The product is 60.
We start out with the information we have. This forms a right triangle, with one leg being 24, the other leg x, and the hypotenuse 30. Using the Pythagorean theorem we have
x²+24²=30²
x²+576=900
Subtract 576 from both sides:
x²+576-576 = 900-576
x²=324
Take the square root of each side:
√x²=√324
x=18
We know that the formula for the volume of a triangular prism is V=(1/2bh)H, where b is the base of the triangle, h is the height of the triangle, and H is the height of the prism. Substituting our known information we have:
720=(1/2*18*24)y
720=216y
Divide both sides by 216:
720/216 = 216y/216
3 1/3 = y
This means the product of x and y would be:
18(3 1/3)
18(10/3)
180/3
60
Answer:
the last option (-5k+4)-8 + 6k
Step-by-step explanation:
-8(-5k+4)+6k
to simplify, begin by distributing the -8 so that parentheses are removed:
=(-8)(-5k) + (-8)(4) + 6k
=40k - 32 + 6k
combine 'like terms':
46k-32
the only answer which simplifies to 46k-32 is the last option:
the only difference between the original problem and the last option is that the -8 value is behind the parentheses instead of in front of it; it simplifies to be 46k-32
Answer:
x = 1
Step-by-step explanation:
Given in the question the equation
y = -x² + 2x - 1
To find the x-intercept, substitute in 0 for y
0 = -x² + 2x - 1
To find value of x use quadratic equation
x = -b ± √b²-4ac / 2a
here a = -1
b = 2
c = -1
x1 = -2 + √2²-4(-1)(-1) / 2(-1)
= -2 + 0 / -2
= -2 / -2
= 1
x2 = -2 - √2²-4(-1)(-1) / 2(-1)
= -2 - 0 / -2
= -2 / -2
= 1
Answer:
Slope (m) =
ΔY
ΔX
=
1
4
= 0.25
θ =
arctan( ΔY ) + 180°
ΔX
= 194.03624346793°
ΔX = 1 – 5 = -4
ΔY = 2 – 3 = -1
Distance (d) = √ΔX2 + ΔY2 = √17 = 4.1231056256177
Equation of the line:
y = 0.25x + 1.75
or
y =
1 x
4
+ 7
4
When x=0, y = 1.75
When y=0, x = -7
Step-by-step explanation:
Answer:
6x-9 = 6x -9
infinite solutions as they are the same equation.
