Which of the following describes the roots of the polynomial function K x) - (x+ 2)(x-4)(x+1)3?

Answer:

The value of the single logarithm is -11 ⇒ answer B

Step-by-step explanation:

* Lets revise the rule of the logarithmic functions

# ㏒ a + ㏒ b = ㏒ ab  

# ㏒ a - ㏒ b = ㏒ a/b

# ㏒ a^n = n ㏒ a  

# ㏒ 1 = 0  

* Now lets solve the problem

∵ [tex]log_{b}(\frac{A^{5}C^{2}}{D^{6}})[/tex]

- Change the single logarithm to an expression by change the

  multiplication to addition and the division to subtraction

∵ [tex]log_{b}A^{5}=5log_{b}A[/tex]

∵ [tex]log_{b}C^{2}=2log_{b}C[/tex]

∵ [tex]log_{b}D^{6}=6log_{b}D[/tex]

∴ The single logarithm = [tex]5log_{b}A+2log_{b}C-6log_{b}D[/tex]

* Now lets substitute the values

∵ [tex]log_{b}A=3;===log_{b}C=2;===log_{b}D=5[/tex]

- Substitute the values into the expression

∴ The value = 5(3) + 2(2) - 6(5) = 15 + 4 - 30 = -11

* The value of the single logarithm is -11

Answer:

The point (2,0) is outside the circle

Step-by-step explanation:

we have

[tex](x-2)^{2}+(y+3)^{2}=4[/tex]

[tex](x-2)^{2}+(y+3)^{2}=2^{2}[/tex]

This is the equation of a circle with center at (2,-3) and radius equal to 2 units

Using a graphing tool

Plot the circle and the given points and verify if the point lie outside  the circle

we have

[tex](1, -4 ),(0, -3),(2, 0),(2,-4)[/tex]

so

The point (2,0) is outside the circle

see the attached figure

Answer:

Step-by-step explanation:

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

We have the points (7, -4) and (7, 9). Substitute:

[tex]d=\sqrt{(7-7)^2+(9-(-4))^2}=\sqrt{0+13^2}=\sqrt{13^2}=13[/tex]

Used [tex]\sqrt{a^2}=a[/tex]

Answer:

The answer is $0.69. This is because there are 32 ounces in the bottle, and $22.08/32=0.69, or $0.69.

Step-by-step explanation:

Answer:

Let's solve your system of equations by elimination.

8x+9y=48;12x+5y=21

Steps:

Multiply the first equation by 5,and multiply the second equation by -9.

5(8x+9y=48)

−9(12x+5y=21)

Becomes:

40x+45y=240

−108x−45y=−189

Add these equations to eliminate y:

−68x=51

Then solve−68x=51for x:

−68x /−68 = 51 /−68  (Divide both sides by -68)

x=  −3 /4

Now that we've found x let's plug it back in to solve for y.

Write down an original equation:

8x+9y=48

Substitute

−3 /4

8x+9y=48:

8( −3 /4 )+9y=48

9y−6=48 (Simplify both sides of the equation)

9y−6+6=48+6 (Add 6 to both sides)

9y=54

9y /9  =  54 /9  (Divide both sides by 9)   y=6

Answer:  x=  −3 /4  and y=6

Hope This Helps!  Have A Nice Day!!

where are the expressions ?

Answer:

3x + 2

Step-by-step explanation:

Answer:

(2, 5)

Step-by-step explanation:

Given the 2 equations

y = x + 3 → (1)

- 2x + y = 1 → (2)

Substitute y = x + 3 into (2)

- 2x + x + 3 = 1

- x + 3 = 1 ( subtract 3 from both sides )

- x = - 2 ( multiply both sides by - 1 )

x = 2

Substitute x = 2 into (1) for corresponding value of y

y = 2 + 3 = 5

Solution is (2, 5)

Answer: y=5, x=2

Step-by-step explanation:

Answer:

Step-by-step explanation:

I think you meant x^(3/2).  This breaks down in at least two ways:

[x^3]^(1/2), or √(x^3)m or √x³), or

[x^(1/2)]^3 = (√x)^3

To write [tex]x^{3/2}[/tex] in radical form, rewrite it as (√x)³or √(x³). This utilizes the relationship between fractional exponents and radicals.

