Answer:
x = 13 and y = 13√3
Step-by-step explanation:
Recall that sin Ф = opposite side / hypotenuse, and that
cos Ф = adjacent sice / hypotenuse.
if we recognize that the angle Ф is 30° here, then we know that:
x = opposite side = hypotenuse * sin 30° = 26*(1/2) = 13.
and....
y = adjacent side = hypotenuse*cos 30° = 26*√3/2 = 13√3
In summary, x = 13 and y = 13√3
Currently the equation 6x - 2y = 18 is in standard form. Convert the standard form equation into a slope-intercept form and we can find the slope easily.
Solve for y.
6x - 2y = 18
-2y = 18 - 6x <-- Subtract 6x from each side. This is to isolate the 2y term
2y / -2 =
<-- Divide each side by 2. This it to
get rid of the 2 coefficient.
y = -9 + 3x
Rearrange the right-hand side a bit.
y = -9 + 3x becomes y = 3x - 9
Now it is in slope-intercept form.
The slope is the coefficient of the x variable.
So, 3 is the slope.
Answer:
sometimes
Step-by-step explanation:
adjacent angles are two angles that share a vertex, common side/ray between them, and do not overlap.
only supplementary adjacent angles always add up to 180 degrees,
both x or y could be any angle, as long as they're sharing a common side and vertex.
Y=4
3y/4=12/3
y=4 3/3=1
12/3=4 so y=4
The answer: " x = ⅓ " .
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Given: " 3x − 2 (x + 3) = 4x −<span> 7 " ; Solve for "x" ;
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Start with the following term on the "left-hand side" of the equation:
" - 2 (x + 3) " ;
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Note the "distributive property of multiplication" :
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a(b + c) = ab + ac ;
a(b </span>− c) = ab <span>− ac ;
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As such,
" -2 (x + 3) = -2(x) + -2(3) = -2x + (-6) = -2x </span>− 6 ;
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So, we can rewrite our equation:
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" 3x − 2 (x + 3) = 4x − 7 " ; substituting: " -2x − 6" (for " −2 (x + 3)" ; as follows:
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3x − 2x − 6 = 4x − 7 ;
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On the left-hand side off the equation;
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We can combine the "like terms" ; as follows:
3x − 2x = 1x = x ; and rewrite the equation:
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x − 6 = 4x − 7 ;
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We can subtract "4x" from each side of the equation; and add "6" to each side of the equation:
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x − 6 − 4x + 6 = 4x − 7 − 4x + 6 ;
to get: -3x = -1 ;
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Now, we divide EACH SIDE of the equation by "-3" ; to isolate "x" on ONE SIDE OF THE EQUATION; and to solve for "x" ;
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-3x / 3 = -1/-3 ;
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to get: x = <span>⅓ .
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</span> → Now, let us check our answer by plugging in "<span>⅓" for all values of "x" in the ORIGINAL GIVEN EQUATION; to see if the equation holds true:
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</span> → 3x − 2 (x + 3) = 4x −<span> 7 ;
</span>→ [3 * (⅓) ] − 2 [ (⅓) + 3) = ? 4(⅓) − 7 ?? ;
<span>
</span>→ (1) − 2(3 ⅓) =? (⁴/₃) − 7 ?? ;
<span>
</span>→ (1) − 2(3 ⅓) =? (⁴/₃) − 7 ?? ;<span>
</span>→ (³/₃) − 2(¹⁰/₃) =? (⁴/₃) − (²¹/₃) ?? ;
→ (³/₃) − (²⁰/₃) =? (⁴/₃) − (²¹/₃) ?? ;
→ ⁽³ ⁻²⁰⁾/₃) =? ⁽⁴⁻²¹⁾/₃) ??
→ ⁻¹⁷/₃ = ? ⁻¹⁷/₃ ?? Yes! Our answer "makes sense"!
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