Answer: 3 Multiply
Step-by-step explanation: u would Multiply 4x7
You just take 1000 and multiply it by .05. Its 50mL.
Based on the definition of a parallel line and the Midsegment Theorem the following are the right answers:
1. a.) BD║AE
b.) BF ║CE
c.) DF║CA
2. a.) YZ║RT
b.) RS ║XZ
c.) XY║TS
3. a.) FH = 24
b.) JL = 74
c.) KJ = 60
d.) FJ = 30
4. a.) AE = 26
b.) AN = 58
c.) CT = 21.5
d.) Perimeter of ΔAEN = 127
5. x = 15
6. x = 6
<h3>What are Parallel lines?</h3>
Parallel lines coplanar straight lines that do not meet each other and are equal distance from each other.
<h3>The Triangle Midsegment Theorem</h3>
- A midsegment is a line that connects the midpoints of the two sides of a triangle together.
- Every triangle three midsegments.
- Based on the Midsegment Theorem of a triangle, the third side of a triangle is always parallel to the midsegment, and thus, the third side is twice the size of the midsegment. In order words, length of midsegment = ½(length of third side).
Applying the definition of a parallel line and the Midsegment Theorem the following can be solved as shown below:
1. The pairs of parallel lines in ΔAEC (i.e. the midsegment is parallel to the third side) are:
a.) BD║AE
b.) BF ║CE
c.) DF║CA
2. The segment parallel to the given segments are:
a.) YZ║RT
b.) RS ║XZ
c.) XY║TS
3. Given:
FG = 37; KL = 48; GH = 30
a.) FH = ½(KL)
FH = ½(48)
FH = 24
b.) JL = 2(FG)
JL = 2(37)
JL = 74
c.) KJ = 2(GH)
KJ = 2(30)
KJ = 60
d.) FJ = ½(KJ)
FJ = ½(60)
FJ = 30
4. Given:
PT = 13
EN = 43
CP = 29
a.) AE = 2(PT)
AE = 2(13)
AE = 26
b.) AN = 2(CP)
AN = 2(29)
AN = 58
c.) CT = ½(EN)
CT = ½(43)
CT = 21.5
d.) Perimeter of ΔAEN = EN + AN + AE
Perimeter of ΔAEN = 43 + 58 + 26
Perimeter of ΔAEN = 127
5. 10x + 44 = 2(8x - 23) (midsegment theorem)
10x + 44 = 16x - 46
10x - 16x = -44 - 46
-6x = -90
Divide both sides by -6
x = 15
6. 19x - 28 = 2(6x + 7) (midsegment theorem)
19x - 28 = 12x + 14
19x - 12x = 28 + 14
7x = 42
x = 6
Learn more about midsegment theorem on:
brainly.com/question/11482568
Answer:
The 6 names to circle are:
- Laverna
- Alfonso
- Autumn
- Ignacio
- Kathyrn
- Lawrence
The underlined letters from those circled names are:
- RN
- ON
- TU
- G
- RN
- WR
The letters form the phrase or "wrong turn". The spacing is done like that in the first version to show the various subgroups of letters.
Unfortunately the mentioned riddle at the bottom is cut off, so I don't know what the riddle is.
======================================================
Explanation:
- Laverna is correct because a translation is applied. "Translation" in geometry settings means "shifting up/down/left/right". In this case, triangle JKL is shifted 5 units right and 3 units up.
- Alfonso is correct. If a figure is labeled ABCD going in clockwise orientation, then a translation will preserve said orientation. The orientation only flips when a reflection occurs.
- Autumn is correct. Why? Because reflections are isometries, meaning they preserve distances and lengths and angles. In other words, the two triangles are twin clones of each other.
- Willa is not correct. The prime notations go on the image and NOT the preimage. In other words, the prime notations go for the "after" and not the "before". Example: triangle JKL in Laverna's diagram is the preimage, while J'K'L' is the image. JKL is "before", and J'K'L' is "after".
- Ignacio is correct. The figure enlarges or shrinks (depending on the scale factor if its larger than 1, or smaller than 1). The orientation stays the same. Refer to Alfonso's scenario where I mentioned the orientation flipping only when a reflection happens.
- Napoleon is incorrect. A reflection ALWAYS changes the orientation. Consider a triangle ABC where the motions from A to B to C goes clockwise. A reflection will flip the orientation to make A to B to C go counterclockwise. Example: Reflections over non-horizontal lines swap the positions of left vs right, which is another way to see why the orientation swaps as well.
- Kathyrn is correct assuming no reflection operations are done.
- Titus is not correct. A rotation is not the same as a reflection. Though I should point out that two reflections simplify to a rotation. The mirror lines must intersect in some way. Parallel mirror lines will have two reflections lead to a translation.
- Lawrence is correct. The order P,Q,R is clockwise, and so is the order P', Q', R'. A rotation preserves orientation. In this case, a 180 degree rotation has been done. The rule for that is any (x,y) point turns into (-x,-y).
Here's a summary table:
Put another way, here are the people to circle (i.e. the people who made true statements):
- Laverna
- Alfonso
- Autumn
- Ignacio
- Kathyrn
- Lawrence
In the order presented above, the letters underlined are:
- RN
- ON
- TU
- G
- RN
- WR
Through a bit of trial and error, the letters make the phrase of:
I'm not sure what to do with the extra "RN". It might be a typo, or it might be the case your teacher wants you to ignore repeats like this.
Answer:
{-3, 8}
Step-by-step explanation:
This rational expression is undefined wherever the denominator is 0.
Thus, our task is to determine the roots of x² - 5x - 24:
This expression factors as follows: (x - 8)(x + 3) = 0
Setting x - 8 = 0 and solving for x yields x = 8.
Similarly, x + 3 = 0 yields x = -3.
This rational expression is undefined for {-3, 8}.