if p= 1/3 what is the answer to 9p2=
When p equals 1/3, 9p^2 calculates to 1 after squaring p and multiplying by 9.
The question involves calculating the expression 9p^2 given that p = 1/3. First, we square the value of 'p' and then multiply it by 9. Following the process, we have:
[tex](\frac{1}{3} )^2 = \frac{1}{9} \\9 \times (\frac{1}{9} ) = 1[/tex]
Therefore, 9p^2 is equal to 1 when p is equal to 1/3.
Question 8
8 pts + 4 pts for the best answer Thanks!
Question is attached.
Which of the following has no solution?
{x | x < 0} and {x | x > 0}
{x | x ≤ 0} and {x | x ≥ 0}
{x | x ≤ 0} or {x | x ≥ 0}
The pair of sets, {x | x < 0} and {x | x > 0}, has no solution because no number can be simultaneously less than zero and greater than zero. The other pairs do have solutions as they include the number zero.
Explanation:The set of mathematical expressions provided in the question represent intervals along the number line. Understanding which intervals overlap and which intervals don't is the key to comprehending which of these options potentially has a solution. To consider when these sets will have no solution, you must find where no numbers exist that can satisfy both conditions simultaneously.
The first pair, {x | x < 0} and {x | x > 0}, means 'the set of all x such that x is less than 0' and 'the set of all x such that x is greater than 0'. Because no number can be both less than zero and greater than zero at the same time, this pair has no solution.
The other pairs, {x | x ≤ 0} and {x | x ≥ 0} and {x | x ≤ 0} or {x | x ≥ 0} do have solutions because they both include 0 itself, so there are numbers that can satisfy both conditions.
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In a triangle, the second angle is twice the measure of the first, and the third angle is three times the measure of the second. Find the measure of the third angle.
A. 20 degrees
B. 30 degrees
C. 120 degrees
D. 180 degrees
Factor
h^2-4k^2+4h-8k
if f(2)=3 and f'(2)=5 find the equation of the tangent line and the normal line to the graph of y=f(x)
The equations of the tangent and normal to f(x) at x = 2 are -
Tangent → y = 5x - 7
Normal → y = -1/2 x + 3.4
What is tangent and normal to a curve?A tangent is a line touching the curve at one distinct point, and this distinct point is called the point of contact.
The normal line to a curve at a particular point is the line through that point and perpendicular to the tangent.
Given is a function f(x) and f(2) = 3 and f'(2) = 5.
We can find the tangent to the curve at x = 2 by finding the value of the derivative of f(x) at x = 2. The slope of the tangent at x = 2 is -
m[T] = (dy/dx) [at x = 2] = f'(2) = 5
Now. the equation of tangent can be written as -
(y - y₁) = m [T] (x - x₁)
and
f(2) = 3
At x = 2, y =3 →
y - 3 = 5 (x - 2)
y - 3 = 5x - 10
y = 5x - 10 + 3
y = 5x - 7
This is the equation of the tangent.
In order to find the slope of Normal at x = 2, use the following formula -
m [T] x m [N] = -1
m [T] = 5
Then -
m [N] = - 1/5
The equation of the normal is given by -
(y - y₁) = m [N] (x - x₁)
(y - 3) = -1/5 (x - 2)
y - 3 = -x/2 + 2/5
y = -x/2 + 2/5 + 3
y = -1/2 x + 3.4
This is the equation of Normal.
Therefore, the equations of the tangent and normal to f(x) at x = 2 are -
Tangent → y = 5x - 7
Normal → y = -1/2 x + 3.4
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show that cos(3theta) = cos^3(theta)-3 cos(theta)sin^2(theta) ... use this to find an equation in rectangular coordinates for the curve r= 4 cos (3theta)......
ANY HELP ? ...?
What are the x and y intercept of (0,0), (10,106), (15,159), (20,212), (30, 318) ?
Vanessa deposited money into a bank account that earned 1.25% simple interest each year. After 1/2 year, she had earned $5.00 in interest on the account. If no other money was deposited into or withdrawn from the account, how much was her initial deposit
The length of a rectangle is 4/5 feet. The width is 5/8 feet. How much greater is the length of the rectangle than the width?
A.)7/40 feet
B.)1/5 feet
C.)3/20 feet
D.)1/3 feet
What is the end of the CD account time when the money can be withdrawn?
Maturity date
End date
Completion date
Withdrawal date
Correct Answer: maturity date
A friend rewrote the expression 5(x 2) as 5x 2.write a few sentences to your friend explaining the error. then rewrite the expression 5(x 2) correctly
Solve Equation
x^2 -4x +8 = 0
Farmer Ed has 7000 meters of fencing and wants to enclose a rectangular plot that borders on a river. If farmer Ed does not fence the side along the river, what is the largest are that can be enclosed? ...?
Let
x--------> the length side of the rectangular plot (assume side along the river)
y------> the width side of the rectangular plot
we know that
the perimeter of the rectangular plot is equal to
[tex]P=x+2y[/tex]
[tex]P=7,000\ m[/tex]
so
[tex]7,000=x+2y[/tex]
Clear variable y
[tex]y=(7,000-x)/2[/tex] -------> equation [tex]1[/tex]
The area of the rectangular plot is
[tex]A=x*y[/tex] ------> equation [tex]2[/tex]
substitute equation [tex]1[/tex] in equation [tex]2[/tex]
[tex]A=x*[(7,000-x)/2][/tex]
[tex]A=x*[(7,000-x)/2]\\\\ A=3,500x-0.5x^{2}[/tex]
we know that
To find the larger area that can be enclosed------> Find the vertex of the quadratic equation
The quadratic equation is a vertical parabola open down
so
the vertex is a maximum
using a graphing tool
see the attached figure
the vertex is the point [tex](3,500,6,125,000)[/tex]
that means
For [tex]x=3,500\ m[/tex]
the largest area is [tex]6,125,000\ m^{2}[/tex]
Find the value of y
[tex]y=(7,000-3,500)/2=1,750\ m[/tex]
the dimensions of the rectangular plot are
[tex]Length=3,500\ m\\Width=1,750\ m[/tex]
therefore
the answer is
The largest area that can be enclosed is [tex]6,125,000\ m^{2}[/tex]
Which relationship between x and y in the equation shows a proportional relationship?
y=3x
y=5(x+3)
y+5=x+3
y=5x+3
When is substitution a useful method for solving systems of equations?
Let h(x)=xg(x), where g(x)=the inverse of f(x). Find h'(5) using the chart.....(type that in a minute) ...?
What is the difference between 7 and -8?
Round each number to the nearest tenth. what is the best estimate for the difference of 264.72 128.49?
a.137
b.136.3
c.136.2
d.130
Joe paid $14.00 for a board game this is 70% of the original price what was the original price
start off by finding 10% of $14. in order to find 10%, divide it by 70 which gives 2. you now need to make the 30% to add to the 70%, by timesing the 2 by 3to give 6. now all you need to do it add the 6 to 14 to make 20!
so your answer is $20
Answer:
The original price was $20.00
Step-by-step explanation:
Joe paid $14.00 for a board game.
This is the 70% of the original price.
Let the original price of a board game be x
70% of x = $14.00
0.70x = 14.00
x = [tex]\frac{14}{0.7}[/tex] = $20.00
The original price was $20.00
Samantha had 7/8 of a yard of ribbon. She used 1/6 of a yard for a bow. How much ribbon does Samantha have left?
18 is 240% of what? basic percent equation ...?
If AB is parallel to CD and the slope of CD is -8, what is the slope of AB ?
Answer:
and only if they have the same slope. Any two vertical lines are parallel. Therefore, the slope of AB is -8 if AB is parallel to CD.
Step-by-step explanation:
mai is saving money to buy a game so far she has saved 20$ which is four fifths of the total cost of the game how much does the game cost
Write 46 over 15 as a decimal rounded to the nearest hundredth
The cone pictured has a surface area of ______ square centimeters. (Use 3.14 for π.)
A scout group is setting up a tent at camp. Because rain is predicted, the scouts decide to build a fly, or rain cover, over the tent. The fly will be 12 feet high and 16 feet wide. The scouts are building the frame for the fly with poles slanted to meet over the top of the tent. What is the minimum length of the poles needed to support the fly?
Wxyz is a parallelogram. name an angle congruent to xyz
Answer: The answer is ∠XWZ.
Step-by-step explanation: Given that WXYZ is a parallelogram. We are to name an angle that is congruent to ∠XYZ.
Attached herewith, an image of parallelogram WXYZ.
We know that the opposite angles in a parallelogram are congruent to each other. So, in the parallelogram WXYZ, we must have
∠WXY ≅ ∠WZY and ∠XYZ ≅ ∠XWZ.
Therefore, angle congruent to ∠XYZ is ∠XWZ.
Thus, the answer is ∠XWZ.
Final answer:
Angle congruent to angle XYZ in parallelogram WXYZ would be angle W since opposite angles in a parallelogram are congruent.
Explanation:
If WXYZ is a parallelogram and you are asked to name an angle congruent to angle XYZ, you should look at the properties of a parallelogram. One key property is that opposite angles are congruent. Therefore, the angle congruent to angle XYZ would be angle W. If we consider the vertices in order around the parallelogram W, X, Y, Z, angle XYZ corresponds to angle WZY, so its opposite angle is angle WXZ (or simply angle W).
It's important to remember that in a parallelogram, consecutive angles are supplementary (their sum is 180 degrees). This supplementary property could help you in other problems related to angles in a parallelogram, but for this particular case—identifying a congruent angle—the opposite angles property directly gives us the answer.
Regular hexagon ABCDEF is inscribed in a circle with a radius of 2 units.
Find measure of central angle AGF
apothem a=GH
side length s=
perimeter P=
hexagon area A=
How many points are shared by concentric circles?
a. 0
b. 1
c. 2
d. infinite points
Answer:
Option a. 0
Step-by-step explanation:
As we know if we draw two circles with same center but with the different radii, they neither touch each other nor intersect. This is true not only for two circles but for infinite number of the circles having the same center. They never have the common points to share. Set of points lying on each concentric circles are different.
Therefore Option a. 0 points is the correct answer.