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3 years ago

Determine if a quadrilateral with the given vertices is an isosceles trapezoid. Show and explain all steps to prove or disprove.

Mathematics

1 answer:

Inga [223]3 years ago

8 0

Step-by-step explanation:

explain all steps to prove or disprove.

A(-5,0) B(5,0)

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PLEASE HELP ASAP WILL GIVE BRAINLEIST

Arada [10]

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3 years ago

A nursery has 10 tree seedlings to give out at 2 workshops. It wants to give out a minimum of 2 seedlings at each workshop. How

11111nata11111 [884]

We are given total 10 tree seedlings.

Number of workshops = 2.

Here order doesn't matters.

When order doesn't matters we apply combination.

We know formula of combination:

$C(n,r) = \frac{n!}{r!(n-r)!}$

For the given situation, we have

n=10 and r=2.

Plugging values in formula, we get

$\frac{10!}{2!(10-8)!} = \frac{10\times 9\times8!}{2!8!}$

$\frac{10 \times 9}{2} = \frac{90}{2} =45$

<h3>Therefore, 45 different ways can the nursery give out seedlings.</h3>

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3 years ago

PLZ HELP BRAINLIEST Which of the following graphs could represent a function?

Serhud [2]

Answer:

Step-by-step explanation:

all other graphs couldnt work because their x axis do not pass the vertical line test.

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3 years ago

Identify the y-intercept for the line 4x – 2y = 4

stellarik [79]

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3 years ago

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

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2 years ago