Answer: The expression that represents the area of Mary's new garden =2x^2
Step-by-step explanation:
The area of a square is given by x^2, where x is the length of one side. The length of the other side is also x. In a square, all sides are equal. each of the four sides equal x
Area = x × x
Area = x^2
She decided to double the area of her garden
New area = 2(x × x)
New area = 2x^2
The expression that represents the area of Mary's new garden =2x^2
Answer:
<x = 31°
Step-by-step explanation:
m<BCA = m<GCJ (vertical angles)
m<BCA = 59° (substitution)
Since line KL is perpendicular to line FG, the angle formed at point B is 90°.
Therefore, m<ABC = 90°
m<BAC + m<ABC + m<BCA = 180° (sum of triangle)
m<BAC + 90° + 59° = 180° (Substitution)
m<BAC + 149° = 180°
m<BAC = 180° - 149°
m<BAC = 31°
<x = <BAC (vertical angles)
m<x = 31° (substitution)
The statement "<span>The rate of change of y with respect to x is inversely proportional to y^4" can be written mathematically as dy/dx = k/y^4
To solve the differential equation, we use variable saparable method.
y^4 dy = kdx
Integrating both sides gives,
y^5 / 5 = kx + A
y^5 = 5kx + 5A = Bx + C; where B = 5k and C = 5A
![y= \sqrt[5]{Bx+C}](https://tex.z-dn.net/?f=y%3D%20%5Csqrt%5B5%5D%7BBx%2BC%7D%20)
</span>
Answer:
4
Step-by-step explanation:
Let's set up an equation using the formula for the area of a triangle.
Hint #22 / 3
\begin{aligned} \text{Area of a triangle} &= \dfrac12 \cdot \text{base} \cdot \text{height}\\\\ 12&= \dfrac12 \cdot 6 \cdot x \\\\ 12&= 3x \\\\ \dfrac{12}{\blueD{3}}&= \dfrac{3x}{\blueD{3}} ~~~~~~~\text{divide both sides by } {\blueD{ 3}}\\\\ \dfrac{12}{\blueD{3}}&= \dfrac{\cancel{3}x}{\blueD{\cancel{3}}}\\\\ x &=\dfrac{12}{\blueD{3}}\\\\ x &=4\end{aligned}
Area of a triangle
12
12
3
12
3
12
x
x
=
2
1
⋅base⋅height
=
2
1
⋅6⋅x
=3x
=
3
3x
divide both sides by 3
=
3
3
x
=
3
12
=4
