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3 years ago

Solve |x| – 17 = 60 What is the correct answer

Mathematics

2 answers:

belka [17]3 years ago

6 0

Answer:

x=77

Step-by-step explanation:

Hope this helps!!!!

Kazeer [188]3 years ago

4 0

Answer:

x = 77, x = -77

Step-by-step explanation:

|x| – 17 = 60

Add 17 to each side

|x| – 17+17 = 60+17

|x| = 77

The absolute value equation has two solutions, one positive and one negative

x = 77, x = -77

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Triangle DEF is a right triangle. Angle F is a right angle and m∠E=29°.<br><br> What is m∠D?

Aleksandr-060686 [28]

All triangles have 180o in them when the 3 angles making them up are added together.

Givens

F = 90

E = 29

D = ???

Equation

<D + <E + <F = 180

Substitute and solve

<D + 90 + 29 = 180

<D + 119 = 180

<D = 180 - 119

<D = 61

5 0

3 years ago

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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 $=\$(30.91-15.01)M$

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3 0

3 years ago

Factor sec^2x-secx+tan^2x

marysya [2.9K]

Answer:

sec²(x) - sec(x) + tan²(x) = (sec(x) - 1)(2sec(x) + 1)

Step-by-step explanation:

sec²(x) - sec(x) + tan²(x) =

= sec²(x) - sec(x) + [sec²(x) - 1]

= sec²(x) - sec(x) + [(sec(x) + 1)(sec(x) - 1)]

= sec(x)[sec(x) - 1] + [(sec(x) + 1)(sec(x) - 1)]

= (sec(x) - 1)(sec(x) + sec(x) + 1)

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

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3 years ago

An angle is 6 more than five times its supplement. Find the measure of the largest angle.

Julli [10]

Supplementary angles add up to 180°

Angle y is the large angle: y= 5x+6

180= x+y
180= (5x+6) + x
180=6x+6
174=6x
x=29

180= y+29
y=151°

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3 years ago

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Nataly [62]

Answer:

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Step-by-step explanation:

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3 years ago

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