which system of inequalities is shown​

Answer:

The x-intercepts are x = 1 , x = 2 , x = 3

The y-intercept is -6

Step-by-step explanation:

* Lets explain how to solve the problem

- To find the x-intercept of a function substitute f(x) by 0

- To find the y-intercept of a function substitute x by 0

- To find the factors of quadratic function use the long division

* Lets solve the problem

∵ f(x) = x³ - 6x² + 11x - 6

∵ (x - 3) is one of its factors

- Use the long division to find the other factors

∵ x³ - 6x² + 11x - 6 ⇒ dividend

∵ x - 3 ⇒ divisor

# Divide the 1st term in the dividend by the 1st term of the divisor

∵ x³ ÷ x = x²

# Multiply x² by the divisor (x - 3)

∵ x²(x - 3) = x³ - 3x²

# subtract it from the dividend

∵ (x³ - 6x² + 11x - 6) - (x³ - 3x²) = (x³ - x³) + (-6x² + 3x²) +11x - 6

∴ The dividend is -3x² + 11x - 6

# Divide the 1st term in the dividend by the 1st term of the divisor

∵ -3x² ÷ x = -3x

# Multiply -3x by the divisor (x - 3)

∴ -3x(x - 3) = -3x² + 9x

# subtract it from the dividend

∵ (-3x² + 11x - 6) - (-3x² + 9x) = (-3x² - 3x²) + (11x - 9x) - 6

∴ The dividend is 2x - 6

# Divide the 1st term in the dividend by the 1st term of the divisor

∵ 2x ÷ x = 2

# Multiply 2 by the divisor (x - 3)

∴ 2(x - 3) = 2x - 6

# subtract it from the dividend

∴ (2x - 6) - (2x - 6) = (2x - 2x) + (-6 + 6) = 0

∴ (x³ - 6x² + 11x - 6) ÷ (x - 3) = x² - 3x + 2

∴ The factors of f(x) are (x - 3)( x² - 3x + 2)

- The factor (x² - 3x + 2) can factorize into two bracket

∵ The last term is positive and the middle term is negative than the

   two brackets have the middle sign (-)

∵ x × x = x² ⇒ 1st terms in the two brackets

∵ 2 × 1 = 2 ⇒ 2nd terms in the two brackets

∵ 2 × x = 2x

∵ 1 × x = x

∵ 2x + x = 3x

∴  (x² - 3x + 2) = (x - 2)(x - 1)

∴ f(x) = (x - 3)(x - 2)(x - 1)

- To find the x-intercept put f(x) = 0

∴ (x - 3)(x - 2)(x - 1) = 0

- That means each bracket = 0

∵ x - 3 = 0 ⇒ add 3 for both sides

∴ x = 3

∵ x - 2 = 0 ⇒ add 2 for both sides

∴ x = 2

∵ x - 1 = 0 ⇒ add 1 for both sides

∴ x = 1

∴ The x-intercepts are x = 1 , x = 2 , x = 3

- To find the y-intercept put x = 0

∵ f(x) = x³ - 6x² + 11x - 6

∵ x = 0

∴ f(0) = 0 - 0 + 0 - 6 = -6

∴ The y-intercept is -6

Answer:

7/4

Step-by-step explanation:

Answer:

4/7

Step-by-step explanation:

To answer this, take the negative reciprocal of -7/4, obtaining 4/7.  

Answer:

The y-intercept is the point (0,2)

see the attached figure                

Step-by-step explanation:

we have

[tex]3y=-5^{x}+7[/tex]

we know that

The y-intercept is the value of y when the value of x is equal to zero

so

For x=0

substitute in the equation and solve for y

[tex]3y=-5^{0}+7[/tex]    

[tex]3y=-(1)+7[/tex]

[tex]3y=6[/tex]

[tex]y=2[/tex]

therefore

The y-intercept is the point (0,2)

using a graphing tool

see the attached figure                      

Answer: For Plato users plot a point on 2 at the y intercept.

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

Using the identity

(a + b + c)³ = a³ + b³ + c³ + 3 [ (a + b + c)(ab + bc + ac) - abc ], then

5³ = a³ + b³ + c³ + 3(5 × 10) - 3abc, that is

125 = a³ + b³ + c³ + 150 - 3abc, hence

a³ + b³ + c³ - 3abc = 125 - 150 = - 25

Using the cubic identity equation and the values given in the question, we can prove that if (a+b+c) = 5 and ab+bc+ac = 10, then a³+b³+c³-3abc equals -25.

The equation required to prove is derived from the expansion of the cubic identity (a+b+c)³. The equation is a³+b³+c³-3abc = (a+b+c)[(a+b+c)²-3(ab+bc+ac)]. Let's use the values given in the question which are (a+b+c) = 5 and ab+bc+ac = 10.

Therefore, we have proved that if (a+b+c) = 5 and ab+bc+ac = 10, then a³+b³+c³-3abc indeed equals -25.

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Answer:

20 movies

Step-by-step explanation:

no of movies= 80

action movies percentage=25%

no of action movies=25/100*80(25% of 80)

Answer: There Ya go

Explanation:

The kind of symmetry the figures have are horizontal line symmetry and vertical line symmetry

From the question, we have the following parameters that can be used in our computation:

The figures

The figures have horizontal line symmetry and vertical line symmetry

Horizontal line symmetry occurs when a shape can be divided into two identical halves by a horizontal line.

In other words, if you fold the shape in half along the horizontal line, the two halves will exactly overlap.

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Answer:

C. x =3

Step-by-step explanation:

Extraneous solution is that root of a transformed equation that doesn't satisfy the equation in it's original form because it was excluded from the domain of the original equation.

Let's solve the equation first

[tex]\sqrt{45-3x} = x-9\\Taking\ square\ on\ both\ sides\\{(\sqrt{45-3x})}^2 = {(x-9)}^2\\45-3x = x^2-18x+81\\0 = x^2-18x+81-45+3x\\x^2-15x+36 = 0\\x^2-12x-3x+36 = 0\\x(x-12)-3(x-12) = 0\\(x-3)(x-12)\\x-3 = 0\\=> x =3\\x-12 = 0\\x = 12\\We\ will\ check\ the\ solutions\ one\ by\ one\\So,\\for\ x=3\\\sqrt{45-3(3)} = 3-9\\\sqrt{45-9} = -6\\\sqrt{36}= -6\\6\neq -6\\For x=12\\\sqrt{45-3(12)} = 12-9\\\sqrt{45-36} = 6\\\sqrt{36}= 6\\6=6[/tex]

Hence, we can conclude that x=3 is an extraneous solution of the equation ..

Answer:

C

Step-by-step explanation:

Answer:

  50 million

Step-by-step explanation:

You don't need to go to the trouble to find the value of k in e^(kt). Rather, you can use the given ratio directly.

When t = years after 1990, the population of 49 million took 12 years to achieve. The estimate desired is for 16 years after the year 1990. The appropriate exponential formula for the population is ...

  P = 46·(49/46)^(t/12)

Then for t=16, this is ...

  P = 46·(49/46)^(16/12) ≈ 50.04 . . . .  million

The population in 2006 is estimated at 50 million.

_____

The form of the exponential equation we used above is ...

  f(x) = (baseline value)·(ratio to baseline)^(x/(interval corresponding to ratio))

Answer:

Option D y=3

Step-by-step explanation:

The question in English is

Which of the following functions is a constant function?

we know that

A constant function is a function whose output value is the same for every input value

so

Verify each case

case A) y=x+1

This is not a constant function, this is a linear equation

Is a function whose output value is different for every input value

case B) y=x+2

This is not a constant function, this is a linear equation

Is a function whose output value is different for every input value

case C) x=y+3

This is not a constant function, this is a linear equation

Is a function whose output value is different for every input value

case D) y=3

This is a constant function

Is a function whose output value is the same for every input value

Answer:

-4

Step-by-step explanation:

To find your answer, plug in 4 for r.

[tex]-3r+8\\-3(4)+8[/tex]

You can start by multiplying -3 by 4.

[tex]-3(4)+8\\-12+8[/tex]

Next, add -12 to 8 and you'll have your answer.

[tex]-12+8\\-4[/tex]

Answer:

-4.

Step-by-step explanation:

Substitute r = 4 into the given expression:

= -3(4) + 8

= -12 + 8

= -4.

Answer:

here is

Step-by-step explanation:

Answer:

The answer would be option B and option C

∠DEF and ∠FED describe an angle with a vertex at E.

The correct answers are option (B) and option (C)

For given question,

We need to find the correct angle with a vertex at E.

We know that the vertex is the common point of the rays of an angle.

It is always written at the middle in an angle.

So, ∠DEF and ∠FED describe an angle with a vertex at E.

The correct answers are option (B) and option (C)

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Answer:

[tex] \sqrt{\frac{668}{\pi} } [/tex] feet  given the area is 167 ft squared

Step-by-step explanation:

Since our sector as a central angle of 90 degree then it is only a 4th of the whole circle.  The area of a circle is pi*r^2.  We will only be using a 4th of that since are sector is only a 4th of the circle.

So the formula will be using for the area of our sector is A=1/4 *pi*r^2.

We are given the area is 167 so replace A with 167.

167=1/4 * pi *r^2

Multiply both sides by 4.

167*4  =pi * r^2

668=pi * r^2

Divide both sides by pi

668/pi =r^2

Square root both sides

[tex] \sqrt{\frac{668}{\pi} } =r [/tex]

Answer:

130°

Step-by-step explanation:

Since there are 360 degrees is a circle, measure of AXC = 260 means the measure of Arc AC is:

360 - 260 = 100

Now if we were to draw 2 lines, one from A to X and another from C to X, we would have an intercepted angle at X originating from AC.

The theorem is when the intercepted angle is at the opposite side of the circumference, the angle is HALF THAT OF THE ARC.

So, half of 100 is 50.

Angle X and Angle B add up to 180, hence Angle ABC is 180 - 50 = 130

Answer:

(f-g)(x) = 4x - x^(-5)

Step-by-step explanation:

Please, enclose that negative exponent inside parentheses:  g(x)=x^(-5).  No need to type in the " + " in f(x)=4x^+1.

g(x) is to be subtracted from f(x).  Write f(x):

f(x)=4x

followed by the negative of g(x):  -g(x) = -x^(-5)

and now combine these two results:

 f(x)=4x

-g(x)= -x^(-5)

---------------------

(f-g)(x) = 4x - x^(-5)

The expression for (f-g)(x) is (f-g)(x) = 4x² + 1 - 1/x⁵

A function is a mathematical formula that describes how the dependent variable and independent variable are related. The dependent variable's value varies in the function together with the independent variable's value.

To find (f-g)(x), we need to subtract g(x) from f(x):

(f-g)(x) = f(x) - g(x)

We are given:

f(x) = 4x² + 1

g(x) = x⁻⁵ = 1/x⁵

Substituting these values into the expression for (f-g)(x), we get:

(f-g)(x) = f(x) - g(x) = (4x² + 1) - (1/x⁵)

Simplifying the expression, we can write:

(f-g)(x) = 4x^2 + 1 - 1/x⁵

Therefore, the expression for (f-g)(x) is:

(f-g)(x) = 4x² + 1 - 1/x⁵

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Answer:

4

Step-by-step explanation:

a term is simply separated by either a + or a - which means the terms here is 4x,2x,3x and 5

Answer:

4

Step-by-step explanation:

There are 4 terms in the equation 4x+2x(3x-5).

4x,2x,3x and 5

have you finished this yet? im doing it rn and i need help on some of them. if you havent i can help you with a couple answers

[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ H(\stackrel{x_1}{2}~,~\stackrel{y_1}{1})\qquad K(\stackrel{x_2}{10}~,~\stackrel{y_2}{7}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{10+2}{2}~~,~~\cfrac{7+1}{2} \right)\implies \left( \cfrac{12}{2}~,~\cfrac{8}{2} \right)\implies (6,4)[/tex]

Answer:

-3

Step-by-step explanation:

4^x = (1/8)^(x+5)

(2^2)^x =  (2^-3)^(x+5)

2^2x = 2^(-3x - 15)

Since both sides have the same base of 2, then the exponents are equal

So

2x = - 3x - 15

5x = -15

 x = -3

Answer:

-3

Step-by-step explanation:

see attached

Answer:

[tex]\large\boxed{x=\dfrac{8}{3}}[/tex]

Step-by-step explanation:

[tex]-3(-x)-6=-3x+10\\\\3x-6=-3x+10\qquad\text{add 6 to both sideS}\\\\3x=-3x+16\qquad\text{add}\ 3x\ \text{to both sides}\\\\6x=16\qquad\text{divide both sides by 6}\\\\x=\dfrac{16}{6}\\\\x=\dfrac{8}{3}[/tex]

Answer:

Step-by-step explanation:

Let assume that x% = 200,000

Lets assume that 100 %  = 131,000,000 because it is the output value:

Therefore we have two equations:

x% = 200,000

100 %  =131,000,000

Now observe that the L.H.S of both the equations have same unit. So we can write it as:

100%/x% = 131,000,000/200,000

Now just simply solve the values:

Multiply both sides by x

100/x *x = 131,000,000/200,000 *x

100=655x

Now divide both the sides by 655.

100/655 = 655x/655

100/655=x

0.15267175572519=x

Therefore the answer is 200,000 is 0.15267175572519% of 131,000,000 ....

just an addition to the reply above, which is correct, so to the risk of sounding redundant.

if we take 131,000,000 to be the 100%, what is 200,000 off of it in percentage?  Bearing in mind that 1% of 131,000,000 is really 1,310,000, notice we simply chopped off two zeros, but that amount is larger than 200,000 and thus whatever 200,000 is, is less than 1%.

[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 131000000&100\\ 200000&x \end{array}\implies \cfrac{131000000}{200000}=\cfrac{100}{x}\implies \cfrac{1310}{2}=\cfrac{100}{x} \\\\\\ 1310x=200\implies x=\cfrac{200}{1310}\implies x\approx 0.1526717557251908[/tex]

Answer:

10 units

Step-by-step explanation:

Points R and S both have y-coordinate 4, so they are on the same horizontal line. The distance between them is the absolute value of the difference of the x-coordinates.

RS = |-2 - 3| = |-5| = 5

Points S and T both have x-coordinate 3, so they are on the same vertical line. The distance between them is the absolute value of the difference of the y-coordinates.

ST = |-1 - 4| = |-5| = 5

The total length of the trail is the sum of the two distances.

total length = 5 + 5 = 10

Answer:

Step-by-step explanation:

Using the formula for distance, D given 2 coordinates (see attached)

Given

R(-2,4)  S(3,4)   T(3,-1)

Distance RS = √ { [ (-2) -3]² + [4-4]² } = √25 =5 units

Distance ST = √ { [ (3 -3]² + [4-(-1)]² } = √25 = 5 units

Total distance = RS + ST = 5 + 5 = 10 units

Answer:

D. X+5y=7

passes through both coordinates

Answer:

all work is shown and pictured

Answer:

3.7

Step-by-step explanation:

Inversely means we are taking the constant and dividing it.

So y varies inversely with x means "y=k/x".

k is a constant.  We can find the constant if they give us a point on this curve.

The constant is a number that doesn't change no matter your input and output.

[tex]y=\frac{k}{x}[/tex]

So they actually give us k=8.88 and y=2.4 so let's input this:

[tex]2.4=\frac{8.88}{x}[/tex]

We need to solve this equation for x.  You can do your favorite thing in cross-multiply. But how, Freckles?  Well just slap a 1 underneath that 2.4.  You can do that because 2.4/1 is still 2.4.

[tex]\frac{2.4}{1}=\frac{8.88}{x}[/tex]

Cross-multiply:

[tex]2.4x=8.88(1)[/tex]

[tex]2.4x=8.88[/tex]

Divide both sides by 2.4:

[tex]x=\frac{8.88}{2.4}[/tex]

[tex]x=3.7[/tex] when [tex]y=2.4[/tex].

seventy five thousand

Answer:

Step-by-step explanation:

I can't add much to this. The answer is 75 thousand.

7-4x= 31

Bring over 7 to the other side

Positive 7 changes into negative 7

7-7-4x= 31-7

-4x= 24

Divide by -4 for -4x and 24

-4x/-4= 24/-4

x= -6

Check answer by using substitution method

7-4x= 31

7-4(-6)= 31

7+24= 31

31= 31

Answer : C. x= -6

Answer:

C. x = -6

Step-by-step explanation:

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

First, subtract 7 from both sides:

7 - 4x = 31

7 (-7) - 4x = 31 (-7)

-4x = 31 - 7

-4x = 24

Divide -4 from both sides to isolate the variable, x:

(-4x)/-4 = (24)/-4

x = 24/-4

x = -6

x = -6, or C. is your answer.

~

Answer:

Step-by-step explanation:

11C4 = 11! / (7!*4!) = 11 * 10 * 9 * 8 * 7!/ 7! * 4!

11C4 = 11*10 * 9 * 8 / 24

11C4 = 11*10 * 3

11C4 = 330

========

You can't do the second one. Permutations and Combinations always give an answer greater than 1 and integers.

Answer:

f[g(6)] = 0

Step-by-step explanation:

f(x) = 6x + 12

g(x) = x - 8

f[g(6)]

First lets find g(6)

g(6) = 6-8 = -2

Then we substitute -2 in for g(6)

Putting -2 into f(x)

f[g(6)] = f(-2) = 6(-2)+12 = -12+12 =0

Answer:

The number is x-6

Step-by-step explanation:

difference of x and a number is 6

Difference means subtract, is means equals

x-n = 6

Add n to each side

x-n+n = 6+n

x = n+6

Subtract 6 from each side

x-6 = n+6-6

x-6 =n

The number is x-6