PLEASE HELP ME,I’ve been trying all morning
If f(x)= x^2 + 2x + 5, what is f(x + 3)?

[tex]a = {5}^{x} \\ b = {5}^{y} \\ {a}^{y} \times {b}^{y} = 25 \\ prove \: ( {5}^{x} )^{y} \times ( {5}^{y} ) ^{x} = 25 \\ {5}^{xy} \times {5}^{yx} = {5}^{2} \\ {5 }^{xy + yx} = 5^{2} \\ 5^{2xy} = {5}^{2} \\ is \: \: 2xy = 2 \\ xy = \frac{2}{2} \\ xy = 1[/tex]

The prove that  xy is equal to 1 is given below.​

When you raise a number with an exponent, there comes a result.

Lets say you get

a^b = c

Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows

[tex]log_a(c) b = \log_a(c)[/tex]

'a' is called base of this log function. We say that 'b' is the logarithm of 'c' to base 'a'

Some properties of logarithm are:

[tex]\log_a(b) = \log_a(c) \implies b = c\\\\\log_a(b) + \log_a(c) = \log_a(b \times c)\\\\\log_a(b) - \log_a(c) = \log_a(\frac{b}{c})\\\\\log_a(b^c) = c \times \log_a(b)\\\\\log_b(b) = 1\\\\\log_a(b) \times log_b(c) = \log_a(c)[/tex]

Log with base e = 2.71828... is written as

ln(x)\ln(x)

simply.

Log with base 10 is written as

[tex]\log(x)[/tex]

We are given that;

a = 5^x, b = 5^y and a^y×b^x = 25.

Now,

To prove that xy = 1, we can use the properties of exponents and logarithms. Here are the steps:

1. Given that a = 5^x and b = 5^y, we can substitute these expressions into the equation a^y×b^x = 25 and get:

(5^x)^y × (5^y)^x = 25

2. Using the property that (a^b)^c = a^(bc), we can simplify the left-hand side of the equation and get:

5^(xy + yx) = 25

3. Using the property that a^b = c is equivalent to log_a(c) = b, we can take the logarithm of both sides of the equation with base 5 and get:

log_5(5^(xy + yx)) = log_5(25)

4. Using the property that log_a(a^b) = b, we can simplify the left-hand side of the equation and get:

xy + yx = log_5(25)

5. Using the property that log_a(b) = log_c(b) / log_c(a), we can change the base of the logarithm on the right-hand side of the equation to any other base, such as 10, and get:

xy + yx = log_10(25) / log_10(5)

6. Using a calculator or a table of logarithms, we can evaluate the right-hand side of the equation and get:

xy + yx ≈ 2 / 0.69897

7. Simplifying the fraction on the right-hand side of the equation, we get:

xy + yx ≈ 2.8614

8. Since xy and yx are symmetric, we can divide both sides of the equation by 2 and get:

(xy + yx) / 2 ≈ 2.8614 / 2

9. Simplifying both sides of the equation, we get:

xy ≈ 1.4307

10. Since x and y are integers, we can conclude that xy must be an integer as well. The only integer that is close to 1.4307 is 1.

Therefore, by logarithm properties we can say that xy = 1.

Learn more about logarithm here:

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Answer:

i believe it would be -3

Step-by-step explanation:

9 + -12 = -3

Answer:

x>2 or x>6

Step-by-step explanation:

2x+6<10 or 2x+8>20

2x>4 or 2x>12

x>2 or x>6

Inequalities help us to compare two unequal expressions. The correct option is D.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

The two of the given inequalities can be solved as shown below.

2x + 6 < 10

Subtract 6 from both sides of the equation,

2x + 6 - 6 < 10 - 6

2x < 4

Divide both the sides of the equation by 2,

2x/2 < 4/2

x < 2

2x + 8 > 20

Subtract 8 from both sides of the equation,

2x + 8 - 8 > 20 - 8

2x > 12

Divide both the sides of the equation by 2,

2x/2 > 12/2

x > 6

Hence, the correct option is D.

