Find the Limit of the following given Function

The if-then statement is:

If angles are vertical angles then their measure is equal.

and converse of the implication is:

If the measure of angles is equal then they are vertical angles.

What is the Converse Statement?

That sort of reversal is called a converse. Definition: The converse of a conditional statement is created when the hypothesis and conclusion are reversed. In Geometry, the conditional statement is referred to as p → q. The Converse is referred to as q → p.

We have given the statement:

Vertical angles are equal in measure.

A). Rewrite the statement as an if-then statement.

If angles are vertical angles then their measure is equal.

B). Write the converse of the implication

If the measure of angles is equal then they are vertical angles.

Hence, the if-then statement is:

If angles are vertical angles then their measure is equal.

and converse of the implication is:

If the measure of angles is equal then they are vertical angles.

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The procedure is correct is  1 + tan²(theta) = sec²(theta)

What is  Fraction?

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.

And

cos²(theta) = 1 - sin²(theta)

Are both valid identities

Keisha and the David.

As per the question Kisha and the David found the same value of the cosine theta as given by the  Sine theta = Negative Start Fraction 8 Over 17 End Fraction. The Keisha solution and the Davis solution for the solution were tan-squared (theta) + 1 = sec-squared (theta).

Thus the answer is both procedures are correct.

As they both wanted to find the solutions to the numerical problems they made two different methods.

Such as the Sine theta = Negative Start Fraction and the tan-squared (theta) + 1 = sec-squared (theta).

Hence both options are the same and true.

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Sandra needs 8 bowls to divide the trail mix equally.

To determine the number of bowls Sandra needs, we need to divide the total weight of the trail mix by the weight of each bowl.

First, we need to convert the weight of the trail mix from pounds to ounces. There are 16 ounces in a pound, so 5.2 pounds is equal to 5.2 x 16 = 83.2 ounces.

Next, we need to convert the weight of each bowl from pounds to ounces. There are 16 ounces in a pound, so 0.65 pounds is equal to 0.65 x 16 = 10.4 ounces.

Now that we have both weights in the same units, we can divide the total weight of the trail mix by the weight of each bowl to find the number of bowls needed.

⇒ 83.2 ounces / 10.4 ounces per bowl

Apply the division operation,

⇒ 8 bowls.

Therefore, she needs 8 bowls to divide the trail mix equally.

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The price of a 10-year $100 par value bond bearing a 10% coupon rate payable semiannually, and redeemable at 105, bought to yield 8% convertible semiannually, is its present value of $115.87.

The price of a bond is its present value.

The present value can be computed by setting the following parameters:

This can be done using an online finance calculator with the results as follows:

N (# of periods) = 20 semiannual periods (10 years x 2)

I/Y (Interest per year) = 8%

PMT (Periodic Payment) = $5 ($100 x 10% x 1/2)

FV (Future Value) = $105

Results:

Present Value (PV) = $115.87

Sum of all periodic payments = $100 ($5 x 20)

Total Interest = $89.13

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Answer: 115.87 (If you don't get this answer then the solution is incorrect.)

Answer:

you cannot

Step-by-step explanation:

you cannot graph something like that, it is not a equation of a line nor a point or if you want to solve it it is x = -10

Answer:

Step-by-step explanation:

given in the question that 5x=-50

     on solving the equation

          we get, x=-10

on the graph on the negative x-axis locate the point x=-10

The product of -2/7 x 7/4 to the simplest form in fraction is -1/2.

In arithmetic, a number expressed as a quotient, in which a numerator is divided by a denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator.

[tex]\frac{-2}{7} x \frac{7}{4}[/tex]

Solving this we multiply the fraction by multiply the numerator by numerator and also Denominator by Denominator  

= [tex]\frac{-14}{28}[/tex]

Simplify further  by dividing the numerator by denominator we have:

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

Therefore, the the product of the fraction to the simplest form is -1/2 and this can also be written in decimal; -0.5

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Answer:

Below

Step-by-step explanation:

1/3 x   = - 2/5      <=====multiply both sides of the equation by 3 to get

x = -6/5   = - 1  1/5

Answer:

[tex] \sqrt{176} [/tex]

[tex] \sqrt{16 + 11} [/tex]

[tex]4 \sqrt{11} [/tex]

Step-by-step explanation:

The answer is

[tex]4 \sqrt{11} [/tex]

We

need to express 176 as the product of its prime factors i.e. 176 = 2 × 2 × 2 × 2 × 11. Therefore, √176 = √2 × 2 × 2 × 2 × 11 = 4 √11 . Thus, the square root of 176 in the lowest radical form is 4 √11.

i hope this helped

Answer: The relationship in quantity, amount, or size between two or more things: proportion.

Answer:B

Step-by-step explanation:

I took the test

If the position of a moving object at a time t the curvature of the earth would be 1/4t.

