To solve the equation 23(x−4)=−10 , Izzy wants to multiply both sides of the equation by the reciprocal of the fraction. Name the reciprocal.(1 point)

Question

____ / ____

Answer 1

To find the reciprocal of a fraction, you swap the numerator and the denominator. In the equation you provided, we can first rewrite it to isolate the fraction:

\[ 23(x - 4) = -10. \]

Now, we can express the left side as a fraction:

\[ \frac{23(x - 4)}{1} = -10. \]

The fraction here is \( \frac{23}{1} \).

The reciprocal of \( \frac{23}{1} \) is \( \frac{1}{23} \).

So, the reciprocal is:

1 / 23.

Answer 2

Noooooo

Answer 3

I apologize for the misunderstanding. Let's carefully analyze the equation \( 23(x - 4) = -10 \).

To find the reciprocal in terms of what Izzy might be trying to achieve, consider that she may want to divide both sides by \( 23 \) in order to isolate \( (x - 4) \).

The equation can be treated like a multiplication by expressing it as:

\[ y = 23(x - 4). \]

If we want to find the reciprocal of the coefficient of \( (x - 4) \) in that multiplication (which is \( 23 \)), we see that the reciprocal of \( 23 \) is:

\[ \frac{1}{23}. \]

So if we focus purely on multiplying both sides by the reciprocal to help solve for \( x \), the equivalent form would look like:

Multiply both sides by \( \frac{1}{23} \):

\[ \frac{1}{23} \cdot 23(x - 4) = \frac{1}{23} \cdot (-10). \]

Thus, the reciprocal is still:

1 / 23.

If you were looking for the reciprocal of a specific fraction from the given equation, or if I misunderstood your request in any way, please clarify, and I'll be happy to assist further!

Answer 4

There are 2 types of tickets to attend an awards dinner—silver and gold. The gold tickets are $8 more than the silver. If Patrick bought 10 tickets at each level and spent a total of $140, find the price of each ticket.(1 point)

$ ___ for each silver ticket and $_____ for each gold ticket

Answer 5

Let's define the prices of the tickets:

• Let \( s \) be the price of each silver ticket.
• Then the price of each gold ticket will be \( s + 8 \) (since gold tickets are $8 more than silver tickets).

Patrick bought 10 tickets of each type, so the total cost can be expressed as follows:

\[ 10s + 10(s + 8) = 140. \]

Now, let's simplify the equation:

\[ 10s + 10s + 80 = 140. \]

Combine like terms:

\[ 20s + 80 = 140. \]

Now, subtract 80 from both sides:

\[ 20s = 60. \]

Next, divide both sides by 20:

\[ s = 3. \]

So, the price of each silver ticket is $3. Now, we can find the price of each gold ticket:

\[ s + 8 = 3 + 8 = 11. \]

Thus, the prices are:

• $3 for each silver ticket
• $11 for each gold ticket

Final answer:

$3 for each silver ticket and $11 for each gold ticket.

Answer 6

Kendra is making bread, but the recipe she’s using makes 4 loaves. She only wants to make one loaf. The changed recipe calls for 2 1/2 cups of flour and sugar combined. If the original recipe calls for 2 cups of sugar, find the amount of flour (in cups) in the original recipe.(1 point)
___cups

Answer 7

To find the amount of flour in the original recipe, we first need to determine how much flour was used in the original recipe based on the information provided.

1. Original Recipe: The original recipe calls for 2 cups of sugar, and the total amount of flour and sugar combined is given as 2 1/2 cups (or \( \frac{5}{2} \) cups) for the modified recipe (for 1 loaf).

2. Since Kendra is using the modified recipe and the total amount of flour and sugar combined is \( 2.5 \) cups, she can define this as:

\[ \text{Flour} + \text{Sugar} = 2.5 \text{ cups} \]

3. From the original recipe, we know the amount of sugar is 2 cups, so we can use this to set up our first equation for the original recipe.

4. Total amount of flour and sugar in the original recipe:

   • Let \( f \) be the amount of flour in cups in the original recipe.
   • The combined amount of flour and sugar in the original recipe would then be: \[ f + 2 = 4 \text{ loaves} \quad \text{(the original recipe)} \]

5. Kendra is making only \( \frac{1}{4} \) of the original recipe (since she’s making 1 loaf instead of 4):

\[ \frac{f + 2}{4} = 2.5 \]

Now, since \( f + 2 \) represents the total for the entire original recipe (for 4 loaves), we can solve directly:

6. Rearranging \( 2.5 = f + 2\)

First, convert \( 2.5 \) into a fraction for ease of calculation:

\[ 2.5 = \frac{5}{2} \]

So now we have:

\[ f + 2 = \frac{5}{2} \] \[ f = \frac{5}{2} - 2 \]

Convert 2 to a fraction:

\[ 2 = \frac{4}{2} \]

So:

\[ f = \frac{5}{2} - \frac{4}{2} \] \[ f = \frac{1}{2} \]

Thus, the original recipe contains:

0.5 cups of flour (or 1/2 cup).

Answer 8

Nope give me a different answer

Answer 9

Let’s go through the problem again step by step to find the correct amount of flour in the original recipe.

1. Original Recipe for 4 Loaves:

   • Sugar: 2 cups
   • Let \( f \) be the amount of flour in cups in the original recipe.

   The total amount for flour and sugar in the original recipe is: \[ f + 2 \text{ cups of sugar} \]

2. When Kendra wants to make only 1 loaf, she will use the modified amounts, which are given as:

   • Total for 1 loaf (flour + sugar) = \( 2 \frac{1}{2} \) cups.

   Converting \( 2 \frac{1}{2} \) to an improper fraction gives: \[ 2 \frac{1}{2} = \frac{5}{2} \text{ cups} \]

3. The total amount for the modified recipe containing flour and sugar must equal the amount used: \[ \text{Flour (for 1 loaf)} + \text{Sugar (for 1 loaf)} = \frac{5}{2} \]

4. From the original recipe, if she is using \( \frac{1}{4} \) of the original amounts to make 1 loaf, the amount of sugar would also be reduced: \[ \text{Sugar (for 1 loaf)} = \frac{2 \text{ cups}}{4} = \frac{1}{2} \text{ cup} \]

5. Now we can substitute the sugar back into the equation: \[ \text{Flour (for 1 loaf)} + \frac{1}{2} = \frac{5}{2} \]

6. Solve for the amount of flour used in the modified recipe: \[ \text{Flour (for 1 loaf)} = \frac{5}{2} - \frac{1}{2} = \frac{4}{2} = 2 \text{ cups} \]

7. Therefore, for the original recipe, the total amount of flour corresponds to the total for the whole recipe (4 loaves): \[ \text{Flour (original recipe)} = 2 \text{ cups (for 1 loaf)} \times 4 = 8 \text{ cups} \]

Since Kendra is wanting to find the amount of flour in the original recipe, after revisiting the calculations:

The original recipe contains:

8 cups of flour.