Answer:
Reflection: A' (5, 3)
B' (2, 3)
C' (2, 1)
D' (5, 1)
Dialation: A"(10, 6)
B" (4, 6)
C" (4, 2)
D" (10, 2)
Step-by-step explanation:
A(−5,3),B(−2,3),C(−2,1),D(−5,1)
To reflect over the y-axis you change the value of x. In this case all of the values for x are negative. You turn them all into a positive.:
A' (5, 3)
B' (2, 3)
C' (2, 1)
D' (5, 1)
To dialate by a scale factor of 2 you multiple everything by 2 and you should get: A"(10, 6)
B" (4, 6)
C" (4, 2)
D" (10, 2)
Hoep this helps!!
Answer:
x² – x – 12 = (x – 4)(x + 3)
Step-by-step explanation:
Identify two numbers that add to -1 and multiply to -12, let's call them p and q.
So ax² + bx + c = (x + p)(x + q)
pq = c
p + q = b.
It is easier to find these numbers by finding factors of -12.
This can be done by splitting the number up until all the numbers are prime.
-12 → 6 × -2 or -6 × 2 → -(3 × 2 × 2)
There can only be two numbers so the only options we have are 6 and -2, -6 and 2, 3, and -4, or -3 and 4.
We can eliminate them by adding them up.
6 + -2 = 4 ≠ -1 so that can't be it.
-6 + 2 = -4 ≠ -1 so that can't be it either.
-3 + 4 = 1 ≠ -1
therefore p and q are 3 and -4 because 3 + -4 = -1.
so x² – x – 12 = (x – 4)(x + 3)
p = -4, and q = 3.
(x – 4)(x + 3) = x(x + 3) – 4(x + 3) = x² + 3x – 4x + 12 = x² – x – 12
Answer:
question (1)
height of building = 308 ft
question (2)
cos 67.11 = 7/18
Explanation:
question (1)
Taking a look at the triangle, we can see that it is a right-angled triangle. This means that we can apply the special trigonometric identities.
The one we will use here is:
tan Θ = opposite / adjacent
where:
Θ = 72
the opposite side is the height of the building
the adjacent side = 100 ft
Substitute to get the height as follows:
tan(72) = height / 100
height = tan(72)*100 = 307.76 which is approximately 308 ft
question (2):
We are given that:
cos Θ = 7/18
therefore:
Θ = cos^-1(7/18)
Θ = 67.114
approximating to the nearest tenth, we would find that:
Θ = 67.11°
Hope this helps :)
Step-by-step explanation:
Solutions, colloids and suspensions are the three main classifications of a mixture based on sizes of the particles.
- A solution is a homogeneous mixture of solutes and solvents.
- Suspensions are mixtures of small insoluble particles of a solid in a liquid or gas.
- Colloids are homogeneous mixtures of two phases.
Solutions have the following characteristics:
- The size of particles is small
- The particles do not settle on standing.
- The particles pass through ordinary filter papers.
- They are clear and do not have color.
- They do not scatter light
Suspensions have the following properties:
- The particles dispersed are large
- They settle on standing.
- The particles do not pass through ordinary filter papers
- They do not pass through permeable membrane
- They are visible with microscope or naked eyes.
- They are cloudy
- Scatters light.
Colloids have the following properties:
- Their particles are between those in solutions and suspensions.
- Their particles do not settle on standing.
- Their particles pass through ordinary filter paper.
- They do not pass through permeable membranes.
- Scatters light
Learn more:
Mixtures brainly.com/question/4592300
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