Answer:
Step-by-step explanation:
Explanation:
Start by writing out your starting expression
x
2
−
5
x
2
+
5
x
−
14
−
x
+
3
x
+
7
Next, factor the denominator of the first fraction
x
2
+
5
x
−
14
x
2
+
7
x
−
2
x
−
14
x
(
x
−
2
)
+
7
(
x
−
2
)
(
x
−
2
)
(
x
+
7
)
Your expression is thus equivalent to
x
2
−
5
(
x
−
2
)
⋅
(
x
+
7
)
−
x
+
3
x
+
7
Since you have to subtract two fractions, you need to find the commonon denominator first. To do that, multiply the second fraction by
x
−
2
x
−
2
x
2
−
5
(
x
−
2
)
⋅
(
x
+
7
)
−
(
x
+
3
)
⋅
(
x
−
2
)
(
x
−
2
)
⋅
(
x
+
7
)
This will get you
x
2
−
5
−
(
x
+
3
)
(
x
−
2
)
(
x
−
2
)
(
x
+
7
)
x
2
−
5
−
x
2
−
x
+
6
(
x
−
2
)
(
x
+
7
)
=
1
−
x
(
x
−
2
)
(
x
+
7
)
The zero of the function is at 33.69 degree , the graph is plotted and attached with the answer.
<h3>What is a Function ?</h3>
A function is a law that relates a dependent variable and an independent variable with each other
It is given that
y = 2tan (x - π/2) +3
To find the zeroes of a function that function has to be equated to zero.
2tan (x - π/2) +3 = 0
2tan (x - π/2) = -3
tan (x - π/2) = -3/2
x - 90 = -56.31
x = 33.69 degree
The zero of the function is at 33.69 degree
For finding the maxima /minima
the derivative is
dy/dx = 2 sec² (x - π/2)
the point at which the slope is zero is substituted in the second derivative to find maxima/minima
d²y/dx² = 4 sec² (x - π/2) tan (x - π/2)
if the value is negative then it is a maxima and if it is positive it is a minima.
The vertical asymptote is found by finding the values that make the function undefined
x = 0+ πn
No horizontal or oblique asymptote
To know more about Function
brainly.com/question/12431044
#SPJ1
Answer:
There are 16 track events and 6 field events
The answer would be 10! I divided the number of plants that you can water with 4 gallons (14) by, well, the number of gallons it takes to water them (4) and got 3.5 (14 / 4 = 3.5), the number of plants you can water with one gallon. I then divided the number of plants you need to water (35) by the number of gallons it takes to water one plant (3.5) and came up with 10. I hope this helps you!
Answer:
7 square units
Step-by-step explanation:
As with many geometry problems, there are several ways you can work this.
Label the lower left and lower right vertices of the rectangle points W and E, respectively. You can subtract the areas of triangles WSR and EQR from the area of trapezoid WSQE to find the area of triangle QRS.
The applicable formulas are ...
area of a trapezoid: A = (1/2)(b1 +b2)h
area of a triangle: A = (1/2)bh
So, our areas are ...
AQRS = AWSQE - AWSR - AEQR
= (1/2)(WS +EQ)WE -(1/2)(WS)(WR) -(1/2)(EQ)(ER)
Factoring out 1/2, we have ...
= (1/2)((2+5)·4 -2·2 -5·2)
= (1/2)(28 -4 -10) = 7 . . . . square units
