Answer:
<em>The required values are a = 29°, b = 20°</em>
Step-by-step explanation:
<u>Angles and Lines</u>
The image shows two lines crossing at a point where three angles are marked: 57°, 7b-17, and 2a-1.
It can be noted that 57° and 7b-17 are linear angles whose sum is 180°:
57° + 7b - 17° = 180°
Solving for b:
7b = 180° + 17° - 57°
7b = 140°
b = 140°/7 = 20°
b = 20°
It can also be noted that 57° and 2a-1 are vertical angles (opposite angles). Vertical angles are congruent, thus:
57° = 2a - 1°
Adding 1:
2a = 58°
a = 29°
The required values are a = 29°, b = 20°
Answer:
As i understand it:
The total park is 2.4 ha
10% of that is paths and 15% of that is a lake.
So a 10% + 15% = 25% is taken.
So we have left a 75% of the park, this is:
Left = (75%/100%)2.4 ha = 0.75*2.4ha = 1.8 ha.
Now we also need to subtract the are of the tennis court.
The tennis court occupies a rectangular plot of 60m by 50m (you actually wrote cm here, but i guess it was a mistake, we can not have a tennis court of 60cm by 50cm)
So the area of the tennis court is:
A = 60m*50m = 3,000 m^2
But we want to write it in ha
We know that:
1ha = 10,000m^2
then 3,000m^2 = (3,000/10,000) ha = 0.3 ha
Then the left area is:
L = 1.8 ha - 0.3ha = 1.5 ha.
Answer:
350
Step-by-step explanation:
We have two points on the demand curve as (10, 450) and (15, 200). Using the two-point form of the equation for the line between them, we can find the "y" value for "x" = 12 as ...
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
y = (200 -450)/(15 -10)(12 -10) +450
= (-250/5)(2) +450
= -100 +450 = 350
We predict the number of tickets sold at $12 will be 350.
_____
<em>Check</em>
The drop in sales of 50 tickets for each $1 increase in price is consistent with other table values.
The equation that gives the coordinates (0,1), (2,5), (3,7) is y =2x + 1.
Step-by-step explanation:
Step 1; We need to determine the equation relating the x to the f(x) values from the given coordinates. y is the dependent value whereas x is the independent value i.e. y's value depends on x's value.
Step 2; If we multiply the x value with 2 and add the resulting answer with 1 we get the y value.
y = 2x + 1 is the equation that relates the values in the table.
Step 3; Now we substitute the values in the equation to see if it's correct.
For x = 0, y = 2(0) + 1 = 0 + 1 = 1,
For x = 2, y = 2(2) + 1 = 4 + 1 = 5,
For x = 3, y = 2(3) + 1 = 6 + 1 = 7.
So the equation that gives the coordinates (0,1), (2,5), (3,7) is y =2x + 1.