Omar paid $23.60 for 29.5 centimeters of wire. Find unit price in dollars per centimeter

[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.

Learn more about Parabola here :

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Answer:

13 pints

Step-by-step explanation:

6 1/2 (6.50) quarts is equal to 13 pints

Answer:

13pt

to go from quarts to pints multiply the value by 2

Answer:

x= -2

x= -3

x= 5

Step-by-step explanation:

Answer:

Square

Step-by-step explanation:

Hope this helps!

Answers:

In other words, it's nearly everything except choice C (octagon).

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Explanation:

Search out "Cross sections of a cube" and you'll see visual examples of what is possible.

Here are the list of possible cross sections

A parallelogram is also possible, but that isn't one of the listed choices so we can ignore it. The triangle can either be equilateral or won't be, depending how the cross section plane is oriented.

Nearly every box is checked except for the octagon, because we simply don't have enough faces to get 8 sides needed for the cross section.

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.

The value of x, y and z from the system of equation are -1, -8 and 5 respectively.

Data;

To solve this problem, we have to solve the system of equation using substitution method.

From equation (iii)

[tex]2z = 10\\z = 5[/tex]

let us substitute the value of z into equation (ii)

[tex]-3y + 7z = 59\\z = 5\\-3y + 7(5) = 59\\-3y + 35 = 59\\-3y = 59 - 35\\-3y = 24\\y = -8[/tex]

Let's substitute the value of x and y into equation (i)

[tex]-2x + 6y + 3z = -31\\y = -8, z = 5\\-2x + 6(-8) + 3(5) = -31\\-2x - 48 + 15 = -31\\-2x - 33 = -31\\-2x = -31 + 33\\-2x = 2\\x = -1[/tex]

From the calculation above, the value of x, y and z are -1, -8 and 5 respectively.

Learn more on system of equations here;

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Explanation:

Refer to the figure below.

Focus on triangle ABF. Angle AFB = 40 is marked in red. Angle BAF = 90 is marked in blue. The missing angle is 180-90-40 = 50 which is angle ABF.

Inscribed angle ABF = 50 doubles to arc AC since this inscribed angle subtends the arc in question. I'm using the inscribed angle theorem.

arc AC = 2*(angle ABF) = 2*50 = 100 degrees

Note: We don't need the fact that angle AGD = 86

Answer:

The Answer is 108 units.

It's number 2.

Answer:

87

Step-by-step explanation:

Answer:

its A and D dont listen to the other person lol

W

Answer:188

Step-by-step explanation:

u have to add all the side which is 46+46+13+13=188

Answer:

See below for answers and explanations

Step-by-step explanation:

Problem 1

Recall that the projection of a vector [tex]u[/tex] onto [tex]v[/tex] is [tex]\displaystyle proj_vu=\biggr(\frac{u\cdot v}{||v||^2}\biggr)v[/tex].

Identify the vectors:

[tex]u=\langle-10,-7\rangle[/tex]

[tex]v=\langle-8,4\rangle[/tex]

Compute the dot product:

[tex]u\cdot v=(-10*-8)+(-7*4)=80+(-28)=52[/tex]

Find the square of the magnitude of vector v:

[tex]||v||^2=\sqrt{(-8)^2+(4)^2}^2=64+16=80[/tex]

Find the projection of vector u onto v:

[tex]\displaystyle proj_vu=\biggr(\frac{u\cdot v}{||v||^2}\biggr)v\\\\proj_vu=\biggr(\frac{52}{80}\biggr)\langle-8,4\rangle\\\\proj_vu=\biggr\langle\frac{-416}{80} ,\frac{208}{80}\biggr\rangle\\\\proj_vu=\biggr\langle\frac{-26}{5} ,\frac{13}{5}\biggr\rangle\\\\proj_vu=\langle-5.2,2.6\rangle[/tex]

Thus, B is the correct answer

Problem 2

Treat the football and wind as vectors:

Football: [tex]u=\langle42\cos172^\circ,42\sin172^\circ\rangle[/tex]

Wind: [tex]v=\langle13\cos345^\circ,13\sin345^\circ\rangle[/tex]

Add the vectors: [tex]u+v=\langle42\cos172^\circ+13\cos345^\circ,42\sin172^\circ+13\sin345^\circ\rangle\approx\langle-29.034,2.481\rangle[/tex]

Find the magnitude of the resultant vector:

[tex]||u+v||=\sqrt{(-29.034)^2+(2.481)^2}\approx29.14[/tex]

Find the direction of the resultant vector:

[tex]\displaystyle \theta=tan^{-1}\biggr(\frac{2.841}{-29.034}\biggr)\approx -5^\circ[/tex]

Because our resultant vector is in Quadrant II, the true direction angle is 6° clockwise from the negative axis. This means that our true direction angle is [tex]180^\circ-5^\circ=175^\circ[/tex]

Thus, C is the correct answer

Problem 3

We identify the initial point to be [tex]R(-2,12)[/tex] and the terminal point to be [tex]S(-7,6)[/tex]. The vector in component form can be found by subtracting the initial point from the terminal point:

[tex]v=\langle-7-(-2),6-12\rangle=\langle-7+2,-6\rangle=\langle-5,-6\rangle[/tex]

Next, we find the magnitude of the vector:

[tex]||v||=\sqrt{(-5)^2+(-6)^2}=\sqrt{25+36}=\sqrt{61}\approx7.81[/tex]

And finally, we find the direction of the vector:

[tex]\displaystyle \theta=tan^{-1}\biggr(\frac{6}{5}\biggr)\approx50.194^\circ[/tex]

Keep in mind that since our vector is in Quadrant III, our direction angle also needs to be in Quadrant III, so the true direction angle is [tex]180^\circ+50.194^\circ=230.194^\circ[/tex].

