Quesdon 8 of 10
Which of the following is a polynomial?

Answer:

[tex]x=2\\x=-\frac{1}{2}[/tex]

Step-by-step explanation:

1) Move terms to the left side.

[tex]3x=2x^{2} -2\\3x-(2x^{2}-2)=0[/tex]

2) Distribute.

[tex]3x-(2x^{2} -2)=0\\3x-2x^{2} +2=0[/tex]

3) Rearrange terms.

[tex]3x-2x^{2} +2=0\\-2x^{2} +3x+2=0[/tex]

4) Common factor.

[tex]-2x^{2} +3x+2=0\\-(2x^{2} -3x-2)=0[/tex]

5) Divide both sides of the equation by the same term.

[tex]-(2x^{2} -3x-2)=0\\2x^{2} -3x-2=0[/tex]

6) Use the quadratic formula.

[tex]x=\frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex]

Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.

[tex]2x^{2} -3x-2=0\\a=2\\b=-3\\c=-2[/tex]

[tex]x=\frac{-(-3)+\sqrt{(-3)^{2} -4*2(-2)} }{2*2}[/tex]

7) Simplify.

Evaluate the exponent

[tex]x=\frac{3+\sqrt{(-3)^{2}-4*2(-2) } }{2*2}[/tex]

[tex]x=\frac{3+\sqrt{9-4*2(-2)} }{2*2}[/tex]

Multiply the numbers

[tex]x=\frac{3+\sqrt{9-4*2(-2)} }{2*2}[/tex]

[tex]x=\frac{3+\sqrt{9+16} }{2*2}[/tex]

Add the numbers

[tex]x=\frac{3+\sqrt{9+16} }{2*2}[/tex]

[tex]x=\frac{3+\sqrt{25} }{2*2}[/tex]

Evaluate the square root

[tex]x=\frac{3+\sqrt{25} }{2*2} \\x=\frac{3+5}{2*2}[/tex]

Multiply the numbers

[tex]x=\frac{3+5}{2*2}[/tex]

[tex]x=\frac{3+5}{4}[/tex]

8) Seperate the equations.

To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.

[tex]x=\frac{3+5}{4}[/tex]

[tex]x=\frac{3-5}{4}[/tex]

9) Solve.

Rearrange and isolate the variable to find each solution.

[tex]x=2\\x=-\frac{1}{2}[/tex]

Answer:

227 sides

Step-by-step explanation:

The sum of the interior angles of a convex polygon is S=180(n-2) where n is the number of sides. If S=40500, then we have our equation 40500=180(n-2) and we can solve for n:

40500 = 180(n-2)

225 = n-2

227 = n

Therefore, the number of sides in the regular polygon is 227.

Answer:

Step-by-step explanation:

Conclusion:

Therefore, 3/8 is the answer.

Hoped this helped.

Answer:

Letter C.

Step-by-step explanation:

Lap 1 be x

Lap 2 be y

Line graph: plot the values, and will get C.

[tex]x^2 -18x \\\\=x^2 - 2 \cdot 9x +9^2 -9^2\\\\=(x-9)^2-81[/tex]

Answer:

A. 5x² - 7 - 72 = 0

5x² - 79 = 0

x = ± √-4ac / 2a

x = ± √- 4 (5) (-79) / 2 (5)

x = ± √ 1580 / 10

x = ± 39.749/10

x = + 39.749/10 x = -39.749/10

= 3.9749 = - 3.9749

B. x² + 2x - 5 = 0

x = - b ± √b² - 4ac / 2a

= - 2 ± √2² - 4 (1) (-5) / 2 (1)

= - 2 ± √4 + 20 / 2

= - 2 ± √ 24 / 2

x = - 2 + 4.898 /2 x = - 2 - 4.898 / 2

= 2.898/2 = -6.898/2

= 1.449 = - 3.449

C. 3x² + 2x - 4 = 0

x = - b ± √b² - 4ac / 2a

= - 2 ± √2² - 4 (3) (-4) / 2 (3)

= - 2 ± √4 + 48 / 6

= - 2 ± √ 52 / 6

x = - 2 + 7.211 /6 x = - 2 - 7.211 / 6

= 5.211/6 = - 9.211 /6

= 0.869 = - 1.535

Hope that helps

Please to re-check answers

Answer:

[tex]y \leqslant -x + 1[/tex]

Step-by-step explanation:

First write the equation of the line with either inequality sign, like so:

[tex]y \geqslant -x + 1[/tex]

Then check to see if the equation is true. The easiest way to do this is to plug the coordinates (0,0) into the equation:

[tex]0 \geqslant -0 + 1 \\ 0 \geqslant 1[/tex]

Since 0 > 1 is false, you know that the correct inequality must be:

[tex]y \leqslant -x + 1[/tex]

If you want to check this, plug the coordinates (0,0) into the equation:

[tex]0 \leqslant -0 + 1 \\ 0 \leqslant 1[/tex]

Since 0 < 1 is true, you know this equation is correct.

I hope that helped! If I made a mistake, just let me know.

Answer:

(1, 4)

Step-by-step explanation:

im assuming that the point is h(1) = 4

this point is basically just h(x) = y

1 is your x

4 is your y

you plot it at the point (1, 4)

Answer:

yes

Step-by-step explanation:

Answer:

well y= mx + b

Step-by-step explanation:

it is going up by 2/5 then your answer is y =2/5+5

Answer:

Step-by-step explanation:

The time it takes to empty the tank = 85/4 + 0.25 = 21.25 minutes.

- because it takes 21 minutes  to empty 84 gallons and the last gallon takes

1/4 of a minute.

The slash is an oblique slanting line punctuation mark /. Once used to mark periods and commas, the slash is now most often used to represent exclusive or inclusive or, division and fractions, and as a date separator.

Note that √(4 - t²) is defined only as long as 4 - t² ≥ 0, or -2 ≤ t ≤ 2. Then the real integral exists only if -2 ≤ x ≤ 2. (Otherwise we deal with complex numbers.)

If x = 2, then the integral corresponds to the area of a quarter-circle with radius 2. This means that the integral has a maximum value of 1/4 • π • 2² = π.

On the opposite end, if x = -2, then the integral has the same value, but the integral from 0 to -2 is equal to the negative integral from -2 to 0. So the minimum value is -π.

For all x in between, we observe that the integrand is continuous over the rest of its domain, so F(x) is continuous.

Then the range of F(x) is the interval [-π, π].

Answer:

y-2 = -11 (x-5)

Step-by-step explanation:

2 is the y value of the point, 5 is the x value and -11 is the m value.

Slope point form: y-y1 = m(x-x1)

Hope that helps

Answer:

The temperature of the liquid 15 minutes later is [tex]151.5[/tex]

Step-by-step explanation:

This is an example of arithmetic progression

We need to find 15 th term

Here

[tex]a=200.5\\\\d=-3.5\\\\t_{15}=200.5+(15-1)\times-3.5\\\\=151.5[/tex]

Answer:

(7,-2)

Step-by-step explanation:

Answer:

(7, - 2 )

Step-by-step explanation:

x - y = 9 ( add y to both sides )

x = y + 9 → (1)

2x + 5y = 4 → (2)

Substitute x = y + 9 into (2)

2(y + 9) + 5y = 4 ← distribute parenthesis and simplify left side

2y + 18 + 5y = 4

7y + 18 = 4 ( subtract 18 from both sides )

7y = - 14 ( divide both sides by 7 )

y = - 2

Substitute y = - 2 into (1)

x = - 2 + 9 = 7

solution is (7, - 2 )

Answer:

(8, 17)

Step-by-step explanation:

y = 3x - 7,  y = 2x + 1

Substitute the second equation into the first for y.

2x + 1 = 3x - 7

8 = x

Now use 8 for x in one of the equations and solve for y.

2(8) + 1 = y

y = 17

(8, 17)

Answer:

1.2 cups

Step-by-step explanation:

6 cups / 5 batches = 1.2 cups/batch

Answer:

Step-by-step explanation:

fff

Answer:

25

Step-by-step explanation:

Answer:

$18,000.

Step-by-step explanation:

When their weekly pay is the same:

185 + 0.03x =  275 + 0.025x

0.03x - 0.025x =  275 - 185

0.005x = 90

x =90/0.005

x = 18,000

Answer:

a^2+b^2=c^2

C=7

b=?

a=4

LET B=x =

[tex] \sqrt{65 } [/tex]

Answer:

0.01

Step-by-step explanation:

i hope this help only that u need to do next time is to divide 966 with a number that is close to the sum