Learning Task 1

1. M is the midpoint of LN and O is the midpoint of NP.

Reptile [31]

1. M is the midpoint of LN and O is the midpoint of NP. This makes the triangle MNO equal to half of LNP. Then you can get this equation
MO= (1/2) LP

If you insert MO = 2x +6 and LP = 8x – 20 the calculation would be:
2x+6= (1/2)( 8x-20)
2x+6= 4x-10
2x-4x= -10 - 6
-2x= -16
x=8

2. Centroid is the point that intersects with three median lines of the triangle. The centroid should divide the median lines into 1:2 ratio. In AC lines, A located in the base so A.F:FC would be 1:2

Then, the answer would be:
A.F= 1/(1+2) * AC
A.F= 1/3 * 12= 4

FC= 2/(1+2) * AC
FC= 2/3 * 12= 8

3. Since
∠BAD=∠DAC
∠ABD=∠ACD
AD=AD
The triangle ABD and ACD are similar. You can get this equation
BD=DC
x+8= 3x+12
x-3x= 12-8
-2x=4
x=-2

DC=3x+12= 3(-2) +12= 6

4. Orthocenter made by intersection of triangle altitude
A
BC lines slope would be (-4)-(-1)/1-4= -3/-3= 1. The altitude line slope would be -1, the function would be:
y=-x +a
0= 1+a
a=-1
y=-x-1
B
AC lines slope would be (-4)-(-1)/1-0= -3. The altitude line slope would be 1/3, the function would be:
y=1/3x+a
-1=1/3(4)+a
a=-7/3
y=1/3x - 7/3

C
BC lines slope would be (-1)-(-1)/4 = 0/4.
The line would be
0=x+a
a=-1
0=x-1
x=1

y=-x-1 = 1/3x-7/3
-x-(1/3x)=-7/3 +1
-4/3x= -4/3
x=1

y=-x-1
y=-1-1= -2
The orthocenter would be (1,-2)

5.
a. Circumcenter: the intersection of perpendicular bisector lines<span>
b. Incenter: the intersection of bisector lines
c. Centroid: </span>the intersection of median lines<span>
d. Orthocenter: </span>the intersection of altitude lines

5 0

3 years ago

Which of these can be the graph of the equation y=mx+b

Lostsunrise [7]

See the explanation

<h2>Explanation:</h2><h2></h2>

Hello! Your figures are missing, so I could help you in a general way. The Slope-intercept form of the equation of a line is given by the form:

$y=mx+b \\ \\ \\ m:Slope \\ \\ b=y-intercept$

Case 1:

$m>0$

If the slope is positive, we will have a line as the form illustrated in figure 1. So as x increases y also increases.

Case 2:

$m$

If the slope is negative, we will have a line as the form illustrated in figure 2. So as x increases y decreases.

Case 3:

$m=0$

If the slope is zero, we will have a line as the form illustrated in figure 3. here we have a constant function.

Case 4:

m: undefined

If the slope is undefined, we will have a line as the form illustrated in figure 4.

<h2>Learn more:</h2>

Linear equations: brainly.com/question/8210863

#LearnWithBrainly

3 0

3 years ago

Micah is a busy college student. He carries a full load of classes and works a full time job to support himself financially whil

Fantom [35]

Answer:

32 school hrs in a week.

Step-by-step explanation:

The reduction percentage =

80 x 0.80 = 64 (hrs)

The distribution =

64/2 = 32hrs

8 0

3 years ago

Sal bought 2 shirts and a hat. Sal remembers each shirt was $10, and the total was $50. Which equation helps answer the question

olganol [36]

Answer:

The answer is B.

Step-by-step explanation:

There are two shirts, both cost 10.

10 + 10.

The variable is the cost of the hat, which we add on.

10 + 10 + x.

Finally, 50 is the total price so that is going to be what it equals.

10 + 10 + x = 50

3 0

3 years ago

The half-life of a certain tranquilizer in the bloodstream is 47 hours. How long will it take for the drug to decay to 93% of

GaryK [48]

Answer:

It will take 4.84 hours for the drug to decay to 93% of the original dosage.

Step-by-step explanation:

We are given that the half-life of a certain tranquilizer in the bloodstream is 47 hours.

The given exponential model is: $A = A_0 e^{kt}$

Now, we know that A becomes half after 47 hours which means that;

$A = 0.5 A_0$

Using this in the above equation we get;

$A = A_0 e^{kt}$

$0.5 A_0 = A_0 e^{(k\times 47)}$ where t = 47 hours

$\frac{0.5 A_0}{A_0} = e^{(47k)}$

$0.5 = e^{47k}$

Taking log on both sides we get;

$ln(0.5) = ln(e^{47k})$

$ln(0.5) =47k$

$k = \frac{ln(0.5)}{47}$

k = -0.015

Now, the time it will take for the drug to decay to 93% of the original dosage is given by;

$0.93 = e^{kt}$ where t is the required time

$0.93 = e^{(-0.015 \times t)}$

Taking log on both sides we get;

$ln(0.93) = ln(e^{-0.015t})$

$ln(0.93) =-0.015t$

$t = \frac{ln(0.93)}{-0.015}$

t = 4.84 hours

Hence, it will take 4.84 hours for the drug to decay to 93% of the original dosage.

8 0

4 years ago