Answer:
3. D) 
2. D) 
1. B) 
Step-by-step explanation:
3.
{y = 3x + 7
{y = x - 9
x - 9 = 3x + 7
-3x - 3x
____________
−2x - 9 = 7
+ 9 + 9
__________
−2x = 16
____ __
−2 −2
[Plug this back into both equations above to get the y-coordinate of −17]; 
__________________________________________________________
2.
{−4x + 3y = 12
{−2x + 3y = −18
−½[−4x + 3y = 12]
{2x - 1½y = −6 >> New Equation
{−2x + 3y = −18
_______________
1½y = −24
____ ____
1½ 1½
[Plug this back into both equations above to get the x-coordinate of −15]; 
__________________________________________________________
1.
{−10x - 3y = −18
{−7x - 8y = 11
−⅜[−7x - 8y = 11]
{−10x - 3y = −18
{2⅝x + 3y = −4⅛ >> New Equation
_________________
−7⅜x = −22⅛
______ _____
−7⅜ −7⅜
[Plug this back into both equations above to get the y-coordinate of −4]; 
I am joyous to assist you anytime.
<u>Answer</u>:
B) The perimeter of the rectangle is 28 units.
E) The coordinates for the fourth vertex of the rectangle are (−5, −3).
<u>Step-by-step explanation</u>:
The length of the rectangle is 9 and width is 5.
- The perimeter is 2( 9 + 5 ) = 28 units
<em>as the upper one is right. Option A eliminated. </em>
- The coordinates for the fourth vertex of the rectangle are (−5, −3).
<em>as the upper one is right. option C and D will be eliminated.</em>
Answer:
A: The x-intercept of k(x) is half the x-intercept of h(x)
Step-by-step explanation:
Answer choices B, C, and D are concerned with slopes and y-intercepts. The coefficients of x in the functions are different and are related by a factor of -2, so the lines are not parallel, and one slope is not twice the other. The y-intercepts (constants) in each function are different, so they graphs do not cross the y-axis at the same place.
Hence answer choices B, C, and D can be eliminated.
The x-intercepts are found by setting y=0 and solving for x:
h(x) = 0 = -2x +4 ⇒ x = 4/2 = 2
k(x) = 0 = 4x -4 ⇒ x = 4/4 = 1
The x-intercept of k(x) is half that of h(x). . . . . . . matches choice A
Answer:
y value = 49
Step-by-step explanation:
You are going to be completing the square
y = - x^2 - 10x + 24 Take a minus outside the brackets for the first 2 terms.
y = - (x^2 + 10x) + 24
Take 1/2 the linear term (1/2 10 and square it. Put that value inside the brackets. 1/2* 10 =5; 5^2 = 25
y = - (x^2 + 10x + 25) + 24
Add 25 outside the brackets.
y = -(x^2 + 10x + 25) + 24 + 25. You should stop here and consider why you are adding 25 outside the brackets. It is because there is a - sign in front of the trinomial and what is inside the brackets is really - 25 when the brackets are removed. Therefore to balance that, you add 25.
Now complete the square.
y = - ( x + 5)^2 + 49
The value you seek is 49.
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I'll confirm this with a graph.
Answer:
The equation is P - 42 = 12
P = 54
Step-by-step explanation:
