describe how you could use the point-slope formula to find the equation of a line that is perpendicular to a given line and passes through a given point

Observe that the x coords of the roots of a polynomial are,

[tex]x_{1,2,3,4}=\{-3,0,1,4\}[/tex]

Which can be put into form,

[tex]y=a(x-x_1)(x-x_2)(x-x_3)(x-x_4)[/tex]

with data

[tex]y=a(x-(-3))(x-0)(x-1)(x-4)=ax(x+3)(x-1)(x-4)[/tex]

Now if I take any root point and insert it into the equation I won't be able to solve for y because they will always multiply to zero (ie. when I pick [tex]x=-3[/tex] the right hand side will multiply to zero,

[tex]y=-3a(-3+3)(-3-1)(-3-4)=0[/tex]

and a will be "lost" in the process.

If we observed a non-root point that we could substitute with x and y and result in a non-loss process then you could find a. But since there is no such point (I don't think you can read it of the graph) there is no other viable way to find a.

Hope this helps :)

Answer:

-2pi/3

Step-by-step explanation:

y = 2 cos 3(x + 2π∕3) +1

y = A sin(B(x + C)) + D  

amplitude is A

period is 2π/B

phase shift is C (positive is to the left)

vertical shift is D

We have a shift to the left of 2 pi /3

Answer:

A

Step-by-step explanation:

The standard cosine function has the form:

[tex]\displaystyle y = a\cos (b(x-c)) + d[/tex]

Where |a| is the amplitude, 2π / b is the period, c is the phase shift, and d is the vertical shift.

We have the function:

[tex]\displaystyle y = 2 \cos 3\left(x + \frac{2\pi}{3}\right) + 1[/tex]

We can rewrite this as:

[tex]\displaystyle y = \left(2\right)\cos 3\left(x - \left(-\frac{2\pi}{3}\right)\right) + 1[/tex]

Therefore, a = 2, b = 3, c = -2π/3, and d = 1.

Our phase shift is represented by c. Thus, the phase shift is -2π/3.

Our answer is A.

Answer:

$1448

Step-by-step explanation:

Tax=rate*amount=(4/100)*36200=1448

Answer:slope 2/3

Y-int 6

Step-by-step explanation:

9514 1404 393

Answer:

  (-2, 4]

Step-by-step explanation:

  -21 ≤ -6x +3 < 15 . . . . given

  -24 ≤ -6x < 12 . . . . . . subtract 3

  4 ≥ x > -2 . . . . . . . . . . divide by -6

In interval notation, the solution is (-2, 4].

__

Interval notation uses a square bracket to indicate the "or equal to" case--where the end point is included in the interval. A graph uses a solid dot for the same purpose. When the interval does not include the end point, a round bracket (parenthesis) or an open dot are used.

Answer: A

Step-by-step explanation: x=-2, y=3, z=-3

Answer:

A. -2, 3, -3

Step-by-step explanation:

x = 7 - 2y + z

y = 21 + 6x + 2z = 21 + 6×(7 - 2y + z) + 2z =

= 21 + 42 - 12y + 6z + 2z = 63 - 12y + 8z

13y = 63 + 8z

y = (63 + 8z)/13

2x + 2y - 3z = 11

2×(7 - 2y + z) + 2×(63 + 8z)/13 - 3z = 11

2×(7 - 2×(63 + 8z)/13 + z) + 2×(63 + 8z)/13 - 3z = 11

14 - 4×(63 + 8z)/13 + 2z + 2×(63 + 8z)/13 - 3z = 11

-2×(63 + 8z)/13 - z = -3

-2×(63 + 8z) - 13z = -39

-126 - 16z - 13z = -39

-29z = 87

z = -3

y = (63 + 8×-3)/13 = (63 - 24)/13 = 39/13 = 3

x = 7 - 2×3 + -3 = 7 - 6 - 3 = -2

Answer:

what three options bro where are the options

Answer:

9 hours, 11 hours, 19 hours.

Answer:

Amanda's box is in this case, the bigger one. Then subtract the Amanda's by Mary's. The Larger box is 70cm^3 larger then the smaller box.

Step-by-step explanation:

Amanda's box: 13.5*10*10= 1350cm^3

Mary's box: 20*8*8= 1280cm^3

1350-1280=70

The larger box is 70cm^3 larger then the smaller box.

If you have any questions regarding my answer tell me in the comments, i will come answer them. Have a good day.

The answer is prime! I hope this helps you out!

