the sum of two numbers is 56. the difference of the 2 numbers is 16. what is the product of the two numbers?

Answer:

The answer is 8.

Step-by-step explanation:

If is

[tex]\sqrt{r^{64}}=\sqrt{r^{32\cdot2}}=\sqrt{(r^{32})^2}=r^{32}[/tex]

Used:

[tex](a^n)^m=a^{nm}\\\\\sqrt{a^2}=a\ for\ a\geq0[/tex]

If is

[tex]\sqrt{64}=8[/tex] because [tex]8^2=64[/tex]

with the distributive property of multiplication you can take ba+ca and rewrite it as a(b+c)=ab+ac=ba+ca

Step 1 = Distributive Property ( multiplying the 2 by each term in parenthesis)

Step 2 = Addition Property ( adding like terms)

Step 3 = Addition Property (adding 34x to each side)

Step 4 = Division Property. ( dividing both sides by 17)

Do you need all the coordinates or just A' and B'

$1.25x + $10 + $15 (less than or equal to) $50

Answer:

So, with the reaming 25 dollars she can play at max 20 games.

Step-by-step explanation:

Given that

Amount Courtney has to spend = $ 50

Amount Spent on Admission = $ 10

Amount Spent on Snacks = $ 15

Price of a Game at Share = $ 1.25

Now, lets find the total amount spent by her already

Amount Spent = 50 - 10 - 15 = $ 25

Suppos x represent the number of games so, we can represent the remaining amount and in term of games that can be purchased by using it

[tex]1.25x\leq25[/tex]

the above inequality can be simplified as follows

[tex]x\leq\frac{25}{1.25}[/tex]

[tex]x\leq20[/tex]

So, with the reaming 25 dollars she can play at max 20 games.

[tex]f(x)=3(x+5)+\dfrac{4}{x}\\\\f(a+2)\to\text{put x = a + 2 to the equation of the function f}\\\\f(a+2)=3(a+2+5)+\dfrac{4}{a+2}=3(a+7)+\dfrac{4}{a+2}[/tex]

Since the ratio is as simple as 1:2, just double each Euro value.

1:2, 2:4, 5:10, 10:20.

Answer:

$4,$10,$20.

Step-by-step explanation:

60 divided by 10 =6

3x6=18

Raul would ride 18 miles.

Hope this helped :)

Raul would ride 18 miles for 60 minutes at the same speed.

To find out how many miles Raul would ride for 60 minutes at the same speed, we can set up a proportion. If Raul rides 3 miles for 10 minutes, then we can say that 3 miles is to 10 minutes as x miles is to 60 minutes. Setting up this proportion, we get: 3/10 = x/60. To solve for x, we can cross multiply and then divide both sides by 10. This gives us: x = (3/10) * 60 = 18 miles.

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y=-1x-6 is your answer

9*54=486  

10x50=500

So, either 450 or 500.

Comparing the probability values for each Container, Hence, both containers give equal chances of winning .

Complete question:

Container __ Red ___ Blue

A ________ 6 ______ 4

B ________ 60 _____ 40

Using the probability formula:

For Container A :

For Container B :

Since the probability values are the same, then both Container gives equal Chances of winning.

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Answer:

[tex]10x-6[/tex]

Step-by-step explanation:

[tex]f(x) = 5x+2x\\g(x)=3x-6[/tex]

[tex](f+g)(x)\\f(x)+g(x)[/tex]

[tex]5x+2x+3x-6\\10x-6[/tex]

The value of (f+g)(x) is 10x - 6

We are taking into consideration the following two functions f(x) and g(x). The sum of these functions can be written f(x) + g(x) or as (f + g)(x). . The sum of the two functions is the sum of the two polynomials. Or in other words, the sum of any two functions gives us the addition of the terms present inside the function.

