Complete the table and answer the questions that follow. (If a root occurs twice, count it twice; if
thrice, count it three times, and so on. The first one is done
Polynomial Equation
1. (x+1)² (x-5) = 0
2. X-9 0
3. (x+8) (x-8)= 0
4. x² + 3x +2=0
(x+1)(x+2) = 0
5. (x² - 4x + 4)(x-3)²
(x-2)(x-2)(x-3)(x-3) = 0
6. 2
7. (x-3)(x + 1)(x - 1) = 0
8. (x²-4)(x-3)³ = 0
(x+2)(x-2)(x-3)(x-3)(x-3)=0
9. x(x-4)(x + 5)(x - 1) = 0
10. (x + 1)5 (x - 1)² =0
Degree
3
Real Roots of the
Equation
-1 (2times); and 5
Number of Real Roots
3

It is possible to determine a line's direction and steepness by looking at its slope.

Finding the slope between lines inside a coordinate plane can aid in anticipating if the lines are perpendicular, parallel, or none at all without physically using a compass.

A line's basic formula in gradient intercept form is y=mx + b. It is rewritable in point-slope form.

When y-b is equal to m(x-0), the location is the y-intercept (0,b).

The basic equation for a line with m=slope and (k,h) a position on the line is y-h=m(x-k).

By determining y and adding constant variables, the equation can be recast in slope-intercept form.

Y = mx-mk + h, where h-mk = b is the y-intercept in this form.

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There are 24,024 different ways to choose a President, Vice President, Treasurer, and Secretary from a group of 14 students.

Permutation is the arrangement of objects in a specific order. It is the number of different ways in which a set of objects can be arranged in a specific order. The formula to calculate permutation is:

[tex]P(n, r) = n! / (n - r)![/tex]

Permutations are commonly used in mathematics, science, and engineering, and are useful for solving problems that involve counting the number of possible arrangements of objects or events.

We can use the formula for permutations to find the number of ways to choose the four officers from a group of 14 students.

The number of permutations of n objects taken r at a time is given by:

[tex]^nP_r = n! / (n - r)![/tex]

where n! denotes n factorial, which is the product of all positive integers up to n. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

In this case, we want to choose 4 students from a group of 14, and the order in which they are chosen matters (since we are electing them to specific positions). So we have:

n = 14

r = 4

The number of ways to choose the four officers is therefore:

[tex]^1^4P_4 = 14! / (14 - 4)! = 14 \times 13 \times 12 \times 11 = 24,024[/tex]

Therefore, there are 24,024 different ways to choose a President, Vice President, Treasurer, and Secretary from a group of 14 students.

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Answer:

6x - 3

Step-by-step explanation:

3 ( 2x - 1  )

= 3 ( 2x ) - 3 ( 1 )

= 6x - 3

Answer:

x=1/2 or 0.5 or just 6x-3

Step-by-step explanation:

3(2x-1)

distribute.

6x-3

get 6x alone

6x=3

divide

x=3/6

x=1/2 or 0.5

For the given triangles the length of the missing side x is 56in.

As given in the question,

Two triangles are given ,

Let the triangle with measurement 40in. and 35in. be A and another is B.

In triangle A,

Let missing angle be α

Sum of all the angles in the interior of a triangle is equal to 180°

51°+ 74° + α = 180°

⇒α = 55°

In triangle B.

Let missing angle be β,

74° + 55° + β = 180°

⇒β= 51°

By AAA both the triangles are similar.

Length of corresponding sides are in proportion.

40: x = 35 : 49

⇒x = ( 40×49)/35

⇒x= 56in.

Therefore, for the given triangles the length of the missing side x=56in.

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The equation for the vertical line that goes through point M(−2, 6) is x = -2.

Answer:

The equation of a straight line is:

y = mx + b;

y, x are variables, m is the slope of the line and b is the y intercept.

The slope of a vertical is undefined. Since the line passes through the point M(−2, 6), hence the equation of the vertical line is:

x = -2

answer:

look

step-by-step explanation:

over? you would have 2 ÷ (5 x 2) ÷ 28. in fraction form.

