Divide using long division or synthetic division:

(10x^3-x^2-29x-30)/(x^2-x-2)

For the given sides AB and BC the angle included would always be Angle B

When we form a triangle we name the vertex as A, B and C. So, the sides AB and BC will always have an Angle B regardless of the naming convention we use.

A triangle is a polygon with three vertices and three edges that has three sides. It is a basic geometric shape. The term "abc" refers to a triangle containing the vertices a, b, and c. Any three non-collinear points in Euclidean geometry combine to create a singular triangle and a singular plane.

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Answer:

umber is greater than or equal to 15.

Step-by-step explanation:

Let number be x

Quotient of number and 3 =

4 more than = 4+

4+ is at least 9

4+≥9

Simplifying it ,we get

≥9-4

≥5

x ≥ 5(3)

x≥15

Number needs to be greater than or equal to 15

    Equation

(x ÷ 3) + 4 ≥ 9

___________

    Solution

x ≥ 15

Step-by-step explanation:

Solve the inequality

[tex]\left(x\div3\right)+4\ge \:9\\x\div 3+4-4\ge \:9-4\\x\div 3\ge \:5\\3x\div 3\ge \:5\cdot \:3\\x\ge \:15[/tex]

Thus, the inequality solution is x ≥ 15

Answer:

[tex]a_1 = 1\\d = 3[/tex]

Step-by-step explanation:

The nth term of an arithmetic progression is [tex]a_n = a_1 + (n - 1)d[/tex].
You are given that [tex]a_5 = 13[/tex] and [tex]a_{11} = 31[/tex].

Therefore, we can solve the following system of equations to get the first term, as well as the difference.

[tex]-\begin{cases}a_1 + 4d = 13\\a_1 + 10d = 31\end{cases}\\\\\to 6d = 18\\\to d = 3\\\\\text{Substitute d = 3 into one of the equations to find }a_1\text{:}\\a_1 + 4 \times 3 = 13\\a_1 + 12 = 13\\\to a_1 = 1[/tex]

Answer:

the coefficient is 5 and 7 the constant is 2

Answer:

Parallel

Step-by-step explanation:

The correct option is D). The element is sodium, and it is highly reactive.

The atomic number of the element sodium (Na) is 11. It means that the sodium has 11 protons in total and because it is neutral it has 11 number of electrons.

Valence electrons (VE) refers to the electrons that usually presents in the outer shell of an atom. Thus, the sodium has only 1 valence electron.

Basically, the mass number of an element tells about the number of protons and neutrons in an atom and sodium is the atom that has 11 atomic number.

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Complete question:- The atoms of a certain element each contain 11 protons and 1 valence electron. Which statement correctly identifies this element and describes its chemical reactivity?

A The element is sodium, and it is highly reactive.

B The element is fluorine, and it is not very reactive.

C The element is sodium, and it is not very reactive.

D The element is fluorine, and it is highly reactive.

Answer:

6/11

Step-by-step explanation:

3/11 + 3/11

to add both of the fractions just add the numerators (the numbers on the top) and u dont needa add the denominators which is the numbers on the bottom

that makes the answer 6/11 and u cant rlly simplify it so try that.

If its wrong mb

Answer:

A) [tex] \sf \frac{3}{11} + \frac{3}{11} = \frac{6}{11} [/tex]

B) [tex] \sf \frac{9}{10} + \frac{3}{5} = 1 \frac{1}{2}[/tex]

There will be 2 roots of the equation 2 ( [tex]x^{2}[/tex] ) + 3 x = - 4 .

2 ( [tex]x^{2}[/tex] ) + 3 x = - 4 is a quadratic equation . This is because it has degree 2  . Degree is the power of variable which is maximum in function .

Since , x is the variable in this equation , therefore it's degree is 2 .

The no . of roots a polynomial will have is equal to the degree of polynomial .

Hence , the eq . will have 2 real roots .

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Answer:

I think the constraint of proportionality is 25 because each dot it increases buy 25.

I also believe that at 10 the total should be at 225.

Answer:

Since 30% of 100 ml = .3*100 = 30 ml

60 % of X ml = .6x which we are trying to solve

add

(X+100).36 = 30+.6x

.36x+36 = 30+.6x

so

6 = .24x

x = 25 ml

Step-by-step explanation:

I hope this helps you

The solution to question 8, in scientific notation is  9.563 x 10¹¹.

The solution to question 9, in scientific notation is  9.83 x 10⁸.

The solution to question 10, in scientific notation is 1.35759 x 10⁹.

The solution to question 11, in scientific notation is  8.70366 x 10⁴.

Scientific notation is a form of presenting very large numbers or very small numbers in a simpler form.

