[Mawar Tanjung]

The tense used to talk about things that happened before another past event is called the past perfect tense.

For example:

• “She had finished her homework before dinner.”

In this sentence, “had finished” (past perfect) indicates that the homework was completed before the event of having dinner (simple past).

[Mawar Tanjung]

Making a paper boat is a fun and simple craft! Here’s a step-by-step guide:

Materials Needed:

• A rectangular piece of paper (like an 8.5 x 11 inch sheet)

Instructions:

1. Fold the Paper in Half:

   • Start with the paper oriented horizontally. Fold it in half lengthwise, then unfold it to create a crease down the center.

2. Fold the Top Corners:

   • Take the top two corners and fold them down to meet the center crease, forming a triangle at the top.

3. Fold the Bottom Edges:

   • Fold the bottom edge of the paper (the rectangle below the triangle) up towards the base of the triangle, creating a flap on each side. You should have a triangle on top with two flaps at the bottom.

4. Fold the Bottom Flaps:

   • Take the bottom flaps (the parts you just folded up) and fold them outwards, one to the left and one to the right.

5. Create the Boat Shape:

   • Now, hold the triangle from the bottom and gently pull the two sides apart to form the base of the boat. Flatten the bottom to help it stand.

6. Adjust and Decorate:

   • Adjust the shape as needed, and you can decorate your boat with markers or stickers if you like!

Enjoy Your Boat!

You can test it out on water or just display it. Making multiple boats can lead to fun races too!

[Mawar Tanjung]

Sound is produced through the vibration of objects, which creates pressure waves in the surrounding medium (such as air, water, or solids). Here’s a simple breakdown of how sound is made:

1. Vibration: An object vibrates, either by being struck, plucked, or blown into. For example, a guitar string vibrates when plucked.

2. Pressure Waves: These vibrations create waves of pressure in the surrounding medium. As the object moves, it compresses and rarefies (creates low pressure) the air particles around it.

3. Transmission: The pressure waves travel through the medium to our ears. The speed of sound varies depending on the medium—it’s faster in solids and liquids than in gases.

4. Detection: When the sound waves reach our ears, they cause the eardrum to vibrate. This vibration is converted into electrical signals that the brain interprets as sound.

Overall, sound is the result of mechanical vibrations traveling through a medium!

[Mawar Tanjung]

To simplify the expression <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mn>3</mn><mo stretchy=”false”>(</mo><mi>y</mi><mo>−</mo><mn>5</mn><mo stretchy=”false”>)</mo><mo>+</mo><mn>2</mn><mo stretchy=”false”>(</mo><mi>y</mi><mo>+</mo><mn>3</mn><mo stretchy=”false”>)</mo></mrow><annotation encoding=”application/x-tex”>3(y – 5) + 2(y + 3)</annotation></semantics></math>3(y−5)+2(y+3), follow these steps:

1. Distribute <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mn>3</mn></mrow><annotation encoding=”application/x-tex”>3</annotation></semantics></math>3 and <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mn>2</mn></mrow><annotation encoding=”application/x-tex”>2</annotation></semantics></math>2 to the terms inside the parentheses:

   <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mn>3</mn><mo stretchy=”false”>(</mo><mi>y</mi><mo>−</mo><mn>5</mn><mo stretchy=”false”>)</mo><mo>=</mo><mn>3</mn><mi>y</mi><mo>−</mo><mn>15</mn></mrow><annotation encoding=”application/x-tex”>3(y – 5) = 3y – 15</annotation></semantics></math>3(y−5)=3y−15
   <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mn>2</mn><mo stretchy=”false”>(</mo><mi>y</mi><mo>+</mo><mn>3</mn><mo stretchy=”false”>)</mo><mo>=</mo><mn>2</mn><mi>y</mi><mo>+</mo><mn>6</mn></mrow><annotation encoding=”application/x-tex”>2(y + 3) = 2y + 6</annotation></semantics></math>2(y+3)=2y+6

2. Combine the results:

   <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mn>3</mn><mi>y</mi><mo>−</mo><mn>15</mn><mo>+</mo><mn>2</mn><mi>y</mi><mo>+</mo><mn>6</mn></mrow><annotation encoding=”application/x-tex”>3y – 15 + 2y + 6</annotation></semantics></math>3y−15+2y+6

3. Combine like terms:

   <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mo stretchy=”false”>(</mo><mn>3</mn><mi>y</mi><mo>+</mo><mn>2</mn><mi>y</mi><mo stretchy=”false”>)</mo><mo>+</mo><mo stretchy=”false”>(</mo><mo>−</mo><mn>15</mn><mo>+</mo><mn>6</mn><mo stretchy=”false”>)</mo><mo>=</mo><mn>5</mn><mi>y</mi><mo>−</mo><mn>9</mn></mrow><annotation encoding=”application/x-tex”>(3y + 2y) + (-15 + 6) = 5y – 9</annotation></semantics></math>(3y+2y)+(−15+6)=5y−9

The simplified expression is:

<math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><menclose notation=”box”><mstyle scriptlevel=”0″ displaystyle=”false”><mstyle scriptlevel=”0″ displaystyle=”false”><mstyle scriptlevel=”0″ displaystyle=”true”><mrow><mn>5</mn><mi>y</mi><mo>−</mo><mn>9</mn></mrow></mstyle></mstyle></mstyle></menclose></mrow><annotation encoding=”application/x-tex”>\boxed{5y – 9}</annotation></semantics></math>5y−9​

[Mawar Tanjung]

To solve for <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mi>y</mi></mrow><annotation encoding=”application/x-tex”>y</annotation></semantics></math>y in the equation <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mn>4</mn><mi>y</mi><mo>+</mo><mn>9</mn><mo>=</mo><mn>2</mn><mi>y</mi><mo>−</mo><mn>5</mn></mrow><annotation encoding=”application/x-tex”>4y + 9 = 2y – 5</annotation></semantics></math>4y+9=2y−5, follow these steps:

1. Subtract <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mn>2</mn><mi>y</mi></mrow><annotation encoding=”application/x-tex”>2y</annotation></semantics></math>2y from both sides:

   <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mn>4</mn><mi>y</mi><mo>−</mo><mn>2</mn><mi>y</mi><mo>+</mo><mn>9</mn><mo>=</mo><mo>−</mo><mn>5</mn></mrow><annotation encoding=”application/x-tex”>4y – 2y + 9 = -5</annotation></semantics></math>4y−2y+9=−5
   <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mn>2</mn><mi>y</mi><mo>+</mo><mn>9</mn><mo>=</mo><mo>−</mo><mn>5</mn></mrow><annotation encoding=”application/x-tex”>2y + 9 = -5</annotation></semantics></math>2y+9=−5

2. Subtract 9 from both sides:

   <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mn>2</mn><mi>y</mi><mo>=</mo><mo>−</mo><mn>5</mn><mo>−</mo><mn>9</mn></mrow><annotation encoding=”application/x-tex”>2y = -5 – 9</annotation></semantics></math>2y=−5−9
   <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mn>2</mn><mi>y</mi><mo>=</mo><mo>−</mo><mn>14</mn></mrow><annotation encoding=”application/x-tex”>2y = -14</annotation></semantics></math>2y=−14

3. Divide by 2:

   <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mi>y</mi><mo>=</mo><mo>−</mo><mn>7</mn></mrow><annotation encoding=”application/x-tex”>y = -7</annotation></semantics></math>y=−7

Thus, the solution is <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mi>y</mi><mo>=</mo><mo>−</mo><mn>7</mn></mrow><annotation encoding=”application/x-tex”>y = -7</annotation></semantics></math>y=−7.

