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emmainna [20.7K]
4 years ago
14

Which statements are true? Check all that apply.

Mathematics
2 answers:
Masteriza [31]4 years ago
6 0

Answer:what the question

Step-by-step explanation:

SpyIntel [72]4 years ago
4 0
What’s the question though
You might be interested in
2. Determine the sum of the first 400 ODD numbers.<br><br>​
il63 [147K]

Odd numbers take the form 2n-1, where n\ge1 is an integer. When n=400, the last odd number would be 799. So we're adding

S=1+3+5+\cdots+795+797+799

By reversing the order of terms, we have

S=799+797+795+\cdots+5+3+1

and we can pair up terms in both sums at the same position to write

2S=(1+799)+(3+797)+(5+795)+\cdots(795+5)+(797+3)+(799+1)

so that we are basically adding 400 copies of 800, and from there we can find the value of the sum right away:

2S=400\cdot800\implies S=160,000

###

We could also make use of the formulas,

\displaystyle\sum_{i=1}^n1=n

\displaystyle\sum_{i=1}^ni=\dfrac{n(n+1)}2

We have

S=\displaystyle\sum_{i=1}^{400}(2i-1)=2\sum_{i=1}^{400}i-\sum_{i=1}^{400}1=400(400+1)-400=400^2=160,000

3 0
4 years ago
Solving separable differential equation DY over DX equals xy+3x-y-3/xy-2x+4y-8​
Ivanshal [37]

It looks like the differential equation is

\dfrac{dy}{dx} = \dfrac{xy + 3x - y - 3}{xy - 2x + 4y - 8}

Factorize the right side by grouping.

xy + 3x - y - 3 = x (y + 3) - (y + 3) = (x - 1) (y + 3)

xy - 2x + 4y - 8 = x (y - 2) + 4 (y - 2) = (x + 4) (y - 2)

Now we can separate variables as

\dfrac{dy}{dx} = \dfrac{(x-1)(y+3)}{(x+4)(y-2)} \implies \dfrac{y-2}{y+3} \, dy = \dfrac{x-1}{x+4} \, dx

Integrate both sides.

\displaystyle \int \frac{y-2}{y+3} \, dy = \int \frac{x-1}{x+4} \, dx

\displaystyle \int \left(1 - \frac5{y+3}\right) \, dy = \int \left(1 - \frac5{x + 4}\right) \, dx

\implies \boxed{y - 5 \ln|y + 3| = x - 5 \ln|x + 4| + C}

You could go on to solve for y explicitly as a function of x, but that involves a special function called the "product logarithm" or "Lambert W" function, which is probably beyond your scope.

8 0
2 years ago
Which is the best estimate for the product of 3,826.301 × 175.6?
dem82 [27]
If you round 3,826.301 and 175.6 to the nearest hundred you will get 3,800 and 200.

Multiply 3,800 * 200 = 760000

760,000 rounded to the nearest hundred thousand is 800,000.

The best estimate for the product 3,826.301 × 175.6 is B. 800,000. 
7 0
3 years ago
Read 2 more answers
...........answers plz
Ira Lisetskai [31]

Answer:

0

Step-by-step explanation:

m = 21, n = 12

so we just plug these into the equation

(1/3)(21) -1 -(1/2)(12)

(21/3) -1 -(12/2)

7 -1 -6

6 -6

0

3 0
3 years ago
How many square feet of outdoor carpet will
jonny [76]

Answer:  30\ ft^2

Step-by-step explanation:

The missing figure is attached.

For this exercise you can divide the given figure into three rectangles.

The formula for calculate the area of a rectangle is:

A=lw

Where "l" is the lenght and "w" is the width.

Knowing this, you can calculate the area of each rectangle.

Then:

Area of the Rectangle A

You can identify that:

l_A=4\ ft\\w_A=2\ ft

Then, its area is:

A_A=(4\ ft)(2\ ft)\\\\A_A=8\ ft^2

Area of the Rectangle B

Observe that:

l_B=4\ ft+2\ ft=6\ ft\\w_B=2\ ft

Then, its area is:

A_B=(6\ ft)(2\ ft)\\\\A_B=12\ ft^2

Area of the Rectangle C

You can identify that:

l_C=5\ ft\\w_C=2\ ft

Then, its area is:

A_C=(5\ ft)(2\ ft)\\\\A_C=10\ ft^2

Add the area of the rectangles in order to find the total area. This is:

Total=8\ ft^2+12\ ft^2+10\ ft^2\\\\Total=30\ ft^2

Therefore, you will need 30\ ft^2 of  outdoor carpet for that hole.

8 0
3 years ago
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