how to factor x^3 + x - 4 = 0

Answer:

1) [tex]x = -1[/tex]  ||     2) [tex]x = 10[/tex]

Explanation:

1)

→ [tex]\log _3\left(\frac{1}{3}\right)=x[/tex]

→ [tex]\frac{1}{3} = 3^x[/tex]

→ [tex]3^{-1} = 3^x[/tex]

→ [tex]x = -1[/tex]

2)

→ [tex]\log _3\left(x-1\right)=2[/tex]

→ [tex]x - 1 = 3^2[/tex]

→ [tex]x -1 = 9[/tex]

→ [tex]x = 9 +1[/tex]

→ [tex]x = 10[/tex]

[tex]\qquad \qquad\huge \underline{\boxed{\sf Answer}}[/tex]

Here's the solution ~

[tex]\qquad \sf  \dashrightarrow \: log_{ {3} }( \frac{1}{3} ) = x[/tex]

[tex]\qquad \sf  \dashrightarrow \: log_{ {3} }( {3}^{ - 1} ) = x[/tex]

[tex]\qquad \sf  \dashrightarrow \: log_{ {3} }( {3})^{ - 1 } = x[/tex]

[tex]\qquad \sf  \dashrightarrow \: - 1 \times log_{3}(3) = x[/tex]

[tex]\qquad \sf  \dashrightarrow \: - 1 \times 1 = x[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = - 1[/tex]

[tex]\qquad \sf  \dashrightarrow \: log_{3}(x - 1) = 2[/tex]

[tex]\qquad \sf  \dashrightarrow \: x - 1 = {3}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 9 + 1[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 10[/tex]

Answer:

5

Step-by-step explanation:

You simply just divide 100 by 20 and get your answer which is 5.

When you distribute something, you are dividing it into parts. In math, the distributive property helps simplify difficult problems because it breaks down expressions into the sum or difference of two numbers

Answer:

[tex] {7}^{2} [/tex]

[tex]7[/tex]

equations

Answer:

Flight arrived in london on 5 : 35 pm Wednesday

Step-by-step explanation:

Time = 16 h 35 min

Time difference = 7 h

Flight time  =  8am

So

     According to perth time flight reached in london is

         8 am + 16 h 35 m =  8 am + ( 12 h + 4h + 35 m) =

         8pm + 4h +35 =  12am + 35m   = 12 : 35 am

The time difference is 7 h ,so minus this from  perth time

      12 : 35 am -  7h  =   5 : 35 pm

Mark brainliest if you understand

Answer:

a = 156°

b = 132°

c = 108°

Step-by-step explanation:

The sum of the exterior angles of a polygon equals 360°. The sum of an interior and exterior angle equals 180°. There are two missing exterior angles that you need to find the measure of so we can find the value of x.

First exterior angle is with the 82° interior angle. Subtract from 180 to find the exterior angle.

180 - 82 = 98°

The second exterior angle is with the 134° interior angle. Subtract from 180 to find the exterior angle.

180 - 134 = 46°

Now add all the exterior angles together and set them equal to 360.

x + 2x + 3x +72 + 98 + 46 = 360

6x + 216 = 360

6x + 216 -216 = 360 -216

6x = 144

6x/6 = 144/6

x = 24

No find the exterior angles then subtract each one from 180°.

To find a.

a + x = 180

a + 24 = 180

a + 24 - 24 = 180 - 24

a = 156°

To find b.

b + 2x = 180

b + 2(24) = 180

b + 48 = 180

b + 48 - 48 = 180 - 48

b = 132°

To find c.

c + 3x = 180

c + 3(24) = 180

c + 72 = 180

c + 72 - 72 = 180 -72

c = 108°

Answer:

Distributive property

Step-by-step explanation:

Shows the breakdown of distributing the 4

4(x+6)

4x + 4(6)

Answer:

[tex]x=750m[/tex]

Step-by-step explanation:

[tex]Assuming[/tex] [tex]That[/tex]:

[tex]1m=3.3ft[/tex]

We can make the conversion from feet per second to meters per second with this procedure:

[tex](165 \frac{ft}{s} ) (\frac{1m}{3.3ft} )=50\frac{m}{s}[/tex]

Let [tex]x[/tex] be the amount of meters the parachutist will fall during 15 seconds of free fall

Having that in 1 second the parachutist falls 50 meters, we can calculate [tex]x[/tex] :

[tex]x=(50\frac{m}{s} )(15s)[/tex]

[tex]x = 750 m[/tex]

Brainliest?!

​

Answer: 3/9 should be the answer :)

Step-by-step explanation:

Answer:

[tex]p=-10[/tex]

Step-by-step explanation:

Given the following question:

[tex]-5=p+5[/tex]

In order to find the answer, we subtract 5 on both sides:

[tex]-5=p+5[/tex]
[tex]5-5=0[/tex]
[tex]-5-5=-10[/tex]
[tex]-10=p[/tex]
[tex]p=-10[/tex]

Hope this helps.

Answer:

here's your answer hope it helps you

Step-by-step explanation:

the upper bound of an interval uses the number of samples to get its value. same is said for the population standard deviation.

Answer:

120/40=3

Step-by-step explanation: Hope this helps

Answer:

for a three hour job it would be £105

Step-by-step explanation:

to find how much he charges an hour, we divide 140 by 4 and get 35.

from there we multiply 35(£) by 3(hours) and get 105(£).

Step-by-step explanation:

[tex]f'(x)=6x^{2}-6x-12[/tex]

So f'(x)=0:

x^2 - x - 2 = 0

(x-2)(x+1)=0

x=-1, 2

So we need to find the value of f at those critical points and also at the endpoints of the interval

f(-1)=-2-3+12+1=8

f(2)=16-12-24+1=-19

f(-2)=-16-12+24+1=-3

f(3)=54-27-36+1=-8

so the max is 8 and the min is -19

Answer:

7cm

Step-by-step explanation:

15 - 8

Hypotenuse is the longest side

Answer:

it's a unit fraction by cancelling it

Answer:

Whole fraction

Step-by-step explanation:

40/40

= 1

☆ Since we get 1 as the answer, the fraction is a whole fraction.

Hope it helps ⚜

Answer:

simple math convert mph to fps and multiply by 72: 105.6

Step-by-step explanation:

Answer:

180m

Step-by-step explanation:

The figure shown in the picture is a right triangle.

We have two of it's sides and need to find the hypotenuse (the side in front of the right angle).

To find that we must use the Pythagorean theorem:

[tex]c^{2} = {a}^{2} + {b}^{2} [/tex]

Side a is 400m and side b is 300m.

Therefore:

[tex]c^{2} = {300}^{2} + {400}^{2} [/tex]

[tex]c = \sqrt{300 \times 300 + 400 \times 400} = 500[/tex]

Now that we know that side c is 500m we must just substract the distance between Marla and the dock with the lenght of the side to find the answer

500 - 320 = 180m

Answer:

She is 180m from the information Center

She walked 240m from the parking lot to the lake.

Step-by-step explanation:

I searched your question and found the key answers. below is my backup explanation, hope this helps! brainliest, please!

Answer:

∠DCA ≅ 56°

Reason: vertical angles theorem

∠DCF ≅ 144°

Reason: Angles on a straight line (DE) add up to 180°

∠ECB ≅ = 37°

Reason: Angles on a straight line (FA) add up to 180°

∠CAB ≅ ∠DCA ≅ 56°

Reason: Alternate interior angles theorem

∠CBA ≅ ∠ECB ≅ 37°

Reason: Alternate interior angles theorem

Step-by-step explanation:

∠DCA ≅ ∠ECF ≅ 56°

Reason: vertical angles theorem

∠DCF ≅ 180 - 56 = 144°

Reason: Angles on a straight line (DE) add up to 180°

∠ECB ≅ 180 - 56 - 87 = 37°

Reason: Angles on a straight line (FA) add up to 180°

∠CAB ≅ ∠DCA ≅ 56°

Reason: Alternate interior angles theorem

∠CBA ≅ ∠ECB ≅ 37°

Reason: Alternate interior angles theorem

Answer:

solution

Step-by-step explanation:

you can separate it back into its original forms

(Reminder: mixtures cannot be separated and cannot return to its original forms. solutions can be separated and can return to its original forms)

A(0;4); x=0, y=4; m=5

General equation of linear function is [tex]y=mx+b[/tex] ⇒

[tex]4=0\times x+b\\b=4[/tex]

Answer: [tex]y=5x+4[/tex]

Answer:

  350

Step-by-step explanation:

The solution to the equation can be found by multiplying by the denominator, then dividing by its coefficient.

  [tex]0.22 = \dfrac{77}{x}\qquad\text{given}\\\\0.22x = 77\qquad\text{multiply by $x$}\\\\x=\dfrac{77}{0.22}=350\qquad\text{divide by the coefficient of x}[/tex]

The missing value in the fraction is 350.

__

Additional comment

Here, we have rewritten the percentage as a decimal fraction. You could also rewrite it as a ratio of two integer: 22% = 22/100. Sometimes there is confusion about percentages. It can help to think of the % symbol as meaning /100:

  22% = 22/100

Of course, that is "twenty-two hundredths" or 0.22.

If you just write the problem using 22/100 for 22%, then you get the proportion ...

  22/100 = 77/x

  22x = 7700 . . . . . "cross multiply" (multiply by 100x)

  x = 7700/22 = 350 . . . . divide by the coefficient of x

__

If you're paying attention, you see that the solution of this kind of equation has the appearance that the denominator variable and the left-side value are simply swapped:

  [tex]0.22 = \dfrac{77}{x}\ \leftrightarrow\ x=\dfrac{77}{0.22}[/tex]

Effectively, we have multiplied both sides of the equation on the left by x/0.22. There is a property of equality that lets us do that. There is no such thing as a property of equality that says "swap with denominator." You must always pay attention to what is allowed by the properties of equality.

We know:-

[tex] \bigstar \boxed{ \rm Volume \: of \: Cone = \frac{1}{3} \pi {r}^{2} h}[/tex]

[tex] \\ \\ [/tex]

So:-

[tex] \leadsto\sf Volume \: of \: Cone = \dfrac{1}{3} \pi {r}^{2} h[/tex]

[tex] \\ \\ [/tex]

[tex] \leadsto\sf Volume \: of \: Cone = \dfrac{1}{3} \times \pi \times {3}^{2} \times 7 \\ [/tex]

[tex] \\ \\ [/tex]

[tex] \leadsto\sf Volume \: of \: Cone = \dfrac{1}{3} \times \pi \times 3 \times 3 \times 7 \\ [/tex]

[tex] \\ \\ [/tex]

[tex] \leadsto\sf Volume \: of \: Cone = \dfrac{1}{\cancel3} \times \pi \times \cancel3 \times 3 \times 7 \\ [/tex]

[tex] \\ \\ [/tex]

[tex] \leadsto\sf Volume \: of \: Cone =\pi \times 3 \times 7 \\ [/tex]

[tex] \\ \\ [/tex]

[tex] \leadsto\sf Volume \: of \: Cone =\pi \times 21\\ [/tex]

[tex] \\ \\ [/tex]

[tex] \leadsto\bf Volume \: of \: Cone = 21\pi[/tex]

[tex] \\ \\ [/tex]

Therefore option C is correct.

The Volume of the cone is 21π cubic units

The formula for calculating the volume of a cone is expressed as:

V = 1/3πr²h

where:

r is the radius = 3 units

h is the height = 7units

The volume of the cone = 1/3π(3)²*7
Volume of the cone = 3π * 7

Volume of the cone = 21π cubic units

Hence the Volume of the cone is 21π cubic units

Learn more on volume of a cone here: https://brainly.com/question/1082469

Answer:

[        [tex]10000(2)^{-n}[/tex]       ]    where n is the number of hours.

Because the beginning will 10000/2 = 50000, then it keeps double the dividing the time.

Answer:

-(x+8) (x-2) I think this is the answer

Step-by-step explanation:

total area

20 × 17 = 340cm²

unshaded region

9 × 6 = 54cm²

area of shaded region

340 - 54 = 286cm²

Answer:

32°

Step-by-step explanation:

Let the angle next to 121° be a,

a+121°=180°

a=180-121=59°

Now we have a=59°,

89° (given) and x, these threes form a triangle, therefore,

x+a+89°=180°

×+59°+89°=180°

x+148°=180°

x=180°-148°

x=32°

Answer:

Therefore has one solution.

explanation:

Given equations:

6x + y = -7

-24x -7y = 25

Make y the subject:

6x + y = -7

y = -7 - 6x ..............equation 1

-24x -7y = 25

-7y = 25 + 24x

y = (25 + 24x)/-7 ..........equation 2

Solve them simultaneously:

(25 + 24x)/-7 = -7 - 6x

25 + 24x = -7 (-7 - 6x)

25 + 24x = 49 + 42x

42x - 24x = 25- 42

18x = -24

x = [tex]-\frac{4}{3}[/tex]

Then y is:

y = -7 - 6x

y = -7 - 6( [tex]-\frac{4}{3}[/tex])

y = 1

Has one separate value of x and y: (  [tex]-\frac{4}{3}[/tex] , 1 ); so it has one solution.

Answer:the answer is d

Step-by-step explanation: it a d bc i know

[tex]9y^2-12y-14=0\\D=(-12)^2-4\times9\times(-14)=144+504=648=(\pm18\sqrt{2})^2 \\\\y_1=\dfrac{12+18\sqrt{2} }{18} =\dfrac{2+3\sqrt{2} }{3} \\\\y_2=\dfrac{12-18\sqrt{2} }{18} =\dfrac{2-3\sqrt{2} }{3}[/tex]

Answer:

Solve the equation for y by finding a,b, and c of the quadratic then applying the quadratic formula.

Desimal Form:  2.08088022…,−0.74754689…

the guy on top of me is right I just gave you the desimal form he/she give you the rest

Step-by-step explanation: