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3 years ago

Please help me almost done

Mathematics

1 answer:

Gnom [1K]3 years ago

3 0

Answer:

x = -8

<XCE = 30

Step-by-step explanation:

Remark

In any question like this, there are 8 possible answers. Of the 8, 4 are acute angles and 4 are obtuse. So any pair are either equal to each other, or they are supplementary. In this case the two given angles are equal.

We have a little bit of both in this question.

Solution

3x + 174 = - 7x + 94 Alternate exterior angles. Add 7x to both sides.

3x+7x +174 = 94 Combine

10x + 174 = 94 Subtract 174 from both sides

10x = 94 - 174

10x = - 80 Divide by 10

x = - 80/10

x = - 8

===================

Check

3x + 174 = -24 + 174 = 150

-7x + 94 = -7*-8 + 94

-7x + 94 = 56 + 94 = 150

<XCE

<XCE = 180 - (3x + 174)

<XCE = 180 - (-24 + 174)

<XCE = 180 - (150)

<XCE = 30

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Please help me out I really can’t afford failing this test

Blizzard [7]

Answer:

I'm not really sure but I think it's 2

Step-by-step explanation:

So here's what I did;

x³+3x-9=x - 1 +2x

x³+3x - x -2x = 9 - 1

x³= 8

x = ³√8

x = 2

I hope this helps

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3 years ago

Which one is greater 0.02 or 0.002

Scrat [10]

Answer:

0.02

Step-by-step explanation:

As you can see 0.002 has another 0 behind the decimal point, since this is the case 0.02 is greater. :)

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4 years ago

Read 2 more answers

Find the critical points of the surface f(x, y) = x3 - 6xy + y3 and determine their nature.

Vedmedyk [2.9K]

Compute the gradient of $f$ .

$\nabla f(x,y) = \left\langle 3x^2 - 6y, -6x + 3y^2\right\rangle$

Set this equal to the zero vector and solve for the critical points.

$3x^2-6y = 0 \implies x^2 = 2y$

$-6x+3y^2=0 \implies y^2 = 2x \implies y = \pm\sqrt{2x}$

$\implies x^2 = \pm2\sqrt{2x}$

$\implies x^4 = 8x$

$\implies x^4 - 8x = 0$

$\implies x (x-2) (x^2 + 2x + 4) = 0$

$\implies x = 0 \text{ or } x-2 = 0 \text{ or } x^2 + 2x + 4 = 0$

$\implies x = 0 \text{ or } x = 2 \text{ or } (x+1)^2 + 3 = 0$

The last case has no real solution, so we can ignore it.

Now,

$x=0 \implies 0^2 = 2y \implies y=0$

$x=2 \implies 2^2 = 2y \implies y=2$

so we have two critical points (0, 0) and (2, 2).

Compute the Hessian matrix (i.e. Jacobian of the gradient).

$H(x,y) = \begin{bmatrix} 6x & -6 \\ -6 & 6y \end{bmatrix}$

Check the sign of the determinant of the Hessian at each of the critical points.

$\det H(0,0) = \begin{vmatrix} 0 & -6 \\ -6 & 0 \end{vmatrix} = -36 < 0$

which indicates a saddle point at (0, 0);

$\det H(2,2) = \begin{vmatrix} 12 & -6 \\ -6 & 12 \end{vmatrix} = 108 > 0$

We also have $f_{xx}(2,2) = 12 > 0$ , which together indicate a local minimum at (2, 2).

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2 years ago

I need help with solving isosceles and equilateral triangles

Scilla [17]

Answer:

60º

Step-by-step explanation:

The interior angles of a triangle equals 180º. And 60+60+60=180, that is your answer.

3 0

2 years ago

Delta makes 12-volt car batteries. These batteries are known to be normally

blondinia [14]

Answer:

The probability that Delta car batteries last between three and four years

P(36≤X≤48) = 0.5188

The percentage of that Delta car batteries last between three and four years

P(3≤X≤4) = 52%

Step-by-step explanation:

Step(i):-

Given that the sample size n =12 -volt car batteries

Let 'X' be a Random variable in a normal distribution

Given that mean of the normal distribution = 45 months

Given that the Standard deviation of the normal distribution = 8months

Step(ii):-

Let X₁ = 3 years = 12 × 3 = 36 months

$Z_{1} = \frac{x_{1} -mean}{S.D} = \frac{36-45}{8} = -1.125$

Let X₂ = 4 years = 12 × 4 = 48 months

$Z_{2} = \frac{x_{2} -mean}{S.D} = \frac{48-45}{8} = 0.375$

Step(iii):-

The probability that Delta car batteries last between three and four years

P(36≤X≤48) = P(-1.125≤Z≤0.375)

= P(Z≤0.375) - P(Z≤-1.125)

= 0.5 +A(0.375) - (0.5-A(1.125)

= 0.5 + 0.1480 - (0.5 -0.3708)

= 0.1480 + 0.3708

= 0.5188

Final answer:-

The probability that Delta car batteries last between three and four years

P(36≤X≤48) = 0.5188

The percentage of that Delta car batteries last between three and four years

P(3≤X≤4) = 52%

5 0

3 years ago