Thus, A is the correct answer

Problem 4

Add the vectors:

[tex]v_1+v_2=\langle-60,3\rangle+\langle4,14\rangle=\langle-60+4,3+14\rangle=\langle-56,17\rangle[/tex]

Determine the magnitude of the vector:

[tex]||v_1+v_2||=\sqrt{(-56)^2+(17)^2}=\sqrt{3136+289}=\sqrt{3425}\approx58.524[/tex]

Find the direction of the vector:

[tex]\displaystyle\theta=tan^{-1}\biggr(\frac{17}{-56} \biggr)\approx-17^\circ[/tex]

Because our vector is in Quadrant II, then the direction angle we found is a reference angle, telling us the true direction angle is 17° clockwise from the negative x-axis, so the true direction angle is [tex]180^\circ-17^\circ=163^\circ[/tex]

Thus, A is the correct answer

Problem 5

A vector in trigonometric form is represented as [tex]w=||w||(\cos\theta i+\sin\theta i)[/tex] where [tex]||w||[/tex] is the magnitude of vector [tex]w[/tex] and [tex]\theta[/tex] is the direction of vector [tex]w[/tex].

Magnitude: [tex]||w||=\sqrt{(-16)^2+(-63)^2}=\sqrt{256+3969}=\sqrt{4225}=65[/tex]

Direction: [tex]\displaystyle \theta=tan^{-1}\biggr(\frac{-63}{-16}\biggr)\approx75.75^\circ[/tex]

As our vector is in Quadrant III, our true direction angle will be 75.75° counterclockwise from the negative x-axis, so our true direction angle will be [tex]180^\circ+75.75^\circ=255.75^\circ[/tex].

This means that our vector in trigonometric form is [tex]w=65(\cos255.75^\circ i+\sin255.75^\circ j)[/tex]

Thus, C is the correct answer

Problem 6

Write the vectors in trigonometric form:

[tex]u=\langle40\cos30^\circ,40\sin30^\circ\rangle\\v=\langle50\cos140^\circ,50\sin140^\circ\rangle[/tex]

Add the vectors:

[tex]u+v=\langle40\cos30^\circ+50\cos140^\circ,40\sin30^\circ+50\sin140^\circ\rangle\approx\langle-3.661,52.139\rangle[/tex]

Find the magnitude of the resultant vector:

[tex]||u+v||=\sqrt{3.661^2+52.139^2}\approx52.268[/tex]

Find the direction of the resultant vector:

[tex]\displaystyle\theta=tan^{-1}\biggr(\frac{52.139}{-3.661} \biggr)\approx-86^\circ[/tex]

Because our resultant vector is in Quadrant II, then our true direction angle will be 86° clockwise from the negative x-axis. So, our true direction angle is [tex]180^\circ-86^\circ=94^\circ[/tex].

Thus, B is the correct answer

Answer:

Step-by-step explanation:

2x + 3y = -7

7x + 9y = -14

-3(2x+3y= -7) = -6x - 9y = 21

-6x - 9y = 21

7x + 9y = -14

add columns (y values cancel)

1x + 0y = 7

x = 7

plug 7 into the x value in either equation to find y

2(7) + 3y = -7

14 + 3y = -7

3y = -21

y = -7

(x,y) = (7,-7)

The expression is rewritten as the greatest common factor multiplied by the sum of two numbers is: 6*(8 + 11)

First, we need to find the greatest common factor between 48 and 66.

To find it, we can write both of these as a product of its prime factors, we get:

48 = 2*24 = 2*2*12 = 2*2*2*6 = 2*2*2*2*3

66 = 2*33 = 2*3*11

The greatest common factor that we can make is 2*3 = 6

Then we rewrite the numbers as:

48 = 6*8

66 = 6*11

Now we can rewrite our expression:

48 + 66 = 6*(8 + 11)

So the correct option is C

If you want to learn more about common factors, you can read:

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Answer: dude idek how to do this

Step-by-step explanation:

not lying still dont know

Answer:

Right angle

Step-by-step explanation:

It is because ANGLE QMS from the given figure denote 90 ° and right angle means 90°.

Pi, or π, is a number that is used to represent the ratio between a circle's circumference and its diameter.

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:

A. both the interest and fees on a loan.

Step-by-step explanation:

An annual percentage rate (APR) includes both the interest and fees on a loan.

[tex]\purple{\boxed{\blue{\boxed{\green{\star{\orange{\ \: \: Sumin-!! \: \: \: {\green{\star}}}}}}}}}[/tex]

Did the math for you.

[tex]|5 - 3x| + 2 = 19\\|5 - 3x| = 17\\(|5 - 3x|) = 17^2\\25 -15x -15x + 9x^2 = 289\\25 - 30x + 9x^2 -289 = 0\\9x^2 - 30x - 264 = 0\\3(x + 4)(3x - 22)[/tex]

Answer:

D

Step-by-step explanation:

its the closest to the answer i got so that must be it

Answer:

B. At most

Gives a maximum that it can be.

Step-by-step explanation:

x > 5, both terms are positive

x < - 5, both terms are negative

This is not clear

If x>5

Hence..

If x<-5 terms are negative

If x=-5

Answer:

-8

Step-by-step explanation:

This is the same as 4 x -2.

The parenthesis just means to multiply the number to the left by whatver is in the paranthesis when it is touching like that.

Answer: 1/3

You can find the complete solution in the given attachment

I hope It helped you

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:

what is the question?

do you have to find how much she is investing?

Yes, I guess so.

Hope this helps!

Answer:

yea actually what if she turned?- but yea its 0 so D

Step-by-step explanation:

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