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3 years ago

X=y+1400 0.08x+0.05=840

Mathematics

2 answers:

jeyben [28]3 years ago

6 0

Answer:

(7000,5600)

Step-by-step explanation:

mezya [45]3 years ago

3 0

Answer:

x = 7000

y = 5600

(7000, 5600)

Step-by-step explanation:

To solve the system of equations means to find the point of intersection (graphically). You are finding what value of 'x' and what value of 'y' fits both equations.

x = y + 1400

0.08x + 0.05y = 840

We can solve using the method <u>substitution</u>, where you replace a variable in one equation with an equivalent expression.

<u>Since "x" is y + 1400, we can replace "x" in the second equation.</u>

0.08x + 0.05y = 840

0.08(y + 1400) + 0.05y = 840

Distribute over brackets by multiplying 0.08 with y, then 0.08 with 1400.

0.08y + 112 + 0.05y = 840 Collect like terms (with "y" variable)

112 + 0.13y = 840

Now isolate "y" in the simplified equation.

112 - 112 + 0.13y = 840 - 112 Subtract 112 from both sides

0.13y = 728

0.13y/0.13 = 728/0.13 Divide both sides by 0.13

y = 5600 Solved for y

We can substitute "y" with 5600 in any other equation that has "x".

x = y + 1400

x = 5600 + 1400 Add

x = 7000 Solved for x

You may express the answer as a coordinate, or an ordered pair (x, y).

The solution is (7000, 5600).

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What are the intercepts of 2x + 3y – 6z = 30?

ycow [4]

Intercept of equation 2x + 3y - 6z = 30 is (15, 0, 0) , (0, 10, 0) and (0, 0, -5)

<h3><u>Solution:</u></h3>

Given equation is:

2x + 3y - 6z = 30

We have to find the intercepts

Intercept are the point where equations cut the x- axis, y- axis and z- axis.

y and z both are zero

So substitute y = 0 and z = 0 in given equation

2x + 3(0) - 6(0) = 30

2x = 30

x = 15

<h3>Thus the intercept is (15, 0, 0)</h3>

x and z both are zero

So substitute x = 0 and z = 0 in given equation

2(0) + 3y -6(0) = 30

0 + 3y + 0 = 30

3y = 30

y = 10

<h3>Thus the intercept is (0, 10, 0)</h3>

x and y are both zero

So substitute x = 0 and y = 0 in given equation

2(0) + 3(0) - 6z = 30

-6z = 30

z = -5

<h3>Thus the intercept is (0, 0, -5)</h3>

Thus, intercept of equation 2x + 3y - 6z = 30 is (15,0,0) ,(0,10,0) and (0,0,-5)

6 0

3 years ago

Find the generating function for the sequence 1,1,1,2,3,4,5,6,....

marin [14]

Answer:

$P(x)=\dfrac{1}{1-x}+\dfrac{x^3}{(1-x)^2} \quad \text{for} \mid x \mid < 1$ [/tex]

Step-by-step explanation:

The generating function of a sequence is the power series whose coefficients are the elements of the sequence. For the sequence

$1,1,1,2,3,4,5,6,...$

the generating function would be

$P(x)=1+x+x^2+2x^3+3x^4+4x^5+5x^6+...\\$

we can multiply P(x) by x to get

$xP(x)=x+x^2+x^3+2x^4+3x^5+4x^6+...$

Note that

$P(x)-xP(x)=1+(2x^3-x^3)+(3x^4-2x^4)+(4x^5-3x^5)+(5x^6-4x^6)+...\\ \\=1+x^3+x^4+x^5+x^6+...=1+x^3(1+x+x^2+x^3+x^4+...)$

which for $\mid x \mid < 1$ can be rewritten as

$(1-x)P(x)=1+\dfrac{x^3}{(1-x)} \quad \Rightarrow \\\\P(x)=\dfrac{1}{(1-x)}+\dfrac{x^3}{(1-x)^2}$

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3 years ago

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Answer:

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Step-by-step explanation:

The n th term of an arithmetic sequence is

$a_{n}$ = a + (n - 1)d

where a is the first term and d the common difference

Here a = 13 and d = - 2.5, thus

$a_{29}$ = 13 + (28 × - 2.5) = 13 - 70 = - 57

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3 years ago

PLEASE HELP ME WITH THIS QUESTION

alekssr [168]

Answer:

The second option, 1,008 cm²

Step-by-step explanation:

This shape has 5 sides to solve for with reguards to surface area.

Let us solve for them all.

[1 & 2 - the triangles]

12 * 9 = 108 cm²

-> I am not going to divide since we have 2 congruent triangles

[3 - the bottom side]

25 * 12 = 300 cm²

[4 - the side facing away]

25 * 9 = 225 cm²

[5 - the side facing up]

25 * 15 = 375 cm²

Now we will add them together for the total.

108 + 300 + 225 + 375 = 1,008 cm²

The surface area for the triangular prism shown is 1,008 cm².

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