what's the constant of proportionality/unit rate.​

Answer:

1)  Given

2)  Given

3)  Segment Addition Postulate

4)  Segment Addition Postulate

5)  Substitution Property of Equality

6)  Transitive Property of Equality

7)  Definition of congruent segments

Step-by-step explanation:

If a line segment has two endpoints, A and C, and a third point B lies somewhere on the line segment AC, the distance from A to B plus the distance from B to C is equal to the distance from A to C:

If two expressions are equal to each other, then we can replace one of them with the other in any equation or expression, and the equality will still hold true

If a = b and b = c, then a = c.

Statements               Reasons                                        

1)   AB ≅ DE               1)  Given

2)  BC ≅ EF               2)  Given

3)  AB + BC = AC      3)  Segment Addition Postulate

4)  DE + EF = DF       4)  Segment Addition Postulate

5)  AB + BC = DF      5)  Substitution Property of Equality

6)  AC = DF               6)  Transitive Property of Equality

7)  AC ≅ DF              7)  Definition of congruent segments

The value of each limit functions are:

Let's try to solve each problem we have:

1. [tex]\lim_{x \to \--3} 2x^2+4x+1[/tex]

= 2(-3)² + 4(-3) +1

= 2(9) + 4(-3) + 1

= 18 - 12 + 1

= 7

2. [tex]\lim_{x \to \-3} \sqrt{x+1}[/tex]

= √(3+1)

=√4 = 2

3. [tex]\lim_{x \to \-3} \frac{\sqrt{x+2} }{x-4}[/tex]

= √(3+2) / (3-4)

= √5 / (-1) = - √5

4. [tex]\lim_{x \to \-2} \frac{x^3-8}{x-2}[/tex]  -->hint: use L'hospital rule

= [tex]\frac{(x^3-8)'}{(x-2)'}[/tex]

= 3x² / 1

= 3(2)²

= 12

5. [tex]\lim_{x \to \--1} \frac{2x^2-x-3}{x+1}[/tex]

= [tex]\lim_{x \to \--1} \frac{(2x-3)(x+1)}{(x+1)}[/tex]

= 2(-1) - 3

= -5

6. [tex]\lim_{x\to \-3} \frac{\sqrt{x+1}-2 }{x-3}[/tex]

= [tex]\frac{(\sqrt{x+1}-2)' }{(x-3)'}[/tex]

= 1/2√(x+1)

= 1/2√(3+1)

= 1/4

7.[tex]\lim_{x \to \-0} \frac{sin x}{5x}[/tex]

= [tex]\lim_{x \to \-0} \frac{sin x}{x} .\frac{1}{5}[/tex]

= 1/5 ([tex]\lim_{x \to \-0} \frac{sin x}{x}[/tex])

= 1/5 (1)

= 1/5

8. [tex]\lim_{x \to \pi/2}\frac{cosx}{cotx}[/tex]

= [tex]\lim_{x \to \pi/2}\frac{cosx}{\frac{cosx}{sinx} }[/tex]

= [tex]\lim_{x \to \pi/2}{cosx}.\frac{sinx}{cosx}[/tex]

= [tex]\lim_{x \to \pi/2}\ sinx[/tex]

= sin (π/2)

= 1

9. [tex]\lim_{h \to \-0} \frac{f(x+h)-f(x)}{h}[/tex] = f'(x)

a. f(x) = 3x - 2

    f'(x) = 3

b. f(x) = √x

   f'(x) = 1/2√x

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Answer:

4658

Step-by-step explanation:

According to the problem the indicated measures are given below:

∠QRS = [tex]90^{0}[/tex], ∠QTR = [tex]42^{0}[/tex], TR=16, QU=8

Measures are actions taken to achieve a desired result. They are the means used to improve, control, or solve a problem. Measures can be taken in any area, such as economics, finance, health, safety, environment, productivity, quality, customer service, etc.

In the given figure:

m∠TRS = [tex]42^{0}[/tex] and QS = 16

Seeing the figure we know that:

∠QRT +∠TRS = [tex]90^{0}[/tex]

∴∠QRT= [tex]90^{0} - 42^{0} = 48^{0}[/tex]

∠QRT+∠QTR+∠TQR = [tex]180^{0}[/tex] as it is a right angled triangle.

∴∠QTR = [tex]180^{0} - 90^{0} -48^{0} = 42^{0}[/tex]

∠QRS = [tex]90^{0}[/tex] as it is a right angled triangle.

