If x + 2 and x - 3 are factors of the following polynomial, then find the values of a and b. F(x) = x^2 + ax^2- 7x + b

Answer:

24

Step-by-step explanation:

13,14,18,21,22,26,32,39,39,42

middle is 22 and 26

therefore you add and divide by 2

then you'll get 24

The given ratio of the volumes indicates that the volume of the cylinder is 9 times the volume of the cone.

Reasons:

The given parameter are;

Ratio of the volume of the cone to the cylinder to the 1 : 9

The height and diameter of the cone  are; 16 cm and 14 cm

The diameter of the cylinder = 28 cm

Required:

To find the height of the cone:

Solution:

[tex]\displaystyle The \ volume \ of \ a\ cone = \frac{1}{3} \cdot \pi \cdot r^2 \cdot h[/tex]

[tex]\displaystyle The \ volume \ of \ the \ cone = \frac{1}{3} \times \pi \times \left(\frac{14}{2} \right)^2 \times 16 = \mathbf{ \frac{784}{3} \cdot \pi}[/tex]

Volume of a cylinder, V = π·r²·h

[tex]\displaystyle Radius \ of \ the \ cylinder = \frac{28 \, cm}{2} = 14 \, cm[/tex]

Volume of the cylinder, V = π × 14² × h = 2,352·π

The volume of the cylinder = 9 × The volume of the cone

Therefore;

[tex]\displaystyle Volume \ of \ the \ cylinder =9 \times \frac{784}{3} \cdot \pi = \mathbf{2,352 \cdot \pi}[/tex]

[tex]\displaystyle Height \ of \ the \ cylinder, \, h = \mathbf{\frac{2,352 \cdot \pi}{14^2 \cdot \pi}} = 12[/tex]

The height of the cylinder, h = 12 cm

Learn more about ratios here:

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Answer:

d)

[tex] {i}^{740} [/tex]

Step-by-step explanation:

i¹= i

i²= -1

i³= -i

i⁴= 1

i¹²⁴= i^(124 +0)

i^124 . i^0

i^(4×31) . i^0 = 1³¹. i^0

1.i^0= i^0

= 1

a) i^179= i^(176+3)

i^176 . i³ = i^(4×44) . i³

1⁴⁴. i³ = 1. i³

= -i

b) i^582 = i^(580 + 2)

i^580 . i²= i^(4×145) . i²

1^145 . i²= 1.i²

= -1

c) i^165= i^(164+1)

i^164 . i¹ = i^(4×41) . i¹

1⁴¹ . i¹ = 1.i

= i

d) i^740= i^(740+0)

i^740 . i^0 = i^(4×185) . i^0

1^185 . i^0 = 1. i^0

= 1

i¹²⁴= i^740 = 1

subtract 2 from both sides

3a - 3y =  15 - 2x

factor out the common term 3

3 (a-y) = 15 - 2x

divide both sides by 3

a - y = 15 - 2x/3

add y to both sides

a = 15-2x/3 + y

then solve put the value for a =

15-2x/3 + y + 7 ÷10​

simplify using the common denominator

10(15-2x)+7*3/30

simplify 7 * 3 to 21

10(15-2x)+21/30

expand

150-20x+21/30

simplify 150-20x+21 to -20x + 171

-20x+171/30

Answer: -20x+171/30

[tex]\huge\bf Question:– [/tex]

[tex]\sf \longmapsto \: 3a+2x−3y=15[/tex]

[tex] \bf \huge \: To \: Find:–[/tex]

[tex] \boxed{\bf \: Value\: of \: A}[/tex]

[tex]\huge\bf Solution:–[/tex]

[tex]\sf \longmapsto \: 3a+2x−3y=15[/tex]

[tex]\boxed{ \bf \: Add -2x \: to \: both \: sides}[/tex]

[tex]\sf \longmapsto \: 3a+2x−3y+−2x=15+−2x[/tex]

[tex]\sf \longmapsto \: 3a−3y=−2x+15[/tex]

[tex]\boxed{ \bf \: Add \: 3y \: to \: both \: sides}[/tex]

[tex]\sf \longmapsto \: 3a−3y+3y=−2x+15+3y[/tex]

[tex]\sf \longmapsto \: 3a=−2x+3y+15[/tex]

[tex] \boxed{\bf \: \: Divide \: both \: sides \: by \: 3}[/tex]

[tex]\sf \longmapsto \: \dfrac{3a}{3} = \dfrac{−2x+3y+15}{3} [/tex]

[tex] \boxed{\bf \: Cross \: Multiply}[/tex]

[tex]\boxed{\sf \longmapsto \: a = \dfrac{ - 2}{3} x + y + 5}[/tex]

______________________________________

[tex]\bf \: Put\:The\: Value[/tex]