Answer:

23 is a prime number. Reason: Prime number are those numbers which are divisible by 1 and itself. Example: 5 is divisible by 1 and 5 only.

Answer:

Step-by-step explanation:

(x-2)(x+4)=x^2+4x-2x-8=0=> x =2, x=0

Answer:

A

Step-by-step explanation:

Answer:

y<=(-2x+4)

Step-by-step explanation:

The equation of line is y=-2x+4. For the region left of it, y<=(-2x+4)

Answer:

speaking giberish

Step-by-step explanation:

cos it is just a word that is rare

Answer:

Consider the following identity:

Let a = 2, b = 1/2

Use the algebraic identity given below

[tex]\boxed{\sf a^3-b^3=(a+b)(a^2-ab+b^2)}[/tex]

[tex]\\ \sf\longmapsto (2+\dfrac{1}{2})(2^2-1+\dfrac{1}{4})[/tex]

[tex]\\ \sf\longmapsto (2+\dfrac{1}{2})(2^2-2\times \dfrac{1}{2}+\dfrac{1}{2}^2)[/tex]

[tex]\\ \sf\longmapsto 2^3-\dfrac{1}{2}^3[/tex]

[tex]\\ \sf\longmapsto 8-\dfrac{1}{8}[/tex]

The unit rate will be "23.5 miles/gallon". In the below segment, a further solution to the given question is provided.

Given values in the question are:

Total distance,

= 188 miles

Total gas used,

= 8

Now,

⇒ The rate of gas consumption will be:

= [tex]\frac{Total \ distance}{Total \ gas \ used}[/tex]

By putting the given values in the above formula, we get

= [tex]\frac{188}{8}[/tex]

= [tex]23.5 \ miles/gallon[/tex]

Thus the above is the appropriate solution.

Learn more about gas consumption here:

https://brainly.com/question/17321062

Answer:

https://linksharing.samsungcloud.com/ul5cX9oOmhzt

Answer:

n=39/5

Step-by-step explanation:

24=5(n-3)

24=5n-15

-5n= -15-24

-5n=39

n= 39/5

Answer:

bacoot anjing

lo siapa hah kan bisa jawab sendiri sok sok minta bantuuuu

Step-by-step explanation:

maluiiin

Answer:

$5250.96

Step-by-step explanation:

Future value= Present value(1+r)^n

=3700(1+0.011)^32

r=4.4÷100÷4

n=8×4

Answer:

Hello,

Answer

[tex]\sigma=457,95...[/tex]

Step-by-step explanation:

p(z<a)=0.9

p(z<1.29)=0.9015

p(z<1.28)=0.8997

using linear interpolation: with 4 decimals

p(z<1.282)<0.9

[tex]\dfrac{1628-1500}{\sigma} =1.282\\\\\sigma =\dfrac{1628-1500}{1.282}\\\\\sigma=457,95...\\[/tex]

Answer:

H0 : correlation is equal to 0

H1 : correlation is not equal to 0 ;

Pvalue < α ;

There is sufficient evidence

r = 0.945 ;

Pvalue = 0.01524

Step-by-step explanation:

Given the data :

Lemon_Imports_(x) Crash_Fatality_Rate_(y)

230 15.8

264 15.6

359 15.5

482 15.3

531 14.9

Using technology :

The regression equation obtained is :

y = 16.3363-0.002455X

Where, slope = - 0.002455 ; Intercept = 16.3363

The Correlation Coefficient, r = 0.945

H0 : correlation is equal to 0

H1 : correlation is not equal to 0 ;

The test statistic, T:

T = r / √(1 - r²) / (n - 2)

n = 5 ;

T = 0.945 / √(1 - 0.945²) / (5 - 2)

T = 0.945 / 0.1888341

T = 5.00439

The Pvalue = 0.01524

Since Pvalue < α ; Reject the Null and conclude that there is sufficient evidence to support the claim.

Answer:

y = -1/4x+1/2

Step-by-step explanation:

y = 4x - 3

This is in slope intercept form, y = mx+b where the slope is m

The slope is 4

Perpendicular lines have slopes that are negative reciprocals

-1/4 is the slope of the perpendicular line

y = -1/4x+b

Using the point (2,0)

0 = -1/4(2)+b

0 = -1/2+b

b = 1/2

y = -1/4x+1/2

Answer:

-7/25

Step-by-step explanation:

1/5 ÷ (-5/7)

Copy dot flip

1/5 * -7/5

-7/25

Answers:

First bottle's unit cost = 27 cents per oz

Second bottle's unit cost = 27 cents per oz

Both have the same unit cost.

