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madreJ [45]
2 years ago
11

☹️someone help me ASAP

Mathematics
1 answer:
Likurg_2 [28]2 years ago
4 0

SAS postulate

SAS postulate proves the two triangles are congruent.

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Is 3(x + 1)2 = (3x + 3)2 an identity? Explain and show your reasoning.
Scilla [17]

Answer:

YES

Step-by-step explanation:

The equation, 3(x + 1)2 = (3x + 3)2, would be an identity if the equation remains true regardless of the value of x we choose to plug in into the equation.

Let's find out if we would always get a true statement using different value of x.

✍️Substituting x = 1 into the equation:

3(x + 1)2 = (3x + 3)2

3(1 + 1)2 = (3(1) + 3)2

3(2)2 = (3 + 3)2

12 = 12 (TRUE)

✍️Substituting x = 2 into the equation:

3(x + 1)2 = (3x + 3)2

3(2 + 1)2 = (3(2) + 3)2

3(3)2 = (6 + 3)2

18 = 18 (TRUE)

✍️Substituting x = 3 into the equation:

3(x + 1)2 = (3x + 3)2

3(3 + 1)2 = (3(3) + 3)2

3(4)2 = (9 + 3)2

24 = 24 (TRUE)

Therefore, we can conclude that the equation, 3(x + 1)2 = (3x + 3)2, is an identity.

8 0
2 years ago
What will happen to the ratios as you increase the number of sides of the regular polygon?
earnstyle [38]

Answer: increase

Step-by-step explanation:

Number of sides of the polygon, The number of sides of a regular polygon and the measure of the exterior angle are inversely proportional. <em><u>As one quantity increases, the other decreases and vice versa.</u></em>

4 0
3 years ago
Please help Cassie uses 1 quart cranberry juice., 1/2 gallon ginger ale, and 1 1/2 pints orange juice to make fruit punch. How m
marta [7]
2 quarts in 1/2 a gallon
2 pints in a quart
1 pint is 16 ounces
7 1/2 pints total
7 1/2 * 16 = 120 ounces
120/ 6= 20 6 ounce servings
5 0
3 years ago
ANSWER NOW PLEASE.Solve this system of equations with substitution<br><br> x = y - 4<br><br> 2y = x
Arada [10]
In points form the answer is (-8,-4) and in equation form the answer is x=-8, y=-4
If this answered help you then please consider marking it as brainliest to help me level up to expert
4 0
2 years ago
Read 2 more answers
Hiiii.. please help me with this limit question ​
Alenkasestr [34]

Answer:

π

Step-by-step explanation:

Solving without L'Hopital's rule:

lim(x→0) sin(π cos²x) / x²

Use Pythagorean identity:

lim(x→0) sin(π (1 − sin²x)) / x²

lim(x→0) sin(π − π sin²x) / x²

Use angle difference formula:

lim(x→0) [ sin(π) cos(-π sin²x) − cos(π) sin(-π sin²x) ] / x²

lim(x→0) -sin(-π sin²x) / x²

Use angle reflection formula:

lim(x→0) sin(π sin²x) / x²

Now we multiply by π sin²x / π sin²x.

lim(x→0) [ sin(π sin²x) / x² ] (π sin²x / π sin²x)

lim(x→0) [ sin(π sin²x) / π sin²x] (π sin²x / x²)

lim(x→0) [ sin(π sin²x) / π sin²x] lim(x→0) (π sin²x / x²)

π lim(x→0) [ sin(π sin²x) / π sin²x] [lim(x→0) (sin x / x)]²

Use identity lim(u→0) (sin u / u) = 1.

π (1) (1)²

π

Solving with L'Hopital's rule:

If we plug in x = 0, the limit evaluates to 0/0.  So using L'Hopital's rule:

lim(x→0) [ cos(π cos²x) (-2π cos x sin x) ] / 2x

lim(x→0) [ -π cos(π cos²x) sin(2x) ] / 2x

-π/2 lim(x→0) [ cos(π cos²x) sin(2x) ] / x

Again, the limit evaluates to 0/0.  So using L'Hopital's rule one more time:

-π/2 lim(x→0) [ cos(π cos²x) (2 cos(2x)) + (-sin(π cos²x) (-2π cos x sin x)) sin(2x) ] / 1

-π/2 lim(x→0) [ 2 cos(π cos²x) cos(2x) + π sin(π cos²x) sin²(2x) ]

-π/2 (-2)

π

8 0
2 years ago
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