Answer:
y=1/2(x-1)
Step-by-step explanation:
If x=t^2 and t>0, then t=sqrt(x).
If t=sqrt(x) or x^(1/2) and y =1-1/t, then y=1-x^(-1/2).
The x-intercept is when y=0.
So we need to solve 0=1-x^(-1/2) to find point P.
Add x^(-1/2) on both sides: x^(-1/2)=1.
Raise both sides to -2 power: x=1
So point P is (1,0).
Let's find tangent line at point (1,0).
We will need the slope so let's differentiate.
y'=0+1/2x^(-3/2)
y'=1/(2x^(3/2))
The slope at x=1 is y'=1/(2[1]^(3/2))=1/(2×1)=1/2.
Recall point-slope form is y-y1=m(x-x1).
So our line we are looking for is y-0=1/2(x-1)
Let's simplify left hand side y=1/2(x-1)
Answer: x = 4
Step-by-step explanation:
2(x+1)=10
Distributive properties
a*(b+c)=(a*b)+(a*c)
Using distributive properties
Then
2*(x+1)=(2*x)+(2*1)
2*(x+1)=2x+2
Now, commutative properties
a*b=b*a
Addition is cumulative
a+(-b)=(-b)+a
Therefore applying to 2x+2
2x+2+(-2)=2x+(-2)+2
Then, applying to the equation
2x+2+(-2)=10+(-2), +×-=-
2x+2 -2=10-2
2x=8
Using division properties
ax=b
If a is none zero
Then ax/a=b/a
Therefore x=b/a
Applying that to 2x=8
2x=8. Divide both side by 2 which is none zero
2x/2= 8/2
x=4
Option B
Subtraction Property of equality
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The answer is C. Systemic random sampling.
By definition, systemic random sampling is a sampling technique where the respondents are selected according to a <em>random starting point </em>(this alone shows that the answer is C.) The researcher then chooses the sample interval, which is the difference between two consecutive numbers in the progression.
In this case, the starting point is 8 and the sample interval is 10.
The answer is C.
The measure of angle A is 55°.
Solution:
Let us take B be the adjacent angle of 145°.
<em>Sum of the adjacent angles in a straight line = 180°</em>
⇒ m∠B + 145° = 180°
Subtract 145° from both sides.
⇒ m∠B + 145° - 145° = 180° - 145°
⇒ m∠B = 35°
The adjacent angle of 145° is 35°.
In the image, angle B and angle A equal to 90°.
⇒ m∠B + m∠A = 90°
⇒ 35° + m∠A = 90°
Subtract 35° from both sides.
⇒ m∠A = 55°
The measure of angle A is 55°.
