<span>4x − 2y = 6 . . . . . (1)
2x + y = 5 . . . . . (2)
(2) x 2 => 4x + 2y = 10 . . . . . (3)
(1) - (3) gives: -4y = -4
y = -4/-4 = 1
From (2), 2x + 1 = 5 => 2x = 5 -1 = 4
x = 4/2 = 2
Solution is (2, 1)
Substituting the solution into the options gives that
</span><span>−4x − 2y = 10
−4y = 4 −4x
has the same solution.
</span>
Answer:
The difference between the area of Texas and Rhode Island in square miles and scientific notation = (2.68 × 10⁵) square miles.
Step-by-step explanation:
Area of Texas = (2.69 × 10⁵) square miles = 269000 square miles
Area of Rhode Island = (1.21 × 10³) square miles = 1210 square miles
Difference between the Area of the Texas and Rhode Island = 269000 - 1210 = 267,790 square miles = (2.68 × 10⁵) square miles.
The difference between the area of Texas and Rhode Island in square miles and scientific notation = (2.68 × 10⁵) square miles.
Hope this Helps!!!
Helena is correct in saying that the point-slope form will generate the equation. The point-slope form is written as:
y-y₁ = m(x-x₁), where,
m = (y₂-y₁)/(x₂-x₁) is the slope of the line
(x₁,y₁) and (x₂,y₂) are the coordinates of the two points
On the other hand, the slope-intercept form is written as:
y = mx + b, where,
m is the slope of the line
b is the y-intercept
In this case, since only two points were given, the y-intercept of the line is not readily known. Thus, it is only through the point-slope form that the equation of the line can be determined. This is because it only requires the substitution of the x and y-coordinates of the points in the equation.
The equation of a line given two points needs to be found. Samuel claims that slope-intercept form will generate the equation and Helena claims that point-slope form will find the equation. Who is correct? Explain your reason by describing both forms.
Answer:
Step-by-step explanation:
1) <u>The two points are</u>:
a) On the first swing she swings forward by 18 degrees: <em>(1, 18)</em>
b) On the second swing she only comes 13.5 degrees forward: <em>(2,13.5)</em>
2) <u>The general equation using the form given is</u>:
3) <u>Substitute the two points</u>:
4) <u>Divide the second equation by the first one</u>:
⇒ 13.5 / 18 = B
⇒ B = 0.75
5) <u>Substitue B = 0.75 into the first equation</u>:
18 = A (0.75) ⇒ A = 18 / 0.75 = 24
Hence, the equation is:
We are given with the expression y<span> = b cos t + t2 sin t and is asked to differentiate the function in terms of t. Based in the power law and law of products, we apply these to the given expresssion. the derivative is y' = -b sin t + t^2 * (cos t) + sin t * 2t. This is equal to </span>y' = sin t (-b +2t) + t^2 cos t.
