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trasher [3.6K]
3 years ago
12

Please helpppppppppppppppppppppppppppppppp

Mathematics
1 answer:
Crank3 years ago
6 0

Answer:


Step-by-step explanation:


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ZA and ZB are complementary angles. If<br> the measure of ZA is 42°, find the measure<br> of ZB.
Sunny_sXe [5.5K]
Answer: ZB = 48 degree

Explanation:

Complementary angle means 2 angel add together and create a right angle (90 degree).

Thus, ZA + ZB = 90 degree
But ZA = 42 degree

=> 42 degree + ZB = 90 degree
=> ZB = (90 - 42)degree
=> ZB = 48 degree
4 0
3 years ago
Explain the steps to finding the vertex of g(x) = 3x2 + 12x + 15
RUDIKE [14]

Answer:

The vertex of this parabola, (-2, 3), can be found by completing the square.

Step-by-step explanation:

The goal is to express this parabola in its vertex form:

g(x) = a\, (x - h)^2 + k,

where a, h, and k are constants. Once these three constants were found, it can be concluded that the vertex of this parabola is at (h,\, k).

The vertex form can be expanded to obtain:

\begin{aligned}g(x)&= a\, (x - h)^2 + k \\ &= a\, \left(x^2 - 2\, x\, h + h^2\right) + k = a\, x^2 - 2\, a\, h\, x + \left(a\,h^2 + k\right)\end{aligned}.

Compare that expression with the given equation of this parabola. The constant term, the coefficient for x, and the coefficient for x^2 should all match accordingly. That is:

\left\lbrace\begin{aligned}& a = 3 \\ & -2\,a\, h = 12 \\& a\, h^2 + k = 15\end{aligned}\right..

The first equation implies that a is equal to 3. Hence, replace the "a\!" in the second equation with 3\! to eliminate \! a:

(-2\times 3)\, h = 12.

h = -2.

Similarly, replace the "a" and the "h" in the third equation with 3 and (-2), respectively:

3 \times (-2)^2 + k = 15.

k = 3.

Therefore, g(x) = 3\, x^2 + 12\, x + 15 would be equivalent to g(x) = 3\, (x - (-2))^2 + 3. The vertex of this parabola would thus be:

\begin{aligned}&(-2, \, 3)\\ &\phantom{(}\uparrow \phantom{,\,} \uparrow \phantom{)} \\ &\phantom{(}\; h \phantom{,\,} \;\;k\end{aligned}.

8 0
3 years ago
Austin collected 30 9/10 kilograms of glass for recycling. Exactly 2/3 of the glass he collected was blue. What was the total am
elena55 [62]

2/3 of 30 9/10 = (30*10 + 9)/10 = 309/10 kilograms of glass is blue or there are:


(2/3)(309/10) = (2*309)/(3*10) = (2*103)/10 = 206/10 = 10.6 kg of blue glass.

3 0
3 years ago
Solve the equations <br> 4c=16
nikitadnepr [17]
C=4



This is the answer to the equation
4 0
3 years ago
How to find length of a triangle given one side and angle
mr_godi [17]

Answer:

Use trigonometric ratio

Step-by-step explanation:

Since it is one side and angle of the triangle that is given, it is assumed that the triangle is a right-angled triangle

To solve for one of the two unknown lengths, use trigonometric ratio

There are 3 basic trigonometric ratio namely Sine (sin), Cosine (cos) and Tangent (tan)

Sine of the angle given = opposite side ÷ hypotenuse side

Cosine of the angle given = adjacent side ÷ hypotenuse side

Tangent of the angle given = opposite side ÷ adjacent side

Assuming the length given is the hypotenuse side and the angle is inclined to the horizontal

To find the opposite side of the triangle, multiply the hypotenuse side by the sine of the angle given

5 0
3 years ago
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