Evaluate each function at the given value using the remainder theorem.

F(x)=x^4+5x^3-18x+1 at x=-4

Please show work , I give brainliest. :)

Answer:

No solution.

Step-by-step explanation:

[tex]\textbf{Given that,}\\\\~~~~~~~~3x = 3(x-1)\\\\\\\implies \dfrac{3x}3 = \dfrac{3(x-1)}{3}~~~~~~~~~~~~~~~~~;\textbf{Dividing both sides by 3}\\\\\\\implies x = x-1\\\\\\\implies x-x = x-1-x~~~~~~~~~~~~~;\textbf{Subtracting}~ x ~ \textbf{from both sides} \\\\\\\implies 0 = -1\\\\\\\textbf{Which is not true, so there are no solutions.}[/tex]

Answer: 5/6, 3/4, 4/12

Step-by-step explanation:

Convert them all into a common denominator, 12.

5/6=10/12, 3/4=9/12, and 4/12 stays the same. 10>9, and 9>4

The number of the years to take for the farmland's market value to reach $125,000 will be 19 years.

The missing function will be given below.

[tex]\rm p(t) = 78,125\ e^{0.025t}[/tex]

Let a is the base and x is the power of the exponent function and b is the y-intercept. The exponent is given as

y = aˣ

A patch of farmland is currently worth $78,125. The expected increase in its market value can be modeled by the function below.

[tex]\rm p(t) = 78,125\ e^{0.025t}[/tex]

Then the number of the years to take for the farmland's market value to reach $125,000 will be

[tex]\rm 78,125 \ e^{0.025t} = 125,000\\\\e^{0.025t} = 1.6[/tex]

Then take log on both sides, then we have

0.025t lne = ln 1.6

     0.025t = 0.47

               t = 18.8

               t = 19 years

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[tex]g = \frac{x}{5} - \frac{6}{5x} - \frac{3}{5} [/tex]

Step-by-step explanation:

[tex]3 + 5g = \frac{ {x}^{2} - 6 }{x} \\ 5g = x - \frac{6}{x} - 3 \\ g = x - \frac{ \frac{6}{x} - 3}{5} \\ g = \frac{x}{5} - \frac{ \frac{6}{x} }{5} - \frac{3}{5} [/tex]

Answer:

x = 68

Explanation:

⇒ log₈(x - 4) = 2

apply log rules: logₐN = x then N = aˣ

⇒ (x - 4) = 8²

simplify

⇒ x - 4 = 64

add 4 on both sides

⇒ x = 64 + 4

add the integers

⇒ x = 68

Answer:

x = 68

Step-by-step explanation:

Given equation:

[tex] \rm log_{8}(x - 4) = 2[/tex]

To Find:

Value of x

Solution:

Rewrite the equation in exponential form which is equivalent to b^y = x.

[tex] \implies {8}^{2} = x - 4[/tex]

Now find the value of x.

[tex] \implies \:64 = x - 4[/tex]

Transpose 4 from RHS to LHS, make sure to change its sign from (-) to (+) .

[tex] \implies \: 64 + 4 = x[/tex]

Overturn the equation

[tex] \implies \: x = 68[/tex]

Thus, value of x is 68.

Answer:

i might just be mind numb right now but you don't use pie on rectangles for area

Area = 6510

Step-by-step explanation:

A = L x W

A = 93 x 70

A = 6510

Check the picture below, so the parabola looks more or less like so, with a "p" distance of 3 and the vertex at the origin, keeping in mind the vertex is half-way between the focus point and the directrix.

[tex]\textit{horizontal parabola vertex form with focus point distance} \\\\ 4p(x- h)=(y- k)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h+p,k)}\qquad \stackrel{directrix}{x=h-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\supset}\qquad \stackrel{"p"~is~positive}{op ens~\subset} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{cases} h=0\\ k=0\\ p=3 \end{cases}\implies 4(3)(x-0)~~ = ~~(y-0)^2\implies 12x=y^2\implies x=\cfrac{1}{12}y^2[/tex]

Answer:

46 degrees

Step-by-step explanation:

Answer: the answer to your question is 42.2

Step-by-step explanation:25 x 25 + 34 X 34 = c^2

Answer:

20

Step-by-step explanation:

34 + 90 = 124

180-124 = 56 degrees

c = 56 degrees

to find x we need to use sin

sin = SOH (Sin = opposite/hypotenuse

sin 56 = x/25

sin 56 x 25 = x

x = 20.72593931

x = 20 (rounded to the nearest 10th)

hope this helped :)

Answer:

[tex] \frac{32}{45} [/tex]

Step-by-step explanation:

if the multiplication of two numbers is 16)9, and one of the numbers is 5/2. then the other number can be found by dividing the number from the product to get the other number.

