Yes I done it happy new year and a happy evening wish you a happy Christmas
Answer:
Step-by-step explanation:
Given a general quadratic formula given as ax²bx+c = 0
To generate the general formula to solve the quadratic equation, we can use the completing the square method as shown;
Step 1:
Bringing c to the other side
ax²+bx = -c
Dividing through by coefficient of x² which is 'a' will give:
x²+(b/a)x = -c/a
- Completing the square at the left hand side of the equation by adding the square of half the coefficient x i.e (b/2a)² and adding it to both sides of the equation we have:
x²+(b/a)x+(b/2a)² = -c/a+(b/2a)²
(x+b/2a)² = -c/a+(b/2a)²
(x+b/2a)² = -c/a + b²/4a²
- Taking the square root of both sides
√(x+b/2a)² = ±√-c/a + b²/√4a²
x+b/2a = ±√(-4ac+b²)/√4a²
x+b/2a =±√b²-4ac/2a
- Taking b/2a to the other side
x = -b/2a±√√b²-4ac/2a
Taking the LCM:
x = {-b±√b²-4ac}/2a
This gives the vertex form with how it is used to Solve a quadratic equation.
Let us bear in mind the equivalent value of these coins:
One dime = $0.10
One quarter = $0.25
Let x = number of dimes
y<span> = number of quarters</span>
Since the boy has 70 coins in total, we can say that:
<span>x + y = </span><span>70 </span>(can be written as x = 70 – y)
Since the boy has a total of $12.40, we can say that:
0.10x + 0.25y = 12.40
To solve this problem, we need to solve this system of equation. We have to substitute the value of x as written in the first equation (x = 70 –y)
0.10(70 – y) + 0.25y = 12.40
7 – 0.10y + 0.25y = 12.40
0.15y = 5.40
y = 36
X = 70 – 36
X = 34
Therefore,<span> the boys </span>has<span> 34 dimes and 36 quarters. To check our answer, we just have to check if his money would total $12.40.</span>
34 dimes = $3.40
36 dimes = $9.00
<span>Total </span><span>$12.40</span>
Answer:
x = 25.6
Step-by-step explanation:
As we can see, this is a right triangle, so there are known relationships
well to start we have to know the relationship between angles, legs and the hypotenuse
α = 43
a: adjacent = x
o: opposite
h: hypotenuse = 35
sin α = o/h
cos α = a/h
tan α = o/a
we see that it has (angle, adjacent, hypotenuse)
cos α = a/h
cos 43° = x / 35
cos 43° * 35 = x
25.59 = x
if we want to round to the nearest tenth
x = 25.59 = 25.6
Answer:
Step-by-step explanation:
The given expression is 
We apply the distributive property to expand the parenthesis
Regroup similar terms to get:
Combine the similar terms to obtain:
The correct option is C.
