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2 years ago

Tell whether (1,10) is a solution of y>5+6x

Mathematics

2 answers:

laila [671]2 years ago

7 0

Yes just plug in x and y so yes

liraira [26]2 years ago

5 0

y > 5 + 6*x

10 > 5 + 6*1 .... replace x with 1, replace y with 10

10 > 5 + 6

10 > 11 ... this is a false statement because 10 is smaller than 11

Since the last statement is false, this means the first inequality is false when (x,y) = (1,10)

The given point is <u>not</u> a solution

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Let u = (1, k) and v = (2, 1). Find k such that The distance between u and v is 1 u and v are orthogonal The angle between u and

SVETLANKA909090 [29]

Answer:k=1,k=-2,k= $8\pm 5\sqrt{3}$

Step-by-step explanation:

Given two vectors

$u=1\hat{i}+k\hat{j}$

$v=2\hat{i}+1\hat{j}$

$\left ( i\right )$ Distance between them is given by

$|u-v|=\sqrt{\left ( 2-1\right )^2+\left ( 1-k\right )^2}=1$

squaring both side

$1^{2}+\left ( 1-k\right )^2=1$

$k^2-2k+1=0$

$\left ( k-1\right )^2=0$

k=1

$\left ( ii\right )$

angle between u and v is 90 i.e. orthogonal

$u\dot v=0$

$\left ( 1\hat{i}+k\hat{j}\right )\dot \left ( 2\hat{i}+1\hat{j}\right )$ =0

2+k=0

k=-2

$\left ( iii\right )$

angle between u & v is $\frac{\pi }{3}$

$u\dot v=|u||v|cos\left (\frac{\pi }{3}\right )$

$|u|=\sqrt{1^2+k^2}$

$|v|=\sqrt{2^2+1^2}$

$2+k=\left ( \sqrt{1+k^2}\right )\left ( \sqrt{5}\right )cos\left ( \frac{\pi }{3}\right )$

$\left ( 4+2\right )^2=\left ( 1+k^2\right )5$

$k^2-16k-11$ =0

k= $8\pm 5\sqrt{3}$

7 0

2 years ago

Find two consecutive odd integers whose sum is 116 (and please have steps) thank you

matrenka [14]

It's 57 and 59
Call (n) is the first odd interger => the second odd interger is (n+2)
=> n + (n + 2) = 116
=> n + n + 2 = 116
=> 2n = 114
=> n = 57
First odd interger is 57 and the second odd interger is 59 .
Sorry my English so bad =)))

6 0

3 years ago

A triangle has the following coordinates: (-15, 10), (0, -20), and (15, 0). Which of these points will not change if the figure

slega [8]

The point that would not be effected would be (15,0).

The other point are located off of the axis in the coordinate plain and would be flipped when reflected over the x-axis. However, this point, because it is located directly on the x-axis, would not be changed as a result of a reflection across the x-axis. It would reflect onto itself.

5 0

2 years ago

16. Shania Oboe wrote a teen fiction novel about vampires. She receives a 10% royalty based on the total ✓

ELEN [110]

Answer:

turn money into a decimal

Step-by-step explanation:

7 0

2 years ago

Any answers or suggestions

STatiana [176]

Answer:

Use Side, angle, side and side, side, side and angle, side, angle.

SAS

SSS

ASA

Find what they have in common, for example the both share side ED.

8 0

2 years ago