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Mice21 [21]
2 years ago
13

If mBGC = 16x - 4 and mCGD = 2x + 13, find the value of x so that BGD is a right angle​

Mathematics
1 answer:
Lelu [443]2 years ago
5 0

Hi there! :)

Answer:

\huge\boxed{x = 4.5}

m∠BGC = 16x - 4

m∠CGD = 2x + 13

m∠BGC + m∠CGD sums up to 90°, therefore:

(16x - 4) + (2x + 13) = 90

Combine like terms and simplify:

16x + 2x - 4 + 13 = 90

18x - 4 + 13 = 90

18x + 9 = 90

18x = 81

18x/18 = 81/8

x = 4.5

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Write 23/18 as a decimal.
nika2105 [10]

Answer:

hi

Step-by-step explanation:

the answer would be 1.2778

3 0
2 years ago
Solve the simultaneous equations<br><br> 3x + 2y = 30<br> 3x - y = 21
Mrac [35]

Answer:

x = 8 , y = 3

Step-by-step explanation:

3x + 2y = 30

3x - y = 21      -> y = 3x - 21

3x + 2 (3x - 21) = 30

3x + 6x - 42 = 30

3x + 6x = 30 + 42

9x = 72

x = 72/9 = 8

y = 3*8 - 21 = 24 - 21 = 3

∴ x = 8 & y = 3

3 0
3 years ago
12.20x=372.10<br> Pls write exactly how to do it not just answer
ANEK [815]
To find x, you divide both sides of the equation by 12.20. This would look like this:
12.20x/12.20 =372.10/12.20 . Then, the answer you get is 30.5, so. X=30.5
6 0
3 years ago
Read 2 more answers
Help me with my test
hjlf

Answer:

the answer is 0.0183

Step-by-step explanation:

7 0
2 years ago
A juggler tosses a ball into the air . The balls height, h and time t seconds can be represented by the equation h(t)= -16t^2+40
malfutka [58]
PART A

The given equation is

h(t) = - 16 {t}^{2} + 40t + 4

In order to find the maximum height, we write the function in the vertex form.

We factor -16 out of the first two terms to get,

h(t) = - 16 ({t}^{2} - \frac{5}{2} t) + 4

We add and subtract

- 16(- \frac{5}{4} )^{2}

to get,

h(t) = - 16 ({t}^{2} - \frac{5}{2} t) + - 16( - \frac{5}{4})^{2} - -16( - \frac{5}{4})^{2} + 4

We again factor -16 out of the first two terms to get,

h(t) = - 16 ({t}^{2} - \frac{5}{2} t + ( - \frac{5}{4})^{2} ) - -16( - \frac{5}{4})^{2} + 4

This implies that,

h(t) = - 16 ({t}^{2} - \frac{5}{2} t + ( - \frac{5}{4}) ^{2} ) + 16( \frac{25}{16}) + 4

The quadratic trinomial above is a perfect square.

h(t) = - 16 ( t- \frac{5}{4}) ^{2} +25+ 4

This finally simplifies to,

h(t) = - 16 ( t- \frac{5}{4}) ^{2} +29

The vertex of this function is

V( \frac{5}{4} ,29)

The y-value of the vertex is the maximum value.

Therefore the maximum value is,

29

PART B

When the ball hits the ground,

h(t) = 0

This implies that,

- 16 ( t- \frac{5}{4}) ^{2} +29 = 0

We add -29 to both sides to get,

- 16 ( t- \frac{5}{4}) ^{2} = - 29

This implies that,

( t- \frac{5}{4}) ^{2} = \frac{29}{16}

t- \frac{5}{4} = \pm \sqrt{ \frac{29}{16} }

t = \frac{5}{4} \pm \frac{ \sqrt{29} }{4}

t = \frac{ 5 + \sqrt{29} }{4} = 2.60

or

t = \frac{ 5 - \sqrt{29} }{4} = - 0.10

Since time cannot be negative, we discard the negative value and pick,

t = 2.60s
8 0
3 years ago
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