At most, how many unique roots will a third-degree polynomial function have?

Answer:

(3x-2)(2x+5)

or

(2x+5)(3x-2) by commutative property

Step-by-step explanation:

Let's try factoring by grouping.

[tex]6x^2-4x+15x-10[/tex]

I'm going to group the first two terms together and the second two terms together.

[tex](6x^2-4x)+(15x-10)[/tex]

Now I'm going to factor what I can from each pair:

[tex]2x(3x-2)+5(3x-2)[/tex]

Now if you look at the terms 2x(3x-2) and 5(3x-2) you should see they have a common factor of (3x-2) so we can factor that out now.

(3x-2)(2x+5)

Factoring by grouping was a successful here.

Answer:

(3x - 2)(2x + 5)

Step-by-step explanation:

Given

6x² - 4x + 15x - 10 ( factor the first/second and third/fourth terms )

=2x(3x - 2) + 5(3x - 2) ← factor out (3x - 2) from each term

= (3x - 2)(2x + 5) ← in factored form

Answer:

vertex = (2, 1)

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

f(x) = 3(x - 2)² + 1 ← is in vertex form

with vertex = (h, k) = (2, 1 )

Answer:

[tex]f(n) = \frac{n}{3} [/tex]

Step-by-step explanation:

Recall that:

[tex]3ft = 1 \: yd[/tex]

This implies that:

[tex] 6ft = 2yds[/tex]

[tex] 9ft = 3yds[/tex]

In general:

[tex] n \: ft = \frac{n}{3} \: \: yds[/tex]

We can therefore write the function rule:

[tex]f(n) = \frac{n}{3} [/tex]

Answer:

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

Step-by-step explanation:

Given

[tex]\frac{5}{2x}[/tex] = [tex]\frac{25}{4}[/tex] ( cross- multiply )

25 × 2x = 5 × 4

50x = 20 ( divide both sides by 50 )

x = [tex]\frac{20}{50}[/tex] = [tex]\frac{2}{5}[/tex]

Answer:

x = 2/5

Step-by-step explanation:

5/2x} = 25/4 (cross- multiply)

25 × 2x = 5 × 4

50x = 20 (divide both sides by 50)

x = 20/50

x = 2/5

14 more points. Do 42-28.

Answer:

17(21) - 14(20) = 357 - 280 = 77 ft²

The correct answer is I.

Answer:

The range is [tex](0,\infty)[/tex]  (in interval notation).

The range is [tex]0<y<\infty)[/tex] or [tex]y>0[/tex] (in inequality notation).

The range is all real numbers greater than 0  (in words).

Step-by-step explanation:

[tex]5^{x}[/tex] we get close to 0 but will never be 0.  [tex]5^{x}[/tex] will also never be negative.

[tex]5^{x}[/tex] is positive for any real input [tex]x[/tex].

Here is a table of values to help try to convince you we are only ever going to get positive outcomes.

[tex]x[/tex]  |  [tex]5^x[/tex]

-4                 5^(-4)=1/625

-3                 5^(-3)=1/125

-2                 5^(-2)=1/25

-1                  5^(-1)=1/5

0                  5^0=1

1                   5^1=5

2                  5^2=25

3                  5^3=125

4                  5^4=625

You can see the y's are increasing as you increase the x value.

Even if you plug in really left numbers on the number like -200 you will still get a positive number like [tex]5^{-200}=\frac{1}{5^{200}}[/tex]. This number will be really close to 0.  You can go more left of -200 and the outcome will be even closer to 0.

I'm just trying to convince you on the left side the y's will approach 0 but never cross the x-axis on the right side the numbers keep getting larger and larger.

The range is [tex](0,\infty)[/tex]  (in interval notation).

The range is [tex]0<y<\infty)[/tex] or [tex]y>0[/tex] (in inequality notation).

The range is all real numbers greater than 0  (in words).

You can also look at the graph and see that the y's for this equation only exist for number y's greater than 0.  You only see the graph above the x-axis.

Answer:

The range is f(x) = all real values above 0.

In interval notation it is (0, ∞).

Step-by-step explanation:

5^x can have any value above 0 . It cannot be negative or 0.

Answer: $5.00 for 1 day

Step-by-step explanation:

Unit price refers to the price of an item in one unit (one), 1 in quantity in particular. $5.00 goes in daily pricing - 1 day. While the others are pricing in multiple units.

Hope it helped!

If you know Heron's formula, this is easy.

[tex]\text{area}=\sqrt{s(s-6)(s-10)(s-14)}=15\sqrt3[/tex]

where [tex]s=\dfrac{6+10+14}2=15[/tex] is the semiperimeter of the triangle.

