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3 years ago

Kite FGHK is shown. What is the value of m?

Mathematics

2 answers:

charle [14.2K]3 years ago

8 0

M=3 i believe is the answer to your problem

Georgia [21]3 years ago

4 0

For this case, the first thing to do is to observe that the figure is symmetrical with respect to the FH axis.

Therefore, the following lengths are the same:

$GH = HK$

So, by equalizing both sides we have:

$5m + 1 = 3m + 7$

From here, we clear the value of m.

We have then:

$5m - 3m = 7 - 1\\2m = 6$

$m = \frac{6}{2}\\m = 3$

Answer:

The value of m is given by:

$m = 3$

You might be interested in

Determine what the solution is to the following system? Y=3/4x-1 & y=4/3x-1

vichka [17]

Answer:

(0, -1)

Step-by-step explanation:

There are multiple ways of solving this however- since both equations are already in Y-Intercept form, we will use the "Equal Values Method"

First, since both equations are equal to Y, we can set them equal to each other and solve for X

$\frac{3 }{4} x - 1 = \frac{4}{3} x - 1$

To start, you must eliminate the fraction using a "fraction buster" multiply EVERYTHING by 4 then simplify.

$3x - 4 = 5 \frac{1}{3}x - 4$

Since we still have a fraction, we shall do it one more time. This time we multiply by 3

$9x - 12 = 6 x - 12$

Now, solve how you normally would.

9x = 6x

-6x

3x = 0

X = 0

Now, since we know what X would equal in the solution, we are able to plug in X as 0 in one of our equations. We can choose the first one!

$y = \frac{3}{4} (0) - 1$

Now solve which would lead to y = -1

You have your solution as

(X,Y)

(0,-1)

Hope this helps!

4 0

3 years ago

This is a map of three towns. It shows the train line and the highway that connects the towns. The north direction is shown. The

vlada-n [284]

Answer:

about 106 km

Step-by-step explanation:

The distance between the two towns can be estimated several ways. In the attachment, we chose to measure the angles on the map. Using the law of sines, we can estimate the unknown distance.

The distance can also be estimated using the Tounouse-Avaria distance as a ruler. For best results, that ruler would need to be subdivided to an appropriate level.

<h3>angle measures</h3>

The angles in the triangle can be measured using a protractor or some other tool. The attachment shows the results from a geometry program:

∠TMA ≈ 107°
∠TAM ≈ 24°

<h3>law of sines</h3>

The law of sines tells us the distances are proportional to the sines of the opposite angles:

TM/sin(TAM) = TA/sin(TMA)

TM = sin(24°)×(250 km)/sin(107°) ≈ 106.3 km

The distance from Tounouse to Mt. Monotti is estimated to be about 106 km.

<em>Alternate solution</em>

Using a compass or dividers to project the TM distance onto TA, we find it is between 0.4 and 0.5 of the TA distance. The difference between 2×TM and TA can be estimated to be about 0.4×TM. That is, ...

TM ≈ TA/2.4 ≈ (250 km)/2.4 ≈ 104.2 km

This estimate is consistent with the one found using angle measures.