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3 years ago

The sum of two numbers is 21. the second number is six times the first number.

Mathematics

1 answer:

Tamiku [17]3 years ago

8 0

Answer:

Therefore first number is 3 and second number is 18

Step-by-step explanation:

Sum of the two numbers is 21 and Second number is six times the first number

x+6x = 21

7x = 21

x = 21/7

x = 3

substitute x value in 6x to find second number,

= 6x

= 6*3

= 18

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What is 83 squared? Plz help

andrew11 [14]

The answer is 6,889. Squared just means the number times itself. In this case, it's 83 x 83. :)

6 0

3 years ago

Consider F and C below. F(x, y, z) = yz i + xz j + (xy + 6z) k C is the line segment from (2, 0, −2) to (5, 4, 2) (a) Find a fun

WITCHER [35]

Answer:

Required solution (a) $f(x,y,z)=xyz+3z^2+C$ (b) 40.

Step-by-step explanation:

Given,

$F(x,y,z)=yz \uvec i +xz\uvec j+(xy+6z)\uvex k$

(a) Let,

$F(x,y,z)=yz \uvec i +xz\uvec j+(xy+6z)\uvex k=f_x \uvec{i} +f_y \uvex{j}+f_z\uvec{k}$

Then,

$f_x=yz,f_y=xz,f_z=xy+6z$

Integrating $f_x$ we get,

$f(x,y,z)=xyz+g(y,z)$

Differentiate this with respect to y we get,

$f_y=xz+g'(y,z)$

compairinfg with $f_y=xz$ of the given function we get,

$g'(y,z)=0\implies g(y,z)=0+h(z)\implies g(y,z)=h(z)$

Then,

$f(x,y,z)=xyz+h(z)$

Again differentiate with respect to z we get,

$f_z=xy+h'(z)=xy+6z$

on compairing we get,

$h'(z)=6z\implies h(z)=3z^2+C$ (By integrating h'(z)) where C is integration constant. Hence,

$f(x,y,z)=xyz+3z^2+C$

(b) Next, to find the itegration,

$\int_C \vec{F}.dr=\int_C \nabla f. d\vec{r}=f(5,4,2)-f(2,0,-2)=(52+C)-(12+C)=40$

3 0

3 years ago

When the positive integer x is divided by 11, the quotient is y and the remainder 3. When x is divided by 19, the remainder is a

Lyrx [107]

Answer:

A) 0

Step-by-step explanation:

When x is divided by 11, we have a quotient of y and a remainder of 3

x/11 = y + 3

x = 11y + 3 ........(1)

When x is divided by 19, we have a remainder of 3 also

x/19 = p + 3 (p = quotient)

x = 19p + 3 ..........(2)

Equate (1) and (2)

x = 11y + 3 = 19p + 3

11y + 3 = 19p + 3

11y = 19p + 3 -3

11y = 19p

Divide both sides by 11

11y/11 = 19p/11

y = 19p/11

y and p are integers. 19 is a prime number. P/11 is also an integer

y = 19(integer)

This implies that y is a multiple of 19. When divided by 19, there is no remainder. The remainder is 0

8 0

3 years ago

A display of seed packets contains 24 zucchini seed packets and 28 other seed packets. What is the probability that a randomly s

Nonamiya [84]

Answer:

The probability is 6/13

Step-by-step explanation:

Number of zucchini seed packets = 24

Number of other seed packets = 28

Total number of packets = 24 + 28 = 52

Probability is given by

$P(E)=\frac{n(E)}{n(s)}\\\\n(E)=24,n(s)=52\\P(E)=\frac{24}{52}\\\\P(E)=\frac{6}{13}$

Hence, the required probability is 6/13

3 0

3 years ago

Solve for x in the literal equation -20=xy +z.

erastovalidia [21]

Answer:

-(20+z)/y = x

Step-by-step explanation:

-20=xy +z

Subtract z from each side

-20 -z = xy+z-z

-20 -z = xy

Divide each side by y

(-20 -z)/y = xy/y

Factor out a negative

-(20+z)/y = x

5 0

3 years ago