Given that f(x) = 2x³-7x²+7ax+ 16 is divisible by x-a, find
(i) the value of the constant a
(ii) the remainder when f(x) is divided by 2x+1.

Answer:

[tex](x + 7) \times (3x - 4)[/tex]

Step-by-step explanation:

[tex] {3}^{2} + 17x - 28[/tex]

[tex]3 {x}^{2} + 21x - 4x - 28[/tex]

[tex]3 \times x(x + 7) - 4x - 28[/tex]

[tex]3x \times ( x + 7) - 4(x + 7)[/tex]

[tex](x + 7) \times (3x - 4)[/tex]

Step-by-step explanation:

since < 5 = < 8, so,

< 7 = < 6 = 29°

and < 5 = 90° - 29° = 61°

Answer:

Step-by-step explanation:

We mark checks as negative and a deposit as positive:

Add up to get the total change of:

Correct choice is D

Answer:

Answer :-

Here, Irene is having a checking account. First she write a check of $160. Then means it has an decrease money. (-160) Now, She deposit $125. This means Now, the balance is -160 + 125 = $-35. She again write a check of $40. (-40). Total change =>

-40 - 35

-75

Option D is correct mate!

Answer:

[tex]25x +10 \\ 25x \\ are \: the \: exprassion \\ thank \: you[/tex]

Answer:

2nd option and last option

Step-by-step explanation:

the first option is an equation: it has a solution.

the second option is an expression, and follows the criteria of an expression (can be made of co-effecients, symbols, operations, numbers, ect.), so it is one of our answers.

the third option is an equation since it has the equal sign, and thus, has a solution.

the fourth option is simply a number- a value. it does not fit as an equation (no solution) or an expression (can be made of co-effecients, symbols, operations, numbers, ect.)

lastly, our fith option is an expression. it is a coefficient (a multiplication problem between a known value and a variable). this is also one of our last answers.

Answer:

csc x sec x

Step-by-step explanation:

csc = 1/sin

1/sin^2    /  cos/sin    =   1 / sin^2    *  sin/cos       =   1 / sin cos  = csc sec

(A)

Step-by-step explanation:

The meal cost $45.25 so 20% of this for tip is

($45.25)(0.20) = $9.05. Since the tip is split between 4 friends, divide this tip by 4 and each one paid ($9.05/4) = $2.26.

Answer:

g(x) = [tex]\frac{1}{x+11}-9[/tex] is my choice

Step-by-step explanation:

I. If move right is +x and move down is -y

               then f(x) = [tex]\frac{1}{x}[/tex]

               +x = 11, -y = -9

                so g(x) = [tex]\frac{1}{x+11}-9[/tex]

Hope that help :D

Answer: x = 8

Step-by-step explanation:

Given

(1/3) (3x + 6) + 2x = 26

Expand parentheses and apply the distributive property

(1/3) · 3x + (1/3) · 6 + 2x = 26

x + 2 + 2x = 26

Combine like terms

(x + 2x) + 2 = 26

3x + 2 = 26

Subtract 2 on both sides

3x + 2 - 2 = 26 - 2

3x = 24

Divide 3 on both sides

3x / 3 = 24 / 3

[tex]\boxed{x=8}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

(1 )= ..x = (2)

Step-by-step explanation:

(1) = x = (2)

Answer: 1 ≤ x ≤ 2

Step-by-step explanation:

Given inequality

3 ≤ 6x - 3 ≤ 9

Add 3 on all sides

3 + 3 ≤ 6x - 3 + 3 ≤ 9 + 3

6 ≤ 6x ≤ 12

Divide 6 on all sides

6 / 6 ≤ 6x / 6 ≤ 12 / 6

[tex]\boxed{1}[/tex] ≤ x ≤ [tex]\boxed{2}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

2-x^2-6x

Step-by-step explanation:

2-x(x+6)

2-x^2-6c

Answer: Student ticket cost $2 and an adult ticket cost $3.

257 kids total attended

Step-by-step explanation:

Answer: g(x) = (x+1)-3

Step-by-step explanation: Assuming you are moving from expression f to expression g, the plus one in the equation moves the vertex to the right one. subtracting three outside of the parenthesis moves the vertex down three, giving you a vertex of (1,-3). hope this helps!

Answer:

[tex]4( \sqrt[5]{ {x}^{2} y} ) + 3( \sqrt[5]{ {x}^{2}y } ) \\ [/tex]

factorise out the 5th root of x²y :

[tex] = \sqrt[5]{ {x}^{2}y } (4 + 3) \\ = 7( \sqrt[5]{ {x}^{2} y} )[/tex]

Answer:

x = 9±sqrt(7)

Step-by-step explanation:

3(x-9)^2 =21

Divide each side by 3

3/3(x-9)^2 =21/3

(x-9)^2 =7

Take the square root of each side

sqrt((x-9)^2) =±sqrt(7)

x-9 =±sqrt(7)

Add 9 to each side

x = 9±sqrt(7)

9514 1404 393

Answer:

  A.  2×10³

Step-by-step explanation:

The ratio of diameters is ...

