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Hatshy [7]
3 years ago
7

7a-5b=28 A (-2,-3) B (0,4) C (4,0) D (-3,-2)

Mathematics
1 answer:
musickatia [10]3 years ago
7 0
It's C because 7x4=28 and 0x5=0 so 28-0 = 28!

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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.

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

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

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

Unit: Integration

3 0
2 years ago
How do you find the lowest common factor of 6 and 14
Gwar [14]
2 divides both numbers, so divide both numbers by 2 to get 3 and 7. These are relatively prime, so 2 is the gcd. The lcm is 6*14/2=42.
3 0
3 years ago
The cost of renting a car is $75/wk plus $0.15/mi traveled during that week. An equation to represent the cost would be y = 75 +
qaws [65]
The answer to the question is 65 miles

5 0
3 years ago
Andre is paid $12 per hour at his caddying job and $9.50 per hour working at a local fast food restaurant. He would like to keep
Fynjy0 [20]

The equation that can be used to model this scenario is 12x + 9.5y ≥ 275 and x + y ≤ 25

Let x represents the number of hours Andre works at his caddying job and y represents the number of hours he works at the restaurant.

Since he earn at least $275.00 a week, hence:

12x + 9.5y ≥ 275   (1)

Also, he can work no more than 25 hours, hence:

x + y ≤ 25   (2)

Therefore the equation that can be used to model this scenario is 12x + 9.5y ≥ 275 and x + y ≤ 25

Find out more at: brainly.com/question/25285332

5 0
3 years ago
Help with this math question thx
KiRa [710]

Answer:

Skewed to the left.

Step-by-step explanation:

The left side of the graph is at 2 and is 4 units from the middle at 6. The right side of the graph is at 9 and is 3 units from the middle. As such the graph is skewed left since it is a greater distance from the left to the center.

3 0
3 years ago
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