Using it's concept, it is found that there is a 0.001 = 0.1% probability that he will forget to brush his teeth three days in a row.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, for each day, there is a 0.1 probability that he forgers to brush his teeth, and days are independent, hence for 3 consecutive days the probability is given by:

p = (0.1)³ = 0.001.

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The growth of the plant is 25 inches last year.

Explanation:

Suppose the growth of the plant last year was y.

From the given situation, the normal growth was 10  inches more than twice the amount of last year.

So the equation will be

= 10 + 2y = 60

= 2y = 50

= y= 25 inches.

Therefore , the growth of the plant was 25 inches last year.

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Answer: 1/6

Step-by-step explanation: there is 6 faces on a standard die, one of them is 5.

Question 13

[tex]{12x+2}=\frac{18+34}{2}\\\\12x+2=26\\\\12x=24\\\\x=\boxed{2}[/tex]

Question 14

Base angles of an isosceles trapezoid are congruent, so:

[tex]73x+1=74\\73x=73\\x=\boxed{1}[/tex]

The solution of the equation when p = -1 is [tex]T=3x^{-2}[/tex]

The equation is given as:

[tex]T=3x^{2p}[/tex]

The value of p is -1.

So, we have:

[tex]T=3x^{2*-1}[/tex]

Evaluate the product

[tex]T=3x^{-2}[/tex]

Hence, the solution of the equation when p = -1 is [tex]T=3x^{-2}[/tex]

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Answer:

200 dollars

Step-by-step explanation:

Let's say p equals the cost price of the article. Since the man made 25% profit, that means he got 100% of what he originally paid plus another 25% of what he originally paid. In other words, he sold the article for 125% of the original price. Converting that to a decimal we get:

250=p*1.25

Some simple division gets us a cost price of 200 dollars.

The resultant speed of the plane is 100 mi/hr along the northeast direction.

Speed can be calculated as the ratio of distance traveled to the time taken

First, we need to find our coordinate axis, we will define the x-axis as the east and the y-axis as the north.

We are given that the plane travels at 150 mi/hr at 100° east of north, notice that if we measure from the positive x-axis, this is equivalent to an angle of -10°.

Then the x-component of the velocity ;

150mi/hr x cos(-10°) = 147.7 mi/hr

The y-component of the velocity;

150mi/hr x sin(-10°) = -26 mi/hr.

So, the vector is:

V = 147.7 mi/hr, -26 mi/hr

Now we know that the wind blowing at 50mi/hr at southwest, exactly southwest would be at an angle of 225°,

Thus, the components of the vector are:

x-component: 50mi/hr x cos(225°) = -35.4 mi/hr

y-component: 50mi/hr x sin(225°) = -35.4 mi/hr.

So, the vector is:

W = < -35.4 mi/hr, -35.4 mi/hr>

The sum of the vectors gives the total velocity of the plane in the wind is;

V + W = < 147.7 mi/hr -35.4 mi/hr , -26 mi/hr -35.4 mi/hr >

V + W = <112.3 mi/hr, -61.4 mi/hr>

The direction of a vector is;

θ = Atan(y/x)

Then, in this case the direction of the plane is:

θ = Atan(-61.4 mi/hr/112.3 mi/hr) = -28.7°

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[tex] \frac{2}{3} (x - 4) = 2x \\ \frac{2}{3} x - \frac{8}{3} = 2x \\ \frac{2}{3} x - 2x = \frac{8}{3} \\ \frac{2}{3} x - \frac{6}{3} x = \frac{8}{3} \\ \frac{ - 4}{3} x = \frac{8}{3} \\ - 12x = 24 \\ x = \frac{24}{ - 12} \\ x = - 2[/tex]

The expression g = 2hm can be written as in terms of g and h when m is the subject is m = g/2h.

