What are the zeros of the polynomial p(x) = x3 – 19x - 30?
-
1.
-10, 1, 3
2.
-6, -5, 1
3.
-3, -2,5
4.
-15, 1, 2

[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\stackrel{vertex}{(\stackrel{h}{2}~~,~~\stackrel{k}{-11})}\qquad y=a(x-2)^2-11\qquad \qquad \textit{we also know that} \begin{cases} x=0\\ y=5 \end{cases} \\\\\\ 5=a(0-2)^2-11\implies 16=4a\implies \cfrac{16}{4}=a\implies 4=a \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=4(x-2)^2-11~\hfill[/tex]

The equation of the parabola that has the vertex at point (2,-11) and passes through the point (0,5) is y = 4 (x - 2)² - 11.

A parabola is a two dimensional figure on a plane which is U shaped and any point on the parabola is at an equal distance from a fixed point called focus and a fixed line called directrix.

The general form of a parabola is,

y = a (x - h)² + k

where (h, k) is the vertex.

Given vertex is (2, -11).

Equation is,

y = a(x - 2)² - 11

Also, given that the parabola passes through the point (0, 5).

Substituting,

5 = a (0 - 2)² - 11

⇒ 5 = 4a - 11

⇒ a = 4

So the required equation is, y = 4 (x - 2)² - 11.

Hence the equation of the given parabola is y = 4 (x - 2)² - 11.

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Answer:

[tex]V=763.407[/tex] yd^3

Step-by-step explanation:

Formula for volume of right circular cylinder.

[tex]V=\pi r^{2}*6[/tex]

[tex]r=\frac{d}{2}[/tex]

We are given the diameter (d) and the height (h).

First solve for r.

[tex]r=\frac{18}{2}[/tex]

[tex]r=9[/tex]

Now we have everything we need to find the volume. Plug in r into the volume formula.

[tex]V=\pi *9^{2} *3[/tex]

[tex]V=763.407[/tex] yd^3

I think the answer is 30km^2

1/2 ×4 × 15 = 30

Answer:

Slope = -3

Y-intercept = (0,-4)

Equation = -3x-4

Step-by-step explanation:

Slope is [tex]\frac{rise}{run}[/tex] or [tex]\frac{Y2-Y1}{X2-X1}[/tex]. Apply this from the data in the table, for example:

[tex]\frac{5-8}{-3-(-4)} = \frac{rise}{run}\\ \frac{-3}{1} = \frac{rise}{run}\\\\-3= \frac{rise}{run}[/tex]

Y-intercept is located where x=0. If we look at the table, we will find that when x=0, y=-4. If we turn it into a (x,y) point format, we will get (0,4).

The function can be found using the Y-intercept and the slope. Since at x=0, y=-4, we know that the function must have a -4 in it, therefore: [tex]y = x-4[/tex]. Our function decreases by 3 for every positive x and increases by 3 for every negative x, therefore [tex]y = -3x-4[/tex].

Answer:

87

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given that length of Rectangular garden is 9 feet more than its width and perimeter of garden is 206 feet.

Let's assume length of Rectangular garden be x + 9 feet and width be x feet respectively. Firstly using the formula of Perimeter of rectangle we'll find the length and width of the garden.

[tex] \\ \\ \dashrightarrow \: \: { \underline { \boxed{ \pink{ \sf {Perimeter _{(rectangle)} = 2(L + W)}}}}} \\ \\ [/tex]

Substituting the required values:

[tex]\\[/tex]

[tex]\dashrightarrow \sf \: \: 2(x + 9 + x) = 206 \\ \\ [/tex]

[tex]\dashrightarrow \sf \: \: 2x + 18 + 2x = 206 \\ \\ [/tex]

[tex]\dashrightarrow \sf \: \: 4x + 18 = 206 \\ \\ [/tex]

[tex]\dashrightarrow \sf \: \: 4x = 206 - 18 \\ \\ [/tex]

[tex]\dashrightarrow \sf \: \: 4x = 188 \\ \\ [/tex]

[tex]\dashrightarrow \sf \: \: x = \dfrac{188}{4 } \\ \\ [/tex]

[tex]\dashrightarrow \sf \: \: x = 47 \\ \\ [/tex]

Hence,

[tex]\\[/tex]

Now,

[tex] \\ \dashrightarrow \: \: { \underline { \boxed{ \pink{ \sf Area _{(rectangle)} = Length \times Width }}}} \\ \\ [/tex]

Substituting the required values:

[tex]\\[/tex]

[tex]\dashrightarrow \sf \: \: Area = 56 \times 47 \\ \\ [/tex]

[tex]\dashrightarrow \sf \: \: Area = 2632~ ft^2 \\ \\ [/tex]

Hence,

Answer:

Area of rectangular garden is 2632 feet²

Step-by-step explanation:

Given:-

To find :-

Solution:-

Let the length of Rectangular garden be x + 9 feet and width be x feet .

We know that , the formula of Perimeter of rectangle is 2 ( L + B )

putting the known values to find the dimensions ,

2 ( L + B ) = 206 feet

2 ( x + 9 + x ) = 206 feet

4 x + 18 = 206 feet

x = 47 feet

putting the values of x in the equation ,

Length :- 56 feet

width :- 47 feet

Now , area of rectangular garden :- L×B

Area => 56×47 feet²

Area => 2632 feet²

Answer:

208.3

Step-by-step explanation:

Since the numbers are decreasing as multiples, its a geometric progression.

[tex]S_{n}=\frac{a(1-r^{n} )}{1-r} ; r\neq 1 \ and\ r \ is\ less\ than\ 1\\common\ ratio=\frac{20}{50}=\frac{2}{5}\\ S_{10}=\frac{125(1-(2/5)^{10} )}{1-(2/5)} \\=208.3[/tex]

Answer:

A=1/2(b*h)

A=(3x2*4xy)

A=1/2(12x3y)

A=6x3y

so the answer is option (d)

1 to 4 2 stays 3 to 1 4 to 3

Step-by-step explanation:

Answer:

468

Step-by-step explanation:

Area of trapezoid=1/2 *h(l1+l2)

=1/2*18*(15+37)

=9*52

=468

Answer:

  a. 3/4 inches per minute

  b. -1 1/8 inches per minute

  c. B is fastest; 1 1/8 is more than 3/4

Step-by-step explanation:

A change is a difference. A rate of change is one difference divided by another, usually the change in y-value divided by the change in x-value.

__

The change in elevation is the difference between the elevation at the end of the period (6 inches) and the elevation at the beginning of the period (3 inches). The change in time period is the difference between the end time (8 min) and the beginning time (4 min).

  change in elevation per minute = (6 -3 inches)/(8 -4 min)

  = (3 inches)/(4 min) = 3/4 inches/minute

__

Similarly, ...

  change in elevation per minute = (3 -7 1/2 inches)/(18 -14 min)

  = (-4 1/2 inches)/(4 min) = -1 1/8 inches/minute

__

We know that 3/4 is more than -1 1/8, but when we talk about the "fastest rate of change", we're generally interested in the magnitude--the value without the sign. That means we understand a rate of change of -1 1/8 inches per minute to be "faster" than a rate of change of 3/4 inches per minute.

The rate of change from Part B is fastest. 1 1/8 inches per minute is more than 3/4 inches per minute.

Answer:

  87%

Step-by-step explanation:

The percentage of normally-distributed data between 45 and 77 in a data set with mean 63 and standard deviation 10.4 can be found by any of a number of calculators, apps, web sites, or spreadsheets.

The percentage is 87%.

Answer: 1/3

You can find the complete solution in the given attachment

I hope It helped you

Answer:

You can't cconstruct any triangle

Step-by-step explanation:

110+50+10=170  A triangle always has 180º

Answer:

D. 19.25^2

Step-by-step explanation:

A = 5.5

H = 3.5

A = 19.25^2

Answer:

f(3) = 9

Step-by-step explanation:

From the table, when can see that when x is 3, f(x) is 9.

Therefore, f(3) = 9

Answer:

[tex]f(3)[/tex]=9

Step-by-step explanation:

[tex]f(x)[/tex] is x times a function.

so if you look at the table on the 'x' side and go down the table until you reach '3' and see what number on the 'f(x)' side corresponds with it, you will see '9'

so [tex]f(3) = 9[/tex]

and that means your answer is D

Answer: 14

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

2 is in the ones place

4 is in the tens

1 is in the hundreds

6 is in the thousands

9 is in the ten thousands

Answer:

The number that is in the ten thousands is 9, whose value is 90,000.

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Thank you so much for participate in the community of Brainly.com

I hope help you :)

Kind regards, Antonio.

Answer:

[tex]\text{k = 4, 5, 6, 7, 8... and onwards}[/tex]

Step-by-step explanation:

The product of k/3 and 12 be greater than 12.

⇒ k/3 × 12 > 12

The first step in determining the possible values of "k" is to simplify the left-hand-side (L.H.S) of the inequality.

⇒ (12 × k)/3 > 12

⇒ (12 ÷ 3) × k > 12

⇒ (4) × k > 12

The next step in determining the possible values of "k" is to isolate the variable. To do this, we can divide 4 both sides.

⇒ [4 × k]/4 > 12/4

⇒ k > 12/4

⇒ k > 3

To satisfy the inequality, the value of k must be greater than 3. Thus, the values of k could be [tex]\text{4, 5, 6... }[/tex] and so on.

In a parallelogram, opposite sides are of equal measure.

QR = TS

find x

1)

2)

Find value of y:

3)

QT:

4)

if x = 5

means the diagram is enlarged.

then y will be:

We need x and y

Opposite sides of a parallelogram are equal

And

Hence

#3

Segment QT is 4

so

Another way

So

scale factor:-

Find y

Answer:

13 7/9

Step-by-step explanation:

You have two mixed numbers right now, so the first step to take would be to add the integers 4 and 8 since those numbers are limited by fractions (1/9 and 2/3 are limited as fractions). This would equal 13, and now you can move on to the fractions 1/9 and 2/3. In order to add those, you will have to find the LCM or the least common multiple, which in this case is 9 since 3 is a multiple of 9 (and 9 is obviously a multiple of 9). Knowing, you would have to convert the 2/3 into something ___/9, which would be 6/9. Adding those two together would result in 7/9. Combine that with the integer 13, and you have 13 7/9. Hope this helps!  

Answer:

318

Step-by-step explanation:

300 + (300 * 6%) = Answer

300 + (300 * 0.06) = 318

Answer:

The Answer is 108 units.

It's number 2.

Answer:

4=3+x

Step-by-step explanation:

First, let the number be x.

The product of 3 and x looks like so:-

3x

Now, add 4 (the sum of 4 and 3x):

[tex]\bigstar\sf{3x+4}[/tex]

Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I'll comment and/or edit my answer :)

If the elements of the cylinder are perpendicular to the planes containing the bases, the cylinder is a right cylinder, otherwise it is called an oblique cylinder. If the bases are disks (regions whose boundary is a circle) the cylinder is called a circular cylinder

Answer:

Remember length times width times height when finding volume.

In non-terms of pi, the answer would be [tex]2[/tex] [tex]ft^2[/tex]

Answer:

Volume is 2ft

Step-by-step explanation:

Multiply the length x width once you find the answer for lengthxwidth.

Multiply the answer you got by height