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3 years ago

How do i find a formula for "1+3+5+7+......+(2n-1)

Mathematics

1 answer:

nata0808 [166]3 years ago

7 0

Answer:

Step-by-step explanation:

common difference d=3-1=2

first term a=1

an=a+(n-1)d

2n-1=1+(l-1)2

2n-1=1+2l-2

2n-1=2l-1

l=n

(i used l for number of terms)

number of terms=n

$S_{n}=\frac{n}{2} (first ~term+last~term)\\=\frac{n}{2} (1+2n-1)\\=n^2$

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F(x) = 5x ^ 2 and g(x) = x + 1 find (fg)(x)

Vilka [71]

According to the question given, $f(x)=5x^2,g(x)=x+1$ (fg)(x) is $f(x).g(x)=5x^3+5x^2$

Which is not given in the options.

Step-by-step explanation:

We are given:

$f(x)=5x^2$

$g(x)=x+1$

We need to find (fg)(x)

Solving:

$(fg)(x)=f(x).g(x)\\f(x).g(x)= 5x^2*(x+1)\\f(x).g(x)=5x^3+5x^2$

According to the question given, (fg)(x) is $f(x).g(x)=5x^3+5x^2$

Which is not given in the options.

Keywords: Composite functions

Learn more about Composite functions at:

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3 years ago

Lucy makes 4/7 of a dress in 3/4. How many dresses does she make in one hour

GREYUIT [131]

Answer:

3/7 of a dress in one hour

Step-by-step explanation:

(4/7)/(3/4)=x/(4/4)

(4/7)(4/3)=x/1

cross product

4/3*x=(4/7)(1)

4/3x=4/7

x=(4/7)/(4/3)

x=(4/7)(3/4)

x=3/7

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4 years ago

Which number line represents the solution set for the inequality 2x - 62 6(x - 2) + 8?

antoniya [11.8K]

Answer:

2x - 6 ≥ 6(x-2) + 8

2x - 6 ≥ 6x - 12 + 8

6x - 2x ≤ - 6 + 4

4x ≤ -2

4x/4 ≤ -2/4

x ≤ -1/2

Interval Notation: (- ∞, -1/2]

The line starts from -1/2 with the arrow going to the left (decreasing). The endpoint or value from where it started, which is -1/2, should be shaded. The inequality symbol x ≤ -1/2 represents the values at most or maximum -1/2.

Step-by-step explanation:

7 0

3 years ago

This is for pre calculus, please help

Harlamova29_29 [7]

Answer:

The correct answer is:

$g(x) = x+1$

Step-by-step explanation:

Given that:

$h(x) = f\circ g(x)= \sqrt[3]{x+3}$

$f(x) = \sqrt[3]{x+2}$

To find:

$g(x) = ?$

Solution:

Let $g(x) = m$

We have

$f\circ g(x)= \sqrt[3]{x+3}\\OR\\f( g(x))= \sqrt[3]{x+3}$ ...... (1)

Now, we have let:

$g(x) = m\\\therefore f(g(x)) = f(m)$

Putting x = in f(x), we get

$f(x) = \sqrt[3]{x+2}\\\Rightarrow f(m) = \sqrt[3]{m+2}$ ....... (2)

Comparing equation (1) and (2):

$\sqrt[3]{x+3} =\sqrt[3]{m+2}$

Taking cubes both sides:

$x+3=m+2\\\Rightarrow m = x+3-2\\\Rightarrow m = x+1$

$\therefore g(x) = x+1$

Hence,

The <em>correct answer </em>is:

$g(x) = x+1$

5 0

3 years ago

VWX and NOP are similar. If mV = 44° and mP = 66°, what is mW?

Sholpan [36]

VWX and NOP are similar triangles. The angle of V is equal to the angle of N, W is equal to O, X is equal to P. The total angle of a triangle is 180. The angle of V = 44. Angle of P = 66, which is just the same angle as X. So we need to find the angle or W, same angle as O.

180 = 44 + 66 + W
W = 180 - 110
W = 70 degrees.

6 0

3 years ago