[Mawar Tanjung]

To solve for <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mi>y</mi></mrow><annotation encoding=”application/x-tex”>y</annotation></semantics></math>y in the equation <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mn>3</mn><mo stretchy=”false”>(</mo><mi>y</mi><mo>−</mo><mn>4</mn><mo stretchy=”false”>)</mo><mo>+</mo><mn>2</mn><mo>=</mo><mn>5</mn><mo stretchy=”false”>(</mo><mi>y</mi><mo>+</mo><mn>1</mn><mo stretchy=”false”>)</mo><mo>−</mo><mn>3</mn></mrow><annotation encoding=”application/x-tex”>3(y – 4) + 2 = 5(y + 1) – 3</annotation></semantics></math>3(y−4)+2=5(y+1)−3, follow these steps:

1. Distribute the terms:

   <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mn>3</mn><mi>y</mi><mo>−</mo><mn>12</mn><mo>+</mo><mn>2</mn><mo>=</mo><mn>5</mn><mi>y</mi><mo>+</mo><mn>5</mn><mo>−</mo><mn>3</mn></mrow><annotation encoding=”application/x-tex”>3y – 12 + 2 = 5y + 5 – 3</annotation></semantics></math>3y−12+2=5y+5−3

2. Simplify both sides:

   <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mn>3</mn><mi>y</mi><mo>−</mo><mn>10</mn><mo>=</mo><mn>5</mn><mi>y</mi><mo>+</mo><mn>2</mn></mrow><annotation encoding=”application/x-tex”>3y – 10 = 5y + 2</annotation></semantics></math>3y−10=5y+2

3. Rearrange the equation to isolate <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mi>y</mi></mrow><annotation encoding=”application/x-tex”>y</annotation></semantics></math>y:

   <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mn>3</mn><mi>y</mi><mo>−</mo><mn>5</mn><mi>y</mi><mo>=</mo><mn>2</mn><mo>+</mo><mn>10</mn></mrow><annotation encoding=”application/x-tex”>3y – 5y = 2 + 10</annotation></semantics></math>3y−5y=2+10
   <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mo>−</mo><mn>2</mn><mi>y</mi><mo>=</mo><mn>12</mn></mrow><annotation encoding=”application/x-tex”>-2y = 12</annotation></semantics></math>−2y=12

4. Divide by -2:

   <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mi>y</mi><mo>=</mo><mo>−</mo><mn>6</mn></mrow><annotation encoding=”application/x-tex”>y = -6</annotation></semantics></math>y=−6

Thus, the solution is <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mi>y</mi><mo>=</mo><mo>−</mo><mn>6</mn></mrow><annotation encoding=”application/x-tex”>y = -6</annotation></semantics></math>y=−6.

[Mawar Tanjung]

Yes! To divide <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mfrac><mn>3</mn><mn>4</mn></mfrac></mrow><annotation encoding=”application/x-tex”>\frac{3}{4}</annotation></semantics></math>43​ by 2, you can multiply by the reciprocal of 2. The reciprocal of 2 is <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow><annotation encoding=”application/x-tex”>\frac{1}{2}</annotation></semantics></math>21​.

So, you can do the calculation like this:

<math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>÷</mo><mn>2</mn><mo>=</mo><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>×</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>=</mo><mfrac><mrow><mn>3</mn><mo>×</mo><mn>1</mn></mrow><mrow><mn>4</mn><mo>×</mo><mn>2</mn></mrow></mfrac><mo>=</mo><mfrac><mn>3</mn><mn>8</mn></mfrac></mrow><annotation encoding=”application/x-tex”>\frac{3}{4} \div 2 = \frac{3}{4} \times \frac{1}{2} = \frac{3 \times 1}{4 \times 2} = \frac{3}{8}</annotation></semantics></math>43​÷2=43​×21​=4×23×1​=83​

Therefore, <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>÷</mo><mn>2</mn><mo>=</mo><mfrac><mn>3</mn><mn>8</mn></mfrac></mrow><annotation encoding=”application/x-tex”>\frac{3}{4} \div 2 = \frac{3}{8}</annotation></semantics></math>43​÷2=83​.

[Mawar Tanjung]

I don’t create art myself, but I love the idea of storytelling through art! Whether it’s painting, writing, or even music, each form has its own way of expressing emotions and ideas, making it a powerful medium for connection and creativity. What about you? Do you have a favorite type of art?

[Mawar Tanjung]

Certainly! To divide <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mn>2</mn><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow><annotation encoding=”application/x-tex”>2 \frac{1}{2}</annotation></semantics></math>221​ by <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mn>1</mn><mfrac><mn>1</mn><mn>4</mn></mfrac></mrow><annotation encoding=”application/x-tex”>1 \frac{1}{4}</annotation></semantics></math>141​, we first convert both mixed numbers to improper fractions.

