}[/tex]

Now to add, the denominator has to stay the same (12), and add up all the numerators

[tex]\frac{40}{12} + \frac{50}{12} = \frac{90}{12} + \frac{66}{12} = \frac{156}{12} = 13 (simplified)[/tex]

Hope this helped!

Answer: 1+1 = 2 :)

Step-by-step explanation:

Answer:

1+1=2

this is a very simple question

Answer: The perimeter is when you add all of the sides together, and the area is when you multiply the sides together

Step-by-step explanation:

Answer:

6. 11.3 Miles

7. 1.5 Miles

8. No he would need 26 Miles , he only has 25 Miles.

9. 11.25 Miles

10. Not really it slightly goes over by about .80

Answer:

6: 15miles

7: 17miles

8: No, because just by going to the grocery is 13miles (times2) that's 26

9: 11.2 (not sure)

10: No, he said 5miles, the park is 5.8miles away from his house. (you don't have to but rounded is 6miles so he cant reach the park)

Step-by-step explanation:

Step-by-step explanation:

[tex] \sqrt{7 \times \frac{1}{9} } - \sqrt[3]{ \frac{297}{11} } \\ = \sqrt{ \frac{7}{9} } - \sqrt[3]{27} \\ = \frac{ \sqrt{7} }{3} - 3 \\ = \frac{ \sqrt{7} - 9}{3} [/tex]

Answer:

(- 1, 4 )

Step-by-step explanation:

Given the 2 equations

3x + 4y = 13 → (1)

2x - 2y = - 10 → (2)

Multiplying (2) by 2 and adding to (1) eliminates the term in y

4x - 4y = - 20 → (3)

Add (1) and (3) term by term to eliminate y, that is

7x + 0 = - 7

7x = - 7 ( divide both sides by 7 )

x = - 1

Substitute x = - 1 into either of the 2 equations and solve for y

Substituting into (1)

3(- 1) + 4y = 13

- 3 + 4y = 13 ( add 3 to both sides )

4y = 16 ( divide both sides by 4 )

y = 4

solution is (- 1, 4 )

Answer:

Solution :

********************************************

Two angles are said to be a pair of

adjacent angles if they have a common

arm and lie on the either sides of the

common arm .

***********************************************

Now ,

i ) a , b are a pair of adjecent angles .

ii ) c , d are pair of adjecent angles.

iii ) e, f are not adjecent angles .

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

Answer:

a = -1

b= 1

Step-by-step explanation:

8's absolute value is 8, so 8 - 9 is -1 but 8-9 = -1 and since the answer is in the absolute value bars, -1's absolute value is 1, so the answer will be 1

but in a, only 8 is in the absolute value bars, not the complete answer

Answer:

9 sleeves for 22.99

Step-by-step explanation

The first pack has a unit rate of $11.49/ 4 balls

=$2.8725

The second pack has a unit rate of $16.79/6balls

=$2.798 per ball

the third pack has a unit rate of $22.99/9balls

=2.554

So, I would definitely go for the third pack since it has the least cost.

Answer:

1. C

2. C

Step-by-step explanation:

1. 5x+12=57

Subtract 12 from both sides

5x=45

Divide both sides by 5

x=9

2.  7-4x=12-3x

Combine like terms =

-4x+3x=-12-7

x=-12-7

x=19

Answer:

F.O.I.L is a method of solving quadratic equations.

P.S, i love the pics.

Plz mark brainliest!!

Answer:

no

Step-by-step explanation:

3 tons is 3,000 and 7,000 is 7 tons

9514 1404 393

Answer:

  2. chord theorem; t = 10.5

  3. chord theorem; x = 5

Step-by-step explanation:

For both of these problems, the relevant theorem is the "intersecting chord theorem", also referred to as the "chord theorem." It tells you the product of the lengths of the parts of one chord is equal to the product of the lengths of the parts of the other chord.