(9.5 x 10¹¹) + (6.3 x 10⁹)

= (950 x 10⁹) + (6.3 x 10⁹)

= (950 + 6.3) x 10⁹

= 956.3 x 10⁹

= 9.563 x 10¹¹

(1.03 x 10⁹) - (4.7 x 10⁷)

= (103 - 4.7) x 10⁷

= 98.3 x 10⁷

= 9.83 x 10⁸

(1.357 x 10⁹) + 590,000

= (1.357 x 10⁹) + (5.9 x 10⁵)

= (13570 x 10⁵) + (5.9 x 10⁵)

= (13570 + 5.9) x 10⁵

= 13,575.9 x 10⁵

= 1.35759 x 10⁹

87,100 - (6.34 x 10¹)

= 87,100 - 63.4

= 87,036.6

= 8.70366 x 10⁴

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Answer:

0.75

Step-by-step explanation:

1. distribute the 2 into the perenthesis

2. combine like terms

3. simplify on both sides

Answer:

x + y = 29   equation 1 

Five more than means add 5+5 three times the smaller number:

 3x equals the larger number:  = y 3x + 5 = y    equation 2

 From equation 1x + y = 29subtract x from both sidesy = 29 - x 

We now have two things that are both equal tothe larger number y.

  They must be equal to each other. 
3x + 5 = 29 - x

 Add x to both sides 3x + x + 5 = 29 - x + x4x + 5 = 29

subtract 5 from both sides 4x + 5 - 5 = 29 - 54x = 24

divide both sides by 44x/4 = 24/4x = 6 

We now know x = 6

We also know y=29-x y = 29 - 6y = 23

 Your numbers are 6 and 23

Step-by-step explanation:

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ Y(\stackrel{x_1}{1}~,~\stackrel{y_1}{-6})\qquad Z(\stackrel{x_2}{-2}~,~\stackrel{y_2}{8}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ -2 +1}{2}~~~ ,~~~ \cfrac{ 8 -6}{2} \right) \implies \left(\cfrac{ -1 }{2}~~~ ,~~~ \cfrac{ 2 }{2} \right)\implies \stackrel{\textit{\LARGE M}}{(-0.5~~,~~1)}[/tex]

The coordinates of the midpoint M are (-1/2, 1), and the length of YZ is approximately 14.32 units.

We have,

To find the coordinates of the midpoint M of the line segment YZ, we can use the midpoint formula:

Midpoint M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)

Where (x₁, y₁) and (x₂, y₂) are the coordinates of the endpoints Y and Z, respectively.

Given:

Y(1, -6) and Z(-2, 8)

Now, apply the midpoint formula:

Midpoint M = ((1 + (-2)) / 2, (-6 + 8) / 2)

Midpoint M = (-1 / 2, 2 / 2)

Simplify:

Midpoint M = (-1/2, 1)

To find the length of YZ, we can use the distance formula:

Length of YZ = √[(x₂ - x₁)² + (y₂ - y₁)²]

Given:

Y(1, -6) and Z(-2, 8)

Now, apply the distance formula:

Length of YZ = √[(-2 - 1)² + (8 - (-6))²]

Length of YZ = √[(-3)² + (8 + 6)²]

Length of YZ = √[9 + 196]

Length of YZ = √205

Length of YZ ≈ 14.32 (rounded to the nearest tenth)

Thus,

The coordinates of the midpoint M are (-1/2, 1), and the length of YZ is approximately 14.32 units.

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The solution of the radical equation of x is 1.

A linear equation in one variable is an equation which can be represented in the form of ax+b where x is the variable and 'a' is the coefficient and 'b' is  the two constants.

A radical equation is defined as an equation where the variable is under a radical or root.

We know that n-th root of a variable x can be written as x to the power of (1/n). Mathematically : [tex]\sqrt[n]{x} =x^{\frac{1}{n} }[/tex]

In the given equation:

∛x-1=√x-1

adding 1 to both sides we get:

or, ∛x=√x

Cross multiplying we get:

or, ∛x/√x =1

We know that (aˣ/aⁿ)=a⁽ˣ⁻ⁿ⁾

therefore :

or, [tex]x^{\frac{1}{3}-\frac{1}{2} }=1[/tex]

or, [tex]x^{-\frac{1}{6} }=1[/tex]

or, x=1

Hence the value of x in the radical equation is 1

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The mode  for the distribution of scores in the following frequency distribution table is 3, which is the second option.

This is a term used in statistics to refer to the number of highest occurrence. Mode refers to the value that highest the number of frequency. In finding the mode, it is better to orderly arrange the given data to help see the value that occurs more frequently as this is the mode.

For the values given in the distribution of scores in the frequency distribution table the mode is three  ( 3 ) and it is the second option

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5x + 8

2(5x+8)

2(5x+8) is the express of twice the sum of 5 times a number and 8

answer: 2 (5x+8) = 12

The measure of each angle of the triangle is 40°, 40° and 100°.

What is the triangle?

Given:

In an isosceles triangle two of the three angles measure the same.

Let the two angles be equal to x.

The third angle is 20 more than twice the measure of either angle, which means 2x+20.

The angles of a triangle add up to 180 degrees.

(x)+(x)+(2x+20)=180

4x+20=180

4x=160

x=40 degrees

So, the two angles measure 40° each and the third angle would be,

2x+20

=2*40+20

=100°

Therefore, the measure of each angle of the triangle is 40°, 40° and 100°.

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The number of large bins that the pieces will completely fill is 3.

Each large bin can contain only one type of colour. In order to determine the number of large bins that would be used for each color, divide the color for each piece.

Number of large bins that would be used for Brown color = 283 / 150 = 1.89.

1 large bins would be completely filled with brown glass color

Number of large bins that would be used for Green color = 116 /1 50 = 0.7

No large bin would be completely filled with the green glass color

Number of large bins that would be used for Clear color = 315 / 150 = 2.1

2 large bins would be completely filled with the clear glass color

The total number of large bins that would be completely filled = 1 + 2 = 3

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Angles ECD and ACB are congruent, since they form a pair of vertical angles. Let their measure by [tex]y[/tex].

The sum of the interior angles of any triangle is 180°. This means

• in ∆CDE, we have

[tex]x + 100^\circ + y = 180^\circ[/tex]

• in ∆ABC, we have

[tex]4x + 49^\circ + y = 180^\circ[/tex]

Solve for [tex]x[/tex] by eliminating [tex]y[/tex].

[tex](x + 100^\circ + y) - (4x + 49^\circ + y) = 180^\circ - 180^\circ[/tex]

[tex]-3x + 51^\circ = 0[/tex]

[tex]3x = 51^\circ[/tex]

[tex]\boxed{x = 17^\circ}[/tex]

Answer: at least 3 more games

Step-by-step explanation:

70% of 72 is 50.4

50.4 - 48 = 2.4

Because one can't win only a fourth of a game, you need to round up. Bringing us to at least 3 more games to win

The step 2 is incorrect angle o and angle p form supplementary angles not alternate interior angle that is :

∠o +  ∠p = 180°

What are alternate interior angle ?

An alternate interior angle is one formed on the inside side of two parallel lines and opposite on the outer side of the transversal when those two parallel lines are intersected by a transversal and they are equal.

Alternate angles between a transverse and parallel lines are equal .

Here, the step 1 is correct :

as the sum of angles of a triangle is 180 degree therefore,

∠m +∠n + ∠o = 180°.............(1)

the step 2 is incorrect :

as angle o and angle p form supplementary angles not alternate interior angle therefore it will be :

∠o +  ∠p = 180°........(2)

after that step 3 and 4 is correct to get the final result as :

step 3 : ∠m +∠n + ∠o = ∠o +  ∠p

step 4 : ∠m +∠n = ∠p

Therefore, the step 2 is incorrect angle o and angle p form supplementary angles not alternate interior angle.

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The length of DC found using Pythagorean theorem given AD = 10.6 and DB = 5.6 and AD and AB are tangent of circle O, is DC = 1.6

The given parameters are;

The tangents of circle O = AD and AB

The segment passing through O = DB

AD = 10.6

DB = 5.6

Required; The length of DC

Solution;

According to Pythagorean theorem, we have;

AB = √(10.6² - 5.6²) = 9

AB = AC = 9

AD = DC + AC

Which gives;

10.6 = DC + 9

DC = 10.6 - 9 = 1.6

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A. Using subtraction, the distance between the two birds = |-2.5 - 2.5| = |-5| = 5 meters.

B. Using additive inverses, the distance = 2.5 + 2.5 = 5 meters

The distance between any two points on a number line is the absolute difference of the coordinates of the two points.

The additive inverse of a number is the number that is added to the number to make it zero. For example, the additive inverse of a is -a.

Part A:

Using subtraction, the distance between the two birds = |-2.5 - 2.5| = |-5| = 5 meters.

Part B:

The additive inverse of -2.5 is 2.5.

Using additive inverses, the distance = 2.5 + 2.5

Using additive inverses, the distance = 5 meters

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Answer:

y = 2

Step-by-step explanation:

- 3x + 9y = 57 ← substitute x = - 13 into the equation

- 3(- 13) + 9y = 57

39 + 9y = 57 ( subtract 39 from both sides )

9y = 18 ( divide both sides by 9 )

y = 2

Answer: y is 2

solved it with a calculator.

After solving the equation In (2m + 3) = 8, the value of m is equal to 5/2.

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

We have been asked to find m in (2 m+3) = 8

⇒ (2 m+3) = 8

⇒ 2m + 3 = 8

⇒ 2m = 8 - 3

⇒ 2m = 5

⇒ m = 5/2

So, m is equal to 5/2 in (2 m+3) = 8

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Answer:

x = 7

Step-by-step explanation:

Ok, so these angle are equal, because they are opposite angle

So we could write as x+16 = 4x - 5

Now we solve the equation:

x+16 = 4x - 5

16+5 = 4x -x

21 = 3x

7 = x

Answer:

20 Songs

Step-by-step explanation:

60 minutes / 3minutes per song =20 songs

Answer:

[tex] \sf \: x=34[/tex]

Step-by-step explanation:

Let's solve your equation step-by-step.

x/2 = 17/1

Step 1: Cross-multiply.

x/2 = 17/1

x*(1)=(17)*(2)

x=34