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Evgen [1.6K]
3 years ago
14

What is the value of x

Mathematics
1 answer:
Ratling [72]3 years ago
4 0
<h3>Answer:</h3>

90°

<h3>Step-by-step explanation:</h3>

The polygon has 7 sides, so the total of internal angles will be ...

... 180°×(7 -2) = 900°

The sum is then ...

... x + 146° +122° +142° +140° +110° +142° = 900°

... x + 802° = 900° . . . . . simplify

... x = 98° . . . . . . . . . . . . .subtract 802°

_____

<em>Comment on angle measure formula</em>

The usual formula for computing the total of internal angles of a convex polygon with n sides is ...

... total angle measure = (n -2)×180°

This can be simplified from the fact that the sum of external angles is always 360°. That is, for internal angles a1, a2, ..., an, the sum of external angles is ...

... (180° -a1) +(180° -a2) +... +(180° -an) = 360°

... n×180° -(a1 +a2 +... +an) = 360° . . . . . . collect terms

... n×180° -360° = (a1 +a2 +... +an) . . . . . . add ∑ak -360°

... 180°×(n -2) = a1 +a2 +... +an . . . . . . . . . factor out 180°

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A line passes through the points (1, 4) and (3, –4). Which is the equation of the line? y = negative 4 x + 8 y = –2x + 6 y = neg
Kruka [31]

Answer:

y = -4x + 8

Step-by-step explanation:

The equation of a line is written in slope-intercept form : y = mx+b

m is the slope

We are given two points, so let's find the slope of the line first:

Slope = ΔY/ΔX = 4 - (-4) / 1 - 3 = 8 / -2 = -4

The slope is -4

So far, our equation is y = -4x + b

We can input a point's x and y value to find b, the y-intercept

Let's use point (1, 4)

4 = -4(1) + b

4 = -4 + b

b = 4 + 4

b = 8

The equation is y = -4x + 8

-Chetan K

8 0
3 years ago
Read 2 more answers
A quarter circle is attached to the side of a square as shown.
Luda [366]

Answer:

28.6 m²

Step-by-step explanation:

The measurements of the square are 4 by 4; this gives us an area of

4(4) = 16 m²

The quarter circle has a radius of 4 m.  The area of a circle is given by

A = πr².

Since we have a quarter circle, we multiply this by 1/4:

A = 1/4πr²

Using 3.14 for π and 4 for r,

A = 1/4(3.14)(4²) = 1/4(3.14)(16) = 3.14(4) = 12.56 m²

Together this gives us a total area of 16+12.56 = 28.56 m².

This rounds to 28.6 m².

3 0
3 years ago
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Rita has a rope 5 m long. She cuts it into 2 pieces of length 2 m 30 cm and 1 m 65 cm.
Diano4ka-milaya [45]

Answer:

3m 95cm

Step-by-step explanation:

its... simple math? i added 2 and 1; and 30 and 65?

6 0
3 years ago
6. Mrs. Sam buys pencils for $15 per one hundred packs.
Alexxx [7]

Answer:

a.) her loss is 5 dollars

b.) her profit is 10 dollars

c.) she should sell them for $0.15

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2 years ago
Given that f(x) = x2 − 3x + 3 and g(x) = the quantity of x minus one, over four , solve for f(g(x)) when x = 5. (1 point)
Anna007 [38]

Rewrite g(x) as    x-1

                           ------

                              4

and then substitute this result for x in f(x) = x^2 - 3x + 3:

f(g(x)) = (x-1)^2 / 4^2 - 3(x-1)/4 + 3.

At this point we can substitute the value 5 for x:

f(g(5)) = (5-1)^2 / 4^2 - 3(5-1)/4 + 3

          = 16/16 - 3(4/4) + 3 = 1 - 3 + 3 = 1

Therefore, f(g(5)) = 1.

6 0
2 years ago
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