A yield sign measures 24 inches on each of its three sides ( equilateral )then the area of the sign is 249.4

Given,

24 inches on each of its three side. (See in attached picture)

Consider ADB,

As it is an equilateral triangle, BD = BC/2 = 12 inches

By Pythagoras theorem,

AB^2 = BD^2 + AD^2

24^2 = 12^2 + AD^2

24^2 – 12^2 = AD^2

576-144 = AD^2

432= AD^2

20.78= AD

Area = ½ (base * height)

       = ½ (24*20.78)

       = 249.4

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Answer:

Step-by-step explanation:

think that there are 15 ways ... call the boxes A, B, and C.

You could put all four b***s into either box A, or box B, or box C  --->  3 ways.

You could put three ball into one box and the other ball into another box:

-- 3 into A, 1 into B, 0 into C; or 3 into A, 0 into B, 1 into C; or 1 into A, 3 into B, 0 into C; or 1 into A, 0 into B, 3 into C; or 0 into A, 3 into B, 1 into C; or 0 into A, 1 into B, 3 into C  --->  6 ways

You could put two balls into one box and the other two balls into another box:

-- 2 into A, 2 into B, 0 into C; or 2 into A, 0 into B, 2 into C; or 0 into A, 2 into B, 2 into C  --->  3 ways.

You could put two b***s into one box and one ball into each of the other two boxes:

-- There are three boxes that could get the two b***s  --->   3 ways

Total:  3 + 6 + 3 + 3  =  15 ways.

Answer:

Get the roundend answer to 10

Step-by-step explanation:

13.80

Step-by-step explanation:

22 - 4% is your answer

The value of [tex](x_{1},y_{1})= (-9,-6)[/tex] and the value of [tex](x_{2},y_{2})= (-1,-12)[/tex],according to the question.

What do you mean by XY coordinates?

The x and y coordinates are a component of the x-axis and y-axis in a 2D space in the Cartesian coordinate system. The x and y coordinates for a point in space are expressed as an ordered pair (x, y). The position of the point on the x-axis is shown by the first number, while its location on the y-axis is indicated by the second number.

According to the data in the given question,

We have:

The coordinates of points A are (-9,-6).

The coordinates of points W are (-1,-12).

In this question,

[tex](x_{1},y_{1})= (-9,-6)[/tex]

[tex](x_{2},y_{2})= (-1,-12)[/tex]

Therefore, the value of [tex](x_{1},y_{1})= (-9,-6)[/tex] and the value of [tex](x_{2},y_{2})= (-1,-12)[/tex].

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The relation that can be formed by obersving the Cartesian Plane is y = 5x

What is Co-ordinate Geometry?

The study of geometry using coordinate points is known as coordinate geometry (or analytic geometry). It is possible to estimate the distance between two points, divide lines in a m:n ratio, identify the midpoint of a line, calculate the area of a triangle in the Cartesian plane, and so on using coordinate geometry.

Solution:

By analysing the given Cartesian Plane

it can be observed that the rate of change of y with respect to x

is 5 times

Therefore, the relation that can be formed by obersving the Cartesian Plane is y = 5x

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Answer:

60x + 35; x = 4.5 hours

(x is not actually equal to 4.5, it is equal to 4.67)

Step-by-step explanation:

The description says that the plumber charges a one time fee of 35 dollars to come to someones house, and then 60 dollars an hour. The total pay is 305 dollars. x will be the number of hours that the plumber works.

60x + 35 = 305

Subtract 35 from both sides: 60x = 280

Divide by 60: x = 280/60

Simplify: x=14/3

Fraction to decimal: x=4.67

Answer: C (60x + 35 = 305; x = 4.5 hours)

It's right trust me! Wish you luck!

Brainliest?

The short word problem that illustrates the given equation is seen below. The value of the variable is 9.

Linear algebra equations are equations that can be expressed in word problems and these equations can be used to solve real-life scenarios. These algebraic equations are designed by the application of the desired set of variables with its arithmetic operations.

A.

In a food factory, Eighteen fried chickens are added to the six times the number of food plates is seventy-two. How much-fried chicken goes into each food plate?

B.

6x + 18 = 72

Subtract 18 from both sides;

6x + 18 - 18 = 72 - 18

6x = 54

Divide both sides by 6.

