Which expression are equivalent to 3/5x + 3

2/5x + 1/5x

4/5x - 1/5x + 3

2/5x + 3 3/5x -1

1 + 3/5x + 2

1 +x/5 + 2

1 + 2/5x +3

The partial fraction expansion will look like

(x - 2)/((x ² + 1) (x - 1)²) = (ax + b)/(x ² + 1) + c/(x - 1) + d/(x - 1)²

Get everything in terms of a common denominator, and compare the numerators on both sides:

x - 2 = (ax + b) (x - 1)² + c (x ² + 1) (x - 1) + d (x ² + 1)

Expand the right side:

x - 2 = (ax + b) (x - 1)² + c (x ² + 1) (x - 1) + d (x ² + 1)

x - 2 = (a + c) x ³ + (-2a + b - c + d) x ² + (a - 2b + c) x + b - c + d

Match up the coefficients and solve the resulting system of equations:

a + c = 0

-2a + b - c + d = 0

a - 2b + c = 1

b - c + d = -2

==>   a = -1, b = -1/2, c = 1, d = -1/2

So the expansion into partial fractions is

(x - 2)/((x ² + 1) (x - 1)²) = (-x - 1/2)/(x ² + 1) + 1/(x - 1) - 1/(2 (x - 1)²)

… = -(2x + 1)/(2 (x ² + 1)) + 1/(x - 1) - 1/(2 (x - 1)²)

Answer: 1/32

Step-by-step explanation:

Answer:

45g

Step-by-step explanation:

The amount of salt left once the whole water is evaporated can be calculated as follows

= 12% × 375

= 12/100 × 375

= 0.12×375

= 45

Hence 45g of salt is left after the evaporation of water

Answer:

45g

Step-by-step explanation:

Answer:

25:4

Step-by-step explanation:

The ratio of the sides is 5:2

The ratio of the areas is the scale factor squares

5^2 : 2^2

25:4

Answer: C. 13/3

Step-by-step explanation:

[tex]slope=\frac{rise}{run} =\frac{y}{x} =\frac{13}{3}[/tex]

1). 210m^2+156m-96=0

2). 35m^2+26x-16

3). 35m^2+40m-14m-16

4). (35m^2+40m)+(-14m-16)

5). 5m(7m+8)-2(7m+8)

6). (5m-2)(7m+8)

7.) m= 2/5, -8/7

On the 2nd step I divided 6 on both sides.

Answer:

Timed test.

Step-by-step explanation:

An operational definition gives exactly what the independent variable means and its mode of measurement. The Independent variable is the variable in a research or experimental study which causes a change in the the measured variable. Hence, the independent variable is the predictor variable. In the study above, the independent variable is the timed test which is used to observe changes in the heart rate of the test taker (test anxiety). The change innheartrate of the test taker is the dependent variable.

Answer:

7 and 1 respectively

Step-by-step explanation:

1/7= 7 ) 1 (, the basic definition of division

Answer:

The two populations living habitats are different. Also they are only similar not the same. Although the physical features may look the same, the actual species may be totally different. :)

Step-by-step explanation:

Step-by-step explanation:

cho f(t)=(t-4)u(t-2)phep bien doi laplace la

F(s)=e^-2s/s^2-2e^-2s/s62

Answer:

see below

Step-by-step explanation:

11a   -2(x^2 -3)

Distribute

-2*x^2 -2(-3)

-2x^2 +6

11b  2x(x+4)

 Distribute

2x*x +2x*4

2x^2 +8x

12 The perimeter is the sum of all sides

The top is equal to the bottom and the left side is equal to the right

x-10 + x+20+x-10+x+20

Combine like terms

4x +20

Answer:

standard= 21.333%

prime= 42.666%

expedited= 6.666%

locker= 29.333%

Answer:

45

Step-by-step explanation:

CHECK ANSWER:

45  *5 = 225

45+5 = 50

50 < 225

sum < times

I hope this helped !

