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3 years ago

Solve the system of linear equations by elimination. 9x−2y=349x−2y=34 5x+2y=−6

1 answer:

4 0

So combine all the x and the Y on the left side and the coefficients on the right and then multiply the variable (x or Y) by the number needed for both. and then whichever variable you have left (x or y) will equal the coefficient and then divide by the coefficient

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The product of 3 consecutive even integers is equal to the cube of the first plus the square of the second plus twice the square

algol [13]

Answer:

6, 8 and 10 and -2, 0, 2

There are two roots x = -2 and 6,

but the since I don't believe 0 is an even number the answer is 6, 8 and 10

I was incorrect according to G0ggle zero is an even number so another answer is -2, 0, 2

Step-by-step explanation:

read the question and convert the English to mathematics

x, y and z even consecutive number

y = x+2

z = y+2 = x+4

and

xyz = x³ + y² + 2z² substitiute x terms in for y and z

x(x+2)(x+4) = x³ + (x+2)² + 2(x+4)² solve for x by graphing on DEMOS

x = -2, 6 solved algebraically below

x = -2 y=0 z=2

x = 6 y=8 z=10

Checked both answers

xyz = x³ + y² + 2z²

-2(0)2 = -8 + 0 + 8 when x = -2

0 = 0

and

6(8)(10) = 6³ + 8² +2(10)² when x = 6

480 = 216+64+200

= 480

x(x+2)(x+4) = x³ + (x+2)² + 2(x+4)² solved algebraically

(x²+2x)(x+4) = x³ + x² +4x +4 + 2x² + 16x + 32

x³ + 6x² + 8x = x³ + x² +4x +4 + 2x² + 16x + 32

x³ + 6x² + 8x = x³ + 3x² + 20x + 36

3x² - 12x - 36 = 0 factor out the 3

3[x² - 4x - 12] = 0

3(x+2)(x-6) = 0 x = -2 and -12

6 0

2 years ago

suppose that you have 3000$ to invest. which investment yields the greater return over a 10 year period: 8.04% compounded daily

Ksenya-84 [330]

Answer: Option A: 8.04% compounded daily

<u>Step-by-step explanation:</u>

$A = P\bigg(1+\dfrac{r}{n}\bigg)^{nt}\qquad where\\\\\bullet A = \text{accrued amount (principal plus interest earned)}\\\bullet P = \text{principal (amount invested)}\\\bullet r = \text{rate (in decimal form)}\\\bullet n=\text{number of times compounded in one year}\\\bullet t=\text{time (number of years)}\\\\\\Option\ A:\\A = \text{unknown}\\P=3000\\r=8.04\%\rightarrow 0.0804\\n=\text{daily}\rightarrow 365\\t=10\\\\A=3000\bigg(1+\dfrac{0.0804}{365}\bigg)^{365\times 10}\\\\.\ =\$ 6,702.79$

$Option\ B:\\A = \text{unknown}\\P=3000\\r=8.1\%\rightarrow 0.081\\n=\text{quarterly}\rightarrow 4\\t=10\\\\A=3000\bigg(1+\dfrac{0.081}{4}\bigg)^{4\times 10}\\\\.\ =\$ 6,689.37$

Option A results in the greater amount of money.

7 0

3 years ago

Two numbers have theses properties . both numbers are greater than 6 . their hcf = 6 . their lcm = 60. what are the two numbers

aleksandrvk [35]

Let the numbers be x and y.
x*y=HCF*LCM=6*60=360
thus
y=360/x
next we find the list of combinations of x and y and test if they satisfy the conditions above:
(6,60),(12,30),(18,20),(24,15)
out of the above, only (6,60) and (12,30) satisfy both conditions. Thus our answer is:
(6,60) or (12,30)

6 0

3 years ago

The ratio of pencils to pens in the drawer is 8:14. If there are actually twice as many pencils as in the ratio, how many pencil

dusya [7]

Yo sup??

let the number of pencils and pens be 8x and 14x

x=2

therefore the number of pens and pencils are

16 pencils and 28 pens

Hope this helps

6 0

3 years ago

Estimate 53.83-36.464 by first rounding each number to the nearest whole number.

Free_Kalibri [48]

Answer:

Step-by-step explanation:

53.83 rounds to 54

36.464 rounds to 36

54-46=18

7 0

3 years ago

Read 2 more answers