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3 years ago

I'll make you brainlist if you answer correctly

Mathematics

1 answer:

pantera1 [17]3 years ago

4 0

Answer:

Value of x = 3 in the given AP sequence.

Fourth term in the sequence is 19.

Step-by-step explanation:

Here, the given sequence is x+4, 2x+5, and 4x+3

So, the First term a = x + 4

Second Term b = 2x + 5

Third Term = 4x + 3

Now, as the given sequence is in AP.

⇒ b-a = c -b = Common Difference

⇒( 2x+5) - (x+4) = (4x+3) - (2x+5)

or, 2x + 5 - x - 4 = 4x + 3 - 2x -5

or, x + 1 = 2x - 2

or, -x = -3, or x = 3

So, the value of x = 3 in the given AP sequence.

⇒ First term = 3+ 4 = 7

⇒ Second term = 2(3) + 5 = 11

So, the Common Difference = Second term - First term

= 11 - 7 = 4

Now, Fourth term in an AP = Third term + Common Difference

= 4x + 3 + = 4x + 7 = 4(3) + 7 = 19

So, the fourth term in the sequence is 19.

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How can you solve 30×20 using compatible numbers

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You could go 3×10 × 10×2

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4 years ago

What two rational expressions sum to 2x+3/x^2-5x+4

Anni [7]

Answer:

$\frac{2x + 3}{(x- 1)(x - 4)} = \frac{-5}{3(x- 1)} + \frac{11}{3(x - 4)}$

Step-by-step explanation:

Given the rational expression: $\frac{2x + 3}{x^2 - 5x + 4}$ , to express this in simplified form, we would need to apply the concept of partial fraction.

Step 1: factorise the denominator

$x^2 - 5x + 4$

$x^2 - 4x - x + 4$

$(x^2 - 4x) - (x + 4)$

$x(x - 4) - 1(x - 4)$

$(x- 1)(x - 4)$

Thus, we now have: $\frac{2x + 3}{(x- 1)(x - 4)}$

Step 2: Apply the concept of Partial Fraction

Let,

$\frac{2x + 3}{(x- 1)(x - 4)}$ = $\frac{A}{x- 1} + \frac{B}{x - 4}$

Multiply both sides by (x - 1)(x - 4)

$\frac{2x + 3}{(x- 1)(x - 4)} * (x - 1)(x - 4)$ = $(\frac{A}{x- 1} + \frac{B}{x - 4}) * (x - 1)(x - 4)$

$2x + 3 = A(x - 4) + B(x - 1)$

Step 3:

Substituting x = 4 in $2x + 3 = A(x - 4) + B(x - 1)$

$2(4) + 3 = A(4 - 4) + B(4 - 1)$

$8 + 3 = A(0) + B(3)$

$11 = 3B$

$\frac{11}{3} = B$

$B = \frac{11}{3}$

Substituting x = 1 in $2x + 3 = A(x - 4) + B(x - 1)$

$2(1) + 3 = A(1 - 4) + B(1 - 1)$

$2 + 3 = A(-3) + B(0)$

$5 = -3A$

$\frac{5}{-3} = \frac{-3A}{-3}$

$A = -\frac{5}{3}$

Step 4: Plug in the values of A and B into the original equation in step 2

$\frac{2x + 3}{(x- 1)(x - 4)} = \frac{A}{x- 1} + \frac{B}{x - 4}$

$\frac{2x + 3}{(x- 1)(x - 4)} = \frac{-5}{3(x- 1)} + \frac{11}{3(x - 4)}$

7 0

3 years ago

Surface Area of a Triangular Pyramid, please help!

8090 [49]

Answer:

surface area of the triangular pyramid

=(1/2×9×7.8)+(3×1/2×9×12.3)

=35.1+166.05

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5 0

3 years ago

Determine which of the following equations, when graphed, intersect at the point (4, 0).

kakasveta [241]

Answer:

Hence, the following equations, when graphed, intersect at the point (4, 0):

x - y = 4 (1)

x + y = 4 (4)

Step-by-step explanation:

" For the graph to intersect at the point (4,0) we mean that when y=0 , x must be equal to 4 or we could say that when x=4 then y=0".

x-y=4

now when y=0 then x=4.

Hence, the graph intersect at the point (4,0).

-x-y=4

When y=0 in the equation then x=-4, Hence the point (4,0) does not lie on the graph of the given function.

2x-y=7

When y=0 then x=7/2.

Hence the graph of the function does not intersect at the point (4,0).

x+y=4

When y=0 then x=4.

Hence the graph of the given function intersect at (4,0).

2x + y = 7

When y=0 then x=7/2.

Hence the graph of the function does not intersect at the point (4,0).

2x + y = -7

When y=0 then x= -7/2.

Hence the graph of the function does not intersect at the point (4,0).

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3 years ago

The quotient x of and 3

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Easy :)

Quotient means dividing something by something else.

So,

Quotient of x and 3 is x3

If the question says Quotient of x and 3 minus 8 then you can write it as x3-8

$\large\sf\red{thank \: you}$

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3 years ago