To write [tex]x^{3/2}[/tex] in radical form, we can use the relationship between exponents and radicals. In general, the expression [tex]x^{a/b}[/tex] can be written in radical form as the b-th root of x raised to the power 'a'. So, applying this rule to the given expression.

[tex]x^{3/2}[/tex]

Step-by-Step Explanation:

Therefore, the radical form of [tex]x^{3/2}[/tex] is √x³ or (√x)³.

Answer:

see explanation

Step-by-step explanation:

(a)

Note the squared value in column 3 which is the square of 1 more than the row number, that is

row 2 → (2 + 1)² →3²

row 3 → (3 + 1)² → 4²

Find the square root of 676 = 26 → (25 + 1)² = 26²

Hence the row number is 25

(b)

The pattern in column 1 is [ row number × (row number + 2 ) + 1 ]

row number is n then n(n + 2) + 1 = n² + 2n + 1

3.142×40^2×150=753,982.237

if1sec =0.2litres

what about 753.982=

753.982×1/0.2

=22.80

To determine if filling a tank takes longer than an hour, calculate the tank's volume, convert it to liters, and then divide by the fill rate. With a 240π liter capacity and a 0.2 L/s fill rate, it takes approximately 1.05 hours, thus longer than 1 hour.

To determine if it takes longer than 1 hour to fill a water tank with a radius of 40 cm and depth of 150 cm at a rate of 0.2 liters per second, we first calculate the volume of the tank and then the total time required to fill it at the given rate.

Step 1: Calculate the Volume of the Tank

Volume of a cylinder = πr²h, where r is the radius and h is the height.
Here, r = 40 cm and h = 150 cm.

Volume = π(40²)(150) = π(1600)(150) = 240000π cm³.

Step 2: Convert the Volume to Liters

Since 1 liter = 1000 cm³, the volume in liters = 240000π / 1000 = 240π liters.

Step 3: Calculate the Filling Time

Time = volume / rate = 240π / 0.2 = 1200π seconds.
To convert to hours, divide by 3600 (the number of seconds in an hour).

Total time in hours = 1200π / 3600 = π/3 hours, which is approximately 1.05 hours.

Since it takes approximately 1.05 hours to fill the tank, it does take longer than 1 hour to fill the tank.

Answer:

Triangle

Step-by-step explanation:

Look at the shape of the red part

The shape of the triangle is the cross-section part of the given figure. Thus, option A is correct.

The cross-section part of the given figure could be the shape fro the inscribed figure.

Here we can see that the three-dimensional figure inscribed in the square is a cone.

The right circular cone is the cone in which the line joining peak of the cone to the center of the base of the circle is perpendicular to the surface of its base.

But for the plane of the square, the triangle is the cross-section part of the given figure.

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Answer: x = 1/6 or 1.6667

3x * 2 + 6x = 2

Multiply the numbers: 3 * 2 = 6

6x + 6x = 2

Add similar elements: 6x + 6x = 12x

12x = 2

Divide both sides by 12

12x / 12  =  2 / 12

Simplify

x = 1/6

Answer:  The required discriminant of the given quadratic equation is 60.

Step-by-step explanation:  We are given to find the discriminant of the following quadratic equation :

[tex]3x^2+6x=2\\\\\Rightarrow 3x^2+6x-2=0~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We know that

the discriminant of a quadratic equation [tex]ax^2+bx+c=0,~a\neq 0[/tex] is given by

[tex]D=b^2-4ac.[/tex]

For the given equation (i), we have

a = 3,  b = 6  and  c = -2.

Therefore, the discriminant of the given equation will be

[tex]D=b^2-4ac=6^2-4\times3\times(-2)=36+24=60.[/tex]

Thus, the required discriminant of the given quadratic equation is 60.

The answer is:

The area of this figure is 946 square inches.

We can see that the figure is composed by two rectangles with diferrent dimensions, so, to calculate the area of the entire figure.

So,

For the first rectangle, we have:

[tex]Base=7in\\Height=28in[/tex]

The area will be:

[tex]Area=Base*Height=7in*28in=196in^{2}[/tex]

For the second rectangle, we have:

[tex]Base=25in\\Height=30in[/tex]

The area will be:

[tex]Area=Base*Height=30in*25in=750in^{2}[/tex]

Now, calculating the area of the entire figure, we have:

[tex]TotalArea=FirstRectangleArea+SecondRectangleArea\\\\TotalArea=196in^{2}+750in^{2}=946in^{2}[/tex]

Have a nice day!

Answer:

The discount is 15% because 6/40 = 0.15 and a percent is multiplied by 100 so the answer is 15%.

To find the percentage discount, subtract the discount amount from the original price and divide by the original price, then multiply by 100.

To find the percentage discount, we need to calculate the amount of the discount first. The discount is given as $6, so we subtract $6 from the original price of $40 to get $34. To find the percentage, we divide the discount amount by the original price and multiply by 100. In this case, the discount percentage would be (6/40) * 100 = 15%.

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Answer:yes

Step-by-step explanation:

2+7=9

12+2=14

12+7=19

Answer:

No

Step-by-step explanation:

the sum of two sides has to be greater than the third side

2+7=9 9 isn't greater than 12

ANSWER

[tex]( \frac{f}{g} )(x) = \frac{1}{3} ( {x}^{2} + 3x + 9)[/tex]

EXPLANATION

The given functions are

[tex]f(x) = {x}^{3} - 27[/tex]

and

[tex]g(x) = 3x - 9[/tex]

[tex]( \frac{f}{g} )(x) = \frac{f(x)}{g(x)} [/tex]

[tex]( \frac{f}{g} )(x) = \frac{ {x}^{3} - 27}{3x - 9} [/tex]

[tex]( \frac{f}{g} )(x) = \frac{ (x - 3)( {x}^{2} + 3x + 9) }{3(x -3 )} [/tex]

Cancel the common factors,

[tex]( \frac{f}{g} )(x) = \frac{ {x}^{2} + 3x + 9 }{3} [/tex]

OR

[tex]( \frac{f}{g} )(x) = \frac{1}{3} ( {x}^{2} + 3x + 9)[/tex]

Answer:

Check the attached graph

Step-by-step explanation:

Given that slope of the line is m = 1

And the line passes through the point (-3,5).

Now we need to graph the line using above information. So begin by graphing the point (-3,5).

Slope means rise/run

Then slope = 1 means rise/run=1=1/1

means move point 1 unit up then 1 unit right

then new point is at (-2,6).

Now draw a line joining both points to get the final graph.

Mode could work but I believe the best answer would be median.

Answer:

median

Step-by-step explanation:

Median is correct. One extreme outlier can "drag" the mean up or down, while it would have little or no effect on the median.

Answer

914 m^2 to the nearest whole number.

Step-by-step explanation:

The area of the hexagonal base is made up of 6 congruent triangles so its area = 6* 1/2 base* height

= 6 * 1/2 * 12 * 6√3

= 216-√3 m^2.

The area of each slanting triangle = 6 * 15 m^2 so the lateral area of the pyramid

= 6*6*15= 540 m^2

Total surface area = 540 + 216√3

= 914.12 m^2.

hope this helps

and to make it simpler its C or 914.12

Answer:

C

Step-by-step explanation:

1 | 4   6   - 2

        4     10

  ------------------

   4   10    8 ← remainder

Answer:

Option C

Step-by-step explanation:

Given is a division in synthetic

We have to find the remainder

The divisor is x-1 and dividend is [tex]4x^2+6x-2[/tex]

By synthetic division we get the following:

1)     4    6   -2\\

             4    10\\

----------------------\\

      4    10    8=R

Thus remainder is 8

Answer:

x=-4 and x=2

Step-by-step explanation:

You are given the function

[tex]f(x)=\dfrac{x^2+2x-8}{x^2-2x-8}[/tex]

The zeros of the function are those value of x, for which [tex]f(x)=0[/tex]

First, find x for which function is undefined

[tex]x^2-2x-8\neq0\\ \\x^2-4x+2x-8\neq 0\\ \\x(x-4)+2(x-4)\neq 0\\ \\(x-4)(x+2)\neq 0\\ \\x\neq 4\text{ and }x\neq -2[/tex]

Now find points at which f(x)=0:

[tex]f(x)=0\Rightarrow x^2+2x-8=0\\ \\x^2+4x-2x-8=0\\ \\x(x+4)-2(x+4)=0\\ \\(x-2)(x+4)=0\\ \\x=2\text{ or }x=-4[/tex]

For both these values (x=-4 and x=2) function f(x) is defined, then x=-4 and x=2 are zeros of the function.