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

Work Shown:

unit cost = price/(number of ounces)

1st bottle unit cost = (1.35)/(5) = 0.27 dollars per oz = 27 cents per oz

2nd bottle unit cost = (2.16)/(8) = 0.27 dollars per oz = 27 cents per oz

Both lead to the same unit cost. Therefore, you can pick either option and it doesn't matter.

volume= a^2 * h

area= a^2+4ah

take the second equation, solve for h

4ah=1100-a^2

h=1100/4a -1/4 a now put that expression in volume equation for h.

YOu now have a volume expression as function of a.

take the derivative, set to zero, solve for a. Then put that value back into the volume equation, solve for Volume.

Cited from jiskha

Answer:

See below

Step-by-step explanation:

a)

[tex]2\sin(x) +\sqrt{3} =0 \implies 2\sin(x)=-\sqrt{3} \implies \boxed{\sin(x)=-\dfrac{\sqrt{3}}{2} }[/tex]

[tex]\therefore x=\dfrac{4\pi }{3}[/tex]

But note, as sine does represent the [tex]y[/tex] value, [tex]\dfrac{5\pi }{3}[/tex] is also solution

Therefore,

[tex]x=\dfrac{4\pi }{3} \text{ and } x=\dfrac{5\pi }{3}[/tex]

This is the solution for [tex]x\in[0, 2\pi ][/tex], recall the unit circle.

Note: [tex]\sin(x)=-\dfrac{\sqrt{3}}{2} \implies \sin(x)=\sin \left(\pi +\dfrac{\pi }{3} \right)[/tex]

b)

[tex]\sqrt{3} \tan(x) + 1 =0 \implies \tan(x) = -\dfrac{1}{\sqrt{3} } \implies \boxed{ \tan(x) = -\dfrac{\sqrt{3} }{3} }[/tex]

Once

[tex]\tan(x) = -\dfrac{\sqrt{3} }{3} \implies \sin(x) = -\dfrac{1}{2} \text{ and } \cos(x) = \dfrac{\sqrt{3} }{2}[/tex]

As [tex]\tan(x) = \dfrac{\sin(x)}{\cos(x)}[/tex]

[tex]\therefore x=-\dfrac{\pi }{6}[/tex]

c)

[tex]4\sin^2(x) - 1 = 0 \implies \sin^2(x) = \dfrac{1}{4} \implies \boxed{\sin(x) = \pm \dfrac{\sqrt{1} }{\sqrt{4} } = \pm \dfrac{1}{2}}[/tex]

Therefore,

[tex]\sin(x)=\dfrac{1}{2} \implies x=\dfrac{\pi }{6} \text{ and } x=\dfrac{5\pi }{6}[/tex]

[tex]\sin(x)=-\dfrac{1}{2} \implies x=\dfrac{7\pi }{6} \text{ and } x=\dfrac{11\pi }{6}[/tex]

The solutions are

[tex]x=\dfrac{\pi }{6} \text{ and } x=\dfrac{5\pi }{6} \text{ and }x=\dfrac{7\pi }{6} \text{ and } x=\dfrac{11\pi }{6}[/tex]

Answer:

A=13×13

=169sqr.units

Answer:

soory i dont know just report me if you angry

Step-by-step explanation:

Sequence is

4

,

7

,

10

,

13

,

16

,

.

.

.

a

1

=

4

,

a

2

=

7

,

a

3

=

10

,

.

.

.

If it is Arithmetic sequence,

a

2

−

a

1

=

a

3

−

a

2

=

a

4

−

a

3

& so on

In the given sum,

a

2

−

a

1

=

7

−

4

=

3

a

3

−

a

2

=

10

−

7

=

3

a

4

−

a

3

=

13

−

10

=

3

Since the difference between the successive terms is same and

hence

common difference

d

=

3

Answer:

48 ÷ 60 = 4/5

Step-by-step explanation:

4/5 is the answer

Answer:

[tex]\frac{1}{30}[/tex]

Step-by-step explanation:

We require the number of minutes in a day.

i hour = 60 minutes

24 hours = 24 × 60 = 1440 minutes ( 24 hours in 1 day )

Then

fraction = [tex]\frac{48}{1440}[/tex] ( divide numerator/ denominator by 12 )

            = [tex]\frac{4}{120}[/tex] ( divide numerator/ denominator by 4 )

            = [tex]\frac{1}{30}[/tex]