[tex] \sf \longmapsto \: \dfrac{−2x+3y+15}{3} +7÷10[/tex]

[tex] \boxed{\bf \: Distribute}[/tex]

[tex]\sf \longmapsto \: \dfrac{ - 2}{3} x+y+5+ \dfrac{7}{10} [/tex]

[tex] \boxed{\bf \: Combine \: Like \: terms}[/tex]

[tex]\sf \longmapsto \: \bigg( \dfrac{ - 2}{3} x\bigg) + y +\bigg( 5 + \dfrac{7}{10} \bigg)[/tex]

[tex]\sf \longmapsto \: \dfrac{ - 2}{3} x + y + \dfrac{57}{10} [/tex]

______________________________________

[tex]\boxed{\bf The Answer\: is:–}[/tex]

[tex]\boxed{{\underline{\bf\dfrac{ - 2}{3} x + y + \dfrac{57}{10}} }}[/tex]

For the function f(0)=sin(0), 0 is the input variable while f(0) is the output.

For the function g(0)=cos(0), 0 is the input variable while g(0) is the output.

The standard form of representing trigonometry functions is f(x) = sinx or f(x) = cos x

From the functions:

Given the trig function f(0)=sin(0), compared with the general equation, we can see that 0 is the input variable while f(0) is the output.

Similarly for the function g(0)=cos(0), 0 is the input variable while g(0) is the output.

Learn more on input variables here: https://brainly.com/question/11451813

Answer:

a)Perimeter= 2(8+2x+4)

=(24+4x)ft

b)Area= 8(2x+4)

=(16x+32)square ft

c)16x+32=80

x=3

width= 2x+4 = 2(3)+4 =10ft

Answer:

8

Step-by-step explanation:

3(x - 2) = 6

3x - 6 = 6

x - 6 = 2

x = 8

hope it helps :)

mark brainliest!!

Answer:

375.5 combined

Step-by-step explanation:

The cost of the dryer is: (825-74)÷2 =375.5 (combined)

Answer:

it represents and the relative amount of energy in the trophic level.i think sorry if I am wrong

The widths of the bars in an energy pyramid represent the units of energy available within each trophic level.

It is defined as the graphical representation of the movement of the energy from one living organism to another in the ecosystem.

When we think of one organism eating another, we usually think of a huge, predatory predator at the top of the food chain. While this depicts the ecological relationships between creatures, it does not depict the energy flow throughout the ecosystem.

Every bar's width indicates the units of energy available within each trophic level, while the height remains constant. The flow of energy goes from the bottom up through the layers of the energy pyramid, gradually decreasing as energy is used up by the creatures at each level.

Thus, the widths of the bars in an energy pyramid represent the units of energy available within each trophic level.

Learn more about the energy pyramid here:

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[tex]2x^2-8x=2x(x-4)[/tex]

Answer:

2x ( x - 4)

Hope that helps?

Answer:

Step-by-step explanation:

The tenure of an FD can vary from 7, 15 or 45 days to 1.5 years and can be as high as 10 years. These investments are safer than Post Office Schemes as they are covered by the Deposit Insurance and Credit Guarantee Corporation (DICGC).

The length of FD in a right-angled triangle with EC as 18 units and CF as 26 units is 20.2 units.

The length of FD can be found using the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is FD, and the other two sides are EC and CF.

EC = 18 units

CF = 26 units

Plugging these values into the Pythagorean Theorem, we get:

[tex]FD^2[/tex] = [tex]EC^2[/tex] + [tex]CF^2[/tex]

[tex]FD^2[/tex] = [tex]18^2[/tex] + [tex]26^2[/tex]

[tex]FD^2[/tex] = 324 + 676

[tex]FD^2[/tex] = 1000

FD = [tex]\sqrt{[/tex](1000)

FD = 10 * [tex]\sqrt{[/tex](10)

FD = 20.2 units

Therefore, the length of FD is 20.2 units.

To learn more about length here:

https://brainly.com/question/32060888

#SPJ2

Correct Question:

In a right-angled triangle with EC as 18 units and CF as 26 units, what is the length of FD.

Answer:

157.47448

Step-by-step explanation:

here you go i did all the math hope this helped

Answer:

128.2189

Step-by-step explanation:

thats the price of the TV including tax

so, you must have some kind of device for you to make a question on brainly. if you are using your phone, there is probably an already installed calculater app on there. if you don't have one, go to app store or play store and download it. if you are using computer, simply search it. of course, you can also use your phone and just search it on the web.

Answer:

by a new one?????

