select shapes which have one line of symmetry

Answers

Answer 1

Answer:

A semicircle has 1 line of symmetry.

Step-by-step explanation:


Related Questions

Luis has $80 in his checking account. He makes a deposit of $100, and the write a check for $40

Answers

Answer: 140 is the answer

Step-by-step explanation: Luis adds 100 to his account  so which makes the account balance 180 and then writes a check so he takes 40 out of his account which means he has 140 left in his account

Question 6
The functions g is defined on the real numbers by g (x) = (x² + 1) (3x - 5). What is the value
of g(4) ?

-51

63

119

175

Answers

Answer: 119

Step-by-step explanation:

(4^2+1)(3*4-5)

=(16+1)(12-5)

=17*7

=119

Answer:

g(4) = 119

Step-by-step explanation:

g(x) = (x² + 1) (3x - 5)

Substitute x for 4 in the equation

g(4) = (4² + 1) (3(4) - 5)

g(4) = (16 + 1) (12 - 5)

g(4) = (17) (7)

g(4) = 119

Hence, the value of g(4) is 119

Barbara borrows $4,500 at 12 percent annually compounded interest to be repaid in four equal annual installments. The actual end-of-year payment is

Answers

The actual end-of-year payment or present value of this ordinary annuity is equal to $1,482.

How to calculate the actual end-of-year payment?

For the rate of interest, we have:

Rate of interest, r = APR/12

Rate of interest, r = 0.12/12

Rate of interest, r = 0.01

Next, we would calculate the present value of this ordinary annuity by using this formula:

Present value, PV = [P ÷ [1 - (1 + r)^{-n}]/r]

Where:

r is the interest rate.P is the principal.n is the number of times compounded.

Substituting the given parameters into the formula, we have;

Present value, PV = 4,500 ÷ ((1 - (1 + 0.12)^(-4))/(0.12))

Present value, PV = 4,500 ÷ ((1 - (1.12)^(-4))/(0.12))

Present value, PV = 4,500 ÷ ((1 - 0.635518078)/(0.12))

Present value, PV = 4,500 ÷ ((0.364481922)/(0.12))

Present value, PV = 4,500/3.0373

Present value, PV = $1,481.58 ≈ $1,482.

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How to find x here if the perimeter, diagonal, and length is given?​

Answers

Answer:

see explanation

Step-by-step explanation:

(a)

perimeter (P) is calculated as

P = 2(l + b) ← l is the length and b the breadth

given l = x and P = 20 , then

2(x + b) = 20 ( divide both sides by 2 )

x + b = 10 ( subtract x from both sides )

b = 10 - x

Using Pythagoras' identity in the right triangle

x² + (10 - x)² = 8²

x² + 100 - 20x + x² = 64 ( subtract 64 from both sides )

2x² - 20x + 36 = 0 ( divide through by 2 )

x² - 10x + 18 = 0 ← as required

(b)

solve using the method of completing the square

x² - 10x + 18 = 0 ( subtract 18 from both sides )

x² - 10x = - 18

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 5)x + 25 = - 18 + 25

(x - 5)² = 7 ( take square root of both sides )

x - 5 = ± [tex]\sqrt{7}[/tex] ( add 5 to both sides )

x = 5 ± [tex]\sqrt{7}[/tex]

Then

x = 5 - [tex]\sqrt{7}[/tex] ≈ 2.35 ( to 3 significant figures )

x = 5 + [tex]\sqrt{7}[/tex] ≈ 7.65 ( to 3 significant figures )

Identify the values of the variables. Give your answers in simplest radical form. Help!

Answers

Considering the right angle triangle given the values of the variables are

n = 2√3k = 4√3How to determine the values of the variables

Information from the question

right angle triangle

The values of the variables is worked using SOH CAH TOA

The right angle triangle of sides as described below

hypotenuse = k

opposite = n

adjacent = 6

The variable n is solved using tan, TOA, the angle is 30

tan 30 = Opposite / Adjacent

tan 30 = n / 6

tan 30 * 6 = n

n = 2√3

The variable k is solved using cos, CAH, the angle is 30

cos 30 = Adjacent / Hypotenuse

cos 30 = 6 / k

k = 6 / cos 30

k = 4√3

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I’m doing my geometry homework and don’t remember the formula or way to solve the lengths of a triangle side with graph points. How do I solve both parts of #1?

Answers

[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ E(\stackrel{x_1}{2}~,~\stackrel{y_1}{3})\qquad F(\stackrel{x_2}{3}~,~\stackrel{y_2}{1}) ~\hfill EF=\sqrt{(~~ 3- 2~~)^2 + (~~ 1- 3~~)^2} \\\\\\ ~\hfill EF=\sqrt{( 1)^2 + ( -2)^2} \implies \boxed{EF=\sqrt{ 5 }}[/tex]

[tex]F(\stackrel{x_1}{3}~,~\stackrel{y_1}{1})\qquad D(\stackrel{x_2}{-1}~,~\stackrel{y_2}{-1}) ~\hfill FD=\sqrt{(~~ -1- 3~~)^2 + (~~ -1- 1~~)^2} \\\\\\ ~\hfill FD=\sqrt{( -4)^2 + ( -2)^2} \implies \boxed{FD=\sqrt{ 20 }} \\\\\\ D(\stackrel{x_1}{-1}~,~\stackrel{y_1}{-1})\qquad E(\stackrel{x_2}{2}~,~\stackrel{y_2}{3}) ~\hfill DE=\sqrt{(~~ 2- (-1)~~)^2 + (~~ 3- (-1)~~)^2} \\\\\\ ~\hfill DE=\sqrt{( 3)^2 + (4)^2} \implies DE=\sqrt{ 25 }\implies \boxed{DE=5} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]E(\stackrel{x_1}{2}~,~\stackrel{y_1}{3})\qquad F(\stackrel{x_2}{3}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{2}}} \implies \cfrac{ -2 }{ 1 } \implies - 2 \\\\[-0.35em] ~\dotfill[/tex]

[tex]F(\stackrel{x_1}{3}~,~\stackrel{y_1}{1})\qquad D(\stackrel{x_2}{-1}~,~\stackrel{y_2}{-1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{-1}-\underset{x_1}{3}}} \implies \cfrac{ -2 }{ -4 } \implies \cfrac{1 }{ 2 } \\\\[-0.35em] ~\dotfill[/tex]

[tex]D(\stackrel{x_1}{-1}~,~\stackrel{y_1}{-1})\qquad E(\stackrel{x_2}{2}~,~\stackrel{y_2}{3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-1)}}} \implies \cfrac{3 +1}{2 +1} \implies \cfrac{4 }{ 3 }[/tex]

Im giving 20 points for this

Answers

Answer:

(B)={8,10,15,18,20}

Step-by-step explanation:

Please help ASAP will mark brainliest
Plot the points ( -3, 7 ) and ( 9, 0)
Find the distance between the points and the midpoint of the line segment joining the points.

Answers

Answer: 13.89 units

PLEASE GIVE BRAINLIEST THANK YOU VERY MUCH!!

Chang will run at least 21 miles this week. So far, he has run 12 miles. What are the possible numbers of additional miles he will run?
Use t for the number of additional miles he will run.
Write your answer as an inequality solved for t.

Answers

Using an inequality to represent the problem, Chang must run at least an additional 9 miles or greater than 9 miles

What is an Inequality

In Mathematics, the relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally, if two values are not equal, we use “not equal symbol (≠)”. But to compare the values, whether it is less than or greater than, different inequalities are used.

To find the number of additional miles he will run, let's set the unknown number equals t

12 + t > 21

t > 21 - 12

t >9

Chang will need to run at least 9 miles

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1. Which expression has a whole-number product?
(A) (4- 2i) (4 - 2i)
(B) (3 + 2i) (3 - 2i)
C (-6+ i)(3- i)
D(-4+3i)(4-3i)

Answers

Option (B) (3 + 2i) (3 - 2i) is the expression that has the whole number product.

