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GenaCL600 [577]

4 years ago

10

Use Gauss's approach to find the following sums (do not use formulas). 1+3+5+7+...999

1 answer:

muminat4 years ago

4 0

$S=1+3+5+\cdots+995+997+999$
$S=999+997+995+\cdots+5+3+1$
$\implies 2S=(1+999)+(3+997)+(5+995)+\cdots+(995+5)+(997+3)+(999+1)$

$2S=\underbrace{1000+1000+\cdots+1000+1000}_{500\text{ times}}$

(We are adding 500 instances of 1000 because that's how many odd numbers there are between 1 and 1000, inclusive.)

$2S=500\times1000=500000$
$\implies S=250000$

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How do i graph the lines when the equations aren’t in slope intercept form????

jekas [21]

Slope-Intercept Form: y=mx+b

Standard Form: ax+by=c

Point- Slope: (y-y1)= m(x-x1)

There are multiple answers to your question-

If you are only missing b(the y-intercept) but are given a set of points, plug the points into x and y and solve for b.
If you are only missing the slope(m) but are given a set of points, plug the points into x and y and solve for m.
If you are given the standard form/point-slope form, change the equation to slope intercept form.
If you are given an complete form(there is an x and y; no missing variables), but are not sure what it is, plug in some numbers in x to find y, then graph.

7 0

3 years ago

Could someone help me understand how to solve this? I'm having trouble with it, it's about Applications of Systems of Linear Equ

Anna35 [415]

Answer:

Therefore the amount in the 4% savings account = $550

Step-by-step explanation:

i) the total amount = $1500

ii) let the amount placed in the 4% interest savings account = x

iii) let the amount placed in the 5% interest savings account = y

iv) therefore fro i) we can say x + y = 1500

v) the total interest gained = $69.5

vi) therefore we can write 0.04x + 0.05y = 69.50

vii) multiplying equation vi) with 100 we get 4x + 5y = 6950

viii) Multiplying the equation in iv) by 5 we get 5x + 5y = 7500

ix) Subtracting equation in vii) from equation in viii) we get x = $550

x) Therefore the amount in the 4% savings account = $550

3 0

3 years ago

Pedro buys 4 books at the fair for $7 each. Pedro hands the cashier 3 ten dollar bills. how much change would he receive? write

garik1379 [7]

4 x 7 = 28 - 30 = -2. His change is 2 dollars.

8 0

3 years ago

A can of crushed tomatoes holds 40 fluid ounces. How can a label designer name the same volume using metric units? Complete the

inn [45]

The metric unit of a quantity is simply the unit of measurement of the quantity

The volumes of the crashed tomato cans are 1184 milliliters and 1.184 liters

The volume of the crushed tomato can is given as:

$\mathbf{Volume = 40oz}$

From the question, we have the following conversion ratio

$\mathbf{1oz \approx 29.6mL}$

So, the volume in milliliters becomes

$\mathbf{Volume = 40 \times 29.6mL}$

Multiply

$\mathbf{Volume = 1184mL}$

To convert the unit to liters, we simply divide the volume by 1000.

So, we have:

$\mathbf{Volume = 1184L \div 1000}$

$\mathbf{Volume = 1.184L}$

Hence, the equivalent volumes are 1184 milliliters and 1.184 liters

Read more about metric units at:

brainly.com/question/2004114

3 0

3 years ago

Express with radical signs instead of fractional exponents. Rationalize the denominator.

CaHeK987 [17]

$x^{\frac{1}{2}} = \sqrt[2]{x}$ and $3^{-\frac{1}{2}} = \frac{1}{3^{\frac{1}{2}} } = \frac{1}{\sqrt[2]{3}}$ so

$3^{-\frac{1}{2}} x^{\frac{1}{2}} = \frac{1}{\sqrt{3}} \cdot \sqrt{x} = \frac{\sqrt{x}}{\sqrt{3}}$

and you rationalize denominator by multiplying numerator and denominatr by $\sqrt{3}$ so that gives--

$\frac{\sqrt{x}}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{3x}}{3}$

Your answer is $\frac{\sqrt{3x}}{3}$

5 0

3 years ago