The expression 2x(3x^2+4) can be simplified into which of the following?


a. 6x^3+4

b. 5x^3+6x

c. 6x^2+8x

d. 6x^3+8x

Rewrite y^4 as (y^2)^2

(y^2)^2 + 14y^2 +49

Rewrite 49 as 7^2

(y^2)^2 + 14y^2 +7^2

Factor using the perfect square rule.

Final answer: (y^2 + 7)^2

The factorization of given expression  [tex]y^{4}[/tex] + 14y² + 49 is a perfect square which is equal to (y² + 7)².

What is factorization ?

The factorization of algebraic expressions is the process of identifying two or more expressions whose product is the given expression.

The given expression is [tex]y^{4}[/tex] + 14y² + 49.

Before factorization if we look at the given expression we can find out that it is a form of perfect square which is :

A² + B² + 2AB.

Let's convert the given expression in the perfect square form. This will be equal to :

(y²)² + (7)² + 2 × y² × 7

We know that the expansion A² + B² + 2AB is equal to (A+B)².

Here ; A = y² and B = 7.

So , the factorization of given expression  [tex]y^{4}[/tex] + 14y² + 49 is equal to :

(y² + 7)²

Therefore , the factorization of given expression  [tex]y^{4}[/tex] + 14y² + 49 is a perfect square which is equal to (y² + 7)².

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Answer:

its the third one i got that

For this case we must simplify the following expression:

[tex]\frac {12y ^ 7} {18y ^ {- 3}}[/tex]

We have that by definition of properties of powers, it is fulfilled that:

[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]

Then, we can rewrite the expression:

[tex]12y ^ 7 * 18y ^ 3[/tex]

By definition of multiplication properties of powers of the same base we have:

[tex]a ^ m * a ^ n = a ^ {m + n}[/tex]

So:

[tex]12y ^ 7 * 18y ^ 3 = (12 * 18) * y ^ {7 + 3} = 216y ^ {10}[/tex]

Answer:

[tex]216y ^ {10}[/tex]

When y = 0 the expression is 0

Answer:

C. y = -4x +10

Step-by-step explanation:

Equation of a line is found by the formula y = mx +b

Where m is the slope and b is the y intercept

we see that y-intercept is given as 10, so b = 10 and we plug in the coordinate (2,2) into the equation to find the slope (m). We plug in x = 2 and y = 2. Shown below:

[tex]y=mx+b\\2=m(2)+10\\2=2m+10\\2-10=2m\\-8=2m\\m=\frac{-8}{2}\\m=-4[/tex]

We know the value of m to be -4 and b to be 10, thus we can write the equation as:

[tex]y=-4x+10[/tex]

Answer choice C is right.

Answer:

c. y = -4x + 10

Step-by-step explanation:

y = mx + b where b = y -intercept = 10

so

y = mx + 10

Plug in (2,2) to find slope m

2 = 2m + 10

2m = -8

m = -4

Slope m = -4

Equation

y = -4x + 10

315 > 131.5 > 131.05 > 13.15 > 1

Answer:

3c=36

c = 12

Step-by-step explanation:

We have 36 sugar flowers

We put 3 on each cupcake

The number of cupcakes times the number of flowers per cupcake equals the total flowers

3*c = 36

Divide each side by 3

3c/3 = 36/3

c = 12

Answer:

12 cupcakes

Step-by-step explanation:

3 sugar flowers on each (1) cupcake

36 sugar flowers on c cupcakes

3c = 36 * 1

3c = 36

 c = 36/3

 c = 12 cupcakes

Answer:

C. F(X) = (X - 3)⁴

Step-by-step explanation:

Hope this helps you.

The graph of F (x) will be;

⇒ F (x) = (x - 3)⁴

A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

Given that;

The function G (x) is,

⇒ G (x) = x⁴

And, The function of G (x) is shown in figure.

And, It is shifted 3 units to the right.

Now,

Here, The function G (x) is,

⇒ G (x) = x⁴

Since, The function of G (x) is shown in figure.

And, It is shifted 3 units to the right.

So, The function of F(x) become;

⇒ F (x) = (x - 3)⁴

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Answer:

[tex]\large\boxed{A=x^2+23x+49}[/tex]

Step-by-step explanation:

Subtract the area of a square (x + 1) × (x + 1)

from the area of a rectangle (x + 10) × (2x + 5)

The area of a square:

[tex]A_s=(x+1)(x+1)[/tex]            use FOIL: (a + b)(c + d) = ac + ad + bc + bd

[tex]A_s=(x)(x)+(x)(1)+(1)(x)+(1)(1)=x^2+x+x+1=x^2+2x+1[/tex]

The area of a rectangle:

[tex]A_r=(x+10)(2x+5)[/tex]              use FOIL

[tex]A_r=(x)(2x)+(x)(5)+(10)(2x)+(10)(5)=2x^2+5x+20x+50=2x^2+25x+50[/tex]

The area of a figure:

[tex]A=A_r-A_s[/tex]

Substitute:

[tex]A=(2x^2+25x+50)-(x^2+2x+1)=2x^2+25x+50-x^2-2x-1[/tex]

combine like terms

[tex]A=(2x^2-x^2)+(25x-2x)+(50-1)=x^2+23x+49[/tex]

Answer:

I would think the answer would be 35

Step-by-step explanation:

Step 1: Round your answer to 2 decimal places.

Step2: Divide or Multiply your answer you got by 2.

cos42= 35/y

y=35/cos42

y= 47.10

is the answer

Answer:

[tex]\large\boxed{V=\dfrac{1600\pi}{3}\ cm^3}[/tex]

Step-by-step explanation:

The formula of a volume of a cone:

[tex]V=\dfrac{1}{3}\pi r^2H[/tex]

r - radius

H - height

We have r = 10cm and H = 16cm. Substitute:

[tex]V=\dfrac{1}{3}\pi(10^2)(16)=\dfrac{1}{3}\pi(100)(16)=\dfrac{1600\pi}{3}\ cm^3[/tex]

Answer:

7.125 feet

Step-by-step explanation:

1. convert both fractions to decimals by dividing numerator by denominator

    10 1/2 = 10.5

    3 3/8 = 3.375

2. Subtract 10.5-3.375 = 7.125 feet left

Answer:

7.125 ft

Step-by-step explanation:

Answer:

The measure of the line segment GE is [tex]18\ units[/tex]

Step-by-step explanation:

we know that

The Intersecting Secant-Tangent Theorem , states that the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment

so

In this problem

[tex]GE*GF=GH^{2}[/tex]

substitute the values

[tex](8+x)(8)=12^{2}[/tex]

solve for x

[tex]8x+64=144[/tex]

[tex]8x=144-64[/tex]

[tex]8x=80[/tex]

[tex]x=10[/tex]

Find the measure of the line segment GE

[tex]GE=8+10=18\ units[/tex]

Answer:

1) The expression to represent the pattern is 11 + 8n

2) The expression to represent the pattern is 80 - 9n

Step-by-step explanation:

1) * Lets study the pattern;

- 19 , 27 , 35 , 43 , ..................

∵ 27 - 19 = 8

∵ 35 - 27 = 8

∵ 43 - 35 = 8

∴ The difference is constant between each two consecutive terms

∴ It is an arithmetic sequence

* Lets take about the arithmetic sequence

- If the first term is a and the constant difference is d

∴ a1 = a , a2 = a + d , a3 = a + 2d , a4 = a+ 3d , ........

∴ an = a + (n - 1)d, where n the position of the term in the sequence

* Now we will use this rule to find the expression of our pattern

∵ a = 19 , d = 8

∴ an = 19 + (n - 1)(8) ⇒ an = 19 + 8n - 8 ⇒ an = 11 + 8n

* Lets check it;

∵ a3 = 11 + 8(3) = 11 + 24 = 35 ⇒ true

∴ The expression to represent the pattern is 11 + 8n

2) * Lets study the pattern;

- 71 , 62 , 53 , 44 , ..................

∵ 62 - 71 = -9

∵ 53 - 62 = -9

∵ 44 - 53 = -9

∴ The difference is constant between each two consecutive terms

∴ It is an arithmetic sequence

* We will use the same rule above to find the expression of the pattern

∵ a = 71 , d = -9

∴ an = 71 + (n - 1)(-9) ⇒ an = 71 + -9n + 9 ⇒ an = 80 - 9n

* Lets check it;

∵ a4 = 80 - 9(4) = 80 - 36 = 44 ⇒ true

∴ The expression to represent the pattern is 80 - 9n

The cost of painting a wall varies jointly with the length and width of the wall, represented by the formula C = k * l * w, where C is the cost, k is the cost per unit area, l is the length, and w is the width.

The cost of painting a wall varies directly with its area. The area of a rectangular wall is found by multiplying its length (l) by its width (w), giving the formula A = l * w for the area. If C represents the cost of painting, and k is the cost per unit area, then the cost formula can be written as C = k * A, which simplifies to C = k * l * w. This means the cost varies jointly with the length and width of the wall, as both dimensions contribute to the total area. Therefore, the cost does not vary directly with l or w alone, but with their product.

Answer:

A. 5/9    B. 1/6.

Step-by-step explanation:

Total possible events = 6*6 = 36.