The area is also equal to half the product of the base and height of the triangle, which happen to be

[tex]15\sqrt3=\dfrac{14x}2\implies x=\dfrac{15\sqrt3}7\approx3.711[/tex]

so the answer is B.

Answer:

D. The minimum y-value of g(x) approaches -3

Step-by-step explanation:

Form a table for values of x with corresponding values for f(x) and g(x)

x                   f(x)=3x²-3                                         g(x)=2^x -3                          

-3                   =3(-3²)-3=24                                       2⁻³ -3 = -2.88

-2                    =3(-2²)-3=9                                        2⁻² -3 = -2.75

-1                     =3(-1²)-3=0                                         2⁻¹-3 = -2.5

0                      =3(0²)-3= -3                                        2⁰ -3 = -2

1                       =3(1²)-3=0                                           2¹ -3 = -1

2                      =3(2²)-3=9                                          2²- 3 = 1

3                     =3(3²)-3=24                                          2³ -3= 5

From the table above, you can see the minimum value of y in g(x)  -2.88 approaches -3

Answer:

The equation that represents the new path is y=(1/2)x-2

Step-by-step explanation:

step 1

Find the slope of the give line

we have

y=-2x-7

so

the slope m is equal to

m=-2

step 2

Find the slope of the perpendicular line to the given line

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal of each other

so

we have

m=-2 -----> slope of the given line

therefore

The slope of the perpendicular line is equal to

m=1/2

step 3

With m=1/2 and the point (-2,-3) find the equation of the line

y-y1=m(x-x1)

substitute

y+3=(1/2)(x+2)

y=(1/2)x+1-3

y=(1/2)x-2 -----> equation that represent the new path

Answer:

Y= 1/2x-2

Step-by-step explanation:

Apex

Hope this helps Have a nice day

[tex]\large\boxed{9\,\text{boys and}\,12\,\text{girls}}[/tex]

In this question, we're trying to find how many boys and girls are in the class.

Lets get some important information that will help us to answer the question:

Important information:

With the information above, we can solve the question.

To make this easier, we could turn the fractions into percents.

[tex]3/7 = 0.42857\,\, \text{or}\,\, 0.43 = 43\%\,\, \text{This is for boys}\\\\4/7 = 0.571428\,\, \text{or}\,\, 0.57 = 57\%\,\, \text{This is for girls}[/tex]

Now, we could just multiply 21 by the right decimal in order to get the right amount of boys and girls in Mrs. Clark's classroom.

[tex]21 *0.43=9\,\,\text{boys}\\\\21*0.53=12\,\,\text{girls}[/tex]

When you solve, you would figure out that there are 9 boys and 12 girls in Mrs. Clark's class.

Step-by-step explanation:

When two straight lines intersect, they form 4 angles around the point. It can be seen that there are two angles in terms of x on a straight line, which sum up to 180 degrees. Therefore:

3y + y + 88 = 180 and 6x + 35 + 8x - 23 = 180.

Solving for x and y gives:

4y = 92 and 14x = 168.

y = 23 and x = 12.

Substituting the values back in the expression gives the angles:

XAW = 3(23) = 69 degrees.

WAY = 23 + 88 = 111 degrees.

ZAY = 8(12) - 23 = 73 degrees.

XAZ = 6(12) + 35 = 107 degrees.

The problem in this question is that whenever straight lines intersect, they form the vertical opposite angles. The vertical opposite angles are equal. In this question, angle XAW = angle ZAY and angle WAY = angle XAZ. However, in this question, these angles are not equal. (69 is not equal to 73 and 111 is not equal to 107). Hence, this is the problem in the question!!!

It appears that you are asking for a solution to a mathematical problem involving variables x and y and are referencing a figure which seems to be related to the problem. However, the values for x and y are not provided, and the figure in question is also missing from your message.
To solve for x and y, we need the full details of the problem including the specific mathematical equations or relationships that involve x and y. If there is a diagram or figure associated with the problem, the details about the figure such as angles, sides, shapes, or any labels are crucial in order to provide a solution.
Without this information, I cannot provide a correct solution to the problem.
To assist you better, please provide the complete problem statement with all necessary details. If there are equations that need to be solved, specify them. If there is a geometric figure involved, please describe it or provide the relevant measurements and properties that relate to x and y.
Once you provide the full context of the problem, I would be glad to help you find the value of x and y and also explain what might be wrong with the figure, if applicable.

