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Answer: The smallest zero is -3.

Step-by-step explanation: Zeros of a function are the values of input for which the function gives 0 output.

Here, the given function is,

p(x) = x(x-5)(x-2)(x+3)

For finding the zeroes of p(x),

p(x) = 0

⇒ x(x-5)(x-2)(x+3) = 0,

⇒ x = 0 or x - 5 = 0 or x-2=0 or x+3=0

⇒ x = 0 or x = 5 or x = 2 or x = -3

Thus, the zeros of the given function are 0, 5, 2, -3

In which -3 is smallest.

Answer:

x = -3

Step-by-step explanation:

x(x-5)(x-2)(x+3) = 0    means at least one of these terms = 0

so  

                        x = 0       or

x-5 = 0     then x = 5        or

x-2 = 0     then x = 2       or

x+3 = 0     then x= -3

f(x) is our regular graph where the y value is determined by the x value that is plugged in.

f(x + 2) = horizontal shift to the left 2 units

---x, the horizontal axis, is what is being altered here because the change occurs within the parenthesis. We always do the opposite action/move the opposite way when the shift occurs within the parenthesis.

f(x) + 2 = vertical shift up 2 units

---y, the horizontal axis, is what is being altered here because the change occurs outside the parenthesis. We move the function as we would expect to when the shift occurs outside the parenthesis.

Hope this helps!

Answer:

(-2,15) (3,0)

Step-by-step explanation:

By substituting the x value in the coordinate (the first number in the bracket) and solving the equation, you must get the y value in the coordinate (second number in the bracket.

So that is to say:

A

y= -3x + 9

y = -3(-2) + 9

y = 6 + 9

y= 15

Also note that B is not one of them, because the y value you get when you substitute the x value in the equation is NOT NEGATIVE 6.

The diameter of the cylindrical rain barrel which Sophie bought to water her garden, and want to build a platform for it is 15 in.

Volume of cylinder is the amount of quantity, which is obtained by it in the 3 dimensional space.

The volume of the cylinder can be given as,

[tex]V=\pi r^2h[/tex]

Here, (r) is the radius of the base of the cylinder and (h) is the height of the cylinder.

Sophie bought a cylindrical rain barrel to water her garden, but she forgot to ask the seller what the diameter of the barrel was.

She needs to know the diameter so that she can build a platform for it to sit on.

The seller told her the volume of the barrel is 6,925pi cubic in and its height is 38 in.

[tex]V=\pi r^2h\\6925=\pi r^2(38)\\\dfrac{6925}{38\pi}= r^2\\r=\sqrt{\dfrac{6925}{38\pi}}\\r\approx7.62 \rm\; in[/tex]

The diameter of the cylinder is twice the radius of it. Thus, the diameter of the cylinder is,

[tex]d=7.62\times2\\d=15.23\rm\\d\approx15\rm\; in[/tex]

Thus, the diameter of the cylindrical rain barrel which Sophie bought to water her garden, and want to build a platform for it is 15 in.

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Hey there!

5x + 30

5(x + 6)

= 5(x) + 5(6)

= 5x + 30

5x + 30 = 5x + 30

Therefore, the answer should be:

5(x + 6)

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

For 50% its 12, for 25% its 6, and for 75% its 18

Step-by-step explanation:

The length of the segment DF is 11 units

The given parameters are:

ED = 2y + 12

DF = 3y + 8

EF = 25

The length EF is:

EF =ED + DF

This gives

2y + 12 + 3y + 8 = 25

Evaluate the like terms

5y + 20 = 25

Subtract 20 from both sides

5y = 5

Divide by 5

y = 1

Substitute y = 1 in DF = 3y + 8

DF = 3(1) + 8

Evaluate

DF = 11

Hence, the length of DF is 11 units

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The value of the x and y is 12 and -10 respectively, and the provided figure is a parallelogram because the diagonals bisect each other.

In two-dimensional geometry, it is a plane shape having four sides, in which two pairs of sides are parallel to each other and equal in length. The sum of all angles in a parallelogram is 360°.

As we know in the parallelogram, the diagonals bisect each other.

Then,

432 = 3x²

x² = 144

x = √144

x = 12

In the parallelogram, the adjacent opposite angles are the same.

∠C+∠B = 240°

= 360 - 240

∠A + ∠D = 120°

∠A = ∠D = 120°/2 = 60

∠D/2 = 60/2 = 3y + 60

3y + 60 = 30

3y = -30

y = -10

From the definition of the parallelogram, the provided figure is a parallelogram.

