What is 12 more than m

351 students in 27 classes _____ students in each class

77julia77 [94]

Answer:

13

Step-by-step explanation:

351 divided by 27 = 13

7 0

3 years ago

Read 2 more answers

List the elements in each set.

atroni [7]

Answer:

2

Step-by-step explanation:

1+1=2

8 0

3 years ago

The slope intercept form of the equation of a line that passes through (-2,13) is y =5x-3what is the point slope form of the equ

Zigmanuir [339]

Answer:

y - 13 = 5(x + 2)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Given y = 5x - 3 in slope- intercept form

with slope m = 5, then

m = 5 and (a, b) = (- 2, 13)

y - 13 = 5(x - (- 2)), that is

y - 13 = 5(x + 2) ← in point- slope form

6 0

3 years ago

Humans have a normal body temperature of 98.6°F. A temperature, x, that differs from normal by at least 2°F is considered unheal

Alecsey [184]

Answer:

$x\geq100.6$ and $x\leq 96.6$

Step-by-step explanation:

It is given that the normal body temperature is $98.6^\circ F$ .

A temperature 'x' that differs from normal by at least $2^\circ F$ is considered unhealthy. So the inequality to represent such situation is,

$\left | x-98.6 \right |\geq 2$

It can be further written as,

$x-98.6\geq 2$ and $x-98.6\leq -2$

$x\geq (98.6+2)$ and $x \leq(-2+98.6)$

$x\geq100.6$ and $x\leq 96.6$

So the inequality to represent such condition is $x\geq100.6$ and $x\leq 96.6$ .

5 0

3 years ago

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Find the volume of the region between the planes x plus y plus 2 z equals 2 and 4 x plus 4 y plus z equals 8 in the first octant

Alex787 [66]

Find the intercepts for both planes.

Plane 1, x + y + 2z = 2:

$y=z=0\implies x=2\implies (2,0,0)$

$x=z=0\implies y=2\implies(0,2,0)$

$x=y=0\implies 2z=2\implies z=1\implies(0,0,1)$

Plane 2, 4x + 4y + z = 8:

$y=z=0\implies4x=8\implies x=2\implies(2,0,0)$

$x=z=0\implies4y=8\impliesy=2\implies(0,2,0)$

$x=y=0\implies z=8\implies(0,0,8)$

Both planes share the same x- and y-intercepts, but the second plane's z-intercept is higher, so Plane 2 acts as the roof of the bounded region.

Meanwhile, in the (x, y)-plane where z = 0, we see the bounded region projects down to the triangle in the first quadrant with legs x = 0, y = 0, and x + y = 2, or y = 2 - x.

So the volume of the region is

$\displaystyle\int_0^2\int_0^{2-x}\int_{\frac{2-x-y}2}^{8-4x-4y}\mathrm dz\,\mathrm dy\,\mathrm dx=\displaystyle\int_0^2\int_0^{2-x}\left(8-4x-4y-\frac{2-x-y}2\right)\,\mathrm dy\,\mathrm dx$

$=\displaystyle\int_0^2\int_0^{2-x}\left(7-\frac72(x+y)\right)\,\mathrm dy\,\mathrm dx=\int_0^2\left(7(2-x)-\frac72x(2-x)-\frac74(2-x)^2\right)\,\mathrm dx$

$=\displaystyle\int_0^2\left(7-7x+\frac74 x^2\right)\,\mathrm dx=\boxed{\frac{14}3}$

3 0

3 years ago