Solve the system of equations -7x - 6y = 4 x= -3y + 8

1 answer:

7 0

You can use the substitution method for this problem
Since -3y+8=x you can
Use the equation -7(-3y+8) -6y=4
You then distribute and solve
21y-56-6y=4
15y=60
Y=4
You then plug y into one of the original equations
X=-12+8
X=-4
(-4,4)

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MArishka [77]

Okay so your answer would be 9

4 0

4 years ago

The radius of the cone is 1.25 inches, and its height is 2.75 inches. If the diameter of the bubble gum ball is 0.5 inches, what

nasty-shy [4]

<h2>Explanation:</h2><h2></h2>

The volume of a cone can be found as:

$V=\frac{1}{3}\pi r^2 h \\ \\ \\ Where: \\ \\ V:Volume \\ \\ r:radius \ of \ base \\ \\ h:height$

Given the radius and height, we can find the volume of the cone:

$V=\frac{1}{3}\pi r^2 h \\ \\ V=\frac{1}{3}\pi (1.25)^2(2.75) \\ \\ V=\frac{1}{3}\pi(1.5625)(2.75) \\ \\ V\approx 4.5in^3$

The volume of a sphere is:

$V=\frac{4}{3}\pi r^3 \\ \\ \text{Each gum ball has a diameter of 0.5in, so the radius is:} \\ \\ r=\frac{0.5}{2}=0.25in$

So, for each gum ball the volume is:

$V=\frac{4}{3}\pi r^3 \\ \\ V=\frac{4}{3}\pi (0.25)^3 \\ \\ V=0.065in^3$

Therefore, the he closest approximation of the volume of the cone that can be filled with flavored ice is:

$4.5-0.065=4.43in^3$

Conclusion: The volume of the cone that can be filled with flavored ice is 4.43 cubic inches.

3 0

4 years ago

Find an equation of the tangent line to the curve 2(x2+y2)2=25(x2−y2) (a lemniscate) at the point (−3,1). An equation of the tan

valina [46]

$2(x^2+y^2)^2=25(x^2-y^2)$

Let $y=y(x)$ , so that differentiating both sides wrt $x$ gives

$4(x^2+y^2)\left(2x+2y\dfrac{\mathrm dy}{\mathrm dx}\right)=25\left(2x-2y\dfrac{\mathrm dy}{\mathrm dx}\right)$

If $x=-3$ and $y=1$ , the above reduces to

$40\left(-6+2\dfrac{\mathrm dy}{\mathrm dx}\right)=25\left(-6-2\dfrac{\mathrm dy}{\mathrm dx}\right)\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac9{13}$