Thus, the value of the x and y is 12 and -10 respectively and the provided figure is a parallelogram because the diagonals bisect each other.

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Answer:1 4/16

Step-by-step explanation: Theres 1 circle thats all shaded so thats a whole then you got the other circle and thats shaded 4.

Answer:

A

Step-by-step explanation:

the circle with all the yellow is a whole so that is 1 the circle with only 4 in yellow is 4 right now we have 1 and 4, then you will count the circle thats NOT FULL and you will get 16. so the answer is 1 4/16

Answer:

Median: 88, First Quartile: 84, Third Quartile: 92, IQR (interquartile range): 8

Step-by-step explanation:

1. Sort the numbers in numerical order (like 1, 2, 3, etc.)2. Find the number that is in the middle3. Find all the quartiles by finding the median of the lower and upper halves of the list4. Subtract Q1 (quartile 1) and Q3 (quartile 3) like this: Q3 - Q1 to get IQR

The maximum number of African cichlids which can put by Chiletso  in this cylindrical fish tank is 19.

Volume of cylinder is the amount of quantity, which is obtained by it in the 3 dimensional space.

The volume of the cylinder can be given as,

V=(πd^2h)4

Here, (d) is the diameter of the base of the cylinder and (h) is the height of the cylinder.

The height of tank is 30 inches and the length of the diameter of the base is 27.5 inches. Thus, the volume of it is,

V=[π(27.5)²(30)] /4

V=17818.72 cubic inches.

One us gallon is equal to approximately 231 cubic inches. Thus, the volume in gallon is,

V=17818.72/231

V=77.12 gallons.

A good rule of thumb is to have about 3 inches of fish per 2 gallons of water. The number of 6 inches cichlids the can put in 77.12 gallons tank is,

V=(77.12 x 3)/(6 x 2)

V=19.28

Thus, the maximum number of African cichlids which can put by Chiletso  in this cylindrical fish tank is 19.

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Answer: 0.227

Step-by-step explanation:

Answer:

B. 0.227

Step-by-step explanation:

Have a great day!

Answer:

c

Step-by-step explanation:

i took the test

Answer:

16 i think

Step-by-step explanation:

Using the normal distribution, it is found that the tree must have heights between 9.49 cm and 10.51 cm.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 10, \sigma = 2[/tex]

Considering the symmetry of the normal distribution, the middle 20% is between the 40th percentile(Z = -0.253) and the 60th percentile(Z = 0.253), hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-0.253 = \frac{X - 10}{2}[/tex]

X - 10 = -0.253 x 2

X = 9.49.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]0.253 = \frac{X - 10}{2}[/tex]

X - 10 = 0.253 x 2

X = 10.51.

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The slope of the line tangent to the polar curve [tex]\rm r =3sin\theta[/tex] is 1.79.

A surface on which one end or side is at a higher level than another; a rising or falling surface.

The slope of the line tangent to the polar curve;

[tex]\rm r =3sin\theta[/tex]

The slope of the tangent is given by the following formula;

[tex]\rm \text{Slope of tangent line} = \dfrac{dy}{dx} =\dfrac{ (\dfrac{dr}{d\theta}sin\theta + cos\theta)}{(\dfrac{dr}{d\theta}cos\theta-rsin\theta)}[/tex]

Differentiate the given polar curve

[tex]\rm r =3sin\theta\\\\\dfrac{dr}{d\theta}=3cos\theta\\\\[/tex]

Substitute all the values in the formula

[tex]\rm \text{Slope of tangent line} = \dfrac{dy}{dx} =\dfrac{ (\dfrac{dr}{d\theta}sin\theta + rcos\theta)}{(\dfrac{dr}{d\theta}cos\theta-rsin\theta)}\\\\\rm \text{Slope of tangent line} = \dfrac{dy}{dx} =\dfrac{ (3cos\theta \times sin\theta +3 sin \theta \times cos\theta)}{(3cos\theta \times cos\theta-3 sin \theta \times sin\theta)}\\\\\rm \text{Slope of tangent line} = \dfrac{dy}{dx} =\dfrac{3 (cos\theta sin\theta + sin \theta cos\theta)}{3(cos\theta cos\theta- sin \theta sin\theta)}\\\\[/tex][tex]\rm \text{Slope of tangent line} = \dfrac{dy}{dx} =\dfrac{ 2sin\theta cos\theta}{(cos^2\theta -sin^2 \theta)}[/tex]

