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Mrac [35]
2 years ago
10

Diagram 5 shows a triangle ABD such that AD = 17 cm, AB = 10 cm and BD = 21 cm. The straight line AC is perpendicular to the str

aight line BD and the value of area of triangle ABD is an integer. Calculate the length of AC, in cm. (4 marks)​

Mathematics
1 answer:
OlgaM077 [116]2 years ago
7 0

Answer:

8

Step-by-step explanation:

100 = x^2 + AC^2

17^2 = AC^2 + (21 - x)^2

289 = AC^2 + 21^2 + x^2 - 2*21*x

289 =<u> AC^2</u> + 441 +<u> x^2</u> - 42x

from 1st equation AC^2 + x^2 = 100

289 = 441 + 100 - 42x

289 = 541 - 42x

42x = 541 - 289 = 252

x = 252/42 = 6

so AC^2 = 100 - 6^2 = 100 - 36 = 64

AC = 8

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Convert to standard form.<br> y-5=-3(x+2)​
Paul [167]

Answer:

Step-by-step explanation:

y-5=3(x+2)

y-5=3x+6

y-5-6=3x+6-6

y-1=3x

7 0
3 years ago
What is the equation of a circle with center (−8, 3) and radius 8?
Genrish500 [490]

Answer:

x^2 + y^2 + 16x + 6y + 9 = 0

Step-by-step explanation:

Using the formula for equation of a circle

(x - a)^2 + (y + b)^2 = r^2

(a, b) - the center

r - radius of the circle

Inserting the values given in the question

(-8,3) and r = 8

a - -8

b - 3

r - 8

[ x -(-8)]^2 + (y+3)^2 = 8^2

(x + 8)^2 + (y + 3)^2 = 8^2

Solving the brackets

( x + 8)(x + 8) + (y +3)(y+3) = 64

x^2 + 16x + 64 + y^2 + 6y + 9 = 64

Rearranging algebrally,.

x^2 + y^2 + 16x + 6y + 9+64 - 64 = 0

Bringing in 64, thereby changing the + sign to -

Therefore, the equation of the circle =

x^2 + y^2 + 16x + 6y + 9 = 0

7 0
3 years ago
If a recipe requires 400 grams of potatoes for four people, how many kilograms would be required for 12 people?
Tasya [4]

Answer:

1.2 kg

Step-by-step explanation:

We need 400 grams of potatoes for 4 people. That means each person will require 400 / 4 = 100 grams.

Now, we have 12 people, so the total number of grams needed will be:

(100 g/person) * (12 people) = 1200 grams

However, we want the answer in kilograms. There are 1000 grams in a kilogram, so divide 1200 by 1000:

1200 / 1000 = 1.2 kg

The answer is 1.2 kg.

6 0
3 years ago
Read 2 more answers
A six sided die is rolled three times. Find the probability that the result is an even number for every roll.
bogdanovich [222]

|\Omega|=6^3\\|A|=3^3\\\\P(A)=\dfrac{3^3}{6^3}=\left(\dfrac{3}{6}\right)^3=\left(\dfrac{1}{2}\right)^3=\dfrac{1}{8}=12.5\%

4 0
2 years ago
Can someone please help me
harkovskaia [24]

Answer:

E

Step-by-step explanation:

\sqrt 6 is an irrational number, as it cannot be written as the ratio of 2 numbers.

It is also a real number, as it does not include the square root of a negative number.

Therefore, E is the correct option.

3 0
3 years ago
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