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3 years ago

Sahil is putting together supply kits and has 36 packs of x pencils, 12 packs of y crayons, and 24 erasers.

Mathematics

2 answers:

Juliette [100K]3 years ago

6 0

Answer:

Step-by-step explanation:

miskamm [114]3 years ago

5 0

Answer:

Step-by-step explanation:

a. use what's given in the question to write an equation

36x + 12y + 24e (using e as the variable for erasers)

b. 12 is the greatest common factor between the coefficients/ constant so factor it out

12 (3x + y + 2e)

12 kits

c. use the factored expression to see how many of each item

3x - 3 pencils

y - 1 crayon

2e - 2 erasers

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Lines m and n are drawn in the coordinate plane. The equation of line m is y=-3x+8 and line n goes through point (-4,-11). When

balandron [24]

Answer:

The equation of line n is;

y = -3x - 23

Step-by-step explanation:

Here, we want to find the equation of line n

For the alternate interior angles to be congruent after drawing the transversal, then both lines must be parallel

If the two lines are parallel, then their slopes are equal

To get the slope of line m, we compare the equation of line m to the standard form

The equation of line m is y = -3x + 8

if we compare this with the standard form which is y = mx + c

Then the slope of line m is -3 and since they are parallel lines, the slope of line n is -3 too

So now, we need to get the equation of line n

It passes through (-4,-11)

What we have already is;

y = -3x + c

we need to get the y-intercept to write the complete equation

To get the y-intercept we simply substitute for (-4,-11)

Thus, we have

-11 = -3(-4) + c

-11 = 12 + c

c = -11-12 = -23

The equation of line n is;

y = -3x - 23

3 0

3 years ago

Find the exact value of cos (1140)°.

slamgirl [31]

now let's recall that a full circle has 360°, so then 1140 = 360 + 360 + 360 + 60.

namely, 1140 is 3 full-go-around the circle and then it lands on the I Quadrant at 60°. Thus cos(1140°) = cos(60°).

what's that cosine of 60°? Check the picture below.

8 0

3 years ago

Find the volume of the solid bounded by z = 2 - x2 - y2 and z = 1. Express your answer as a decimal rounded to the hundredths pl

butalik [34]

Answer:

The answer is " $(\frac{\pi}{2})$ ".

Step-by-step explanation:

$z = 2 - x^2 - y^2.........(1) \\\\z = 1.............(2)$

Let add equation 1 and 2:

Using formula: $x^2+y^2=1 \\\\$

convert to polar coordinates

$r=2$

$\theta \varepsilon (0=\pi)=z\\\\V=\int^{2\pi}_{\theta=0}\int^{1}_{\pi=0}\int^{z_{2}}_{z_1} r \ dr \d \theta\\\\$

$=\int^{2\pi}_{0}\int^{1}_{0} (Z_2-z_1)r \ dr \d \theta\\\\=\int^{2\pi}_{0}\int^{1}_{0} 1- (-1-x^2-y^2) r \ dr \d \theta\\\\=\int^{2\pi}_{0}\int^{1}_{0} (+1 \pm r^2) r \ dr \d \theta\\\\=\int^{2\pi}_{0}\int^{1}_{0} (-r^3 + r) \ dr \d \theta\\\\=\int^{2\pi}_{0} (-\frac{r^4}{4}+\frac{r^2}{1})^{1}_{0} \d \theta\\\\=\int^{2\pi}_{0} (\frac{1}{4}) \d \theta\\\\=(\frac{2 \pi}{4}) \\\\=(\frac{\pi}{2}) \\\\$