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Answer:

answer is in photo. please try again yourself.

Answer:

5 by the power of 5

3125 is the answer

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\large\textsf{5(5)(5)(5)(5)}[/tex]

[tex]\huge\textbf{Solving for your equation:}[/tex]

[tex]\large\textsf{5(5)(5)(5)(5)}[/tex]

[tex]\large\textsf{= 25(25)(5)}[/tex]

[tex]\large\textsf{= 625(5)}[/tex]

[tex]\large\textsf{= 3,125}[/tex]

[tex]\huge\textbf{Or you could simply say:}[/tex]

[tex]\large\textsf{5(5)(5)(5)(5)}\\\uparrow\ \uparrow \ \ \ \uparrow \ \ \ \uparrow \ \ \uparrow\\\large\textsf{1 2 \ 3 \ \ 4 \ 5}\\\\\large\text{Seems to me that you have a 5 fives. So, most likely your exponent: }\\\large\boxed{\rm{5^5}}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{{Original\ answer \rightarrow \frak{3,125}}}\huge\checkmark\\\\\\\huge\boxed{Exponenential\ form \rightarrow \frak{5^5}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

[tex](s.t)(x) = 4x^2+24x^2\\(s-t)(x) = x+6-4x^2\\(s+t)(-3) = 39[/tex]

Step-by-step explanation:

Given functions are:

[tex]s(x)= x+6\\t(x)= 4x^2[/tex]

We have to find:

(s.t)(x) => this means we have to multiply the two functions to get the result.

So,

[tex](s.t)(x) = s(x)*t(x)\\= (x+6)(4x^2)\\=4x^2.x+4x^2.6\\=4x^3+24x^2[/tex]

Also we have to find

(s-t)(x) => we have to subtract function t from function s

[tex](s-t)(x) = s(x) - t(x)\\= (x+6) - (4x^2)\\=x+6-4x^2[/tex]

Also we have to find,

(s+t)(-3) => first we have to find sum of both functions and then put -3 in place of x

[tex](s+t)(x) = s(x)+t(x)\\= x+6+4x^2[/tex]

Putting x = -3

[tex]= -3+6+4(-3)^2\\=-3+6+4(9)\\=3+36\\=39[/tex]

Hence,

[tex](s.t)(x) = 4x^2+24x^2\\(s-t)(x) = x+6-4x^2\\(s+t)(-3) = 39[/tex]

Ans 7, 9, 11

Step-by-step explanation:

Think of it as an equation.  You have 3 integers x, y, and z.

x + 2y = z + 14.  

Plug in consecutive odd integers, picking your next set of trial and error integers based on how far off the equation is.

In this case, 7 + (2 * 9) = 11 + 14

In this example, it took me three attempts to get the correct answer.

Answer:

Yes.

Step-by-step explanation:

We'll substitute in the values in both equations.

[tex]2x-3y=-5[/tex]        [tex]4x-4y=-4[/tex]

[tex]2(2)-3(3)=-5[/tex]   [tex]4(2)-4(3)=-4[/tex]

Distribute.

[tex]4-9=-5[/tex]             [tex]8-12=-4[/tex]

Simplify.

[tex]-5=-5[/tex]                [tex]-4=-4[/tex]

Yes, it is a solution. You can plug the equations into Desmos to check.

Answer:. 30 : 48

40:64

Step-by-step explanation: The hint is in the table where the rows highlighted in pink, multiples of 5 and 8, contain the values of the original given ratio, 10:16

Equivalent ratios include any of the corresponding values in columns AND that are in the pink rows.

5:8, 10:16, 15:24, 20:32 . . .

We can see the pattern; pairs of multiples of the factors of the numbers in the original ratio are equivalent ratios.

Answer:

She buys 2/8 more pound of granola than banana chips

Step-by-step explanation:

Answer:

1,200 out of 2000 doctors use X aspirin

Step-by-step explanation:

Answer:

Slope = 3

Step-by-step explanation:

For a proportional relationship, the slope of the line is simply y/x.

So using any given pair of values from the table, say (1, 3), the slope is:

y/x = 3/1

Slope = 3

Answer: g it is 2x+21 ansd h is 3x+24

Step-by-step explanation:

Answer:

Area of big rectangle - area of mini rectangle

56in2 - 3in2

B. 53 in2

Step-by-step explanation:

Separate the two rectangleulsr shapes. 3x6 which equals 18.

8-3=5

5×7= 35

35+18= 53

B. 53 in sq

Answer:

the answer is

12 = y - 5

y=17

x+2 = 4

x=2

Answer:I zoom in but it blurry .

Sorry but have a great day.

Step-by-step explanation:

Answer:

Jan would have traveled about 1500 miles

Answer:Yes

Step-by-step explanation:

Answer:

78ft

I got it off of apec

Answer:

NO

Step-by-step explanation:

Answer:

To run one lap Lin takes 1.6 minutes.

Step-by-step explanation:

To find this answer you would do 8 divided by 5. Always remember when dividing time goes first unless the instructions / directions / your teacher says differently. So, when you do 8 divided by 5 the answer you get is 1.6, and there is your answer. Also to check your answer you can do 1.6 times 5, and you get 8, so you know that 1.6 is the correct answer.

Answer: there's one more screen shot but the limit is 5... so ill type it out!

7. Are the two products the same when you multiply them vertically? (1 point)

Yes they are

Making a Decision:

8. Who was right, Emily or Zach? Are the products the same with the three different methods of multiplication? (1 point)

They were both correct

9. Which of these three methods is your preferred method for multiplying polynomials? Why? (1 point)

I prefer the first one, Table method. To me it is easier and the fastest out of them all.

Answer: 850

Step-by-step explanation:

if  250 miles takes 5 gallons then 7 gallons may give you about 850.

It looks like your just adding on 2 more.

Answer:

350 miles

Step-by-step explanation:

5 gallons of gas - 250 miles

7 gallons of gas - [tex]\frac{7}{5}[/tex] × 250 miles = 350 miles

Answer:

5

Step-by-step explanation:

y ∝ x

y = k times x

where 'k' is constant

substitute y for -7 and x for -28

-7 = k times -28

-7 = -28k

Divide through by -28

[tex]\frac{-7}{-28}[/tex] = [tex]\frac{-28k}{-28}[/tex]

= [tex]\frac{1}{4}[/tex] =k

formula y = [tex]\frac{1}{4}[/tex] times x

y = [tex]\frac{1}{4}[/tex] times 20

y = 5

 By using the proportionality relation, at x = 20 the value of y will be 5.

Given in the question → y ∝ x

                                       y = kx

                                       Here, k = Proportionaility constant

It's given, when x = -28, value of y = -7

By substituting these values in the expression,

-7 = k(-28)

[tex]k=\frac{-7}{-28}[/tex]

k = [tex]\frac{1}{4}[/tex]

Therefore, given expression for the proportional relation will be,

[tex]y=\frac{1}{4}x[/tex]

If x = 20, we have to calculate the value of y,

Substitute x = 20 in the same expression,

[tex]y=\frac{1}{4}(20)[/tex]

y = 5

    Therefore, for the value of x = 20, value of y will be 5.

Learn more about the proportional relation here,

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Answer:

A square field has a perimeter if 3.6km what is the length of one side in metres

Step-by-step explanation:

A square field has a perimeter if 3.6km what is the length of one side in metres

Given,

We need to find,

As we know that,

→3600=4s

→3600/4=side

→Side=900m

Answer:

3692

Step-by-step explanation:

Multiply the starting amount, by the percent, and them multiply by how many years (2600*0.03%*14)