Math help please What is the value for y?

Mathematics

1 answer:

Nat2105 [25]3 years ago

7 0

Answer:

y =14

Step-by-step explanation:

we know that <a = <b since it is an isosceles triangle

<a = <b = 50

the triangle add to 180 degrees

<a + <b + <c =180

50 + 50 + <c = 180

add like terms

100 + <c = 180

subtract 100 from each side

<c = 180-100

<c = 80

<c = 5y+ 10

80 = 5y+10

subtract 10 from each side

80 -10 = 5y+10-10

80-10 = 5y

70 = 5y

divide by 5

70/5 =5y/5

14 = y

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Use Cramer's Rule to solve the following system: –2x – 6y = –26 5x + 2y = 13

andriy [413]

$\bf \begin{cases}
-2x-6y&=-26\\
\quad 5x+2y&=13
\end{cases}\stackrel{\textit{determinant of the coefficients}}{D=
\begin{bmatrix}
-2&-6\\5&2
\end{bmatrix}}\implies (-4)-(-30)
\\\\\\
D=-4+30\implies \boxed{D=26}\\\\
-------------------------------\\\\$

$\bf x=\cfrac{D_x}{D}\implies x=\cfrac{
\begin{bmatrix}
\boxed{-26}&-6\\\\ \boxed{13}&2
\end{bmatrix}}{D}\implies x=\cfrac{(-52)-(-78)}{26}
\\\\\\
x=\cfrac{-52+78}{26}\implies x=\cfrac{26}{26}\implies \boxed{x=1}\\\\
-------------------------------\\\\
y=\cfrac{D_y}{D}\implies y=\cfrac{
\begin{bmatrix}
-2&\boxed{-26}\\\\ 5&\boxed{13}
\end{bmatrix}}{D}\implies y=\cfrac{(-26)-(-130)}{26}
\\\\\\
y=\cfrac{-26+130}{26}\implies y=\cfrac{104}{26}\implies \boxed{y=4}$

4 0

3 years ago

Find the total surface area of this triangular prism. 17 cm 8 cm 2 cm 15 cm

kumpel [21]

Answer:

200cm²

Step-by-step explanation:

Total surface area of the prism = bh + L(s1+s2+s3)

b is the base of the triangle = 15cm

h is the height of the triangle = 8cm

Perimeter of the triangular base = s1 + s2 + s3 = 8+17+15

Perimeter of the triangular base = 40cm