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If the lengths of two sides of a triangle are 5 and 9, respectively, which of the following could be the length of the third sid

slamgirl [31]

There are two answers:

B) 5

C) 8

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Explanation:

If we had a triangle with sides a, b and c, then we can say

b-a < c < b+a

where b is larger than 'a'. This is the triangle inequality theorem

In this case, a = 5 and b = 9 so,

b-a < c < b+a

9-5 < c < 9+5

4 < c < 14

Telling us that c is some number between 4 and 14, not including either endpoint. If c is a whole number, then c could be any value from this set: {5,6,7,8,9,10,11,12,13}

We see that the numbers 5 and 8 are in this set. The values 3 and 15 are not in the set.

3 0

3 years ago

Thrush us a landscape architect. For his first public project he is asked a small scale drawing of a garden to be placed in the

ehidna [41]

Answer:

Therefore, on the graph;

The height = 7.5 units

And base = 5.0 units

Attached is an image for further information;

Step-by-step explanation:

Given that;

1 unit on the grid represent 2m of the garden;

Ratio = 1/2 unit/m

For the height;

height h = 15m

On the graph;

h = 15m × 1/2 unit/m

h = 7.5 units

For the base;

Base b = 10m

On the graph;

b = 10m × 1/2 unit/m

b = 5 units

Therefore, on the graph;

The height = 7.5 units

And base = 5.0 units

6 0

3 years ago

A rhombus has four 6-inch sides and two 120-degree angles. From one of the vertices of the obtuse angles, the two latitudes are

nikitadnepr [17]

Answer:

Area(A)=Area(C)= $9 in^{2}$

Area(B)= $13.2 in^{2}$

Step-by-step explanation:

We begin with finding the angles a and b that from the drawing attached you can see that a=b.

Now, the sum of the internal angles of a rhomboid is equal to 360 degrees, with that we have:

120+120+a+b=360

240+2a=360

2a=120

a=60=b

Next, in the image you can see that the lines coming from the angle at the top 120 degrees vertex, divide the opposite sides by half, thus making two triangles with one side of 6 in and another of 3 in.

We can say from the drawing as well:

Area(A)+Area(B)+Area(C)=Area(rhomboid)

But, we can also say that Area(A)=Area(C)

So, starting with Area(A)

Area(A)=Area(triangle)= $\frac{b*h}{2}$ = $\frac{6*3}{2}$ = $9 in^{2}$

We can then calculate the area B, a rhomboid, or better, take the Total area of the figure and subtract the area of the two triangles.

Area(B)=Area(rhomboid)-Area(A)-Area(C)

Area(rhomboid)=b*h where b=6in and h is the perpendicular distance from the base to the top.

$h=[tex]6*cos(30)=5.20in$ The 30 degrees come from: 120-30-60=30, since the latitudes split the 120 angle in two equal parts and one that is the half of the obtuse angle.

Area(rhomboid)=5.20*6= $31.2 in^{2}$

Area(B)=Area(rhomboid)-Area(A)-Area(C)= $31.2 in^{2}$ - $9 in^{2}$ - $9 in^{2}$ = $13.2 in^{2}$

3 0

3 years ago

matt rode his bike to the store by traveling 5 km east and the 3 km north. what distance (a) did he travel? and what was his dis

slamgirl [31]

A = 5 km is your distance it is how far he traveled.

b = 3 km is your displacement it's the length in which he when north.

8 0

3 years ago

Simplify: StartRoot StartFraction 576 Over 64 EndFraction EndRoot The prime factorization of 576 is. The prime factorization of

riadik2000 [5.3K]

The prime factor of the 576 is $2^6 * 3^2$ and the prime factor of the 64 is $2^6$ . And the expression $\sqrt{\dfrac{576}{64}}$ is equal to 3.