MATHEMATICS MIDDLE SCHOOL

Triangle ABC has a perimeter 22cmAB= 8 cm
BC= 5cm

By calculation, deduce whether triangle ABC is a right-angled triangle

Answers

Answer 1

Answer:

Answer:

ΔABC is not a right- angled triangle

Step-by-step explanation:

Given AB = 8, BC = 5

Then AC = 22 - (8 + 5) = 22 - 13 = 9 cm

Using the converse of Pythagoras' identity

If the square of the longest side equals the sum of the squares of the other 2 sides then triangle is right.

AC² = 9² = 81

AB² + BC² = 8² + 5² = 64 + 25 = 89

81 ≠ 89, hence ΔABC is not right- angled

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a box of 10 markers weighs 105 grams. if the empty box weights 15 grams, how much does each marker weigh?

Answers

first, ,how much do all the markers weight? the box with the markers weights 105, so without the box all the markers weigh 105-15=90 grams.

so 90 grams is the weight of 10 markers together, and each of them will weigh one tenth of this: 90/10=9

so each marker weights 9 grams.

Final answer:

The weight of each marker can be found by first subtracting the weight of the empty box from the total weight to get the weight of all markers, then dividing by the number of markers. Each marker weighs 9 grams.

Explanation:

Firstly, we can find the total weight of the markers by subtracting the weight of the empty box from the total weight of the box with the markers. Doing this calculation (105 grams - 15 grams) gives us the total weight of the markers, which is 90 grams. As there are 10 markers, we can find the weight of each marker by dividing the total weight of the markers by the number of markers. This calculation (90 grams / 10) results in each marker weighing 9 grams.

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0.75 turn into a percent

Answers

1. Move the decimal to places to the right.

2. Remove the zero

3. And the answer is 75%

75%, hun! Let us know if you need any more help haha

Find the area of the image below:A. 24.6 square units
B. 25.8 square units
C. 26.3 square units
D. 27.5 square units

Answers

Answer:

Option D. $27.7\ units^(2)$

Step-by-step explanation:

we know that

The area of the image is equal to the area of the complete square minus the area of triangle 1, minus the area of triangle 2, minus the area of triangle 3, minus the area of trapezoid 4

see the attached figure to better understand the problem

Find the area of the complete square

$A=8^(2)=64\ units^(2)$

Find the area of triangle 1

$A=(1/2)(4)(5)=10\ units^(2)$

Find the area of triangle 2

$A=(1/2)(3)(3)=4.5\ units^(2)$

Find the area of triangle 3

$A=(1/2)(3)(3)=4.5\ units^(2)$

Find the area of triangle 4

$A=(1/2)(3+4)(5)=17.5\ units^(2)$

The area of the image is equal to

$A=64-10-4.5-4.5-17.5=27.7\ units^(2)$

The area of the given image, calculated using the Shoelace Formula based on the coordinates of its vertices, is 27.5 square units.

The correct answer is option D.

To determine the area of the provided image formed by the points H(0,0), L(1,5), K(4,8), J(-1,8), and I(-4,5), we can employ the Shoelace Formula. This formula calculates the area of a polygon based on the coordinates of its vertices. For a polygon with vertices (x₁, y₁), (x₂, y₂), ..., (xₙ, yₙ), the formula is:

Area = 1/2 * |x₁y₂ + x₂y₃ + ... + xₙy₁ - y₁x₂ - y₂x₃ - ... - yₙx₁|

Applying this formula to the given points:

Area = 1/2 * |(0 * 5 + 1 * 8 + 4 * 8 + (-1) * 5 + (-4) * 0) - (0 * 1 + 5 * 4 + 8 * (-1) + 8 * (-4) + 5 * 0)|

Area = 1/2 * |(0 + 8 + 32 - 5 - 0) - (0 + 20 - 8 - 32 + 0)|

Area = 1/2 * |35 - (-20)|

Area = 1/2 * 55

Area = 27.5 square units

Therefore, the correct answer is D. 27.5 square units.

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determine wheter 3x+12+x is equivalent to 4(3+x). use properties of operations to justify your answer. please help! answer only if you know!

Answers

3x + 12 + x = 4x + 12 becuase 3x and x are like terms so you can add them
4(3 + x) = 12 + 4x because 4 times 3 is 12 and 4 times x is 4x so you add them to get 12 + 4x which can be rearranged to equal 4x + 12
So in short: 3x + 12 +x is equivalent to 4(3+x)

there are 20 ounces of water in a glass. someone drinks 55%of the water. how many ounces of water is left?

Answers

Given:
20 ounces of water
someone finishes 55% of water
What is left?

20 × 0.55 (55% = $(55)/(100)$ = 0.55)
11

20 - 11 = 9
There are 9 ounces of water left

How would you solve x in this equation: 0.85x=200

Answers

The value of x in the equation is 235.294.

What is an Equation?

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

The given equation is 0.85x = 200.

In order to solve the equation, we need the variable x on one side and a number on the other side.

0.85x = 200

Dividing both sides of the equation by 0.85,

0.85x / 0.85 = 200 / 0.85

x = 235.294

Hence after solving, the value of x is 235.294.

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Well, you would have to divide to get the answer. What you do to one side you do to the other. So, you would divide 0.85 by 0.85. and then you would divide 200 by 0.85. Then the answer would be estimated to 235.294.

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