select shapes which have one line of symmetry

The sum of the first and second integer is 44.

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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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).

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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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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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.

(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.

(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.

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]

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.

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

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.

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

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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Answer:

96, $ 144

Step-by-step explanation:

The missing side length of  triangle XYZ is 7.

Given,

Triangle ABC and triangle XYZ are similar.

Length of AB = 4

Length of BC = 8

Length of AC = x

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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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

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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Answer: (7, 12)

Step-by-step explanation:

The x-coordinate is 7.

The y-coordinate is 12.

Thus, the coordinates are (7, 12).

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

[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]

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

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.

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

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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Answer:

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

Step-by-step explanation:

Answer: 13.89 units

PLEASE GIVE BRAINLIEST THANK YOU VERY MUCH!!

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

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:

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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Total: 499.75

Step-by-step explanation:

4 × 110.5 = 442

3 × 19.25 = 57.75

442 + 57.75 = 499.75

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

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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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 )

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]

The width across Keala book cover is 40cm

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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answer:

we need the table.

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°

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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