Answer:

0, 1.32

Step-by-step explanation:

16cos(t)*sin(t)=4sin(t)

cos(t)=1/4 or sin(t)=0

t=1.32 or 0

Answer:

19

Step-by-step explanation:

Add 7 onto 12 to find answer.

Answer:

b = 19

Step-by-step explanation:

b = 12 + 7

Simplify 12+7 to 19.

Answer:

I don't know what to do so I just answered the volume of this tell me if I am wrong

Step-by-step explanation:

radius : 3.5 cm

volume : ?

now,

volume (v) : π × r (2)

: 22/7 × 3.5(2)

:22×3.5×3.5 by 7

therefore,

the volume is 38.5

We know

[tex]\boxed{\sf cos\theta=\dfrac{Base}{Hypotenuse}}[/tex]

[tex]\\ \sf\longmapsto cos59=\dfrac{x}{28}[/tex]

[tex]\\ \sf\longmapsto 0.5=\dfrac{x}{28}[/tex]

[tex]\\ \sf\longmapsto x=28\times 0.5[/tex]

[tex]\\ \sf\longmapsto x\approx 14[/tex]

Answer:

[tex]x = 14[/tex]

Step-by-step explanation:

[tex] \cos( \theta) = \frac{a}{h} \\ \cos(59) = \frac{x}{28} \\ 0.5 \times 28 = x \\ 14 = x[/tex]

Answer:

Step-by-step explanation:

(b)

(i)

(ii)

(a) Cumulative frequency is 500, median is at 249, 250, the horizontal line from point 250 on y-axis intersecting the graph at approximately 52%, this is the median

(b)  Vertical line from the 45% mark intersects the graph at approximately 177th point. The number of candidates passed the test:

(iii) P(pass) = 323/500 = 0.626 or 62.6%

We know

[tex]\boxed{\sf M_o=3M_d-2M}[/tex]

[tex]\\ \sf\longmapsto M_o=3(25)-2(28)[/tex]

[tex]\\ \sf\longmapsto M_o=75-56[/tex]

[tex]\\ \sf\longmapsto M_o=19[/tex]

Explanation:

When multiplying fractions, we multiply the numerators together, and the denominators are handled separately.

The numerators in this case are -1 and 3. They multiply to -3

The denominators multiply to 2*4 = 8

So that's how we end up with -3/8 as the final answer

This fraction cannot be reduced any further, because 3 and have 8 no factors (other than 1) in common.

Answer: Third proportion is 21/5.

Step-by-step explanation:

Let the proportion be x

so,

3:5:x:7

so

3:5 = x:7

or, 3/5 = x/7

or, 21 = 5x

or, x = 21/5

If both are similar ratio of sides will be same

[tex]\\ \sf\longmapsto \frac{x}{25} = \frac{7}{5} \\ \\ \sf\longmapsto 5x = 7 \times 25 \\ \\ \sf\longmapsto 5x = 175 \\ \\ \sf\longmapsto x = \frac{175}{5} \\ \\ \sf\longmapsto x = 35[/tex]

Step-by-step explanation:

The triangle is equilateral (OPTION D) because any triangle that has 3 equal side lengths is an equilateral triangle.

Answer:

the area of right angle is 1.5×2.5=3.75

Answer:

1.5 units^2

Step-by-step explanation:

If we say that the missing side is x, we can use the pythatgorean theorem to find it.

1.5^2 + x^2 = 2.5^2  =>  2.25 + x^2 = 6.25  =>  x^2 = 4  =>  x=2

The area of a triangle is hieght * base * 1/2 => 1.5 * 2 * 1/2 = 1.5

Answer:

domain = {-6,-7,-7,-7}

Answer:

952

Step-by-step explanation:

34 = (30 + 4)

28 = (20 + 8)

34 x 28 = (30 + 4) x (20 + 8)

34 x 28 = 30 x 20 + 30 x 8 + 4 x 20 + 4 x 8

34 x 28 = 600 + 240 + 80 + 32

34 x 28 = 952

952 = 952

Answer:

4.5

Step-by-step explanation:

9/2 = 4.5

Answer:

x + 3

Step-by-step explanation:

Image below