What is the maximum number of relative extremes contained in the graph of this function f(x)=3x^4-x^2+4x-2

Answer: [tex]6x^2+11[/tex]

Step-by-step explanation:

Given the polynomial of degree 3:

[tex]24x^3 - 54x^2 + 44x -99[/tex]

You can observe make two groups or two terms each:

[tex](24x^3 + 44x) - (54x^2 + 99)[/tex]

The Greatest Common Factor (GCF), is the highest number that divides into two or more numbers without leaving remainder.

 You can observe that the GCF of both set are factored out ([tex]4x[/tex] and [tex]9[/tex]), then, you can find  the common factor that is missing from both sets of parentheses with this procedure:

[tex](\frac{24x^3}{4x}+\frac{44x}{4x})-(\frac{54x^2}{9}+\frac{99}{9})=(6x^2+11)-(6x^2+11)[/tex]

You can observe that the common factor that is missing from both sets of parentheses is:

[tex]6x^2+11[/tex]

Final answer:

The solutions of the given system can be found by solving the equations simultaneously using the method of substitution. The solution is (x, y) = (-30, 55).

Explanation:

The solutions of the given system of equations can be found by solving it simultaneously. We have the following equations:

X+y = 25

| 2x+y= -5

To solve this system, we can use the method of substitution or elimination. Let's use the method of substitution:

Therefore, the solution to the system is (x, y) = (-30, 55).

Answer:

C 18%

Step-by-step explanation:

To find  the percent increase ,take the new amount and subtract the old amount

12.39 - 10.50 = 1.89

Divide this by the original amount

1.89/10.50 = .18

Multiply this by 100 to get the percent

.18*100% = 18%

Answer:

The inequality is y > 1/2 x - 2

Step-by-step explanation:

* To solve this problem we must to know how to make an equation

  of the line from two point

- If the line passes through points (x1 , y1) and (x2 , y2)

- The form of the equation is y = mx + c, where m is the slope of the

 line and c is the y-intercept

- The rule of the slope is m = (y2 - y1)/(x2 - x1)

- The y-intercept means the line intersect the y-axis at point (0 ,c)

* Now lets solve the problem

- To write the inequality we must to make the equation of the line

  from any two points on it

∵ The line passes through points (4 , 0) and (0 , -2)

- Let (4 , 0) is (x1 , y1) and (0 , -2) is (x2 , y2)

∵ m = (y2 - y1)/(x2 - x1)

∴ m = (-2 - 0)/(0 - 4)

∴ m = (-2)/-4 = 1/2

- Lets write the form of the equation

∵ y = mx + c ⇒ substitute the value of m

∴ y = 1/2 x + c

- The line intersects the y-axis at point (0 , -2)

∴ c = -2

∴ y = 1/2 x + -2

∴ y = 1/2 x - 2

- lets look to the line if it is dashed line then there is no equal with the

 inequality (> , <) sign, if it is solid line then there is equal with the

 inequality sign (≥ , ≤)

∵ The line is dashed line

∴ The sign of inequality is > or <

- Lets look to the shaded part, if it is over the line then the inequality

 will be y > 1/2 x - 2, if it is under the line then the inequality will

 be y < 1/2 x - 2

∵ The shaded part is over the line

∴ y > 1/2 x - 2

* The inequality is y > 1/2 x - 2

The value of c=12 will makes the equation true. for the given expression.

Here in the question we have expression:

[tex]\dfrac{3\sqrt{x^3}}{cy^4}}=\dfrac{x}{4y^3\sqrt{y}}[/tex]

By solving the above equation we will get:

[tex]12\sqrt{x}=c\sqrt{y}[/tex]

So value of c=12 will makes the equation true. for the given expression.

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The correct value of [tex]\( c \)[/tex] that makes the equation true is [tex]\( c = 64 \)[/tex].

To find the value of [tex]\( c \)[/tex], we start by simplifying the given equation:

[tex]\[ 3\sqrt{\frac{x^3}{cy^4}} = \frac{x}{4y}(3\sqrt{y}) \][/tex]

First, we simplify the left side of the equation by applying the cube root to both the numerator and the denominator:

[tex]\[ \frac{3\sqrt{x^3}}{3\sqrt{cy^4}} = \frac{x}{4y}(3\sqrt{y}) \][/tex]

The cube root of [tex]\( x^3 \)[/tex] is [tex]\( x \)[/tex] , and the cube root of [tex]\( y^4 \)[/tex] is [tex]\( y \)[/tex] times the cube root of [tex]\( y \)[/tex], which is [tex]\( y \cdot y^{1/3} \)[/tex]. Simplifying further, we get:

[tex]\[ \frac{x}{3\sqrt{c} \cdot y} = \frac{x}{4y}(3\sqrt{y}) \][/tex]

Now, we simplify the right side of the equation:

[tex]\[ \frac{x}{3\sqrt{c} \cdot y} = \frac{x \cdot 3\sqrt{y}}{4y} \][/tex]

Since [tex]\( x \)[/tex] and [tex]\( y \)[/tex] are positive, we can multiply both sides by [tex]\( 4y \)[/tex] to eliminate the denominators:

[tex]\[ \frac{4yx}{3\sqrt{c} \cdot y} = x \cdot 3\sqrt{y} \][/tex]

Simplifying, we get:

[tex]\[ \frac{4x}{3\sqrt{c}} = 3x\sqrt{y} \][/tex]

Now, we can divide both sides by [tex]\( x \)[/tex] since [tex]\( x > 0 \)[/tex]:

[tex]\[ \frac{4}{3\sqrt{c}} = 3\sqrt{y} \][/tex]

Next, we square both sides to eliminate the square root:

[tex]\[ \left(\frac{4}{3\sqrt{c}}\right)^2 = (3\sqrt{y})^2 \][/tex]

[tex]\[ \frac{16}{9c} = 9y \][/tex]

Since [tex]\( y > 0 \)[/tex], we can multiply both sides by [tex]\( 9c \)[/tex] to get rid of the denominator:

[tex]\[ 16 = 81cy \][/tex]

Now, we divide both sides by [tex]\( y \)[/tex]:

[tex]\[ \frac{16}{y} = 81c \][/tex]

Finally, we multiply both sides by [tex]\( y \)[/tex] to solve for [tex]\( c \)[/tex]:

[tex]\[ 16 = 81c \][/tex]

[tex]\[ c = \frac{16}{81} \][/tex]

[tex]\[ c = \left(\frac{2^4}{3^4}\right) \][/tex]

[tex]\[ c = \left(\frac{2}{3}\right)^4 \][/tex]

[tex]\[ c = \left(\frac{3}{2}\right)^{-4} \][/tex]

[tex]\[ c = 64 \][/tex]

Therefore, the value of [tex]\( c \)[/tex] that makes the equation true is [tex]\( c = 64 \)[/tex].

Hello there!

The answer is the first option.

Remember that congruent = same size and same shape, and this is the only option that has both of those things. In the second and forth options, the sizes are different making those options not correct. In the 3rd option, the shape is slightly different since one triangle is not as stretched out as the other.

I hope this was helpful and have a great day!

Since the two sides and one angle in figure 1 are the same as a result they are congruent.

Congruent triangles are those that are exactly the same size and shape. Congruent is represented by the symbol ≅ When the three sides and three angles of one triangle match the dimensions of the three sides and three angles of another triangle, they are said to be congruent.

While the similarity law for triangles is defined as the law to prove that two triangles have the same shape, it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.

Thus, the two sides and one angle in figure 1 are the same as a result they are congruent.

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Answer:

Global extrema:  none.  Local extrema:  (0, 0) and (4, -32)

Step-by-step explanation:

ƒ(x) = x3 – 6x2 should be written as  ƒ(x) = x^3 – 6x^2.  Use " ^ " to denote exponentiation, please.

One way to answer this problem would be to make a careful graph of ƒ(x) = x^3 – 6x^2.  Notice that this graph begins in Quadrant III and ends in Quadrant I; this is one outcome of its being an ODD function.  The graph will increase, reach a peak (a local max), decrease, reach a valley (a local min) and then grow from then on.

Another way is to use calculus.  You don't say what course you're in, so I can't be sure that calculus would make sense to you.

Find the first derivative of  ƒ(x) = x^3 – 6x^2.  It is f '(x) = 3x^2 - 12x.  Set this derivative = to 0 and find the roots.  Hint:  find the roots of 3x^2(x - 4).  They are x = 0 and x = 4.  At x = , y = f(0) = 0.  Thus, the local max is

(0, 0).  At x = +4, y = f(4) = 64 - 6(16) = -32.  Thus, the local min is at (4, -32 ).

This graph rises without bound as x goes to ∞, and decreases without bound as x goes to -∞.  Thus, there is neither a global max nor a global min.  

A leap year consists of 366 days.

52 weeks + 2 days.

These 2 days can be: (mon,tue),(tue,wed),(wed,thu),(thu,fri),(fri,sat)(sat,sun)(sun,mon)

Thus, the total number of cases = 7.

The number of cases in which we get Friday = 2(Thu, Fri)(Fri, Sat).

Therefore the required probability = 2/7.

Answer:

x = z - w

Step-by-step explanation:

Given

w + x = z ( isolate x by subtracting w from both sides )

x = z - w

Answer:

x = z - w

Step-by-step explanation:

Take w to the other side and subtract with z to make x the subject

Since m<4 and m<8 both add up to 180 degrees. Combine 2x + 20 and 3x - 5 and set it equal to 180. By subtracting 15 to the other side and dividing five to the other side you get x=33. Plug 33 back into the angle measurement separate equations to find degree angle measurement. Your welcome.

Answer:

The dose in milligrams of a 6-year-old child is 60.

Step-by-step explanation:

The formula is:

[tex]C = \frac{a}{(a+ 12)}A[/tex]

We know that

A= adult dosage in milligrams=180 milligrams

a = age of the child = 6 years-old

So the child’s dosage in milligrams is:

[tex]C = \frac{6}{(6+12)}*180[/tex]

[tex]C = \frac{1}{(3)}*180[/tex]

[tex]C = \frac{180}{(3)}[/tex]

[tex]C = 60\ milligrams[/tex]

Final answer:

To find the child's dosage of medicine, apply the formula C = a/(a+12) x A with a being the child's age and A the adult dosage. For a 6-year-old, the dosage is 60 milligrams.

Explanation:

To calculate the prescribed dosage of medicine for a 6-year-old child when the adult dosage is 180 milligrams, we use the formula C = a/(a+12) ⋅ A, where C is the child’s dosage in milligrams, a is the age of the child, and A is the adult dosage in milligrams.

Plugging the given values into the formula we get:

C = 6 / (6 + 12) ⋅ 180
C = 6 / 18 ⋅ 180
C = 1 / 3 ⋅ 180
C = 180 / 3
C = 60 milligrams

Therefore, the prescribed dosage for a 6-year-old child is 60 milligrams.

Answer:

Every hour he drives 60 miles and if he drives 8 hours a day ( 8x60 ), that means that he drives 480 miles a day. Then you would do, 2641 / 480, to find the number of days it should take. The answer is around 5.5 days.

Answer:

15.5 or 15 1/2

arrange all numbers least to greatest and cross out each number until u get to the last two, once u get to the last two add them and divide them by two:

Answer:

q = 20

Step-by-step explanation:

1/5q = 4

q = 20

[tex]\bf \qquad \textit{perfect square trinomial} \\\\ (a\pm b)^2\implies a^2\pm \stackrel{\stackrel{\text{\small 2}\cdot \sqrt{\textit{\small a}^2}\cdot \sqrt{\textit{\small b}^2}}{\downarrow }}{2ab} + b^2 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf x^2+15x+\boxed{?}^2\implies \stackrel{\textit{we know the middle term is}}{2\sqrt{x^2}\cdot \sqrt{\boxed{?}^2}\implies 2x\boxed{?}}\qquad then\qquad 2x\boxed{?}=15x \\\\\\ \boxed{?}=\cfrac{15x}{2x}\implies \boxed{?}=\cfrac{15}{2}\qquad \impliedby \textit{we should add that much \underline{squared}} \\\\[-0.35em] ~\dotfill\\\\ x^2+15x+\left( \cfrac{15}{2} \right)^2\implies \left(x+ \cfrac{15}{2} \right)^2[/tex]

where are the signs between the 5 and 48j, and k and 2? is at multiplication? cause you use parentheses only for that.

If it is multiplication... then 3j * 3k = 9jk

48j * 5 = 240j * k =240jk * 2 = 480jk / 9jk = 53.3333333333jk

I dont know how to help you bud give me a geometry and I could maybe solve it lol

To express 12X+36Y in different terms, we can use other variables or coefficients while maintaining the same relationship between X and Y. Two equivalent expressions are 4A+12B and 6C+18D.

To express the expression 12X+36Y in terms of equivalent mathematical expressions using different variables or coefficients, we can use any other variables or coefficients as long as they maintain the same relationship between X and Y. Here are two distinct expressions:

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The probable question may be:

Express the expression 12X+36Y in terms of equivalent mathematical expressions using different variables or coefficients. Provide at least two distinct expressions that are equivalent to 12X+36Y.

Check the picture below.

so the triangle has a height of 9 and a base of 9, since it's the radius anyway.

if we subtract the area of that triangle from the area of the circle's sector, what's leftover is just the shaded area.

20.25π - 40.5.

Answer:

Step-by-step explanation:

A function is a relation that associates each element x of a set X, to a single element y of another set Y.

In D) for x = 0 we have three values of y = f(x): -1, 4 and 6.

Therefore this table does not represent a function.

Answer:

for the first graph it is

a=1

b= 1/16

c=1/256

for the second graph it is

d=1

e=4/9

f=16/81

An Isosceles triangle means it has two sides that measures the same.

When we have two sides that measures the same also means that they have the same angles.

If one angel measures 140 that means that the other angles are 20 and 20

Because the angles of the triangle has to sum to 180

In an isosceles triangle, two angles are same and the sum of all angles is 180 degrees. If one angle is 140 degrees, the other two angles must sum to 40 degrees, and since they are equal, each would measure 20 degrees.

In an isosceles triangle, two of the angles are equal, and the third angle, also known as the base angle, is different. The total sum of the angles in any triangle, including an isosceles triangle, is always 180 degrees. Thus, if one of the angles measures 140 degrees, the remaining two angles must sum up to 40 degrees. Since these two angles are equal (as it is an isosceles triangle), each of them would measure 20 degrees. Thus, in the given isosceles triangle, the other two angles would measure 20 degrees each.

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Answer: D

Step-by-step explanation:

Answer:

Option A is correct.

Step-by-step explanation:

Zeros at -8, -1 and 3 means these are the factors of the polynomial.

x=-8, x=-1 and x =3

It can be written as:

x+8=0, x+1=0 and x-3=0

Factors can be written as:

(x+8)(x+1)(x-3)=0

Multiplying the first two terms and then their product with third terms:

[tex](x(x+1) +8(x+1))(x-3) =0\\(x^2+x+8x+8)(x-3)=0\\Adding\,\, like\,\, terms\,\,:\,\,\\(x^2+9x+8)(x-3) =0\\x(x^2+9x+8) -3(x^2+9x+8)=0\\x^3+9x^2+8x-3x^2-27x-24=0\\Adding\,\, like\,\, terms\,\,:\,\,\\x^3+9x^2-3x^2+8x-27x-24=0\\x^3+6x^2-19x-24=0\\or\,\,f(x) = x^3+6x^2-19x-24[/tex]

So, Option A is correct.

Answer:

Question 10: [tex]f(x)=1/2x-1[/tex] Question 13: [tex]f(-2)=-1[/tex] Question 11: [tex]f(8)=60[/tex]

Step-by-step explanation:

For Question 10:

The functionis in the form of [tex]f(x)[/tex]. We know the slope is [tex]\frac{1}{2}[/tex] (rise 1 run 2)and the y intercept is -1 (where the line goes through the y axis). We can then put the function is slope intercept form ([tex]y=mx+b[/tex]) and we would have [tex]f(x)=1/2x-1[/tex].

For Question 13:

To evaluate the function[tex]f(x)=\frac{3}{2} x-4[/tex] for [tex]f(-2)[/tex] we need to plug -2 into the function as x. [tex]f(-2)=\frac{3}{-2} (-2)-4[/tex]. [tex]\frac{3}{-2}[/tex] times -2 would equal 3 because the negatives cancle out. 3-4 equals -1 so the solution is [tex]f(-2)=-1[/tex].

For question 11:

Same as question 13. plug 8 into x in [tex]f(x)=x^2-4[/tex]. This would be [tex]f(8)=(8)^2-4[/tex]. 8 squared is 64 and 64-4 is 60. Therefore [tex]f(8)=60[/tex].

Answer:

Step-by-step explanation:

We have

2 rectangles 3ft × 5ft

2 rectangles 5ft × 6ft

2 rectangles 3ft × 6ft

The formula of an area of a rectangle:

A = lw

l, w - dimensions of a rectangle

Calculate:

A₁ = (3)(5) = 15 ft²

A₂ = (5)(6) = 30 ft²

A₃ = (3)(6) = 18 ft²

The total area of the solid figure:

A = 2A₁ + 2A₂ + 2A₃ = 2(A₁ + A₂ + A₃)

Substitute:

A = 2(15 + 30 + 18) = 2(63) = 126 ft²

It will take them 20 hours, since the question is asking how long it will take them when working together you add each of their hours together,9+11=20

The measure of the angle is 6°

A complementary angle consists of two angles who's sum is 90 degrees. Since there are two we know this for sure:

1st angle: x (unknown value)

2nd angle: x-78 (78 less then its complement)

total: 90

If we put the equation together we get:  x+x-78= 90

x+x-78+78=90+78

2x=168

2x/2=168/2

x=84

Now we know that x = 84, know we gonna find the 2nd angle:

1st: x=84

2nd: 84-78 = 6

total: 84+6=90

Answer:

The total weight of the packages of fruit that weigh less than half a pound is, 7/8.

Step-by-step explanation:

This reason being is because 2 of the 1/8ths are under 1/2 of a pound, and the 1/4th and the 3/8 is all under 1/2 of a pound. You add the 2 1/8ths together and get 2/8 + the 3/8 = 5/8. Then you add the 5/8 together with the only 1/4th and you get 7/8, as your answer.

Hope this helps!! :)

Answer: 150 is divisible by 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.

I hope that this helps! :D

Answer:

2,3,5,6, and 10

Step-by-step explanation:

If you get a whole number when you divide by one of these numbers that means the number is divisible, if you get a fraction/decimal then it isn't divisible