Step-by-step explanation:

Answer:

a.8

Step-by-step explanation:

y=-16

-16=-2x

16=2x

x=16/2=8

Answer:

35/5

Step-by-step explanation:

7/1 divded by 3/5. flip 3/5 to its reciprocal so it becomes 5/3, then times 7/1 by 5/3

Answer:

13 ft, 17 ft, 22 ft

Step-by-step explanation:

let x be the shortest side, then second side is x + 4 and the third side is

2x - 4

sum the 3 sides and equate to 52

x + x + 4 + 2x - 4 = 52 , simplify

4x = 52 ( divide both sides by 4 )

x = 13

x + 4 = 13 + 4 = 17

2x - 4 = 2(13) - 4 = 26 - 4 = 22

lengths of 3 sides are 13 ft, 17 ft and 22 ft

Answer:

0.75 liters

Step-by-step explanation:

1000ml in 1 liter so 0.75*1000=750ml

750ml > 350ml

Answer:

5

x

2

−

11

(

x

)

+

6

Step-by-step explanation:

[tex]5x^2-11x+6\\\\=5x^2-5x-6x+6\\\\=5x(x-1) - 6(x-1)\\\\=(x-1)(5x-6)[/tex]

Answer:

Step-by-step explanation:

12a + 3.50t x 6rides

Answer:

20.

Step-by-step explanation:

That's the correct answer

Answer:

20

Step-by-step explanation:

To divide by a fraction, such as 1/4, we invert the fraction and then multiply instead of dividing.  Thus:

5÷1/4 = 5*(4/1) =20

Answer:

HF = 14.9

Step-by-step explanation:

Answer:

hope it helps

..........

The statement that a ratio of two measurements having different units of measure IS ONE is false

Ratios are used to relate measurements of different quantities.

The measures of the quantities may or may not be one (1).

When the second quantity has a measure of one, then the ratio is called a unit rate.

So, the quantities may be one, but it is not a requirement that the measure of one or both quantities be one.

Hence, the statement is false

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Answer: Max has 4 cards.

Step-by-step explanation: 2/6 is equal to 1/3 so 4/6 is equal to 2/3

Also an easier way is to divide 4 by 2 to get 2 and 6 by 2 to get 3.

Answer:

4 cards

Step-by-step explanation:

Each card takes  [tex]\frac{1}{6}[/tex] of an hour to be completed, and Max works for [tex]\frac{2}{3}[/tex] of an hour, so Max must've completed x amount of cards in

[tex]\frac{1}{6} x=\frac{2}{3}[/tex]

And we can solve the equation by multiplying the reciprocal of [tex]\frac{1}{6}[/tex] , which is [tex]\frac{6}{1}[/tex],to solve for x:

[tex]\frac{6}{1} * \frac{1}{6} x = \frac{2}{3} * \frac{6}{1} \\ \frac{6 *1}{6*1} x=\frac{2*6}{3*1} \\ \frac{6}{6} x=\frac{12}{3} \\[/tex]

And for any fraction, if the denominator and the numerator are the same number (except for 0), then it will result in 1.

[tex]1x=\frac{12}{3}[/tex]

The 1 isn't necessary when multiplying it with a variable, so we can simply remove it:

[tex]x=\frac{12}{3}[/tex]

And we can simplify the fraction...:

[tex]x=4[/tex]

And we are done!

Couldn't make a fraction bar but hopes this helps :(

Let [tex]f^{-1}(x)[/tex] be the inverse of

[tex]f(x) = 3 \log_3 (x + 3) + 1[/tex]

Then by definition of inverse function,

[tex]f\left( f^{-1}(x) \right) = 3 \log_3 \left(f^{-1}(x) + 3\right) + 1 = x[/tex]

Solve for the inverse :

[tex]3 \log_3 \left(f^{-1}(x) + 3\right) + 1 = x[/tex]

[tex]3 \log_3 \left(f^{-1}(x) + 3\right) = x - 1[/tex]

[tex]\log_3 \left(f^{-1}(x) + 3\right) = \dfrac{x - 1}3[/tex]

[tex]3^{\log_3 \left(f^{-1}(x) + 3\right)} = 3^{\frac{x-1}3}[/tex]

[tex]f^{-1}(x) + 3 = 3^{\frac{x-1}3}[/tex]

[tex]f^{-1}(x) = 3^{\frac{x-1}3} - 3[/tex]

Answer:

132 in /12 in/ft + 3 yd(3ft/yd) = 11 + 9 = 20 ft

Step-by-step explanation:

Answer:

20 ft

Step-by-step explanation:

12 inches = 1 foot

12 : 1 = 132 : y

[tex]\frac{132:y}{12:1}[/tex]

12 × y = 132 × 1

12y = 132

12y ÷ 12 = 132 ÷ 12

y = 11

11 ft

1 yard = 3 feet

1 : 3 = 3 : y

[tex]\frac{1:3}{3:y}[/tex]

1 × y = 3 × 3

1y = 9

y = 9

9 ft

11 ft + 9ft = 20 ft