TR = QS as diagonals bisect each other.

∴TR=16

QU=1/2QS=16/2=8

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The expected value of the rate of return is 23.5%

It is a branch of mathematics that deals with the occurrence of a random event.

Given is a table which gives the probability distribution of the annual rate of return on the stock of MNP Company, Inc. We have to find out  the expected value of the rate of return

Let X be the return and p probability

Then

X     15%     20%    30%     35%  Total

p     0.2       0.4     0.3       0.1        1

x(p)  3           8        9          3.5     23.5

Hence Expected rate of return

E(x)= 23.5%

Hence, the expected value of the rate of return is 23.5%

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Based on the student's work, the equation was solved incorrectly. B. The equation solved correctly would show that it has one solution(s).

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For instance, 2x - 5 = 13. Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign.

In correct solution of the equation is given as:

4(2 - 3x) = x - 2(2x + 1)

8 - 12x = x - 4x - 2

8 - 12x = -3x - 2

8 + 2 = 12x - 3x

10 = 9x

x = 10/9

Hence, based on the student's work, the equation was solved incorrectly.

The equation solved correctly would show that it has one solution(s).

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Answer:

See below for truth tables and proofs

Step-by-step explanation:

Let's understand what a tautology is and what a contradiction is

statement which is always true is called a tautology. A statement which
is always false is called a contradiction.

A proposition p ⇒ q has a hypothesis p and a conclusion q

p ⇒ q is False

a) p  ⇒ q is False if p is True and q is False. It is True for all other values of p and q

The truth table for p ⇒ q therefore is::

p q (p ⇒ q)

F F T

F T T

T F F

T T T

We have to prove that p AND q ⇒ p is a tautology for all p, q i.e. it is True no matter what the values of p and q are

p AND  q ⇒ p can be re-written as (p AND q) ⇒ p since the AND operator has precedence over the implies operator

Here is the truth table for (p ∧ q) ⇒ p.
(∧ is the symbol for logical AND)

Here the hypothesis is (p ∧ q)  and the conclusion is p.

It is False if and only if the hypothesis  (p ∧ q) is T and p is False. That combination never occurs in the truth table

p q   p ∧ q      (p ∧ q)  ⇒ p  
------------------------------------------------------
T T      T                 T                      

T F      F       T  

F T      F   T  

F F      F   T

Since the expression  (p ∧ q)  ⇒ p  is True for all values of p and q it is a tautology

b)

Truth Table for (p ∨ ¬p) where ¬p represents not p or p'

p ¬p       (p ∧ ¬p)
---------------------------
F   T            F

T   F            F

Since the expression is False for any p value, it is a contradiction

For a nonempty set of real numbers, A it is proved that inf A = -sup(-A)

Let A be a nonempty set of real numbers that is bounded below

suppose inf A = K

claim:- -sup (-A) = K where -A is the set of all numbers -x show that [tex]$ x \in A$[/tex]

To show that sec (-A) = -K

First, we show that -k is the upper bound of - A

Let [tex]$-x \in-A$[/tex] be any element [tex]$\Rightarrow x \in A \ldots$[/tex] (by definition of -A ).

But inf A = K

K is the lower bound of A

[tex]& \Rightarrow \quad k \leq x \quad \forall x \in A \\[/tex]

Multiply by -1

[tex]& \Rightarrow-k \geqslant-x \quad \forall x \in A \\[/tex]

[tex]& \Rightarrow-k \geqslant-x \quad \forall-x \in-A[/tex]

Therefore -K is the upper bound of -A

suppose l is another upper bound of -A.

[tex]-x \leqslant l & \forall-x \in-A \\[/tex]

Multiply by -1

[tex]x \geqslant-l && \quad $\forall \quad x \in A \\[/tex]

[tex]\Rightarrow-k \geqslant-x \quad & \forall-x \in-A[/tex]

Therefore -k is the upper bound of -A.

Suppose l is another upper bound of -A.

[tex]\Rightarrow-x \leq l \quad \forall-x \in-A[/tex]

Multiply by -1

[tex]$\Rightarrow \quad x \geqslant-1 \quad \forall x \in A$[/tex]

-l is the lower bound of A

But k is the greatest lower bound of A

[tex]-l \leq k$[/tex]

Multiply by -1

[tex]$-l \geqslant-k$[/tex].

-K is the least upper bound of A.

sup (-A) = -k

-sup (-A) = k

inf (A) = -sup (-A)

Hence proved.