Given functions,  f(x) = 5x + 2x

and g(x) = 3x - 6

Sum of the two functions -

∴ (f+g)(x) = f(x) + g(x) = 5x + 2x + 3x - 6 = 10x - 6

Therefore (f+g)(x) = 10x - 6

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b represents rate of change

Answer:

rate of change

Step-by-step explanation:

Answer:

18 rolls of nickles

Step-by-step explanation:

One roll of dimes would be the same value as 2 rolls of nickles. If she has 9 rolls of dimes, she would have 18 rolls of nickles.

Dont forget to thanks and rate!

Alysha has 13 nickel rolls.

Let x be the number of dime rolls and y be the number of nickel rolls.

A linear equation only has one or two variables. No variable in a linear equation is raised to a power greater than 1 or used as the denominator of a fraction. When you find pairs of values that make a linear equation true and plot those pairs on a coordinate grid, all of the points lie on the same line.

Each dime roll has 50 dimes, then x dime rolls are worth 50×10×x=500x cents or $5x.

Each nickel roll has 40 nickels, and then y nickel rolls are worth 40×5×y=200y cents or $2y.

A. The total value of Alysha's rolls is 500x+200y cents or $(5x+2y).

If the total value of the coins is $71 and she has 9 rolls of dimes, then x = 9 and 5×9+2y=71.

⇒45+2y=71

⇒2y=71-45

⇒2y=26

⇒y=13

Therefore, Alysha has 13 nickel rolls.

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Alysha has a collection of dime and nickel rolls that she'd like to take to the bank. Each dime roll has 50 dimes and each nickel roll has 40 nickels.

a) Write an equation to represent the total value of

b) If the total value of the coins is $71 and she has 9 rolls of dimes, how many does she have?

I think it is 25 sorry if im wrong

Answer:

There were 25 guest in Dan's party.

Step-by-step explanation:

We are given the following information in the question:

Number of classmates came to Dan’s birthday party = 5

Number of friends from his summer camp = Number of classmates came to Dan’s birthday party = 5

Number of relatives in Dan's party =

Let x be the number of relatives, then,

[tex]\displaystyle\frac{x}{3} = 5\\\\x = 15[/tex]

Total number of guest in Dan's party =

[tex]\text{Number of classmates came to Dan’s birthday party} +\\ \text{Number of friends from his summer camp } + \\\text{Number of relatives}\\= 5 + 5 + 15\\=25[/tex]

Hence, there were 25 guest in Dan's party.

we are given

[tex]f(x)=e^x sin(x)[/tex]

(a)

Firstly, we will find critical numbers

so, we will find derivative

[tex]f'(x)=e^x sin(x)+e^x cos(x)[/tex]

now, we can set it to 0

and then we can solve for x

we get

[tex]x=\frac{3\pi }{4} ,x=\frac{7\pi }{4}[/tex]

now, we can draw a number line and then locate these values

and then we can find sign of derivative on each intervals

increasing intervals:

[tex][0,\frac{3\pi}{4} )U(\frac{7\pi}{4} , 2\pi][/tex]

Decreasing interval:

[tex](\frac{3\pi}{4} ,\frac{7\pi}{4} )[/tex]

(b)

Local maxima:

It is the value of x where function changes from increasing to decreasing

so, local maxima is at

[tex]x=\frac{3\pi}{4}[/tex]

Local minima:

It is the value of x where function changes from decreasing to increasing

so, local minima is at

[tex]x=\frac{7\pi}{4}[/tex]

now, we will plug critical numbers and end values into original function

and we get

At x=0:

[tex]f(0)=e^0 sin(0)[/tex]

[tex]f(0)=0[/tex]

At [tex]x=\frac{3\pi}{4}[/tex]:

[tex]f(\frac{3\pi}{4})=e^{\frac{3\pi}{4}} sin(\frac{3\pi}{4})[/tex]

[tex]f(\frac{3\pi}{4})=7.46049[/tex]

At [tex]x=\frac{7\pi}{4}[/tex]:

[tex]f(\frac{7\pi}{4})=e^{\frac{7\pi}{4}} sin(\frac{7\pi}{4})[/tex]

[tex]f(\frac{7\pi}{4})=-172.640[/tex]

At [tex]x=2\pi [/tex]:

[tex]f(2\pi)=e^{2\pi} sin(2\pi )[/tex]

[tex]f(2\pi )=0[/tex]

Global maxima:

It is the largest value among them

so, we get

[tex]f(\frac{3\pi}{4})=7.46049[/tex]

Global minima:

It is the largest value among them

so, we get

[tex]f(\frac{7\pi}{4})=-172.640[/tex]

(c)

now, we can find second derivative

[tex]f'(x)=e^x sin(x)+e^x cos(x)[/tex]

[tex]f''(x)=\frac{d}{dx}\left(e^x\sin \left(x\right)+e^x\cos \left(x\right)\right)[/tex]

[tex]=\frac{d}{dx}\left(e^x\sin \left(x\right)\right)+\frac{d}{dx}\left(e^x\cos \left(x\right)\right)[/tex]

[tex]=e^x\sin \left(x\right)+\cos \left(x\right)e^x+e^x\cos \left(x\right)-e^x\sin \left(x\right)[/tex]

[tex]f''(x)=2e^x\cos \left(x\right)[/tex]

now, we can set it to 0

and then we can solve for x

[tex]f''(x)=2e^x\cos \left(x\right)=0[/tex]

so, we get

[tex]x=\frac{\pi}{2} ,x=\frac{3\pi}{2}[/tex]

now, we  can draw number line and locate these values

and then we can find sign of second derivative on each intervals

concave up intervals:

[tex][0,\frac{\pi}{2})U(\frac{3\pi}{2}, 2\pi][/tex]

Concave down intervals:

[tex](\frac{\pi}{2} ,\frac{3\pi}{2})[/tex]

Turning points:

All values of x for which concavity changes

so, we get turning points at

[tex]x=\frac{\pi}{2} ,x=\frac{3\pi}{2}[/tex]

fff

[tex]f(x) = e^x sin (x)[/tex]

To find increasing and decreasing intervals we take derivative

[tex]f'(x) = e^xsin(x)+e^x(cosx)= e^x(sinx+cosx)[/tex]

Now we set the derivative =0  and solve for x

[tex]e^x(sinx+cosx)=0[/tex]

sinx + cosx =0

divide whole equation by cos x

[tex]\frac{sinx}{cosx} + \frac{cosx}{cosx} =0[/tex]

tanx +1 =0

tanx = 1

[tex]x=\frac{3\pi }{4}[/tex] and  [tex]x=\frac{7\pi}{4}[/tex]

Now we pick a number between 0 to  [tex]\frac{3\pi }{4}[/tex]

Lets pick  [tex]\frac{\pi }{2}[/tex]

Plug it into the derivative

[tex]f'(x) =e^{\frac{\pi }{2}}(sin(\frac{\pi}{2})+cos(\frac{\pi }{2}))[/tex]

= 4.810 is positive

So the graph of f(x) is increasing on the interval [0, [tex]x=\frac{3\pi }{4}[/tex])

Now we pick a number between   [tex]\frac{7\pi}{4}[/tex] to 2pi

Lets pick  [tex]\frac{11\pi}{6}[/tex]

Plug it into the derivative

[tex]f'(x) =e^{\frac{11\pi}{6}}(sin(\frac{11\pi}{6})+cos(\frac{11\pi }{6}))[/tex]

= 116 is positive

So the graph of f(x) is increasing on the interval [tex](\frac{7\pi }{4}, 2\pi)[/tex]

Increasing interval is [tex](0,\frac{3\pi }{4}) U (\frac{7\pi }{4}, 2\pi)[/tex]

Decreasing interval is [tex](\frac{3\pi}{4}, \frac{7\pi}{4})[/tex]

(b)

The graph of f(x) increases and reaches a local maximum at [tex]x=\frac{3\pi}{4}[/tex]

The graph of f(x) decreases and reaches a local minimum at [tex]x=\frac{7\pi}{4}[/tex]

(c)

f(0) = 0

[tex]f(2\pi)=0[/tex]

[tex]f(\frac{3\pi }{4})=7.46[/tex]

[tex]f(\frac{7\pi}{4})=-172.64[/tex]

Here global maximum at [tex]x=\frac{3\pi}{4}[/tex]

Here global minimum at [tex]x=\frac{7\pi}{4}[/tex]

Hello, Jssoyg! I've solved the problem for you below. I hope it helps.

Slope equation is[tex]\frac{y2 - y1}{x2 - x1}[/tex]. The two points are (0,1) and (4,2), so the equation becomes [tex]\frac{2 - 1}{4 - 0} = \frac{1}{4}[/tex]. We now know that the slope is 1/4, so now let's write it in the [tex]y = mx + b[/tex] format. Plug in the m, x, and y values:[tex]2 = 4*\frac{1}{4} + b[/tex].

This becomes [tex]2 = 1 + b[/tex] which means b = 1.

Your answer is y = 1/4x + 1. Hope this was helpful. :D

Here we are given the information that an insurance agent receives 16% commission on every premium paid.

Now we are given that a premium of $497.69 is paid.

Let us say $x is the commission paid on the policy with a premium of $497.69.

Let us try to find the amount x here.

So we have to find 16% of 497.69 to get the commission amount x.

So finding 16% of 497.69.

x= 16% of 497.69 = 0.16*497.69 = 79.63

Answer: Commission of $79.63 is paid on a policy with a premium of $497.69.

Answer:

$ 79.6304 of commission was paid on policy with a premium of $497.69.

Step-by-step explanation:

Percentage on amount received on every premium = 16% of the premium

So, when the premium of the $ 497.69 was paid , the commission received by an agent will be: 16% of the $497.69 .

[tex]\$497.69\times \frac{16}{100}=\$79.6304[/tex]

$ 79.6304 of commission was paid on policy with a premium of $497.69.

a.) [tex]769-362 = 407[/tex]

Checking: Since, [tex]407+362 = 769[/tex]

Therefore, our answer is correct.

b.) [tex]502+17 = 519[/tex]

Checking: Since, [tex]519-17 = 502[/tex]

Therefore, our answer is correct.

c.) [tex]7802-3461 = 4341[/tex]

Checking: Since, [tex]4341+3461 = 7802[/tex]

Therefore, our answer is correct.

d.) [tex]1432+2568 = 4000[/tex]

Checking: Since, [tex]4000-2568 = 1432[/tex]

Therefore, our answer is correct.

Answer:

Consider the numbers:

a) 769 - 362 = ?

Subtract the numbers.

769 - 362 = 702

Therefore, the value is 702.

Now, check using the inverse operation.

407 + 362

Add the numbers.

407 + 362 = 769

Thus, the answer is correct.

Consider the numbers:

b) 502 + 17 = ?

Add the numbers.

502 + 17 = 519

Therefore, the value is 519.

Now, check using the inverse operation.

519 - 17

Subtract the numbers.

519 - 17 = 502

Thus, the answer is correct.

Consider the numbers:

c) 7802 - 3461 = ?

Subtract the numbers.

7802 - 3461 = 4341

Therefore, the value is 4341.

Now, check using the inverse operation.

4341 + 3461

Add the numbers.

4341 + 3461 = 7802

Thus, the answer is correct.

d) 1432 + 2568 = ?

Add the numbers.

1432 + 2568 = 4000

Therefore, the value is 4000.

Now, check using the inverse operation.

4000 - 2568

Subtract the numbers.

4000 - 2568 = 1438

Thus, the answer is correct.

