Matt is showing his work in simplifying (6.2 − 1.6) − 4.4 + 7.8. Identify any error in his work or reasoning.

Mathematics

1 answer:

shusha [124]2 years ago

6 0

Start with the parentheses first

4.6 -4.4+7.8 then calculate from left to right
= 0.2+7.8 = 8

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find the gradient of the line joining (3,7) and (6,9). Hence, find the acute angle it makes with the positive x-y axis

stiv31 [10]

Answer:

33.7 degrees

Step-by-step explanation:

As we go from (3,7) to (6,9), x increases by 3 and y increases by 2. Thus, the gradient (slope) of the line connecting these two points is

m = rise / run = 2/3. Using the slope-intercept formula y = mx + b, we obtain

7 = (2/3)(3) + b, or 7 = 2 + b, so we see that b = 5 and y = (2/3)x + 5. The y-intercept is (0, 5).

Next we find the x-intercept. We set y = (2/3)x + 5 = to 0 and solve for x:

(2/3)x = -5, or (3/2)(2/3)x = -5(3/2), or x = -15/2, so that the x-intercept is

(-15/2, 0). This line intersects the x-axis at (-15/2, 0).

Now look at the segment of this line connecting (-15/2, 0) and (0, 5). Here x increases by 15/2 and y increases by 5, and so the tangent of the acute angle in question is

tan Ф = 5 / (15/2) = 10 / 15 = 2/3.

Using the inverse tangent function, we get Ф = arctan 2/3, or approx.

33.7 degrees.

I believe you meant "the acute angle it makes with the positive x-axis."

3 0

2 years ago

What is the domain of the function f(x) = x + 2 ? a. all real numbers greater than -2 b. all real numbers greater

dsp73

The domain of the function is represented by option C. All real numbers.

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3 years ago

Write an equation in slope-intercept form for the line passing through the pair of points.

Umnica [9.8K]

First find your slope! by doing
y2-y1/x2-x1
in this case it would be
2-(-3)/-1-(-6)
It would give you 5/5 which would reduce to 1 meaning your slope equals 1
with your slope now you should use the point slope formula y-y1=m(x-x1)

i’m going to use the point (-1,2) so the equation would be

y-2=1(x-(-1))

simplifying that you would get

y-2=1x+1

then put it in y=mx+b form and get

y=x+3

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3 years ago

How do I find the y value for point I such that DI and EI form a 3:5 ratio.

liraira [26]

3:5 ratio mean there are 8 "parts" (3 + 5 = 8)

The distance between the x-coordinates is |-3 - 5| = 8.
So each "part" is 8/8 = 1 unit long in the x-direction.
You want I to be 3(1) = 3 units from D, so the x-coordinate of I is -3 + 3 = 0.

Same deal for y.
|2 - 5| = 3 is the distance between D and E
Each part is 3/8.
3(3/8) = 9/8
2 + 9/8 = 25/8

So the point I is (0, 25/8)