Answer:

(2/3)n(n+1)(2n+1)

Step-by-step explanation:

First you have to find the general term formula which is here (2k)^2 which is equal to 4k^2. Sum(k=1 to n) of 4k^2=4•n(n+1)(2n+1)/6

simplified to (2/3)n(n+1)(2n+1)

Answer:

The percentage change is 7.67%

Step-by-step explanation:

Cost of stock in a restaurant when bought= $300

Cost of stock in a restaurant now = $323

Change in cost = 323 -300 = $23

The percentage change is = (change in cost/Cost of stock in a restaurant when bought) * 100

The percentage change is = (23/300) * 100 = 7.67 %

The percentage change is 7.67%

To calculate the percentage change in the value of Jorge's stock, you follow these steps:
1. Find the change in value by subtracting the initial value from the current value.
2. Divide the change in value by the initial value to get the fraction that represents the change.
3. To find the percentage change, multiply the fraction from step 2 by 100.
Let's do this for Jorge's stock:
1. Change in value: \( $323 - $300 = $23 \)
2. Fraction of change: \( \frac{23}{300} \)
3. Percentage change: \( \left(\frac{23}{300}\right) × 100 \)
Now let's compute the percentage change:
\( \left(\frac{23}{300}\right) × 100 = \left(\frac{23}{3}\right) \)
After calculating this, you would get the percentage change as:
\( \frac{23}{3} = 7.666... \)
Rounded to two decimal places, the result would be 7.67.
So the complete statement is:
The percentage change is 7.67%.

Answer:

N'

Step-by-step explanation:

L corresponds to L'

M corresponds to M'

N corresponds to N'

O corresponds to O'

P corresponds to P'

After the transformation if you copy and paste your picture over the new picture, the corresponding angles should lay on top of each other.

Polygon LMNOP was transformed to create polygon L'M'N'O'P'.  The angle N corresponds to N'.

A polygon is a two-dimensional geometric figure that has a finite number of sides. The sides of a polygon are made of straight line segments connected to each other end to end. Thus, the line segments of a polygon are called sides or edges.

Here,

L corresponds to L'

M corresponds to M'

N corresponds to N'

O corresponds to O'

P corresponds to P'

Hence, The N corresponds to N'.

To know more about polygons refer to

https://brainly.com/question/1513726

#SPJ2

Answer:

Both of those are functions.

Step-by-step explanation:

[tex]y=x^2[/tex] is a parabola that opens up.

Any upward or downward parabola is a function because they pass the vertical line test.

[tex]x=\pm \sqrt{1-y}{/tex]

Square both sides:

[tex]x^2=1-y[/tex]

Subtract 1 on both sides:

[tex]x^2-1=-y[/tex]

Multiply both sides by -1:

[tex]-x^2+1=y[/tex]

So this is a another parabola and it is faced down.  So this is also a function.

[tex]y=ax^2+bx+c[/tex] wit [tex]a \neq 0[/tex] willl always be a parabola.  

If [tex]a>0[/tex] then it is open up.

If [tex]a<0[/tex] then it is open down.

Upwards and downward parabolas will always be functions.

[tex]x=ay^2+by+c[/tex] are also parabolas but these open to the left or right.  These will not be functions because they will not pass the vertical line test.  

Answer:

obtuse, because 6^2+10^2 is greather than 12^2

Step-by-step explanation:

The triangle with side lengths 6 cm, 10 cm, and 12 cm is a right triangle. This is determined by applying the Pythagorean theorem (a^2 + b^2 = c^2) to the side lengths of the triangle.

The classification of a triangle can be determined by its side lengths. In this context, you have a triangle with side lengths 6 cm, 10 cm, and 12 cm. This is not an acute triangle, contrary to the original statement. It is, in fact, a right triangle.

To determine this, one can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as a^2 + b^2 = c^2.

If we apply the Pythagorean theorem to our triangle, we find that 6^2 + 10^2 equals 36 + 100, which is 136. Similarly, 12^2 equals 144. Since 136 is less than 144, the triangle is indeed a right triangle, not an acute triangle.

https://brainly.com/question/4028542

#SPJ3

Answer:

6 and up

Step-by-step explanation:

this is beacuse when you add all the angels up you you would have to have a minimum of 6 to pass the negative 5

Answer:

x = 80°

Step-by-step explanation:

The sum of the interior angles of a hexagon is 720 degrees. So,

x + (x - 5) + (x - 5) + (2x - 5) + (2x - 5) + (2x + 20) = 720

Eliminating parenthesis

x + x - 5 + x - 5 + 2x - 5 + 2x - 5 + 2x + 20 = 720

Adding and subtracting

9x + 0 = 720

Isolating x

x = 720/9

x = 80

Answer:

y-intercept of y=4x-3 is -3

Step-by-step explanation:

The given equation is:

y = 4x -3

The equation is in slope-intercept form.

The standard equation of slope-intercept form is:

y = mx + b

where m is the slope and b is the y-intercept

So, comparing the given equation with the standard equation the y-intercept is -3

y-intercept of y=4x-3 is -3

Answer:

Step-by-step explanation:

The y intercept of any equation that is a function is the y value taken on when x = 0

So in this case it is y = - 3 because 4*0 = 0. All that is left for y is y = -3.

The point of interception is (0.-3). The way to confirm many answers is to graph the point.

[tex]\huge{\boxed{32\%}}[/tex]

We can find this information using the table. The number of female students that like peas is 64, and the total number of students is 200. That gives us the following fraction. [tex]\frac{64}{200}[/tex]

Now, turn this into a percentage by making the denominator 100. This is done by dividing the numerator and denominator each by 2, since the denominator is 100. [tex]\frac{64 \div 2}{200 \div 2}= \frac{32}{100}=32%[/tex]

Required probability that one of these students is female and

likes peas is 32/100 or 32%

According to the problem,

∴ Required probability = 64/200 = 32/100 = 32%

Find more about "Probability" here : https://brainly.com/question/25870256

#SPJ2

Answer:

see below

Step-by-step explanation:

Take the 4 lb container.  Pour out rice and fill the 3 lbs container.  What is left in the 4 lb container is 1 lb  (4-3 =1)

Empty the 3 lbs container and put the 1lbs into it

Now measure rice into the 4 lbs container

We  have 1lbs ( in the 3lbs container)

and 4 lbs ( in the 4 lbs container)

for a total of 5 bs

Answer:

Option 90°

Step-by-step explanation:

AB is the perpendicular bisector of XY

The result of intersection will give 4 right angles

So,the measure of the angle of intersection when AB is the perpendicular bisector of XY = 90°

See the attached figure.

Answer:

Option A. ∠ECB=25°

Step-by-step explanation:

we know that

The measurement of the outer angle is the semi-difference of the arcs it encompasses.

so

∠ECB=(1/2)[arc DB-arc EB]

substitute the given values

(x+10)°=(1/2)[146°-(6x+6)°]

solve for x

2x+20=140-6x

2x+6x=140-20

8x=120

x=15

Find the measure of angle ECB

∠ECB=x+10=15+10=25°

Answer:

25

Step-by-step explanation:

A scalene triangle has all different side lengths and different sized angles. This means that a scalene can NOT have two congruent angles.

This means that the answer is:

True

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

it is actually false

cause you can change the angles or sides to turn it scalene

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]y=-3x-9\qquad(1)\\\\y=\dfrac{1}{3}x-39\qquad(2)\\\\\text{Substitute (1) to (2)}\\\\-3x-9=\dfrac{1}{3}x-39\qquad\text{multiply both sides by 3}\\\\-9x-27=x-117\qquad\text{add 27 to both sides}\\\\-9x=x-90\qquad\text{subtract}\ x\ \text{from both sides}\\\\-10x=-90\qquad\text{divide both sides by (-10)}\\\\x=9[/tex]

[tex]\text{Put the value of x to (1):}\\\\y=-3(9)-9\\\\y=-27-9\\\\y=-36[/tex]

Answer:

It is A

Step-by-step explanation:

Answer:

U' = (-4,-5)

V' = (-6,-2)

Step-by-step explanation:

Vertex U has coordinates

U = (-4,5)

Vertex V has coordinates

V = (-6,2)

When a quadrilateral is reflected across x- axis the sign of x coordinate remains same and sign of y coordinate changes.

So, U= (-4,5)

then U' is:

U' = (-4,-5)

V = (-6,2)

then V' is

V' = (-6,-2)

Answer:

(-4, -5) and V' is at (-6, -2)

Answer:

5x^3 +2x -1

Step-by-step explanation:

f(x)=5x^3-2 and g(x) = 2x+1

(f+g)(x) = 5x^3-2 + 2x+1

Combine like terms

           = 5x^3 +2x -1

Answer:

y - 1 = (1/3)(x + 1)

Step-by-step explanation:

Look carefully at (0, -3) and (2, 3).  As we move from the first to the second, x increases by 2 (from 0 to 2) and y increases by 6 (from -3 to 3).  Therefore, the slope of this line is m  = rise / run, or m = 6/2, or m = 1/3.  Both lines have the same slope, 1/3, because they are parallel.

Now let's apply the point-slope form of the equation of a straight line.  Here the point in question is (-1, 1) and the slope is 1/3.  Therefore, we have:

y - 1 = (1/3)(x + 1)

Answer:

Step-by-step explanation: