The equation of the parabola could be written as y-k = a(x-h)^2, where (h,k) is the vertex. Thus, y-(-3) = a(x+4)^2, or y+3 = a(x+4)^2.
The coordinates of one x-intercept are (-11,0). Thus, y+3 = a(x+4)^2 becomes
0+3 = a(-11+4)^2, so that 3 = a(-7)^2, or 3 = 49a. Therefore, a = 3/49, and the equation of the parabola becomes
y+3 = (3/49)(x+4)^2.
To find the other x-intercept, let y = 0 and solve the resulting equation for x:
0+3 = (3/49)(x+4)^2, or (49/3)*2 = (x+4)^2
Taking the sqrt of both sides, plus or minus 49/3 = x+4.
plus 49/3 = x+4 results in 37/3 = x, whereas
minus 49/3 = x+4 results in x = -61/3. Unfortunatelyi, this disagrees with what we are told: that one x-intercept is x= -11, or (-11,0).
Trying again, using the quadratic equation y=ax^2 + bx + c,
we substitute the coordinates of the points (-4,-3) and (-11,0) and solve for {a, b, c}:
-3 = a(-4)^2 + b(-4) + c, or -3 = 16a - 4b + c
0 = a(-11)^2 - 11b + c, or 0 = 121a - 11b + c
If the vertex is at (-4,-3), then, because x= -b/(2a) also represents the x-coordinate of the vertex, -4 = b / (2a), or -8a = b, or
0 = 8a + b
Now we have 3 equations in 3 unknowns:
0 = 8a + 1b
-3 = 16a - 4b + c
0 = 121a - 11b + c
This system of 3 linear equations can be solved in various ways. I've used matrices, finding that a, b and c are all zero. This is wrong.
So, let's try again. Recall that x = -b / (2a) is the axis of symmetry, which in this case is x = -4. If one zero is at -11, this point is 7 units to the left of x = -4. The other zero is 7 units to the right of x = -4, that is, at x = 3.
Now we have 3 points on the parabola: (-11,0), (-4,-3) and (3,0).
This is sufficient info for us to determine {a,b,c} in y=ax^2+bx+c.
One by one we take these 3 points and subst. their coordinates into
y=ax^2+bx+c, obtaining 3 linear equations:
0=a(-11)^2 + b(-11) + 1c => 0 = 121a - 11b + 1c
-3 = a(-4)^2 +b(-4) + 1c => -3 = 16a - 4b + 1c
0 = a(3)^2 +b(3) + c => 0 = 9a +3b + 1c
Solving this system using matrices, I obtained a= 3/49, b= 24/49 and c= -99/49.
Then the equation of this parabola, based upon y = ax^2 + bx + c, is
y = (1/49)(3x^2 + 24x - 99) (answer)
Check: If x = -11, does y = 0?
(1/49)(3(-11)^2 + 24(-11) - 99 = (1/49)(3(121) - 11(24) - 99
= (1/49)(363 - 264 - 99) = (1/49)(0) YES!
y = (1/49)(3x^2 + 24x - 99) (answer)
Answer:
it depends how many weeks look below
Step-by-step explanation:
1 week=$100.00
2 weeks=$115.00
3 weeks=$130.00
4 weeks=$145.00
and so on
pretty much every week you go up, she earns 15 bucks
hope this helps! have a good day :)
Answer:
Biotic, Abiotic
Step-by-step explanation:
Interconnected pathways through which water is recycled through the biotic and abiotic components of the biosphere.
The water cycle is driven by the Sun’s energy. The sun warms the ocean surface and other surface water, causing liquid water to evaporate and ice to sublime—turn directly from a solid to a gas. These sun-driven processes move water into the atmosphere in the form of water vapor.
Over time, water vapor in the atmosphere condenses into clouds and eventually falls as precipitation, rain or snow. When precipitation reaches Earth's surface, it has a few options: it may evaporate again, flow over the surface, or percolate—sink down—into the ground.
In land-based, or terrestrial, ecosystems in their natural state, rain usually hits the leaves and other surfaces of plants before it reaches the soil. Some water evaporates quickly from the surfaces of the plants. The water that's left reaches the soil and, in most cases, will begin to move down into it.
In general, water moves along the surface as runoff only when the soil is saturated with water, when rain is falling very hard, or when the surface can't absorb much water. A non-absorbent surface could be a rock in a natural ecosystem or asphalt or cement in an urban or suburban ecosystem.
Water evaporates to form the ocean surface and forms clouds by condensation. Water in clouds may fall as precipitation over either the land or the sea. Clouds formed over the sea may move over the land. When rain falls over the land, it may flow along the surface, infiltrate the soil—move into it from above ground—and percolate through the soil, moving downward to become groundwater. Groundwater in upper levels may flow into rivers, lakes, or oceans. Water near the soil surface may be taken up by plants and move out of their bodies through transpiration from the leaves. Snowmelt runoff and sublimation of snow and ice are other processes that contribute to the water cycle.
Water evaporates to form the ocean surface and forms clouds by condensation. Water in clouds may fall as precipitation over either the land or the sea. Clouds formed over the sea may move over the land. When rain falls over the land, it may flow along the surface, infiltrate the soil—move into it from above ground—and percolate through the soil, moving downward to become groundwater. Groundwater in upper levels may flow into rivers, lakes, or oceans. Water near the soil surface may be taken up by plants and move out of their bodies through transpiration from the leaves. Snowmelt runoff and sublimation of snow and ice are other processes that contribute to the water cycle.
Image credit: The water cycle by NOAA National Weather Service Jetstream, CC BY 2.0
Water in the upper levels of the soil can be taken up by plant roots. Plants use some of the water for their own metabolism, and water that's in plant tissues can find its way into animals’ bodies when the plants get eaten. However, most of the water that enters a plant's body will be lost back to the atmosphere in a process called transpiration.
Answer:
If there is a negative tile and a positive tile, it creates a zero pair.
Like terms can occur with the same variables (except for terms with exponents)
Step-by-step explanation:
Answer:
I think that you forgot to post the picture
Step-by-step explanation:
