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marissa [1.9K]
3 years ago
14

Helen draws three parallelograms. In each figure, she measures a pair of angles, as shown.

Mathematics
2 answers:
kakasveta [241]3 years ago
6 0

Answer:

<em>D. In a parallelogram, opposite angles are congruent.</em>

Step-by-step explanation:

In each case, she measures two opposite angles, and they are congruent.

D. In a parallelogram, opposite angles are congruent.

drek231 [11]3 years ago
6 0

Answer:

D.In a parallelogram, opposite angles are congruent.

Step-by-step explanation:

We are given that Helen draws  three parallelograms.

We have to find conjecture which is reasonable for Helen to make.

We know that in parallelogram opposite angles are congruent.

Opposite sides of parallelogram are equal and parallel.Consecutive angles are supplementary.

In each figure, opposite angles are congruent.

Therefore, option D is true.

Answer:D.In a parallelogram, opposite angles are congruent.

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One circle has a 96 cm diameter and another circle has a 295.16 cm circumference. Which circle has a larger radius?
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Answer: The first one.

Step-by-step explanation:

One circle has a 96 cm diameter

and another circle has a 295.16 cm circumference.

Which has a larger radius?

Radius of the first circle is 48 cm.

Radius of the second circle is 47 cm

The first circle has a larger radius.

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Answer:

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Step-by-step explanation:

55 + x + 74 + 54 = 180

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Determine the area enclosed by y=2x+3, the x-axis and the ordinates x=3 and x=4​
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Answer:

\displaystyle \int\limits^4_3 {2x + 3} \, dx = 10

General Formulas and Concepts:
<u>Calculus</u>

Integration

  • Integrals

Integration Rule [Reverse Power Rule]:                                                           \displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C

Integration Rule [Fundamental Theorem of Calculus 1]:                                 \displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)

Integration Property [Multiplied Constant]:                                                     \displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx

Integration Property [Addition/Subtraction]:                                                   \displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx

Area of a Region Formula:                                                                               \displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify.</em>

y = 2x + 3

<em>x</em>-interval [3, 4]

<em>x</em>-axis

<em>See attachment for graph.</em>

<u>Step 2: Find Area</u>

  1. Substitute in variables [Area of a Region Formula]:                               \displaystyle A = \int\limits^4_3 {2x + 3} \, dx
  2. [Integral] Rewrite [Integration Property - Addition/Subtraction]:           \displaystyle A = \int\limits^4_3 {2x} \, dx + \int\limits^4_3 {3} \, dx
  3. [Integrals] Rewrite [Integration Property - Multiplied Constant]:           \displaystyle A = 2 \int\limits^4_3 {x} \, dx + 3 \int\limits^4_3 {} \, dx
  4. [Integrals] Integrate [Integration Rule - Reverse Power Rule]:               \displaystyle A = 2 \bigg( \frac{x^2}{2} \bigg) \bigg| \limits^4_3 + 3(x) \bigg| \limits^4_3
  5. [Integrals] Integrate [Integration Rule - FTC 1]:                                       \displaystyle A = 2 \bigg( \frac{7}{2} \bigg) + 3(1)
  6. Simplify:                                                                                                     \displaystyle A = 10

∴ the area bounded by the region y = 2x + 3, x-axis, and the coordinates x = 3 and x = 4 is equal to 10.

---

Learn more about integration: brainly.com/question/26401241

Learn more about calculus: brainly.com/question/20197752

---

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

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