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3 years ago

What is the value of x? Enter your answer in the box. x =

Mathematics

1 answer:

tresset_1 [31]3 years ago

5 0

These are vertical angles, meaning they are congruent by definition. Thus, you can set the angles' expressions equal to each other and solve for x this way:

3x + 50 = 6x - 10
3x + 60 = 6x
60 = 3x
20 = x

Answer:
x = 20

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An aircraft manufacturer wants to determine the best selling price for a new airplane. The company estimates that the initial co

Blizzard [7]

Answer:

$(a)$ $C(x)=500+20x-5x^{\frac{3}{4}}+0.01x^2$

$p(x)=320-7.7p$

$R(x)=(320-7.7p)p=320p-7.7p^2$

$(b)$ $x=82 \text{planes}$

$(c)$ $p=\$30.91 M\;\; \text{per plane}$

$(d)$ maximum profit $=\$ 15.90M$

Step-by-step explanation:

Given that,

The company estimates that the initial cost of designing the aeroplane and setting up the factories in which to build it will be 500 million dollars.

The additional cost of manufacturing each plane can be modelled by the function.

$m(x)=20x-5x^{\frac{3}{4}}+0.01x^2$

$(a)$ Find the cost, demand (or price), and revenue functions.

$C(x)=500+20x-5x^{\frac{3}{4}}+0.01x^2$

$p(x)=320-7.7p$

$R(x)=(320-7.7p)p=320p-7.7p^2$

$(b)$ Find the production level that maximizes profit.

$f=R(x)-C(x)$

$\Rightarrow f=320p-7.7p^2-(500+20x-5x^{\frac{3}{4}}+0.01x^2)$

$\Rightarrow df=320dp-15.4pdp-20dx+5(\frac{3}{4} )x^{\frac{-1}{4} }dx-0.02xdx$

$x=320-7.7p$

$p=\frac{320-x}{7.7}$

$\frac{dp}{dx} = \frac{-1}{7.7}$

$\frac{df}{dx}=\frac{320}{-7.7} -\frac{15.4(320-x) }{7.7(\frac{-1}{7.7} )}-20+5\frac{3}{4} x^{\frac{-1}{4}} -0.02x=0$

$\Rightarrow -41.5584+83.1169-0.2597x-20+3.75x^{\frac{-1}{4} }-0.02x=0$

$\Rightarrow 21.5585+3.75x^{\frac{-1}{4} }-0.279x=0$

$\Rightarrow x=82 \text{planes}$

$(c)$ Find the associated selling price of the aircraft that maximizes profit.

$p=\frac{320-82}{7.7}$

$\Rightarrow p=\$30.91 M\;\; \text{per plane}$

$(d)$ Find the maximum profit.

Manufacturing cost of one plane is:

$m(1)=20-5+0.01$

$=\$15.01 M$

maximum profit $=\$(30.91-15.01)M$

$=\$15.90M$

3 0

3 years ago

Suppose that a recent article stated that the mean time spent in jail by a first-time convicted burglar is 2.5 years. A study wa

Sladkaya [172]

Answer:

The null hypothesis is $H_0: \mu = 2.5$ .

The alternative hypothesis is $H_1: \mu > 2.5$

Step-by-step explanation:

Suppose that a recent article stated that the mean time spent in jail by a first-time convicted burglar is 2.5 years.

At the null hypothesis, we test if the mean is of 2.5 years, that is:

$H_0: \mu = 2.5$

A study was then done to see if the mean time has increased in the new century.

At the alternative hypothesis, we test if the mean has increased, that is, if it is above 2.5 years. So

$H_1: \mu > 2.5$

8 0

3 years ago

Help help help help help

Mkey [24]

Answer:

x = 42

Step-by-step explanation:

The marked angles are supplementary, so their sum is 180°.

(2x +8) +(2x +4) = 180

4x +12 = 180 . . . . . . . . . simplify

x +3 = 45 . . . . . . . divide by 4 (because we can)

x = 42 . . . . . . subtract 3

_____

<em>Additional comment</em>

A "two-step" linear equation like this one is usually solved by subtracting the unwanted constant, then dividing by the coefficient of the variable. Here, we have done those steps in reverse order. This makes the numbers smaller and eliminates the coefficient of the variable. Sometimes I find it easier to solve the equation this way.

5 0

2 years ago

Which equation is equivalent to x + x - (-3) = 12?

Bogdan [553]

Answer:

C.) 2x+3 = 12

Step-by-step explanation:

x+x=2x

2x-(-3) is 2x+3

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3 0

3 years ago

6 + 4/6 show all work

zvonat [6]

To answer, change the 6 into a fraction

6 x 6/6 = 36/6

36/6 + 4/6 = 40/6

Simplify

40/6 = 6 4/6, or 6 2/3 (simplified)

hope this helps

6 0

3 years ago

Read 2 more answers