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3 years ago

What is the slope of the line through (-7.-2) and (-6,7)

Mathematics

2 answers:

bija089 [108]3 years ago

8 0

Answer:

$\boxed {\tt m=9}$

Step-by-step explanation:

The slope formula is:

$m=\frac{y_2-y_1}{x_2-x_1}$

where (x₁, y₁) and (x₂, y₂) are the points the line passes through.

The points given are: (-7,-2) and (-6,7). Therefore,

$x_1= -7 \\y_1= -2 \\x_2=-6 \\y_2= 7$

Substitute the values into the formula.

$m=\frac{7--2}{-6--7}$

$m=\frac{7+2}{-6+7}$

Solve the numerator by adding 7 and 2.

$m=\frac{9}{-6+7}$

Solve the numerator by adding 7 to -6.

$m=\frac{9}{1}$

Divide 9 by 1.

$m=9$

The slope of the line is 9.

Xelga [282]3 years ago

5 0

Answer:

gradient = 9

Step-by-step explanation:

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Which of the following shows 2 + (x + 3y) rewritten using the Associative Property of Addition?

Paha777 [63]

B (2+x) +3y

Other examples include (14 + 6) + 7 = 14 + (6 + 7)
because Adding 14 + 6 easily gives the sum of 20 to which we can add 7. The right hand side of the equation is where we add 14 and 13. Both sides will result in 27.

8 0

3 years ago

HELP!

maksim [4K]

Part A

$4x^2 -7x-15=0\\\\(4x+5)(x-3)=0\\\\x=-\frac{5}{4}, 3$

So, the x-intercepts are $\boxed{\left(-\frac{5}{4}, 0 \right), (3,0)}$

Part B

The vertex will be a minimum because the coefficient of $x^2$ is positive.

The x-coordinate of the vertex is $x=-\frac{-7}{2(4)}=\frac{7}{8}$

Substituting this back into the function, we get $f\left(\frac{7}{8} \right)=4\left(\frac{7}{8} \right)^2 -7\left(\frac{7}{8} \right)^2 -15=-\frac{289}{16}$

So, the coordinates of the vertex are $\boxed{\left(\frac{7}{8}, -\frac{289}{16} \right)}$

Part C

Plot the vertex and the x-intercepts and draw a parabola that passes through these three points.

The graph is shown in the attached image.

7 0

2 years ago

The one-to-one functions g and h are defined as follows

Debora [2.8K]

Answer:

$g^-^1(x)=-8$

$h^-^1(x)=\frac{x-4}{3}$

$(h^-^1 \ o\ h)(-3)=-3$

Step-by-step explanation:

When given the following functions,

$g=[(-2,-7),(4,6),(6,-8),(7,4)]$

$h(x)=3x+4$

One is asked to find the following,

1. Question 1

$g^-^1(4)$

When finding the inverse of a function that is composed of defined points, one substitutes the input given into the function, then finds the output. After doing so, one must substitute the output into the function, and find its output. Thus, finding the inverse of the given input;

$g^-^1(4)$

$g(4)=6\\g(6)=-8\\g^-^1(4)=-8$

2. Question 2

$h^-^1(x)$

Finding the inverse of a continuous function is essentially finding the opposite of the function. An easy trick to do so is to treat the evaluator (h(x)) like another variable. Solve the equation for (x) in terms of (h(x)). Then rewrite the equation in inverse function notation,

$h(x)=3x+4\\\\h(x)-4=3x\\\\\frac{h(x)-4}{3}=x\\\\\frac{x-4}{3}=h^-^1(x)$

$h^-^1(x)=\frac{x-4}{3}$

3. Question 3

$(h^-^1 \ o\ h)(-3)$

This question essentially asks one to find the composition of the function. In essence, substitute function (h) into function ( $h^-^1$ ) and simplify. Then substitute (-3) into the result.