TODAY, Kyle has 11 pounds to lose to get to his goal weight. Tuesday he was 196 lbs. TODAY, he is down 3 lbs.

Find the equation of the line passing through point (4,2) and perpendicular to AB

Setler [38]

Answer:

a. -⅓

b. 3

c. y = 3x - 10

Step-by-step explanation:

a. Gradient of line AB:

A(1, 3), B(7, 1)

$Gradient = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 3}{7 - 1} = \frac{-2}{6} = -\frac{1}{3}$

Gradient (m) = -⅓

b. The of the line that is perpendicular to line AB would be the negative reciprocal of the gradient of line AB.

Thus, the negative reciprocal of -⅓ = 3

Gradient of the line perpendicular to line AB = 3

c. Equation of the line that passes through (4, 2) and is perpendicular to line AB:

We can write the equation using the point-slope form equation, y - b = m(x - a), where,

(a, b) represents a point on the line, and,

m = gradient/slope

We know that the gradient/slope (m) = 3

Also, a point, (a, b) = (4, 2).

Therefore, substitute a = 4, b = 2, and m = 3 into y - b = m(x - a)

Thus:

y - 2 = 3(x - 4)

y - 2 = 3x - 12

Add 2 to both sides

y = 3x - 12 + 2

y = 3x - 10

5 0

3 years ago

Original Equation:8 - 7x^2 + 3 = 4x^2 - 1Frist step:11 - 7x^2 = -4x^2 - 1Which property justifies the first step?A. Division pro

Tpy6a [65]

8 - 7x^2 + 3 = 4x^2 - 1

8+3-7x^2 = 4x^2-1

11-7x^2 = 4x^2-1

B. Commutative property of addition

We can swap numbers and obtain the same results.

In this case, we swapped 8+3 and added them.

7 0

1 year ago

Please help me w the answer

evablogger [386]

Answer:

$\frac{2(x-6)(x-10)}{(x-4)(x-5)}$

Step-by-step explanation:

In essence, one needs to work their way backwards to solve this problem. Use the information to construct the function.

The function has verticle asymptotes at (x = 4) and (x = 5). This means that the denominator must have (x - 4) and (x - 5) in it. This is because a verticle asymptote indicates that the function cannot have a value at these points, the function jumps at these points. This is because the denominator of a fraction cannot be (0), the values (x - 4) and (x - 5) ensure this. Since if (x) equals (4) or (5) in this situation, the denominator would be (0) because of the zero product property (this states that any number times zero equals zero). So far we have assembled the function as the following:

$\frac{()}{(x-4)(x-5)}$

The function has x-intercepts at (6, 0), and (0, 10). This means that the numerator must equal (0) when (x) is (6) or (10). Using similar logic that was applied to find the denominator, one can conclude that the numerator must be ( $(x - 6)(x-10)$ ). Now one has this much of the function assembled

$\frac{(x-6)(x-10)}{(x-4)(x-5)}$

Finally one has to include the y-intercept of (0, 120). Currently, the y-intercept is (60). This is found by multiplying the constants together. (6 * 10) equals (60). One has to multiply this by (2) to get (120). Therefore, one must multiply the numerator by (2) in order to make the y-intercept (120). Thus the final function is the following:

$\frac{2(x-6)(x-10)}{(x-4)(x-5)}$

6 0

3 years ago

Solve for x. PLEASE HELP ASAP

Paha777 [63]

Answer:

x = 6

Step-by-step explanation:

the tangent- tangent angle UVW is half the difference of the intercepted arcs, that is

∠ UVW = $\frac{1}{2}$ (UW - WU ) , then

5x + 17 = $\frac{1}{2}$ (37x + 5 - (23x - 5) ) ← multiply both sides by 2

10x + 34 = 37x + 5 - 23x + 5

10x + 34 = 14x + 10 ( subtract 14x from both sides )

- 4x + 34 = 10 ( subtract 34 from both sides )

- 4x = - 24 ( divide both sides by - 4 )

x = 6

7 0

2 years ago

Vehicle a averages 14 miles per gallon of gasoline, and vehicle b averages 36 miles per gallon of gasoline. at these rates, how

Dima020 [189]

72 or 28 is the answer i hope this helped you :)

3 0

4 years ago