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3 years ago

Simplify 36p^16q^12r^15 + 18p^10q^13r^11 + 72p^8q^16r^12

1 answer:

6 0

The three terms are not like terms, so they cannot be added together.
The expression is simplified.
If you need to factor the expression, then the instructions should be factor the expression, not simplify.

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4/5 ÷ 7/6 + 2/7 ∙2 1/5

Aleksandr [31]

<h2>The value of $\dfrac{4}{5}$ ÷ $\dfrac{7}{6}$ + $\dfrac{2}{7}.2\dfrac{1}{5}$ $=\dfrac{8}{7}$ </h2>

Step-by-step explanation:

We have,

$\dfrac{4}{5}$ ÷ $\dfrac{7}{6}$ + $\dfrac{2}{7}.2\dfrac{1}{5}$

To find, the value of $\dfrac{4}{5}$ ÷ $\dfrac{7}{6}$ + $\dfrac{2}{7}.2\dfrac{1}{5}$ = ?

∴ $\dfrac{4}{5}$ ÷ $\dfrac{7}{6}$ + $\dfrac{2}{7}.2\dfrac{1}{5}$

$=\dfrac{4}{5}\times \dfrac{6}{7} +\dfrac{2}{7}.\dfrac{8}{5}$

$=\dfrac{24}{35} +\dfrac{16}{35}$

Taking LCM of denominator, we get

$=\dfrac{24+16}{35}$

$=\dfrac{40}{35}$

Dividing numerator and denominator by 5, we get

$=\dfrac{8}{7}$

∴ The value of $\dfrac{4}{5}$ ÷ $\dfrac{7}{6}$ + $\dfrac{2}{7}.2\dfrac{1}{5}$ $=\dfrac{8}{7}$

Hence, the value of $\dfrac{4}{5}$ ÷ $\dfrac{7}{6}$ + $\dfrac{2}{7}.2\dfrac{1}{5}$ is equal to $\dfrac{8}{7} .$

4 0

3 years ago

Letang Industrial Systems Company (LISC) is trying to decide between two different conveyor belt systems. System A costs $280,00

Vanyuwa [196]

We have to calculate the EAC for both the conveyor belt system.

Solutions :

<u>Equivalent Annual Cost or (EAC) for the SYSTEM-A</u>

$\text{Operating cash flow } = \text{Pre-tax annual operating cost (1-tax rate )} + (\text{depreciation expense} \times$ tax rate )

$=-855,000(1-0.23)+\left[\left(\frac{280,000}{4}\right)\times 0.23\right]$

$= (-85,000 \times 0.77 ) + (70,000 \times 0.23)$

= $ 49,350

Year Annual Cost flow Present value factor Present Value of Annual

at 10% cash flow

1 -49,350 0.909091 -44,863.64

2 -49,350 0.826446 -40,785.12

3 -49,350 0.751315 -37,077.39

4 -49,350 <u> 0.683013 </u> <u>-33,706.71 </u>

Total $ 3.169865 $ -156,432.86

Therefore, Net Present value = present value of the annual cash flow - initial investment.

= 156,432.86 - 280,000

= $ 436,432.86 (negative)

Now the EAC or the Equivalent Annual Cost for System A :

$\text{EAC}= \text{Net present value / (PVIFA 10 percent, 4 years)}$

$=\frac{436,432.86}{3.169865}$

$= 137,681.86$ dollar (negative)

$\text{Operating cash flow } = \text{Pre-tax annual operating cost (1-tax rate )} + (\text{depreciation expense} \times$ tax rate)

$=79,000(1-0.23)+\left[\left(\frac{360,000}{6}\right) \times 0.23\right]$

$=(-78,000 \times 0.77)+(60,000 \times 0.23)$

= -$ 47,030

Year Annual Cost flow Present value factor Present Value of Annual

at 10% cash flow

1 -47,030 0.909091 -42,754.55

2 -47,030 0.826446 -38,867.77

3 -47,030 0.751315 -35,334.34

4 -47,030 0.683013 -32,122.12

5 -47,030 0.620921 -29,201.93

6 -47,030 <u> 0.564474 </u> <u> -26,547.21 </u>

Total $ 4.355261 $ -204,827.91

Net Present Value = Present Value of annual cash inflows – Initial Investment

$= 204,827.91 - 360,000$

= -$ 564,827.91 (negative)

EAC for system B:

Equivalent Annual Cost for system B $=\frac{\text{net present value}}{\text{PVIFA 10 \text percent, 6 years}}$

$=\frac{-564,827.91}{4.355261}$

= -$129,688.66 (negative)

7 0

2 years ago

Which constant term would mean that the expression is completely factored? x2 – 3x

kolbaska11 [484]

Factor x2−3x−10x2−3x−10=(x+2)(x−5) Answer: (x+2)(x−5)

have a nice day !!!

7 0

2 years ago

liubo4ka [24]

Answer:

<h3>The answer is option D.</h3><h3 /><h3>3</h3>

Step-by-step explanation:

From the table above f(-2) = 3

Hope this helps you

4 0

3 years ago

I NEED HELP ASAP PLZZZZ LOOK AT THE PIC

umka2103 [35]

Answer:

The red line is g(x)

Step-by-step explanation:

* To solve this problem you must to know some fact about

transformation

- If the function f(x) translated horizontally to the left

by h units, then the new function g(x) = f(x + h)

- If the function f(x) translated vertically up

by k units, then the new function g(x) = f(x) + k

- If the function f(x) translated vertically down

by k units, then the new function g(x) = f(x) – k

- A vertical stretching is the stretching of the graph away from

the x-axis

• if k > 1, the graph of y = k•f (x) is the graph of f (x) vertically

stretched by multiplying each of its y-coordinates by k.

- A vertical compression is the squeezing of the graph toward

the x-axis.

• if 0 < k < 1 (a fraction), the graph is f (x) vertically compressed

by multiplying each of its y-coordinates by k.

• if k should be negative, the vertical stretch or compress is

followed by a reflection across the x-axis.

* Now lets solve the problem

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

# x + 2 ⇒ means the graph moved 2 units to the left

# -1/2 ⇒ means the graph has vertical compressed followed

by a reflection across the x-axis, then multiply

each y-coordinate by -1/2

- The graph of f(x) intersects x-axis at point (3 , 0)

∴ The point will be (1 , 0) on g(x)

- The graph of f(x) intersects y-axis at point (0 , -6)

∴ The point will be (-2 , 3) on g(x)

* Look to the graph

# The red line is g(x)

# The blue line is f(x)

- To check your answer

# The equation of f(x) is f(x) = 2x - 6

∵ g(x) = -1/2f(x + 2)

∴ g(x) = -1/2[2(x + 2) - 6] = -1/2[2x + 4 - 6] = -1/2[2x - 2] = -x + 1

* g(x) intersect x-axis at point (1 , 0) and y-axis at point (0 , 1)

3 0

3 years ago