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3 years ago

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Choose one of the following theorems and prove it: Vertical Angles are congruent, Alternate interior angles are congruent, Corre

sponding angles are congruent. Demonstrate on a whiteboard.
(Just tell me how to write it on a whiteboard)

1 answer:

True [87]3 years ago

5 0

As can be seen from the figure above, when two lines intersect, four angles are formed. Each opposite pair are called vertical angles and are always congruent. The red angles ∠JQM and ∠LQK are equal, as are the blue angles ∠JQL and ∠MQK. Vertical angles are also called opposite angles.

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What is (f-g)(x)?<br><br> f(x)=x^4-x^2+9<br> g(x)=x^3+3x^2+12

sweet-ann [11.9K]

X^4 - x^2 + 9 - (x^3 + 3x^2 + 12) =

x^4 - x^3 - 4x^2 - 3

6 0

3 years ago

lys-0071 [83]

Answer:

The number of quarters Josie has in her collection of 92 coins 28 quarters

Step-by-step explanation:

The given information are

The total number of coins Josie has = 92

Let the number of quarters she has = x

Therefore, 92 = 8 + 3×x

8 + 3×x = 92

3×x = 92 - 8 = 84

3×x = 84

x = 84/3 = 28

x = 28

The number of quarters Josie has in her collection of 92 coins = 28 quarters.

4 0

3 years ago

If you have a cubic polynomial of the form y = ax^3 + bx^2 + cx + d and lets say it passes through the points (2,28), (-1, -5),

nikklg [1K]

Step-by-step explanation:

<u>Step 1: Solve using the first point</u>

<em>(2, 28)</em>

$28 = a(2)^3 + b(2)^2 + c(2) + d$

$28 = 8a + 4b + 2c + d$

<u>Step 2: Solve using the second point</u>

<em>(-1, -5)</em>

$-5 = a(-1)^3 + b(-1)^2 + c(-1) + d$

$-5 = -a + b - c + d$

<u>Step 3: Solve using the third point</u>

<em>(4, 220)</em>

$220 = a(4)^3 + b(4)^2 + c(4) + d$

$220 = 64a + 16b + 4c + d$

<u>Step 4: Solve using the fourth point</u>

<em>(-2, -20)</em>

$-20 = a(-2)^3 + b(-2)^2 + c(-2) + d$

$-20 = -8a + 4b - 2c + d$

<u>Step 5: Combine the first and fourth equations</u>

<u /> $28 - 20 = 8a - 8a + 4b + 4b + 2c - 2c + d + d$

$8 = 8b + 2d$

$8 - 8b = 8b - 8b + 2d$

$(8 -8b)/2 = 2d/2$

$4 - 4b = d$

<u>Step 6: Solve for c in the second equation</u>

$-5 + 5 = -a + b - c + d + 5$

$0 + c = -a + b - c + c + d + 5$

$c = -a + b + d + 5$

<u>Step 7: Substitute d with the stuff we got in step 5</u>

$c = -a + b + (4 - 4b) + 5$

$c = -a + b + 4 - 4b + 5$

$c = -a - 3b + 9$

<u>Step 8: Substitute d and c into the first equation</u>

<u /> $28 = 8a + 4b + 2(-a - 3b + 9) + (4 - 4b)$

$28 = 8a + 4b - 2a - 6b + 18 + 4 - 4b$

$28 - 22 = 6a - 6b + 22 - 22$

$6 / 6 = (6a - 6b) / 6$

$1 + b = a - b + b$

$1 + b = a$

<u>Step 9: Substitute a, b, and c into the third equation</u>

$220 = 64(1 + b) + 16b + 4(-(1 + b) - 3b + 9) + (4 - 4b)$

$220 = 64 + 64b + 16b + 4(-1 - b - 3b + 9) + 4 - 4b$

$220 - 100 = 60b + 100 - 100$

$120 / 60 = 60b / 60$

$2 = b$

<u>Step 10: Find a using b = 2</u>

$a = b + 1$

$a = (2) + 1$

$a = 3$

<u>Step 11: Find c using a = 3 and b = 2</u>

$c = -a - 3b + 9$

$c = -(3) - 3(2) + 9$

$c = -3 - 6 + 9$

$c = 0$

<u>Step 12: Find d using b = 2</u>

$d = 4 - 4b$

$d = 4 - 4(2)$

$d = 4 - 8$

$d = -4$

Answer: $a = 3, b = 2, c = 0,d = -4$

6 0

2 years ago

Read 2 more answers

Let f(x) = 6x - 5 and g(x) = 8x, for x E R.<br> Write down g(2).<br><br> Find (fog)(x)

ziro4ka [17]

Answer:

48x -5

Step-by-step explanation:

(fog)(x) = f(g(x)) = 6(8x)-5 =48-5

5 0

2 years ago

Which traingle are congruent by asa

hjlf

Im pretty sure that the answer is B.

3 0

3 years ago