Answer:
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Step-by-step explanation:
Answer:
Mostly correct
For Q3, you are doing great, you remembered that negative numbers can happen if the exponent is an odd number.
For Q4, I think you were confused with the fractions,
4(i)
4(ii) is also wrong but I'll let you try to fix it yourself following what I given you for 4(i). You should get 1/64
Hope this helps!
Considering there is a function (relationship) and that it is linear, the distance will change proportionally to time constantly. In other words, we are taking the speed to be constant throughout the journey.
If we let:
t = time (min's) driving
d = distance (miles) from destination
Then we can represent the above information as:
t = 40: d = 59
t = 52: d = 50
If we think of this as a graph, we can think of the x-axis representing time and the y-axis representing the distance to the destination. Being linear, the function will be a line, i.e. it will have a constant gradient. If you were plot the two points inferred from the information and connect the two dots, you will get a declining line (one with a negative gradient) representing the inversely proportional relationship or equally, the negative correlation between the time driving and the distance to the destination. The equation of this line will be the linear function that relates time and the distance to the destination. To find this linear function, we do as follows:
Find the gradient (m) of the line:
m = Δy/Δx
In this case, the x-values are t-values and our y-values are d-values, so:
Δy = Δd
= 50 - 59
= -9
Δx = Δt
= 52 - 40
= 12
m = -9/12 = -3/4
Note: m is equivalent to speed with units: d/t
Use formula to find function and rearrange to give it in the desired format:
y - y₁ = m(x - x₁)
d - 50 = -3/4(t - 52)
4d - 200 = -3t + 156
4d + 3t - 356 = 0
Let t = 70 to find d at the time:
4d + 3(70) - 356 = 0
4d + 210 - 356 = 0
4d - 146 = 0
4d = 146
d = 73/2 = 36.5 miles
So after 70 min's of driving, Dale will be 36.5 miles from his destination.
#9 You have to make the fraction a decimal, then multiply 11.8 by 6.5. This is because 11.8 is per hour.
#10 here is a hint, one quarter of an hour is 15 minutes. again change the fraction to a decimal
#11 just multiply the 2 numbers
1.4
×2.9
---------
126
+ 280
------------------
3.06
Given that triangle <span>STU
is reflected once to map onto
triangle S'T'U'.
Given that triangle STU has
vertices S(8, 6), T(2, 2), U(5, 1).
If vertex T' is at
(2, −2), this means that triangle STU is refrected across the x-axis.
A refrection across the x-axis results in an image that has the same x-value as the pre-image but a y-value that has the opposite sign of the y-value of the pre image.
Thus, a point, say (x, y), refrected over the x-axis will result in an image with coordinate (x, -y)
Therefore, given that the coordinate of S is (8, 6), then the coordinates of vertex S'</span> is (8, -6).
