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4 years ago

How many integers between 14 and 3,452 can be divided by 42 with a remainder of zero?

1 answer:

4 0

_______
42 I 3,452

82 with a remainder

There are <u>82</u> integers between 14 and 2452 that can be divided with a remainder of 0

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Using the attached link below.

Serhud [2]

$\text{Use the Pythagorean theorem:}\\\\r-hypotenuse\\\\r^2=7^2+5^2\\\\r^2=49+25\\\\r^2=74\to r=\sqrt{74}$

$\sin=\dfrac{opposite}{hypotenuse}\\\\\cos=\dfrac{adjacent}{hypotenuse}\\\\\tan=\dfrac{opposite}{adjacent}\\\\\cot=\dfrac{adjacent}{opposite}\\\\\text{We have}\\\\for\ the\ angle\ y:\\\text{opposite = 7}\\\text{adjacent = 5}\\\text{hypotenuse = }\ \sqrt{74}\\\\for\ the\ angle\ x:\\\text{opposite = 5}\\\text{adjacent = 7}\\\text{hypotenuse = }\ \sqrt{74}$

$\csc x=\dfrac{1}{\sin x}\\\\\sec x=\dfrac{1}{\cos x}$

$A.\\\\\sin x=\dfrac{5}{\sqrt{74}}=\dfrac{5\sqrt{74}}{74}\\\\\csc y=\dfrac{1}{\frac{7}{\sqrt{74}}}=\dfrac{\sqrt{74}}{7}\\\\B.\\\\\tan x=\dfrac{5}{7}\\\\\cot y=\dfrc{5}{7}\\\\C.\\\\\cos x=\dfrac{7}{\sqrt{74}}=\dfrac{7\sqrt{74}}{7}\\\\\sec y=\dfrac{1}{\frac{5}{\sqrt{74}}}=\dfrac{\sqrt{74}}{5}$

$D.\\\sin\theta=\dfrac{2}{3}\\\\\sin^2\theta+\cos^2\theta=1\to\left(\dfrac{2}{3}\right)^2+\cos^2\theta=1\\\\\dfrac{4}{9}+\cos^2\theta=1\qquad\text{subtract}\ \dfrac{4}{9}\ \text{from both sides}\\\\\cos^2\theta=\dfrac{5}{9}\to\cos\theta=\sqrt{\dfrac{5}{9}}\to\cos\theta=\dfrac{\sqrt5}{3}\\\\\tan\theta=\dfrac{\sin\theta}{\cos\theta}\to\tan\theta=\dfrac{\frac{2}{3}}{\frac{\sqrt5}{3}}=\dfrac{2}{3}\cdot\dfrac{3}{\sqrt5}=\dfrac{2}{\sqrt5}=\dfrac{3\sqrt5}{5}$

6 0

3 years ago

PLEASE HELP ITS AN EMERGENCY

raketka [301]

Answer:

y = -40

Step-by-step explanation:

|y/5+8| - 3 = -3

|y/5+8| = -3 + 3 = 0

y/5+8 = 0 or -0 but 0 and -0 are the same so there would be only 1 answer for this:

Subtract both side by 8

y/5 = -8

Times 5, we got:

y = -40

Hope this help you :3

8 0

3 years ago

Solve the system using substitution<br> 8x+9y=15<br> 5x-2y=17

Otrada [13]

$5x-2y=17\ \ \ \ |-5x\\-2y=-5x+17\ \ \ \ |:(-2)\\y=2.5x-8.5\\\\\text{substitute to the first equation}\\\\9x+9(2.5x-8.5)=17\ \ \ \ |\text{use distributive property}\\9x+22.5x-76.5=17\ \ \ \ |+76.5\\31.5x=93.5\ \ \ \ |:31,5\\x=3\\\\\text{substitute the value of x to the equation}\ y=2.5x-8.5\\\\y=2.5(3)-8.5=7.5-8.5=-1\\\\Answer:\ x=3,\ y=-1\to(3;\ -1)$

8 0

3 years ago

Please help I need this ASAP

nalin [4]

C , i think . correct me

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3 years ago

A line with the equation y = x and a circle with the

Alik [6]

Step-by-step explanation:

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3 years ago

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