Answer/Step-by-step explanation:
The reasons for the stated numbered angles that are congruent to the given angles are written in the parentheses as follows:
7. <7 ≅ 65° (alternate interior angles)
<4 ≅ 65° (corresponding angles)
<1 ≅ 65° (vertical angles)
8. <4 ≅ 51° (alternate interior angles)
<5 ≅ 51° (corresponding angles)
<7 ≅ 51° (vertical angles)
9. <1 ≅ 120° (corresponding angles)
<3 ≅ 120° (alternate angles)
Answer:
hat: $12
t-shirt: $8
Step-by-step explanation:
Let the price of 1 hat = h.
Let the price of 1 t-shirt = t.
Julie: h + 2t = 28
Raj: 2h + t = 32
We have a system of 2 equations in 2 variables.
h + 2t = 28
2h + t = 32
Let's use the substitution method to solve the system of equations.
Solve the first equation for h.
h = 28 - 2t
Substitute 28 - 2t for h in the second equation.
2(28 - 2t) + t = 32
56 - 4t + t = 32
56 - 3t = 32
-3t = -24
t = 8
h = 28 - 2t
h = 28 - 2(6)
h = 12
Answer:
hat: $12
t-shirt: $8
Answer: A) 0 triangles
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Explanation:
Adding up the two smaller sides gets us 9.6+11.6 = 21.2, but this result is not larger than the third side of 21.2
For a triangle to be possible, we need to be able to add any two sides and have the sum be larger than the third remaining side. This is the triangle inequality theorem.
I recommend you cutting out slips of paper with these side lengths and trying it out yourself. You'll find that a triangle cannot be formed. The 9.6 cm and the 11.6 cm sides will combine to form a straight line that is 21.2 cm, but a triangle won't form.
As another example of a triangle that can't be formed is a triangle with sides of 3 cm, 5 cm, and 8 cm. The 3 and 5 cm sides add to 3+5 = 8 cm, but this does not exceed the third side. The best we can do is form a straight line but that's not a triangle.
In short, zero triangles can be formed with the given side lengths of 9.6 cm, 11.6 cm, and 21.2 cm
Answer:
Should be 39 years.
there is 12 inches in a foot. and if the tree grows 4 inches every year, then in 3 years the tree would be 1 foot. 13 x 3 = 39, thus proving that in 39 years, it will be 13 feet tall. I may be wrong but this sounds correct.
Answer:
a) no real solutions
Step-by-step explanation:
the discriminant (b² - 4ac) is negative which indicates no real solutions
