Please help me make you show how to solve it please

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.

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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]

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:

1 = YES

2 = NO

Answer:

52

Step-by-step explanation:

AB is the hypotenuse of the right triangle

sin34 = opp/hyp = 29/hyp

hyp = 29/sin34 = 51.860457849...

Answer:

[tex]let \: |ab| \: be \: x \\ \\ \frac{ \sin(90) }{x} = \frac{ \sin(34) }{29} \\ x \sin(34) = 29 \sin(90) \\ x = \frac{29 \sin(90) }{ \sin(34) } \\ x = 51.86(2.d.p) \\ |ab| = 51.86[/tex]

Answer:

n = -6

Step-by-step explanation:

2n + (n + 2) = -16

3n + 2 = -16

3n = -18

Answer:

D. [tex] 5.1[/tex]

Step-by-step explanation:

[tex] \frac{ - 44.288 - 31.6}{ - 3.1(6 - 1.2)} [/tex]

➡️ [tex] \frac{ - 75.888}{ - 3.1 \times 4.8} [/tex]

➡️ [tex] \frac{24.48}{4.8} [/tex]

➡️ [tex] = 5.1[/tex]

Answer:

B____C____D_____E

BC+ CE = BD + DE

(3x+47) + (x+26) = ( x+27) + (10)

4x + 73 = x + 37

4x – x = 37 – 73

3x = ‐ 36

x = – 36/ 3 —> x = – 12

BC = 3x + 47 = 3(-12) + 47 = - 36 + 47 = 11

BD = x+ 27 = –12+27 = 15

CE = x + 26 = –12+26= 14

I hope I helped you^_^

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:

p=2l+2w

=2*12'7"+2*11'3"

Answer:

$1080

Step-by-step explanation:

s=30w+750

s=30(11)+750

s=330+750

s=1080

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:

14

Step-by-step explanation:

√36+√64

√36=6

√64=8

6+8

14

THANK YOU

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:

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: 60th

Step-by-step explanation:

First order the values from least to greatest:

47, 49, 61, 76, 79, 88, 92, 92, 94, 94.

We can note that the 88 is the 6th of 10 values, so 6/10 = 0.60 or the 60th percentile.

Theresa is in 60 percentile.

A test that is administered and scored in a consistent, or "standard," manner is known as a standardized test. The questions and interpretations on standardized tests are designed to be consistent and are administered and scored in a predetermined, standard manner.

A standardized test is one in which the same test is given to all test takers in the same way and graded in the same way for everyone.

Given scores

88, 49, 92, 47, 61, 94, 94, 76, 79, and 92.

arrange in increasing order,

47, 49, 61, 76, 79, 88, 92, 92, 94, 94

Theresa got 88, which is sixth term

percent = term x 10

 percent = 6 x 10 = 60%

Hence, she is in 60%.

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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.

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:

54.895

Step-by-step explanation:

hopes it's help you

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:

C

E

Step-by-step explanation:

Answer:

Step-by-step explanation:

t=2g+3.

-7 x = -28

Divide both sides by -7.

x = 4

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]

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:

1. (6,3)

2. x = 850, y = 150

Step-by-step explanation:

1. 3x-5y=3

4x-15y=-21

-9x +15y=-3 (multiply by -3)

4x-15y=-21

-5x=-30

x = 6

3(6)-5y=3

18-5y=3

-5y= -15

y= 3

so, x = 6, y = 3

2.

let x be regular

let y be reserved

x+y=1000

x= 5, y= 5+2=7 ("2 dollar more")

5x+7y=5300

x+y=1000

use the elimination method

x=850, y=150

so, the regular tickets were 850 and reserved tickets were 150 sold.