Find the missing value so that the two points have a slope of 1/2.
(9, 1) and (3, y)

Please explain

Given:

The equation is

[tex]y=5x^3-6x^2-4x+8[/tex]

To find:

The coordinates of the turning point.

Solution:

We have,

[tex]y=5x^3-6x^2-4x+8[/tex]

Differentiate with respect to x.

[tex]\dfrac{dy}{dx}=5(3x^2)-6(2x)-4(1)+(0)[/tex]

[tex]\dfrac{dy}{dx}=15x^2-12x-4[/tex]

For the turning points [tex]\dfrac{dy}{dx}=0[/tex].

[tex]15x^2-12x-4=0[/tex]

Using quadratic formula:

[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]x=\dfrac{-(-12)\pm \sqrt{(-12)^2-4(15)(-4)}}{2(15)}[/tex]

[tex]x=\dfrac{12\pm \sqrt{144+240}}{30}[/tex]

[tex]x=\dfrac{12\pm \sqrt{384}}{30}[/tex]

Now,

[tex]x=\dfrac{12+\sqrt{384}}{30}\text{ and }x=\dfrac{12-\sqrt{384}}{30}[/tex]

[tex]x\approx 1.053\text{ and }x\approx-0.253[/tex]

Putting x=1.053 in the given equation, we get

[tex]y=5(1.053)^3-6(1.053)^2-4(1.053)+8[/tex]

[tex]y\approx 2.973[/tex]

Putting x=−0.253 in the given equation, we get

[tex]y=5(-0.253)^3-6(-0.253)^2-4(-0.253)+8[/tex]

[tex]y\approx 8.547[/tex]

Therefore, the turning points are (1.053,2.973) and (-0.253, 8.547).

Answer:

no solution

Step-by-step explanation:

when you distribute, the 6x on each side cancel out leaving there to be no solution to the problem. I attached a photo of my work as well.

Answer:

The answer is False meaning it's no solution

Step-by-step explanation:

1. Distribute 3 through the parentheses which will be 6x+12=6x+10

2.Cancel equal terms on both sides of the equation and you will get 12=10 which isn't a true statement.

Step-by-step explanation:

Answered 1 year, 9 months ago

Given,

Principal, P =Rs.10000,  Rate, R = 8% per annum compounded half yearly for 1 year. 

Now, There are two half years in a year. Therefore compounding has to be 2 times. 

And rate = half of 10% = 5% half yearly.

Therefore, the required amount =   = Rs. 10816

And Compound Interest, C.I. = Amount - Principal = Rs. (10816 - 10000) = Rs. 816.

hope it helps you

Answer:

1) B. the labels can he make to the tape

2) D. he can make 73 labels

Step-by-step explanation:

1) We are told that He will make labels 1.25 inches long each. We are asked the number of labels he can make.

Thus, correct answer is option B.

2) He wants to make labels 1.25 inches long out of 91.25 inches of plastic.

Thus, number of labels he can make = 91.25/1.25 = 73 labels

Answer:

What is the area, in square inches, of the trapezoid below? 15.7 in 8 in 6.6 in​-by-step explanation:

The area, in square inches, of the trapezoid, is 89.2 in².

We have given that,

A = 89.2 in²

The area (A) of a trapezoid is calculated as,

A = 1/2 h (b₁ + b₂ )

where h is the perpendicular height and b₁, b₂ the parallel bases

Here h = 8, b₁ = 6.6, b₂ = 15.7 , then

A = 1/2 × 8 × (6.6 + 15.7)

A= 4 × 22.3

A= 89.2 in²

The area, in square inches, of the trapezoid, is 89.2 in².

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Answer:

54 inches

Step-by-step explanation:

6/18=7/x

6x=7(18)

6x=126

x=21

21+15=18=54

Answer:

B

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

x² + 30² = 50²

x² + 900 = 2500 ( subtract 900 from both sides )

x² = 1600 ( take the square root of both sides )

x = [tex]\sqrt{1600}[/tex] = 40 → B

Answer:

What's the nth term for 7,10,13,16? The nth term = 3n + 4. The formula for the nth term of an arithmetic progression is a(n) = dn + a(1) - d. Therefore in your sequence, the difference d = 3, and the first term a(1) = 7.

Step-by-step explanation:

Answer:

7/8 > 3/4

Step-by-step explanation:

Find a common denominator first and here it is 8. To get 3/4 to 8ths, you multiply the numerator and denominator by 2 to get 6/8 and 7/8 is greater

Answer:

[tex]A_1 = 24m^2[/tex] -- Swing set

[tex]A_2 = 16m^2[/tex] -- Slide

[tex]A_3 = 5m^2[/tex] --- Pathway

Step-by-step explanation:

Missing part of the question:

Fill in the table above to show the area of each section (see attachment for table)

The area of each section is calculated as:

[tex]Area = Length * Width[/tex]

For the Swing set

[tex]A_1 = 8m * 3m[/tex]

[tex]A_1 = 24m^2[/tex]

For the Slide

[tex]A_2 = 8m * 2m[/tex]

[tex]A_2 = 16m^2[/tex]

For the Pathway

[tex]A_3 = 5m * 1m[/tex]

[tex]A_3 = 5m^2[/tex]

The total area is:

[tex]Area=A_1 + A_2 + A_3[/tex]

[tex]Area = 24m^2 + 16m^2 + 5m^2[/tex]

[tex]Area = 45m^2[/tex]

Answer:

I DONT KNOW!!

