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Yanka [14]
3 years ago
13

Triangle A'B'C' is formed using the translation (x + 2 y + 0) and the dilation by a scale factor of 1/2 from the origin. Which e

quation explains the relationship between
AB and A"B"?

Mathematics
1 answer:
Scorpion4ik [409]3 years ago
6 0

Answer:

A"B" = \frac{AB}{2}

Step-by-step explanation:

Given

k = \frac{1}{2} --- scale factor

Required

Relationship between AB and A"B"

k = \frac{1}{2} implies that the sides of A"B"C" are smaller than ABC

i.e.

A"B" = k * AB

A"B" = \frac{1}{2} * AB

This gives:

A"B" = \frac{AB}{2}

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There are 180 students participating in after school activities. Of those students 40% are boys . How many girls are participati
Nezavi [6.7K]

i dont want to assume all the other people participating in after school activities are girls but if they are, the answer is 108.

180 = 100%

x = 40%

the information above shows that 60% are girls

60% of 180 = 108 or 0.60 x 180 = 108

the answer is 108

hope this is helpful!

7 0
3 years ago
One half of a number (use x) is equal to 8 less than the same number.
Rudiy27
Your answer is 16
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Step-by-step explanation:

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3 years ago
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Explain why the equations X - 13 = 4 and 13 - X = 4 do NOT have the same solution.
Aloiza [94]

Answer:

they have different answers

Step-by-step explanation:

X - 13 = 4 and 13 - X = 4

for x- 13 = 4

x=4+13=17

x=17

for 13 - x = 4

13-4-x=0

9-x=0

9=x

x=9

6 0
3 years ago
Determine the area enclosed by y=2x+3, the x-axis and the ordinates x=3 and x=4​
jok3333 [9.3K]

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

3 0
2 years ago
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