If triangle RST is congruant to triangle ABC, the measure of angle A equals x^2-8x, and the measure of angle C equals 4x-5, and the measure of angle R equals 5x+30 find the measure of angle C [ only an algebraic solution can receive full credit.]

Answers

Answer 1

Answer: In any statement like this one: $\triangle RST \cong \triangle ABC$ you can assume that the points match up in the order that you are given them.
This means that $\angle A \cong \angle R$ .
We know that $m\angle A = x^2-8x$ and $m\angle R=5x+30$ , and because they are congruent we can set the two equal to each other.

$x^2-8x=5x+30$
Let's get everything to one side.
$x^2-13x-30=0$
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.
$x^2-15x+2x-30=0$
$x(x-15)+2(x-15)=0$
$(x+2)(x-15)=0$
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.
$m\angle C=4x-5\ where\ x=15\nm\angle C=4(15)-5\nm\angle C=60-5\n\boxed{m\angle C = 55\°}$

Answer 2

Answer:    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

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Answers

Answer:

Al will receive $1770 for his work.

Step-by-step explanation:

Given : Al Johnson is a word processor. He is paid $2.95 a page.

To Find: A normal job has 600 pages and requires about 225 words per page. About how much will Al receive for his work?

Solution:

Cost of 1 page = $2.95

So, cost of 600 pages = $2.95 * 600$

= $1770$

Hence Al will receive $1770 for his work.

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"A survey reported that out out 50 teenagers 9 said they get their news from a newspaper at this rate how mant 300 teenagers would get a newspaper"

Answers

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The ordered pair (2, 36) is a solution for which equation(s)? Check all that apply. A. y = (x + 4)2
B. y = 7x2 + 2
C. y = (3x)2
D. y = 2x2

Answers

plug it into each equation and see if both sides are equal:
A. 36 = (2+4)^2 -> 36 = 36 works
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How do you find the domain of a function?

Answers

ok so domain means the set of numbers you are alowed to use

bsaically
domain=all real numbers except for those that make strange things happen

strange things are
1. dividing by zero
2. taking square root of negative
3. might be more, dunno

example
if y ou have
f(x)=3/x, domain is all real number except 0 since if x=0, then 3/0 is undifined
f(x)=3/(2+x), domain is all real except x=-2

for the negative sqrt
f(x)=√x, x cannot be negative, it goes from zero to positive infinity
f(x)=√(x-1), x cannot be less than 1, it has to be any number more than or equal to 1 (√0=0)

basically domain=all real number except for ones that make function comlex or undefined

You just see what's the range of x values the function covers.

Given this equation, what is the largest possible value for z?

Answers

Hello,
z=-2x²+15x-3y²+21y-6
=-2(x²-2*15/2*x+(15/2)²) -3(y²-2*7/2y+(7/2)²)-6+2*225/4+3*49/4
=-2(x-15/2)²-3(y-7/2)²+573/4

The max is for x-15/2=0 and y-7/2=0 thus 537/4

Shown are lines p , r , t , and w. Suppose angles 8 and 10 are congruent. Given this fact, which two line must be congruent? Show all work to receive credit.

Answers

Answer:

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Step-by-step explanation:

Angles 8 and 10 are alternate interior angles with respect to transversal r across lines t and w. If those angles are congruent, then lines t and w must be parallel.

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