[tex]|\Omega|=20\cdot19=380\\|A|=4\cdot12=48\\\\P(A)=\dfrac{48}{380}\approx0.13[/tex]

x=16/3 or 5.33333333

Answer:

Step-by-step explanation:

multiply by 3 the whole equation

6×3 = (x)×3  + (2/3) ×(3)

18 =3x + 2

subtracting 2 both sides

18-2 = 3x +2-2

16= 3x

dividing by 3 both sides

16/3 = 3x / 3

16/3 = x

100th customer is your answer

Find the first number that shows up on both answers when they are added

Add 20 each time for $5 gift card:

20, 40, 60, 80, 100

Add 50 each time for $10 gift card:

50, 100

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

As seen above, the first number that shows up on both is 100, therefore, 100 is your answer

hope this helps

No, it is not.

Hope it helped! :)

Solve:

(3x    −   4)(2x^2     +      2x    −   1)

Simplify:

(3x     −      4)(2x^2      +       2x     −    1)

=      (3x     +    −4)(2x^2     +        2x        +        −1)

=   (3x)(2x^2)    +   (3x)(2x)   +   (3x)(−1)    +    (−4)(2x2)   +    (−4)(2x)     +     (−4)(−1)

=      6x^3    +   6x^2    −   3x    −  8x^2   −   8x   +   4

Answer   =      6x^3    −   2x^2     −   11x   +   4

Hope that helps!!!!                                         : )

Final answer:

The product of (3x - 4) and (2x² + 2x - 1) is calculated by multiplying each term in the first polynomial by each term in the second and combining like terms, resulting in the final expression 6x³ - 2x² - 11x + 4.

Explanation:

The product of the polynomials (3x − 4) and (2x2 + 2x − 1) is obtained by applying the distributive property, otherwise known as FOIL (First, Outer, Inner, Last) method in this context. Each term in the first polynomial is multiplied by each term in the second polynomial and then the results are summed together. The step-by-step calculation is as follows:

Multiply the First terms: (3x) × (2x2) = 6x3.

Multiply the Outer terms: (3x) × (2x) = 6x2.

Multiply the Inner terms: (− 4) × (2x2) = − 8x2.

Multiply the Last terms: (− 4) × (− 1) = 4.

Once these calculations are done, we combine like terms:

6x3 (no like terms to combine here)

6x2 − 8x2 = -2x2

(3x) × (2x) = 6x2 (already accounted for in the previous step)

(3x) × (−1) = -3x

(− 4) × (2x) = − 8x

4 (no like terms to combine here)

So, adding all these up, we get:

6x3 − 2x2 − 3x − 8x + 4

Combining the x terms, we have:

− 3x − 8x = − 11x, so the final answer is:

6x3 − 2x2 − 11x + 4

You can solve this using long division. The answer should end up being 2.3.

Answer:

2.3

Step-by-step:

To find (f+g)(x), add f(x) and g(x) together. (f + g)(x) is calculated as (5x - 2) + (2x + 1), which simplifies to 7x - 1. Therefore, the correct answer is C. 7x - 1.

The question asks to find the sum of two functions, f(x) and g(x).

To find (f+g)(x), we add the two functions together.

Here's how we calculate it:
First, we take the function f(x) = 5x - 2 and the function g(x) = 2x + 1.
Then, we add them together: (f + g)(x) = f(x) + g(x).
So, (f + g)(x) = (5x - 2) + (2x + 1).
Combining like terms, we get (f + g)(x) = 5x + 2x - 2 + 1.
This simplifies to (f + g)(x) = 7x - 1.

Therefore, the correct answer is C. 7x - 1.

Final answer:

To find (f+g)(x), we need to add the functions f(x) and g(x) together. The function f(x) is given as f(x) = 5x-2 and the function g(x) is given as g(x) = 2x+1. To add the functions, we simply add the coefficients of the variable and the constant terms. So, (f+g)(x) = (5x-2) + (2x+1) = 7x-1. Therefore, the correct answer is C. 7x-1.

