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2 years ago

What is the slope of the line through the points (-6, 3) and (-7, -4)?

Mathematics

1 answer:

klio [65]2 years ago

7 0

Answer: slope: 7, y-intercept: 45, equation: y=7x+45

Step-by-step explanation:

y=mx+b

3=-6m+b

-4=-7m+b

subtract 1 from 2

-7=-m

m=7

-4=-49+b

b=45

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3 years ago

Evaluate [(40 + 5) − 3^2] ÷ 9 ⋅ 2. (1 point)

Ostrovityanka [42]

Answer:

[(40 + 5) − 32] ÷ 9 ⋅ 2

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Step-by-step explanation:

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3 years ago

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2 years ago

Given the following three points, find by the hand the quadratic function they represent (0,6, (2,16, (3,33)

Lisa [10]

Answer:

$f(x) = 4x^2 - 3x + 6$

Step-by-step explanation:

Quadratic function is given as $f(x) = ax^2 + bx + c$

Let's find a, b and c:

Substituting (0, 6):

$6 = a(0)^2 + b(0) + c$

$6 = 0 + 0 + c$

$c = 6$

Now that we know the value of c, let's derive 2 system of equations we would use to solve for a and b simultaneously as follows.

Substituting (2, 16), and c = 6

$f(x) = ax^2 + bx + c$

$16 = a(2)^2 + b(2) + 6$

$16 = 4a + 2b + 6$

$16 - 6 = 4a + 2b + 6 - 6$

$10 = 4a + 2b$

$10 = 2(2a + b)$

$\frac{10}{2} = \frac{2(2a + b)}{2}$

$5 = 2a + b$

$2a + b = 5$ => (Equation 1)

Substituting (3, 33), and c = 6

$f(x) = ax^2 + bx + x$

$33 = a(3)^2 + b(3) + 6$

$33 = 9a + 3b + 6$

$33 - 6 = 9a + 3b + 6 - 6$

$27 = 9a + 3b$

$27 = 3(3a + b)$

$\frac{27}{3} = \frac{3(3a + b)}{3}$

$9 = 3a + b$

$3a + b = 9$ => (Equation 2)

Subtract equation 1 from equation 2 to solve simultaneously for a and b.

$3a + b = 9$

$2a + b = 5$

$a = 4$

Replace a with 4 in equation 2.

$2a + b = 5$

$2(4) + b = 5$

$8 + b = 5$

$8 + b - 8 = 5 - 8$

$b = -3$

The quadratic function that represents the given 3 points would be as follows:

$f(x) = ax^2 + bx + c$

$f(x) = (4)x^2 + (-3)x + 6$

$f(x) = 4x^2 - 3x + 6$

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3 years ago

What is the difference between the smallest 6-digit whole number and the greatest four digit whole number

kupik [55]

First, lets start with the greatest 4-digit number. That would be 9,999.99999999999, with 9 to ∞, because the next number is a 5-digit number. The smallest 6-digit number is 100,000, because the number preceding 100,000 is a 4 digit number. To find difference, you have to subtract. 100,000 minus 9,999.9999 continued gives you 90,000.000000 to ∞ with a one with 1 at the end. You would write 90,000.01 with bar notation over only the 0 to indicate that it goes on to infinity.

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3 years ago