Express in algebraic terms: five less than four times a number.

Answer:

63

Step-by-step explanation:

∫₂⁴ f(x) g"(x) dx

Integrate by parts.

If u = f(x), then du = f'(x) dx.

If dv = g"(x) dx, then v = g'(x).

∫ u dv = uv − ∫ v du

= f(x) g'(x) − ∫ g'(x) f'(x) dx

f'(x) is constant at 3, so:

= f(x) g'(x) − ∫ 3 g'(x) dx

= f(x) g'(x) − 3 g(x)

Evaluate from x=2 to x=4.

[f(4) g'(4) − 3 g(4)] − [f(2) g'(2) − 3 g(2)]

[(13) (7) − 3 (9)] − [(7) (1) − 3 (2)]

64 − 1

63

The required value of [tex]\int\limits^4_2 {f(x)g"(x)} \, dx (1)[/tex] is 63.

Given that,

The table above gives selected values of twice-differentiable functions f and g,

The first two derivatives of g. If f′ (x) = 3 for all values of x.

We have to determine,

What is the value of [tex]\int\limits^4_2 {f(x)g"(x)} \, dx (1)[/tex].

According to the question,

To obtain the value of given function, integrating the function,

[tex]= \int\limits^4_2 {f(x)g"(x)} \, dx (1)[/tex]

Integrating by using by-parts.

[tex]= \int\limits^4_2 {f(x)g"(x)} \, dx (1)\\\\if\ u = f(x), \ then \ du = f'(x)dx\\\\if \ dv = g"(x)dx, \ then \ v = g'(x)\\\\[/tex]

Then,

[tex]\int u\ dv = uv\ - \ \int v \ du\\\\= f(x) \ g'(x) - \int g'(x) f'(x) \ dx\\[/tex]

if f'(x) is constant at 3,

Then,

[tex]= f(x) g'(x) - \int g'(x)\dx\\\\= f(x) g'(x) -3g(x)[/tex]

Substitute from x = 2 to x = 4 then evaluate,

[tex]= [f(4)\ g'(4) - 3 \ g (4)]- [f(2)\ g'(2) - 3 \ g (2)]\\\\= [(13).(7) - 3.(9)] - [7.(1)- 3.(2)]\\\\= [91-27} - {7-6}\\\\= 64-1\\\\= 63[/tex]

Hence, The required value of [tex]\int\limits^4_2 {f(x)g"(x)} \, dx (1)[/tex] is 63.

To know more about Integration click the link given below.

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Answer:

$13.75

Step-by-step explanation:

0 weeks = 260

4 weeks = 315

8 weeks = 370

Every 4 weeks, the rate of change is $55 as can be seen by 315 - 260 = 55 and 370 - 315 = 55.

Per week, the rate of change is $13.75 This is because $55 ÷ 4 weeks = rate of change per week

55 ÷ 4 = 13.75

Answer:115.38

Step-by-step explanation:

115.378

=115.38

The hundredth digit is seven

Answer:

the domain or set of departure of a function is the set into which all of the input of the function is constrained to fall.

Step-by-step explanation:

didn't know if you needed the definition or not :)

Answer:

28

Step-by-step explanation:

I hope this helps!

Answer:

28!

Step-by-step explanation:

Answer:

B. all real numbers

Step-by-step explanation:

hope that helps

Answer:

B  hope this helps :)

Step-by-step explanation:

Answer:

31

Step-by-step explanation:

Since be is in the middle its connecting the two.

So you will add the 11 and 20 to get 31

Answer:

-16

Step-by-step explanation:

did the math

Answer:

[tex]\frac{965777}{55555}[/tex]

Step-by-step explanation:

The answer is quite simple, just divide both sides and rewrite the equation to get it. Maybe focus more on the question rather than yourself next time :)

Answer:

-1.5

Step-by-step explanation:

The product of slopes of two perpendicular lines = -1

If line one has a slope of 2/3;

Let line two, perpendicular to line one, has a slope of a

2/3 × a = -1

a = -1 ÷ 2/3 = -3/2 = -1.5

Answer: 9m^4- 30m^3 +37m^2 - 20m + 4  

Step-by-step explanation:

(3m^2 -5m +2)^2  is the same as (3m^2 -5m +2)(3m^2 -5m +2)  

Now apply the distributive property 3 times to solve.

3m^2(3m^2 -5m + 2) =   9m^4 - 15m^2 + 6m^2

-5m(3m^2 -5m+2) = -15m^3 +25m^2 -10m

2(3m^2 -5m +2)  =  6m^2 - 10m + 4

Now add the solutions

(9m^4 - 15^2 + 6m^2) (-15m^3 + 25m^2 -10m)(6m^2 -10m +4) =

9m^4- 30m^3 +37m^2 - 20m + 4

Answer:

4567

Step-by-step explanation:

add 2

add 88

sub 99

Answer:

First one.

Step-by-step explanation:

4+(-8) -10+22 =12

24+(-12) 0+ (-12) =-24

Please brainliest! Im on my way to another rank!

The expression 24 + (-12) has a sum of 12 after applying the arithmetic operation options (b) and (c) is correct.

The study of numbers and their operations, which are relevant to all other fields of mathematics, is part of the discipline of arithmetic operations. Addition, subtraction, multiplication, and division are the basic operations that make up this system.

It is given that:

The expressions are shown in the picture.

After solving using Arithmetic operation:

Take the expression:

= 24 - 12

= 12

-10 + 22

= 12

Thus, options (b) and (c) are correct.

Learn more about the arithmetic operations here:

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Answer:

56mph

Step-by-step explanation:

If d=rt,

then s=d/t,

so if d=67.2 and t=1.2,

then 67.2/1.2=56

8+3a-2a+7=0

8+a+7=0

a+15=0

a= (-15)

Hope it helped

Answer:

perimeter of new room = 2[(l+20)*b]

Step-by-step explanation:

Answer:

2000

Step-by-step explanation:

just muliply

Answer:

c

Step-by-step explanation:  3 is not bigger than 9 so it can't bump it up so it stays like that.

Answer: Rate of water flow is 12/5 gallon per minute

Step-by-step explanation:

Given the following :

Volume of faucet pot = 2 gallon

Time taken to fill the faucet pot = 5/6 of a minute = (5/6) minute.

Rate of water flow:

Volume of faucet pot / time taken

= 2 gallon ÷ (5/6) minute

= 2 gallon × (6/5) minutes

= (12 /5) gallon / minute

= 2 2/5 gallon / minute

Hence rate of water flow is 12/5 gallon per minute.

Answer:

2 2/5

Step-by-step explanation:

2 2/5

Since A is the midpoint of BC, we can assume BA and AC are equal to each other.

We also know that BC = BA + AC = 23 + 23 = 46

Answer: x = -10

Step-by-step explanation:

Answer:

∛8 = 2

Step-by-step explanation:

[tex]\sqrt[3]{8}[/tex]

=2

2*2*2 = 8

Answer:

you can fit 1000 hairs in 10 cm

Step-by-step explanation:

[tex]10^2= .01[/tex]

[tex].01*1000 = 10[/tex]

Answer: [tex](1,-\frac{3}{2})[/tex]

Step-by-step explanation:

To find the midpoint, you use the formula [tex]midpoint=(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex].

The points are (-2,-1) and (4,-2).

[tex]midpoint=(\frac{-2+4}{2} ,\frac{-1+(-2)}{2} )[/tex]              [add]

[tex]midpoint=(\frac{2}{2} ,\frac{-3}{2} )[/tex]                            [divide]

[tex]midpoint=(1 ,\frac{-3}{2} )[/tex]

Now, we know the midpoint is [tex](1,-\frac{3}{2})[/tex].

Step-by-step explanation:

By Pythagoras' Theorem, z^2 + (2.7)^2 = (4.2)^2.

This means that z^2 = (4.2)^2 - (2.7)^2 = 10.35.

So z = 3.2 (1 d.p.)

Step-by-step explanation:

x=4.2

y=2.7

z=x

(×+y=×

(4.2+2.7=×)

×=6.9

Answer:

about 39%

Step-by-step explanation:

In order to find the percent, you need to find the total amount of games they played first.

9 games + 7 games + 2 games = 18 games total

Divide the number of games they won by the total amount of games they played:

7 games / 18 games = about 39%

Given:

Point O is on line segment NP.

OP=10, NP=2x, and NO=x+7.

To find:

The numerical length of NO.

Solution:

If point O is on line segment NP, then by segment addition property, we get

[tex]NP=NO+OP[/tex]

[tex]2x=(x+7)+10[/tex]

[tex]2x=x+17[/tex]

Subtract both sides by x.

[tex]2x-x=17[/tex]

[tex]x=17[/tex]

The value of x is 17.

Now,

[tex]NO=x+7[/tex]

[tex]NO=17+7[/tex]

[tex]NO=24[/tex]

Therefore, the numerical length of NO is 24units.

Answer:

(a) [tex]x \leq 2.5[/tex]

(b) [tex]x \geq 2[/tex]

Step-by-step explanation:

Solving (a):

[tex]0.4x - 1 \leq 0[/tex]

Add 1 to both sides

[tex]0.4x - 1 + 1\leq 0 + 1[/tex]

[tex]0.4x \leq 1[/tex]

Solve for x

[tex]x \leq 1/0.4[/tex]

[tex]x \leq 2.5[/tex]

Solving (b):

[tex]2.3x \geq 4.6[/tex]

Solve for x

[tex]x \geq 4.6/2.3[/tex]

[tex]x \geq 2[/tex]

Hey there!

[tex]6x+2y=12[/tex]

Let's start by adding -2y to both sides.

[tex]6x+2y+-2y=12+-2y\\\text {This equals: 6x=-2y+12}[/tex]

Our second and final step is to divide both sides by 6.

[tex]\frac{6x}{6}=\frac{-2y+12}{6} \\x=\frac{-1}{3}y+2(ANSWER)[/tex]

If you are looking to solve y, the answer is 6 - 3x.

If you are looking for x, the answer is x = 2 - y/3

Hope this helps and have a great weekend!

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