Answer:
Step-by-step explanation:
Let equal sides of an isosceles triangle = a inches
Base = 
inches
Perimeter = 32 inches
a + a + = 32
Subtract 2 from both sides
a = 12 inches
base = 
= 6 + 2
Base = 8 inches
Answer:
Eq: (x+a/2)²+(y+1)²=(a²-8)/4
Center: O(-a/2, -1)
Radius: r=0.5×sqrt(a²-8)
Mandatory: a>2×sqrt(2)
Step-by-step explanation:
The circle with center in O(xo,yo) and radius r has the equation:
(x-xo)²+(y-yo)²=r²
We have:
x²+y²+ax+2y+3=0
But: x²+ax=x²+2(a/2)x+a²/4-a²/4= (x+a/2)²-a²/4
And
y²+2y+3=y²+2y+1+2=(y+1)²+2
Replacing, we get:
(x+a/2)²-a²/4+(y+1)²+2=0
(x+a/2)²+(y+1)²=a²/4-2=(a²-8)/4
By visual inspection we note that:
- center of circle: O(-a/2, -1)
- radius: r=sqrt((a²-8)/4)=0.5×sqrt(a²-8). This means a²>8 or a>2×sqrt(2)
Answer:
The center of the circle is
Step-by-step explanation:
Let the equation of the circle be
, where (-a,-b) is the center of this circle.
The points lying the circle must satisfy the equation of this circle.
A(0,0)
We substitute this point to get;
B(-3,0)
But c=0
C(1,2)
Put the value of 'a' and 'c' to find 'b'
b=-2
Hence the center of the circle is
Step1: Define an odd integer.
Define the first odd integer as (2n + 1), for n = 0,1,2, ...,
Note that n is an integer that takes values 0,1,2, and so no.
Step 2: Create four consecutive odd integers.
Multiplying n by 2 guarantees that 2n will be zero or an even number.
Therefore (2n + 1) is guaranteed to be an odd number.
By adding 2 to the odd integer (2n+1), the next number (2n+3) will also be an odd integer.
Let the four consecutive odd integers be
2n+1, 2n +3, 2n +5, 2n +7
Step 3: require that the four consecutive integers sum to 160.
Because the sum of the four consecutive odd integers is 160, therefore
2n+1 + 2n+3 + 2n+5 + 2n +7 = 160
8n + 16 = 160
8n = 144
n = 18
Because 2n = 36, the four consecutive odd integers are 37, 39, 41, 43.
Answer: 37,39,41,43
The class which generally had the highest pulse of students recorded by the science teacher after climbing the stairs is class 3.
<h3>What is box plot representation of data?</h3>
Box plot is the way of representation of data which gives the graphical image of the data set to understand better.
The minimum and the maximum values in the box plot is plotted at the end points.
- A science teacher recorded the pulse of each of the students in her classes after the students had climbed a set of stairs.
- She displayed the results, by class, using the box plots shown.
In this box plot, the class 3 has the highest value compare to all the box plot.
Thus, the class which generally had the highest pulse of students recorded by the science teacher after climbing the stairs is class 3.
Learn more about the box plot here;
brainly.com/question/14277132
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