Answer:
The ordered pair (7, 19) is a solution to the first equation because it makes the first equation true
The ordered pair (7, 19) is not a solution to the system because it makes at least one of the equations false
Step-by-step explanation:
we have
-----> First equation
-----> Second equation
Solve the system of equations by graphing
Remember that the solution of the system is the intersection point both graphs
The solution is the point (1,7)
The ordered pair (7,19) lie on the first line, so is a solution of the first equation
see the attached figure
<u><em>Verify each statement</em></u>
case 1) The ordered pair (7, 19) is a solution to the first equation because it makes the first equation true
The statement is true
case 2) The ordered pair (7, 19) is a solution to the second equation because it makes the second equation true
The statement is false, because the ordered pair (7,19) not lie on the second line
case 3) The ordered pair (7, 19) is not a solution to the system because it makes at least one of the equations false
The statement is true
case 4) The ordered pair (7, 19) is a solution to the system because it makes both equations true
The statement is false,because it makes only the first equation true
Answer:
86in²
Step-by-step explanation:
Find the complete question attached
Area of the circle = πr²
Area of the square = L²
Length of the side of the square
r is the radius of the circle
r = L/2 = 20/2 =10in
Given
Length of the side of the circle = 20in
Area of the square = 20²
Area of the square = 400in²
Area of the circle =π(10)²
Area of the circle = 3.14(100)
Area of the circle= 314in²
Amount of plywood left over = 400in²-314in² = 86in²
Answer:
Step-by-step explanation:
In order to solve this problem, we must start by drawing a diagram of the cylinder. (See attached picture)
This diagram will help us visualize the problem better.
So we start by determining what data we already know:
Height=6in
Diameter=3.8in
Radius = 1.9 in (because the radius is half the length of the diameter)
The problem also states that the radius will increase on thousandth of an inch every 3 minutes. We can find the velocity at which the radius is increasing with this data:
which yields:
with this information we can start solving the problem.
First, the problem wants us to know how fast the volume is increasing, so in order to find that we need to start with the volume formula for a cylinder, which is:
where V is the volumen, r is the radius, h is the height and π is a mathematical constant equal approximately to 3.1416.
Now, the height of the cylinder will not change at any time during the reborning, so we can directly substitute the provided height, so we get:
or
We can now take the derivative to this formula so we get:
Which simplifies to:
We can now substitute the data provided by the problem to get:
which yields:
The size of angle PRQ is 15°
Step-by-step explanation:
In any regular polygon of n-sided
∵ PQ and QR are two sides of a regular 12-sided polygon
∴ PQ = QR
∵ PR is a diagonal
∴ ∠PQR is an interior angle of the polygon
- By using the rule of the interior angle above
∵ n = 12
∴ m∠PQR =
∴ m∠PQR = 150°
In Δ PQR
∵ PQ = QR ⇒ sides in a regular polygon
- Δ PQR is an isosceles Δ
∴ m∠PRQ = m∠RPQ ⇒ base angles of an isosceles Δ
The sum of the measures of the interior angles of a triangle is 180°
∵ m∠PQR + m∠PRQ + m∠RPQ = 180°
∴ 150 + m∠PRQ + m∠RPQ = 180°
- Subtract 150 from both sides
∴ m∠PRQ + m∠RPQ = 30
∵ m∠PRQ = m∠RPQ
- Divide their sum by 2 to find the measure of each one
∴ m∠PRQ = m∠RPQ = 30 ÷ 2 = 15°
∴ m∠PRQ = 15°
The size of angle PRQ is 15°
Learn more:
You can learn more about the triangles in brainly.com/question/3945600
#LearnwithBrainly
Basic properties that will be used:
All of these expression can be written to match on or more of the patterns above.