Choose the inequality that matches this situation.

Question

Sarah will spend at most $26 on candy. Each item costs $3, and she has a coupon for a $5 discount.

Answer 1

To represent the situation with an inequality, let's define the variable:

• Let \( x \) be the number of candy items Sarah buys.

The cost of each candy item is $3, so the total cost for \( x \) items will be \( 3x \). Additionally, Sarah has a coupon for a $5 discount, which means her total cost after applying the discount will be \( 3x - 5 \).

Since Sarah will spend at most $26, we can set up the inequality as follows:

\[ 3x - 5 \leq 26 \]

This inequality represents the situation where Sarah's total spending on candy, after applying the discount, does not exceed $26.

Answer 2

what is the sighn

Answer 3

In the inequality we set up, the sign used is "less than or equal to" (≤). This indicates that the amount Sarah spends after using her coupon can be equal to or less than $26.

The complete inequality is:

\[ 3x - 5 \leq 26 \]

Answer 4

choose the inequality that matches this situation.

Company A charges $312 to power-wash the siding of a house plus $12 for each window. Company B charges $36 per window, and the price includs the siding. How many windows must a house have to make the total cost from Company A be less expensive than Company B?

Answer 5

Let's define the variable:

• Let \( x \) be the number of windows.

Company A's cost:

• Fixed cost for power-washing the siding: $312.
• Additional cost for \( x \) windows: $12 per window.
• Total cost for Company A: \[ \text{Cost}_A = 312 + 12x \]

Company B's cost:

• Cost for \( x \) windows at $36 each:
• Total cost for Company B: \[ \text{Cost}_B = 36x \]

We want to find out when Company A's cost is less than Company B's cost: \[ 312 + 12x < 36x \]

To isolate \( x \), we can first subtract \( 12x \) from both sides: \[ 312 < 36x - 12x \] \[ 312 < 24x \]

Finally, we can divide both sides by 24: \[ \frac{312}{24} < x \] \[ 13 < x \]

This means that \( x > 13 \).

So the inequality that matches the situation is: \[ 312 + 12x < 36x \]

Answer 6

Choose the inequality that matches this situation.

Company A charges a fee of $25 plus $0.20 per brouchure to print and deliver them. Company B charges $0.30 per brochure. How many would need to be ordered for Company A to cost more than Company B

Solve this equation for x:

5(2x + 3) = 7x - 3

Answer 7

First, let's set up the inequality for the given situation with Company A and Company B.

Company A's cost:

• Fixed fee: $25
• Cost per brochure: $0.20
• Total cost for \( x \) brochures: \[ \text{Cost}_A = 25 + 0.20x \]

Company B's cost:

• Cost per brochure: $0.30
• Total cost for \( x \) brochures: \[ \text{Cost}_B = 0.30x \]

We want to find when Company A's cost is more than Company B's cost: \[ 25 + 0.20x > 0.30x \]

Now solve the inequality:

1. Subtract \( 0.20x \) from both sides: \[ 25 > 0.30x - 0.20x \] \[ 25 > 0.10x \]

2. Divide both sides by \( 0.10 \): \[ \frac{25}{0.10} > x \] \[ 250 > x \] or \[ x < 250 \]

The inequality that matches the situation is: \[ 25 + 0.20x > 0.30x \]

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Now, solving the equation:

Equation:
\[ 5(2x + 3) = 7x - 3 \]

1. Distribute on the left side: \[ 10x + 15 = 7x - 3 \]

2. Subtract \( 7x \) from both sides: \[ 10x - 7x + 15 = -3 \] \[ 3x + 15 = -3 \]

3. Subtract 15 from both sides: \[ 3x = -3 - 15 \] \[ 3x = -18 \]

4. Divide both sides by 3: \[ x = -6 \]

So, the solution to the equation \( 5(2x + 3) = 7x - 3 \) is: \[ x = -6 \]

Answer 8

What is it called when heat and pressure change one type of rock into another?(1 point)
Responses

erosion
erosion

metamorphism
metamorphism

crystallization
crystallization

deposition
deposition

What is the theory that Earth’s surface is composed of several rock plates that fit together like the pieces of a puzzle?(1 point)
Responses

geological shift
geological shift

plate tectonics
plate tectonics

metamorphism
metamorphism

divergent plate boundary

Where are most deposits of natural resources found?(1 point)
Responses

at present and past plate boundaries
at present and past plate boundaries

in the earth's oceans
in the earth's oceans

in very tall mountain ranges
in very tall mountain ranges

near rivers and streams
near rivers and streams

Answer 9

Here are the correct responses to your questions:

1. What is it called when heat and pressure change one type of rock into another?

   • Response: metamorphism

2. What is the theory that Earth’s surface is composed of several rock plates that fit together like the pieces of a puzzle?

   • Response: plate tectonics

3. Where are most deposits of natural resources found?

   • Response: at present and past plate boundaries

If you have any more questions or need further clarification, feel free to ask!

Answer 10

What does discovery of giant rabbit fossils on an island in the Mediterranean Sea tell scientists about the Earth’s changing landforms?(1 point)
Responses

The island had been underwater in the past.
The island had been underwater in the past.

The island had remained unchanged since its formation.
The island had remained unchanged since its formation.

The island was formed by a volcanic eruption in the past.
The island was formed by a volcanic eruption in the past.

The island had to be connected to the mainland in the past.

Answer 11

The discovery of giant rabbit fossils on an island in the Mediterranean Sea suggests that:

• Response: The island had to be connected to the mainland in the past.

This is because the presence of land mammals, like rabbits, typically indicates that there was once a land connection between the island and a larger landmass, as these animals would have needed a pathway to migrate to the island. If you have any further questions or need clarification, feel free to ask!