Final answer:

To find the zeros of the given function, set the numerator equal to zero and solve for x. The zeros are x = -4 and x = 2.

Explanation:

We can notice that both the numerator and denominator share the same factors (x² - 2x - 8). This means that f(x) is undefined where the denominator is zero.

Therefore, the zeros of the function f(x) = x² + 2x - 8 / x² - 2x - 8 can be found by setting the numerator equal to zero and solving for x.

By factoring the numerator and denominator, it becomes easier to identify the zeros.

x² - 2x - 8 = 0

Factoring the expression:

(x - 4)(x + 2) = 0

Therefore, the zeros of the function f(x) are x = 4 and x = -2.

Answer:

We have the following equations:

5 + 3x - 2 and x + 2(x+1) + 1

Before checking the statements. Let's solve the syste of equations:

5 + 3x - 2 = x + 2(x+1) + 1

5 + 3x - 2 = x + 2x+2 + 1

3x + 3 = 3x + 3

Both equations are equivalent. Now, let's judge the statements:

1. The expressions are only equivalent when evaluated with odd values.

Given that the both expression are the same, the expressions are equivalent for ALL values.

Therefore, the statement IS FALSE ❌

2. The expressions are only equivalent for x=3 and x=7.

Given that the both expression are the same, the expressions are equivalent for ALL values, not only x=3 and x=7.

Therefore, the statement IS FALSE ❌

3. The expressions should have been evaluated with one odd value and one even value.

If two expressions are equivalent, they should be equivalent for ALL values. Sometimes, evaluating just one odd and one even value isn't enough. That's why the best approach is to solve the system of equations.

Therefore, the statement IS FALSE ❌

4. The expressions have equivalent values when x=6.

Given that the both expression are the same, the expressions are equivalent for x=6 (And all the real values too).

Therefore, the statement IS TRUE ✅

5. When x=0, the first expression has a value of 3 and the second expression has a value of 4.

Given that BOTH expressions are equvalent, they have the same value when x=0, which is 3.

Therefore, the statement IS FALSE ❌

6. The expressions have equivalent values for any value of x.

Given that the both expression are the same, the expressions are equivalent for ALL values of x.

Therefore, the statement IS TRUE ✅

7. When x=10, both expressions have a value of 33

Given that the both expression are the same, the expressions are equivalent for ALL values of x. That's why when x=0, both expressions have a value of 33.

Therefore, the statement IS TRUE ✅

Answer:

D,F,G

Step-by-step explanation:

It Makes Sense.

Answer:

(2x)+3

Step-by-step explanation:

I'm sure most of you just want the answer, but if you want me to educate you, keep reading!!

The product of two and a number x can be written as 2x.

Three more than something means that we add 3 to it.

If we add 3 to 2x, we have 3+2x.

So in conclusion, the answer would be (2x)+3.

Hope this helps! :)

The final value will be 2x+3

Firstly,

∴If we add 3 to 2x, we have 3+2x.

So the answer would be (2x)+3.

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The answer is .22222..., 3/10, .53, and 3/5.

Hope this helps!

Hello there!

The numbers in order from least to greatest are:

0.2222, 3/10, 0.53, 3/5

Start by turning all the numbers into either decimals. To do this, take the two fractions, 3/5 and 3/10 and divide them out.

3 divided by 5 = 0.6

3 divided by 10 = 0.3

Now let's look at our numbers again.

0.3, 0.222, 0.6, 0.53.

We know that 2 is less than 3, and 3 is less than 5, and 5 is less than 6, so lets rearrange the numbers into that order.

