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kati45 [8]
3 years ago
11

Two thirds of a number added to six is at least twenty-two

Mathematics
1 answer:
Stella [2.4K]3 years ago
8 0
2/3x + 6 \geq 22.


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Triangle PQR is transformed to triangle P'Q'R'. Triangle PQR has vertices P(4, 0), Q(0, −4), and R(−8, −4). Triangle P'Q'R' has
Whitepunk [10]

Answer:

Please find attached the required plot accomplished with an online tool

Part A:

1/4

Part B:

P''(-1, 0),  Q''(0, -1), and R''(2, -1)

Part C:

Triangle PQR is similar to triangle P''Q''R'' but they are not congruent

Step-by-step explanation:

Part A:

Triangle ΔPQR has vertices P(4, 0), Q(0, -4), R(-8, -4)

Triangle ΔP'Q'R' has vertices P'(1, 0), Q'(0, -1), R'(-2, -1)

The dimensions of the sides of the triangle are given by the relation;

l = \sqrt{\left (y_{2}-y_{1}  \right )^{2}+\left (x_{2}-x_{1}  \right )^{2}}

Where;

(x₁, y₁) and (x₂, y₂) are the coordinates on the ends of the segment

For segment PQ, we place (x₁, y₁) = (4, 0) and (x₂, y₂) = (0, -4);

By substitution into the length equation, we get;

The length of segment PQ = 4·√2

The length of segment PR = 4·√10

The length of segment RQ = 8  

The length of segment P'Q' = √2

The length of segment P'R' = √10

The length of segment R'Q' = 2

Therefore, the scale factor of the dilation of ΔPQR to ΔP'Q'R' is 1/4

Part B:

Reflection of (x, y) across the y-axis gives;

(x, y) image after reflection across the y-axis = (-x, y)

The coordinates after reflection of P'(1, 0), Q'(0, -1), R'(-2, -1) across the y-axis is given as follows;

P'(1, 0) image after reflection across the y-axis = P''(-1, 0)

Q'(0, -1) image after reflection across the y-axis = Q''(0, -1)

R'(-2, -1) image after reflection across the y-axis = R''(2, -1)

Part C:

Triangle PQR is similar to triangle P''Q''R'' but they are not congruent as the dimensions of the sides of triangle PQR and P''Q''R'' are not the same.

6 0
3 years ago
I have four bills that need to be paid this week. The electric bill is 182.17 the water bill is 92.55 the cell phone bill is 225
tangare [24]
The answer would be 200 + 200 +200+100 = 700
7 0
2 years ago
Read 2 more answers
0.00000000828860 in scientific notation
azamat

0.00000000828860 upto which decimal?


6 0
3 years ago
Find the measure of 2<br><br> A 38<br> B 92<br> C 112<br> D 136
NikAS [45]

Answer:

The answer is C

Step-by-step explanation:

(180-46)/2=67

67+45=112

4 0
3 years ago
A bracelet that regulaurly sells for $44 is on sale for 25% off. Find the sale price of the bracelet.
Alchen [17]
Since it is on sale of 25% then it is 25% off. So minus 100% by 25% which is 75%
Then u find 75% of 44 the. Then answer you get it is the final answer.

8 0
2 years ago
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