The quotient rule for exponents states that if we divide exponents with the same base, then we can subtract the exponents and keep the base unchanged. The exponents have the same base so we can apply the quotient rule and rewrite the given expression
1)
a. y=mx+b
m=slope
b=y-intercept
y=20x+40
The slope is 20.
The y-intercept is 40.
b. y =cost
x= # of shirts
y=20x+40
15 sweatshirts would make the equation y=20(15)+40
y=300+40
y=340
15 shirts would cost $340.
c. y=20x+40
$1000 would make the equation 1000=20x+40
1960=20x
98=x
Paying $1000 would get the swim team 98 shirts.
2)
(1,5) (4,11)
(x,y) (x1, y1)
y+y1=m(x+x1)
Pick a point and substitute it into the equation.
y+5=m(x+1)
To find the slope of a line, use the following equatIon:
y-y1/x-x1
11-5/4-1
6/3=2
The slope of the line is 2. Plug it into the equation for m.
y+5=2(x+1)
Solve the equation.
y+5=2x+2
y+3=2x
Put the equation in slope-intercept form.
y=2x-3
3)
y=x-25
y=6x-5
Plug one equation into the other.
x+25=6x-5
Solve.
x+30=6x
30=5x
6=x
Now plug 6 into one of the equations.
y=6x-5
y=6(6)-5
y=36-5
y=31
The answer should be in the form of a point.
(6,31)
5) I'm sorry, don't know how to solve this. You can Google how to graph two inequalities, though.
6)
Antonio's age can be represented by x.
Sarah's age can be represented by y.
2x+y=35
5x=y
Plug 5x into the first equation.
2x+5x=35
Solve.
7x=35
x=5
Antonio is 5 years old.
To find Sarah's age, plug Antonio's age into the equation for Sarah's age.
5x=y
5(5)=y
25=y
Sarah is 25 years old.
Answer:
[ 0 ]
Step-by-step explanation:
The order of the matrix [ 3 1 1 ] is 1 by 3 and the order of the other matrix is 3 by 1 so this means that the order of the answer matrix is 1 by 1. So we multiply matrices row by columns.
[ 3 1 1 ] × | 2|
| -6|
| 0|
[ 3 × 2 + 1 × -6 + 1 × 0 ]
[ 6 - 6 + 0 ]
[ 0 ]
Answer:
Polygon A is reflected across x- axis followed by the reflection across y-axis.
Step-by-step explanation:
A polygon A has been transformed by a rigid transformation to form an image polygon B.
Let one of the vertex of polygon A is (-2, 1).
When polygon is reflected across the x - axis,
Image point will be,
A(x, y) → A'(x, -y)
By this rule,
A(-2, 1) → A'(-2, -1)
Now the image point is further reflected across the y-axis,
Rule for the reflection across y-axis is,
A'(x, y) → B'(-x, y)
By this rule, image of A' will be,
(-2, -1) → (2, -1)
Therefore, Polygon A is reflected across x- axis followed by the reflection across y-axis.
9514 1404 393
Answer:
(a)
Step-by-step explanation:
Add A to both sides of the equation:
X -A +A = B +A
X = B + A
The sum of the two matrices is the matrix that is the sum of corresponding terms.
x11 = B11 +A11 = -9+2 = 7
x12= B12 +A12 = 5-7 = -2
These calculations are sufficient to match the answer with choice (a).