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3 years ago

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The measures of three angles of a triangle are given by (8x - 5), (2x)º, and (3x – 10). What is the measure of the largest angle

? A 15° B 115° C. 35° D 150°

1 answer:

zhannawk [14.2K]3 years ago

3 0

Answer: 115°

Step-by-step explanation:

We should note that the sum of the angles that are in a triangle is equal to 180°, therefore we will add the angles given and equate them to 180°. This will be:

(8x - 5) + (2x) + (3x - 10) = 180

8x - 5 + 2x + 3x - 10 = 180

Collect like terms

8x + 2x + 3x = 180 + 5 + 10

13x = 195

x = 195/13

x = 15

The angles are:

8x - 5 = 8(15) - 5 = 120 - 5 = 115°

2x = 2(15) = 30°

3x - 10 = 3(15) - 10 = 45 - 10 = 35°

Therefore, the largest angle is 115°

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masya89 [10]

Answer:

9.95

Step-by-step explanation:

you add 4 miles + 5.2 miles which is 9.2 miles then u add the 3/4 mile which is .75 in a decimal form which equals 9.95

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3 years ago

In the 2009-2010 school year in country A, there were 92,000 foreign students from country B. This number I 23% more than the nu

max2010maxim [7]

Answer:

$\approx74796$

Step-by-step explanation:

GIVEN: In the $2009-10$ school year in country A, there were $92,000$ foreign students from country B. This number is $23\%$ more than the number of students from country C.

TO FIND: How many foreign students were from country C.

SOLUTION:

Total foreign students from country B $=92000$

let the foreign students from country C be $x$

As the students from country B is $23\%$ more than the country C

Students from country B

$92000=\frac{123}{100}x$

$x=\frac{9200000}{123}$

$x\approx74796$

Hence the number of students from country C are $74796$

8 0

3 years ago

Use the Fundamental Theorem of Calculus to find the "area under curve" of

lozanna [386]

Answer:

$\displaystyle A = 300$

General Formulas and Concepts:

<u>Calculus</u>

Integrals

Definite Integrals
Area under the curve
Integration Constant C

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>

f(x) = 6x + 19

Interval [12, 15]

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

Substitute in variables [Area of a Region Formula]: $\displaystyle A = \int\limits^{15}_{12} {(6x + 19)} \, dx$
[Integral] Rewrite [Integration Property - Addition/Subtraction]: $\displaystyle A = \int\limits^{15}_{12} {6x} \, dx + \int\limits^{15}_{12} {19} \, dx$
[Integrals] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle A = 6\int\limits^{15}_{12} {x} \, dx + 19\int\limits^{15}_{12} {} \, dx$
[Integrals] Integrate [Integration Rule - Reverse Power Rule]: $\displaystyle A = 6(\frac{x^2}{2}) \bigg| \limits^{15}_{12} + 19(x) \bigg| \limits^{15}_{12}$
Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: $\displaystyle A = 6(\frac{81}{2}) + 19(3)$
Simplify: $\displaystyle A = 300$

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

Unit: Integration

Book: College Calculus 10e

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3 years ago

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Thepotemich [5.8K]

Answer:

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General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Step-by-step explanation:

<u>Step 1: Define</u>

6² + x - x²

x = 3

<u>Step 2: Evaluate</u>

Substitute: 6² + 3 - (3)²
Exponents: 36 + 3 - 9
Add: 39 - 9
Subtract: 30

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Step-by-step explanation:

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