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

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

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.

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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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!!

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

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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Total: 499.75

Step-by-step explanation:

4 × 110.5 = 442

3 × 19.25 = 57.75

442 + 57.75 = 499.75

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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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

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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Answer: (7, 12)

Step-by-step explanation:

The x-coordinate is 7.

The y-coordinate is 12.

Thus, the coordinates are (7, 12).

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]

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

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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Answer:

96, $ 144

Step-by-step explanation:

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.

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:

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]

Answer: The answer is D ( 2/5 < 1/2

Step-by-step explanation:

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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a) The 90% confidence interval of the percentage of all mangoes on the truck that fail to meet the standards is: (7.55%, 12.45%).

b) The margin of error is: 2.45%.

c) The 90% confidence is the level of confidence that the true population percentage is in the interval.

d) The needed sample size is: 271.

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The margin of error is given by:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The variables are listed as follows:

The confidence level is of 90%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.90}{2} = 0.95[/tex], so the critical value is z = 1.645.

The sample size and the estimate are given as follows:

[tex]n = 150, \pi = \frac{15}{150} = 0.1[/tex]

The margin of error is of:

[tex]M = z\sqrt{\frac{0.1(0.9)}{150}} = 0.0245 = 2.45\%[/tex]

The interval is given by the estimate plus/minus the margin of error, hence:

For a margin of error of 3% = 0.03, the needed sample size is obtained as follows:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.03 = 1.645\sqrt{\frac{0.1(0.9)}{n}}[/tex]

[tex]0.03\sqrt{n} = 1.645\sqrt{0.1(0.9)}[/tex]

[tex]\sqrt{n} = \frac{1.645\sqrt{0.1(0.9)}}{0.03}[/tex]

[tex](\sqrt{n}})^2 = \left(\frac{1.645\sqrt{0.1(0.9)}}{0.03}\right)^2[/tex]

n = 271 (rounded up).

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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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There were 500 times more views were on Saturday than Sunday

In this question, we have been given a website got 4 × 10^9 views on Saturday and 8 × 10^6 views on Sunday.

We need to find the number of times more views were on Saturday than Sunday.

We need to divide 4 × 10^9 by 8 × 10^6

( 4 × 10^9) / (8 × 10^6)

= (4/8) * 10^(9 - 6)                   ..............(rule of exponents)

= 0.5 * 10^3

= 500      

Therefore, there were 500 times more views were on Saturday than Sunday.

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[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]

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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⇒ Supplementary angles are angles that add up to 180°

⇒ ∠1+∠2=180°(angles on a straight line)

∠2=∠4( Corresponding angles are equal m||n)

⇒*NOTE THE FOLLOWING STATEMENT IS TO MAKE YOU UNDERSTAND,IT MUST NOT BE INCLUDED IN YOUR ANSWERBOOK)

If ∠2=∠4

in the place of ∠2 in the equation ∠1+∠2=180° we can substitute ∠4 since the two angles (∠2 and ∠4) are equal by corresponding angles

______________________________________________________

⇒You may include this step now as you now know how ∠4 came up.

∴∠1+(∠4)=180°

∠1+∠4=180°

Now from the above equation we can see that ∠1 and ∠4 are supplementary angles as they both add up to 180°

answer:

we need the table.