A.  The possible combinations for the sum  being <= 6 are:

1 ,1  2,2   3,3   1,2  1,3  1,4  1,5  2,1   2,3  2,4  3,1   3,2  3,3  4,1  4,2  5,1

= 16

So Probability of Sum > 6 =  (36-16) / 36

= 20/36

= 5/9.

B.   Possible combinations where the sum is divisible by 6  are

3,3  2,4  4,2  1,5  5,1. 6,6   =   6.

So the required probability =  6/36

= 1/6.

Answer:

none

Step-by-step explanation:

y = -4x^2 +3x-2

To find the x intercepts, let y =0

0 = -4x^2 +3x-2

Using the discriminant

a=-4, b=3  c=-2

b^2 -4ac

3^2 -4(-4)(-2)

9 -32

-23

Since this is negative all the roots are complex, so it has no real roots

none

Answer:

9 hours.

Step-by-step explanation:

Average rate = distance / time

=  871 / 13

=  67 mph

So the time to travel 603 miles

=  distance / rate

= 603 / 67

=  9 hours.

Answer:

  c. Reflect across the y-axis, translate 3 right and 2 down

Step-by-step explanation:

You want a description of the transformation of g(x) = ln(x) into f(x) = ln(3 -x) -2.

Reflection across the y-axis is the result of replacing x by -x in a function. That is, f(x) = g(-x) will reflect g(x) across the y-axis.

Translation right h units and up k units is the result of the transformation ...

  f(x) = g(x -h) +k

The given function f(x) can be written as ...

  f(x) = g(-(x -3)) -2

The first transformation is replacement of x by -x:

  f(x) = g(-x) . . . . . . . . reflection over the x-axis

The second transformation is replacement of x by x-3, and adding -2 to the function value:

  f(x) = g(-(x -3)) -2 . . . . translation of the reflected function right 3, down 2

The graph of g(x) = ln(x) is transformed to the graph of f(x) = ln(3 -x) -2 by reflection over the y axis, then translation right 3 and down 2, choice C.

Answer:

basketball hoop= 10 feet high

steve=5 feet tall

hes standing 12 feet away

so  i would say 3 feet away

The distance from the top of Steve's head to the hoop is 13 feet.

Given information in the question is the height of basketball hoop is 10 feet, height of Steve 5 feet and the distance from hoop to him is 12 feet.

Therefore the distance from the top of Steve's head to the hoop is also 12 feet.

Also the distance from the top of Steve's head and the top of Hoop is (10 - 5) feet = 5 feet.

Therefore calculating the distance from top of Steve's head to the hoop by using Pythagoras Theorem -

Let the required distance is d feet .

⇒  [tex]d = \sqrt{12^{2} + 5^{2} }[/tex]

⇒  [tex]d = \sqrt{169} = 13[/tex] feet

Therefore the distance from the top of Steve's head to the hoop is 13 feet.

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Answer:

D

Step-by-step explanation:

We need to graph both  [tex]6^x[/tex]  and  [tex]3^x[/tex]  and figure out the x-value at which the graph of  [tex]6^x[/tex] is LESS THAN that of the graph of [tex]3^x[/tex].

The attached picture shows the graph of  [tex]6^x[/tex] in BLUE and the graph of  [tex]3^x[/tex] in RED.

We need to find x-value where the BLUE graph is "BELOW" the RED graph. We can see that this occurs when x < 0.

Thus the correct answer is  D

Answer:

Long diagonal: 12.12 yd

Short diagonal: 7 yd.

Step-by-step explanation:

As you can see, 4 righ triangles are formed.

The larger diagonal divides the angle ∠AFM=60° into two angles of 30° each.

Then,  choose one the triangles that has the angles of 30°. The hypotenuse will be the side lenght of 7 yards, the long diagonal (D) will be twice the adjacent side and the short diagonal (d) will be twice the opposite side.

Then:

- Long diagonal:

[tex]\frac{D}{2}=7*cos(30\°)=6.06yd\\\\D=2(\frac{D}{2})=2(6.06yd)=12.12yd[/tex]

- Short diagonal:

[tex]\frac{d}{2}=7*sin(30\°)=3.5yd\\\\d=2(\frac{d}{2})=2(3.5yd)=7yd[/tex]

Answer:

The length of diagonals are 7 yd and 12.12 yd

Step-by-step explanation:

Let the point of intersection called as 'D'

<AFD = <MFD =60/2 = 30°

Then < AFM = <AFD + <MFD

Consider the ΔAFD

The angles are 30°, 60° and 90 then sides are in the ratio

1 : √3 : 2

The two diagonals are MA and FR

MA = MD + AD = 7/2 + 7/2 = 7 yd

FR = FD + RD =  7√3/2 +  7√3/2 =  7√3 = 12.12 yd

Therefore the length of diagonals are 7 yd and 12.12 yd

Answer:

The shape includes a curve.

