At Westonci.ca, we provide clear, reliable answers to all your questions. Join our vibrant community and get the solutions you need. Get immediate answers to your questions from a wide network of experienced professionals on our Q&A platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
Sagot :
ΔRST ≡ ΔABC
<R = <A
(5x + 30)° = (x² - 8x)°
5x + 30 = x² - 8x
-x² + 5x + 30 = x² - x² - 8x
-x² + 5x + 30 = -8x
+ 8x + 8x
-x² + 13x + 30 = 0
x = -(13) ± √((13)² - 4(-1)(30))
2(-1)
x = -13 ± √(169 + 120)
-2
x = -13 ± √(289)
-2
x = -13 ± 17
-2
x = -13 + 17 U x = -13 - 17
-2 -2
x = 4 U x = -30
-2 -2
x = -2 x = 25
<C = 4x - 5 U <C = 4x - 5
<C = 4(-2) - 5 U <C = 4(25) - 5
<C = -8 - 5 U <C = 100 - 5
<C = -13° U <C = 95°
or
ΔRST ≡ ΔABC
<A + <C = <R
(x² - 8x)°+ (4x - 5)° = (5x + 30)°
(x² - 8x) + (4x - 5) = (5x + 30)
(x² - 8x + 4x - 5) = (5x + 30)
x² - 4x - 5 = 5x + 30
- 5x - 5x
x² - 9x - 5 = 30
- 30 - 30
x² - 9x - 35 = 0
x = -(-9) ± √((-9)² - 4(1)(-35))
2(1)
x = 9 ± √(81 + 140)
2
x = 9 ± √(221)
2
x = 9 ± 14.86
2
x = 9 + 14.86 U x = 9 - 14.86
2 2
x = 23.86 U x = -4.14
2 2
x = 11.93 U x = -2.07
<R = <A
(5x + 30)° = (x² - 8x)°
5x + 30 = x² - 8x
-x² + 5x + 30 = x² - x² - 8x
-x² + 5x + 30 = -8x
+ 8x + 8x
-x² + 13x + 30 = 0
x = -(13) ± √((13)² - 4(-1)(30))
2(-1)
x = -13 ± √(169 + 120)
-2
x = -13 ± √(289)
-2
x = -13 ± 17
-2
x = -13 + 17 U x = -13 - 17
-2 -2
x = 4 U x = -30
-2 -2
x = -2 x = 25
<C = 4x - 5 U <C = 4x - 5
<C = 4(-2) - 5 U <C = 4(25) - 5
<C = -8 - 5 U <C = 100 - 5
<C = -13° U <C = 95°
or
ΔRST ≡ ΔABC
<A + <C = <R
(x² - 8x)°+ (4x - 5)° = (5x + 30)°
(x² - 8x) + (4x - 5) = (5x + 30)
(x² - 8x + 4x - 5) = (5x + 30)
x² - 4x - 5 = 5x + 30
- 5x - 5x
x² - 9x - 5 = 30
- 30 - 30
x² - 9x - 35 = 0
x = -(-9) ± √((-9)² - 4(1)(-35))
2(1)
x = 9 ± √(81 + 140)
2
x = 9 ± √(221)
2
x = 9 ± 14.86
2
x = 9 + 14.86 U x = 9 - 14.86
2 2
x = 23.86 U x = -4.14
2 2
x = 11.93 U x = -2.07
In any statement like this one: [tex]\triangle RST \cong \triangle ABC[/tex] you can assume that the points match up in the order that you are given them.
This means that [tex]\angle A \cong \angle R[/tex].
We know that [tex]m\angle A = x^2-8x[/tex] and [tex]m\angle R=5x+30[/tex], and because they are congruent we can set the two equal to each other.
[tex]x^2-8x=5x+30[/tex]
Let's get everything to one side.
[tex]x^2-13x-30=0[/tex]
Let's solve by factoring, since it's easy to do with these whole numbers.
We're looking for two number thats add to -30 and multiply to -13...
These would be -15 and 2.
Since our leading coefficient (_x²) is 1, we can factor straight to (x-15)(x+2).
Here's what it would look like if you went through all the steps anyways, though.
[tex]x^2-15x+2x-30=0[/tex]
[tex]x(x-15)+2(x-15)=0[/tex]
[tex](x+2)(x-15)=0[/tex]
Any value which causes either factor to equal 0 is a solution.
(The second factor wouldn't matter b/c 0 times anything is still 0)
Therefore x = -2 or 15.
Only one of these is possible, however!
If you use x = -2, you will find that the angle measure 4x-5 is negative, which is impossible. In this case, x must be 15.
Let's find the measure of angle C.
[tex]m\angle C=4x-5\ where\ x=15\\m\angle C=4(15)-5\\m\angle C=60-5\\\boxed{m\angle C = 55\°}[/tex]
This means that [tex]\angle A \cong \angle R[/tex].
We know that [tex]m\angle A = x^2-8x[/tex] and [tex]m\angle R=5x+30[/tex], and because they are congruent we can set the two equal to each other.
[tex]x^2-8x=5x+30[/tex]
Let's get everything to one side.
[tex]x^2-13x-30=0[/tex]
Let's solve by factoring, since it's easy to do with these whole numbers.
We're looking for two number thats add to -30 and multiply to -13...
These would be -15 and 2.
Since our leading coefficient (_x²) is 1, we can factor straight to (x-15)(x+2).
Here's what it would look like if you went through all the steps anyways, though.
[tex]x^2-15x+2x-30=0[/tex]
[tex]x(x-15)+2(x-15)=0[/tex]
[tex](x+2)(x-15)=0[/tex]
Any value which causes either factor to equal 0 is a solution.
(The second factor wouldn't matter b/c 0 times anything is still 0)
Therefore x = -2 or 15.
Only one of these is possible, however!
If you use x = -2, you will find that the angle measure 4x-5 is negative, which is impossible. In this case, x must be 15.
Let's find the measure of angle C.
[tex]m\angle C=4x-5\ where\ x=15\\m\angle C=4(15)-5\\m\angle C=60-5\\\boxed{m\angle C = 55\°}[/tex]
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.