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2 years ago

Write a two-column proof. Given: 7y = 8x - 14; y = 6. Prove that : x = 7.

Mathematics

2 answers:

svet-max [94.6K]2 years ago

4 0

Answer:

Given: $7y =8x-14$ , y =6

To prove: x =7

On substituting the value of y =6 in the equation 7y = 8x -14 to solve for x.

$7(6)= 8x - 14$

42 = 8x -14 ......[1]

Addition Property of equality states that you add the same number to both sides of an equation.

Add 14 to both sides in equation [1];

42+14 =8x -14+14

Simplify:

56 = 8x

8x =56 ......[2]

Division Property of equality states that you divide the same number to both sides of an equation.

Divide by 8 to both sides of an equation [2];

$\frac{8x}{8} =\frac{56}{8}$

Simplify:

x =7 Hence proved!

A two Column proof:

Statement Reason

1. 7y = 8x -14 Given

y= 6

2. 7(6) = 8x -14 Substitution property

3. 42+14 = 8x Addition property of equality

4. 56 =8x Simplify

5. x =7 Division Property of equality

trasher [3.6K]2 years ago

4 0

Given - 7y=8x-14 : y=6

Substitution Property - 7(6)=8x-14

Distributive Property - 8x-14=42

Addition Property - 8x=56

Division Property - x=7

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2 years ago

Rumor of the cancellation of final exams began to spread one day on a college campus with a population of 80 thousand students.S

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Answer:

P(t) is directly proportional to N and N'.

Where P is the increase in numbers of students who have heard the exam's cancellation rumor at any time t;

N is numbers of students who have heard the rumor of the exam's cancellation;

N' is numbers of students who have not heard the rumor of the exam's cancellation;

N' = (80 - N). Since the total number of students is 80;

K is the constant of the proportionality.

K is calculated to be 9/700

Therefore,

P(t) = KNN'

P(t) = (9/700) x N x (80 - N)

Step-by-step explanation:

The total number of students is 80. For N, N' = 80 - N.

Initially, 1 thousand people heard the rumor.

Within/after a day, the increased in number of students who have heard the rumor is P = 10 - 1 = 9

P = 9 = K x 10x (80-10)

9 = K x 10 x 70 = 700K.

Divide both sides by 700,

9/700 = (700/700)K

K = 9/700

Subtitle K into the equation P(t) = KNN'

P(t) = (9/700) x N x N'

P(t) = (9/700) x N x (80 - N), where N' = 80 - N

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2 years ago

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2 years ago

What is 2 (log Subscript 3 Baseline 8 + log Subscript 3 Baseline z) minus log Subscript 3 Baseline (3 Superscript 4 Baseline min

Ilya [14]

Answer:

Value of expression in single logarithm is $\log_3\left(2z^2\right)$ .

Step-by-step explanation:

Given expression is,

$2\left(\log_3\left(8\right)+\log_3\left(z\right)\right)-\log_3\left(3^4-7^2\right)$

Now using logarithmic rule to solve the expression as follows,

Applying product rule of logarithmic,

$\log_c\left(a\right)+\log_c\left(b\right)=\log_c\left(ab\right)$

Therefore,

$2\log_3\left(8z\right)-\log_3\left(3^4-7^2\right)$

Applying power rule of logarithmic,

$a\log_c\left(b\right)=\log_c\left(b^a\right)$

Therefore,

$\log_3\left(\left(8z\right)^2\right)-\log_3\left(3^4-7^2\right)$

$\log_3\left(\left(64z^2\right)\right)-\log_3\left(3^4-7^2\right)$

Applying quotient rule of logarithmic,

$\log_c\left(a\right)-\log_c\left(b\right)=\log_c\left(\frac{a}{b}\right)$

Therefore,

$\log_3\left(\dfrac{\left(64z^2\right)^2}{3^4-7^2}\right)$

Simplifying,

$\log_3\left(\dfrac{\left(64z^2\right)^2}{81-49}\right)$

$\log_3\left(\dfrac{\left(64z^2\right)^2}{32}\right)$

$\log_3\left(2z^2\right)$

Therefore value of expression is $\log_3\left(2z^2\right)$

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2 years ago

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