Answer:
24 pennies
Step-by-step explanation:
120 x 0.2 go get 24 and other will get 48
The correct answer; w = 2 :)
<span>7x − (1/2)(8x + 4) = 6
Step 1: 7x − 4x − 2 = 6
Step 2: 3x − 2 = 6
Step 3: 3x − 2 + 2 = 6
Step 4: 3x = 6
Step 5: x = 2
The error is in step 3, where 2 was added to the left side but not to the right side. The additive property of equality states that you can add the same number to both sides of an equation. Here 2 was added only to the left side. That is incorrect. 2 should have been added to both sides.
3x - 2 + 2 = 6 + 2
3x = 8
x = 8/3
The correct solution is x = 8/3, not x = 2.
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Answer:
Step-by-step explanation:
(a)
For the quadratic equation of the form 
,
The discriminant is given as: 
Simplifying the given quadratic equation:
[(x-7)^2] - 62 = 19
∴ (x^2) - 14x + 49 = 81
∴ (x^2) - 14x - 32 = 0
Comparing with the standard form of quadratic equation:
a = 1; b = -14; c = -32
∴ Discriminant = (b^2) - 4ac = 196 + 128 = 324
Since Discriminant > 0,
The roots will be real and distinct.
(b)
This equation can be factored as:
(x - 16)(x + 2) = 0;
∴ x = 16 ; x = -2, are the two roots of the equation.
Here's your illustration:
I don't know if you can see that picture, but it's not showing up on my screen, so I'll describe it to you:
-Draw a right triangle
(It's a right triangle because the wall is vertical so the wall creates a right angle with the ground)
-The hypotenuse [the slanted side opposite the right angle] is your ladder. The length of the ladder is 25, so the length of your hypotenuse is 25.
-The long leg of the triangle [the long side that is not the hypotenuse] is your wall. We don't know the length of the wall, but that's okay for this problem.
-The short leg of the triangle [your shortest side] is the distance between the bottom of the ladder and the bottom of the wall. That's 10.
So you have your triangle. The angle the ladder makes with the wall is the angle between the top of the ladder and the top of the wall.
Your answer depends on the equation you're going to use to find this angle.
That depends on what lengths are given to you, which in this case is the hypotenuse and the short leg.
Your angle is opposite the short leg. This means the angle is not the right angle, and not an angle touching the short side.
The sine ratio is opposite side/hypotenuse
You have both the opposite side of the angle and the hypotenuse, so your formula would be this:
sin(angle)=10/25
So your answer would use the sine ratio, meaning your answer is...
sin-10.4
And there's your answer.
