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2 years ago

Square inch for 30 stones

Mathematics

1 answer:

Anna71 [15]2 years ago

8 0

1 stone = 20 square inches

1 stone * 30 = 20 square inches * 30

30 stones = 600 square inches

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write a linear equation that intersects y=x^2 at two points. Then write a second linear equation that intersects y=x^2 at just o

Liula [17]

We know that $y = x^2$ is a parabola, concave up, with vertex in the origin $(0,0)$

So, we may use three horizontal lines for our purpose: any horizontal line above the x axis will intersect the parabola twice. The x axis itself intersects the parabola once on the vertex, while any horizontal line below the x axis won't intercept the parabola.

Here's the examples:

The horizontal line $y = 4$ intercepts the parabola twice: the system $y = x^2,\ y = 4$ is solved by $x^2=4 \implies x = \pm 2$
The horizontal line $y=0$ intercepts the parabola only once: the system is $y=x^2,\ y=0$ which yields $x^2=0\implies x=0$ which is a repeated solution
The horizontal line $y=-5$ intercepts the parabola only once: the system is $y=x^2,\ y=-5$ which yields $x^2=-5$ which is impossible, because a squared number can't be negative.

5 0

3 years ago

∠CAT and ∠MUD are supplementary. If m∠CAT=11x+16 and m∠MUD=4x+14, find the measure of each angle.

Georgia [21]

Answers:

x = 10
angle CAT = 126 degrees
angle MUD = 54 degrees

=========================================================

Explanation:

∠CAT and ∠MUD are supplementary, which means the angle measures add to 180. They form a straight line.

( m∠CAT ) + ( m∠MUD ) = 180

( 11x+16 ) + ( 4x+14 ) = 180

11x+16 + 4x+14 = 180

(11x+4x) + (16+14) = 180

15x+30 = 180

15x = 180-30

15x = 150

x = 150/15

x = 10

Let's find each angle based on this x value

m∠CAT=11x+16 = 11*10+16 = 110+16 = 126 degrees
m∠MUD=4x+14 = 4*10+14 = 40+14 = 54 degrees

Those two angles add to 126+54 = 180 to confirm we do indeed have supplementary angles, and confirm the correct answers.

8 0

1 year ago

Question 12<br> With steps please

34kurt

$Answer:\ \boxed{5^2}$

$\sqrt[n]{a}=a^\frac{1}{n}\\\\\text{therefore}\\\\\sqrt5=5^\frac{1}{2}\\----------------\\25=5^2\\----------------\\78,125=5^7\\----------------\\\text{use}\\\\a^n\cdot a^m=a^{n+m}\\\\\dfrac{a^n}{a^m}=a^{n-m}\\----------------\\\\\dfrac{\sqrt5\times78,125}{25\times5^{\frac{7}{2}}}=\dfrac{5^\frac{1}{2}\times5^7}{5^2\times5^\frac{7}{2}}=\dfrac{5^{\frac{1}{2}+7}}{5^{2+3\frac{1}{2}}}=\dfrac{5^{7\frac{1}{2}}}{5^{5\frac{1}{2}}}=5^{7\frac{1}{2}-5\frac{1}{2}}=\boxed{5^2}$