use the derivative f′(x)=(x−2)(x 1)(x 4) to determine the local maxima and minima of f and the intervals of increase and decrease. sketch a possible graph of f (f is not unique).

Answer:

26.1 to the nearest  tenth.

Step-by-step explanation:

tan 43 = x / 28

x = 28 tan 43

  = 26.1102

The difference between two numbers are [tex]3[/tex] and numbers are [tex]x[/tex] and [tex]y[/tex] so the equation is [tex]x-y=3[/tex]

How to find the equation and what is the equation ?

equation, statement of equality between two expressions consisting of variables and/or numbers. In essence, equations are questions, and the development of mathematics has been driven by attempts to find answers to those questions in a systematic way.

if the difference of two numbers are [tex]3[/tex]

And one number is [tex]x[/tex] and another is [tex]y[/tex]

So we write the equation with operation of subtraction

[tex]x-y=3[/tex]

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The perimeter of the new rectangular piece of glass is 80m.

Here, a rectangular piece of glass has a perimeter of 20 meters.

As we know the perimeter P of a rectangle is given by the formula,

P = 2l+2w...(1)

Therefore,

20 = 2l + 2w

20 = 2(l + w)

20/2 = l + w

10 = l + w ....(2)

Now, both the length and width of the rectangle are multiplied by 4,

That is,

The new length of the rectangle is, l = 4l

The new width of the rectangle is, w = 4w

Therefore by substituting this in the equation(1) we get,

P = 2(4l) + 2(4w)

P = 8l + 8w

P = 8(l+w)....(3)

Substitute equation (2) in (3),

That is,

P = 8*10

P = 80m

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The number the teacher gave Ross is 5127

From the question, we are to determine the number that the teacher gave Ross

From the given information,

Mr. David gave Ross a number and asked him to divide it by 15.

Let the number be x

That is,

x/15

The quotient and remainder obtained by ross are 341 and 12 respectively

That is,

x/15 = 341 + 12/15

Now, we will solve the equation for x

x/15 = 341 + 12/15

Multiply through by 15

x = 15×341 + 12

x = 5115 + 12

x = 5127

Hence, the number the teacher gave Ross is 5127

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Using proportions, it is found that there are 5 cups of milk in each bowl of chocolate pudding.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The cafeteria used 10 quarts for 8 bowls, hence the number of quarts per bowl is:

10/8 = 1.25

Each quart has 4 cups, hence the number of cups is:

4 x 1.25 = 5 cups.

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The values of x is 1 and 6.

According to the statement

we have two tangents which are represented by x+5 and x+1 then

we have to find the value of x to get the perfect value of tangent

so, due to interior values of tangent they are equal to each other but in opposite sign.

But here we have to find the value of x one by one.

It means

Here we take interior value of tangent and exterior value of tangent equal to each other

So, the equations become are written below

X+5= 6 then x = 1

X+1= 7 then x = 6

So, The values of x is 1 and 6.

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Answer:

     2√2

Step-by-step explanation:

We can find the relationship of interest by solving the given equation for A, the mean distance.

  [tex]T^3=A^2\\\\A=\sqrt{T^3}=T\sqrt{T}\qquad\text{take the square root}[/tex]

The mean distance of planet X is found in terms of its period to be ...

  [tex]D_x=T_x\sqrt{T_x}[/tex]

The mean distance of planet Y can be found using the given relation ...

  [tex]T_y=2T_x\\\\D_y=T_y\sqrt{T_y}=2T_x\sqrt{2T_x}=(2\sqrt{2})T_x\sqrt{T_x}\\\\D_y=2\sqrt{2}\cdot D_x[/tex]

The mean distance of planet Y is increased from that of planet X by the factor ...

  2√2

Answer:

D.  d = √(V/5)

E.  A = √(b/c).

Step-by-step explanation:

V = 5d^2

Divide both sides by 5:

V/5 = d^2

Now take the square root of both sides:

d = √(V/5)

Note - it's the square root of the whole term (V/5).

b = cA^2

A^2 = b/c

A = √(b/c).

The value of N is 28.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.

