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3 years ago

What is the value of z?

Mathematics

1 answer:

andreyandreev [35.5K]3 years ago

4 0

Answer:

122 degrees, because x and z are alternate interior angles

122 degrees, because 58 degrees and z are same side interiors which add to 180

Step-by-step explanation:

1) we know that

m∠x=m∠z -----> by alternate interior angles

m∠x+58°=180° ----> by supplementary angles (form a linear pair)

m∠x=180°-58°=22°

therefore

m∠z=22°

2) m∠z+58°=180° ----> by same side interior angles

solve for z

m∠z=180°-58°=122°

therefore

122 degrees, because x and z are alternate interior angles

122 degrees, because 58 degrees and z are same side interiors which add to 180

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F(x) = x4 - x3 - 2x- 4 factor the polynomial function over the complex numbers

olchik [2.2K]

Answer:

Step-by-step explanation:

The given function is f(x) = x⁴ - x³ -2x -4

factor the polynomial function

f(x) = x⁴ - x³ -2x -4 = (x⁴ - 4) - (x³ + 2x ) ⇒ take (-) as a common from (- x³ -2x)

= (x² + 2 ) (x² - 2) - x (x² + 2) ⇒ take (x² + 2) as a common

= (x² + 2 ) ( x² - x - 2)

= (x + √2 i) (x - √2 i) (x -2 ) ( x+1)

Notes: (x⁴ - 4) = (x² + 2 ) (x² - 2)

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2 years ago

There are seven cats in my neighborhood, with an average of $41$ whiskers each. If one of the cats has $17$ whiskers, how many w

harkovskaia [24]

Answer:

Each of the other cats have 45 whiskers on average.

Step-by-step explanation:

Let x represent the average number of whisker of each cat.

We have been given that there are 7 cats in my neighborhood, with an average of 41 whiskers each.

The total number of whiskers of six cats would be $6x$ .

Since one of the cats has 17 whiskers, so the total number of whiskers of 7 cats would be $6x+17$

We will use average formula to solve our given problem.

$\text{Average}=\frac{\text{Sum of data points}}{\text{Number of data points}}$

Upon substituting our given values, we will get:

$41=\frac{6x+17}{7}$

Let us solve for x.

$41*7=\frac{6x+17}{7}*7$

$287=6x+17$

$287-17=6x+17-17$

$270=6x$

Switch sides:

$6x=270$

$\frac{6x}{6}=\frac{270}{6}$

$x=45$

Therefore, the each of the other cats have 45 whiskers on average.

8 0

3 years ago

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yan [13]

Answer:

The best estimate for the solution is the ordered pair $(-6.5,-3.5)$

Step-by-step explanation:

we have

$y=\frac{3}{2}x+6$ ------> equation A

$y=\frac{1}{4}x-2$ ------> equation B

we know that

using a graphing tool, the solution of the system of equations is the intersection point both graphs

The intersection point is $(-6.4,-3.6)$

therefore

The best estimate for the solution is the ordered pair $(-6.5,-3.5)$

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2 years ago

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Ierofanga [76]

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hichkok12 [17]

Answer:

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Step-by-step explanation:

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2 years ago