In one baseball season, Peter hit twice the difference of the number of home runs Alice hit and 6. Altogether , they hit 18 home runs.How many runs did each player hit that season. Write and solve an equation .

The logic of a conditional statement ('if-then') is followed here. Given 'If Kyle is from Texas, then he is a football fan' and 'Kyle is from Texas', we can validly conclude 'Kyle is a football fan'.

The statement 'if Kyle is from Texas then he is a football fan' is known as a conditional statement in logic. Conditional statements have an 'if' part (the hypothesis) and a 'then' part (the conclusion). In this case, the hypothesis is 'Kyle is from Texas' and the conclusion is 'he is a football fan'. The statement 'Kyle is from Texas' confirms the hypothesis. Therefore, following the logic of the conditional statement, we can conclude that 'Kyle is a football fan'. This conclusion is based on the given condition, in real life, of course, being from Texas doesn't automatically make someone a football fan, but within the confines of this logic, it does.

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Answer:

D

Step-by-step explanation:

The equivalent expression of the expression m - n will be m + (-n). Then the correct option is D.

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ m - n

The equivalent expression of the expression m - n will be written as,

⇒ m - n

⇒ m + (-n)

The equivalent expression of the expression m - n will be m + (-n). Then the correct option is D.

More about the equivalent link is given below.

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Answer:

20) 10x - 10 = 120

10x = 130

x = 13

21) 6x + 10 + 8x + 2 = 180

14x + 12 = 180

14x = 168

x = 12

22) 5x + 5x + 6 + 94 = 180

10x + 100 = 180

10x = 80

x = 8

23) 2x + 3 + 4x + 1 = 124

6x + 4 = 124

6x = 120

x = 20

Hey there!

Equation given :

50 + 5y - 20 = 14y - 12 - 2y

Combining like terms :

30 + 5y = 12y - 12

Adding 12 on both sides :

42 + 5y = 12y

Subtracting 5y on both sides :

7y = 42

Dividing by 7 on both sides :

y = 6

The value of y is 6.

Hope my answer helps!!

Answer is: Solve for x by simplifying both sides of the equation, then isolating the variable.

x = 20.2

-56mi in 4 minutes is (56mi/4) in 1 minutes = 14mi/minute.

Therefore, the submarine was 14 miles below sea level after 1 minute.

Answer:

The submarine's depth relative to sea level after the first minute is -14 miles.

Step-by-step explanation:

Consider the provided information.

Starting at sea level, a submarine descended at a constant rate to a depth of −56 mile relative to sea level in 4 minutes.

This can be written as:

[tex]-56\ miles=4\ minutes[/tex]

To find the submarine's depth relative to sea level after the first minute, divide both the sides by 4.

[tex]\frac{-56}{4}\ miles=\frac{4}{4}\ minutes[/tex]

[tex]-14\ miles=1\ minutes[/tex]

Hence, the submarine's depth relative to sea level after the first minute is -14 miles.

perimeter = 4m + 3

the perimeter is the sum of the 3 sides of the triangle, thus

perimeter = 3m + 4 - m + 2m - 1 = 4m + 3

Answer: 4m + 3

Step-by-step explanation:

This is because the perimeter of a triangle is the same as adding all of its sides.

3m+(4-m)+(2m-1)

Group like terms:

(3m-m+2m) + (4-1)

Then combine like terms to get your final answer of:

4m + 3

None of them are equivalent to 0.3, unless it's 0.3 with a bar over the 3, in which case the answer is 1/3.

Solution:

Convert all the numbers to decimal form;

1/3 = 0.3 (where 3 is recurring)

33/100 = 0.33

5/6 = 0.83 (where 3 is recurring)

2/3 = 0.6 (where 6 is recurring)

The correct choice is  1/3 since its the only choice that don't give a limitation on rounding up the decimal value to 1 decimal place.

Answer:

The value that optimizes this inequality is x = 1, since it represents the vertex of the parabola. Therefore, $ 0.25 is the price that must be discounted to maximize revenues

With x = 1 the value of the new income will be = $ 1983.75

Step-by-step explanation:

Revenue with the current sale price is:

6 * 330 = $ 1980

Let's call x the number of times the price of a sandwich decreases, that is, if x = 1 then the price of the sandwich decreases by $ 0.25

Then, the price would be:

Price = (6-0.25x)

Then, if the price is decreased by a factor of x, then the number of sandwiches sold will increase by a factor of 15x. Therefore the number of clients will be:

Sale = (330 + 15x)

Now we need an equation for income. The income will be equal to the sale price, for the number of sandwiches sold

Income = price * sale

Income = (6-0.25x) (330 + 15x)

In order for this restaurant pricing model to be profitable, the revenues with the new sale price must be greater than the revenues with the sale price of $ 6. So:

New income> current income.

[tex](6-0.25x) * (330 + 15x)> 330 * 6\\ (6-0.25x) * (330 + 15x)> 1980[/tex]

The left side of the inequality represents a parabola:

[tex]-3,750x ^ 2 + 7.5x + 1980> 1980[/tex]

The value that optimizes this inequality is x = 1, since it represents the vertex of the parabola. Therefore, $ 0.25 is the price that must be discounted to maximize revenues

The attached image shows the region that satisfies the proposed inequality and the vertex of the parabola:

[tex]x = \frac{-b}{2a}[/tex]

With x = 1 the value of the new income will be = $ 1983.75

Rental car agency charge:

Let's assume number of miles in as week as x miles

and total rent as R(x)

A rental car agency charges $240 per week plus $0.25 per mile to rent a car

so, we get equation as

[tex]R(x)=240+0.25x[/tex]

Minivan charge:

Let's assume number of miles in as week as 'x' hours

and total charge of minivan as M(x)

The charge for a minivan is $180 per week plus $0.40 per mile

so, we get

[tex]M(x)=180+0.40x[/tex]

now, we can set them equal

and then we can solve for x

[tex]240+0.25x=180+0.40x[/tex]

Subtract both sides by 0.25x

[tex]240+0.25x-0.25x=180+0.40x-0.25x[/tex]

[tex]240=180+0.15x[/tex]

Subtract both sides by 180

[tex]240-180=180+0.15x-180[/tex]

[tex]60=0.15x[/tex]

divide both sides by 0.15

and we get

[tex]x=400 miles/tex]............Answer

The total charge for each vehicle, a car and a minivan, is the same when 400 miles are driven.

The subject you're dealing with here is algebra, specifically, finding the point where two linear functions intersect which shows when the cost of renting the two different vehicles will be the same.

Let's use the formula for the cost of each vehicle, where C is the total cost, W is the flat weekly charge, M is the price per mile, and X is the number of miles driven:

For the car: C = $240W + $0.25M X

For the minivan: C = $180W + $0.40M X

Set these two equations equal to each other to solve for X, the number of miles driven when the two costs are equal:

$240W + $0.25M X = $180W + $0.40M X

Subtracting $180W from both sides and $0.25M X from both sides, you get:

$60W = $0.15M X

Finally, divide by $0.15M to solve for X:

X = $60W/$0.15M = 400 miles

Therefore, the total charge for each vehicle is the same when 400 miles are driven.

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Answer:

Step-by-step explanation:

Let [tex] x[/tex] be the greater number and [tex] y [/tex] be the smaller number. We know that their difference is 15, so we have

[tex] x-y=15 [/tex]

Then, we have the following information: if we add twice the greater (2x) and 8 (2x+8), the result is 3 times the lesser (3y) minus four (3y-4). So, we have

[tex] 2x+8 = 3y-4 \iff 2x-3y = -12 [/tex]

So, we have the follwing system:

[tex] \begin{cases} x-y=15\\2x-3y = -12\end{cases} [/tex]

From the first equation, we can derive [tex] x = y+15 [/tex], and substitute this expression in the second equation to get

[tex] 2(y+15)-3y = -12 \iff 2y + 30 -3y = -12 \iff -y = -42 \iff y = 42 [/tex]

Substitute this value for y in the first equation to get

[tex] x-42=15 \iff x=15+42 \iff x = 57 [/tex]

Firstly, we need to write down the information given in the form of algebraic equations. We can represent our two unknown numbers, the greater and the lesser, as x and y respectively.

From the given information, we can form two equations. The first equation is from "the difference between the two numbers is 15", which gives us x - y = 15, where x is the larger number and y is the smaller one.

Also, we know that "If 8 is added to twice the greater number, the result is 4 less than 3 times the lesser number", this gives us the second equation: 2*x + 8 = 3*y - 4.

We now have a system of two equations that we can solve simultaneously:

1) x - y = 15
2) 2*x + 8 = 3*y - 4

To make it easier, let's multiply the first equation by 2, which gives us 2*x - 2*y = 30.