According to the question,

a+b+c=60

a-7=N

b+7=N

7c=N

From the above three equations,

a=N+7

b=N-7

c=N/7

So, N+7+N-7+N/7=60

2N+N/7=60

14N+N=420

15N=420

N=28

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Answer:

sin a = -3/5

Step-by-step explanation:

sin^2(a)+cos^2(a)=1

sin^2(a)+ (4/5)^2 = 1

sin^2(a) = 1 - 16/25 = 9/25

sin a = 3/5 ( in Quadrant 1)

In quadrat IV the sine is negative

so sin a = -3/5

The researcher is using a within-subjects factorial design.

According to statement

A researcher conducts an experiment to determine whether the type of car and color of the car impact how fast people drive.

This can be done by within-subjects factorial design.

In a within-subjects factorial design, all of the independent variables are manipulated within subjects. This would mean that each participant was tested in all conditions.

Another common example of a within-subjects design is medical testing.

So, The researcher is using a within-subjects factorial design.

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The design of the experiment above will center around:

The aim of this study is to know  and compare student's level of satisfaction with school cafeteria food services so as to improve the quality of food served at school meal service.

Hence The design of the experiment above will center around:

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Answer:

3, 7, 14

Step-by-step explanation:

small brain

Answer:

Hector makes a tent shaped like a rectangular pyramid the volume is 56 cubic feet and the area is 24 square feet how tall is the tent

Step-by-step explanation:

17.49 is the magnitude of the resultant vector. This can be obtained by adding the vectors and finding magnitude.

Resultant vector: vector that gives the combined effect of all the vectors. When we add two or more vectors, the outcome is the resultant vector.

For example,

(3,4) + (5,7) = (3+5,4+7) = (8,11)

(8,11) is the resultant vector of vector (3,4) and vector (5,7)

Magnitude of a vector: the length of the vector. The magnitude of the vector a is denoted as ∥a∥.

Magnitude of a = (a₁, a₂)

∥a∥=[tex]\sqrt{a_{1}^{2} +a_{2}^{2} }[/tex]

In the given question,

v (8,10) and w (7, -1)

Adding the vectors,

resultant vector = (8,10) + (7, -1) = (15, 9)

Magnitude of a vector (a,b) = √a²+b²

Here, magnitude = √15²+9² = √225+81 = √306 ≈ 17.49

Hence 17.49 is the magnitude of the resultant vector.

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Answer:

[tex]x=6[/tex]

Step-by-step explanation:

Given equation:

[tex]x-\left(2x-\dfrac{3x-4}{7}\right)=\dfrac{4x-27}{3}-3[/tex]

Expand the left side:

[tex]\implies x-2x+\dfrac{3x-4}{7}=\dfrac{4x-27}{3}-3[/tex]

Let all terms on the left side have the same denominator of 7:

[tex]\implies \dfrac{7x}{7}-\dfrac{14x}{7}+\dfrac{3x-4}{7}=\dfrac{4x-27}{3}-3[/tex]

Join the terms on the left side:

[tex]\implies \dfrac{7x-14x+3x-4}{7}=\dfrac{4x-27}{3}-3[/tex]

[tex]\implies \dfrac{-4x-4}{7}=\dfrac{4x-27}{3}-3[/tex]

Let all the terms on the right side have the same denominator of 3:

[tex]\implies \dfrac{-4x-4}{7}=\dfrac{4x-27}{3}-\dfrac{9}{3}[/tex]

Join the terms on the right side:

[tex]\implies \dfrac{-4x-4}{7}=\dfrac{4x-27-9}{3}[/tex]

[tex]\implies \dfrac{-4x-4}{7}=\dfrac{4x-36}{3}[/tex]

Cross multiply:

[tex]\implies 3(-4x-4)=7(4x-36)[/tex]

Expand:

[tex]\implies -12x-12=28x-252[/tex]

Add 12x to both sides:

[tex]\implies -12=40x-252[/tex]

Add 252 to both sides:

[tex]\implies 240=40x[/tex]

Divide both sides by 40:

[tex]\implies 6=x[/tex]

[tex]\implies x=6[/tex]

The vertex form of the function is f(x) = -2(x-4)^2 + 2

The standard vertex form of a function is expressed according to the expression;

f(x) = a(x-h)^2+k

where

a is a constant = -2

(h, k) is the vertex = (4, 2)

Substitute

f(x) = -2(x-4))^2+2

f(x) = -2(x-4)^2 + 2

Hence the vertex form of the function is f(x) = -2(x-4)^2 + 2

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The length and the width of the rectangle are 10 inches and 6 inches respectively.

