Answer:
Tom has 70 cards, and Harry has 28 cards.
Step-by-step explanation:
Let h = number of cards Harry has.
Then the number of cards Tom has is 2 1/2 * h = 2.5h.
Together they have 2.5h + h = 3.5h number of cards.
Together they have 98 cards.
3.5h = 98
h = 98/3.5
h = 28
Harry has 28 cards.
Tom has 2.5h = 2.5 * 28 = 70
Answer: Tom has 70 cards, and Harry has 28 cards.
Answer: lower bound = 9550
<u>Step-by-step explanation:</u>
Since the number is rounded to the nearest hundred, the actual value is somewhere between 9550 (which rounds up to 9600) and 9649 (which rounds down to 9600).
The lower bound is: 9550
The upper bound is: 9649
Answer:
4 x minus 5 y = negative 5 and 3 x + 10 y = negative 20
Step-by-step explanation:
The equations
4 x - 5 y = 5 (red)
3 x + 10 y = 20 (blue)
4 x - 5 y = -5 (green)
3 x + 10 y = -20 (purple)
are shown in the picture attached. As we can see there, the point (–2.7, –1.2) is on the intersection of the purple and green lines. Therefore is the solution of the system:
4 x - 5 y = -5
3 x + 10 y = -20
Answer:
y = -24 + -2x + 2x2
Step-by-step explanation:
Simplifying:
y = 2(x + 3)(x + -4)
reorder the terms:
y = 2(3 + x)(x + -4)
multiply (3 + x) * (-4 + x)
y = 2(3(-4 + x) + x(-4 + x))
y = 2((-4 * 3 + x * 3) + x(-4 + x))
y = 2((-12 + 3x) + x(-4 + x))
y = 2(-12 + 3x + (-4 * x + x * x))
y = 2(-12 + 3x + (-4x + x2))
Combine like terms 3x + -4x = -1x
y = 2(-12 + -1x + x2)
y = (-12 * 2 + -1x * 2 + x2 * 2)
y = (-24 + -2x + 2x2)
Solving:
y = -24 + -2x + 2x2
solving for variable 'y'
Move all terms containing y to the left, all other terms to the right.
Simplifying:
y = -24 + -2x + 2x2
<h3>Answers are:
sine, tangent, cosecant, cotangent</h3>
Explanation:
On the unit circle we have some point (x,y) such that x = cos(theta) and y = sin(theta). The sine corresponds to the y coordinate of the point on the circle. Quadrant IV is below the x axis which explains why sine is negative here, since y < 0 here.
Since sine is negative, so is cosecant as this is the reciprocal of sine
csc = 1/sin
In quadrant IV, cosine is positive as x > 0 here. So the ratio tan = sin/cos is going to be negative. We have a negative over a positive when we divide.
Because tangent is negative, so is cotangent.
The only positive functions in Q4 are cosine and secant, which is because sec = 1/cos.
