OK, I ASSUME YOU MEAN 4 / (SQRT(2) + 3) CORRECT ?? IF SO, TO RATIONALIZE WE NEED TO REMOVE THE SQRT FROM THE DENOM. WE DO THAT BY MULTIPLYING NUMBERATOR AND DENOMINATOR BY THE CONJUGATE THE CONJUGATE IS USING...

OK, I ASSUME YOU MEAN 4 / (SQRT(2) + 3) CORRECT ?? IF SO, TO RATIONALIZE WE NEED TO REMOVE THE SQRT FROM THE DENOM. WE DO THAT BY MULTIPLYING NUMBERATOR AND DENOMINATOR BY THE CONJUGATE THE CONJUGATE IS USING...

CIRCUMFERENCE = 2*PI*R WHERE R=RADIUS SO 188 = 2*PI*R R = 188/(2*PI) = 29.921 METERS (TO 3 DECIMALS)

Problem with ratios, please help (answer)

let X = NUMBER OF EGG SANDWICHES let Y = NUMBER OF TUNA SANDWICHES SO THE RATIO X/Y = 2/3 NOW, X / (Y + 15) = 1/3 SO WE HAVE 2 EQUATIONS, 2 UNKNOWNS. CROSS MULTIPLY...

1/2 DIVIDED BY 3, OR 1/2 x 1/3 = 1/6 pound each to check: 1/6 + 1/6 + 1/6 = 3/6 or 1/2 pound

MEDIAN - SAME NUMBER OF VALUES LESS THAN AND GREATER THAN EX: 1, 2, 3, 4, 7, 9, 10, 13, 14 7 IS THE MEDIAN BECAUSE THERE ARE 4 VALUES BELOW, AND 4 VALUES ABOVE.

DIST = 90 MI MILES PER GAL = 25 SO TO COMPUTE HOW MANY GALLONS, DIV 90 MI/25 MPG = 3.6 (THAT IS, 25 MI GOES INTO 90, 3.6 TIMES) 3.6 GAL X $2.50 DOLLARS/GAL = $9.00

Check for extraneous solutions (answer)

if I read this right, and the square root is of the quantity (2x+5) SQRT(2X+5) = X + 3 square both sides 2X + 5 = (X+3)^2 2X + 5 = X2 + 6X + 9 combine terms, and put all on...

Interest = 2.65% Initial Value = $10,000 after 1 year, the value is 10,000 x 1.0265 = 10,265.00 after 2 years, the value is 10,000 x 1.0265 x 1.0265 so each year the previous value is just mult by 1.0265 i year ...

Assuming the 324 square feet of fabric is square in shape, each side would be 18 feet (18 x 18 = 324) an inscribed circle on this square would have a diameter of 18, or a radius of 9 feet.

mean = 82 1 std dev = 5 2 std dev = 10 for a normal distribution +/- 1 std dev = 68.2 % or 34.1% to each side of the mean +/- 2 std dev = 95.4 % or 47.7% to each side of the mean I hope this graphically shows the...

I will assume you know how to do synthetic division for testing factors If not long division should also work For synthetic division we write the coeff of the polynomial, then use the X value of the zero (or root) For (X - 1) we then use X=1 For the 1st eqn...

POTENTIAL ENERGY = MGH KINETIC ENERGY = MV2/2 G = 9.8 M/S2 (Gravity accel at earth surface) THE SUM OF POT ENERGY AND KINETIC ENERGY SHOULD BE EQUAL AT POINTS (FROM H=0 - 15M) IN THE FALL. ...

Find the time (answer)

THE PHYSICS EQN IS JUST X = ACC*T2/2 + V*T + X0 FOR BOTH CARS, THEY HAVE NO INITIAL SPEED V1 OR DISPLACEMENT X0 SO X = ACC*T2/2 CAR A HAS ACC = 5.5 BUT LEAVES 1.5 SEC AFTER CAR B CAR B HAS ACC = 4.4 XB...

the number of each coin times their value is the total amount, so P = number of pennies N = number of nickels D = number of dimes so we can write our total cents equation: P(1) + N(5) + D(10) = 64 ! numbers...

David is 17 pounds lighter than Pablo . The total weight is 259 pounds . Find David's weight. (answer)

Let D = Davids weight and P = Pauls weight if David is 17 lbs less than Paul, we can wright that as D = P - 17 Together they weigh 259, so D + P = 259 Now just replace D in the 2nd eqn with D from the 1st eqn (P-17)...

The speed (or rate) of the bike is distance divided by time OR 7.5 mi / hr . Rate x Time = Distance so, 7.5 mi/hr x 1/3 hr = 7.5/3 = 2.5 mi in 1/3 hr she'd ride 2.5 miles

Just use the ratio of 150 M to 0.03 (Note: 150 M = 15,000,000) think of it as 150 Million years is to 3% History as X years is to 100% History express 3% as 0.03 and 100% as 1.0 M = Million H = HISTORY...

the question doesn't say how many dolls. there would be an infinite number. But we'll just form the equation for the nth doll. Largest doll = 12 inches 2nd doll = (12) x 0.7 3rd doll = (12...

Let M = cost of 1 muffin Let Q = cost of 1 quart of milk then the cost equations are: #1 8M + 2Q = $18 #2 3M + 1Q = $7.50 We can solve two ways. 1) use one eqn to solve for one variable in terms of the other, then...

The rate of work x time = Task (or amount of Work) Let Shirley's rate = Sdot Let Cora's rate = Cdot (xx"-dot" is typically used for a rate) So, if we take rate x time = T (T = task) 1)...