MATHEMATICS COLLEGE

On Monday, a local hamburger shop sold a combined total of 544 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times thenumber of hamburgers sold. How many hamburgers were sold on Monday?

Answers

Answer 1

Answer:

Answer:

136 hamburgers

Step-by-step explanation:

Create an equation where x is the number of hamburgers sold.

The number of cheeseburgers sold can be represented by 3x, since it was 3 times the number of hamburgers.

3x + x = 544

Solve for x:

4x = 544

x = 136

So, 136 hamburgers were sold on Monday

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Please help me thank you

Answers

Uhm I’m not sure, haven’t did fraction math in a long time

Malory isn’t putting money in two savings accounts.Account A started with $150 and Account B started with $300.Malory deposits $16 in Account A and $12 in Account B each month.In how many months will Account A have a balance at least as great as Account B?What will that balance be?

Answers

Given:

There are two savings accounts - account A has $150 and account B has $300 to begin with.
Malorie deposits $16 in account A and $12 in account B every month.

To Find:

The number of months where the balance of both is equal and the balance itself.

Solution:

In 37.5 months, the account balances in both accounts will be equal.

This balance will be equal to $750 in both account A and B.

Calculation:

Let x be the number of months where both the accounts have equal balance.

So, at the end of x months, 16x is the amount of money that will be added to account A (since $16 is added every month).

And the total amount at the end of x months will therefore be $(150+16x)

Similarly, at the end of x months, 12x is the amount of money that will be added to account B (since $12 will be added every month).

And the total amount at the end of x months will therefore be $(300+12x)

By our assumption, x is the number of months it will take for both the accont balances will be equal. Therefore, we have the equation

$150+16x=300+12x\n4x=150\nx=37.5$

Therefore, in 37.5 months, the account balances in both accounts will be equal.

This balance will be equal to $150+16(37.5)=750$ i.e. $750 will be the balance in both account A and B.

Determine what information you would need to know in order to use SAS to show that the triangles are congruent

Answers

Answer:

Option D

Step-by-step explanation:

We already have two reasons to support two sides. We have the reflexive property and that the base is divided by a midpoint. So we will need an angle.

Also, AC is the median so it divides into two congruent angles and parts

Option D, because the reflexive property is then included in that part

Find the Derivative.
f(x) = -xcos3x

Answers

Answer:

$(d)/(dx)(-xcos3x)= 3x \ sin(3x)- cos(3x)$

Step-by-step explanation:

Use the Product Rule for derivatives, which states that:

$(d)/(dx) =[f(x)g(x)]= f(x)g'(x)+f'(x)g(x)$

In the function we are given, $f(x)=-x \cos3x$ , we can break it up into two factors: -x is being multiplied by cos3x.

Now, we have the factors:

$-x \n $cos 3x$

Before using the product rule, let's find the derivative of cos3x using the chain rule and the power rule.

$(d)/(dx)(cos3x)= (d)/(dx) (cos3x) * (d)/(dx) (3x) \n (d)/(dx)(cos3x)= (-sin3x) * 3 \n (d)/(dx) (cos3x) = -3sin(3x)$

Now let's apply the product rule to f(x) = -xcos3x.

$(d)/(dx)(-xcos3x)= (-x)(-3sin3x) + (-1)(cos3x)$

Simplify this equation.

$(d)/(dx)(-xcos3x)= (x)(3sin3x) - (cos3x)$

Multiply x and 3 together and remove the parentheses.

$(d)/(dx)(-xcos3x)= 3x \ sin(3x)- cos(3x)$

Therefore, this is the derivative of the function $f(x)=-xcos3x$ .

Hi there!

$\large\boxed{f'(x) = -cos3x + 3xsin3x}$

$f(x) = -xcox3x\n\n\text{Use the product rule and chain rule to solve for the derivative:}\n\n(dy)/(dx)= -cos3x + (-x * (-sin3x) * 3)\n\n= -cos3x + 3xsin3x$

A library contains only paperback and hardback books. If the ratio of paperback books to the total number of books is 3 to 5, which statement must be true? The ratio of paperback books to hardback books is 2 to 3. The ratio of paperback books to hardback books is 2 to 3. The ratio of paperback books to hardback books is 3 to 2. The ratio of paperback books to hardback books is 3 to 2. There are exactly 2 paperback books in the library. There are exactly 2 paperback books in the library. There are exactly 8 hardback books in the library. There are exactly 8 hardback books in the library.

Answers

Answer:

A library contains only paperback and hardback books. If the ratio of paperback books to the total number of books is 3 to 5, the true statement is:

The ratio of paperback books to hardback books is 3 to 2.

Step-by-step explanation:

The number of books in the library = 5

The number of paperback books in the library = 3

Therefore, the number of hardback books in the library = 2 (5 - 3)

Then, the relationship between the paperback books and the hardback books in the library can be expressed as a ratio of 3:2. This still gives the sum of the ratios as 5, which is the total number of books in the library, including paperback and hardback books.

Final answer:

The correct statement is that the ratio of paperback to hardback books is 3:2. The ratios provided do not indicate the exact quantity of books in the library.

Explanation:

The ratio of paperbacks to the total number of books is 3:5. This means that for every 5 books, 3 are paperbacks and therefore, the remaining 2 must be hardbacks. Hence the ratio of paperback to hardback books is actually 3:2, not 2:3.

Note that the ratios given do not indicate the exact number of books. Therefore, we cannot confidently say that there are exactly 2 paperback books or exactly 8 hardback books in the library.

Learn more about Ratios here:

brainly.com/question/32531170

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Which set of ordered pairs could represent the same function as y = x2 ?A (1, 1), (2, 4), (3,6)
B (1,1),(3,9), (7,49)
© (1,2), (4,16), (8, 64)
D (4,8), (5, 25), (6,36)