A curved path having various radii of curvature is known as a variable-curvature path. from: 2020 Control Systems Design of Bio-Robotics and Bio-mechatronics with Advanced Applications.

A straight line has zero curvature. In contrast to the tangent, which is a vector quantity, the curvature at a point is often a scalar quantity or one that can be described by a single real integer.

|| r (t) || = 3[tex]t^{2}[/tex], || r' (t) || = 2t, || T (t) || = 1

|| T' || = 1/2

Curvature K = || T' (t) || / || r' (t)  || = (1/2) / 2t

K = 1/4t

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Answer:

Step-by-step explanation:

w

The degree to turn before walking 673 paces is 59 degrees

From the question, we have the following parameters that can be used in our computation:

Lengths = 989 paces, 673 paces and 861 paces

These paces can be represented as

x = 989

y = 673

z = 861

The measure of the required angle (angle Z) i.e.  the degree to walk can be calculated using the following cosine rule

z² = x² + y² - 2xy * cos(Z)

Substitute the known values in the above equation, so, we have the following representation

861² = 989² + 673² - 2 * 989 * 673 * cos(Z)

Evaluate the exponents, the products and the summation

So, we have the following representation

741321 = 1431050 - 1331194 * cos(Z)

Evaluate the like terms

- 1331194 * cos(Z) = -689729

Divide both sides by  - 1331194

cos(Z) = 0.51812808651

Take the arc-cos of both sides

Z = 58.7

Approximate

Z= 59 degrees

Hence, the measure of the angle is 59 degrees

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66°

Step-by-step explanation:

X=22°

3x= 3*22=66°

to find value of x:

(2x+3)+3x+67=180°

5x+70=180°

x=22°

Answer: She needs to ride 13.9 more kilometers on her bike to finish the race.

Step-by-step explanation:

==> 30 = 3.75 + 12.35 + x

Take 16.1 from both sides:

==> 30 = 16.1 + x

==> 30 = 13.9km

Answer:

Step-by-step explanation:

The answer would be 13.9, if you add 12.35 to 3.75 you get 16.1, then 16.1 added to 13.9 equals 30

Answer:

A

Step-by-step explanation:

as the graphic suggests : reflect (mirror) ABD across the line BD, and CBD is a mirrored but otherwise equal copy of ABD, which also makes angle C equal to angle A.

all the other answer options are creating new triangle that do not map to CBD.

three digit odd numbers are 450.

What is odd number?

Whole numbers that cannot be split perfectly into pairs are referred to be odd numbers. When two is divided by an odd number, one is left over.

Odd numbers 1, 3, 5, 7, 9, 11, 13, etc. are in order.

In the place of the ones, odd numbers have the digits 1, 3, 5, 7 or 9.

9 digits = (1,2,3,4,5,6,7,8,9) are the digits that may be used to fill in any spot.

There are nine different methods to fill the thousand's position, hence the 100 spot cannot be zero.

There are 10 different methods to fill the number ten.

There are 5 different methods to fill the unit location (1,3,5,7,9)

Three-digit odd totals are (9*10*5), which equals 450.

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Answer:

x≤12

Step-by-step explanation:

-3x≥36

÷-3  ÷-3

Answer: 160 inches

Step-by-step explanation:

To put lights around the window, you will need a total of 32 + 48 + 32 + 48 = <<32+48+32+48=160>>160 inches of lights. You will need this much light to go completely around the window.

Answer:

x = - 3

Step-by-step explanation:

2(x - 6) + 2 = 4x - 4 ← distribute parenthesis on left side and simplify

2x - 12 + 2 = 4x - 4

2x - 10 = 4x - 4 ( subtract 4x from both sides )

- 2x - 10 = 4x - 4 ( add 10 to both sides )

- 2x = 6 ( divide both sides by - 2 )

x = - 3

Answer:

SOLUTION

2(X-6)+2=4X-4

open the blanket by multiplication

2x-12+2=4x-4

2x-10=4x-4

collect like term

2x+4x=-4+10

6x=6

divide both side by 6

x=1

The volume of the pentagonal prism as per the given values is obtained as 2.5 cm³.

A pentagonal prism has two pentagonal surfaces on the top and the bottom. It has ten vertices, 15 edges and 7 faces. The number of rectangular surfaces are five.

The expression for the volume of a regular pentagon is given as V =  5/2 × abh

Where h is the height and a and b are the length of the sides.

Now, the value of a, b and h as per the question is given as,

a = b = h = 1.

Then, the volume can be calculated as,

V = 5/2 × 1 ×1 × 1
   = 2.5

Hence, the volume of the regular pentagonal prism  is given as 2.5 cm³.

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By graphing, the solution to the system, y = 5x + 2 and y = x - 2 is: A. (-1, -3)

The solution to a system of equations is the coordinates of an ordered pair that will make both of the equations to be true. This coordinates is determined by graphing.

To do this, plot both lines on a coordinate plane, then determine the coordinates of the point of intersection of both lines.