0.2222, 0.3, 0.53, 0.6

Now, convert any fractions that were converted into decimals back into their original forms.

0.2222, 3/10, 0.53, 3/5

This is your final answer. I hope this helps and have a great day!

The ratio in option (D), 15 boys to 40 girls is equivalent to 3 : 8.

Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.

If a and b are two values, their ratio will be a:b,

The given ratio of boy to girls is 3 : 8.

To find the equivalent ratio to 3:8.

Solve with the help of option,

(A)

15 boys to 55 girls.

The ratio 15 : 55 = 3 : 11

(B)

55 boys to 15 girls,

The ratio 55 : 15 = 11 : 3.

(C)

40 boys to 15 girls,

The ratio 40 : 15 = 8 : 3

(D)

15 boys to 40 girls,

The ratio 15 : 40 = 3 : 8.

The ratio of 15 boys to 40 girls is 3:8.

Hence, the correct option is (D).

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Answer:

Multiply the length and the width of the shape together to get the area of the square or rectangle in square feet.

10 multiplied by 8 equals 80 square feet

Step-by-step explanation:

Got a 100 on it.

Final answer:

To cover a rectangular garden measuring 10 feet by 8 feet, multiply the length by the width to get an area of 80 square feet, which is the amount of material needed.

Explanation:

Calculating the Area of a Rectangular Garden

To determine the number of square feet required to cover your rectangular garden, you need to calculate the area of the garden. The area of a rectangle is found by multiplying the length by the width. In this case, the garden has a length of 10 feet and a width of 8 feet.

Steps to Calculate the Area

Measure the length and width of the garden using a measuring tape.

Multiply the length by the width to get the area in square feet: 10 feet (length) × 8 feet (width) = 80 square feet.

Therefore, you would need 80 square feet of material to cover the entire garden.

Answer:

a) yes they are similar

b)Proved below

c)Proved below

Step-by-step explanation:

a) rectangle 1 and 2 are similar by definition of similar rectangles.

Definition of similar rectangles states that two rectangles are similar if they have same shape but different sizes. The ratio between their corresponding sides are same, in this case as rectangle 2 is made by multiplying each dimension of Rectangle 1 by a

factor of k, where k>0 thus providing same proportion in length of different corresponding sides of two rectangles hence rectangle 1 and 2 are similar.

b) Perimeter of rectangle 1, P1= s1+ s2+ s3 + s4

As each side of rectangle 2 is formed by multiplying each dimension of Rectangle 1 by k, therefore

  Perimeter of rectangle 2, P2= k.s1+ k.s2+ k.s3 + k.s4

Taking k common

                                                  = k(s1+ s2+ s3 + s4)

Substituting P1 in above expression

                                               P2  =k(P1)

Hence the perimeter of Rectangle 2 is k times the perimeter of Rectangle 1.

c) Area of rectangle 1, A1= 2(s1)(s2)

As each side of rectangle 2 is formed by multiplying each dimension of Rectangle 1 by k, therefore

Area of rectangle 2, A2= 2(k.s1)(k.s2)

                                       = 2k^2(s1)(s2)

                                        = k^2 [2(s1)(s2)]

Substituting A1 in above expression

                                        A2 = k^2(A1)

Hence the area of Rectangle 2 is k2 times the area of Rectangle 1 !

Answer:

a rectangle with two triangles.

Step-by-step explanation:

this way you will  be able to find the area of the rectangle then add it to the area of the two triangles.

Answer:

the correct answer is b

Step-by-step explanation:

[tex]\bf h=\cfrac{1}{5}w+\cfrac{8}{5}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{5}}{5(h)=5\left( \cfrac{1}{5}w+\cfrac{8}{5} \right)}\implies 5h=w+8\implies 5h-8=w[/tex]

The equation that can be used to find the number of weeks since planting is (b) w = 5h - 8

The equation is given as:

h = (1/5)w + (8/5)

Multiply through by 5

5h = w + 8

Subtract 8 from both sides

5h - 8 = w

Make w the subject

w = 5h - 8

Hence, the equation that can be used to find the number of weeks since planting is (b) w = 5h - 8

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