The shaded region is a triangle. Triangle area can be determined with formula
a = 1/2 × b × h
From the question, we know that the triangle consists of
base = 10 - 6 = 4 m
and the height is the dimension which is perpendicular to the base,
height = 6 m
Find the triangle area
a = 1/2 × b × h
a = 1/2 × 4 × 6
a = 1/2 × 24
a = 12
The area of the shaded region is 12 m²
The absolute value
returns the "positive version" of a number.
In other words, if the number is positive, it remains positive; if the number is negative, it changes sign.
So, if we want
, we want the "positive version" of x to be 9.
This can happen in two ways: if x is already 9, then its absolute value is still nine. If instead x=-9, its positive value will be 9 again.
In formula, we have

because

I think that first you need to understand what CPCTC is used for.
Let's start with the definition of congruent triangles.
Definition of congruent triangles
Two triangles are congruent if each side of one triangle is congruent to a corresponding side of the other triangle and each angle of one triangle is congruent to a corresponding angle of the other triangle.
A definition works two ways.
1) If you are told the sides and angles of one triangle are congruent to the corresponding sides and angle of a second triangle, then you can conclude the triangles are congruent.
2) If you are told the triangles are congruent, then you can conclude 6 statements of congruence, 3 for sides and 3 for angles.
Now let's see what CPCTC is and how it works.
CPCTC stands for "corresponding parts of congruent triangles are congruent."
The way it works is this. You can prove triangles congruent by knowing fewer that 6 statements of congruence. You can use ASA, SAS, AAS, SSS, etc. Once you prove two triangles congruent, then by the definition of congruent triangles, there are 6 congruent statements. That is where CPCTC comes in. Once you prove the triangles congruent, then you can conclude two corresponding sides or two corresponding angles are congruent by CPCTC. These two corresponding parts were not involved in proving the triangles congruent.
Problem 1.
Statements Reasons
1. Seg. AD perp. seg. BC 1. Given
2. <ADB & <ADC are right angles 2. Def. of perp. lines
3. <ADB is congr. <ADC 3. All right angles are congruent
4. Seg. BD is congr. seg CD 4. Given
5. Seg. AD is congr. seg. AD 5. Congruence of segments is reflexive
6. Tr. ABD is congr. tr. ACD 6. SAS
7. Seg. AB is congr. seg. AC 7. CPCTC
Answer:
a. N=25
b. X[bar]= 60.52
c. Y[bar]= 106.72
d. SSx= 115.24
e. ∑X*∑Y = 4036684
f. SSxy= 202020.3296
g. √(SSx*SSy)= 449.46
Step-by-step explanation:
Hello!
Using the attached data you need to calculate some statistics.
a) N
The sample size is listed under the first column "subject" You can see that 25 subjects qhere studied so N=25.
b.
The mean of set X is equal to X[bar]= ∑X/n= 1513/25= 60.52
∑X is listed in the second table.
c.
The mean of ser Y is Y[bar]= ∑Y/n= 2668/25= 106.72
∑Y is listed in the second table.
d.
Sum of Squares of set X SSx= ∑X²-[(∑X)²/n]= 91682-[(1513)²/25]= 115.24
e.
∑X*∑Y =1513*2668= 4036684
f.
SSxy= (∑X²-[(∑X)²/n]) * (∑Y²-[(∑Y)²/n])= (91682-[(1513)²/25]) * (286482*[(2668)²/25])= 202020.3296
g.
√(SSx*SSy)= √(115.24*1753)= 449.46
I hope you have a SUPER day!
Answer:
(15,16)
Step-by-step explanation:
C=halfway between A to B
A to B on the x axis goes across by 24
24/2 =12
3+12=15
A to B on the y axis goes up by 28
28/2 = 14
2+14=16
(15,16)