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3 years ago

Perform the indicated operation. 10 3/7 + 19 5/9

2 answers:

4 0

Given expression is

$10 \frac{3}{7} + 19 \frac{5}{9}$

Now convert mixed fraction as improper fraction as

$10 \frac{3}{7} + 19 \frac{5}{9} = \frac{10*7 + 3}{7} + \frac{19*9+5}{9}$
                                                         $= \frac{73}{7} + \frac{176}{9}$
                                                          $= \frac{73*9 + 176 * 7}{63}$
                                                         $= \frac{657 + 1232}{63} = \frac{1889}{63}$
Now we can convert $\frac{1889}{63 } = 29 \frac{62}{63}$

So the answer is $29 \frac{62}63}$

ratelena [41]3 years ago

3 0

Answer:

29 62/63

Step-by-step explanation:

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A local park is in the shape of a square. A map of the local park is made with the scale 1 inch to 200 feet.

ICE Princess25 [194]

1 inch to 100 feet

12 inches = 1200 feet.

Just multiply both sides by 12.

The answer is 1200 feet.

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2 years ago

How does knowing the double 6+6=12 help you solve the near double 6+7=13

forsale [732]

Answer:

6 + 7 = 13

Step-by-step explanation:

We are given the following information in the question:

We know that

$6 + 6 = 12$

We need this information to evaluate

$6+7$

The evaluation can be done with the help of using associative property and distributive property.

Associative property: (a + b) + c = a + (b + c)

The evaluation can be shown as:

$6 + 7\\= 6 + 6 + 1\\=(6 + 6) + 1\\= 12 + 1\\=13$

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2 years ago

3x + 2z - 4y - 6 + 4z + 7y

Anon25 [30]

Answer:

3x(2z+4z)+(−4y+7y)−6

Step-by-step explanation:

1 Collect like terms.

3x+(2z+4z)+(−4y+7y)−6

2 Simplify.

3x+(2z+4z)+(−4y+7y)−6

3x+6z+3y−6

5 0

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