In the question, we are given that the length of a rectangle exceeds its width by 4 inches, and the area is 60 square inches.

We are asked for the length and the width of the rectangle.

We assume the width (w) of the rectangle to be x inches.

Its length (l), exceeds its width (w) by 4 inches.

Thus, its length (l) = x + 4 inches.

Now, the area can be calculated using the formula, A = l*w, where A is its area, l is its length, and w is its width.

Thus, the area = (x + 4)x = x² + 4x.

But, we are given that the area is 60 square inches.

Putting the value, we get a quadratic equation:

x² + 4x = 60.

or, x² + 4x - 60 = 0,

or, x² + 10x - 6x - 60 = 0,

or, x(x + 10) - 6(x + 10) = 0,

or, (x - 6)(x + 10) = 0.

By the zero-product rule, we get:

Either, x - 6 = 0, or, x = 6,

or, x + 10 = 0, or, x = -10, but this is not possible as the width of a rectangle cannot be negative.

Thus, the width = x = 6 inches.

The length = x + 4 = 10 inches.

Thus, the length and the width of the rectangle are 10 inches and 6 inches respectively.

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Step-by-step explanation:

Since there is 2 unknown variable ,

so we need 2 equation to find their values.

Answer:

z = 5

Step-by-step explanation:

To solve for z, means to get z all by itself on one side of the equation. In your equation z has had two things done to it. First, z has been times by 4, then 10 is subtracted. So, you "un-do" that in reverse order.

FIRST, add 10. To reverse or "un-do" subtracting.

4z - 10 = 10

4z -10+10 = 10+10

4z = 20

Then, divide by 4 to reverse the multiplying.

4z/4 = 20/4

z = 5

see image.

Also, you can check you answer.

put in 5 in place of z and be sure that you get a true statement.

4(5) - 10 = 10

20 - 10 = 10

10 = 10 Checked!

Answer:

[tex]z=5[/tex]

Step-by-step explanation:

First, substitute in 5 for z: [tex]4(5) -10=10[/tex]

Since [tex]4*5=20[/tex], we can now simplify the equation to [tex]20-10=10[/tex].

Now, check the equation to make sure that the value of z is correct. Do this by subtracting [tex]20-10[/tex] to see if it results in a solution of 10.

Since the equation [tex]20-10=10[/tex] is equal/true, we can conclude that [tex]z=5[/tex].

The volume of the oblique prism is 16261 cubic units

The given parameters are:

Height = 23

Base area = 707

The volume is calculated as:

V = base area * height

So, we have:

V = 707 * 23

Evaluate

V = 16261

Hence, the volume of the oblique prism is 16261 cubic units

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The variation given in the first question is not a direct variation and there is no constant of variation.

y = k × x

when

y = -40 and x = -0.5

y = k × x

-40 = k × -0.5

-40 = -0.5k

k = -40/-0.5

k = 80

When y = 8 and x = 2.5

y = k × x

8 = k × 2.5

8 = 2.5k

k = 8 / 2.5

k = 3.2

When y = 4 and x = -3

y = k × x

4 = k × -3

4 = -3k

k = -4/3

when y = 8 and x = -6

y = k × x

8 = k × -6

8 = -6k

k = 8/-6

k = -4/3

This is a direct variation and the constant of proportionality is -4/3

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Answer:

A. x=5 is a solution, but x=3 is not

Step-by-step explanation:

When x=5, 11-5<7, 6<7, this is a solution

When x=3, 11-3<3l, 8<7, this is not a solution

The standard deviation is approximately 3.84

Step 1: Find the mean
Find the sum of the values, and divide by number of terms.
Mean (average) = (36+32+38+28)/4 = 134/4 = 33.5

We must use Standard Deviation formula which is attached as an image below.

