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2 years ago

Angles and transversals thank you

Mathematics

1 answer:

faltersainse [42]2 years ago

7 0

Answer:

#11-13: 118 , 97 , 62

#7-10: 92 , 125 , 56 , 130

Step-by-step explanation:

#11. Supplementary angles (A + B = 180)

(n + 7) + (3n - 47) = 180
n = 55
<ABC = 3(55) - 47 = 118 degrees

#12. Supplementary angles

83 + x = 180
x = 97
<ABC = 97 degrees

#13. Congruent angles (A = B)

(8x - 34) = (5x +2)
x = 12
<DEF = 5 (12) + 2 = 62 degrees

#7. Congruent angles

(3x +23) = 4x
x = 23
<ABC = 4(23) = 92 degrees

#8. Congruent angles

5x = (3x + 50)
x = 25
<MPQ = 3(25) + 50 = 125 degrees

#9. Congruent angles

(a + 28) = 2a
a = 28
<MNP = (28) + 28 = 56 degrees

#10. Congruent angles

5y = (2y + 78)
y = 26
<WXZ = 5(26) = 130 degrees

I hope this helps!

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Help evaluating the indefinite integral

Dafna11 [192]

Answer:

$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \boxed{ -\sqrt{4 - x^2} + C }$

General Formulas and Concepts:
Calculus

Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]:
$\displaystyle (cu)' = cu'$

Derivative Property [Addition/Subtraction]:
$\displaystyle (u + v)' = u' + v'$
Derivative Rule [Basic Power Rule]:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Integration

Integrals

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

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

Integration Methods: U-Substitution and U-Solve

Step-by-step explanation:

Step 1: Define

Identify given.

$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx$

Step 2: Integrate Pt. 1

Identify variables for u-substitution/u-solve.

Set u:
$\displaystyle u = 4 - x^2$
[u] Differentiate [Derivative Rules and Properties]:
$\displaystyle du = -2x \ dx$
[du] Rewrite [U-Solve]:
$\displaystyle dx = \frac{-1}{2x} \ du$

Step 3: Integrate Pt. 2

[Integral] Apply U-Solve:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \int {\frac{-x}{2x\sqrt{u}}} \, du$
[Integrand] Simplify:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \int {\frac{-1}{2\sqrt{u}}} \, du$
[Integral] Rewrite [Integration Property - Multiplied Constant]:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \frac{-1}{2} \int {\frac{1}{\sqrt{u}}} \, du$
[Integral] Apply Integration Rule [Reverse Power Rule]:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = -\sqrt{u} + C$
[u] Back-substitute:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \boxed{ -\sqrt{4 - x^2} + C }$

∴ we have used u-solve (u-substitution) to find the indefinite integral.

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Learn more about integration: brainly.com/question/27746495

Learn more about Calculus: brainly.com/question/27746485

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

Unit: Integration

5 0

2 years ago

What is the factored form of the expression 9x^2+24x+16?

igor_vitrenko [27]

This is the product of the square of a binomial expression. Therefore, it will have two factors.

Square of a binomial: a² + 2ab + b² = (a+b)²

The process:

9x² + 24x + 16

= (3x)² +2(3x)(4) + (4)²

= (3x + 4)² or (3x+4)(3x+4)

I hope this helps :)

4 0

3 years ago

15. Xavier filled a 36 ounce cup with water. He

aniked [119]

Answer:28.8 ounces

Step-by-step explanation:20% -36 =22.8

4 0

2 years ago

How do i write this ?

Makovka662 [10]

Answer:

1 $\frac{5}{9\\}$

Step-by-step explanation:

When turning remainders into mixed numbers remember Place the remainder as the numerator, or the top number, in your fraction. Put the divisor on the bottom of the fraction, or the denominator.

Proceed to check your work :)

hope this helps

4 0

3 years ago

The sum of two numbers is 72 and their difference is 26. find two numbers?

Archy [21]

9514 1404 393

Answer:

23, 49

Step-by-step explanation:

Let s represent the smaller of the two numbers. Then the larger is s+26, and the sum is ...

s + (s+26) = 72

2s = 72 -26

s = (72 -26)/2 = 23

Then the larger number is

s +26 = 49

The two numbers are 23 and 49.

_____

The reason we wrote the solution this way is to show you that the smaller number is half the difference between the given sum (72) and difference (26). This is the generic solution to a "sum and difference" problem. The smaller number is always half the difference of the give sum and difference. (Similarly, the larger is always half the sum of the given sum and difference.)

That is, the two numbers are always half the sum ± half the difference:

72/2 ± 26/2 = {36+13, 36-13} = {49, 23}

7 0

2 years ago