Whole number:

Whole number refers the numbers without fractions and it is a collection of positive integers and zero and represented by the symbol “W” and the set of numbers are {0, 1, 2, 3, 4, 5, 6, 7, 8, 9,……………}.

Given,

Here we have the following expression:

(A) (4- 2i) (4 - 2i)

(B) (3 + 2i) (3 - 2i)

(C) (-6+ i)(3- i)

(D) (-4+3i)(4-3i)

Now, we need to find the whole number product.

In order to find the solution we have to perform the multiplication on the given expression,

First expression will gives the following,

(A) (4 - 2i) (4 - 2i)

When we apply the (a-b)² formula in it then we get,

=> 4²+ (2i)² - (2 x 4 x 2i)

=> 16 - 4 - 16i

=> 12 - 16i

Which is not a whole number product.

Second expression,

(B) (3 + 2i) (3 - 2i)

Apply the (a + b)(a - b) formula in it,

Then we get,

=> 3² - (2i)²

=> 9 + 4

=> 13

Therefore, this one is the whole number product.

Third expression,

(C) (-6 + i) (3 - i)

When we perform the multiplication on it, then we get,

=> -18 + 6i +3i -i²

=> -18 + 9i + 1

=> -17 + 9i

his one is not a whole number product.

Final expression,

(D) (-4 + 3i) (4 - 3i)

When we perform the multiplication on it, then we get,

=> -16 + 12i + 12i - (3i)²

=> -16 + 24i + 9

=> -7 + 24i

This one is also no the whole number product.

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For which equation would x = 5 be a solution?
3x+6=21
12-2x = 13
7+ 6 x = 27
4x-7=27

Answers

4x-7=27 is the answer to x = 5
No, for each equation x=5 would not be a solution.

If you plug 5 into x for each equation, only a couple of the equations would be true, while the others would be false.

Your answer is no

Michel is taking 4 credit hours of courses at his local community college. Each credit hour costs $110.50. He is also to pay three technology fees of $19.25. Determine the total amount that he will pay in tuition.

Answers

Total: 499.75

Step-by-step explanation:

4 × 110.5 = 442

3 × 19.25 = 57.75

442 + 57.75 = 499.75

Gabriel has a stack of nickels that is 2 inches tall. The thickness of a nickel is
0.08 inch. How many nickels does Gabriel have?
Show your work.
Answer: Gabriel has
nickels.

Answers

Gabriel owns a stack of nickels which is 2 inches tall and thickness of each nickel is 0.08 inch then number of nickels with Gabriel is equal to 25.

As given in the question,

Gabriel has 2 inches tall stack of nickel

Thickness of each nickel = 0.08inch.

Let 'n' be the number of nickels Gabriel has .

Required equation to get the number of nickel is equal to :

0.08 × n = 2

⇒ n = 2 / 0.08

⇒ n = 200/ 8

⇒ n = 25

Therefore,  Gabriel owns a stack of nickels which is 2 inches tall and thickness of each nickel is 0.08 inch then number of nickels with Gabriel is equal to 25.

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Answer 0.04

Step-by-step explanation:

because 0.08 divided by two is 0.04

What is the image of (12,-12) after a dilation by a scale factor of 1/4 ​centered at the origin?

Answers

The image of (12, -12) after a dilation by a scale factor of 1/4 ​centered at the origin would have these coordinates (3, -3).

What is dilation?

In Geometry, dilation simply refers to a type of transformation which typically changes the size of a geometric object based on the scale factor applied, but not its shape.

Next, we would dilate the coordinates of the preimage (12, -12) by using a scale factor of 1/4 centered at the origin (0, 0) as follows:

Coordinate A (12, -12) → Coordinate A' (12 × 1/4, -12 × 1/4) = Coordinate A' (3, -3).

In conclusion, the coordinates of the image after a dilation by using a scale factor of 1/4 are (3, -3).

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Keala is making a new book cover before giving their favorite picture book to their little brother. The cover is 22 1 4 cm 22 4 1 ​ cm22, start fraction, 1, divided by, 4, end fraction, start text, c, m, end text tall. It has a rectangular shape and an area of 890 cm 2 890cm 2 890, start text, c, m, end text, squared. How wide across is Keala's book cover? cm

Answers

The width across Keala book cover is 40cm

What is a rectangle?

A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel. It is a four-sided polygon that has four angles, equal to 90 degrees

From the question,

The length of the cover

= 22 1/4

= 89/4

The area of the cover

=890 cm²

From the formula

Area of a Rectangle = Length x Breadth

890=89/4×Breadth

Breadth = 890×4/89

Breadth=40cm

Hence, the width of the book cover is 40cm

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ABC and △XYZ are similar. Find the missing side length. A B C X Y Z 4 8 ? 42 24 48 (The triangles are not drawn to scale.)

Answers

The missing side length of  triangle XYZ is 7.

Given,

Triangle ABC and triangle XYZ are similar.

Triangle ABC;

Length of AB = 4

Length of BC = 8

Length of AC = x

Triangle XYZ;

Length of XY = 24

Length of YZ = 48

Length of XZ = 42

We have to find the missing length x.

Here,

Triangle ABC and triangle XYZ are similar.

So,

AB : XY = BC : YZ = AC : XZ

Then,

Take AB : XY = AC : XZ

= 4 : 24 = x : 42

= 4 × 42 = 24x

x = 4 × 42 / 24

x = 42/6

x = 7

That is,

The missing side length of  triangle XYZ is 7.

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Many Texas cities have experienced substantial growth in population over the last 20 years. The growth of Houston, Texas, since 2015 is shown in the scatterplot. A least-squares equation that relates the number of years since 2015 to the population of that year (in millions) is given by Population = 0.025 (year) + 2.01.

Based on the residual plot, is a linear model suitable for modeling the population growth of Houston?

A linear model is suitable because a pattern is evident in the residual plot.
A linear model is not suitable because the residuals do not cluster around zero.
A linear model is not suitable because the residual plot shows a curved pattern.
A linear model is suitable because the residuals seem to be randomly scattered.

Answers

Based on the given residual plot, as regards the linear model, we can say that; A linear model is not suitable because the residual plot shows a curved pattern.

What is a residual Plot?

A residual plot is a plot that shows the difference between the observed response and the fitted response values.

The ideal residual plot is usually called the null residual plot, and it shows a random scatter of points that form an approximately constant width band around the identity line.

When it comes to finding out if a linear model will be suitable, we can say that the points will form a pattern when the model function is not correct.

Now, you might be able to transform variables or even add polynomial and interaction terms in order to remove the pattern.

Now, looking at the given graph, we can say that a linear model is not suitable because from the definitions above, we can see that the residual plot shows a curved pattern.

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A chemist is mixing a 30% salt solution with a 15% salt solution to make 60 L of a new solution that will contain 20% salt. How much of the 30% solution
should the chemist use?

Answers

20 amount of 30% salt solution

How to find the salt solution percentage?

Divide the solute's gram weight by the total weight of the solution, then multiply the result by 100 to get the mass/mass percent of the solution. The amount of solute (measured in grams) per milliliter of solution is known as the mass/volume percent.

Let x be the amount of 30% salt solution

Then, 60-x = amount of 15% salt solution

Salt content of the first solution + salt content of second solution = salt content of the mixture

∴ 0.30x + 0.15(60-x) = 0.20*60

  0.30x + 9 - 0.15x = 12

             0.15x = 3

                   x = 20

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WHat is 5/1 x 4/5 This is a hard one

Answers

5 times 20 equals 1000

4

Step-by-step explanation:

[tex]{ \tt{ \frac{5}{1} \times \frac{4}{5}}} [/tex]

[tex]{ \tt{ \frac{5 \times 4}{5}}} [/tex]

[tex]{ \tt{ = \frac{20}{5}}} [/tex]

[tex] = { \green{ \boxed{ \pink{ \sf{4}}}}}[/tex]

there are three consecutive odd integers such that if the second is subtracted from twice the sum of the first and third,the result is 52 more than the first. find the sum of the first and second

Answers

The sum of the first and second integer is 44.

How to illustrate the information?

Let the numbers be x, x+2 and x+4.

If the second is subtracted from twice the sum of the first and third,the result is 52 more than the first. This will be:

2(x + 2 + x + 4) - (x + 2) = x + 52

2(2x + 6) - (x + 2) = x + 52

4x + 12 - x - 2 = x + 52

Collect like terms

4x - x - x = 52 - 12 + 2

2x = 42

Divide

x = 42/2

x = 21

Second Integer = x + 2 = 21 + 2 = 23

Third integer = x + 4 = 21 + 4 = 25

Sum = 21 + 23 = 44

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A bottle maker assumes that 24% of his bottles are defective. If the bottle maker is right, what is the probability that the proportion of defective bottles in a sample of 546 bottles would differ from the population proportion by greater than 4%? Round your answer to four decimal places.

Answers

The probability that the proportion of defective bottles in a sample of 546 bottles would differ from the population proportion by greater than 4% is: 10.9069.

What is the probability that the population proportion will be greater than 4%?

To obtain the correct value, we need to use the formula for the Z score. This formula requires that we subtract the average or mean value from the data point provided and divide the remaining value by the standard deviation.

Here is the formula:

z = (x-μ)/σ

First population proportion = 0.24

The sample proportion, hat p = 0.04

​Z score =

[tex]0.04 - 0.24 / \sqrt 0.24 (1 - 0.24) / 546[/tex]

So, the Z score will

= -10.9469

So, when the z score = - 10.9469, the probability that Z is greater than - 10.9469,  is = 10.9069

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carolina and her friends are training for a kayaking competition. the average distance and time traveled by each is shown in the table below. if the distance kayaked in the competition is 3 miles, predict who will win based on the rates shown. predict how long it will take the winner to complete the race if their rate remains constant

Carolina, 7/8 mi in 1/2 hr
Leslie, 1 mi in 1/3 hr
Bryan 3/4 mi in 3/4 hr
Javier 1 mi in 2/3 hr

Answers

The winner of the race among the friends would be Leslie.

Who would win the race?

The person who has the highest average speed will win the race. Average speed is the total distance travelled per time.

Average speed = total distance / total time

Carolina's average speed = 7/8 ÷ 1/2

7/8 x 2 = 7/4 = 1 3/4 miles per hour

Leslie's average speed = 1 ÷ 1/3

1 x 3 = 3 miles per hour

Bryan's average speed = 3/4 ÷ 3/4

3/4 x 4/3 = 1 mile per hour

Javier's average speed = 1 ÷ 2/3

1 x 3/2 = 1 1/2 miles per hour

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12. Use the coordinate grid below to answer the question.
What are the coordinates of Point A?

Answers

Answer: (7, 12)

Step-by-step explanation:

The x-coordinate is 7.

The y-coordinate is 12.

Thus, the coordinates are (7, 12).

11/7 Thursday Math Math Hw. Fractions

Answers

Answer:

96, $ 144

Step-by-step explanation:

The frequency table gives information about the numbers of mice in some nests

Answers

answer:


we need the table.

parallel lines, traversal, and algebra

need help!

Answers

The values of the variables, x and y in the angles formed by the parallel lines that have a common transversal are;

x = 4°, y = 10°

11. x = 9°, y = 12°

12. x = 14°, y = 5°

13. x = 8°, y = 11°

14. x = 16°, y = 23°

15. x = 9°, y = 13°

What are parallel lines?

Parallel lines are lines that maintain the same distance from each other along their lengths.

From the figure, we get;

(29·x - 3) and (15·x + 7) are linear pair angles, therefore;

(29·x - 3) + (15·x + 7) = 180°

44·x + 4 = 180

x = (180 - 4)/44 = 4

x = 4°

(15·x + 7) and (13·y - 17) are same side exterior angles between parallel lines, therefore;

(15·x + 7) + (13·y - 17) = 180°

(15×4 + 7) + (13·y - 17) = 180°

67 + 13·y - 17 = 180°

50 + 13·y = 180

13·y = 180 - 50 = 130

y = 130 ÷ 13 = 10

y = 10°

11. (18·x - 44)° and  (8·x - 10)° are same side exterior angles, therefore;

(18·x - 44)° +  (8·x - 10)° = 180°

26·x - 54 = 180

x = (180 + 54)/26 = 9

x = 9°

(8·x - 10)° and (13·y - 38)° are linear pair angles, therefore;

(8·x - 10)° + (13·y - 38)° = 180°

(8 × 9 - 10)° + (13·y - 38)° = 180°

62 - 38 + 13·y = 180

13·y = 180 - (62 - 38) = 156

y = 156 ÷ 13 = 12

y = 12°

12. (9·x - 2)° and (5·x + 54)° are corresponding angles, therefore;

(9·x - 2)° = (5·x + 54)°

(9·x - 2)° = (5·x + 54)°

9·x - 5·x = 54 + 2 = 56°

4·x = 56°

x = 56° ÷ 4 = 14°

x = 14°

(9·x - 2)° and (10·y + 6)° are linear pair angles, therefore;

(9·x - 2)° + (10·y + 6)° = 180°

(9 × 14 - 2)° + (10·y + 6)° = 180°

124 + 6 + 10·y = 180

10·y = 180 - 130 = 50

y = 50 ÷ 10 = 5

y = 5°

13. The angle to which the angle (8·x - 1)° is an alternate interior angle is a corresponding angle to the angle (11·x - 25)°, therefore;

(8·x - 1)° is congruent to angle (11·x - 25)°

(8·x - 1)° = (11·x - 25)°

11·x - 8·x = 25 - 1 = 24

3·x = 24

x = 24 ÷ 4 = 8

x = 8°

Angles (15·y - 48)° and (8·x - 1)° are linear pair angles, therefore;

(15·y - 48)° + (8·x - 1)° = 180°

(15·y - 48)° + (8 × 8 - 1)° = 180°

(15·y - 48)° + 63° = 180°

15·y + 15° = 180°

15·y = 180° - 15° = 165°

y = 165° ÷ 15 = 11°

y = 11°

14· The angle (4·x + 4)° and (7·x - 44)° are alternate exterior angles, therefore;

(4·x + 4)° = (7·x - 44)°

7·x - 4·x = 44° + 4° = 48°

3·x = 48°

x = 48° ÷ 3 = 16°

x = 16°

The vertical angle to angle 39° is a linear pair angle to the angle (8·y - 43)°

Therefore;

39 + 8·y - 43 = 180°

8·y  = 180 + 43 - 39 = 184

y = 184 ÷ 8 = 23

y = 23°

15. The diagram indicates that the angles (15·x - 26)° and (12·x + 1)° are congruent, therefore;

(15·x - 26) = (12·x + 1)

(15·x - 12·x) = (26 + 1)

3·x = 27

x = 27 ÷ 3 = 9

x = 9°

The vertical angle to (2·x + 1) is therefore;

12·x + 1 = 12 × 9 + 1 = 109

The angle sum property indicates that we have;

28° + 109° + (4·y - 9)° = 180°

(4·y - 9)° = 180° - (28° + 109°) = 43°

(4·y - 9)° = 43°

(4·y)° = 43° + 9° = 52°

y = 52°/4 = 13°

y = 13°

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Can someone please help me solve this, I’m so stressed

Answers

Answer:

  3a.  $8493.42

  3b.  139.0 months

  4a.  10

  4b.  10.2 years

Step-by-step explanation:

Given exponential equations, you want values for specific times, and you want times for specific values.