2. 20t = 10·21

  t = 210/20 . . . . divide by 20

  t = 10.5 . . . . . . . simplify

__

3. 10(x +4) = 15(x +1)

  10x +40 = 15x +15 . . . . . eliminate parentheses

  25 = 5x . . . . . . . . . . . . . subtract 10x+15

  5 = x . . . . . . . divide by 5

Answer:

69.08

Step-by-step explanation:

circumference is pi times diameter

22×3.14=69.08 inches

Answer:

C = 69.08 in

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Geometry

Step-by-step explanation:

Step 1: Define

d = 22 in

Step 2: Find r

Step 3: Find C

Answer:

x= 95/2  or  x=47.5  or   47 1/2

Step-by-step explanation:

3x + 10 = 5(x - 17)

First Step:

multiply and combine the right side (parentheses)

5 times x = 5x         5 times -17 = -85

3x + 10 = 5x -85

Second Step:

Add like terms ----> which is: 3x and 5x -----10 and -85

BUT since you only want one x on one side, you combine x first.

3x + 10 = 5x -85

-5x         -5x

-2x + 10 = -85

NOW

Third Step:     Add the integers---> 10 and -85

you want to get 10 on the same side as the -85, so you subtract it from BOTH sides.

which brings you:

-2x + 10 = -85

       -10    -10

NOW that we've subtracted -10 from -85 it's technically just adding 85 and 10 then putting a negative sign on it.

so now we have:

-2x = -95

Step Four:

divide -2 from each side to get X alone

-2x = -95

-2      -2

ANSWER:

x=47.5

Answer:

Angle E is 30⁰

Explanation:

If triangle ABC= triangle DFE then they are both the same it's just that in this case the triangles are mirrored meaning that Angle C= Angle E

Making Angle E: 30⁰

Answer:

A) 3:9 => 1:3

B) 12:36 => 1:3

C) 13:39 => 1:3

D) 71:213 => 1:3

E) 142:213 => 2:3

F) 38:57 => 2:3

G) 33:44 => 3:4

H) 31:42 => 31:42 or 21:42 => 1:2

Step-by-step explanation:

The simplest form of the ratios are as follows:

A) 3:9

Dividing the ratio by 3

1:3

B) 12:36

Dividing the ratio by 12

1:3

C)13:39

Dividing the ratio by 13

1:3

D) 71:213

Dividing the ratio by 71

1:3

E) 142:213

Dividing the ratio by 71

2:3

F) 38:57

Dividing the ratio by 19

2:3

G) 33:44

Dividing the ratio by 11

3:4

H) 31:42

The ratio is already in simplest form as 31 and 42 don't have a common multiple.

Or it might be mistakenly typed 31 instead of 21

Then the simplest form will be:

21:42

1:2

Hence,

A) 3:9 => 1:2

B) 12:36 => 1:3

C) 13:39 => 1:3

D) 71:213 => 1:3

E) 142:213 => 2:3

F) 38:57 => 2:3

G) 33:44 => 3:4

H) 31:42 => 31:42 or 21:42 => 1:2

Answer:  11/3 or 3.6 or 3 2/3

Step-by-step explanation:

All you have to do is simplify the expression

Answer:

f(g(x)) = 722, and g(f(x)) = 154

Step-by-step explanation:

f(x) = 2x²

g(x) = 3x + 4

g(f(x)) = 3(2x²) + 4

g(f(5)) = 3(2 × 5²) + 4

g(f(5)) = 3(2 × 25) + 4

g(f(5)) = 3 × 50 + 4

g(f(5)) = 154

f(g(x)) = 2(3x + 4)²

f(g(5)) = 2(3 × 5 + 4)²

f(g(5)) = 2 × 19²

f(g(5)) = 2 × 361

f(g(5)) = 722

Answer:

one solution:  x = -3,  y = 26

Step-by-step explanation:

3x + y = 17

x + 2y = 49

If you multiply the first equation by -2 and then add you will eliminate the 'y' term

-2(3x + y) = -2(17)

  -6x - 2y = -34

+    x + 2y = 49

   -5x = 15

     x = -3

-3 + 2y = 49

2y = 52

y = 26