  (189,869 mm)/(98 mm) ≈ 1927.3 ≈ 2000 = 2×10³

The diameter of the peach became about 2×10³ times as large.

Answer:

use the formula sn= n(a1+an)/2

Step-by-step explanation:

2982=28(228+an)/2

5964=28(228+an)

5964/28=228+an

213=228+an

an=-15(last term)

to find difference use formula

an = a+(n-1)d

-15=228+(28-1)d

-243=27d

d=-243/27

d=-9

arithmetic sequence  can be found be keep on subtracting 9 from 228

hence the arithmetic sequence is

228, 219, 210, 201, 192, 183, 174........-15

Answer:

when x = 18. Putting x = 18 into the equation y = 6/x, we have y = 6/18. Simplifying the fraction gives us y = 1/3.

Step-by-step explanation:

Answer:

the point (9,-12) is also on the line

Step-by-step explanation:

by using the 2 points the equation is y=-4/3x

use x of 9

y = -12

it will also represent a direct variation function

so two of the 4 will be correct

Answer:

The point (9,-12) is also on the line

Step-by-step explanation:

Please give brainliest

Answer:

The first choice.

Step-by-step explanation:

Domain = x value (first value in a coordinate pair: (x,y))

Range = y value

A function cannot have a repeating Domain value.

This eliminates the last option since -4 is used twice.

The second option has 11 as a y value but it is not in the range.

The third option has 10 as an x value but it is not in the domain.

Step-by-step explanation:

[tex] - \frac{5}{6} + ( - 2 \frac{5}{8} )[/tex]

[tex] = - \frac{5}{6} - \frac{21}{8} [/tex]

[tex] = \frac{ - 20 - 63}{24} [/tex]

[tex] = \frac{ - 83}{24} (ans)[/tex]

Answer:

[tex]radius \: of \: first \: circle \: = \frac{3}{2} = 1.5cm \\ radius \: of \: \: second = \frac{4}{2} = 2cm \\ radius \: of \: third = \frac{6}{2} = 3cm \\ then \: ab \: length \\ = radius \: of \: first + diameter \: of \: second \: +r adius \: of \: third \\ = 1.5 + 4 + 3 \\ = 1.5 + 7 \\ = 8.5 cm\\ thank \: you[/tex]

Answer:

405 gallons

Step-by-step explanation:

Let it be that the amount of gallons of a 70% antifreeze solution  is x, when a mixture that is 60 percents of antifreeze is placed in y gallons

x+90=y - the equation of dependence between solutions

The amount of antifreeze in the first one is x/100*70= 0.7x (in gallons), in the second solution (15percents) antifreeze is 90/100*15=13.5 (in gallons).

In the mixture we should get there will be y/100*60=0.6y - gallons of antifreeze

0,7x+13.5=0.6y

We have two equations x+90=y and 0,7x+13.5= 0.6y

0.6x+54=0.6y

0.7x+13.5=0.6y

0.7x+13.5-0.6x-54= 0.6y-0.6y

0.1x-40.5=0

x=405- the answer

p.s. sorry, I don't know what the six-step method is. But the answer is right.

Answer:

$9000

Step-by-step explanation:

36000:4=$9000

Answer:

1 hour 12 minutes

Step-by-step explanation:

1.2 × 60 = 72 minutes

72-60 = 12 minutes

Step-by-step explanation:

The arithmetic mean of a distribution is 5. The second and the third moments about the mean are 20 and 140 respectively. What is the third moment of the distribution about 10?

Call the random variable x.

Now, define a new variable y = x - 5. Note that x - 10 = y - 5.

So, it is clear that (x-10)^3 = (y-5)^3

Also, note that (y-5)^3 can be expanded as follows:

Expand (y-5)³

Result ; y³-15 y²+75 y - 125

Letting E denote expectation with respect to the random variable x, we see that

E[(y-5)^3 ] = E(y^3) -15 E(y^2) + 75 E(y) - 125

Again, recalling that y = x - 5, have

E(y^3) = 140

E(y^2) = 20

E(y) = E(x) - 5 = 5 - 5 = 0

Thus,

E[(y-5)^3 ] = 140 -15(20) + 75(0) -125 = -285

Finally, note that

E[(y-5)^3] = E[({x-5} -5)^3] = E[(x-10)^3]

So, we get E[(x-10)^3] = -285.

The percentage of 45 out of 120 is 38%  thus 38% calories from fat.

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

Given that,

Total calories = 120

Calories from fat = 45

Fraction of calories from fat = 45/120 = 0.38

Percentage of calories from fat out of total calories ⇒

(45/120) × 100 = 38%

Hence "The percentage of 45 out of 120 is 38%  thus 38% calories from fat".

For more about the percentage,

brainly.com/question/13450942

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Answer:

None

Step-by-step explanation:

Simply, the absence of s^-1 shows the answer as none

Answer:

the answer is C

Step-by-step explanation:I hope you understand.... if you don't, let me know. pls make this your brainliest answer.

cheers

Answer:

B. [tex]\frac{5}{8}[/tex]

Explanation:

Because the denominators (bottom numbers) of both fractions are the same, we simply just add the numerators (top numbers) and keep 8 as the denominator.