C = child tickets
a = adult tickets
Solve this with the substitution method.
Make two equations:
6.30c + 9.90a = 1,246.50
c + a = 159
Solve for c.
Subtract 9.90a from both sides.
6.30c = 1,246.50 - 9.90a
Divide both sides by 6.30.
c = 197.86 - <span>1.57a (rounded to hundredths)
Plug c into second equation.
</span>197.86 - 1.57a + a = 159
Combine like terms.
197.86 - 0.57a = 159
Subtract 197.86 from both sides.
-0.57a = -38.86
Divide both sides by -0.57.
a = <span>68.18
round up to ones: 68
</span>

were sold.<span>
</span>
ANSWER
45.6cm to the nearest tenth.
EXPLANATION
The diagonal of the rectangular painting is 62cm.
The height of the painting is 42 cm.
The height of the painting h , the diagonal, and the width of the painting forms a right triangle with the diagonal being the hypotenuse.
From the Pythagoras Theorem,





The width of the painting is 45.6cm to the nearest tenth.
Answer:
In the explanation
Step-by-step explanation:
Going to start with the sum identities
sin(x+y)=sin(x)cos(y)+sin(y)cos(x)
cos(x+y)=cos(x)cos(y)-sin(x)sin(y)
sin(x)cos(x+y)=sin(x)cos(x)cos(y)-sin(x)sin(x)sin(y)
cos(x)sin(x+y)=cos(x)sin(x)cos(y)+cos(x)sin(y)cos(x)
Now we are going to take the line there and subtract the line before it from it.
I do also notice that column 1 have cos(y)cos(x)sin(x) in common while column 2 has sin(y) in common.
cos(x)sin(x+y)-sin(x)cos(x+y)
=0+sin(y)[cos^2(x)+sin^2(x)]
=sin(y)(1)
=sin(y)
Answer:
(x + 6)(x + 13)
Step-by-step explanation:
Given
x² + 19x + 78
Consider the factors of the constant term (+ 78) whuch sum to give the coefficient of the x- term (+ 19)
The factors are + 6 and + 13 , since
6 ×13 = + 78 and 6 + 13 = + 19 , then
x² + 19x + 78 = (x + 6)(x + 13) ← in factored form
Answer:
Step-by-step explanation:
Because dividing any term by the previous term gives a constant this is a geometric sequence of the form an=y^(n-1). Since each term is four times the previous term y=4 so
an=4^(n-1)