X=the units digit
y=the tens digit.
The number is: 10y + x
The reversed number is: 10x+y
The units digit is twice the tens digit, then: x=2y
a)we suggest this system of equations:
x=2y
2(10y+x)=12+(10x+y)
We can solve this system of equations by substitution method:
2(10y+2y)=12+[10(2y)+y]
2(12y)=12+21y
24y=12+21y
24y-21y=12
3y=12
y=12/3
y=4
x=2y
x=2(4)=8
The number is: 10y+x=10*4+8=48
Answer: the number is 48.
b)
the number is: 10x+y
we can suggest this system of equations:
8(x+y)=(10x+y)+19
x=y-2
We can solve this system of equations by substitution method.
8(y-2+y)=[10(y-2)+y]+19
8(2y-2)=11y-20+19
16y-16=11y-1
16y-11y=-1+16
5y=15
y=15/5
y=3
x=y-2
x=3-2=1
The number is: 10x+y=10*1+3=13
Answer:the number is 13.
c)
The number is: 10x+y
The number reversed is: 10y+x
we can suggest this system of equations:
y=2x
2(10x+y)=9+(10y+x)
We solve this system of equations by substitution method:
2(10x+2x)=9+[10(2x)+x]
2(12x)=9+21x
24x=9+21x
24x-21x=9
3x=9
x=9/3
x=3
y=2x
y=2*3=6
The number is: 10x+y=10*3+6=36
Answer: the number is 36
Answer:
7
Step-by-step explanation:
First, you need to plug in the values for x. Here, we know that x = 5. So, when we plug it in we get 2^5 - 5^2. When we simplify, we then get 32 - 25. Thus, 32 - 25 = 7.
Answer:
Step-by-step explanation:
we know that
The total area of the figure is equal to the area of the square plus the area of the triangle
step 1
Find the area of triangle
The area of triangle is equal to
where
b is the base of triangle (is the same that the length side of the square)
h is the height of triangle
we have
Applying the Pythagorean Theorem
Find the length side b
Area of triangle
step 2
Find the area of the square
The area of the square is
we have
substitute
step 3
Find the total area of the figure
Adds the areas
Answer:
A
Step-by-step explanation:
Note the following 3 points with respect to a function given as y = f(x).
1. The function y = f(-x) is a reflection across the y-axis
2. The function y = f(x+a) is a horizontal translation a units left and y = f(x-a) is a horizontal translation a units right
3. the function y = f(x) + a is a vertical translation a units up and y = f(x) - a is a vertical translation a units down
Dissecting the transformed function of f(x) = ln (3-x) -2 w.r.t f(x) = ln x, we see:
<em>1. x is replaced with -x, so </em><u><em>reflection across y-axis</em></u>
<em>2. we have a horizontal shift in left side because the argument of ln is (3-x) or (-x+3)</em>
<em>3. We have vertical shift 2 units down because there is a -2 after the functional part of ln(3-x)</em>
<em />
Looking at the choices, A is the right answer.
