Given that,
Julia completes a 20-mile bike ride in 1.2 hours.
The distance Julia covers is 20 miles and her time taken is 1.2 hours.
Therefore, Julia's speed = 
= 16.67 mph
Katie finishes the same 20-mile ride in 1.6 hours.
Katie’s distance is 20 miles and her time is 1.6 hours.
Hence, Katie's speed = 
= 12.5 mph
To determine how much faster Julia rides compared to Katie, subtract Katie’s speed from Julia’s speed.
Thus, 16.67 mph minus 12.5 mph equals 4.17 mph, approximately 4.2 mph.
Consequently, Julia cycles 4.2 mph faster than Katie.
Each tweet could cost anywhere from 1 to 140 pennies, which can be expressed as an inequality [1 ≤ x ≤ 140]. Since it's impossible to tweet 0 characters or exceed 140. If required in pounds, simply divide by 100. A) 1 ≤ x ≤ 140 B) The cost per character is a penny, and tweeting fewer than 1 character or more than 140 is not permitted.
The question clearly seeks the highest values from both functions, meaning the vertices of each.
<span>The graph depicting the path of Ed’s football indicates the vertex's coordinates (the peak of the graph).
</span>
Specifically,
(h,k) = (1.5, 7.5)
Where (h,k) represents the vertex's location.
Conversely,<span>the trajectory of Steve's football is defined by the equation:
y = - 2x
²</span>
+ 5x + 4<span>
To find the axis of symmetry, we use the formula:x = - b
÷ 2a
Where:
a = -2</span>
b = 5
Consequently,
x = - 5 ÷ - 4
x = 5 / 4
x = 1.25
Now substituting this x-value back into the main equation to determine y.
y = - 2x² + 5x + 4y = - 2(1.25)² + 5(1.25) + 4
y = - 3.125 + 6.25 + 4
y = 7.125
Thus, the vertex (h,k) = (1.25, 7.125)
As observed from the calculationsEd’s
<span>football attains a higher height.
</span>
T<span>he area of a figure signifies the measure of space within a two-dimensional shape, typically expressed as square units based on the figure's dimensions.
For instance, with a shape having dimensions of k, its area can be given by
.
</span>
<span>Consider that one similar figure possesses an area nine times that of another.
As these figures are similar, their areas correspond to the proportionality of their dimensions.
Let the smaller shape's dimensions be k, while the larger is p times the dimensions of the smaller shape. The smaller shape's area is
and the larger shape's area is
.
Now, knowing the larger figure's area is nine times the area of the smaller figure, we have:
</span>
Thus, the dimensions of the larger figure must be 3 times those of the smaller figure.
Answer:
(B) There is a single solution: x = 0.
Step-by-step explanation:
The equation that Kate is attempting to solve is: 
Consequently, this equation results in one solution: x = 0.