Given the system of equations,

y = 5x + 2

y = x - 2

The graph that shows both equations are attached below where the red line is y = 5x + 2, and y = x - 2 is the blue line.

The point of intersection is at (-1, -3). Therefore, the solution is:

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(a) Using y the manufacture can find the required diameter of the hole.

(b) The mean of the random variable y is 0.003.

(c) The standard deviation of the y is 0.0063.

(d) It is reasonable to assume that x1 and x2 are independent since peg and hole are made of different wood.

(e)  We can see that mean of y is greater than standard deviation of y, So mostly the peg maybe bigger than hole.

Given that x1 be the peg diameter with mean 0.25 in. and standard deviation 0.0006 in.and x2 be the hole diameter with mean 0.253in. and deviation 0.002 in.

a) y=x2-x1 denote the difference between hole and peg diameter

if y<0 , the peg won’t go inside the hole and

if y>0 ,the peg be loose to the hole

So using y the manufacture can find the required diameter of the hole.

b)Now, we have to find the mean of the random variable y

μ(y) = μ(x2) - μ(x1)

μ(y) = 0.253-0.25

μ(y) = 0.003

c) Now we have to find the standard deviation of the y

σ(y) = √{var(x1)+ var(x2)}(x1 and x2 are independent)

σ(y) = √0.000036+0.000004

σ(y) = √0.00004

σ(y) = 0.0063

d) It is reasonable to assume that x1 and x2 are independent since peg and hole are made of different wood.

e) With a standard deviation larger than the mean , it would be fairly likely to observe a negative value of y, so it would be a relatively common occurrence to find a peg that was too big to fit in the predrilled hole. We can see that mean of y is greater than standard deviation of y, So mostly the peg maybe bigger than hole.

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The correct matching regarding the linear functions are given as follows:

i. A set of points where the coordinates of each point has a sum of 2: Line n.

ii. A set of points where the y-coordinate of each point is 10 less than the x-coordinate: Line m.

b - i) Two numbers with a sum of 2: A and C.

b - ii) Two numbers where the y-coordinate is 10 less than the x-coordinate: D and E.

b - iii) Two numbers with a sum of 2 and where the y-coordinate is 10 less than the x-coordinate: B.

The set of points where the coordinates of each point has a sum of 2 is defined by the following linear function

x + y = 2.

In slope-intercept form, it is of:

y = 2 - x.

Which is the decreasing line n, with an intercept of 2.

A set of points where the y-coordinate of each point is 10 less than the x-coordinate is defined by the following linear function

y = x - 10.

Which is the increasing line m, which an intercept of m.

The coordinates of each point are given as follows:

These points are then used to match the sentences in item b.

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The maximum no. of fish tacos they can order is 8.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

let, The no. of fish taco be 'F'.

Therefore, 2F + 3.75 ≤ 20.  

So, The no. of fish tacos they order is,

2F ≤ 20 - 3.75.

2F ≤ 16.25.

F ≤ 16.25/2.

F ≤ 8.125 Or 8 as the no. of fish tacos must be in integers.

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Answer:

It is a reciprocal function

Step-by-step explanation:

f(x) = x, the reciprocal function is f(x) = 1/x

The total income from the machines over the first 5 years is $185.89

From the question, we have the following parameters that can be used in our computation:

f(t) = 160e0.03t

Where

Rewrite the function properly

so, we have the following representation

f(t) = 160e⁰.⁰³ⁿ

The above function is an exponential function

So: In the first 5 years, we have the value of t to be 5

This is represented as follows

t = 5

Substitute the known values in the above equation, so, we have the following representation

f(5) = 160e⁰.⁰³ ˣ ⁵

Evaluate the product of the exponents

f(5) = 160e⁰.¹⁵

The products above give

f(5) = 185.89

Hence, the total income is $185.89

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The z-scores correspond to the oldest and youngest senators of ages 87 and 44 are 2.57 and -1.17. The z-score corresponding to the oldest senator of age 85 is 2.39.

A Z-score is a metric that quantifies how closely a value relates to the mean of a set of values. The formula to calculate this score [tex]z=\frac{x-\mu}{\sigma}[/tex].  Where z is the z-score, x is the observed value, μ is the sample mean, and σ is the sample standard deviation.

Given μ = 57.5 and σ = 11.5.

When x = 87, the z-score value is,

[tex]\begin{aligned}z&=\frac{87-57.5}{11.5}\\&=2.57\end{aligned}[/tex]

When x = 44, the z-score value is,

[tex]\begin{aligned}z&=\frac{44-57.5}{11.5}\\&=-1.17\end{aligned}[/tex]

When x = 85, the z-score value is,

[tex]\begin{aligned}z&=\frac{85-57.5}{11.5}\\&=2.39\end{aligned}[/tex]

The required answers are 2.57, -1.17, and 2.39.

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