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3 years ago

What is the slope of the line that passes through the points (3, -2) and (9, -2)?

Mathematics

1 answer:

emmasim [6.3K]3 years ago

5 0

Answer:

a) 0

Step-by-step explanation:

the equation of the slope (m) for a line from two points is given as (y2-y1)/(x2-x1)

we are given the points (3,-2) and (9,-2)

we can label the points:

x1=3

y1=-2

x2=9

y2=-2

now substitute into the equation:

m=(-2--2)/(9-3)

simplify

m=(-2+2)/6

m=0/6

m=0

the slope of the line is 0, which is option a

Hope this helps!

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

svet-max [94.6K]

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

4 0

3 years ago

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NEED HELP IMMEDIATELY. 50 POINTS TO THE BEST ANSWER.

Reil [10]

Answer:

See below

Step-by-step explanation:

r=0 means there is zero correlation between the independent and dependent variables. Most likely, some other regression model will help to bring the value of r closer to -1 or 1 to show a strong correlation.

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2 years ago

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What is the value of f(x)=2•2^x for f(-2)

Zigmanuir [339]

Answer:

The value of f(-2) is 1/2 or it can be written as 0.5.

Step-by-step explanation:

The given function is

$f(x)=2\cdot 2^x$

We have to find the value of f(-2).

Substitute x=-2 in the given function to find the value of f(-2).

$f(-2)=2\cdot 2^(-2)$

$f(-2)=2\cdot \frac{1}{2^(2)}$

$f(-2)=\frac{1}{2}$

$f(-2)=0.5$

Therefore the value of f(-2) is 1/2 or it can be written as 0.5.

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3 years ago

What is the fourth term in the binomial expansion (a+b)^6)

Dafna11 [192]

Answer:

$20a^3b^3$

Step-by-step explanation:

<u>Binomial Series</u>

$(a+b)^n=a^n+\dfrac{n!}{1!(n-1)!}a^{n-1}b+\dfrac{n!}{2!(n-2)!}a^{n-2}b^2+...+\dfrac{n!}{r!(n-r)!}a^{n-r}b^r+...+b^n$

<u>Factorial</u> is denoted by an exclamation mark "!" placed after the number. It means to multiply all whole numbers from the given number down to 1.

Example: 4! = 4 × 3 × 2 × 1

Therefore, the fourth term in the binomial expansion (a + b)⁶ is:

$\implies \dfrac{n!}{3!(n-3)!}a^{n-3}b^3$

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$\implies \dfrac{6!}{3!3!}a^{3}b^3$

$\implies \left(\dfrac{6 \times 5 \times 4 \times \diagup\!\!\!\!3 \times \diagup\!\!\!\!2 \times \diagup\!\!\!\!1}{3 \times 2 \times 1 \times \diagup\!\!\!\!3 \times \diagup\!\!\!\!2 \times \diagup\!\!\!\!1}\right)a^{3}b^3$