Answer:
254.34
Step-by-step explanation:
m∠A=3x+105 ; m∠B=−6x−39 Given
m∠A+m∠B=90° Definition of complementary angles
3x+105−6x−39=90 Substitution Property of Equality
−3x+105−39=90 Simplify.
−3x+66=90 Simplify.
−3x=24
x=−8
m∠B=−6(−8)−39
m∠B=48−39 Simplify.
m∠B=9°
Answer:
Statement: -3x=90-66
Reason: By subtraction property of equality..
Statement: -3x=24
Reason: By simplification.
Statement: x=
Reason: By division property of equality.
Statement:
Reason: By substitution property of equality.
Statement:
Reason: By simplification.
Step-by-step explanation:
Given and are complementary angles.
To prove that
Proof:
1.Statement: are complementary angles .
Reason: Given .
2.Statement: ;
Reason: Given .
3. Statement:
Reason: By definition of complementary angles.
4.Statement:
Reason: By substitution property of equality.
5. Statement:
Reason: By simplification.
6. Statement:
Reason: By simplification.
7. Statement:
Reason: By subtraction property of equality .
8.Statement:
Reason: By simplification.
9.Statement:
Reason : By division property of equality.
10. Statement: x=-8
Reason: By simplification.
11. Statement:
Reason : By substitution property of equality.
12. Statement:
Reason: By simplification.
13. Statement:
Reason : By simplification.
Hence,
Hence proved.
Given: and are complementary angles.
and .
To prove:
Proof:
Statement 1: and are complementary angles.
Reason 1: Given
Statement 2: and .
Reason 2: Given
Statement 3:
Reason 3: Definition of complementary angles.
Statement 4:
Reason 4: Substitution property of equality
Statement 5:
Reason 5: Simplification
Statement 6:
Reason 6: Simplification
Statement 7:
Reason 7: Simplification
Statement 8:
Reason 8: Multiplication property of equality
Statement 9:
Reason 9: Substituting the value of 'x'
Statement 10:
Reason 10: Simplification
Answer:
The distance Conner walks each day is 10 miles
The distance Kevin walks each day is 7 miles
The distance John walks each day is 12 miles
Step-by-step explanation:
The question is a word problem
Let the number of miles Conner walks per day = x
The given inforf the totmation in the question are;
The distance Kevin walks per day = x - 3 miles
The distance John walks per day = x + 2 miles
In three days, the difference between the total distance John walks and the total distance Kevin walks is equal to half the total distance Conner walks
The number of miles each person walks per day is found as follows;
3×(x + 2) - 3×(x - 3) = 3·x/2
3·x + 6 - 3·x - (-9) = 3·x/2
3·x + 6 - 3·x + 9 = 3·x/2
3·x - 3·x + 6 + 9 = 3·x/2
0 + 6 + 9 = 3·x/2
15 = 3·x/2
x = 15×2/3 = 10 miles
x = 10 miles
Therefore, the distance Conner walks each day = 10 miles
The distance Kevin walks per day = (x - 3) miles = (10 - 3) miles = 7 miles
The distance Kevin walks per day = 7 miles
The distance John walks per day = (x + 2) miles = (10 + 2) miles = 12 miles
The distance John walks per day = 12 miles.
For this case, we have that by definition, the proportions can be expressed in different ways. Example, if we have a dog and three cats:
75%: It's percentage
0.75: In decimal (75% are cats)
: In fraction. (There are of cats)
: Using ":" to separate sample values. (For every three cats there is a dog)
Care should be taken with the proportions, always multiplying the numbers in the proportion by the same value.
Example:
Answer:
Care should be taken with the proportions, always multiplying the numbers in the proportion by the same value.
The numbers are 40 and 22.
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Let the numbers be m and n.
The two expressions are:
m + n = 62 ______(1)
m = 62 - n ______(2)
m - n = 18 ______(3)
From (2) and (3)
(62 - n) - n = 18
62 - n - n = 18
62 - 2n = 18
62 - 18 = 2n
n = 44/2
n = 22
Now,
m + n = 62
m = 62 - 22
m = 40
Thus,
m = 40 and n = 22.
Learn more about expressions here:
#SPJ3
The answer is Always
Step-by-step explanation: