Consider the equation below. − 5 ⁢ n + 31 = − 14 ⁢ n − 5 Select the equation that has the same solution. − 1 − 22 ⁢ n = − 20 ⁢ n − 9 3 − 6 ⁢ n + 3 ⁢ n = − 3 + 4 − 4 ⁢ n 1 = 0.75 ⁢ n + 3.25

[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - b^2}=a \qquad \begin{cases} c=\stackrel{hypotenuse}{12}\\ a=adjacent\\ b=\stackrel{opposite}{9}\\ \end{cases} \\\\\\ \sqrt{12^2 - 9^2}=a\implies \sqrt{144 - 81}=a\implies \sqrt{63}=a[/tex]

Answer:

To determine whether the three points P, Q, and R are colinear, we can calculate the distances between pairs of points using the distance formula:

d(P,Q) = √((-8 - (-7))^2 + (4 - 6)^2 + (-11 - (-8))^2) = √((-1)^2 + (-2)^2 + (-3)^2) = √14

d(Q,R) = √((-9 - (-8))^2 + (3 - 4)^2 + (-14 - (-11))^2) = √((-1)^2 + (-1)^2 + (-3)^2) = √9

d(P,R) = √((-9 - (-7))^2 + (3 - 6)^2 + (-14 - (-8))^2) = √((-2)^2 + (-3)^2 + (-6)^2) = √19

If the three points are collinear, the distance between any two points should be a multiple of the distance between the other two points. Since √14, √9, and √19 are not multiples of each other, it can be concluded that the three points P, Q, and R are not collinear.

The height of the radio tower observed by the person is approximately 554.75 feet.

The tangent function is a mathematical function that maps an angle to its corresponding tangent value. It is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle in a right triangle.

We can use trigonometry to solve this problem. The angle of elevation from the window to the top of the tower is 38°, and the angle of depression from the window to the bottom of the tower is 29°. We can use these angles to form two similar right triangles, one with the tower and the window and one with the height of the tower and the difference between the height of the window and the height of the tower.

Let H be the height of the tower. Then the difference between the height of the window and the height of the tower is H - 300.

Using the tangent function, we can write:

tan(38°) = H / 300

and

tan(29°) = (H - 300) / 300

Solving for H, we find:

H = 300 * tan (38°) = 554.75 feet

So, the height of the tower is approximately 554.75 feet.

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Answer: To solve for t in terms of P, I and r, we'll use algebraic manipulation of the given formula:

I = Prt

To solve for t, we'll divide both sides of the equation by Pr:

I/Pr = t

So, t = I/Pr

So we can say that the time (in years) is the ratio of the interest earned over the product of principal and the interest rate.

Step-by-step explanation:

Answer:

I/Pt

Step-by-step explanation:

bottom one wrong ash

The indicated congruency of the angles ∠BEC and ∠AED (∠BEC ≅ ∠AED) and ∠BEA and ∠CED (∠BEA ≅ ∠CED), according to the alternate interior angles postulate, shows that [tex]\overline{AB}[/tex]║[tex]\overline{CD}[/tex] and  [tex]\overline{BC}[/tex]║[tex]\overline{AC}[/tex] are parallel.

Two segments on a plane are parallel if the distance between the segments remain the same, through the lengths of the segments.

The specified details of the dimensions of the segments in ABCD are;

Segments [tex]\overline{AC}[/tex] bisects segment [tex]\overline{BD}[/tex] and vice versa

Required to prove that [tex]\overline{AB}[/tex] ║ [tex]\overline{CD}[/tex] and [tex]\overline{BC}[/tex] ║ [tex]\overline{AD}[/tex]

The two column consisting of the statements and reasons to prove that the specified sides are parallel is presented as follows;

Step [tex]{}[/tex]        Statement                                    Reasons

1.    [tex]{}[/tex]   [tex]\overline{AC}[/tex] and [tex]\overline{BD}[/tex] bisect each other           Given

2. [tex]{}[/tex]    [tex]\overline{BE}[/tex] ≅ [tex]\overline{ED}[/tex] and  [tex]\overline{CE}[/tex] ≅ [tex]\overline{AE}[/tex]                   Definition of bisected segments

3.   ∠BEC ≅ ∠AED and  ∠BEA ≅ ∠CED     Vertical angles theorem

4. [tex]{}[/tex] ΔBCE ≅ ΔADE and ΔBEA ≅ ΔCED      SAS congruency rule

5.  [tex]{}[/tex] ∠EBC ≅ EDA and ∠EBA ≅ ∠EDC        CPCTC

6.  [tex]{}[/tex] [tex]\overline{AB}[/tex] ║ [tex]\overline{CD}[/tex] and [tex]\overline{BC}[/tex] ║ [tex]\overline{AD}[/tex]                     Converse of alt. int. ∠s theorem

The details of the reasons in the above table are;

Vertical angles theorem

The vertical angle theorem states that the vertical angles formed by two intersecting straight lines are congruent.

SAS congruency rule

The SAS (acronym for Side-Angle-Side) congruency rule states that if two sides and an included angle in one triangle are congruent to two sides and an included angle in a second triangle, the two triangles are congruent

CPCTC

CPCTC is an acronym for Corresponding Parts of Congruent Triangle are Congruent.

Converse Alt, Int, ∠s theorem

The converse of the alt. int. ∠s (abbreviation for alternate interior angles) theorem state that if the the alternate interior angles formed by two lines and a common transversal are congruent, then the two lines are parallel

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Answer: A. AB = BC can be proven true.

An isosceles triangle has two equal side lengths, and since the vertex angle is angle C, it means that sides AB and BC are the equal sides.

B. angle A = angle B can be proven true.

In an isosceles triangle, since the two sides are equal, the base angles are also equal.

D. segment BC = segment AC can be proven true.

In an isosceles triangle, since the two sides are equal, the base segments are also equal.

E. segment AB = segment AC can be proven true.

In an isosceles triangle, since the two sides are equal, the base segments are also equal.

C. angle B = angle C is not true.

Because the vertex angle is angle C, and it is formed by the two base segments, so it will be different than angle B and angle A.

Step-by-step explanation:

Answer:

  B, D

Step-by-step explanation:

You want to know what you can prove, given that the vertex angle of isosceles triangle ABC is angle C.

A triangle is isosceles if it has two congruent sides or two congruent angles. In either case, the angles opposite the congruent sides are congruent, and vice versa.

The vertex angle is opposite the "base" of the isosceles triangle. The sides of the vertex angle are the congruent sides, and the angles that are not the vertex angle are the congruent angles.

These sides share point B, which is not the vertex. This cannot be proven.

These are the base angles of the triangle, hence congruent. This can be proven.

These angles cannot be proven congruent using the given information. This will be true if and only if the isosceles triangle is also an equilateral triangle.

These sides share point C, which is the vertex. This can be proven.

These sides share point A, which is not the vertex. This cannot be proven.

Refer to the image attached.

The consecutive numbers are 21 and 22.

Consecutive numbers are numbers that follow each other in order and they have a difference of 1 between every two numbers. 

We shall represent the consecutive numbers with n and (n + 1) so that:

3(n + 1) = 2n + 24 {open bracket}

3n + 3 = 2n + 24

3n - 2n = 24 - 3 {collect like terms}

n = 21

since the lesser number is 21, then the greater number is 21 + 1= 22.

Therefore, the two consecutive numbers such that 3 times the greater number exceeds twice the lesser by 24 are 21 and 22.

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Answer:

Step-by-step explanation:

poop

To solve the equation for x, locate squares a, b, and c and use the quadratic formula. x= [tex]-1\±I[/tex]

A second order polynomial can be used to define a square. It has at least one term that needs to be squared, in other words. They go by the name quadratic equations as well. The quadratic equation's generic form is

[tex]ax^2\+ bx + c = 0[/tex]

Where x is an unknown variable and a, b, and c are numerical coefficients, the formula is: ax2 + bx + c = 0. An example of a quadratic equation is x2 + 2x + 1. in which a 0. The equation becomes a linear equation when this value is zero and ceases to be a quadratic equation.

bx+c=0

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Answer: x is 17

Step-by-step explanation:

Distribute the -5: -5x + 50 = -35

Subtract 50 from both sides: -5x = -85

Divide both sides by -5: x = 17

Answer: x is representing here.

Step-by-step explanation: as the equation is -5(x-10) = -35

(-) sign in both sides will cancel out each other so the equation will become 5(x-10)= 35

now we will solve the equation

5x-50 = 35

5x = 35+50

5x = 85

x=85/5 = x =

Answer:

It can be represented as a fraction, 276/1000. It isn't non-terminating.

0.276 is a rational number because we can write it as a fraction, where both denominator and numerator are integers.

Answer: A, B, and E can be used to satisfy the equation

Step-by-step explanation:

A applies because 45 is the same exact number as 45, so the equal sign accurately compares them.

B applies because that symbol means less than or equal to, and 45 is not less than but is equal to 45.

C does not apply because that symbol means is not equal to, but 45 is equal to 45.

D does not apply because that is the less than symbol, and 45 is not less than 45.

E applies because it is greater than or equal to symbol, and 45 is not greater than but is equal to 45.

F does not apply because that is the greater than symbol and 45 is not greater than 45.

Hope this helps!

An ordered pair (x, y) that is a solution to the equation include the following: (x, y) = (-3, 0).

In Mathematics, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph.

In order to determine the ordered pairs that represent points on the graph of the given function, we would plot its equation by using an online graphing calculator and then read all the ordered pairs that lie on the line.

By critically observing the graph of the given function (see attachment), the required solutions are include following;

Ordered pair = (0.75, 0).

Ordered pair = (-3, 0).

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The possible lengths for the third side 8² + 11² < x²,  8² + 11² = x²

and 8² + 11² ≥ x².

If a² + b² < c² then it is an acute angle triangle.

If a² + b² = c² then it is a right-angle triangle.

If a² + b² ≥ c² then it is an obtuse angle triangle.

Given, Two sides of a triangle have lengths 8 and 11.

Let, The third side be 'x'.

Therefore, The possible lengths for the third side are,

8² + 11² < x²...(i)

8² + 11² = x²...(ii)

8² + 11² ≥ x²...(iii)

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Answer:

Step-by-step explanation:

System I: This system has one solution. To solve, you would need to first solve for one of the variables, say x. Then, substitute the value of x into the other equation to solve for y.

System II: This system has an infinite number of solutions. To solve, you would need to first solve for one of the variables, say x. Then, substitute the value of x into the other equation to solve for y. Since both equations are linear, they will have an infinite number of solutions.

The domain and range of the the function are given below -

Domain → [-5, 10)

Range → [-3, 3)

Given is a graph of the function.

The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that function takes. So, we can write the domain as -

Domain → [-5, 10)

Range → [-3, 3)

Therefore, the domain and range of the the function are given below -

Domain → [-5, 10)

Range → [-3, 3)

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The angles forming the triangle must be equal to prove that they are parallel.

Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.

Given here: AX/AB=XY/BC=AY/AC

Thus the triangles are similar (ΔAXY≈ABC)

Therefore ∠x=∠B & ∠Y=∠C , so we can conclude that the two lines (XY||BC)

Hence, The angles forming the triangle must be equal to prove that they are parallel.

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Answer:

It means there is no solution.

Step-by-step explanation:

When you work on a system of equations and the variable falls out of the equation and you're left with a false statement...that means there is no solution.

Answer: The value represented by the digit 6 is 100 times greater.

Step-by-step explanation: The digit 6 in the number 84,362 is in the tens place, whereas the digit 6 in the number 6,419 is in the thousandths place. One thousand is equal to 10 x 100, meaning that the value is 100 times greater. Hope this helps and have a great day!

The value of digit 6 in 6419 is 100 times greater than the value of the digit 6 in 84362.

Place value describes the position or place of a digit in a number. Each digit has a place in a number.

When we represent the number in general form, the position of each digit will be expanded.

Those positions start from a unit place, or we also call it one’s position. The order of place value of digits of a number of right to left is units, tens, hundreds, thousands, ten thousand, a hundred thousand, and so on.

Given that are two numbers 6419 and 84362, we need to determine that the value digit 6 in 6419 is how much times greater than the value of the digit 6 in 84362.

So, the expanded form of the numbers =

6419 = 6000 + 400 + 10 + 9

84362 = 80000 + 4000 + 300 + 60 + 2

Place values of 6 in each =

In 84362 = 60

In 6419 = 6000

∴ 6000 / 60 = 100

Hence, the value of digit 6 in 6419 is 100 times greater than the value of the digit 6 in 84362.

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Sara's average speed for the entire race is

3.6 meters per second

The first 50 meters of the race is ran at a constant speed of 4.6 m/s.

Let's compute the time taken for this portion

distance = rate*time

time = distance/rate

time = 50/(4.6)

time = 10.869

It takes approximately 10.869 seconds to run the first 50 meters (at a constant speed of 4.6 m/s).

Add on the other time values from the other sections (10 and 23) to get 10.869+10+23 = 43.869

The entire 200 m race takes about 43.869 seconds.

So Sara's average speed over the entire race is about 200/43.869 = 4.559 which rounds to 4.6 m/s when rounding to one decimal place.

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Answer:

Step-by-step explanation:

Let's start by labeling the sides of the triangle ABC:

A = 12

B = x

C = 10

Using the Law of Cosines, we can write the following equation:

C² = A² + B² - 2ABcos(C)

Substituting the values we have, we get:

10² = 12² + x² - 2(12)(x)cos(10)

Simplifying, we get:

100 = 144 + x² - 24xcos(10)

Rearranging, we get:

x² - 24xcos(10) + 44 = 0

Solving for x, we get:

x = [24cos(10) ± √(576cos²(10) - 176)]/2

Calculating the values, we get:

x = [24cos(10) + √(5232)]/2 ≈ 18.3

x = [24cos(10) - √(5232)]/2 ≈ 7.7

Therefore, BC = 18.3 or BC = 7.7

Answer:

19.7

Step-by-step explanation:

A^2 + B^2 = C^2

8^2 + 18^2 = sqrt(388)

Answer: Hello how are you doing today?

Step-by-step explanation: How may I help you?

Answer: The sum of the first 10 terms of the given geometric sequence is 3069.

Step-by-step explanation:

A geometric sequence is a sequence of numbers such that any two consecutive terms are in a constant ratio.

The first term of the given sequence is 3 and the common ratio is 2 (6/3 = 12/6 = 24/12 = ...).

To find the sum of the first 10 terms of a geometric sequence, we can use the formula:

S = a(1 - r^n)/(1 - r)

where a is the first term, r is the common ratio and n is the number of terms.

So for this geometric sequence:

S = 3(1 - 2^10)/(1 - 2) = 3(1 - 1024)/(-1) = 3(-1023)/(-1) = 3069

Explanation: By using the formula for the sum of a geometric sequence, the sum of the first 10 terms of the sequence was found by substituting the first term, common ratio and number of terms into the formula.

Answer:

C)  3069

Step-by-step explanation:

A geometric series is the sum of the terms of a geometric sequence.

[tex]\boxed{\begin{minipage}{7 cm}\underline{Sum of the first $n$ terms of a geometric series}\\\\$S_n=\dfrac{a(1-r^n)}{1-r}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $r$ is the common ratio.\\\end{minipage}}[/tex]

Given geometric sequence:

From inspection of the sequence, the first term is 3:

[tex]\implies a=3[/tex]

To find the common ratio, divide consecutive terms:

[tex]\implies r=\dfrac{a_2}{a_1}=\dfrac{6}{3}=2[/tex]

To find the sum of the first 10 terms, substitute the found values of a and r together with n=10 into the geometric series formula:

[tex]\implies S_{10}=\dfrac{3(1-2^{10})}{1-2}[/tex]

[tex]\implies S_{10}=\dfrac{3(1-1024)}{1-2}[/tex]

[tex]\implies S_{10}=\dfrac{3(-1023)}{-1}[/tex]

[tex]\implies S_{10}=\dfrac{-3069}{-1}[/tex]

[tex]\implies S_{10}=3069[/tex]

Therefore, the sum of the first 10 terms of the given geometric sequence is:

The number of zeroes that the product has at the end 50 x 49 x 48 x ... x 3 x 2 x 1 will be 12.

The factor of n is given as the production of the number n, (n - 1), (n - 2)... and 1. Then the factorial of n is given as

n! = n x (n - 1) x (n - 2) x ... 3 x 2 x 1

The expression is given below.

⇒ 50 x 49 x 48 x ... x 3 x 2 x 1

⇒ 50!

Then the number of zeroes in the product at the end will be given as,

⇒ 50 / 5 + 50 / 5²

⇒ 50 / 5 + 50 / 25

⇒ 10 + 2

⇒ 12

The number of zeroes that the product has at the end 50 x 49 x 48 x ... x 3 x 2 x 1 will be 12.

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Answer:To estimate the number of steps the average man takes in 1 week, we can multiply the number of steps per day by the number of days in a week.

A week has 7 days so the number of steps the average man takes in a week would be 7,912 steps/day * 7 days/week = 55,384 steps/week

So the correct answer for the number of steps the average man takes in one week is 55,384 steps/week or in scientific notation is 5.5 x 10^4. So the answer is D. 7.9 x 10^4

Step-by-step explanation:

Answer:

A: 5.5*10⁴

Step-by-step explanation:

1 week = 7 days

7 * 7912 = 55384 steps/week

Scientifin notation:

55384 =

              5538.4*10¹

               553.84*10²

               55.384*10³

                5.5384*10⁴

Then:

the answer is:

5.5*10⁴

Answer:

square root 27

Step-by-step explanation:

3³/² =

(3×3×3 )½ =27½

Answer:

Step-by-step explanation:

The company breaks even, meaning the profits are $0, only when it sells 10,000 boxes.

a. The mean stock price of Cenovus Energy is 15.437.

b. The standard deviation for the sample prices of Cenovus Energy is

3.93.

c. The median stock price for Cenovus Energy is 14

d.  The range in Cenovus Energy's stock price is 11.5.

e. The coefficient of variation for each stock are 28.071% Cenovus Energy for % and 9% for TD Bank.

f. As the coefficient of variation is more for TD Bank it is riskier to buy.

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the mean.

a. The mean stock price of Cenovus Energy is,

= (18 + 19 + 12 + 16 + 17.50 + 12 + 7.50 + 10)/8.

= 112/8.

= 14.

b. The variance for the sample prices of Cenovus Energy is,

= [tex]\frac{1}{n}\[ \sum_{i=1}^{n}[x_i - \overline{x}]^2[/tex].

= (1/8)×[(18 - 14)² + (19 - 14)² + (14 - 12)² + (16 - 14)² +(17.50 - 14)² +(14 - 12)² +(14 - 7.50)² + (14 - 7.50)² +(14 - 10)²].

= (1/8)×[16 + 25 + 4 + 4 + 12.25 + 4 + 42.25 + 16].

= (1/8)×(123.5).

= 15.437.

Standard deviation = √(15.437).

= 3.93.

c. To find the median stock price for Cenovus Energy first we have the data set in ascending order.

7.50, 10.00, 12.00, 12.00, 16.00, 17.50, 18.00, 19.00.

So, The median of the stock price for Cenovus Energy is,

= (12 + 16)/2.

= 28/2.

= 14.

d. The range in Cenovus Energy's stock price is (19.00 - 7.50).

= 11.5.

e. The coefficient of variation for each stock is,

CV = {(Standard Deviation)/(Mean)}×100%.

CV = (3.93/14)×100%.

CV = 28.071 for Cenovus Energy.

CV = (6.30/70)×100%.

CV = 9% for TD Bank.

f. TD Bank's higher coefficient of variance makes investing riskier.

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