x² + 8x = 10 solve this quadratic equation by completing the square

[tex]\text{L.H.S}\\\\=\cot^2 \dfrac{\pi}6 -2\cos^2 \dfrac{\pi}{3}-\dfrac 34 \sec^2 \dfrac{\pi}4-4\sec^2 \dfrac{\pi}6\\\\\\=\cot^2 30^\circ -2 \cos^2 60^\circ- \dfrac 34 \sec^2 45^{\circ} -4 \sec^2 30^{\circ}~~~~~~~;[\pi= 180^{\circ}]\\\\\\=\left(\sqrt 3 \right)^2 -2 \left( \dfrac 12 \right)^2 -\dfrac 34 \left(\sqrt 2 \right)^2 -4 \left(\dfrac 2{\sqrt 3} \right)^2\\\\\\=3-2 \cdot \dfrac 14 - \dfrac 34 \cdot 2 -4 \cdot \dfrac 43\\ \\\\=3-\dfrac 12-\dfrac 32 - \dfrac{16}3\\\\\\[/tex]

[tex]\\=\dfrac{9-16} 3 - \dfrac 42 \\\\\\=\dfrac{-7}{3}-2\\\\\\=\dfrac{-7-6}3\\\\\\=-\dfrac{13}3\\\\\\=-4\dfrac 13 \\\\\\=\text{R.H.S}\\\\\\\text{Proved.}[/tex]

There are 43 small dogs signed up in the competition

Represent the small dogs with x and the large dogs with y.

So, we have the following equations

x + y = 50

x = 36 + y

Make y the subject in x = 36 + y

y = x - 36

Substitute y = x - 36 in x + y = 50

x + x - 36 = 50

Evaluate the like terms

2x = 86

Divide both sides by 2

x = 43

Hence, there are 43 small dogs in the competition

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First product

Second and final product

Answer:

Given polynomials

The product of the given polynomials:

[tex]\begin{aligned}(2ab+b)(a^2-b^2) & = 2ab(a^2-b^2)+b(a^2-b^2)\\& = 2a^3b-2ab^3+a^2b-b^3\end{aligned}[/tex]

The product of the given polynomials multiplied by [tex](2a+b)[/tex]:

[tex]\begin{aligned}(2a+b)(2a^3b-2ab^3+a^2b-b^3) & = 2a(2a^3b-2ab^3+a^2b-b^3)+b(2a^3b-2ab^3+a^2b-b^3)\\& = 4a^4b-4a^2b^3+2a^3b-2ab^3+2a^3b^2-2ab^4+a^2b^2-b^4\\& = 4a^4b+2a^3b^2-4a^2b^3-2ab^4+2a^3b+a^2b^2-2ab^3-b^4\end{aligned}[/tex]

Therefore, the resulting polynomial has 8 terms.

Answer:

13.3 km/h

Step-by-step explanation:

getting the neutral is adding both the hours and distance, after adding them you can then dicixe the distance by the time getting your average speed (the upstream is what balances the downstream)

Answer:

[tex]\tan \theta = \dfrac{8}{15}[/tex]

Step by step explanation:

[tex]\text{Given that,}\\\\~~~~~~~\sin \theta = \dfrac{8}{17}\\\\\implies \sin^2 \theta = \dfrac{64}{289}\\\\\implies 1-\cos^2 \theta = \dfrac{64}{289}\\\\\implies \cos^2 \theta = 1-\dfrac{64}{289}\\\\\implies \cos^2 \theta = \dfrac{225}{289}\\\\\implies \cos \theta =\pm\sqrt{\dfrac{225}{289}}\\\\\implies \cos \theta = \pm\dfrac{15}{17}[/tex]

[tex]\text{In quadrant I, all ratios are positive, so,}~ \cos \theta = \dfrac{15}{17}\\\\\text{Now,}\\\\\tan \theta = \dfrac{\sin \theta }{\cos \theta}\\\\\\~~~~~~~~=\dfrac{\tfrac{8}{17}}{\tfrac{15}{17}}\\\\\\~~~~~~~~=\dfrac{8}{17} \times \dfrac{17}{15}\\\\\\~~~~~~~=\dfrac{8}{15}[/tex]

Answer: C

Step-by-step explanation: I know it trust me

Answer:

16 less than two times a number "x"

The solution of the inequality  3-x/2≥12 is x≤-18

a relationship between two expressions or values that are not equal to each other is called 'inequality.

The given inequality is 3-x/2≥12

Three minus x by two greater than or equal to twelve

Subtract 3 from both sides

-x/2≥9

-x≥18

x≤-18

Hence, the solution of the inequality  3-x/2≥12 is x≤-18

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Inequalities help us to compare two unequal expressions.  The inequality that represents losing more than 500 points is x<-500.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.

It is mostly denoted by the symbol <, >, ≤, and ≥.

Given In a computer game positive numbers represent earning points and negative numbers represent losing points. Therefore, the loss of more than 500 points is given by the inequality,

x< -500

Hence, the inequality that represents losing more than 500 points is x<-500.

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Answer:

Vertex(1,7)

Vertex form: [tex]f(x)=-2\left(x-1\right)^2+7[/tex]

Step-by-step explanation:

Vertex form equations for x is [tex]v=-\frac{b}{2a}[/tex]

which the vertex here is

[tex]-\frac{4}{2\left(-2\right)}[/tex]

->

x = 1, plugin to find y, y = 7

Answer:

y=3

Step-by-step explanation:

y=mx+b where m = slope and b=y-intercept
slope: 0, y-intercept: 3

y=(0)x + 3

y=3

Answer:

[tex]\left(12x^5-3x^1+2x-5\right)+\left(8x^1-3x^3+4x+1\right)[/tex]

=> Expand

[tex]12x^5-3x^1+2x-5+8x^1-3x^3+4x+1[/tex]

=> simplify and group like terms

[tex]12x^5-3x^3+5x^1+6x-4[/tex]

=> simplify further

[tex]12x^5-3x^3+11x-4[/tex]

Answer:

3.14 × 16 is 18,84

Method in picture

[tex]{\color{aqua}{\boxed{\mathfrak{LordKeyarga23}}\:}}[/tex]

The value of the multiplication of the numbers 3.14 and 16 will be 50.24.

Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.

The numbers are given below.

3.14 and 16

Then the multiplication of the numbers 3.14 and 16 will be given by putting a cross sign between them. Then we have

⇒ 3.14 x 16

⇒ 50.24

The value of the multiplication of the numbers 3.14 and 16 will be 50.24.

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An irrational number is the square root of 5 since it cannot be written as a ratio of two integers.

Irrational numbers are number that cannot be written as a ratio of two integers.

Most irrational numbers are repeating decimals. From the given options, an irrational number is the square root of 5 since it cannot be written as a ratio of two integers.

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Answer:

The choice A.

[tex]y > \frac{3}{2} x + 2[/tex]

Answer:

Exact Form:−2/3

Decimal Form:−0.666…

Step-by-step explanation:

Hello, the answer of each option is given below.

Good luck! These are four-operation-equations. We should calculate by our hand or try to use calculator to get the result. Anyway, If you have any question(s), then feel free to ask in comments!

The slope of the linear equation, y = -9x - 8 is determined as: -9.

If the equation of a line is given in a slope-intercept form, y = mx + b, the slope value is represented as m.

Thus, given the equation y = -9x - 8, the slope in the linear equation is -9.

Therefore, slope of y = -9x - 8 is: -9.

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Step-by-step explanation:

you must do it by step

Solution ,

here,

x+32=180 [Sum of straight angle]

x=180 - 32

x=148

ans

The graph that shows the solution set for the system of inequalities is graph C.

Here we have the system of linear inequalities:

[tex]y < (-1/3)*x + 1\\\\y \geq 2x- 1[/tex]

For the first one, we can see a line with a negative slope, and y is strictly smaller than that. So we will have a dashed line that goes down, and we need to shade the region below that line.

For the second inequality, we can see that y can be equal to or larger than the line, so this time we will use a solid line (because the points on the line are solutions). and we will shade above that line.

Also notice that this time the slope is positive, so this line goes upwards.

With that general description, we conclude that the correct option will be graph C.

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Answer:

B.

Step-by-step explanation:

Because the point on the top on the original would still be on top so it is 100% B

Hope This Helped

Answer:

936

Step-by-step explanation:

You multiply 31.2 by 10, so you move the decimal one place to the right, so it's 312, And then, you multiply those numbers by 6 like 3, 1, and 2. For the ones digit 2 x 3 = 6,  for the tens digit, 1 x 3 = 3, and for the hundreds digit, 3 x 3 = 9. Therefore, the answer is 936!

Answer:

0.25

Step-by-step explanation:

1,800 laps ÷ 12 weeks = 150 laps

150 laps ÷ 5 days each week = 30 laps per day

30 laps per day ÷ 120 hours per week = 0.25 per hour

Answer:

  19 units

Step-by-step explanation:

A regular polygon has equal-length sides. This fact can be used to solve for the value of x, and for the side length. Knowing the side length, we can find the perimeter.

__

 5 -2x = 4x +9 . . . . . marked sides are the same length

  -4 = 6x . . . . . add 2x -9

  -2/3 = x . . . . . divide by 6

  5 -2(-2/3) = 5 +4/3 = 6 1/3 . . . . length of one side

The perimeter is the sum of the side lengths, or 3 times the length of one side.

  P = 3s = 3(6 1/3)

  P = 19 . . . . units

The perimeter of the polygon is 19 units.

Step-by-step explanation:

To answer this, we need to plug in 3 as x in the equation f(x) = 5 + 4x².

That would look like this: f(3) = 5 + 4(3)²

f(3) = 5 + 4(3)²

f(3) = 5 + 36

f(5)=41

Therefore, the answer is 41.

I hope this helps!! :)

By the quadratic formula, we find that the two zeroes of the quadratic function y = x² - 20 · x + 32 are x₁ = 10 + 2√17 and x₂ = 10 - 2√17, respectively.

A value of x is a zero of a polynomial if and only if [tex]\sum\limits_{i=0}^{n} c_{i}\cdot x^{i} = 0[/tex], the quadratic formula for second order polynomials of the form a · x² + b · x + c = 0 is presented below:

[tex]x =\frac{-b \pm \sqrt{b^{2}-4\cdot a \cdot c}}{2\cdot a}[/tex]

If we know that a = 1, b = -20 and c = 32, then the roots of the second order polynomial are:

[tex]x = \frac{20 \pm \sqrt{(-20)^{2}-4\cdot (1)\cdot (32)}}{2\cdot (1)}[/tex]

[tex]x = 10 \pm 2\sqrt{17}[/tex]

By the quadratic formula, we find that the two zeroes of the quadratic function y = x² - 20 · x + 32 are x₁ = 10 + 2√17 and x₂ = 10 - 2√17, respectively.

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Answer:

Step-by-step explanation:

-2/3 * (-1/4) =

2/3 * 1/4 =

2/12 =

1/6