Substitute the value of [tex]\theta[/tex] in the equation

[tex]\rm \text{Slope of tangent line} = \dfrac{dy}{dx} =\dfrac{ 2sin \dfrac{\pi }{6} cos\dfrac{\pi }{6} }{(cos^2\dfrac{\pi }{6} -sin^2 \dfrac{\pi }{6} )}\\\\\text{Slope of tangent line} = \dfrac{dy}{dx} =\dfrac{2 \times 0.5 \times 0.86}{0.86^2 -0.5^2}\\\\\text{Slope of tangent line} = \dfrac{dy}{dx} =\dfrac{0.86}{0.73- 0.25}\\\\\text{Slope of tangent line} = \dfrac{dy}{dx} =\dfrac{0.86}{0.48}\\\\\text{Slope of tangent line} = \dfrac{dy}{dx} =1.79[/tex]

Hence, the slope of the line tangent to the polar curve [tex]\rm r =3sin\theta[/tex] is 1.79.

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Check the picture below.

the axis of symmetry is the line, in this case a vertical one, where the graph begins to mirror itself.

the range is simply the vertical distance in this case, the parabola goes as low as 0 then back up, the arrows mean the graph keeps on +∞.

Answer: 100ft 113.6ft 200ft

Step-by-step explanation:

These new lengths are all ⅘of the original length

Answer:

B. 12/16

Step-by-step explanation:

12/16 divided by 4/4 = 3/4

Answer:

5=18

Step-by-step explanation:

they are counting by 2s      10,12,14,16,18

Hope this helps!

Answer:

18

Step-by-step explanation:

It seems like for this pattern, as the x-value(base value) increases, the corresponding y-value(value changing with the base value) increases by 2 given that the function starts with a y-intercept of 8. So at the value 0, the corresponding number would be 8. So in this case, by creating a function regrading this information we can solve for the corresoponding value of 5: y = 2x + 8

y = 2 * 5 + 8

y = 10 + 8

y = 18

5 = 18

Another way to approach this is just by following the pattern given to us in the description. We see that the pattern starts at 10, and increases by 2 for each increasing base value. Therefore, if 4 = 16, then 16 + 2 = 5, so 5 = 18.

Answer:

1

:)

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

because you do 1 by its self

like

1 x 2 = 1 + 1 = 2

if you were doing 1 x 1

1 + 0 = 1

you would add 0 because there's not another number

The prime factors that the numbers 24 and 36 have in common are found out to be; 2 × 2 × 3

A prime factor of a number is simply factor of that number that is a prime number. This means that any of the prime numbers that can be multiplied to give the original number.

Now, we have;

Prime factors of 36; 2 × 2 × 3 × 3

Prime factors of 24; 2 × 2 × 2 × 3

The prime factors that they have in common will be; 2 × 2 × 3

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The volume of the box made by cardboard box company which has a depth of n, a height of 2n+1, and a width of 3n+2, is 6n³+7n²+2n

Volume of rectangular prism is the amount of quantity, which is obtained in it in the 3 dimensional space.

Volume of a rectangular prism is the product of its width, height and length.

V=w×h×l

Here, (w) is the width of the base (l) is the length and (h) is the height of the rectangular prism.

A cardboard box company designs all of its boxes suc that they have the measure of depth of n, a height of 2n+1, and the measure of width of 3n+2.Thus, the volume of this box is,

V=w×h×l

V=(3n+2)×(2n+1)×(n)

V=(3n+2)×(2n²+n)

V=6n³+3n²+4n²+2n

V=6n³+7n²+2n

Thus, the volume of the box made by cardboard box company which has a depth of n, a height of 2n+1, and a width of 3n+2, is 6n³+7n²+2n

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Step-by-step explanation:

remember the rules of exponents.

a "minus" sign means 1/...

like 2^-1 = 1/2

and 2^-3 = 2^(3(-1))

so, it is 1/2³ = 1/8.

so, now here in our case

y = 3×(1/2)^-2 = 3×(1/2)^(2(-1)) = 3×((1/2)²)^-1 = 3×(1/4)^-1 =

= 3× 1 / 1/4 = 3×4 = 12

Answer:

0.50 or 50%

Step-by-step explanation:

40 x 125 = X

1.25 as a decimal or 125%

40 x 1.25 = 0.50

0.50 --->50%

40 x 125% = 50%

Answer:

see below

Step-by-step explanation:

C

Because the first day reaches up to 8 in c, while all the others don't

Answer:

y=3x bro I'm pretty sure this is wrong tho I'm not good at math

Answer:

I'm not sure but I think it's +3

Step-by-step explanation:

more than = +