It is defined as the combination of constants and variables with mathematical operators.

We have an expression:

g  = 2hm

To make m as the subject and solve it:

Divide the above expression by 2h on both sides:

g/2h = m  or

m = g/2h

Thus, the expression g = 2hm can be written as in terms of g and h when m is the subject is m = g/2h.

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Based on the calculations, the solutions of this system of linear inequalities are equal to:

An inequality simply refers to a mathematical relation that's used to compare two (2) or more integers (variables) in an equation based on any of the following:

In order to determine the solutions of this system of linear inequalities, we would find the slope of each line.

For line A, we have:

Slope, m = (11 - 3)/(4 - 0) = 8/4

Slope, m = 2.

Mathematically, the standard equation of a line is given by y = mx + b.

y = 2x + 3

y ≤ 2x + 3.

For line B, the slope is equal to 4. Also, the y-intercept from the graph is equal to 5.

Therefore, the standard equation of a line is given by:

y = 4x + 5

y < 4x + 5

In conclusion, the solutions of this system of linear inequalities are equal to:

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Answer:

A ≈ 9.6 units²

Step-by-step explanation:

the area (A) of the triangle is calculated as

A = product of 2 sides × sin (angle between them ) , that is

A = 3 × 5 × sin40° = 15 × sin40° ≈ 9.6 units² ( to the nearest tenth )

The volume of the right squared pyramid with the given base edges and slant height is 32768 cubic centimeters.

The volume of a square pyramid is expressed as;

V = (1/3)a²h

Where a is the base length and h is the height of the pyramid

Given that;

First, we determine the height of the pyramid using Pythagorean theorem.

c² = a² + b²

(40cm) = (32cm)² + h²

1600cm² = 1024cm² + h²

h² = 1600cm² - 1024cm²

h² = 576cm²

h = √576cm²

h = 24cm

Now, we calculate the volume of the right square pyramid;

V = (1/3)a²h

V = (1/3) × (64cm)² × 24cm

V = (1/3) × 409664cm² × 24cm

V = 32768cm³

Therefore, the volume of the right squared pyramid with the given base edges and slant height is 32768 cubic centimeters.

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If Aleka earns her regular pay or $14 per hour for up to 40 hours of work per week. For each hour over 40 hours of work per week, Aleka earns 14 times her regular pay. Then $728 she earns in a week in which she works 48 hours

Two or more expressions with an equal sign is called as Equation.

Given that Aleka earns her regular pay or $14 per hour for up to 40 hours of work per week.

14x40=560

For each hour over 40 hours of work per week, Aleka earns 14 times her regular pay.

Fourteen plus seven equal to twenty one

14+7=21

Twenty one times of eight is equal to one hundred sixty eight

21x8=168

Now let us add five hundred sixty and one hundred sixty eight

560+168=728

Hence she earns $728 in a week in which she works 48 hours.

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The approximate equation is n = (ln 6)/10 and approximate value is n = 0.179.

In mathematics, an exponential function is a function of form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

Here, given equation; (we are using n in place of t)

          -5.e¹⁰ⁿ = -30

      On dividing -5 both sides, we get

           -5.e¹⁰ⁿ/-5 = -30/-5

                e¹⁰ⁿ  = 6

 Taking 'ln' on both side, we get

             10n = ln 6

              n = (ln 6)/10

              n = 1.791759/10

              n = 0.179

Thus, the approximate equation is n = (ln 6)/10 and approximate value is n = 0.179.

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Answer:

16

Step-by-step explanation:

The range is the distance between the largest number and the smallest number. To find the range, you take the smallest number and subtract it from the largest number. In this case, the smallest number is -9 and the largest number is 7. 7 minus -9 is a double negative, so you can also do 7+9=16. 16 is the range.

then for 5 tablespoons you use 12.5 ounces of milk

Answer:

Improper fraction

Step-by-step explanation:

2×3/5

=6/5 i.e Improper fraction