Response:
If there are "p" pounds of peanuts and "m" pounds of a mixture containing '20% peanuts and 80% almonds', then we can formulate the following equations:
p + m = 10 -----------(1) and
4m/5 = 4 ------------(2)
The solution yields 5 lb peanuts and 5 lb mixture.
Detailed explanation:
In the mixture that Delaney desires to create, there will be
lb
= 6 lb of peanuts
Thus, there will be (10 - 6) lb
= 4 lb of almonds
If Delaney has "p" pounds of peanuts and "m" pounds of the '20% peanuts and 80% almonds' mixture, then based on the problem statement,
p + m = 10 -----------(1) and
4m/5 = 4 ------------(2)
From equation (2), we derive
m = 5 --------------(3)
From (1) and (3), we find that
p = (10 - 5) = 5
Response:
(A)
A symmetrical outcome occurs when both figures are identical.
The half section of the illustration is tilted downward; therefore, to achieve symmetry, we must shift the figure upwards.
Then, we reflect upon the inverted image.
Thus, we achieve reflectional and translational symmetry.
Response:
The answer to the inquiry is 8 hours.
Step-by-step breakdown:
Information
Ladder length = 200 cm
Distance between rungs = 20 cm
Tide rise rate = 10 cm/h
Fifth rung =?
Procedure
1.- Determine the total height the tide must reach
Height = 20 cm x 4
= 80 cm as the first rung is touching the water.
2.- Calculate the time needed
Rate = distance / time
-Solve for time
Time = distance / rate
-Substitute values
Time = 80 cm / 10 cm/h
-Final outcome
Time = 8 hours.
The cubic equation formed is L^3 - 52L +144 = 0. Dimensions: Length = 4 inches, Width = 2 inches, Height = 3 inches. To determine this, let L be the length, W the width, and H the height. The box volume is 24 cubic inches, and its total surface area is 52 sq. inches. Setting W = L/2 leads to Volume = L * W * H, thus substituting W gives us the equation 0.5L^2 * H = 24 resulting in H = 48/L^2. The surface area equation simplifies to (L*W) + (L+H) + (W+H) = 26. Introducing W = 0.5L yields 0.5L^2 + 1.5LH = 26. Substituting H into this gives 0.5L^2 + 72/L = 26. Multiplying throughout by L to eliminate denominators yields 0.5L^3 - 26L + 72 = 0. After multiplying through by 2: L^3 - 52L +144 = 0. Testing L=4 confirms a factor, thus Length (L) = 4 inches, and subsequently, W and H calculate to 2 inches and 3 inches respectively.
We understand that a rectangle has been altered into the one shown in Figure 1 using this rule:
It is known that the origin is the center of rotation and two rules apply to perform a rotation of 90 degrees, namely:
1. Clockwise
The rule to convert a point in this case is:
This rule has already been implemented to create the image, so we need to reverse the outcome using this formula, hence:
2. Counterclockwise
Applying the same concept as before but with new rules for the scenario:
Reversing the outcome gives us:
