An airplane allows each passenger 36 kilograms of luggage. Carl has to lower the weight of his suitcase by 25% to stay within the limit. How much did the suitcase originally weight?

Answer: The correct option is option third, i.e.,25 cm square.

Explanation:

From the given figure it is easily noticed that the shaded region contains two congruent parallelograms and 4 congruent triangles.

Area of a parallelogram is the product of base and height.

[tex]\text{Area of a parallelogram}=4\times 3=12[/tex]

The area of a parallelogram is 12 cm square.

Area of a triangle is half of the product of base and height.

[tex]\text{Area of a triangle}=\frac{1}{2}\times 2\times 0.25=0.25[/tex]

The area of a triangle is 0.25 cm square.

Since there are 2 parallelograms and 4 triangles in the figure, therefore the total area is,

[tex]A=2(12)+4(0.25)[/tex]

[tex]A=24+1=25[/tex]

Therefore, the area of figure is 25 cm square and the third option is correct.

Answer:

25 units²

Step-by-step explanation:

Count each whole box as one cm and count the ones that aren't whole as half a cm and you get 25 units²

Out of given expressions, only expression A results in a positive value. Expression B, C, and D all result in a negative value.

To determine which expression results in a positive value, evaluate each:

So, "only expression A results in a positive value".

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Answer: Angle addition postulate.

Explanation: If [tex]\angle TRV= 60^{\circ}[/tex] and [tex]\angle TRS=4x^{\circ}[/tex]

here, if we have to prove x=30

If there is a condition that TR is a line which meets with the line segment VS at point R then by the Angle addition postulate,  we can say that [tex]\angle TRV+\angle TRS=180^{\circ}[/tex]⇒[tex]x=30^{\circ}[/tex]

But,

In option (1) substitution property of equality

If there is condition that  [tex]\angle TRV=\angle TRS[/tex]

then we can use  substitution property of equality,

And, in this case [tex]4x^{\circ}=60^{\circ}[/tex]⇒[tex]x=15^{\circ}[/tex]

which is wrong. So, we can not use this property here.

In option (3) subtraction property of equality

There is no use of this property to find the value x.

In option (4) addition property of equality

There is no use of this property to find the value x.

The omitted reason in step 3 should be the angle addition postulate.

From the diagram attached ;

mTRV = 60 ; ∠TRS = 4x

According to the addition postulate :

mTRV + ∠TRS = 180° (sum of linear pair of angles).

Hence, the missing reason for the third step is the angle addition postulate.

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To calculate 7 x 12 using distributive property and partial products, decompose 12 into 10 and 2, then multiply 7 by each part and add the results. The sum of 70 and 14 gives you 84, which is the product of 7 and 12.

To find the product of 7 x 12 using the distributive property and partial products, we first break down the number 12 into 10 + 2. Then we use the distributive property to multiply 7 by each of these parts separately:

Now, we add these partial products together to find the total:

70 + 14 = 84

Therefore, 7 x 12 equals 84 when we use distributive property and partial products.

The clown bought a total of 70 heart-shaped balloons. This is found by multiplying the number of bags (5) by the number of balloons in each bag (14).

The question involves a basic multiplication operation in mathematics. The clown bought 5 bags of heart-shaped balloons and each bag contains 14 balloons. To find the total number of balloons, you multiply the number of bags (5) by the number of balloons in each bag (14). This is done as follows:

So, the clown bought a total of 70 heart-shaped balloons.

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The mean, median, and mode are measures of central tendency. The median value is based on the median , while the arithmetic average is based on the mean. The most frequently occurring value in a data set is based on the mode .

For example, if we have the following data set: {4, 18, 18, 19, 19, 19, 19, 19, 20, 20}, the mean is 17.5 (170/10), the median is 19, and the mode is 19.

Final answer:

By applying the Pythagorean theorem, it's determined that the set of line segments that could create a right triangle is option b. (15, 36, 39), as it's the only set that satisfies the equation a² + b² = c².

Explanation:

The question asks which set of line segments could create a right triangle. To solve this, we apply the Pythagorean theorem, which states for a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as a² + b² = c², where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

Therefore, the set of line segments that could create a right triangle is option b. (15, 36, 39).

Answer:

  b.  15, 36, 39

Step-by-step explanation:

You want the set of line segments that could form a right triangle.

A set of 3 integers is a Pythagorean triple if it satisfies the Pythagorean theorem:

  a² +b² = c²

The most common primitive triples are {3, 4, 5}, {5, 12, 13}. If two of three numbers match these, but the third does not, a right triangle cannot be formed.

We note that {3, 4, 5} has the smallest first number of any Pythagorean triple, and it is the only triple that is an arithmetic sequence.

We can reduce the given numbers to their lowest form to see if we can determine whether any is a Pythagorean triple:

  a. 15 : 30 : 35 = 3 : 6 : 7 . . . . . not a right triangle

  b. 15 : 36 : 39 = 5 : 12 : 13 . . . . forms a right triangle

  c. 15 : 20 : 29 = 3 : 4 : 5.8 . . . . . not a right triangle

  d. 5 : 15 : 30 = 1 : 3 : 6 . . . . not a triangle

__

Additional comment

The attachment shows the values of a² +b² -c² for the different answer choices. That expression will evaluate to 0 if the numbers form a right triangle. If the sum is negative, any triangle formed would be obtuse. As we noted above, choice D values do not even form a triangle.

Other Pythagorean triples commonly seen in algebra problems are ...

  {7, 24, 25}, {8, 15, 17}, {9, 40, 41}, {20, 21, 29}

You may also notice that when the two largest numbers differ by 1, the smallest is the root of their sum: 3 = √(4+5), 5 = √(12+13), 7 = √(24+25), and so on. This is another way we can tell {3, 6, 7} is not a Pythagorean triple: 3 ≠ √(6+7).

it started at -10.5 then rose 5.2

 -10.5 +5.2 = -5.3

then fell 3.6

-5.3 - 3.6 = -8.9

 so it was -8.9 degrees Celcius

Answer:

[tex]\frac{-\sqrt{2}-\sqrt{6}}{4}[/tex]

Step-by-step explanation:

PLATO

To find the initial amount of water in the pail, set up a system of equations based on the total volume and the information provided after transferring some water. Solve the equations to obtain the initial quantity of 957 milliliters in the pail.

A student posed a problem: A tank and a pail contain a total of 5136 milliliters of water. Jacob pours 314 milliliters of water from the pail into the tank. The amount of water in the tank is now 7 times what is left in the pail. How much water was in the pail at first?

Let's denote the initial amount of water in the tank as T milliliters and in the pail as P milliliters. According to the given information, the combined quantity of water in both is 5136 milliliters:

After transferring 314 milliliters from the pail to the tank, the tank now has T + 314 milliliters, and the pail has P - 314 milliliters. It is also given that the water in the tank is now 7 times the water left in the pail:

Now, we have a system of two equations:
   

By solving these equations, we can find the initial amount of water in the pail, P. First, modify the second equation to isolate T:

Next, substitute the expression for T from the second equation into the first equation and solve for P:

Initially, there were 957 milliliters of water in the pail.

Answer:9 Groups

Step-by-step explanation:

Given

There are 126 boys and 135 girls

The greatest no of groups that could be form is determine by factorizing 126 and 135

[tex]126=2\times 7\times 9[/tex]

[tex]135=3\times 5\times 9[/tex]

both contains 9 as highest multiplying factor thus 9 groups can be formed.

Answer: 74:111

Step-by-step explanation: To find 185 in ratio 2:3:

First, add the ratios: 2 + 3 = 5

Second, each ratio will be put over the total: [tex]\frac{2}{5}[/tex] and [tex]\frac{3}{5}[/tex]

Third, multiply the number by the fraction of each proportion:

185 . [tex]\frac{2}{5}[/tex] = 74

185 . [tex]\frac{3}{5}[/tex] = 111

So, 185 in ration 2:3 gives ratio 74:111.

Lucy and 3 friends = 4 people

 30 ounces /  4 people = 7.5 ounces each