Rick started his retirement account with \$5,000 when he was 23. When he retired at age 65 , he had 2.2 * 10 ^ 6 dollars in his retirement account . How many times greater was his account when he retired ?

Answer:

A

Step-by-step explanation:

To reflect a function over the x-axis, we multiply the function by -1. So, if f(x) is the original function, then -f(x) is the function across the x-axis.

To reflect a function over the y-axis, we multiply the inside of the function by -1. So, if f(x) is the original function, then f(-x) is the function across the x-axis.

We have:

[tex]f(x)=(x-1)^2+1[/tex]

Then:

[tex]f(-x)=(-x-1)^2+1=f ^\prime(x)[/tex]

We can see that the choice that resembles this is A. If we let:

[tex]f(-4x)=(-4x-1)^2+1[/tex]

This is a reflection over the y-axis followed by a horizontal compression by a factor of 4.

Hence, our answer is A.

=====================================================

Explanation:

Since the range of [tex]y = \sqrt{x}[/tex] is [tex]y \ge 0[/tex], this means that [tex]\sqrt{53+20\sqrt{7}}[/tex] cannot be negative.

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

Let's set the given nested radical expression equal to the form a+b*sqrt(c), and then square both sides to see what happens

[tex]\sqrt{53+20\sqrt{7}} = a+b\sqrt{c}\\\\\left(\sqrt{53+20\sqrt{7}}\right)^2 = \left(a+b\sqrt{c}\right)^2\\\\53+20\sqrt{7} = a^2+2ab\sqrt{c}+b^2c\\\\53+20\sqrt{7} = (a^2+b^2c)+2ab\sqrt{c}\\\\[/tex]

Equating the corresponding parts shows that

[tex]53=a^2+b^2c \text{ and } 20\sqrt{7} = 2ab\sqrt{c}\\\\[/tex]

Therefore c = 7 must be the case to allow the radicands to match up.

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

Since c = 7, we can update the first equation like so

[tex]53=a^2+b^2c\\\\53=a^2+b^2*7\\\\53=a^2+7b^2\\\\[/tex]

We'll come back to this later.

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

Focus on [tex]20 = 2ab\sqrt{7}[/tex]

Note how 20 and 2ab are coefficients outside the root. So 20 = 2ab leads to ab = 10.

Here are all the ways to multiply to 10 where a,b are integers

So we could have these possibilities.

If you try all of those a,b combinations with [tex]53 = a^2 + 7b^2[/tex], then you should find that a = 5 and b = 2 works. I'm skipping a bunch of steps here. All you basically do is plug and chug.

Due to symmetry, we could have a = -5 and b = -2 as another solution to [tex]53 = a^2 + 7b^2[/tex]. However, if a < 0 and b < 0, then [tex]a+b\sqrt{c}[/tex] would be negative which contradicts the fact that [tex]\sqrt{53+20\sqrt{7}}[/tex] is positive. So we'll ignore any case where a,b are negative.

Therefore, the only combination that works is a = 5 and b = 2

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

Overall, we found that

And therefore,

[tex]\sqrt{53+20\sqrt{7}} = a+b\sqrt{c}\\\\\sqrt{53+20\sqrt{7}} = 5+2\sqrt{7}\\\\[/tex]

You can confirm this with your calculator by taking advantage of the idea "If x = y, then x-y = 0". In other words, if you subtract the left and right sides, you should get 0 as a result (the order of subtraction doesn't matter in this case). Don't forget to use parenthesis correctly, or you may not get 0. It might help to think of it as the form (x) - (y) = 0.

After we confirmed we have the correct a,b,c values, we simply add them up to get a+b+c = 5+2+7 = 14.

Answer:

true

Step-by-step explanation:

Answer:

true

Step-by-step explanation:

because with evidence you can verify if a claim is correct, leading you to an answer.

Answer:

they forgot to add the 3x

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

This is because mas and weight is converted into grams then kilograms and more.

Answer:

what is the question

Step-by-step explanation:

Answer:

Step-by-step explanation:

Absolute value inside the brackets will always be positive*

1. 7

2.15

3.0

4. -5

5.-3

6.3

7.17

8.5

9.-101

10.0

11.16

12.1

Hope this helped!

Answer:

About 45 pens would be bought

GIVEN,

3 pens can be bought for 65 cents

☞TO FIND

The number of pens that can be bought for $9.75

ANSWER

$9.75 = 975 cents

Therefore the number of pens that can be bought for $9.75 is,

[tex] \frac{975}{65} \times 3 \\ = 15 \times 3 \\ = 45[/tex]

So 45 pens can be bought

Answer:

Step-by-step explanation:

2x+2.5+3(x-4)

2x+10+3(x-4)

2x+10+3x+3.-4

2x+10+3x-12

5x+10-12

5x-2

Answer:

???

Step-by-step explanation:

Answer:

x/13.5 feet = 12 inches/1 foot

So, the answer would be

162 inches/13.5 feet = 12 inches/1 foot

Answer:

Player 1's position is Player 2's position reflected across the y-axis; only the signs of the x-coordinates of Player 1 and Player 2 are different.

Step-by-step explanation:

Answer:

Player 1's position is Player 2's position reflected across the x-axis; only the signs of the x-coordinates of Player 1 and Player 2 are different.

Since you flip across the grid you would get the same coordinates but the number things would be answer blah blah blah

listen I know this is the answer I don’t have to explain myself.

Answer:

5

Step-by-step explanation:

The question says a proportional relationship, of not stated otherwise, this means a directly proportional relationship, where,

y=kx

Now if, k=1, substituting in the equation would give,

y=x,

Therefore, whatever the value of x is, so is that the value of y,

thus, if x=5,

y=5

Answer:

i think it is 15,840 because if you multiply 3 by 5,280 you will get 15,840

Step-by-step explanation:

Answer:

z=2

Step-by-step explanation:

When you subtract a negative, you are adding the number, so the question simplify into 14= z + 12, which is 2

Brainliest Maybe?

Answer:

Ted is 14 years old, and Ed is 21 years old.-B

Step-by-step explanation:

Answer:

a=7

Step-by-step explanation:

Answer:A.

A. The cost of zero bags of caramel corn

Step-by-step explanation:

Answer:

w+ (9+3)

Step-by-step explanation:

pretty simple if I remember how to use that property

Answer:

The equivalent expression for the given expression (w+9)+3 using associative property is w + 12

Solution:

Given that, expression is ( w + 9 ) + 3

We have to find how do we can use the associative property to write an expression equivalent to ( w + 9 ) + 3

The associative property states that you can add or multiply regardless of how the numbers are grouped

By above definition, we get

(a + b) + c = a + (b + c)

So, now let us apply the above property to the given expression,

Then, ( w + 9 ) + 3 = w + ( 9 + 3 ) = w + 12

Hence, the equivalent expression for the given expression is w + 12

Step-by-step explanation:

Its the same thing but I put it it the comments bc why not

Answer:

[tex]a-(-b)>a[/tex]

Step-by-step explanation:

ok so lets round  =-3 and b=2

ok so now lets solve -3-(-2)=-3+2

remember when you subtract a negative it is just like adding

so -3+2=-1 and -1 is greater than -3

i hope this helps

Answer:

yes

Step-by-step explanation:

Correct-a-mundo !

4000 * .06 * 5 = 1200

Answer:

80.027

Step-by-step explanation:

139.65 - 59.623= 80.027

hope this helps!