Step-by-step explanation:

Answer:

95km

Step-by-step explanation:

5 days = 375km

4 days = 67km + 78km + 46km + 89km= 280km

5 days - 4days = the 5th day

375km - 280km = 95km

Answer:

72 apples will be used and 4 will not

Answer:

She will use 72 apples and 4 apples will not be used.

Step-by-step explanation:

If she requires 9 apples for one pie... the she can make only 8 pies out of 76 apples.

hence she uses 72 apples...

Answer:

its 4.8

Step-by-step explanation:

i divided 7.5 by 12.5 and got 0.6 and added 4.2 and got 4.8

Equation is formed of two expressions. The amount of water that is used by Sofia to make the slime is 4.8 fl oz.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the amount of salt solution used by Sofia be x, and the amount of water used by Sofia be y.

As it is given that the amount of glue used is 12.5 times the amount of salt solution used, and the amount of glue used is 7.5 fl oz. Therefore, the equation can be written as,

Amount of glue = 12.5 x Amount of salt solution

[tex]7.5 = 12.5 \times x\\\\x = \dfrac{7.5}{12.5}\\\\x = 0.6[/tex]

Also, it is given that the amount of water used is 4.2 fl oz. less than the amount of salt solution used, since we know the amount of salt solution used, therefore, the equation can be written as,

Amount of salt solution = Amount of water - 4.2 oz

[tex]x = y -4.2\\\\(0.6)=y-4.2\\\\y = 4.8[/tex]

Hence, the amount of water that is used by Sofia to make the slime is 4.8 fl oz.

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Answer:

Step-by-step explanation:

Answer:

63+ 2x- 17 = 180 degree

or, 2x+46=180degree

or, 2x=180-46=134degree

or, x = 134÷2=67 degree ans.

Answer:

m<J = 83

m<L = 97

m<M = 97

Step-by-step explanation:

The corners across (left to right/right to left) from each other of a trapezoid are always equal.

So, it would be like this:

Angle J is equal to angle K

Angle M is equal to angle L

See how they are across from each other?

Therefore, Angle J will be 83 degrees.

To find the other 2 angles subtract 83 from 180

180 - 83 = 97

So, Angle L and M are 97 degrees.

To check your answer you can add up all the corners and they should equal 360 degrees:

83 + 83 + 97 + 97 = 360

360 = 360

Hope this helps!!

- Kay :)

Answer:

The unit rate[tex]\frac{4}{1}[/tex] of the graph is 4, the slope of the graph is 4, and the comparison between answers is that they are equal.

Step-by-step explanation:

For every increase of 1 in the X value of the graph, the Y value increases by 4, so the slope would be [tex]\frac{4}{1}[/tex] or 4.

Answer:

60000

Step-by-step explanation:

You should treat the first son with the 1 ratio as x. Because of this, the second son would be 3x and the third would be 6x. All of them need to equal 120000 so 10x=120000. Next you isolate the and x= 12000. Fill in 1200 for x and the first son gets 12000, the second gets 36000, and the third gets 72000. Lastly you subtract and you get 60000.

Answer:

nicki monaj is the queen of rap

Step-by-step explanation:

periodt purr

Answer:

 It's C) -6y

Step-by-step explanation:

I know someone already answered but I figured I could explain since it looks like you are getting a little confused. The reason it's not A is because its

-5 + 5 which is zero. So it gets rid of x so your just left with -6y. If it was

5x+5x then it would 10x but the negative makes it 0

Answer:

12.4 did this before

Step-by-step explanation:

Answer:

sɪʀ ʏᴏᴜʀ ᴀɴsᴡᴇʀ ɪs 12.4

ᴀᴄᴄᴏʀᴅɪɴɢ ᴛᴏ ᴍɪᴅ ᴘᴏɪɴᴛ ᴛʜᴇʀᴏᴇᴍ

Find quarts per hour:

140 quarts / 10 hours = 14 quarts per hour.

Now multiply quarts per hour by hours:

14 quarts per hour x 12 hours = 168 quarts

Answer:

7x + 3y = 3

7x + 3y = 3

7x + 3y = 3

Answer:

[tex]8x=32\\2y=-24[/tex]

Step-by-step explanation:

When solving for 1 variable, set the other to 0 and solve.

[tex]3x-y(0)=12\\3x=12\\x=4\\4*8=32\\8x=32\\\\3(0)-y=12\\-y=12\\y=-12\\-12*2=-24\\2y=-24[/tex]

Answer:

yes but no

Step-by-step explanation:

one is bigger than the other by prolly 1 foot

Answer:

1 is bigger by abt a foot or so

Step-by-step explanation: