MATHEMATICS COLLEGE

3x + 6y = -18
2y = 3x - 22
The solution to the system is ( _, _ ).

Answers

Answer 1

Answer:

Answer:

(4, -5)

Step-by-step explanation:

3x + 6y = -18

2y = 3x - 22

In the second equation, move 3x to the other side:

3x + 6y = -18

-3x + 2y = -22

Since they have opposite signs, the x terms can cancel out. Add together the equations in order to cancel out x:

3x + 6y = -18

-3x + 2y = -22

8y = -40

Solve for y:

y = -5

Then, plug in -5 in as y into one of the equations, then solve for x:

3x + 6y = -18

3x + 6(-5) = -18

3x - 30 = -18

3x = 12

x = 4

So, the solution to the system is (4, -5)

Answer 2

Answer:

Answer:

(4, -5)

Step-by-step explanation:

the next question (on slide 2) is:

C. (the third option).

then B. (second choice).

then ( 0.5, 3)

3rd slide:

C. 6

A. add

(-2, -4)

4th slide

B C

B Exactly one

(0, -3)

Edge 2021

Logarithm

A log function is a way to find how much a number must be raised in order to get the desired number.

$a^c=b$

can be written as

$\rm{log_ab=c$

where a is the base to which the power is to be raised,

b is the desired number that we want when power is to be raised,

c is the power that must be raised to a to get b.

For example, let's assume we need to raise the power for 10 to make it 1000 in this case log will help us to know that the power must be raised by 3.

$\rm{log\ 1000 = 3$

Given to us

log a = 3,

log b = 4,

log c = -1,

Logarithm Values

log a = 3

$10^3 = a\n1000 = a\na=1000$

lob b = 4,

$10^4=b\n10000=b\nb=10,000$

log c = -1,

$10^(-1) = c\n\n(1)/(10) = c\n\nc = 0.1$

Simplifying

$\rm{log(b^7)/(a^5c^6)\n$

$=\rm{log(10,000^7)/(1,000^5* 0.1^6)\n$

$=\rm{log 10^(19)$

Hence, the value of $\rm{log\ 10^(19)$ is 19.

Answer:

Step-by-step explanation:

Given:

$(b^7)/(a^5c^6)$

log a = 3,

log b = 4,

log c = -1

Required:

Numerical value of the log expression

SOLUTION:

To solve this, we need to recall the rules to apply in each step:

$(b^7)/(a^5c^6)$

Step 1: Apply log of quotients => i.e. $log (a)/(b) = log(a) - log(b)$

$log(b^7) - (log(a^5c^6))$

Step 2: Apply log of products. i.e. log ab = log a + log b.

$log(b^7) - (log(a^5) + log(c^6))$

Step 3: Apply log of exponents. i.e. $log(a^n) = nlog(a)$ .

$7log(b) - (5log(a) + 6log(c))$

Step 4: Substitute log a = 3, log b = 4, log c = -1, into the equation.

$7(4) - (5(3) + 6(-1))$ .

$28 - (15 - 6)$ .

$28 - 9$ .

$= 19$ .

Three 3.0 g balls are tied to 80-cm-long threads and hung from a single fixed point. Each of the balls is given the same charge q. At equilibrium, the three balls form an equilateral triangle in a horizontal plane with 20 cm sides. What is q?

Answers

Answer:

q = 0.105uC

Step-by-step explanation:

We can determine the force on one ball by assuming two balls are stationary, finding the E field at the lower right vertex and calculate q from that.

Considering the horizontal and vertical components.

First find the directions of the fields at the lower right vertex. From the lower left vertex the field will be at 0° and from the top vertex, the field will be at -60° or 300° because + charge fields point radially outward in all directions. The distances from both charges are the same since this is an equilateral triangle. The fields have the same magnitude:

E=kq/r²

Where r = 20cm

= 20/100

= 0.2m

K = 9.0×10^9

9.0×10^9 × q /0.2²

9.0×10^9/0.04

2.25×10^11 q

These are vector fields of course

Sum the horizontal components

Ecos0 + Ecos300 = E+0.5E

= 1.5E

Sum the vertical components

Esin0 + Esin300 = -E√3/2

Resultant = √3E at -30° or 330°

So the force on q at the lower right corner is q√3×E

The balls have two forces, horizontal = √3×E×q

and vertical = mg, therefore if θ is the angle the string makes with the vertical tanθ = q√3E/mg

mg×tanθ = q√3E.

