ST is a midsegment, which tells you that BD=2(ST) or ST=½BD. Use that to substitute the values and find ST.
BD=2(ST)
29+x=2(2x+31)
29+x=4x+62
29=3x+62
-33=3x
x=-11
Now that we know x, we can substitute that into 2x+31 to find ST
ST=2x+31
ST=2(-11)+31
ST=-22+31
ST=9
Answer:
18
Step-by-step explanation:
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The sample space (list of outcomes) is:
DFNR; DFRN; DRFN; DRNF; DNFR; DNRF;
NFDR; NFRD; NRFD; NRDF; NDRF; NDFR;
RFDN; RFND; RNFD; RNDF; RDFN; RDNF;
FRDN; FRND; FNRD; FNDR; FDRN; FDNR
P(Dave beside Natalie) = 1/2
P(B,G,B,G or G,B,G,B) = 1/3
P(boys in the middle) = 1/6
P(Frida beside Natalie) = 1/2
P(Robbie between Frida & Natalie) = 1/6
P(Natalie between Dave & Robbie) = 1/6
Explanation
Letting D=Dave, R=Robbie, N=Natalie, and F=Frida you get the list of possibilites above.
For P(Dave beside Natalie), look for DN or ND. This appears 12 times out of the 24 possibilities above; 12/24 = 1/2.
For P(B,G,B,G or G,B,G,B), we have the possibilities DFRN, DNRF, RFDN, RNDF, FRND, FDNR, NDFR, NRFD. There are 8 possibilites out of 24; 8/24 = 1/3.
For P(Frida beside Natalie), look for NF or FN. This appears 12 times out of the 24 possibilities; 12/24 = 1/2.
For Robbie between Frida and Natalie, look for FRN or NRF. This appears 4 times out of 24; 4/24 = 1/6.
For Natalie between Robbie and Dave, look for RND or DNR. This appears 4 times out of 24; 4/24 = 1/6.
Yes, the two triangles are similar.
Similar triangles have equal corresponding angles and proportionate sides.
We can see that the corresponding angles of the two triangles are equal because although the smaller triangle is rotated, the angle measurements of both triangles are 23°, 67°, and 90°.
The corresponding sides are proportionate because they have a set ratio. The sides of the smaller triangle are all 1/4 the length of the corresponding sides of the bigger triangle.
Answer: 3
Step-by-step explanation: m=2 so 7.5x2 = 15
15/5 is 15 divided by 5 so the answer is 3
