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nataly862011 [7]
3 years ago
11

Need help fast! need the value of x and please show the work!

Mathematics
1 answer:
lions [1.4K]3 years ago
6 0

By the external angle of a triangle theorem

m < ABD = m < BDC + m < BCD

That is  5x + 2 = x^2 - 1 + 4x - 3

x^2  + 4x - 5x - 1 - 3 - 2 = 0

x^2 - x - 6 = 0

(x - 3)(x + 2) = 0

x = 3,  -2

x cannot be -2 because that would make the external angle, 5x-2 negative.

Answer x = 3

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Please help find them <br>1 AB<br><br>2 BC​
spin [16.1K]

Answer:

AB ≈ 15.7 cm, BC ≈ 18.7 cm

Step-by-step explanation:

(1)

Using the Cosine rule in Δ ABD

AB² = 12.4² + 16.5² - (2 × 12.4 × 16.5 × cos64° )

       = 153.76 + 272.25 - (409.2 cos64° )

       = 426.01 - 179.38

       = 246.63 ( take the square root of both sides )

AB = \sqrt{246.63} ≈ 15.7 cm ( to 1 dec. place )

(2)

Calculate ∠ BCD in Δ BCD

∠ BCD = 180° - (53 +  95)° ← angle sum in triangle

∠ BCD = 180° - 148° = 32°

Using the Sine rule in Δ BCD

\frac{BC}{sin53} = \frac{BD}{sin32} = \frac{12.4}{sin32} ( cross- multiply )

BC × sin32° = 12.4 × sin53° ( divide both sides by sin32° )

BC = \frac{12.4sin53}{sin32} ≈ 18.7 cm ( to 1 dec. place )

         

6 0
2 years ago
4 of 7<br> June rolls a fair dice 234 times.<br> How many times would June expect to roll a one?
alexandr402 [8]

Answer: 39 times

Step-by-step explanation: A fair dice has 6 sides with each side having a different number between 1 and 6. Therefore, the probability of rolling a 1 is 1/6. To find out how many times June would expect to roll a 1 after rolling the dice 234 times, you must multiply 234 by 1/6 to get the answer of 39.

7 0
2 years ago
Ashton purchased a new vacuum for $1,150 at the Best Buy. He has a 15% coupon. How much will he save?
Kipish [7]

Answer:

$172.50

Step-by-step explanation:

1150(0.15)

172.50

6 0
3 years ago
Find the GCF ( Greatest Common Factor)<br><br><br>18;45<br><br><br>24;16
nika2105 [10]
18;45 = 9

24;16 = 8

I hope this helps
8 0
3 years ago
The length of the rectangle is twice the width. Find the length of the rectangle if the perimeter is 42m.
kompoz [17]

Answer:

28m

Step-by-step explanation:

2x+x=42

3x=42

x=14

However, since the length of the rectangle is twice the width, we'll need to multiply it by 2.

So: 14 times 2=28

8 0
3 years ago
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