Now subtract the second equation (2*x + 8 = 3*y - 4) from the first (2*x - 2*y = 30), it yields: -2*y - 3*y = 30 - (-4 - 8).

This simplifies to -5y = 30 + 4 + 8, or -5*y = 42.

To get the value of y, divide by -5, therefore y = -42 / -5 = 42.

Now to find x, we can substitute y = 42 in the first equation (x - y = 15), so we get x = 42 + 15 = 57.

Hence, the greater number is 57 and the lesser number is 42.

Hi, here is the solution...

The Fibonacci series  1, 1, 2, 3, 5, 8, 13, 21, 34...

3rd number = Sum of the first two numbers.

2 = 1 + 1

4th number = Sum of the two numbers before it

That is, 3 = 2 + 1

5th number is 5.

5 = 3 + 2 (Sum of the two numbers before 5).

6th number is 8

8 = 5 + 3

7th number is 13

13 = 8 + 5

8th number is 21

21 = 13 + 8

Therefore, the conjecture is " Each number in the series is The Sum of Two Numbers Before it."

Hope you understand the concept.

Thank you :)

(gog)(-3) basically means g(g(-3)).

g(-3) = (-3)^2 - 3(-3) - 6

g(-3) = 12

g(12) = 102

So the answer is 102.

Assuming Ellies was 8 /13 feet long

9 1/2 + 6 1/3 + 8 1/3 =

getting a common denominator of 6

9 3/6 + 6 2/6 + 8 2/6

23 7/6

24 1/6 feet

If all movies took the same time to download (unlikely), you could download (5 1/4) / (1 2/5) movies

= (21/4) / (7/5) = (21/4)*(5/7) = 15/4 = 3 3/4 movies.

If it takes 1 2 5 hours to download 1 movie, then in 5 1 4 hours, you will download 4 movies.

Hello!

To solve this problem we first need to find the value of each given item.

12^4 is equal to 12·12·12·12, or 20,736

12·12·12·12·12 is equal to 12^5, or 248,832

With this information being provided, it can be said that 12^4 < 12x12x12x12x12

Hope this helps.

Let H = number of hours worked.

He gets $15 for every hour worked, so you need to multiply 15 by h which is written as 15h

You then need to add that to the $200 he gets for showing up.

Total pay = 15h + 200

B) The consumer pays less per item.

If a bag of chips cost .15, but if 20 bags cost $2, you are saving $1.

Hope I helped!

Good Luck!

Answer:

B.) The consumer pays less per item

Step-by-step explanation:

If you buy items in bulk, you will pay a higher total price but a lower price per item. For instance, buying a package of four rolls of paper towels will usually be cheaper than buying one roll four times.

27 x $42 = $1,134

Hope this helps you

-AaronWiseIsBae

The correct answer is A) as the x values go to positive infinity, then the graph goes to negative infinity.

We can tell this by looking at the graph values as x goes up. You'll notice, as we get higher and higher, the graph disappears down. This means it is heading towards negative infinity for the rest of the graph.

The statement  which is true about the end behavior of the graphed function is:

We know that the end behavior of the function is the value where it approaches when x tends to plus infinity and minus infinity.

 From the graph of the function we see that the graph first decreases continuously and then it increases and again it decreases to minus infinity.

Also,

when x → -∞ we see that  f(x) → ∞

and when  x → ∞ then f(x) → -∞

As the function has opposite behavior in both the directions this means that the function is odd.

At x=0 the value of function is: -2

Hello.

The answer is: 24

length=3*width, this can be written as 3w

area=27 sq cm

Formula for the area of a rectangle=27 (area)= 3w (length) * w (width)

27=3w^2

then divide both sides by 3: 9=w^2

take the square root of both sides to get: w=3

Now that we know what the width is, we can substitute that and find the length: 3w= 3*3=24

have a nice day

3(1 - 2x) > 3 - 6x    use distributive property

(3)(1) + (3)(-2x) > 3 - 6x

3 - 6x > 3 - 6x    add 6x to both sides

3 > 3 FALSE

Answer: NO SOLUTION

32=8*4 This is how the equation would be written. Hope I helped :)

The equation that represents this comparison sentence 32 is 8 times as many as 4 is [tex]32 = (8 \times 4)[/tex]

Times also means multiplication

8 times as many as 4 is expressed as [tex](8\times 4)[/tex]

If 32 is 8 times as many as 4, this is expressed as

Hence the equation that represents this comparison sentence 32 is 8 times as many as 4 is [tex]32 = (8 \times 4)[/tex]

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