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This formula is used to get the values of the sine and cosine products for angle A and to solve different trigonometry issues.

SinA cosA = sin2A / 2 is the formula for sinA and cosA. This formula is used to get the values of the sine and cosine products for angle A and to solve different trigonometry issues.

Let LHS =

[tex]\frac{tan A}{1+ tan^{2} A} + \frac{cot A}{1+ cot^{2} A}[/tex]

= [tex]\frac{tan A}{(sec^{2}A) ^{2} } +\frac{cot A}{(cosec^{2}A) ^{2} }[/tex]

= [tex]\frac{\frac{sin A}{cos A} }{\frac{1}{cos^{4}A } } + \frac{\frac{cos A}{sin A} }{\frac{1}{sin^{4}A } }[/tex]

= [tex]sin A cos^{3} A + cos A sin^{3}A[/tex]

= [tex]sin A cos A (sin^{2}A + cos^{2}A)[/tex]

= [tex]sin A cos A[/tex] = R.H.S

Hence proved  as L.H.S= R.H.S

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The complete question is:

Prove that (tan A)/((1 + tan2 A) 2) + (cot A)/((1 + cot2 A) 2) for cotA  = sinA cosA.

Answer:16

Step-by-step explanation:

the height of fall of the bungee jumper is 9216 feet.

What is Distance?

a velocity is a unit of measurement for the Distance an object travels in a predetermined period of time. Here is a word equation that illustrates the connection between space, speed, and time: velocity is calculated by dividing the total Distance traveled by the journey time.

Diane and Douglas both drive at an average rate of 50 miles per hour. So if they travel for the same time they will end up covering the same Distance as well.

As we know velocity = rate of change of displacement

The distance the bungee jumper falls is estimated as follows when the time of motion is 6 seconds;

6 = [tex]\frac{\sqrt{d} }{16}[/tex]

√d = 16*6

√d = 96

d = 9216

Hence the height of fall of the bungee jumper is 9216feet.

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Number of track practices it would take roger to run 20 miles are 10 track practices.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

Given;

Roger ran a total of 6 miles over the course of 3 track practices

3track practices= 6miles

1mile= 1/2 track practices

20miles= 1/2*20

=10 track practices

Therefore, the answer by unitary method will be 10.

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Step-by-step explanation:

collect like terms

Answer:

A) 6centimeters (cm) LONG

B) 6 gallons/Liters of water

C) 32 milligrams

Step-by-step explanation: contact me through discord Acathia#0103, its easier to help, I can help with multiple questions aswell or send me ur SC

Answer:

1.339 Canisters

Step-by-step explanation:

Because you are making 5 meatloafs for a party, and according to the recipe you need 1 1/4 cup of breadcrumbs per each meatloaf. In each canister there is 14/3 cups of breadcrumbs which you can see by multiplying the serving size by the servings per container.

Since you need five meatloafs, you can figure out how many cups of breadcrumbs you need by multiplying 1 1/4 cups by 5. This gives you 6 1/4 or 6.25 cups.

In each canister of breadcrumbs, there are 14/3 cups or 4.667 cups of breadcrumbs.

To figure out how many canisters you need, you divide the amount of breadcrumbs you need (6.25 cups) by the amount of breadcrumbs you have (4.667) which gives you 1.339 canisters.

The polynomial y = x⁶ + 7 · x⁴ - 17 · x² + 9 has two real zeros: x = 1, x = - 1. The polynomial diverges to + ∞ when x → ± ∞.

Sextic equations are polynomials of grade six, whose form is described below:

y = a · x⁶ + b · x⁵ + c · x⁴ + d · x³ + e · x² + f · x + g

Where a, b, c, d, e, f, g are real coefficients.

According to Bolzano's theorem, given a function f(x) defined for interval [a, b], there is at least a value of x such that f(x) = 0. For polynomials with integer coefficients, zeros may be divisors of grade zero coefficient. Then, the possible candidates for zeros of the sextic equation:

Possible roots = - 9, + 9, - 3, + 3, - 1, + 1

Now we proceed to check possible roots:

x = - 9

y = (- 9)⁶ + 7 · (- 9)⁴ - 17 · (- 9)² + 9

y = 576000

x = 9

y = 9⁶ + 7 · 9⁴ - 17 · 9² + 9

y = 576000

x = - 3

y = (- 3)⁶ + 7 · (- 3)⁴ - 17 · (- 3)² + 9

y = 1152

x = 3

y = 3⁶ + 7 · 3⁴ - 17 · 3² + 9

y = 1152

x = - 1

y = (- 1)⁶ + 7 · (- 1)⁴ - 17 · (- 1)² + 9

y = 0

x = 1

y = 1⁶ + 7 · 1⁴ - 17 · 1² + 1

y = 0

The end behavior of polynomial is defined by sign of lead coefficient, that is, the real coefficient of the highest exponent of the polynomial. In addition, polynomials does not converge at any value for x → ± ∞.

