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ss7ja [257]
2 years ago
9

Elliot has a total of 26 books. He has 12 more fiction books than nonfiction books. Let x represent the number of fiction books

and y represent the number of nonfiction books.
The system of equations models the total costs for each.
x + y = 26
x – y = 12
Elliot added the two equations and the result was
2x = 38.
Solve the equation. How many of each type of book does Elliot have?

fiction books

nonfiction books
Mathematics
2 answers:
AlladinOne [14]2 years ago
4 0

<u>Answers</u>

19 fiction books

7 nonfiction books


<u>Explanation</u>

x + y = 26  ............................................. (i)

x – y = 12  ............................................ (ii)

Elliot added the two equations and the result was

2x = 38.

Dividing both sides by 2;

x = 19

There are 19 fiction books.

Substituting x in equation (i),

x + y = 26             when x = 19

19 + y = 26

y = 26 - 19

   = 7

There are 7 nonfiction books

lidiya [134]2 years ago
4 0

Answer:

Which equation represents the situation? x+(x-12)=26

Step-by-step explanation:

Check marks prove it

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Emma went to a salon to get her hair cut. The price of the haircut is $65. She wants to leave a 20% tip. What is the total amoun
Rudiy27

Answer:

She should leave a total of $78.

Step-by-step explanation:

To find this, we first need to find the tip amount. We can do this by multiplying the total by the tip percentage.

$65 * 20% = $13

Now that we have that, we need to add it to the cost.

$65 + $13 = $78

8 0
2 years ago
A child has a box full of colored building blocks. She will choose one block without looking. The odds against choosing a blue b
Mama L [17]

(a) A child has a box full of colored building blocks. She will choose one block without looking. The odds against choosing a blue block are 4/7. What is the probability of choosing a blue block?

Answer:

7/11 is the probability of choosing a blue block.

Step-by-step explanation:

We need the probability of choosing a blue block,

Odds:

The odds of an event is the ratio of the probability of an event to the probability of its complement. In other words, it is the ratio of favorable outcomes to unfavorable outcomes.

The odds against choosing a blue block are 4/7 means. In 11 chances, 4 events will happen in which blue block will not be chosen and 7 events will happen in which blue blocks will be chosen.

So, the probability of not choosing the blue block is 4/11.

Probability of choosing blue block: complement of 4/11 which is equal to 7/11.

(b) Amanda is playing a role-playing game with her friends. She will roll dice to determine if her character unlocks a treasure chest. The probability of her character unlocking the treasure chest is 13/20. Find the odds in favor of her character unlocking the treasure chest.

Answer:

The odds in favor of her character unlocking the treasure chest are 13/7.

Step-by-step explanation:

The probability of Amanda's character unlocking the treasure chest is 13/20.

It means, in 20 total chances, 13 times an event will happen where Amanda's character unlocks the treasure chest while the rest 7 times, her character would not open treasure chest.

Favorable events: 13

Unfavorable events: 7

Hence, the odds in favor of her character unlocking the treasure chest are 13/7.

7 0
2 years ago
A local museum charges $25 per adult and $12 per child for admission fees. At the end of a day, the museum made $9,014 in total
Natali [406]

Answer:

There were 172 guests that were children and 278 guests that were adults

Step-by-step explanation:

Step 1: State what is known

It is $25 per adult

It is $12 per child

The made $9014 dollars

There were 450 guests

Step 2: Define equations

25y + 12x = 9014 -----1

x + y = 450 ------------2

Step 3: Rearrange equation 2 for x

x + y = 450

x = 450 - y --------------3

Step 4: Substitute 3 into 1 for y and solve for y

25y + 12(450 - y) = 9014

25y + 5400 - 12y = 9014

13y = 3614

y = 3614/13

y = 278

Step 5: Substitute y = 278 into 3 to solve for x

x = 450 - (278)

x = 172

Therefore 172 children and 278 adults visited the museum

4 0
2 years ago
What value for c will make the expression a perfect square trinomial? x2 – 7x + c negative StartFraction 49 Over 4 EndFraction n
puteri [66]

Answer: c=\frac{49}{4}

Step-by-step explanation:

You can find the value of "c" that will make it a perfect square trinomial by Completing the square.

Given the following expression provided in the exercise:

x^2 - 7x + c

You can notice that it is written in this form:

ax^2-bx+c

Then, you can identify that the coefficient "b" is:

 b=-7

Since to complete the square you must add and subtract the half of square of coefficient "b", you can conclude that:

c=(\frac{b}{2})^2

Therefore, substituting "b" into c=(\frac{b}{2})^2, you get:

c=(\frac{-7}{2})^2\\\\c=\frac{49}{4}

6 0
2 years ago
Read 2 more answers
Which statement justifies that 3x2 − 2x − 4 multiplied by 2x2 + x − 3 obeys the closure property of multiplication? The result 6
zalisa [80]

We have been given two polynomials 3x^2-2x -4 \text{ and } 2x^2+x-3

Let us first multiply these polynomials.

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Now, we know that polynomials follows closure property of multiplication.

It means that when we multiply two polynomials, the result will be a polynomial.

Since, when we multiplied the given polynomials, we got 6 x^4 - x^3 - 19 x^2 + 2 x + 12 which is a polynomial.

Therefore, the correct option is

The result 6 x^4 - x^3 - 19 x^2 + 2 x + 12   is a polynomial.


4 0
2 years ago
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