In part (a), the value is found by substituting an appropriate value for t and doing the arithmetic.

In part (b), logarithms will be involved in solving for t.

3. Investment

(a) Use t=12, the number of months in one year. You want the value of ...

  S = 8000·1.005^12 ≈ 8493.42

The amount after 1 year is $8493.42.

(b) The time it takes to double the investment is the value of t such that ...

  16000 = 8000·1.005^t

  2 = 1.005^t . . . . . . divide by 8000

  log(2) = t·log(1.005) . . . . . take logarithms

  t = log(2)/log(1.005) ≈ 138.976

The investment will double in about 139.0 months.

4. Otters

(a) Use t=0 and evaluate.

  y = 2500 -2490e^(-0.1·0) = 2500 -2490 = 10

The population of otters was 10 when they were reintroduced.

(b) The time it takes for the population to reach 1600 is the value of t such that ...

  1600 = 2500 -2490e^(-0.1t) . . . . use 1600 for y

  -900 = -2490e^(-0.1t) . . . . . . . . . subtract 2500

  900/2490 = e^(-0.1t) . . . . . . . . . divide by -2490

  ln(900/2490) = -0.1t . . . . . . . . . take natural logs

  t = ln(900/2490)/-0.1 . . . . . . . . divide by the coefficient of t

  t ≈ 10.176 ≈ 10.2

It will be 10.2 years before the otter population reaches 1600.

A doll sold for $209 in 1977 and was sold again in 1989 for $467. Assume that the growth in the value V of the collector's item was exponential.
a) Find the value k of the exponential growth rate. Assume V0=209
b) Find the Exponential growth function in terms of t, where t is the number of years since 1977
c) Estimate the value of the doll in 2009.
d) What is the doubling time for the value of the doll to the nearest tenth of a year?
e) Find the amount of time after which the value of the doll with be $2221

Answers

Step-by-step explanation:

the exponential growth function is

f(t) = v0 × (1 + k)^t

1977 to 1989 is 12 years (t).

a)

so, we have

467 = 209 × (1 + k)¹²

467/209 = (1 + k)¹²

12th root(467/209) = 1 + k = 1.069295033...

k = 0.069295033...

b)

f(t) = 209 × 1.069295033...^t

c)

2009 = 32 years after 1977

f(32) = 209 × 1.069295033...³² = $1,783.478472... ≈

≈ $1,783.48

d)

double the value of 209 is 418.

418 = 209 × 1.069295033...^t

2 = 1.069295033...^t

t = log1.069295033...(2) =

= log(2)/log(1.069295033...) = 10.34554457... ≈

≈ 10.3 years

e)

2221 = 209 × 1.069295033...^t

2221/209 = 1.069295033...^t

t = log1.069295033...(2221/209) =

= log(2221/209)/log(1.069295033...) =

= 35.27452616... years ≈

≈ 35.3 years

35 years would mean end of 2012. so, 35.3 years would be early 2013.

From ratio proportion for the following using
2 different way

45 members of Glee Club to 30 members of Dance
Club

Answers

Answer:

see explanation

Step-by-step explanation:

this can be expressed in ratio form and fractional form , that is

45 : 30 ( divide each part by 15 )

= 3 : 2 ← in simplest form

= [tex]\frac{3}{2}[/tex]

India's hourly wage is $10.50. If she
regularly works 40 hours per week, what is
her regular weekly pay?

Answers

10.50 * 40 = 420

Her regular weekly pay is $420

Step-by-step explanation:

10 hours per week: $10.50 x 10 = $105.00

20 hours per week: $105.00 x 2 = $210.00

40 hours per week: $210.00 x 2 = $420.00

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