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OLEGan [10]
3 years ago
5

PLEASE HELP!!!!!!

Mathematics
1 answer:
Sauron [17]3 years ago
7 0

Part A; The height of the base is 15 cm.

Part B; Approximately 320 cm of cardboard is used to make the candy box.

Step-by-step explanation:

Step 1; We split the triangle into two right-angled triangles. So each triangle has an 8 cm long adjacent side and a 17 cm long hypotenuse. As we have two sides of the triangle, we can solve for the other side's length by using Pythagoras' theorem. Assume the opposite side of the triangle measures x cm. According to Pythagoras theorem, 17² = 8² + x²,

289 = 64 + x², x² = 289 - 64 = 225, x = √225 = 15 cm.

So the height of the base is 15 cm.

Step 2; To find the amount of cardboard needed, we need to determine the perimeter. There are 2 triangular faces and 3 rectangular faces.

A triangle's perimeter is the sum of all the side lengths.

The perimeter of the triangular face = 16 + 17 + 17 = 50 cm.

The perimeter for two triangular faces = 2 × 50 = 100 cm.

Step 3; A rectangle's perimeter is determined by multiplying the rectangle's length with the rectangle's width.

Of the three rectangular faces, two are similar.

The perimeter for the face along the side of the triangle = 2 × (20 + 17) =

2 × 37 = 74 cm.

The perimeter for two similar rectangular planes = 2 × 74 = 148 cm.

The perimeter for the face along the base of the triangle = 2 × (16 + 20) =

2 × 36 = 72 cm.

The perimeter of the entire shape = 100 + 148 + 72 = 320 cm.

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3 years ago
The length of a rectangle is 4 meters less than twice its width. The are of a rectangle is 70m^2. Find the dimensions of the rec
igomit [66]

Answer:

The length is 7 m

The width is 10 m

Step-by-step explanation:

length = x

width = 2x - 4

length * width = area

It is given that the area is 70 m^{2}

From there

x * (2x - 4) = 70

2x^{2} - 4x = 70

2x^{2} - 4x - 70 = 0

x^{2} - 2x - 35 = 0

Now we have a quadratic equation, which is  ax^{2} + bx + c = 0, where a \neq 0

In this equation a = 1, b = -2 and c = -35

Discriminant (D) formula is b² - 4ac

D = -2^{2}  - 4 * 1 * (-35) = 144 > 0

This discriminant is more than 0, so there are two possible x

Their formulas are  \frac{- b - \sqrt{D}  }{2a} and \frac{- b + \sqrt{D}  }{2a}

x_{1} =  \frac{- (-2) - \sqrt{144} }{2} = -5 < 0 (the length of the rectangle has to be more than 0, so we don't use this x)

x_{2} = \frac{- (-2) + \sqrt{144} }{2} = 7 > 0 (this one is right)

Calculating the dimensions

length = x = 7 (m)

width = 2x - 4 = 2 * 7 - 4 = 10 (m)

8 0
3 years ago
The perimeter of a rectangular window is 324 cm.
padilas [110]

Answer:

76 cm

Step-by-step explanation:

P=2L+2w

324=2(86)+2w

324=172+2w

324-172=2w

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4 0
3 years ago
Determine the solution to f(x) = g(x) using the following system of equations: (5 points) f(x) = 3x − 23 g(x) = −4.5x + 7
jeka94

Answer:

(The solution is (4, -11).

Step-by-stp explanation:

Let f(x) = g(x) = y:

y = 3x − 23

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0 = 7.5x - 30

7.5x = 30

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Plug this into the first equation:

y = 3(4) - 23

y =  -11.

5 0
3 years ago
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Answer:

A

Step-by-step explanation:

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