According to given information, the lead coefficient of polynomial y = x⁶ + 7 · x⁴ - 17 · x² + 9 diverges to + ∞ when x → ± ∞, since grade of polynomial is an even number.

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The number of calories that you would consume if you eat 3 mini-muffins is 41.66.

To know the number of calories per muffin, let's divide the total of calories (250) by the number of muffins.

Regular muffins: 250 / 12 = 20.83 calories

Mini-muffins: 250 / 18 = 13.88 calories.

This shows that one mini-muffin contains 13.88 calories, while the original recipe contains 20.83 calories per muffin.

13.88 calories x 3 = 41.66 calories

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The uncertainty of the total distance is 0.2 cm.

As per the given data, the distance between the diffraction slit and the screen on which the pattern forms,

[tex]x_{1}[/tex] = (15.8 ± 0.2) cm

[tex]x_{2}[/tex] = (6.7 ± 0.1) cm

[tex]x_{3}[/tex] = (11.3 ± 0.1) cm

Let, the uncertainty in the measurements,

[tex]x_{1}[/tex], [tex]x_{2}[/tex] and [tex]x_{3}[/tex]  is [tex]e_{1}[/tex], [tex]e_{2}[/tex] and [tex]e_{3}[/tex] respectively.

So,

[tex]e_{1}[/tex] = 0.2 cm

[tex]e_{2}[/tex] = 0.1 cm

[tex]e_{3}[/tex] = 0.1 cm

Again, let the uncertainty in the total distance

[tex]\mathrm{x} =\mathrm{x}_1+\mathrm{x}_2+\mathrm{x}_3[/tex] is e(error propagation).

The impact of a variable's uncertainty on the uncertainty of a function depending on it is known as propagation of uncertainty. When the variables are experimental measurement values, measurement limits cause uncertainties that are propagated via the function's combination of variables.

Then the error propagation is given as,

e = [tex]\sqrt{\mathrm{e}_1^2+\mathrm{e}_2^2+\mathrm{e}_3^2} \\[/tex]

So, e = [tex]\sqrt{(0.2)^2+(0.1)^2+(0.1)^2} \\[/tex]

Therefore e = [tex]\sqrt{0.06} \\[/tex]

e = 0.245 cm

e ≅ 0.2 cm

Therefore uncertainty of the total distance 0.2 cm

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The events described are known as a compound probability experiment.

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Experience shows that few students hand in their statistics exams early and most prefer to hand them in near the end of the test period. This means that the time taken by students to write exams is positively skewed.

In statistics, a positively skewed (or right-skewed) distribution is a type of distribution in which most values are clustered around the left tail of the distribution while the right tail of the distribution is longer. The positively skewed distribution is the exact opposite of the negatively skewed distribution.

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Answer:

To find the y-intercept, set x = 0 and solve for y:

13 * 0 - 21 * y = 7

-21 * y = 7

y = -7/21

y = -1/3

So the y-intercept is at (0, -1/3).

Answer: -1/3

Step-by-step explanation:

13x-21y=7

y=13x/21-1/3

y=-1/3

Answer: 44

Step-by-step explanation:

The interior and exterior in these type of problems equal 180. 180 – 136 = 44

The average velocity for the time period beginning when t=3 and lasting for

1) 0.01 s: -9051.12 ft/sec

2) 0.005 s: -18051.06 ft/sec

3) 0.002 s: -45051.1 ft/sec

4) 0.001 s: -90051  ft/sec

Here, a ball is thrown with initial velocity of 46 ft/s.

The height of the ball in feet after t seconds is given by an equation,

 y = 21t - 12t²

Let us assume that P represents the average velocity.

