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Westkost [7]
3 years ago
6

What is

Mathematics
1 answer:
Marina86 [1]3 years ago
4 0
If you multiply
63,178 by 2,741 you get a result of
173,170,898
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What substitution should be used to rewrite 4x^4-21x^2+20=0 as a quadratic function?
pogonyaev

Answer:

see explanation

Step-by-step explanation:

Let u = x² ( choice of variable is flexible ), then

4u² - 21u + 20 = 0 ← expressed as a quadratic

This can now be solved for u and converted back into terms of x

3 0
3 years ago
Read 2 more answers
Find the surface area of each figure pls 7-10
Vlad [161]

Answer:

7) 42 inches^{2}

8) 358 meters^{2}

9) 320 yards^{2}

10) 288 miles^{2}

Step-by-step explanation:

Problems 7, 8, and 10 all use the same formula: the formula for the surface area of a rectangular prism.

Formula: 2 * (lw + lh + hw)

where l = length, w = width and h = height

This is a condensed form of the sum lw + lw + lh + lh + hw + hw where each product is a face of the prism.

replace each variable in the formula above with the values given in your problems for 7, 8 and 10:

7) 2 * (3*3 + 3*2 + 2*3) = 2 * (9 + 6 + 6) = 2 (21) = 42

8) 2 * (12*7 +12*5 + 5*7) = 2 * (84 + 60 + 35) = 2(179) = 358

10) 2* (12*4 + 12*6 + 4*6) = 2 * (48 + 72 + 24) = 2(144) = 288

Now 9 is a little different, as it contains a regular pentagon. However it is not much different from the other problems as it is also a prism.

The formula for the area of any regular polygon can be in the form:

Area = \frac{1}{2}ap where the a stands for apothem (which is the distance from the center of a regular polygon to its side, in this case it is 5.5 yds) and the p is the perimeter of the polygon.

The reason for this formula involves the polygon being divided into as many congruent triangles as it has sides, but that is for another time : )

Given this formula for the area of the pentagon, you can substitute values:

Area = \frac{1}{2}(5.5)(number of sides * length of a side)

Area =  \frac{1}{2}(5.5)(5 * 8) = 110

And get that the area of the face is 110 yd^2

the rest of the faces are rather straightforward as they contain rectangles of sides 4 yds and 5 yds, and you would end up with 5 of them (for each side of the pentagon)

Therefore by adding up each of the bases and the sides, you should get:

110 + 110 + 20 + 20 + 20 + 20 + 20 = 320

Hope that helped : )

3 0
3 years ago
Determine area under the standard normal curve given the z score, z less than 1.25
FromTheMoon [43]

Answer:

0.8944

Step-by-step explanation:

Use a calculator or table.

Using a z-score table:

P(z < 1.25) = 0.8944

7 0
3 years ago
Does the function g(x) = -2x2 + 10x + 2 have a minimum or a maximum? Identify its value.<br> +
Hitman42 [59]

Answer:

(5/2, 29/2), and this represents a maximum

Step-by-step explanation:

g(x) = -2x^2 + 10x + 2 is a quadratic function with coefficients {-2, 10, 2}.

The formula for the axis of symmetry (which passes through the vertex) is

x = -b/ [2a].  Here, a = -2; b = 10.  Therefore, the axis of symmetry is

x = -10/ [2(-2)] = -10/(-4) = 5/2

Evaluate the function g(x) = -2x^2 + 10x + 2 at x = 5/2 to determine the y-coordinate of the vertex:

g(5/2) = -2(5/2)^2 + 10(5/2) + 2, or

g(5/2) = -2(25/4) + 25 + 2, or

g(5/2) = -25/2 + 27, or

g(5/2) = 14.5

The vertex is thus (5/2, 29/2), and this represents a maximum, because the coefficient of the x^2 term is negative (the curve opens downward).

3 0
3 years ago
Help please, need to show work.
stiks02 [169]

9514 1404 393

Answer:

  3.  m∠A < 80°

Step-by-step explanation:

The exterior angle NGS, marked as 80°, has a measure that is the sum of the measures of the remote interior angles: GAN, GNA.

If we assume that angle measures cannot be zero, then we must have ...

  m∠A +m∠N = 80°

  m∠A = 80° -m∠N

Since m∠N > 0, the measure of angle A must be less than 80°.

This conclusion matches choice 3.

8 0
2 years ago
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