X is the mean here, so lets plug in 33.5

Step 2. Distance from the mean squared |x-mean∣²

For each data point, we will plug in the numbers.
|36-33.5|²=2.5²=6.25

|32-33.5|²=1.5²=2.25

|38-33.5|²=4.5²=20.25

|28-33.5|²=5.5²=30.25
Step 3: Find the sum (∑)
We find the sum here by adding all the distances from the mean squared
∑|x-mean|²=59

Step 4: Divide the sum by the amount of points, 4
59/4=14.75
Step 5: Take the square root of step 4
[tex]\sqrt{14.75}[/tex] is about 3.84

The standard deviation is approximately 3.84

Answer:

[tex]\dfrac{991}{40\sqrt{2}}[/tex]

Step-by-step explanation:

Given expression:

[tex]\sqrt{72}-\dfrac{48}{\sqrt{50}}-\dfrac{45}{\sqrt{128}}+2\sqrt{98}[/tex]

Rewrite 72 as 36·2, 50 as 25·2, 128 as 64·2 and 98 as 49·2:

[tex]\implies \sqrt{36 \cdot 2}-\dfrac{48}{\sqrt{25 \cdot 2}}-\dfrac{45}{\sqrt{64 \cdot 2}}+2\sqrt{49 \cdot 2}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]

[tex]\implies \sqrt{36}\sqrt{2}-\dfrac{48}{\sqrt{25}\sqrt{2}}-\dfrac{45}{\sqrt{64}\sqrt{ 2}}+2\sqrt{49}\sqrt{2}[/tex]

Rewrite 36 as 6², 25 as 5², 64 as 8² and 49 as 7²:

[tex]\implies \sqrt{6^2}\sqrt{2}-\dfrac{48}{\sqrt{5^2}\sqrt{2}}-\dfrac{45}{\sqrt{8^2}\sqrt{ 2}}+2\sqrt{7^2}\sqrt{2}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0[/tex]

[tex]\implies 6\sqrt{2}-\dfrac{48}{5\sqrt{2}}-\dfrac{45}{8\sqrt{ 2}}+2\cdot 7\sqrt{2}[/tex]

Simplify:

[tex]\implies 6\sqrt{2}-\dfrac{48}{5\sqrt{2}}-\dfrac{45}{8\sqrt{ 2}}+14\sqrt{2}[/tex]

Combine like terms:

[tex]\implies 20\sqrt{2}-\dfrac{48}{5\sqrt{2}}-\dfrac{45}{8\sqrt{ 2}}[/tex]

Make the denominators of the two fractions the same:

[tex]\implies 20\sqrt{2}-\dfrac{384}{40\sqrt{2}}-\dfrac{225}{40\sqrt{ 2}}[/tex]

Rewrite 20√2 as a fraction with denominator 40√2:

[tex]\implies 20\sqrt{2}\cdot\dfrac{40\sqrt{2}}{40\sqrt{2}}-\dfrac{384}{40\sqrt{2}}-\dfrac{225}{40\sqrt{ 2}}[/tex]

[tex]\implies \dfrac{1600}{40\sqrt{2}}-\dfrac{384}{40\sqrt{2}}-\dfrac{225}{40\sqrt{ 2}}[/tex]

Combine fractions:

[tex]\implies \dfrac{991}{40\sqrt{2}}[/tex]

The average speed is 50 meters per second

The given parameters are:

Laps = 4

Time = 2 minutes

1 lap = 25 meters

Start by calculating the total distance

Distance = Laps * Meters

Distance = 4 * 25 meters

Distance = 100 meters

The average speed is then calculated as:

Speed = Distance/Time

This gives

Speed = 100 meters/2 minutes

Evaluate

Speed = 50 meters per second

Hence, the average speed is 50 meters per second

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If the base angles of a trapezoid are congruent, the diagonals are congruent.

A trapezium is a quadrilateral and the sum of the interior angles is 360 degrees. Therefore, the properties of a trapezium includes the following:

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[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{14+10y\geq 3(y+14) } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{Simplify \ both \ sides \ of \ the \ inequality. }} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{Subtract \ 3y \ from \ both \ sides. }} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{ Subtract \ 14 \ from \ both \ sides. }} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{Divide \ both \ sides \ by \ 7. }} \end{gathered}$}[/tex]

The total mass of Adrian and Chang at birth is 7.41 kilograms

Total mass of the babies = Adrian weight + Chang weight

= 2.87 kilograms + 4.54 kilograms

= 7.41 kilograms

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