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svetoff [14.1K]
3 years ago
9

Prove ||a+b|| ≤ ||a||+|b||​

Mathematics
1 answer:
ANTONII [103]3 years ago
4 0

Step-by-step explanation:

|a+b|=✓(a²+b²)

|a|+|b|=a+b

||a+b|| ≤ ||a||+|b||

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Write an equation in slope-intercept form for the line that has a slope of -4/5 and passes through (0, 7).
patriot [66]

Answer:

A. y = -\frac{4}{5}x + 7

Step-by-step explanation:

Slope intercept form is y = mx + b where m is the slope and b is the y-intercept

<em>It gives us the slope, so we can plug that in:</em> y = -\frac{4}{5}x + b

<em>Next, it gives us a point, so we can plug in the x and y into our equation and solve for b when (x, y)</em>

y = -\frac{4}{5}x + b

7 =  -\frac{4}{5}(0) + b

7 = b

<em>Last, complete our equation:</em>

y = -\frac{4}{5}x + b

y = -\frac{4}{5}x + 7

4 0
3 years ago
I am really confused about this question for math.. any help would be really appreciated:
Elina [12.6K]

y= (\frac 1 4 )^x

A reflection about the x axis, about y=0, is the mapping (x',y')=(x,-y) so

y'= -y = - (\frac 1 4)^{x'}

A dilation of 2 is the mapping (x'',y'')=(2x', 2y')

So

x'=x''/2, y'=y''/2

y''/2= - (\frac 1 4)^{x''/2}

y'' =  - 2((\frac 1 4)^{1/2})^{x''}

y''= - 2(\frac 1 2)^{x''}

We can rewrite that without the primes and combine the powers of 2.

y =  - 2^{1-x}

Let's graph these and see if we're close,

Plot y= (1/4)^x, y= - (1/4)^{x}, y = - 2^{1-x}

6 0
3 years ago
The ratio of two complementary angles is 17:13. What is the measure of the smaller angle?
Mariana [72]
We know by definition that complementary angles add up to 90 degrees. We can set up an equation using the ration given:

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x=3

We now know that the number we multiply the ratio by is 3. The smaller number in the ratio is 13, and so therefore we multiply it by 3.

3*13=39

The answer is 39 degrees.
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Send a picture so i can answer it
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3 years ago
Gia is painting her wall. 1 liter of paint can cover 10 square meters. She has a rectangular wall that
garik1379 [7]
5*4 equals 20 so her wall is 20 square meters
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