Based on the definition of congruent angles, the value of x is: 23.
<h3>What are Congruent Angles?</h3>
Congruent angles have the same measure. Examples of angles that are congruent are:
- Alternate interior angles
- Alternate exterior angles
- Corresponding angles
Thus:
(5x + 16) = (6x - 7) -- congruent angles
Combine like terms
5x - 6x = -16 - 7
-x = -23
x = 23
Therefore, based on the definition of congruent angles, the value of x is: 23.
Learn more about congruent angles on:
brainly.com/question/1675117
The easiest way to find the vertex is to convert this standard form equation into vertex form, which is y = a(x - h)^2 + k.
Firstly, put x^2 - 10x into parentheses: y = (x^2 - 10x) + 30
Next, we want to make what's inside the parentheses a perfect square. To do that, we need to divide the x coefficient by 2 and square it. In this case, the result is 25. Add 25 inside the parentheses and subtract 25 outside of the parentheses: y = (x^2 - 10x + 25) + 30 - 25
Next, factor what's inside the parentheses and combine like terms outside of the parentheses, and your vertex form is: y = (x - 5)^2 + 5.
Now going back to the formula of the vertex form, y = a(x - h)^2 + k, the vertex is (h,k). Using our vertex equation, we can see that the vertex is (5,5).
Answer:
a) ∅ ∈ {∅} TRUE
b) ∅ ∈ {∅,{∅}} TRUE
c) {∅} ∈ {∅} FALSE
d) {∅} ∈ {{∅}} TRUE
e) {∅} ⊂ {∅,{∅}} TRUE
f ) {{∅}} ⊂ {∅,{∅}} TRUE
g) {{∅}} ⊂ {{∅},{∅}}FALSE
Step-by-step explanation:
To assess whether these statements are true or false, first observe the symbol:
"∈" means that element, as it is and as it is, belongs to the set. To belong to the set it must be within the symbols "{}"
On the other hand, the symbol "⊂" means "subset", that is, it is a subset that is included in the main set.
So:
c) is false because "{∅}" is not included in the set
g) is false because " {{∅}}" is not included in the set
Answer:Jason is 5 years old.
John is 4 years old.
Jackson is 12 years old.
Step-by-step explanation:
Let x represent the age of Jason.
Let y represent the age of John.
Let z represent the age of Jackson.
The ages of three siblings Jason John and Jackson totals 21 years. It means that
x + y + z = 21 - - - - - - - - - - -1
Jason is one year older than John. It means that
x = y + 1
Jackson is three times as old as John. It means that
z = 3y
Substituting x = y + 1 and z = 3y into equation 1, it becomes
y + 1 + y + 3y = 21
5y = 21 - 1 = 20
y = 20/5 = 4
x = y + 1 = 4 + 1
x = 5
z = 3y = 3 × 4
z = 12
Answer:
Step-by-step explanation:
Let X be average interest paid monthly by a bank's Visa cardholders
Given that X is N(28, 8)
In the following to find out probability we convert X to z score and use std normal distribution table
Z = 
Probability being less than 1 is here equal to the proportion also.
A) P(X>32) = P(Z>0.5)=0.5-0.1915=0.3085
B) P(X>40) = P(Z>1)=0.5-0.3413=0.1687
C) P(X<19) = P(Z<-1.125)=0.5-0.0438=0.4562
D) We have to find 19th percentile here
Z =-0.88
