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3 years ago

GI bisects with angle DGH so that m angle DGI is x - 3 and m angle IGH is 2x-13. What is x?

Mathematics

2 answers:

11111nata11111 [884]3 years ago

7 0

X-3 = 2x-13
+x +x

-3 = 3x-13
+13 +13

10 = 3x
10/3 3/3

3.3=x

leonid [27]3 years ago

3 0

Answer:

x=10

Step-by-step explanation:

We are given that GI bisects the angle DGH.

$m\angle DGI=x-3$

$m\angle IGH=2x-13$

We have to find the value of x

$m\angle DGI=m\angle DGH$ (GI bisect angle DGH)

$x-3=2x-13$

$-3+13=2x-x$

$10=x$

Hence, the value of x=10

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3 years ago

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Vsevolod [243]

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3 years ago

Please help! Thanks in advance.

alukav5142 [94]

In this problem, we need to plug in the given x values for $f(x)=0$ and find a and b.

When we plug in 1, we get: $2 \times {1}^{4} - 5 \times {1}^{3} - 14 \times {1}^{2} + a \times 1 + b = 0$

Simplify:
$2 - 5 - 14 + a + b = 0$
$- 17 + a + b = 0$
$a + b = 17$

We got our first statement about the values of the variables. If we find one more we can find those 2 variables.

We have another given root: 4.

Plug it in:
$2 \times {4}^{4} - 5 \times {4}^{3} - 14 \times {4}^{2} + a \times 4 + b = 0$
$512 - 320 - 224 + 4a + b = 0$
$- 32 + 4a + b = 0$
$4a + b = 32$

Now we have our second one. We can combine them:
$a + b = 17 \\ 4a + b = 32$

I use elimination method which is easier here.

Multiply the top equation by -1: $- a - b = - 17 \\ 4a + b = 32$

Add them up:
$3a = 15$

Simplify:
$a = 5$

Now we have a, we can plug in one of those equations to find b:
$5 + b = 17$
$b = 17 - 5$
$b = 12$

So, the answers are $a=5$ and $b=12$ .

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3 years ago