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4 years ago

Solve the equation 2x - 3 plus 4x = 21

Mathematics

1 answer:

vichka [17]4 years ago

4 0

Answer:

$x=3$

Step-by-step explanation:

Add like terms and get x by itself.

$2x-3+4x=21\\6x-3=21\\6x=18\\x=3$

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5√-54 in simplest radical form

rjkz [21]

YOUR ANSWER IS 15i radical 6

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3 years ago

Perimeter. 6) A quadrilateral can have 2 reflex angles.

madreJ [45]

Answer:

False

Step-by-step explanation:

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4 years ago

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Ben has b dollars. Cam has 7 fewer dollars than ben. How many dollars does cam have?

aleksley [76]

Answer:

b - 7 = the amount of money Cam has

Step-by-step explanation:

We don't know how much money ben has so we have to subtract 7 from b to find the amount of money Cam has.

Hope this helps!

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3 years ago

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What is the largest possible integral value in the domain of the real-valued function

kotegsom [21]

Answer:

Max Value: x = 400

General Formulas and Concepts:

Algebra I

Domain is the set of x-values that can be inputted into function f(x)

Calculus

Antiderivatives
Integral Property: $\int {cf(x)} \, dx = c\int {f(x)} \, dx$
Integration Method: U-Substitution
[Integration] Reverse Power Rule: $\int {x^n} \, dx = \frac{x^{n+1}}{n+1} + C$

Step-by-step explanation:

Step 1: Define

$f(x) = \frac{1}{\sqrt{800-2x} }$

Step 2: Identify Variables

Using U-Substitution, we set variables in order to integrate.

$u = 800-2x\\du = -2dx$

Step 3: Integrate

Define: $\int {f(x)} \, dx$
Substitute: $\int {\frac{1}{\sqrt{800-2x} } } \, dx$
[Integral] Int Property: $-\frac{1}{2} \int {\frac{-2}{\sqrt{800-2x} } } \, dx$
[Integral] U-Sub: $-\frac{1}{2} \int {\frac{1}{\sqrt{u} } } \, du$
[Integral] Rewrite: $-\frac{1}{2} \int {u^{-\frac{1}{2} }} \, du$
[Integral - Evaluate] Reverse Power Rule: $-\frac{1}{2}(2\sqrt{u}) + C$
Simplify: $-\sqrt{u} + C$
Back-Substitute: $-\sqrt{800-2x} + C$
Factor: $-\sqrt{-2(x - 400)} + C$

Step 4: Identify Domain

We know from a real number line that we cannot have imaginary numbers. Therefore, we cannot have any negatives under the square root.

Our domain for our integrated function would then have to be (-∞, 400]. Anything past 400 would give us an imaginary number.

7 0

3 years ago

Find the area of the shaded region. round answers to the nearest tenth. assume all inscribed polygons are regular. 29.3 units2

FromTheMoon [43]

The picture in the attached figure

we know that
the area of the shaded region is equal to
(2/3)*[area of the circle - the area of the triangle]

step 1
Find the area of a circle Ac
Ac = π r²
Ac = π (6)²
Ac = 113.10 units²

step 2
find the area of the triangle At
The triangle is an equilateral triangle with angles on each corner equal to 60 degrees. Meanwhile,
the 3 angles at the center is 120 degrees each since a circle is 360 degree.
We know that the radius (line from centerpoint to corner) is equivalent to 6.
Using the cosine law,
we can calculate for the length of one side.
s² = 6^ + 6² – 2 (6) (6) cos 120
s² = 108
s = 10.4 units
Since this is an equilateral triangle, therefore, all sides are equal.
The area for this is:
At = (sqrt3 / 4) * s²
At = 46.77 units²

step 3
the area of the shaded region=(2/3)*[area of the circle - the area of the triangle]
the area of the shaded region=(2/3)*[113.10-46.77]------> 44.22 units²

therefore

the answer is
the area of the shaded region is 44.22 units²

5 0

3 years ago