Explanation:

To find (f+g)(x), we need to add the functions f(x) and g(x) together. The function f(x) is given as f(x) = 5x-2 and the function g(x) is given as g(x) = 2x+1.

To add the functions, we simply add the coefficients of the variable and the constant terms. So, (f+g)(x) = (5x-2) + (2x+1) = 7x-1. Therefore, the correct answer is C. 7x-1.

Answer: The correct reason for [tex]\angle4\cong \angle7[/tex] is property of corresponding angles and the reason for [tex]\angle4+\angle6=180[/tex] is substitute [tex]\angle7=\angle4[/tex] and the third error is the forget the property that the sum of consecutive interior angles is 180.

Explanation:

It is given that m is parallel to n.

When  two parallel lines intersected by a transversal eight angles are produced as shown in the given figure, where m and n are parallel and l is the transversal line.

In this case corresponding angles are congruent. Example [tex]\angle1\cong \angle5[/tex],[tex]\angle2\cong \angle6[/tex] etc.

So, [tex]\angle4\cong \angle7[/tex] by the property of corresponding angles.

[tex]\angle7+\angle6=180[/tex] because these are supplementary angles.

Substitute [tex]\angle7=\angle4[/tex]

[tex]\angle4+\angle6=180[/tex]

So, the correct reason is substitution.

Hence proved [tex]\angle4+\angle6=180[/tex]

The third error is the forget the property that the sum of one side interior angles is 180. Since the alternate interior angles are congruent therefore the consecutive interior angles are supplementary angles around the sum of consecutive interior angles is 180 degree.

Lets x and y are the value of two numbers.

x + y = 16

x - y = 2.4

If x + y = 16 then x = 16 - y

Substitute x = 16 - y into x - y = 2.4

16 - y - y = 2.4

16 - 2y = 2.4

2y = 13.6

 y = 6.8

x = 16 - y

x = 16 - 6.8

x = 9.2

Answer:

The value of two numbers are 9.2 and 6.8

Answer:

For step three she could multiply the two parenthesis against each other to get 3(x² - 10x + 25) - 2 + 4x

Step-by-step explanation:

step 1: 3(x - 5)² - 2 + 4x

step 2: 3(x - 5)(x - 5) - 2 + 4x

For step three she could multiply the two parenthesis against each other to get 3(x² - 10x + 25) - 2 + 4x

d. distribute the 3 to each term in the parentheses by multiplying.

First, simplify within parentheses: [tex]\(3(2x - 6 - x)^2 = 3(x - 6)^2\)[/tex]. Next, expand the exponent to get [tex]\(3x^2 - 36x + 108\)[/tex].

Sure, let's break down the steps:

Given expression:

[tex]\[ 3(2x - 6 - x)^2 - 24x \][/tex]

Step 1: Simplify within the parentheses.

[tex]\[ 3(2x - 6 - x)^2 = 3(x - 6)^2 \][/tex]

Step 2: Expand the exponent.

[tex]\[ 3(x - 6)^2 = 3(x^2 - 12x + 36) \][/tex]

[tex]\[ = 3x^2 - 36x + 108 \][/tex]

Now, combine this result with the given expression:

[tex]\[ 3x^2 - 36x + 108 - 24x \][/tex]

Step 3: Combine like terms.

[tex]\[ = 3x^2 - 60x + 108 \][/tex]

So, the simplified expression is:

[tex]\[ 3x^2 - 60x + 108 \][/tex]

The correct question is:

sharina simplified the expression 3(2x – 6 – x 1)^2 – 2 4x. in step 1 she simplified within the parentheses. in step 2 she expanded the exponent. which is a possible next step?

a. simplify the expression by adding and subtracting from left to right.

b. combine like terms within the parentheses.

c. combine all x-terms.

d. distribute the 3 to each term in the parentheses by multiplying.