Step-by-step explanation:

A polygon consists of joined straight lines - no curves.

Set (x+3) to 0. X+3=0. X=-3

Set (x+2) to 0 X+2=0. X=-2

Answer:

r = - [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

The common ratio r of a geometric sequence is

r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{a_{3} }{a_{2} }[/tex] = .....

Hence

r = [tex]\frac{-52}{104}[/tex] = [tex]\frac{26}{-52}[/tex] = - [tex]\frac{1}{2}[/tex]

To compute the mean and standard deviation of the random variable X, the number of adults who believe that the overall state of moral values is poor, we use formulas for a binomial distribution. The mean is 78 and the standard deviation is 6.34. The interpretation of the mean is that for every 150 adults, the mean is the number of them that would be expected to believe that the overall state of moral values is poor.

To compute the mean and standard deviation of the random variable X, the number of adults who believe that the overall state of moral values is poor, we can use the formulas for a binomial distribution. The mean is found by multiplying the total number of trials (150) by the probability of success (0.52): mean = 150 × 0.52 = 78. The standard deviation is found by taking the square root of the product of the number of trials, the probability of success, and the probability of failure (1 - 0.52): standard deviation = √(150 × 0.52 × 0.48) = 6.34.

The interpretation of the mean is that for every 150 adults, the mean is the number of them that would be expected to believe that the overall state of moral values is poor, which in this case is 78.

It would not be unusual if 71 out of the 150 adults surveyed believe that the overall state of moral values is poor, as this value falls within one standard deviation from the mean.

Answer:b

Step-by-step explanation:

Answer:

Step-by-step explanation:

The first triangle is a 30-60-90 right triangle.  We have a Pythagorean triple associated with this type of triangle that is

 (x , x√3, 2x) which represent the side lengths across from the

(30°, 60°, 90°)

We have the side length across from the 30° as 14.  That means that x = 14.  In our figure, "y" is across from the 60° which means that the side length is

14√3, which has a decimal equivalency of 24.24871131; in our figure "x" is the hypotenuse which is 14(2) which is 28.

For the intents and purposes of keeping you not confused:

x = 28, y = 14√3 (or 24.24871131)

The next triangle is also a right triangle but this one is a 45-45-90.  The Pythagorean triple for that triangle is

( x , x , x√2 ) as the side lengths across from the

(45°, 45°, 90°)

We have a side length across from the 90° as 18 units long; therefore, according to our Pythagorean triple:

x√2 = 18 and

x = [tex]\frac{18}{\sqrt{2} }[/tex] and, rationalizing the denominator:

[tex]x=\frac{18\sqrt{2} }{2}[/tex] so

x = 9√2, which has a decimal equivalency of 12.72792206.

Summing up again:

x = 9√2 (or 12.72792206)

Answer:

d = 50 in.

Step-by-step explanation:

A = Pi*r^2

625Pi = Pi*r^2

625 = r^2

r = 25 in

Diamenter = 2(radius=

d = 50 in

Best regards

Answer:

a) The function is constantly increasing and is never decreasing

b) There is no local maximum or local minimum.

Step-by-step explanation:

To find the intervals of increasing and decreasing, we can start by finding the answers to part b, which is to find the local maximums and minimums. We do this by taking the derivatives of the equation.

f(x) = ln(x^4 + 27)

f'(x) = 1/(x^2 + 27)

Now we take the derivative and solve for zero to find the local max and mins.

f'(x) = 1/(x^2 + 27)

0 = 1/(x^2 + 27)

Since this function can never be equal to one, we know that there are no local maximums or minimums. This also lets us know that this function will constantly be increasing.

To find the interval of increase and decrease, we need to find where the derivative of the function is positive and negative, respectively. The derivative is positive when x > 0 and negative when x < 0.

To find the interval of increase and decrease, we need to find where the derivative of the function is positive and negative, respectively. The derivative of f(x) = ln(x^4 + 27) can be found using the chain rule: f'(x) = (4x^3)/(x^4 + 27).

The derivative is positive when (4x^3)/(x^4 + 27) > 0, which occurs when x > 0.

The derivative is negative when (4x^3)/(x^4 + 27) < 0, which occurs when x < 0.

Therefore, the interval of increase is (0, infinity) and the interval of decrease is (-infinity, 0).

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Answer:

An angle showing a turn through 1/5 of a circle is greater

Step-by-step explanation:

we know that

A complete circle represent [tex]360\°[/tex]

so

An angle showing a turn through 1/6 of a circle is

[tex](360\°)*(\frac{1}{6})=60\°[/tex]

An angle showing a turn through 1/5 of a circle is

[tex](360\°)*(\frac{1}{5})=72\°[/tex]

therefore

An angle showing a turn through 1/5 of a circle is greater