1. Convert <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mn>2</mn><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow><annotation encoding=”application/x-tex”>2 \frac{1}{2}</annotation></semantics></math>221​:

   <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mn>2</mn><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>=</mo><mfrac><mrow><mn>2</mn><mo>×</mo><mn>2</mn><mo>+</mo><mn>1</mn></mrow><mn>2</mn></mfrac><mo>=</mo><mfrac><mrow><mn>4</mn><mo>+</mo><mn>1</mn></mrow><mn>2</mn></mfrac><mo>=</mo><mfrac><mn>5</mn><mn>2</mn></mfrac></mrow><annotation encoding=”application/x-tex”>2 \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{4 + 1}{2} = \frac{5}{2}</annotation></semantics></math>221​=22×2+1​=24+1​=25​

2. Convert <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mn>1</mn><mfrac><mn>1</mn><mn>4</mn></mfrac></mrow><annotation encoding=”application/x-tex”>1 \frac{1}{4}</annotation></semantics></math>141​:

   <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mn>1</mn><mfrac><mn>1</mn><mn>4</mn></mfrac><mo>=</mo><mfrac><mrow><mn>1</mn><mo>×</mo><mn>4</mn><mo>+</mo><mn>1</mn></mrow><mn>4</mn></mfrac><mo>=</mo><mfrac><mrow><mn>4</mn><mo>+</mo><mn>1</mn></mrow><mn>4</mn></mfrac><mo>=</mo><mfrac><mn>5</mn><mn>4</mn></mfrac></mrow><annotation encoding=”application/x-tex”>1 \frac{1}{4} = \frac{1 \times 4 + 1}{4} = \frac{4 + 1}{4} = \frac{5}{4}</annotation></semantics></math>141​=41×4+1​=44+1​=45​

Now, we can divide the two improper fractions by multiplying by the reciprocal:

<math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mfrac><mn>5</mn><mn>2</mn></mfrac><mo>÷</mo><mfrac><mn>5</mn><mn>4</mn></mfrac><mo>=</mo><mfrac><mn>5</mn><mn>2</mn></mfrac><mo>×</mo><mfrac><mn>4</mn><mn>5</mn></mfrac></mrow><annotation encoding=”application/x-tex”>\frac{5}{2} \div \frac{5}{4} = \frac{5}{2} \times \frac{4}{5}</annotation></semantics></math>25​÷45​=25​×54​

The <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mn>5</mn></mrow><annotation encoding=”application/x-tex”>5</annotation></semantics></math>5s cancel out:

<math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mo>=</mo><mfrac><mn>4</mn><mn>2</mn></mfrac><mo>=</mo><mn>2</mn></mrow><annotation encoding=”application/x-tex”>= \frac{4}{2} = 2</annotation></semantics></math>=24​=2

Thus, <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mn>2</mn><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>÷</mo><mn>1</mn><mfrac><mn>1</mn><mn>4</mn></mfrac><mo>=</mo><mn>2</mn></mrow><annotation encoding=”application/x-tex”>2 \frac{1}{2} \div 1 \frac{1}{4} = 2</annotation></semantics></math>221​÷141​=2.

[Mawar Tanjung]

1. Convert <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mn>3</mn><mfrac><mn>3</mn><mn>4</mn></mfrac></mrow><annotation encoding=”application/x-tex”>3 \frac{3}{4}</annotation></semantics></math>343​:

   <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mn>3</mn><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>=</mo><mfrac><mrow><mn>3</mn><mo>×</mo><mn>4</mn><mo>+</mo><mn>3</mn></mrow><mn>4</mn></mfrac><mo>=</mo><mfrac><mrow><mn>12</mn><mo>+</mo><mn>3</mn></mrow><mn>4</mn></mfrac><mo>=</mo><mfrac><mn>15</mn><mn>4</mn></mfrac></mrow><annotation encoding=”application/x-tex”>3 \frac{3}{4} = \frac{3 \times 4 + 3}{4} = \frac{12 + 3}{4} = \frac{15}{4}</annotation></semantics></math>343​=43×4+3​=412+3​=415​

