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2 years ago

11

Please help!!!

1 answer:

sweet [91]2 years ago

4 0

Answer:

<u>A</u> He should ask his students to know what they prefer

Step-by-step explanation:

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Solve using quadratic formula for 2x^(2)-10x+5=0

sergij07 [2.7K]

Answer:

$x=\frac{5+\sqrt{15}}{2},\:x=\frac{5-\sqrt{15}}{2}$

Step-by-step explanation:

$\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}$

$x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\mathrm{For\:}\quad a=2,\:b=-10,\:c=5$

$x_{1,\:2}=\frac{-\left(-10\right)\pm \sqrt{\left(-10\right)^2-4\cdot \:2\cdot \:5}}{2\cdot \:2}$

$\sqrt{\left(-10\right)^2-4\cdot \:2\cdot \:5}$

Apply exponent rule: (-a)^n=a^n, if n is even

$\left(-10\right)^2=10^2$

$=\sqrt{10^2-4\cdot \:2\cdot \:5}$

$\mathrm{Multiply\:the\:numbers:}\:4\cdot \:2\cdot \:5=40$

$=\sqrt{10^2-40}$

$10^2=100$

$=\sqrt{100-40}$

$\mathrm{Subtract\:the\:numbers:}\:100-40=60$

$=\sqrt{60}$

$60\:\mathrm{divides\:by}\:2\quad \:60=30\cdot \:2$

$=2\cdot \:30$

$30\:\mathrm{divides\:by}\:2\quad \:30=15\cdot \:2$

$=2\cdot \:2\cdot \:15$

$15\:\mathrm{divides\:by}\:3\quad \:15=5\cdot \:3$

$=2\cdot \:2\cdot \:3\cdot \:5$

$2,\:3,\:5\mathrm{\:are\:all\:prime\:numbers,\:therefore\:no\:further\:factorization\:is\:possible}$

$=2\cdot \:2\cdot \:3\cdot \:5$

$=2^2\cdot \:3\cdot \:5$

$=\sqrt{2^2\cdot \:3\cdot \:5}$

Apply Radical Rule:

$=\sqrt{2^2}\sqrt{3\cdot \:5}$

Apply Radical Rule:

$\sqrt{2^2}=2$

$=2\sqrt{3\cdot \:5}$

$\mathrm{Refine}$

$=2\sqrt{15}$

$x_{1,\:2}=\frac{-\left(-10\right)\pm \:2\sqrt{15}}{2\cdot \:2}$

$\mathrm{Separate\:the\:solutions}$

$x_1=\frac{-\left(-10\right)+2\sqrt{15}}{2\cdot \:2},\:x_2=\frac{-\left(-10\right)-2\sqrt{15}}{2\cdot \:2}$

$\frac{-\left(-10\right)+2\sqrt{15}}{2\cdot \:2}$

Apply Rule -(-a)=a

$=\frac{10+2\sqrt{15}}{2\cdot \:2}$

$\mathrm{Multiply\:the\:numbers:}\:2\cdot \:2=4$

$=\frac{10+2\sqrt{15}}{4}$

$=\frac{2\left(5+\sqrt{15}\right)}{4}$

$\mathrm{Cancel\:the\:common\:factor:}\:2$

$=\frac{5+\sqrt{15}}{2}$

$\frac{-\left(-10\right)-2\sqrt{15}}{2\cdot \:2}$

$=\frac{10-2\sqrt{15}}{2\cdot \:2}$

$\mathrm{Multiply\:the\:numbers:}\:2\cdot \:2=4$

$=\frac{10-2\sqrt{15}}{4}$

$=\frac{2\left(5-\sqrt{15}\right)}{4}$

$\mathrm{Cancel\:the\:common\:factor:}\:2$

$=\frac{5-\sqrt{15}}{2}$

$\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}$

$x=\frac{5+\sqrt{15}}{2},\:x=\frac{5-\sqrt{15}}{2}$

8 0

2 years ago

The table shows the temperatures in degrees Celsius, y, inside a shed at x hours past noon. The maximum and minimum temperatures

kolbaska11 [484]

Answer:

B

y = 3 cos (pi/12x - pi/4) + 17

Step-by-step explanation:

First find the average temperature which is 20 + 14/2 = 17

Find the amplitude

20 - 17 = 3

This means that that at noon, the shift is 3hrs past

the best equation that represents this scenario is $y = 3 cos (\frac{\pi}{12}x - \frac{\pi}{4}) + 17$

5 0

2 years ago

Hunter-Best [27]

Answer:

It would b A

Step-by-step explanation:

7 0

3 years ago

A 20 ft flag pole casts a shadow 32 ft long. What is the angle of elevation of the sun?

Nookie1986 [14]

Answer:

<em>The angle of elevation of the sun is 32°</em>

Step-by-step explanation:

<u>Right Triangles</u>

The flagpole and the ground form a right angle (90°). In triangles with right angles, the trigonometric ratios are satisfied.

Each acute angle has an adjacent leg and an opposite leg. The tangent ratio relates to both legs.

$\displaystyle \tan x=\frac{\text{opposite leg}}{\text{adjacent leg}}$

The opposite leg to angle x is 20 ft and the adjacent leg is 32 ft, thus:

$\displaystyle \tan x=\frac{20}{32}=0.625$

Calculate x by using the inverse tangent:

$x=\arctan 0.625$

$x=32^\circ$

The angle of elevation of the sun is 32°

7 0

3 years ago

What is: 5x + x - 3 = 9

Allisa [31]

5x+x-3=9

6x-3=9

cancel out 3 3+3 9+3

6x=12 divide six by 6 and by 12 too.

x=12/6=2

x=2

8 0

3 years ago

Read 2 more answers