graph the sequence 2, 4, 6, 8, 10

Answer:

a = 5, b = - 13

Step-by-step explanation:

The Remainder theorem states that the remainder when f(x) is divided by (x - a) is equal to f(a)

Thus the remainder for division by (x + 2) is zero , then by substituting x = - 2 into the expression.

2(- 2)³ + a(- 2)² + b(- 2) - 30 = 0

2(- 8) + 4a - 2b - 30 = 0

- 16 + 4a - 2b - 30 = 0

- 46 + 4a - 2b = 0 ( add 46 to both sides )

4a - 2b = 46 → (1)

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Similarly when f(x) is divided by (cx - a) the remainder is f([tex]\frac{c}{a}[/tex] )

The remainder on dividing by (2x - 1) is - 35, then by substituting x = [tex]\frac{1}{2}[/tex]

2([tex]\frac{1}{2}[/tex] )³ + a([tex]\frac{1}{2}[/tex] )² + [tex]\frac{1}{2}[/tex] b - 30 = - 35

2([tex]\frac{1}{8}[/tex] ) + [tex]\frac{1}{4}[/tex] a + [tex]\frac{1}{2}[/tex] b - 30 = - 35 ( add 30 to both sides )

[tex]\frac{1}{4}[/tex] + [tex]\frac{1}{4}[/tex] a + [tex]\frac{1}{2}[/tex] b = - 5 ( multiply through by 4 to clear the fractions )

1 + a + 2b = - 20 ( subtract 1 from both sides )

a + 2b = - 21 → (2)

Solve (1) and (2) simultaneously )

Add (1) and (2) term by term to eliminate b

5a = 25 ( divide both sides by 5 )

a = 5

Substitute a = 5 into (2)

5 + 2b = - 21 ( subtract 5 from both sides )

2b = - 26 ( divide both sides by 2 )

b = - 13

According to the remainder theorem, when a polynomial P(x) is divided by (x-t) then the remainder of the division is equal to P(t). The value of a and b are 5 and -13, respectively.

According to the remainder theorem, when a polynomial P(x) is divided by (x-t) then the remainder of the division is equal to P(t). If P(t)=0, then the (x-t) is the factor of the polynomial.

Using the remainder theorem we can write,

f(x) = 2x³+ ax² + bx - 30

f(-2) = 2(-2)³ + a(-2)² + b(-2) - 30 = 0

-16 + 4a - 2b - 30 = 0

4a - 2b = 46   ........ equation 1

f(x) = 2x³+ ax² + bx - 30

f(1/2) = 2(1/2)³ + a(1/2)² + b(1/2) - 30 = -35

(1/4) + a(1/4) + b(1/2) = -35 + 30

(1+a+2b)/4 = -5

1 + a + 2b = -5 × 4

a + 2b = -21   .......... equation 2

Adding the two equations,

4a + 2b + a - 2b = 46 - 21

5a = 25

a = 25/5

a = 5

Substitute the value of a in any one of the equation,

a + 2b = -21

5 + 2b = -21

2b = -21 - 5

2b = -26

b = -26/2

b = -13

Hence, the value of a and b are 5 and -13, respectively.

Learn more about the Remainder Theorem here:

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Answer:

$1080

Step-by-step explanation:

s=30w+750

s=30(11)+750

s=330+750

s=1080

Answer:

f(2)=4

Step-by-step explanation:

[tex]\\ \rm\longmapsto f(x)=x^2,x>1[/tex]

[tex]\\ \rm\longmapsto f(2)=2^2[/tex]

[tex]\\ \rm\longmapsto f(2)=4[/tex]

Answer:

56-x=728+2x

1.) rearrange

[tex]56x = 728 + 2x \\ \ - x + 56 = 728 + 2x[/tex]

[tex] - x + 56 = 728 + 2 x \\ \\ - x + 56 = 2x + 728[/tex]

2.)subtract 56 on both side

[tex] - x + 56 = 2x + 728 \\ \ - x + 56 - 56 = 2x + 728 - 56[/tex]

3.) simplify

[tex] - x = 2x + 672[/tex]

4.)Subtract 2 on both sides

[tex] - x = 2x + 672 \\ \\ - x - 2x = 2x + 672 - 2x[/tex]

5.) simplify

[tex] - x - 2x = 2x + 672 - 2x \\ \\ - 3x = 2x + 672 - 2x \\ \\ - 3x = 672[/tex]

6.)divide both sides on the same equation

[tex] - 3x = 672 \\ \\ \frac{ - 3x}{ - 3} = \frac{672}{ - 3} [/tex]

7.) simplify

[tex]x = - 224[/tex]

8.) answer

[tex]x = - 224[/tex]

if u need any help, just let me know

Answer:

y = - [tex]\frac{1}{2}[/tex] x - 4

Step-by-step explanation:

( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )

y -  [tex]y_{1}[/tex] = m ( x - [tex]x_{1}[/tex] )

~~~~~~~~~~~~~~~~~

m = - [tex]\frac{1}{2}[/tex]

( - 10, 1 )

y - 1 = - [tex]\frac{1}{2}[/tex] [ x - ( - 10 )]

y - 1 =  - [tex]\frac{1}{2}[/tex] x + ( - [tex]\frac{1}{2}[/tex] )(10)

y = - [tex]\frac{1}{2}[/tex] x - 4

Answer:

C

E

Step-by-step explanation:

Answer:

Step-by-step explanation:

first one: 1/4

second one: 1/4

last one: 1/4

8 divided by 2=4 and 4 becmes the denominator

the answer is basicallly 1/4

What grade is this btw

Answer:

radius is 7 cm

Step-by-step explanation:

formular for volume:

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

r is radius

h is height

[tex]1540 = 3.14 \times {r}^{2} \times 10 \\ {r}^{2} = 49.0 \\ r = 7 \: cm[/tex]

-7 x = -28

Divide both sides by -7.

x = 4

Answer:

1 = YES

2 = NO

Answer:

y = -|x + 1| - 4

Step-by-step explanation:

Answer:

An integer is any positive whole number or its opposite. Here, opposite means sign. So a positive integer has a negative opposite and vice versa

Step-by-step explanation:

-5 and 5 are an example.

Answer:

Step-by-step exA wall is 1200 sq ft.

A gallon of paint covers 200 sq ft.

Complete the conversion factor: 1 gallon / ? sq ftplanation:

Answer:

ethethe

Step-by-step explanation:

thethetht

Answer:

54.895

Step-by-step explanation:

hopes it's help you

Answer:

If sum were 75 the integers would be 24, 25 and 26, so the next lowest/smallest sum would be 23 + 24 + 25 is 72. The answer is 23.

Answer:

smallest value=24

Step-by-step explanation:

steps are in picture.

Note:If you have any confusion you can ask me.

Answer:

2.0km

Step-by-step explanation:

Answer:

1/2

Explanation:

22 ÷ 11 = 2

Exactly half of the cakes were made in the morning

Answer:

11:22

Simplified=

1:2

Answer:

0.25 or 25%

Step-by-step explanation:

because the area of circle is 2πr^2 or two radius times together so that both are decreased by 50%

Answer:

Answer is 9.

Step-by-step explanation:

a (5, 3),  b (5, -6)

[tex]\sqrt(x^2 - x^1) ^2+(y^2- y^1)^2\\\sqrt(5 - 5)^2 +(-6- 3)^2\\\\\sqrt(0)^2 +(-9)^2\\\\\sqrt(81)\\\\9[/tex]

Answer: 9

Step-by-step explanation:

Sqrt (5-5)^2+(-6-3)^2 =

Sqrt (0)+(-9)^2

Sqrt 81 = 9

Answer:

x1=-4,y1=-1,x2=2,y2=3

Now,

slope (m)=3/2

By formula,

(y-y1)=m (X-x1)

y-(-1)=3/2(x+4)

y+1=3/2(x+4)

2y+2=3x+12

3x-2y+10=0,which is required equation.

Step-by-step explanation:

Given line y=1/3x-4

slope of given line m=1/3

Slope of required line :

m=1/3

As lines are parallel then slope of lines are equal.

Using point slope form:

y-y1=m(x-x1)

p(x1,y1)=(9,8)

y-8=1/3(x-9)

3y-24=x-9

x-3y-9+24=0

x-3y+15=0

Note:if you need to ask any question please let me know.

Answer:

m = -3

Step-by-step explanation:

15 - (4m - 5) = 32            (Given)

15 - 4m + 5 = 32             (Distributed)

20 - 4m = 32                  (Added like terms)

20 - 4m - 20 = 32 - 20  (Subtract 20 on both sides)

-4m = 12                         (Simplify)

-4m/-4 = 12/-4                (Divide -4 on both sides)

m = -3                             (Simplify)

Answer:

n | 0 | 0 1

| y 2 | 2 y 3 | 3 años

Step-by-step explanation:

The answer is 56. work is shown below.

Step 1: apply 2nd power to everything inside parentheses

(7 - 1)² = 7² - 1²

Step 2: apply exponents (remember, exponents are a shorter way to express a number multiplied by itself a number of times).

1 x 1 = 1

7 x 7 = 49

Step 3: subtract

49 - 1 = 48

Step 4: apply exponent

2 x 2 x 2 x 2 = (2 x 2) x (2 x 2)

2 x 2 = 4

2 x 2 = 4

4 x 4 = 16

2⁴ = 16

Step 5: add

48 + 16 = 64

Step 6 (final step): subtract

64 - 8 = 56

final answer: 56

The bottom row x axis) is seconds and goes to 6 seconds

Each peak is a heartbeat, there are 9 in the 6 seconds.

A minute is 60 seconds.

60 seconds / 6 seconds = 10

9 beats every 6 seconds x 10 = 90 beats per minute.

The heart rate is 90 beats per minute

Answer:

Step-by-step explanation:

t=2g+3.