6x/6 = 54/6

x = 9

C.

The value of the variable is 9, and according to the example we used, it represents the number of chickens that goes into each plate of food.

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Answer: 300

Step-by-step explanation:

[tex]\sum^{3n}_{k=1} k=\frac{3n(3n+1)}{2}\\\\\sum^{n}_{k=1} k=\frac{n(n+1)}{2}\\\\\therefore \frac{3n(3n+1)}{2}-150=\frac{n(n+1)}{2}\\\\3n(3n+1)-300=n(n+1)\\\\9n^2 +3n-300=n^2 +n\\\\8n^2 +2n-300=0\\\\4n^2 +n-150=0\\\\(n-6)(4n+25)=0\\\\n > 0 \implies n=6\\\\\therefore 4n=24\\\\\implies \sum^{4n}_{k=1} k=\sum^{24}_{k=1} k=\frac{24(25)}{2}=300[/tex]

Step-by-step explanation:

9x + 3y = 153

6x + 5y = 147

the first equation can be divided by 3 and then multiplied by 2. and from that we can subtract equation 2 :

9x + 3y = 153 | /3

3x + y = 51 | ×2

6x + 2y = 102

- 6x + 5y = 147

-----------------------

0 -3y = -45

3y = 45

y = 15

3x + y = 51

3x + 15 = 51

3x = 36

x = 12

1 bottle of water costs Rs 12.

1 bottle of juice costs Rs 15.

The terms of the algebraic equation 3+6ab+c are (d) 3, 6ab  and c

The algebraic equation is given as

3 + 6ab + c

Consider an equation represented as

x + y

The terms of the equation are x and y

Also, for an equation represented as

x + y + z;

The terms are x, y and z

Using the above as a guide, the terms of 3 + 6ab + c are 3, 6ab  and c

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Answer:

Step-by-step explanation:

The length of the entire line which is subdivided according to golden ratio is 13.09 meters.

What is Golden Ratio?

The golden ratio is a special number approximately equal to 1.618

We find the golden ratio when we divide a line into two parts so that, the whole length divided by the long part is also equal to the long part divided by the short part

Let smaller part of a line be b and long part be a

Golden ratio = a + b/a = a/b = 1.618

According to the given question:

Length of smaller part of line = 5 meters

Let the longer length of the line be x

∴ Total length of line = 5 + x

Using Golden ratio to find the entire length of line

x/5 = 1.618

x = 8.09

Calculating length of entire line = 5 + x = 5 + 8.09 = 13.09

∴ Length of entire line is 13.09 meters

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The value of [tex]f.f^{-1}(x)[/tex] is 3 from the given function.

The  given function is f(x)=x-7/2.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The inverse of the given function is

y=x-7/2

Replace y with x and x with y, we get

x=y-7/2

y=x+7/2

[tex]f^{-1}(x)[/tex]=x+7/2

When x=3

[tex]f^{-1}(3)=3+7/2[/tex]

=6.5

f(6.5)=6.5-7/2

=6.5-3.5

=3

Therefore, the value of [tex]f.f^{-1}(x)[/tex] is 3 from the given function.

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The equation from the given graph is y=-2/3 x²+5.

From the given graph the vertex is (h, k)=(0, 5).

A quadratic function is one of the form f(x) = ax² + bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola.

The vertex form of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola. The coefficient a determines whether the graph of a quadratic function will open upwards or downwards.

Here, point on the given line from the graph is (3, -1)

Put (x, y)=(3, -1) and (h, k)=(0, 5) in y = a(x - h)² + k, we get

-1=a(3-0)²+5

⇒ 9a=-6

⇒ a=-2/3

Now, y=-2/3(x-0)²+5

y=-2/3 x²+5

Hence, the equation from the given graph is y=-2/3 x²+5.

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The x-intercept and y-intercept of the graph is (5,0) and (0,4)

How to find the intercept ?

When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b). The y value of the y intercept point is represented by b in the equation.

1. To find the x-intercept we put y=0

The equation becomes

4x + 5(0) = 20

4x = 20

 x =  [tex]\frac{20}{4}[/tex]

 x = 5

∴ The x-intercept is (5,0)

2. To find the y-intercept we put x=0

The equation becomes

4(0) + 5y = 20

5y = 20

 y =  [tex]\frac{20}{5}[/tex]

 y =  4

∴ The y-intercept is (0,4)

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The system of equation to describe the situation below is x= 1.

What is equation?

an equation is a formula that is to expresses the equality of two expressions, by the  connecting them with in the equals sign.

The process of equting one thing with another is called the equation of science with objective.

Sol- Based on the given condition-

The formulate is- 36+2x=35+3x

Rearrange variables to the left side of the equation

2x-3x=35-36

Combine like terms

-x= 35-36

Calculate the sum or difference

-x=-1

Devide both side of the equation by the coefficient of variable we get

X=1

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A) The equation is 22 + (d * 1/2) = 30

B) The plant that still have to grow 8 cm more

C) d = 16 days, d represents the number of days

Step-by-step explanation:

Given:

Initial height (basil plant at buying) = 22cm

Plant grows on everyday = 1/2cm

A) Given:

Total  height (to be grown) = 30 cm.

The equation is,

Initial height+ ( number of days * plant grows on everyday) =  Total height

22 + (d * 1/2) = 30  →  equation 1

B) The plant that still have to grow = Total height - Initial height

= 30 - 22

= 8 cm

C) Solving the value d using equation 1:

22 = 30 - (d * 1/2)

    44 = 60 - d 

      d = 16 days

Hence, A) The equation is 22 + (d * 1/2) = 30.

B) The plant that still have to grow 8 cm more.

C) d = 16 days, d represents the number of days.

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Step-by-step explanation:

imagine a circle with J being the center, and JK being the radius.

then

sin(J) = 15.1/JK

cos(J) = 9.4/JK

we have one trigonometric function, where we don't need to calculate JK first : tangent.

tan(J) = sin(J)/cos(J) = 15.1/JK / 9.4/JK = 15.1/9.4 =

= 1.606382978...

J = 58.09705252...° ≈ 58.1°

The angle that the ramp makes with the ground rounded off to two decimal places is 10.48°.

What is trigonometry?
The study of the relationship between the sides and angles of the right-angle triangle is essentially the focus of the field of mathematics known as "trigonometry". Therefore, employing trigonometric formulas, functions, or trigonometric identities can be helpful in determining the missing or unknown angles or sides of a right triangle. Angles in trigonometry can be expressed as either degrees or radians.

Given, the length of the ramp = h = 17 feet
Height at which ramp is placed on truck = p = 4 feet
Let the angle that the ramp makes with the ground = ∅
Taking the length and height of ramp as basis, on assuming a right triangle with the length as hypotenuse and the height as perpendicular, we have:
sin ∅ = Perpendicular/Hypotenuse = h / p = 17/4 = 4.25
⇒ ∅ = sin⁻¹ (4.25) ⇒ ∅ = 10.48°
Thus, the angle that the ramp makes with the ground rounded off to two decimal places is 10.48°.

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Answer:

x = -72

Step-by-step explanation:

So first you need to get x on its own, so you you need to get rid of -16 by adding +16 which you get 0.

so now x=-88

whatever you do on one side you do on the other, so add 16 to the other side (-88) so you get -72.

x = -72

so the answer is -72

Thank you <3

The required expression is: [tex]| 17 - \frac{5}{2}x|[/tex] = 48

An algebraic expression (or) a variable expression is a aggregate of phrases through the operations together with addition, subtraction, multiplication, division, etc. For instance, allow us to have a study the expression 5x + 7. Thus, we will say that 5x + 7 is an instance of an algebraic expression.

Words can be expressed algebraically.

The algebraic expression is: [tex]| 17 - \frac{5}{2}x|[/tex] = 48

Let the number be x.

Five-halves of x is: 5/2x

So the difference between  and 17 is:

5/2x - 17 = 48 or 17 - 5/2x = 48

Combine both expressions

[tex]| 17 - \frac{5}{2}x|[/tex] = 48

Hence, the required expression is:  [tex]| 17 - \frac{5}{2}x|[/tex] = 48

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Answer:

600ml

Step-by-step explanation: