The quadratic equation x^2 - 8x = -4 is rewritten in the form (x + p)^2 = q. when q is a constant. What is the value of p ?
Answers
Answer:
-4
Step-by-step explanation:
If you multiply out the square, you can see ...
(x +p)^2 = q
x^2 +2px +p^2 = q
The coefficient of the x-term is 2p, so ...
2p = -8
p = -8/2 = -4
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Answers
Answer:
491400
Step-by-step explanation:
Given : A club has 28 members.
To Find : . How many ways are there to choose four members of the club to serve on an executive committee?
Solution:
We are supposed to choose four members of the club out of 28.
So, we will use combination
Formula :
n = 28
r = 4
Substitute the values :
Hence there are 491400 ways o choose four members of the club to serve on an executive committee
Answers
The solution is x = 9 and y = 4, meaning Brody would work 9 hours babysitting and 4 hours cleaning tables to satisfy both conditions (total hours ≤ 13 and total earnings ≥ $150).
Given:
Brody can work a maximum of 13 hours: x + y ≤ 13
Brody must earn at least $150: 10x + 15y ≥ 150
These are the two inequalities we need to solve graphically.
Graph the first inequality: x + y ≤ 13
This inequality represents the total number of hours Brody can work, which cannot exceed 13 hours. We'll plot the line x + y = 13 and shade the region below it.
Graph the second inequality: 10x + 15y ≥ 150
This inequality represents the total earnings Brody needs to make, which should be at least $150. Let's simplify it to 2x + 3y ≥ 30. We'll plot the line 2x + 3y = 30 and shade the region above it.
Now, let's find the point where the shaded regions of both inequalities overlap. This point will represent the feasible solution where Brody's working hours and earnings satisfy both conditions.
Solving the system of inequalities graphically, you will find the point of intersection. However, since I can't create a graphical representation here, I'll explain how to calculate the solution point algebraically:
First, solve the equation x + y = 13 for y:
y = 13 - x
Now substitute this value of y into the equation 2x + 3y = 30:
2x + 3(13 - x) = 30
2x + 39 - 3x = 30
-x = -9
x = 9
Now substitute the value of x back into the equation y = 13 - x:
y = 13 - 9
y = 4
So, the solution is x = 9 and y = 4, meaning Brody would work 9 hours babysitting and 4 hours cleaning tables to satisfy both conditions (total hours ≤ 13 and total earnings ≥ $150).
To know more about inequalities:
#SPJ3
Graph y≤13−x (shading down)
graph y≥10− 3/2x (shading up)
B. They are complementary angles
C. They are supplementary angles.
D. They are vertical angles.
Answers
Answer:
A. They are adjacent angles
Step-by-step explanation:
Angles 1 and 2 are next to each other, that makes them adjacent angles
A They are adjacent angles (next to each other and share a side) True
B. They are complementary angles (add to 90 degrees) False- Angle 2 is 90 degrees)
C. They are supplementary angles. (add to 180) False, they do not form a straight line
D. They are vertical angles. (opposite angles) False, they are not made by intersecting lines
Answer:
The answer is adjacent angles:)
Step-by-step explanation:
Answers
Answer:
Discount = Original Price x Discount %/100
Discount = 2.88 × 1/100
Discount = 2.88 x 0.01
You save = $0.03
Final Price = Original Price - Discount
Final Price = 2.88 - 0.0288
Final Price = $2.85
Answers
Answer:
(a) True
(b) False
(c) True
(d) False
(e) False
(f) True
(g) False
(h) True
(i) True
(k) True
Step-by-step explanation:
(a) Two lines parallel to a third line are parallel
True
(b) Two lines perpendicular to a third line are parallel
Only for lines on the same plane
Therefore, false
(c) Two planes parallel to a third plane are parallel
True
(d) Two planes perpendicular to a third plane are parallel
The two planes can be at an angle to each other and so intersect
Therefore, false
(e) Two lines parallel to a plane are parallel
Where the two lines are on a plane parallel to the first plane but the lines are not themselves parallel to each other they intersect
Therefore, false
(f) Two lines perpendicular to a plane are parallel
True
(g) Two planes parallel to a line are parallel
Where the planes are not parallel to each other, they will intersect
Therefore, false
(h) Two planes perpendicular to a line are parallel
True
(i) Two planes either intersect or are parallel
True
(k) A plane and a line either intersect or are parallel
True.
What is the area of the circle using π = 3.14?
113.04 in2
452.16 in2
1,017.36 in2
4,069.44 in2
Answers
Answer:
1017.36 in²
Step-by-step explanation:
Information we need to know:
Radius = diameter ÷ 2
Area of circle = πr²
1) Find the radius of the circle
We have to make sure the we are using the radius of the circle instead of the diameter as the formula using the value of r. If we were to use the diameter our answer would be wrong.
- 36 ÷ 2 = 18
2) Find the area
To find area we can distribute the numbers given into the formula...
- 3.14 (π) x 18 (r)² = 1017.36
Hope this helps, have a lovely day! :)
A = 1,017.36 in²
The answer is option C
Step by step solved:
The formula to calculate the area of a circle is
A = πr²,
where A is the area and r is the radius of the circle. In this case, the diameter of the circle is given as 36 inches, so the radius is half of that, which is 18 inches.
Using the value of π as 3.14, we can plug in the values and calculate the area as follows:
A = πr²
A = 3.14 x 18²
A = 3.14 x 324
A = 1,017.36 in²
Therefore, the area of the circle with a diameter of 36 inches using π = 3.14 is 1,017.36 in². The answer is option C