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1 year ago

If mAD=85 degrees and mBC=31 degrees find the value

Mathematics

1 answer:

Eddi Din [679]1 year ago

7 0

Answer: x = 11

To start, we know that a whole circle equals 360 degrees. If we subtract the 2 arcs we know, 85 and 31, we have 244 degrees left for the 2 congruent arcs. Dividing that by 2 gives us 122 for each arc.

Now, write the equation: 122 = 13x - 21

Solve this, to find the x = 11.

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A parallelogram with sides of 6 and 10 has an area of 30. Find the measure of the small angle of the parallelogram.

dmitriy555 [2]

<span>A = 2 * (0.5ab) + b (10 - a) = ab + 10b - ab = 10b

10b = 30√2; b = 3√2

sin α = 3√2 / 6; α = 45 degrees

Small angle: 45°; Large angle: 135°</span><span>
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Stacey owns a lot that has 180 feet of front footage and contains 36,000 square feet. She purchases two lots adjacent to each si

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The graph of the function f(x)=(x+2)(x+6) is shown

The statement the function is negative for all real values of x where x <-2

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Which graph could represent a car that begins by increasing its speed, then travels at a constant speed, and then decreases its

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The graph would almost look like this

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1 year ago

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Anton will be constructing a segment bisector with a compass and straightedge, while Maxim will be constructing an angle bisecto

Genrish500 [490]

The similarities are;

Compass and a straight edge required for both construction

Both construction includes a line drawn from the intersection of arcs to bisect a segment or an angle

The bases for the construction of both bisector are the ends of segment and the angle to be bisected

The width of the compass when drawing intersecting arcs, is more than half the width of the segment or angle being bisected

The differences are;

Two points of intersection of arcs are used in the segment bisector while only one is requited in an angle bisector
The bisecting line crosses the segment in a segment bisector, while it stops at the vertex of the angle being bisected in an angle bisector

The sources of the above equations are as follows;

The steps to construct a segment bisector are;

Place the needle of the compass at one of the ends of the line segment to be bisected

Widen the compass so as to extend more than half of the length of the segment to be bisected

Draw two arcs, one above, and the other below the line

Place the compass needle at the other end and with the same compass width draw arcs that intersects with the arcs drawn in the above step

Draw a line segment by placing the ruler on the points of intersection of the arcs above and below the line

The steps to construct an angle bisector are;

With the compass needle at the vertex, open the pencil end such that arcs can be drawn on the rays (lines) forming the angle

Draw an arc on both lines forming the angle

Place the compass needle at one of the intersection points and draw an arc in between the lines forming the angle

Repeat the above step with the same compass width from the other intersection point with the rays forming the angle

Join the point of intersection of the two arcs to the vertex of the angle to bisect the angle

Therefore, we have;

The similarities are;

A compass and a straight edge can be used for both construction

A straight line is drawn from the point of intersection of arcs to bisect the segment or the angle

The arcs are drawn from the ends of the segment or angle to be bisected

The width of the compass is more than half the width of the line or angle when drawing the arcs

The differences are;

In a segment bisector, the intersection point is above and below the line, while in an angle bisector only one pair of arcs are drawn to intersect above the line

The bisecting line passes through the segment being bisected, while the line stops at the vertex in an angle bisector

Learn more about the construction of segment and angle bisectors here;

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1 year ago

Greg is trying to solve a puzzle where he has to figure out two numbers, x and y. Three less than two-third of x is greater than

Fittoniya [83]

Inequation 1:

$\frac{2}{3}x-3 \geq y$

to plot the pairs (x, y) for which the inequation holds, draw the line $y=\frac{2}{3}x-3$

then pick a point in either side of the line. If that point is a solution of the inequation, than color that region of the line, if that point is not a solution, then color the other part of the line.

we do the same for the second inequation. Then the solution, is the region of the x-y axes colored in both cases.

inequation 2:

$y+ \frac{2}{3}x\ \textless \ 4$

$y\ \textless \ - \frac{2}{3} x+ 4
$

draw the lines

i) $y=\frac{2}{3}x-3$ use points (0, -3), (3, -1)

ii) $y=- \frac{2}{3} x+ 4$ use points ( 0, 4), (3, 2)

let's use the point P(3, 3) to see what region of the lines need to be coloured:

$\frac{2}{3}x-3 \geq y$ ;
$\frac{2}{3}(3)-3 \geq 3$
$2-3 \geq 3$ , not true so we color the region not containing this point

$y+ \frac{2}{3}x\ \textless \ 4$
$(3)+ \frac{2}{3}(3)\ \textless \ 4$
$3+ 5\ \textless \ 4$ not true, so we color the region not containing the point (3, 3)

The graph representing the system of inequalities is the region colored both red and blue, with the blue line not dashed, and the red line dashed.

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