MATHEMATICS
MIDDLE SCHOOL

Answer:

Answer:

Step-by-step explanation:

To write the factored form, multiply a*c from the standard form . Here it is 4*1 = 4.

Then find factors of 4 that add to b=-4.

4: 1,2,4

-2+-2 = -4

Split the middle term into -2x+-2x and factor by grouping.

MIDDLE SCHOOL

How many ways can you make a 3-letter arrangements out of the letters in the word trapezoid?

You can make 81 words from 3-letter arrangements out of the letters in trapezoid.

3-LETTER ARRANGEMENTS:

Ado, adz, aid, air, ait, ape, apo, apt, are, art, ate, azo, dap, dei, die, dip, dit, doe, dor, dot, ear, eat, era, eta, ire, oar, oat, oda, ode, ope, opt, ora, ore, ort, pad, par, pat, pea, ped, per, pet, pia, pie, pit, pod, poi, pot, pro, rad, rai, rap, rat, red, rei, rep, ret, rai, rid, rip, rod, roe, rot, tad, tae, tao, tap, tar, tea, ted, tie, tip, tod, toe, top, tor, zap, zed, zep, zip, zit, zoa

3-LETTER ARRANGEMENTS:

Ado, adz, aid, air, ait, ape, apo, apt, are, art, ate, azo, dap, dei, die, dip, dit, doe, dor, dot, ear, eat, era, eta, ire, oar, oat, oda, ode, ope, opt, ora, ore, ort, pad, par, pat, pea, ped, per, pet, pia, pie, pit, pod, poi, pot, pro, rad, rai, rap, rat, red, rei, rep, ret, rai, rid, rip, rod, roe, rot, tad, tae, tao, tap, tar, tea, ted, tie, tip, tod, toe, top, tor, zap, zed, zep, zip, zit, zoa

MIDDLE SCHOOL

Mom wants to make 5 lbs of the sugar syrup. How much water and how much sugar does he need to make 20% syrup?

Answer:

Let x pound of the sugar to make 20% syrup.

As per the statement:

Mom wants to make 5 Ibs of the sugar syrup.

We have to find how much water and sugar does she need to make 20% syrup.

By definition of proportion; we have

Simplify:

Multiply both sides by 5 we get;

Remaining = 5 -1 = 4 pounds of water

Therefore, 1 pounds of sugar and 4 pounds of water does she need to make 20% syrup.

HIGH SCHOOL

The gas law for an ideal gas at absolute temperature T (in kelvins), pressure P (in atmospheres), and volume V (in liters) is PV = nRT, where n is the number of moles of the gas and R = 0.0821 is the gas constant. Suppose that, at a certain instant, P = 8.0 atm and is increasing at a rate of 0.14 atm/min and V = 13 L and is decreasing at a rate of 0.16 L/min. Find the rate of change of T with respect to time at that instant if n = 10 mol. (Round your answer to four decimal places.)dT/dt = ___ K/min

Answer:

Step-by-step explanation:

We have to calculate the time derivative of T=PV/nR with P and V variable and n and R constants. This is:

What we have to do is the derivative of a product:

Substituting, we have:

where all these values are given since the time derivatives of P and V are their variation rate, using minutes.

We then substitute everything, noticing that already everything is in the same system of units so they cancel out:

And then just calculate:

MIDDLE SCHOOL

Write an expression for y more than 7

Answer:

y>7

Step-by-step explanation:

y is greater than 7 I think. Your Welcome.

Answer:

y > 7

Step-by-step explanation: