which is the correct domain and range for this graph?

The number of real zeros of the function f(x) = x3 + 4x2 + x − 6 is 3

The equation of the function is given as:

f(x) = x^3 + 4x^2 + x - 6

Expand the function

f(x) = x^3 + 5x^2 - x^2 + 6x - 5x - 6

Reorder the terms of the function

f(x) = x^3 + 5x^2 + 6x - x^2 - 5x - 6

Factor the expression

f(x) = x(x^2 + 5x + 6) -1(x^2 + 5x + 6)

Factor out x -1

f(x) = (x^2 + 5x + 6)(x -1)

Expand

f(x) = (x^2 + 3x + 2x + 6)(x -1)

Factorize

f(x) = [x(x + 3) + 2(x + 3)](x - 1)

Factor out x + 2

f(x) = (x + 3)(x + 2)(x- 1)

The function has been completely factored;

And it has 3 linear factors

Hence, the number of real zeros of the function f(x) = x3 + 4x2 + x − 6 is 3

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Step-by-step explanation:

= ( +2 ) × ( + 6 ) ( -3 )

= + 12 (- 3 )

[tex] = - 36[/tex]

hence - 36 is the answer...

Answer:

D, E, and A

Step-by-step explanation:

Because 4 is also equivelent to square root of 16 and square root of 16 times square root of 3 is equal to square root of 48 which is D, and E is also correct because square root 24 x square root 2 is also square root 48 and same concept with A.

Answer:

[tex] \boxed{\rm \: Volume_{(Drum)} = 5024 \: in {}^{3} }[/tex]

Step-by-step explanation:

Given :

To Find:

The volume of the drum.

Solution:

We all know that drum is cylindrical.So we'll use the formulae of the volume of cylinder,to find its volume.

[tex] \boxed{\rm \: Volume_{(Cylinder)} = \pi{r} {}^{2} h}[/tex]

Where,

The value of radius ain't given,but the diameter is given.We can use the formulae of radius.

[tex] \rm \: Radius = D/2[/tex]

Substitute the value of diameter:

[tex] \rm \: Radius = \cfrac{20}{2} = 10[/tex]

Hence,the radius is 10.

So we could now use the formulae of the volume of cylinder:

[tex] \rm \: Volume_{(Cylinder)} = \pi{r} {}^{2} h[/tex]

[Firstly bring the answer in terms of π then plug π = 3.14 and then simplify.]

[tex] \rm \: Volume_{(Drum)} = \pi(10) {}^{2} (16)[/tex]

[tex] \rm \: Volume_{(Drum)} =\pi100(16)[/tex]

[tex] \rm \: Volume_{(Drum)} = 1600\pi[/tex]

[tex] \rm \: Volume_{(Drum)} = 1600 \times 3.14[/tex]

[tex] \boxed{\rm \: Volume_{(Cylinder)} = 5024 \: in {}^{3}} [/tex]

Hence, we can conclude that:

The volume of this drum is 5024 in^3.

The statement "151.8​​ is what percent of 69​​ is expressed as 0.69p =  151.8

Equations are expressions separated by an equal sign. Words can be translated to equations.

Let the unknown variable be "p". If p percent of 69is 151.8, this is expressed as;

p% of 69 = 151.8

Convert to decimals

p/100 * 69 = 151.8

0.01p * 69 = 151.8
0.69p =  151.8

Hence the statement "151.8​​ is what percent of 69​​ is expressed as 0.69p =  151.8

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Since 0.3 is divided by 100, we will shift the decimal point backward in 2 places to have 0.003

Decimal numbers are numbers that includes the dot in between. Given the percentage value expressed as:
0.3%

This can be expressed as;

0.3% = 0.3/100

Since 0.3 is divided by 100, we will shift the decimal point backward in 2 places to have 0.003

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The probability of P(A|B) will be; P(A|B) = 2/5 = 0.4

From the Venn diagram attached, it displays sports played by 10 students.

Let event A = The students play basketball.

Let event B = The student plays soccer.

Then the probability of P(A|B) will be;

P(A|B) = P(A ∩ B)/P(B)

P(A|B) = (2/10)/(5/10)

P(A|B) = 0.40

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Answer:

18ft

Step-by-step explanation:

i can't lay out the formula

#1

Find y intercept

#2

Y intercept

Both graphs attached

An point should be (1,6)

Answer:

< or > = dashed line

≤ or ≥ = solid line

< or ≤ = shade below the line

> or ≥ = shade above the line

To draw:

[tex]y < \dfrac{2}{3}x+6[/tex]

Treat as a linear equation.

Find 2 points:

[tex]x=0 \implies y=\dfrac{2}{3}(0)+6=6 \implies (0,6)[/tex]

[tex]x=3 \implies y=\dfrac{2}{3}(3)+6=8 \implies (3,8)[/tex]

Plot the 2 points and draw a dashed straight line through them.

To draw:

[tex]y > 1.5^x+4[/tex]

Treat as an exponential equation.

Find y-intercept:

[tex]x=0\implies y=1.5^0+4=5\implies (0,5)[/tex]

End behaviors:

[tex]\textsf{As } x \rightarrow \infty, f(x) \rightarrow \infty[/tex]

[tex]\textsf{As } x \rightarrow - \infty, f(x) \rightarrow 4[/tex]

Draw the curve as a dashed line.

Once both lines are drawn, shade the overlapping region below the linear inequality and above the exponential inequality.  

A point that belongs to the solution is any point in the shaded area,
e.g. (1, 6)

Answer:

20 miles

Step-by-step explanation:

We are finding the difference.  Take the larger number and subtract the smaller number

40-20 = 20

The difference is 20 miles

Answer:

B; because it has two points where x is once 2 and once -4

Step-by-step explanation:

mark me brainlist!! hope this helps

Answer:

c

Step-by-step explanation:

its just the dilate of the triangle which both add up to 180

The car would travel a distance of 400 km using 20 litres of petrol

The given parameters can be represented using the following scale ratio :

Scale = 340 km : 17 litres

For 20 litres of petrol, we have:

Distance : 20 = 340 km : 17

Express as fraction

Distance/20 = 340 km/17

Multiply both sides by 20

Distance = 400 km

Hence, the car would travel a distance of 400 km using 20 litres of petrol

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Answer:

Peter spent 14 dollars on movie tickets. Henry spent 10 dollars on popcorn.

Step-by-step explanation:

I hope this helps! :)

Given the following parameters DB = 18 ft, AB = 3 ft, and CB = 10 ft. Therefore, The length of the CE is 4.6 ft.

The secant-secant rule states that if two secants are drawn from an external point to a circle, then the product of the measures of one secant's external part and that entire secant is equal to the product of the measures of the other secant's external part and that entire secant.

Mathematically:

(BA + AD)BA = (BE + EC)BE

Given the following parameters

DB = 18 ft, AB = 3 ft, and CB = 10 ft.

Substitute to check if we can find CE

(BA + AD)BA = (BE + CE)BE

(3+ 15) x 3 = (10 + CE ) x 10

18 x 3 = 100 + 10CE

54 = 100 + 10CE

CE = 4.6

Therefore, The length of the CE is 4.6 ft.

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For a quadrilateral to be a square, the diagonals must be congruent and must be perpendicular.

An equation is formed of two equal expressions. The correct option is A.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Ms. Banerjee bought a car for $22,500. The amount she paid for her new car was twice the amount she paid for her previous car, which she bought 8 years ago. Therefore, the equation shows p, the price in dollars that she paid for her previous car,

Price of new car = 2 (Price of the previous car)

22,500 = 2p

Hence, the correct option is A.

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Answer: a

Step-by-step explanation:

The term used to describe the equidistance from a given directrix and focus is: C. a locus of points called a parabola.

A parabola can be defined as a curve on a plane where any given point is at equal distance from the focus (fixed point), and from a directrix (fixed straight line).

Thus, we can conclude that what is a locus of points called a parabola is equidistant from a given directrix and focus.

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Answer:

A reflection of a point over the y -axis is shown. The rule for a reflection over the y -axis is (x,y)→(−x,y) .

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

The statement which is true about the thrown ball is that A. The ball attains a maximum height of 70 meters at 4 seconds

This refers to the highest vertical projectile that an object can attain when acted upon by an external force.

Given the attached diagram that shows the graph of the projectile of the ball, we can observe that its maximum height before it began to fall is 70 meters at 4 seconds based on the values on the x and y-axis.

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Answer:

10π (31.415926)

√101(10.0498756)

9.92749...

0.99853...

Step-by-step explanation:

For 10π, we can simplify π into 3.14 for an approximate amount. 3.14*10=31.4

For the square root of ten, we can estimate it's between 10 and 11 since 10 squared is 100 and 11 squared is 121.

Answer:

See explanation

Step-by-step explanation:

First, we have to put the expressions into numbers. For the square root of 101, it doesn't divide evenly into any whole number. We do know that 10^2 is 100, and 11^2 is 121. That means the square root of 101 is between 10 and 11. Pi is equal to 3.14, so we just multiply 10 by 3.14. If we do this, we get 31.4. From here we can rank the numbers in order from greatest to smallest.

31.4 (10pi) is greater than

The square root of 101 which is greater than

9.92749... which is greater than

0.99853...

Hope this helps!

[tex]\sqrt x > \sqrt{25} \qquad( x\geq 0)\\\sqrt x > 5\\x > 25[/tex]

When [tex]x > 25[/tex].

Answer: [tex]\{x|x \exists \mathbb{R}, x > 3 \}[/tex]

Step-by-step explanation:

Adding 5 to both sides, we get x > 3.

Answer:

x^2+2x+y^2−2y−7=0

Step-by-step explanation:

The method from converting to standard to general is very simple

this equation in standard form would be

(x+1)^2+(y-1)^2=9

This is because whatever the center of the circle is, you take the negative/positive version of that number

The center is at -1, 1.  So it would flip to be put into the equation as 1, -1.

9 is the radius^2.

The radius is 3.

To convert to general form you just simplify

x^2+1+2x = (x+1)^2

y^2 + 1 -2y = (y-1)^2

x^2 - 2x + y^2 - 2y + 2 = 9

get the nine on the left side

x^2 -2x +y^2 - 2y 2 - 9 = 0

x^2+2x+y^2−2y−7=0

Give brainliest, please!

Hope this helps :)

To expand an expression, use FOIL method.

-7y and y are the first terms in each expression.

(-7y)(y) = -7y²

-7y is the first term in the first expression

-4 is the last term of the second expression

(-7y)(-4) = 28y

-8 is the last term in the first expression

y is the first term in the second expression

(-8)(y) = -8y

-8 is the last term of the first expression

-4 is the last term of the second expression

(-8)(-4) = 32

Combine all simplified terms.

Answer:

Wxndy~~