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IgorC [24]
3 years ago
15

Find the length of BC if ABC is equilateral with AB=12x+4 and AC=8x+12

Mathematics
1 answer:
Citrus2011 [14]3 years ago
4 0

Answer:

BC = 28

Step-by-step explanation:

Since the triangle is equilateral then all 3 sides are congruent.

Equate AB and AC and solve for x, that is

12x + 4 = 8x + 12 ( subtract 8x from both sides )

4x + 4 = 12 ( subtract 4 from both sides )

4x = 8 ( divide both sides by 4 )

x = 2, thus

AC = 8x + 12 = (8 × 2) + 12 = 16 + 12 = 28

Since the 3 sides are congruent then BC = 28

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What is the five-number-summary of the following data set? Write the numbers separated by commas.
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If there are 9 girls and 11 boys in a class, what percentage of the class are girls
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1. Find the total number of class members
    9 + 11 = 20

2. Find 9 as a percentage of 20
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3 years ago
Which statement explains the equation (6 × 3) 2 = 6(3 × 2)?
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8990 9000

Step-by-step explanation:

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7 0
3 years ago
Determine the projection of vector w onto vector u. u=9i-6j, v=-3i-2j, w=19i+15j
Naily [24]

Answer:

proj_uw=6.2i-4.2j

Step-by-step explanation:

The projection of a vector v onto a vector u is defined as the projection of the vector v on the line that contains the vector u. It can be calculated  using the following formula:

proj_uv=\frac{u\cdot v}{||u||^2} u

Where:

u\cdot v

Is the dot product between u and v which is given by:

u\cdot v= $$\sum_{i=1}^{n} u_iv_i= u_1v_1+u_2v_2+...+u_nv_n$$

and:

||u||

Is the magnitude of vector which can be calculated as follows:

||u||=\sqrt{u_1^2+u_2^2+...+u_n^2}

In this sense, the projection of vector w onto vector u is:

proj_uw=\frac{u\cdot w}{||u||^2} u

Where the dot product between u and w is:

u\cdot w =(9*19)+(-6*15)=171-90=81

And the magnitude of u is:

||u||=\sqrt{9^2+(-6)^2} = 3 \sqrt{13}

Thus:

proj_uw=\frac{u\cdot w}{||u||^2} u=\frac{81}{117} \langle9,-6\rangle=\langle6.23,-4.15\rangle\approx6.2i-4.2j

8 0
3 years ago
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