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3 years ago

If the adjacent is 8, the opposite is 15, and the hypotenuse is 17. Express sin H as a fraction in simplest terms.

Mathematics

1 answer:

Serggg [28]3 years ago

5 0

Answer:

$\frac{15}{17}$

Step-by-step explanation:

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Find an equation of the line in the form ax+by=c whose x-intercept is 12 and y-intercept is 4, where a, b, and c are integer

Lostsunrise [7]

Answer:

The equation of the line in $ax+by=c$ form where $a,b,c$ are integers with no factor common to all three, and greater than or equal 0 is:

$x+3y=12$

Step-by-step explanation:

Given:

x-intercept = 12

y-intercept = 4

To find the equation of line in the form $ax+by=c$ where $a,b,c$ are integers with no factor common to all three, and greater than or equal 0.

Solution:

The x-intercept is the point at which the line cuts the x-axis. The point of x-intercept is given as $(x,0)$

Thus, on point of the line is (12,0)

The y-intercept is the point at which the line cuts the y-axis. The point of y-intercept is given as $(0,y)$ .

Thus, on point of the line is (0,4)

Using the two points we can find the slope of the line using the slope formula.

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

So, slope of the line can b given as:

$m=\frac{4-0}{0-12}$

$m=\frac{4}{-12}$

$m=-\frac{1}{3}$

The slope intercept form of the equation of he line is given as:

$y=mx+b$

where $m$ represents slope of the line and $b$ represents the y-intercept.

So, the equation of the line can be given as:

$y=-\frac{1}{3}x+4$

Multiplying each term by 3 to remove fraction.

$3y=3.-\frac{1}{3}x+4(3)$

$3y=-x+12$

Adding $x$ both sides.

$3y+x=-x+x+12$

$3y+x=12$

Thus, the equation of the line in $ax+by=c$ form where $a,b,c$ are integers with no factor common to all three, and greater than or equal 0 is:

$x+3y=12$

8 0

3 years ago

the bottom of a ladder must be placed 10 feet from a building. The ladder is 26 feet. How far above the ground does the ladder t

Sauron [17]

Answer:

<em>The ladder touches the wall at 24 feet from the ground.</em>

Step-by-step explanation:

The wall of the building, the ground, and the ladder form a right triangle, whose longer side is the length of the ladder.

In any right triangle, we can apply Pythagora's theorem to find any missing side length.

The ladder is 26 feet in length, the distance from the bottom of the ladder and the building is 10 feet. Calling H to the distance above the ground where the ladder touches the wall, then:

$26^2=10^2+H^2$

Calculating:

$676=100+H^2$

Solving:

$H^2=676-100$

$H^2=576$

$H=\sqrt{576}$

H=24 feet

The ladder touches the wall at 24 feet from the ground.

8 0

3 years ago

f a bag contains 12 quarters, 6 dimes, and 18 nickles, what is the part-to-whole ratio of dimes to all coins?

Anna35 [415]

There are 6 dimes and a total of 36 coins in all so the part to whole ratio is 6:36 or 1:6

3 0

3 years ago

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Pleaseeeeeeee help .......ASAP

fenix001 [56]

Answer:

Option A

Step-by-step explanation:

Given:

Center of circle = (h,k)= (3,8)

Radius = r = 5

The standard form of equation of circle with center and radius is:

$(x-h)^2+(y-k)^2=r^2\\Putting\ the\ values\\(x-3)^2+(y-8)^2=(5)^2\\Simplifying\\x^2+9-6x+y^2+64-16y=25\\x^2+y^2-6x-16y+9+64=25\\x^2+y^2-6x-16y+73=25\\x^2+y^2-6x-16y+73-25=0\\x^2+y^2-6x-16y+48=0$

Therefore, the general form of the equation of circle given is:

$x^2+y^2-6x-16y+48=0$

Hence, option A is correct ..

5 0

4 years ago

U like fruit WELL ANSWER THIS. lol pls help!!!

Y_Kistochka [10]

Answer:apple

Step-by-step explanation:

6 0

2 years ago

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