2. Convert <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mn>2</mn><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow><annotation encoding=”application/x-tex”>2 \frac{1}{2}</annotation></semantics></math>221​:

   <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mn>2</mn><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>=</mo><mfrac><mrow><mn>2</mn><mo>×</mo><mn>2</mn><mo>+</mo><mn>1</mn></mrow><mn>2</mn></mfrac><mo>=</mo><mfrac><mrow><mn>4</mn><mo>+</mo><mn>1</mn></mrow><mn>2</mn></mfrac><mo>=</mo><mfrac><mn>5</mn><mn>2</mn></mfrac></mrow><annotation encoding=”application/x-tex”>2 \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{4 + 1}{2} = \frac{5}{2}</annotation></semantics></math>221​=22×2+1​=24+1​=25​

Now, we multiply the two improper fractions:

<math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mfrac><mn>15</mn><mn>4</mn></mfrac><mo>×</mo><mfrac><mn>5</mn><mn>2</mn></mfrac><mo>=</mo><mfrac><mrow><mn>15</mn><mo>×</mo><mn>5</mn></mrow><mrow><mn>4</mn><mo>×</mo><mn>2</mn></mrow></mfrac><mo>=</mo><mfrac><mn>75</mn><mn>8</mn></mfrac></mrow><annotation encoding=”application/x-tex”>\frac{15}{4} \times \frac{5}{2} = \frac{15 \times 5}{4 \times 2} = \frac{75}{8}</annotation></semantics></math>415​×25​=4×215×5​=875​

To convert <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mfrac><mn>75</mn><mn>8</mn></mfrac></mrow><annotation encoding=”application/x-tex”>\frac{75}{8}</annotation></semantics></math>875​ back to a mixed number:

1. Divide 75 by 8, which gives 9 with a remainder of 3.
2. So, <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mfrac><mn>75</mn><mn>8</mn></mfrac><mo>=</mo><mn>9</mn><mfrac><mn>3</mn><mn>8</mn></mfrac></mrow><annotation encoding=”application/x-tex”>\frac{75}{8} = 9 \frac{3}{8}</annotation></semantics></math>875​=983​.

Thus, <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mn>3</mn><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>×</mo><mn>2</mn><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>=</mo><mn>9</mn><mfrac><mn>3</mn><mn>8</mn></mfrac></mrow><annotation encoding=”application/x-tex”>3 \frac{3}{4} \times 2 \frac{1}{2} = 9 \frac{3}{8}</annotation></semantics></math>343​×221​=983​.

[Mawar Tanjung]

1. Distribute the terms:

   <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mn>4</mn><mi>z</mi><mo>−</mo><mn>8</mn><mo>−</mo><mn>5</mn><mi>z</mi><mo>−</mo><mn>3</mn><mo>+</mo><mn>2</mn><mi>z</mi><mo>−</mo><mn>8</mn></mrow><annotation encoding=”application/x-tex”>4z – 8 – 5z – 3 + 2z – 8</annotation></semantics></math>4z−8−5z−3+2z−8

2. Combine like terms:

   • <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mn>4</mn><mi>z</mi><mo>−</mo><mn>5</mn><mi>z</mi><mo>+</mo><mn>2</mn><mi>z</mi><mo>=</mo><mn>1</mn><mi>z</mi></mrow><annotation encoding=”application/x-tex”>4z – 5z + 2z = 1z</annotation></semantics></math>4z−5z+2z=1z or simply <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mi>z</mi></mrow><annotation encoding=”application/x-tex”>z</annotation></semantics></math>z
   • Combine the constants: <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mo>−</mo><mn>8</mn><mo>−</mo><mn>3</mn><mo>−</mo><mn>8</mn><mo>=</mo><mo>−</mo><mn>19</mn></mrow><annotation encoding=”application/x-tex”>-8 – 3 – 8 = -19</annotation></semantics></math>−8−3−8=−19

3. Putting it all together:

   <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mi>z</mi><mo>−</mo><mn>19</mn></mrow><annotation encoding=”application/x-tex”>z – 19</annotation></semantics></math>z−19

So, the simplified expression is <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mi>z</mi><mo>−</mo><mn>19</mn></mrow><annotation encoding=”application/x-tex”>z – 19</annotation></semantics></math>z−19.

[Mawar Tanjung]

To solve the equation <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mn>3</mn><mo stretchy=”false”>(</mo><mi>y</mi><mo>−</mo><mn>4</mn><mo stretchy=”false”>)</mo><mo>=</mo><mn>15</mn></mrow><annotation encoding=”application/x-tex”>3(y – 4) = 15</annotation></semantics></math>3(y−4)=15:

1. Distribute the 3:

   <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mn>3</mn><mi>y</mi><mo>−</mo><mn>12</mn><mo>=</mo><mn>15</mn></mrow><annotation encoding=”application/x-tex”>3y – 12 = 15</annotation></semantics></math>3y−12=15

2. Add 12 to both sides:

   <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mn>3</mn><mi>y</mi><mo>=</mo><mn>27</mn></mrow><annotation encoding=”application/x-tex”>3y = 27</annotation></semantics></math>3y=27

3. Divide by 3:

   <math xmlns=”http://www.w3.org/1998/Math/MathML” display=”block”><semantics><mrow><mi>y</mi><mo>=</mo><mn>9</mn></mrow><annotation encoding=”application/x-tex”>y = 9</annotation></semantics></math>y=9

So, <math xmlns=”http://www.w3.org/1998/Math/MathML”><semantics><mrow><mi>y</mi><mo>=</mo><mn>9</mn></mrow><annotation encoding=”application/x-tex”>y = 9</annotation></semantics></math>y=9.

[Mawar Tanjung]

Making a homemade card holder is simple and fun! Here’s a quick guide:

Materials Needed:

• Cardboard or cardstock
• Scissors
• Glue or tape
• Ruler
• Pencil
• Decorative materials (markers, stickers, washi tape, etc.)

Instructions:

1. Cut the Base:

   • Use the ruler to measure and cut a rectangle from the cardboard (e.g., 6×8 inches) for the base.

2. Create the Slots:

   • Cut additional strips of cardboard about 1 inch wide. These will form the slots for holding cards. You can cut 3-4 strips, each around 4-6 inches long.

3. Attach the Slots:

   • Space the strips evenly on the base and glue or tape them down vertically. Leave some space between them to fit cards.

4. Make the Back:

   • Cut another rectangle for the back, slightly larger than the base (e.g., 7×9 inches) to give it support. Attach it to the back of the base.

5. Decorate:

   • Use markers, stickers, or any decorative materials to personalize your card holder.

6. Let it Dry:

   • If you used glue, let it dry completely before using it.

Finished!

Your homemade card holder is now ready to display your favorite cards or notes!

[Mawar Tanjung]

To form a negative sentence using a verb, you generally add “not” after the auxiliary (helping) verb or use “do not” (or “does not,” “did not”) with the main verb. Here are some examples:

1. With an auxiliary verb:

   • Positive: “She is going.”
   • Negative: “She is not going.”

2. With a main verb using “do”:

   • Positive: “He likes apples.”
   • Negative: “He does not like apples.”

3. In the past tense:

   • Positive: “They finished the project.”
   • Negative: “They did not finish the project.”

This structure helps convey that something is not happening or is untrue.

[Mawar Tanjung]

Research is crucial for several reasons:

1. Knowledge Expansion: It helps expand our understanding of various subjects, leading to new discoveries and insights.

2. Informed Decision-Making: Research provides the evidence needed for making informed decisions in fields like medicine, policy, and education.

3. Problem Solving: It identifies issues and explores potential solutions, driving innovation and improvement in society.

4. Critical Thinking: Engaging in research fosters critical thinking and analytical skills, which are essential for evaluating information and arguments.

5. Social Progress: Research contributes to advancements in technology, health, and social structures, ultimately improving quality of life.

Overall, research is foundational for growth and development in both individual and collective contexts.