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3 years ago

Four more than twice a number is -10

Mathematics

2 answers:

Anna [14]3 years ago

7 0

Answer:

-7

Step-by-step explanation:

Fantom [35]3 years ago

4 0

Answer: the twice a number would be -3 x2 =-6 plus the four -10

Step-by-step explanation:

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krek1111 [17]

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Peyton is altering her new jacket to enter it into the Bodacious Bedazzling Contest. In order for a garment to be considered "be

horrorfan [7]

248 to 370 gems
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3 years ago

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Centerville is the headquarters of Greedy Cablevision Inc. The cable company is about to expand service to two nearby towns, Spr

NeX [460]

Answer:

20.2057 Units.

Step-by-step explanation:

First, we determine the length of the cable.

Distance between Centerville (8,0) and point (x,0) is given as:

$\sqrt{(8-x)}^2=8-x$

Distance between point (x,0) and Springfield(0,7) is:

$\sqrt{(7-0)^2+(0-x)^{2}}=\sqrt{(7)^2+(x)^{2}}$

Distance between point (x,0) and Shelvyfield(0,-7) is:

$\sqrt{(-7-0)^2+(0-x)^{2}}=\sqrt{(7)^2+(x)^{2}}$

Therefore the Length of the Cable L(x)

$L(x)=(8-x)+2\sqrt{(7)^2+(x)^{2}}$

To find the critical point, we set the derivative of L(x)=0

$L^{'}(x)=-1+\frac{2x}{\sqrt{\left( 49 - x^{2}\right) }}$

$\frac{-\sqrt{\left( 49 - x^{2}\right)}+2x}{\sqrt{\left( 49 - x^{2}\right)}}=0\\-\sqrt{\left( 49 - x^{2}\right)}+2x=0\\\sqrt{\left( 49 - x^{2}\right)}=2x\\(\sqrt{\left( 49 - x^{2}\right)})^2=(2x)^2\\49 - x^{2}=4x^2\\49=5x^2\\x^2=\frac{49}{5}\\x= 3.1305$

To verify that L(x) has a minimum at this critical number we compute the second derivative L″(x) and find its value at the critical number.

$L^{''}(x)=\frac{\left( 98\right) \,\sqrt{\left( 49 - x^{2}\right) }}{{\left( 7 - x\right) }^{2}\,{\left( 7+x\right) }^{2}}\\At \:x=3.1305, L^{''}=0.3993$

Since $L^{''}(x)$ is positive, the minimum point of L(x) exists.

Next, we find the minimum length by substituting z=3.1305 into L(x)

$L(3.1305)=(8-3.1305)+2\sqrt{(7)^2+(3.1305)^{2}}$

Minimum Length, L=20.2057

The minimum length of the cable is 20.2057 Units.

6 0

3 years ago

Which functions are equivalent to f (x) = RootIndex 4 StartRoot 162 EndRoot Superscript x? Check all that apply.

Delvig [45]

Answer:

1,3,5

Step-by-step explanation:

5 0

3 years ago

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The vertex of this parabola is at (4, -3). When the x-value is 5, the

NeTakaya

Parabola equation with a vertex at (h, k) is given by y = a(x - h)^2 + k
For the give parabola, y = a(x - 4)^2 - 3
y = a(x^2 - 8x + 16) - 3
At (5, -6)
-6 = a((5)^2 - 8(5) + 16) - 3 = a(25 - 40 + 16) - 3 = a - 3
a = -6 + 3 = -3

Therefore, the coefficient of the squared expression is -3.

3 0

3 years ago