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Rashid [163]
3 years ago
13

Find the value of x, y, and z.

Mathematics
1 answer:
egoroff_w [7]3 years ago
8 0

Answer:

x = 61°

y = 61°

z = 58°

Step-by-step explanation:

In the given triangle, measures of two sides are equal. So, measures of angles opposite to them are also equal.

Therefore,

x + x + 58 \degree = 180 \degree \\  \\ 2x = 180 \degree - 58 \degree \\  \\ 2x = 122 \degree \\  \\ x =  \frac{122 \degree}{2}  \\  \\ x = 61\degree  \\  \\ y = 61\degree  \\  ( \angle s \: in \: the \: alternate \: segment) \\ \\ z = 58\degree  \\  ( \angle s \: in \: the \: alternate \: segment) \\

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Paul bought a photo frame which measured 10 inches in length and 8 inches in width. Determine the diagonal length of the photo f
Katyanochek1 [597]

Answer:

≈12.8

Step-by-step explanation:

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7 0
2 years ago
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A store has 263 board games. Sit has 100 fewer puzzles than board games. The store has 10 more action figures than puzzles. Writ
Yuri [45]

so is it has 100 puzzles less than board games and you have 263 board games just subtract 263-100 which is 163. if it has 10 more action figures than puzzles and you have 163 puzzles you would add 10 to 163 which would give you 173 action figures.

163 puzzles and 173 action figures is the answer

4 0
3 years ago
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Write an equation of the line with a slope of<br> 3 and y-intercept of -8
Yuki888 [10]

Answer:

3x-8=y

Step-by-step explanation:

3 0
3 years ago
Factor f(x)=x4-x3-7x2+13x-6 completely. Then Sketch the graph
Dennis_Churaev [7]

ANSWER TO QUESTION 1


f(x)=(x-2)(x+3)(x-1)^2.



EXPLANATION


The function given to us is,


f(x)=x^4-x^3-7x^2+13x-6


According to rational roots theorem,


\pm1,\pm2,\pm3,\pm6 are possible rational zeros of  


f(x)=x^4-x^3-7x^2+13x-6.


We find out that,


f(-3)=(-3)^4-(-3)^3-7(-3)^2+13(-3)-6


f(-3)=81+27-63-39-6



f(-3)=6-6



f(-3)=0


Also




f(2)=(2)^4-(2)^3-7(2)^2+13(2)-6



f(2)=16-8-28+26-6



f(2)=6-6



f(2)=0


This implies that  


x-2 and x+3 are factors of



f(x)=x^4-x^3-7x^2+13x-6 and hence (x-2)(x+3)=x^2+x-6 is also a factor.



We perform the long division as shown in the diagram.



Hence,


f(x)=(x-2)(x+3)(x-1)^2.


ANSWER TO QUESTION 2

Sketching the graph

We can see from the factorization that the roots  

x=2 and x=-3 have a multiplicity of 1, which is odd. This means that the graph crosses the x-axis at this intercepts.


Also the root x=1 has a multiplicity of 2, which is even. This means the graph does not cross the x-axis at this intercept.



Now we determine the position of the graph on the following intervals,


x\le -3


f(-4)=(-4)^4-(-4)^3-7(-4)^2+13(-4)-6


f(-4)=150\:>0



-3\le x \le 1


f(0)=-6\:


1\le x\le 2


f(1.5)=-0.56\:



x \ge 2



f(3)=24\:>0



We can now use these information to sketch the function as shown in diagram



4 0
3 years ago
Length of the rectangle 11 cm, width 3x, find the perimeter of the rectangle
Vikentia [17]

​Length of the rectangle 11 cm, width 3X, find the perimeter of the rectangle.

​The perimeter of a rectangle is calculated by adding its four sides that are equal two to two.

​Perimeter = 2*Length + 2*width = 2*11cm +2*3Xcm = 22cm + 6*Xcm

​Answer : perimeter = 22cm + 6*Xcm

​Hope this helps!​​​​

\textit{\textbf{Spymore}}​​​​​​​

6 0
3 years ago
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