All categories

3 years ago

3x + ky = 8

Mathematics

1 answer:

sattari [20]3 years ago

4 0

Answer:

(a): x is 3 and ky is -1

(b): k is -2

Step-by-step explanation:

Let: 3x + ky = 8 be equation (a)

x - 2 ky = 5 be equation (b)

Then multiply equation (a) by 2:

→ 6x + 2ky = 16, let it be equation (c)

Then equation (c) + equation (b):

${ \sf{(6 + 1)x + (2 - 2)ky = (16 + 5)}} \\ { \sf{7x = 21}} \\ { \sf{x = 3}}$

Then ky :

${ \sf{2ky = 3 - 5}} \\ { \sf{ky = - 1}}$

${ \bf{y = \frac{1}{2} }} \\ { \sf{ky = - 1}} \\ { \sf{k = - 2}}$

You might be interested in

Simplify (4x^2+2)÷(2x^2-9x-5)

frosja888 [35]

Answer:

4.1 Pull out like factors :

4x2 + 2 = 2 • (2x2 + 1)

Polynomial Roots Calculator :

4.2 Find roots (zeroes) of : F(x) = 2x2 + 1

Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient

In this case, the Leading Coefficient is 2 and the Trailing Constant is 1.

The factor(s) are:

of the Leading Coefficient : 1,2

of the Trailing Constant : 1

Let us test ....

P Q P/Q F(P/Q) Divisor -1 1 -1.00 3.00 -1 2 -0.50 1.50 1 1 1.00 3.00 1 2 0.50 1.50

Polynomial Roots Calculator found no rational roots

Trying to factor by splitting the middle term

4.3 Factoring 2x2 - 9x - 5

The first term is, 2x2 its coefficient is 2 .

The middle term is, -9x its coefficient is -9 .

The last term, "the constant", is -5

Step-1 : Multiply the coefficient of the first term by the constant 2 • -5 = -10

Step-2 : Find two factors of -10 whose sum equals the coefficient of the middle term, which is -9 .

-10 + 1 = -9 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -10 and 1

2x2 - 10x + 1x - 5

Step-4 : Add up the first 2 terms, pulling out like factors :

2x • (x-5)

Add up the last 2 terms, pulling out common factors :

1 • (x-5)

Step-5 : Add up the four terms of step 4 :

(2x+1) • (x-5)

Which is the desired factorization

Final result :

2 • (2x2 + 1) —————————————————— (x - 5) • (2x + 1)

5 0

2 years ago

Tasha invests $5,000 annually at 6% and an additional $5,000 annually at 8%. Thomas invests $10,000 annually at 7%. Which statem

Setler79 [48]

Answer:

B is correct.

Step-by-step explanation:

Compound Interest Formula:

$V(t)=P(1+\frac{r}{n})^{nt}$

Tasha invests in two ways

Case 1:

Principal P=$5,000
Rate of Interest r=0.06
Time t=t
n=1

$V(t)=5000(1+0.06)^t$

$V(t)=5000(1.06)^t$

Case 2:

Principal P=$5,000
Rate of Interest r=0.08
Time t=1
n=1

$V(t)=5000(1+0.08)^t$

$V(t)=5000(1.08)^t$

Total amount yield by Tasha = $5000[(1.06)^t+(1.08)^t]$

Thomas Investment

Principal P=$10,000
Rate r= 0.07
t=t
n=1

Total amount yield by Thomas = $10000(1.07)^t$

Now we make table for Tasha and Thomas different value of t

t Tasha Thomas

1 $10,700 $10,700

2 $11,450 $11,449

3 $12,254 $12,250

4 $13,115 $13,108

In table we can see Tasha investment will yield more from Thomas.

Thus, Tasha’s investment will yield more over many years because the amount invested at 8% causes the overall total to increase faster.

8 0

3 years ago

Read 2 more answers

Ski rentals are $100 plus $18 per hour, as shown in the table above.

lisabon 2012 [21]

Answer:

1. f(x)=18X +100

2:108

3. 7.5

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Please help me with disss

Westkost [7]

Answer:

-4

Step-by-step explanation:

3 0

3 years ago

What is the DOMAIN of this relation? Write your answer.

pashok25 [27]

Answer: Domain = {-4, -1, 0, 2, 7, 8, 13}

The domain is the set of allowed x inputs. So all we do is list the set of x values in the top row of the table.

In contrast, the range is the set of possible y outputs. So the range would be {5,2,-3,7,4,9}. Any duplicate items in the range are tossed out. Optionally you can order the set from smallest to largest, but that's not required. This is because order in a set doesn't matter.

6 0

3 years ago

Read 2 more answers