Answer: OPTION C.
Step-by-step explanation:
It is essential to consider the following:
Dilation:
- A transformation where the image retains the same shape as the original but differs in size.
- Dilation maintains the order of points.
- Measurements of angles remain unchanged.
Translation:
- A transformation that keeps the image identical in size and shape to the original.
- Translation preserves the ordering of points.
- The angle measurements do not change.
Consequently, since Square T underwent translation followed by dilation to form Square T'', we conclude that the rationale explaining why they are similar is:
Translations and dilations maintain the order of points; thereby, the corresponding sides of squares T and T″ are proportional.
First note the ratio is
7:2 so divide 7 by 2 to get 7/2 = 3.5. Then add 3.5 to 2, yielding the result 5.5
Answer:
The fat percentage in the blend amounts to 8%.
Step-by-step explanation:
Let
x -----> represent the fat percentage in the mix.
We understand that
The total of milk's volume times its fat percentage, added to cream's volume times its fat ratio, must match the overall mixture's volume times its fat percentage.
Keep in mind that
15% = 15/100 = 0.15
3% = 3/100 = 0.03
therefore
Now, solve for x
Convert that into a percentage
Answer:
a) The first inequality is 100 + 55x > 150 + 51x;
b) The final inequality results in x > 12.5
c) Sal's mother will need to use the second phone for at least 13 months.
Step-by-step explanation:
a) Let x represent the number of months.
1. The first phone is priced at $100, with a monthly fee of $55 for unlimited use, leading to a total cost of $(100 + 55x) for x months.
2. The second phone costs $150 with a monthly fee of $51 for unlimited use, resulting in a total of $(150 + 51x) for x months.
3. For the second phone to be cheaper, we set up the inequality:
150 + 51x < 100 + 55x
which simplifies to
100 + 55x > 150 + 51x
b) Now solve this:
55x - 51x > 150 - 100
4x > 50
so x > 12.5
c) This means Sal's mother has to retain the second phone for at least 13 months (since x > 12.5).
Answer:
In total, Henry requires 15 pints of paint.
Step-by-step explanation:
Henry starts with 2 pints of red and 3 pints of yellow to achieve a certain color, but he has already used 9 pints of yellow paint. Thus, this is represented by:
3 x 3 = 9 (yellow)
Since whatever is done on one side must also be applied to the other, we calculate the red paint:
2 x 3 = 6 (red)
Now we consolidate the amounts:
9 + 6 = 15. (Total red and yellow paint)
This leads to the conclusion that 15 pints are needed.
