Answer:
y=-9
Step-by-step explanation:
If x equals 2, then we can substitute that into the equation, resulting in the equation 2*2-2y=22
We can solve for multiplication first:
4-2y=22
Then we can subtract four on both sides, canceling out the four on the left side:
-2y=18
Now to isolate y, we divide both sides by -2, resulting in the solution:
y=-9
Hope this helps!
X²+15x+36<0
at first solve quadratic equation
D=b²-4ac= 225-4*1*36= 81
x=(-b+/-√D)/2a
x=(-15+/-√81)/2= (-15+/-9)/2
x1=(-15-9)/2=-12
x2=(-15+9)/2=-3
we can write x²+15x+36<0 as (x+12)(x+3)<0
(x+12)(x+3)<0 can be 2 cases, because for product to be negative one factor should be negative , and second factor should be positive
1 case) x+12<0, and x+3>0,
x<-12, and x>-3
(-∞, -12) and(-3,∞) gives empty set
or second case) x+12>0 and x+3<0
x>-12 and x<-3
(-12,∞) and (-∞,-3) they are crossing , so (-12, -3) is a solution of this inequality
Answer
That should be it!
Step-by-step explanation:
Question 1 (Multiple Choice Worth 1 points) (04.03) The expression below shows the population of foxes in a forest after 12x years: f(x) = 50(1.05)12x Which of the following is an equivalent function? f(x) = 50(1.7959)x f(x) = 50(12.6000)x f(x) = 600(1.05)x f(x) = 4.2(1.05)x Question 2 (Multiple Choice Worth 1 points) (04.01) Which of the following best defines 3 to the power of 2 over 3? Square root of 9 Cube root of 9 Cube root of 3 Square root of 3 Question 3 (Multiple Choice Worth 1 points) (04.06) A sequence has its first term equal to 4, and each term of the sequence is obtained by adding 2 to the previous term. If f(n) represents the nth term of the sequence, which of the following recursive functions best defines this sequence? f(1) = 2 and f(n) = f(n − 1) + 4; n > 1 f(1) = 4 and f(n) = f(n − 1) + 2n; n > 1 f(1) = 2 and f(n) = f(n − 1) + 4n; n > 1 f(1) = 4 and f(n) = f(n − 1) + 2; n > 1 Question 4 (Multiple Choice Worth 1 points) (05.05) Look at the graph below: First line joins ordered pairs negative 4, 3 and 2, negative 3. Second line joins negative 4, negative 3 and 2, 3. Part A shaded above first and second line. Part B shaded below first line and above second line. Part C shaded below first and second lines. Part D shaded above first line and below second line. Which part of the graph best represents the solution set to the system of inequalities y ≤ x + 1 and y + x ≤ −1? Part A Part B Part C Part D Question 5 (Multiple Choice Worth 1 points) (04.03) The number of bacteria in a sample increased by a factor of 2 every minute from 9:05 AM to 9:55 a.m.. The function below shows the number of bacteria in the sample f(x) after x minutes from 9:05 a.m.: f(x) = 10(2)x Which of the following is a reasonable domain for the function? 0 ≤ x ≤ 10 5 ≤ x ≤ 55 0 ≤ x ≤ 50 All positive integers Question 6 (Multiple Choice Worth 1 points) (03.05) The graph below shows the velocity f(t) of a runner during a certain time interval: graph of line going through ordered pairs 0, 2 and 6, 8. Graph of another line through ordered pairs 6, 8 and 8, 0. Label on the x axis is time in second and label on the y axis is velocity in meters per second Which of the following describes the intercepts on the graph? The initial velocity of the runner was 8 m/s, and the runner stopped after 2 seconds. The initial velocity of the runner was 2 m/s, and the runner stopped after 8 seconds. The initial acceleration of the runner was 8 m/s2, and the runner stopped after 2 seconds. The initial acceleration of the runner was 2 m/s2, and the runner stopped after 8 seconds. Question 7 (Multiple Choice Worth 1 points) (03.03) Choose the equation that represents the graph below: Graph of a line passing through points negative 3 comma 0 and 0 comma 3 y = x − 3 y = −x + 3 y = −x − 3 y = x + 3 Question 8 (Multiple Choice Worth 1 points) (04.03) Jake forgot to replace the cap on a bottle of cologne. The cologne began to evaporate at the rate of 18% per day. If the original amount of cologne in the bottle was 50 grams, which of the following graphs best represents the amount of cologne f(x) remaining in the bottle after x days? graph of function f of x equals 30 multiplied by 0.88 to the power of x graph of exponential function going down from left to right in quadrant 1 through the point 0, 40 and approaching the x axis graph of function f of x equals 50 multiplied by 0.82 to the power of x graph of exponential function going down from left to right in quadrant 1 through the point 0, 4 and approaching the x axis
A butterfly can fly 82 feet in 4 seconds.
Distance traveled by butterfly = 82 feet.
Time taken by butterfly =4 seconds
Speed = distance /time
Speed of butterfly = 82/4 = 20.5 feet/second
A dragonfly can fly 50 feet in 2 seconds.
Distance traveled by dragonfly =50 feet.
Time taken by dragonfly =2 seconds.
Speed of dragonfly = 50/2 = 25 feet/second
So dragonfly can fly faster than the butterfly.
Difference in speed = speed of dragonfly - speed of butterfly = 25-20.5 = 4.5
So The dragonfly is 4.5 feet per second faster than butterfly.
Answer: B) The dragonfly is 4.5 feet per second faster.
The midpoint lines are half the opposite side length.
Line DE is given as 7 , So Line F = 7 x 2 = 14
Line EF is given as 12, so Line D = 12 x 2 = 24
Line DF is given as 16, so line E = 16 x 2 = 32
The perimeter is the sum of the 3 sides:
Perimeter = 14 + 24 + 32 = 70