The average velocity is given by formula,

P = [y(t₂) - y(t₁)]/[t₂ - t₁]

i) the average velocity for the time period beginning when t=3 and lasting  0.01 s

Here, t₂ = 3.01 s and  t₁ = 3 s

y(t₂) =  21(3.01) - 12(3.01)²

      = -45.5112

y(t₁) =  21(3) - 12(3)²

      = 45

y(t₂) - y(t₁) = -45.5112 - 45

                = -90.5112

So, P = -90.5112 / (0.01)

     P = -9051.12 ft/sec

ii) the average velocity for the time period beginning when t=3 and lasting  0.005 s

Here, t₂ = 3.005 s and  t₁ = 3 s

y(t₂) - y(t₁) = -45.5112 - 45

                = -90.2553

So, P = -90.2553 / (0.005)

     P = -18051.06 ft/sec

iii) the average velocity for the time period beginning when t=3 and lasting  0.002 s

Here, t₂ = 3.002 s and  t₁ = 3 s

y(t₂) - y(t₁) = -45.1021 - 45

                = -90.1021

So, P = -90.1021 / (0.002)

     P = -45051.1 ft/sec

iv) the average velocity for the time period beginning when t=3 and lasting  0.001 s

Here, t₂ = 3.001 s and  t₁ = 3 s

y(t₂) - y(t₁) = -45.051 - 45

                = -90.051

So, P = -90.051 / (0.001)

     P = -90051 ft/sec

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The complete question is:

A ball is thrown into the air by a baby alien on a planet in the system of Alpha Centauri with a velocity of 46 ft/s. Its height in feet after t seconds is given by   y = 21t - 12t² .  A. Find the average velocity for the time period beginning when t=3 and lasting  .01 s:     .005 s:      .002 s:   .001 s:      NOTE: For the above answers, you may have to enter 6 or 7 significant digits if you are using a calculator.  Estimate the instanteneous velocity when t=3.  

The speed of the faster cyclist is 3 miles per hour.

We can use the information given to set up the following equation:

r + (2r) = (r + 2r) / 2t

Where r is the speed of the slower cyclist, (2*r) is the speed of the faster cyclist, t is the time in hours, and the distance between the two cyclists is (r + 2r) miles.

We can use the given information that the two cyclists meet 2 hours later to solve for r:

r + (2r) = 30 / 22

Simplifying the equation we get:

r + (2*r) = 15

3r = 15

r = 5

We know that the faster cyclist is going 2 times faster than the slower cyclist, so we can use the value of r to find the speed of the faster cyclist:

2r = 25 = 10

So, the speed of the faster cyclist is 10 miles per hour.

Pythagorean Theorem states that the area of the blue square + the area of the red square = the area of the purple square.

Consider the triangle

Where “a” is the perpendicular,

“b” is the base,

“c” is the hypotenuse.

According to the definition, the Pythagoras Theorem formula is given as:

Hypotenuse² = Perpendicular² + Base²

c² = a² + b²

The side opposite to the right angle (90°)  is the longest side (known as Hypotenuse) because the side opposite to the greatest angle is the longest.

Pythagoras theorem states that “In a right-angled triangle,  the square of the hypotenuse side is equal to the sum of squares of the other two sides“.

Hence, Pythagorean Theorem states that the area of the blue square + the area of the red square = the area of the purple square.

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The area of hubcap in shape of circle is 121π cm^2.

What is a circle?

A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident. A circle is also termed as the locus of the points drawn at an equidistant from the center. The distance from the center of the circle to the outer line is its radius. Diameter is the line which divides the circle into two equal parts and is also equal to twice of the radius.

The equation of circle in the plane is given as:

(x-h)^2 + (y-k)^2 = r^2

where (x, y) are the coordinate points

(h, k) is the coordinate of the center of a circle

and r is the radius of a circle.

and Area of circle = πr²

Circumference of circle=2πr

Now,

As shape of hubcap is circular.

Area of circle = πr^2

where r=D/2  D=diameter

Given diameter of hubcap is 22cm. --> r=11 cm.

Therefore,

                Area=π*11^2=121π cm^2

Hence,

          The area of hubcap in shape of circle is 121π cm^2.

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The number of rolls of paper used per wall will be 1.5 rolls per wall.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Andy is hanging wallpaper in his kitchen. He is to cover 2 2/5 of the walls in the room using 6 rolls of paper. We know that the room has 4 walls.

Then the number of rolls of paper used per wall is given as,

⇒ 6 / 4

⇒ 1.5 rolls per wall

The number of rolls of paper used per wall will be 1.5 rolls per wall.

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Step-by-step explanation:

that's your answer im hoping so