..1

Then θ will be...

Since the hypotenuse = 80cm

80cm/100

= 0.8m

The distance from the centroid to the lower right vertex is 0.1/cos30 =

0.1/0.866

= 0.1155m

Hence,

0.8×sinθ = 0.1155

Sinθ = 0.1155/0.8

Sin θ = 0.144375

θ = arch sin 0.144375

θ = 8.3°

From equation 1

mg×tanθ = q√3E

g = 9.8m/s^2

m = 3.0g = 0.003kg

0.003×9.8×tan(8.3)

0.00428 = q√3E

0.00428 = q×1.7320×E

Where E=kq/r²

Where r = 0.2m

0.0428 = kq^2/r² × 1.7320

K = 9.0×10^9

0.0428/1.7320 = 9.0×10^9 × q² / 0.2²

0.02471×0.04 = 9.0×10^9 × q²

0.0009884 = 9.0×10^9 × q²

0.0009884/9.0×10^9 = q²

q² = 109822.223

q = √109822.223

q = 0.105uC

The third and the sixth term of a geometric progression are 24 and 64/9 respectively. Finda) the first term and common ratio
b) the sum of the first five terms

Answers

Answer:

Ai. Common ratio = 2/3

Aii. First term = 54

B. Sum of the first five terms = 422/3

Step-by-step explanation:

From the question given above, the following data were obtained:

3rd term (T3) = 24

6Th term (T6) = 64/9

First term (a) =?

Common ratio (r) =?

Sum of the first five terms (S5) =?

Ai. Determination of the common ratio (r).

T3 = ar²

T3 = 24

24 = ar²....... (1)

T6 = ar⁵

T6 = 64/9

64/9 = ar⁵......... (2)

The equation are:

24 = ar²....... (1)

64/9 = ar⁵......... (2)

Divide equation 2 by equation 1.

64/9 ÷ 24 = ar⁵ / ar²

64/9 × 1/24 = r³

8/27 = r³

Take the cube root of both side

r = 3√(8/27)

r = 2/3

Thus, the common ratio is 2/3

Aii. Determination of the first term (a).

T3 = ar²

3rd term (T3) = 24

Common ratio (r) = 2/3

First term (a) =?

24 = a(2/3)²

24 = 4a/9

Cross multiply

24 × 9 = 4a

216 = 4a

Divide both side by 4

a = 216/4

a = 54

Thus, the first term (a) is 54

B. Determination of the sum of the first five terms.

Common ratio (r) = 2/3

First term (a) = 54

Number of term (n) = 5

Sum of first five terms (S5) =?

Sn = a[1 –rⁿ] / 1 – r

S5 = 54[1 – (⅔)⁵] / 1 – ⅔

S5 = 54 [1 – 32/243] / ⅓

S5 = 54 (211/243) × 3

S5 = 54 × 211/81

S5 = 6 × 211/9

S5 = 2 × 211/3

S5 = 422/3

Thus, the sum of the first five terms is 422/3

I would appreciate if you solved number 2

Answers

Answer:

the answer for #2 is 6

Step-by-step explanation:

Formula for a triangle:

Area = Base x Height ÷ 2

Write the ratio in fractional notation in lowest terms. 28 inches to 42 inches

Answers

28 to 42 means 28/42

We now reduce 28/42 to lowest terms.

28 ÷ 7 = 4

42 ÷ 7 = 6

We now have 4/6.

We now reduce 4/6.

4 ÷ 2 = 2

6 ÷ 2 = 3

Final answer: 2/3

HELP! i'll mark you brainliest . find y

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Answer: Thanks for points by the way what grade are you in ???

Step-by-step explanation:

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3x + 6y = -18 2y = 3x - 22 The solution to the system is ( ___, ___ ).

Answers

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Logarithm

Given to us

Logarithm Values

Simplifying

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3x + 6y = -18
2y = 3x - 22
The solution to the system is ( _, _ ).