Five years ago, Alan was thrice as old as Aron. After ten years, Alan will be twice as old as Aron. How old are Alan and Aron?

Answer:

Step-by-step explanation:

by looking at the given image...

the shape ABCD is a parallelogram.

Required:

is to prove ∡A and ∡B are supplementary

and ∡C and ∡D are supplementary.

so, m∠A + m∠B = 180°

and m∠C + m∠D = 180°

the  Statement    

1. ABCD is a parallelogram                

the reason is..    

It is Given!

the  Statement  

2.m∠A=m∠C and m∠B=m∠D        

the reason is..

Definition of parallelogram.

the  Statement  

3.m∠A+m∠B+m∠C+m∠D=360°    

the reason is..

Definition of quadrilateral

the  Statement  

4. m∠A+m∠B+m∠A+m∠B=360°    

the reason is..

By substitution

⇒ 2( m∠A + m∠B ) = 360°

⇒ m∠A + m∠B = 180°

it is also similar  m∠C + m∠D = 180°

the  Statement  

5.∠A and ∠C are supplementary

the reason is..

by the definition of Supplementary   ∠ B and ∠D are supplementary

Hope it helps!

Answer:

see below

Step-by-step explanation:

by looking at the given image...

the shape ABCD is a parallelogram.

Required:

is to prove ∡A and ∡B are supplementary

and ∡C and ∡D are supplementary.

so, m∠A + m∠B = 180°

and m∠C + m∠D = 180°

the  Statement    

1. ABCD is a parallelogram                

the reason is..    

It is Given!

the  Statement  

2.m∠A=m∠C and m∠B=m∠D        

the reason is..

Definition of parallelogram.

the  Statement  

3.m∠A+m∠B+m∠C+m∠D=360°    

the reason is..

Definition of quadrilateral

the  Statement  

4. m∠A+m∠B+m∠A+m∠B=360°    

the reason is..

By substitution

⇒ 2( m∠A + m∠B ) = 360°

⇒ m∠A + m∠B = 180°

it is also similar  m∠C + m∠D = 180°

the  Statement  

5.∠A and ∠C are supplementary

the reason is..

by the definition of Supplementary   ∠ B and ∠D are supplementary

Hope it helps!

Answer:

Step-by-step explanation:

Add the equations in order to solve for the first variable. Plug this value into the other equations in order to solve for the remaining variables.

Point Form:

(

−

1

,

10

3

)

Equation Form:

x

=

−

1

,

y

=

10

3

Tap to view steps...

image of graph

Tap to hide graph...

Answer:

Dimensions of square shaped pit = 6m [tex]\times[/tex] 6m

Dimensions of rectangular pit = 1m [tex]\times[/tex] 36m or 2m [tex]\times[/tex] 18m or 3m [tex]\times[/tex] 12m or 4m [tex]\times[/tex] 9m

Step-by-step explanation:

Given:

Two pits in the school playground area (one square shaped and one rectangular shaped).

Each pit must have an area = 36 [tex]m^2[/tex]

To find:

Dimensions of each pit = ?

Solution:

First of all, let us have a look at the formula for area of a square and a rectangle:

[tex]Area_{square} = (Side)^2[/tex]

[tex]Area_{Rectangle} = Length\times Width[/tex]

Now, let us try to find out dimensions of square:

[tex]36 = Side^2\\\Rightarrow Side = 6\ m[/tex]

So, dimensions of Square will be 6m [tex]\times[/tex] 6m.

Now, let us try to find out dimensions of rectangle.

[tex]36 = Length\times Width[/tex]

We are not given any restrictions on the Length and Width of the rectangle.

So, let us explore all the possibilities by factorizing 36:

[tex]36 = 1 \times 36\\36 = 2 \times 18\\36 = 3 \times 12\\36 = 4 \times 9[/tex]

6 [tex]\times[/tex] 6 factors not considered because then it will become a square and which is not the required case.

Dimensions of rectangular pit = 1m [tex]\times[/tex] 36m or 2m [tex]\times[/tex] 18m or 3m [tex]\times[/tex] 12m or 4m [tex]\times[/tex] 9m

Answer:

The translation from triangle IJK to triangle I'J'K' is [tex]T_{(2, 6)}[/tex] which is 2 units to the right and 6 units up

Step-by-step explanation:

The coordinates of triangle JKI are;

J has coordinates (1, - 1)

K has coordinates (1, - 4)

I has coordinates (-3, - 2)

While, the coordinates of translation triangle J'K'I' are;

J' has coordinates (3, 5)

K' has coordinates (3, 2)

I' has coordinates (-1, 4)

Which give the translation as follows

Translation in the y-coordinate (y values);

For J = 5 - (-1) = 6

For K = 2 - (-4) = 6

For I = 4 - (-2) = 6

Translation in the x-coordinate (x values);

For J = 3 - 1 = 2

Therefore, the translation from triangle IJK to triangle I'J'K' is T(2, 6) which is 2 units to the right and 6 units up

Answer:

interquartile range=21.05

Step-by-step explanation:

3.5, 12, 19.1, 25.8, 31.8

median is 19.1

Quartile 1= (3.5+12)/2=7.75

Quartile 3=(25.8+31.8)/2=28.8

interquartile range=Q3-Q1=28.8-7.75= 21.05

Answer:

Rectangle

Step-by-step explanation:

Well if point A is on (2,3) and you reflect it over the x axis point B would be located at (2,-3).

Then over the y axis point C would be located at (-2,-3), then reflecting that over the x axis point D is (-2,3)

Points

__________

A. (2,3)

B. (2,-3)

C. (-2,-3)

D. (-2,3)

__________

So graphing all these points we get a rectangle.

Because it has 4 sides that are 90 degrees and the sides opposite from each other are the same.

The most precise name of the quadrilateral will be rectangle .

Given,

Point A : (2,3) .

Here,

If point A is on (2,3) and you reflect it over the x axis point B would be located at (2,-3).

Then over the y axis point C would be located at (-2,-3), then reflecting that over the x axis point D is (-2,3)

Points

A. (2,3)

B. (2,-3)

C. (-2,-3)

D. (-2,3)

So, graphing all these points we get a rectangle.

Because it has 4 sides that are 90 degrees and the sides opposite from each other are the same.

Know more about rectangle,

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Answer:

Step-by-step explanation:

(-100*0.9)(x)==-90x

Blake should first multiply the numbers in parenthesis and then multiply by x, even the answer is right but the process is wrong Blake has to follow the rule

Parenthesis , Exponent, Multiplication/Division, Addition/ Subtraction

P E M D A S

Answer:

Step-by-step explanation:

We have f(x) and g(x). We are to evaluate each of these functions at the domain values given (1, 2, 3, 4, 5, and 6) and see where the output is the same.

[tex]f(1)=-(1)^2+4(1)+12[/tex] and f(1) = 15

[tex]f(2)=-(2)^2+4(2)+12[/tex] and f(2) = 16

[tex]f(3)=-(3)^2+4(3)+12[/tex] and f(3) = 15

[tex]f(4)=-(4)^2+4(4)+12[/tex] and f(4) = 12

[tex]f(5)=-(5)^2+4(5)+12[/tex] and f(5) = 7

[tex]f(6)=-(6)^2+4(6)+12[/tex] and f(6) = 0

Now for g(x) at each of these domain values:

g(1) = 1 + 2 and g(1) = 3

g(2) = 2 + 2 and g(2) = 4

g(3) = 3 + 2 and g(3) = 5

g(4) = 4 = 2 and g(4) = 6

g(5) = 5 + 2 and g(5) = 7

g(6) = 6 + 2 and g(6) = 8

It looks like the outputs are the same at f(5) and g(5). Actually, the domains are the same as well! f(5) = g(5)

Answer:

[tex] x+2-2 <-5-2[/tex]

And after operate we got:

[tex] x <-7[/tex]

And then the solution would be [tex]x<-7[/tex]

Step-by-step explanation:

For this problem we have the following inequality:

[tex] x+2 <-5[/tex]

The first step would be subtract 2 from both sides of the equation and we got:

[tex] x+2-2 <-5-2[/tex]

And after operate we got:

[tex] x <-7[/tex]

And then the solution would be [tex]x<-7[/tex]

Answer:

Step-by-step explanation

√144²

12²

144

√9 + √16

3 + 4

7

√9 + √16 × √400 = ​

3 + 2^{4} x 5

3 + 80

83

Answer:

6/35

Step-by-step explanation:

add ¹/7+¹/5 =12/35

divide 12/35 by 2

=6/35

Answer: The fifth piece of paper could have any number 9 and less or 14 and greater.

Step-by-step explanation:  The list of choices is not given in the question, but it makes sense that the new number would not be a duplicate of any of the numbers 10, 11, 12, 13. Otherwise that would change the probability to 5/5.

So any other number could be a possibility.

Answer:  The value of b= 15.6

Step-by-step explanation:

The given equation:  [tex]4\dfrac{1}{3}b+b=6b-10.4[/tex]

To find : Value of b.

Since, we can write [tex]4\dfrac{1}{3}=\dfrac{13}{3}[/tex]

So, the given equation becomes [tex]\dfrac{13}{3}b+b=6b-10.4[/tex]

[tex]\Rightarrow\dfrac{13b+3b}{3}=6b-10.4\Rightarrow\dfrac{16b}{3}=6b-10.4[/tex]

Subtract 6b from both sides , we get

[tex]\Rightarrow\dfrac{16b}{3}=6b-10.4\\\\\Rightarrow\dfrac{16b-18b}{3}=-10.4\\\\\Rightarrow\dfrac{-2b}{3}=-10.4\\\\\Rightarrow b=-10.4\times\dfrac{-3}{2}\\\\\Rightarrow\ b= 15.6[/tex]

hence, the value of b= 15.6

Answer:

39 units²

Step-by-step explanation:

The figure is composed of a rectangle VEDR and Δ RMV

Area of rectangle = VE × ED = 5 × 6 = 30 units²

Area of Δ = 0.5 × RV × perpendicular from M to RV

                = 0.5 × 6 × 3 = 9 units²

Thus

Area of polygon = 30 + 9 = 39 units²

Answer:

a.

Explanation:

In the chart, the average temperature of each month at the beginning of the year gradually rises until August, where it begins to decrease. This trend is displayed in graph a. Additionally, each month on the x-axis is shown correctly because the months should only span numbers 1-12.

Answer: the answer is A

Step-by-step explanation: hope this helps :D can u plz give a brainliest

Answer:

y = -2x + 5

Step-by-step explanation:

You use the equation y = mx + b, where m is the slope and b is the y-intercept. We see that the line hits the y-axis at 5, so that will be your b. To find the slope, use [tex]\frac{rise}{run}[/tex]. You have to go down 4 and right 2, so your slope will be [tex]-\frac{4}{2}[/tex] which simplifies to -2. Hope this helps!

Answer: y=2/-5x+5

Step-by-step explanation:

Answer:

78.5 yds

Step-by-step explanation:

The circumference is given by

C = pi *d

C = 3.14 * 25

C =78.5

Answer:

[tex]\huge\boxed{C=25\pi\ yd\approx78.5\ yd}[/tex]

Step-by-step explanation:

The formula of a circumference of a circle:

[tex]C=d\pi[/tex]

d - diameter

We have d = 25yd.

Substitute:

[tex]C=25\pi\ yd[/tex]

Use [tex]\pi\approx3.14[/tex]:

[tex]C\approx(25)(3.14)=78.5\ yd[/tex]

Answer:

$2,500 was invested in the first account while $7,500 was invested in the second account

Step-by-step explanation:

Here in this question, we want to find the amount which was invested in each of the accounts, given their individual interest rates and the total amount that was accorded as interest from the two investments

Now, since we do not know the amount invested , we shall be representing them with variables.

Let the amount invested in the first account be $x and the amount invested in the second account be $y

Since the total amount invested is $10,000, this means that the summation of both gives $10,000

Mathematically;

x + y = 10,000 ••••••(i)

now for the $x, we have an interest rate of 5%

This mathematically translates to an interest value of 5/100 * x = 5x/100

For the $y, we have an interest rate of 6% and this mathematically translates to a value of 6/100 * y= 6y/100

The addition of both interests, gives 575

Thus mathematically;

5x/100 + 6y/100 = 575

Multiplying through by 100, we have

5x + 6y = 57500 •••••••••(ii)

From 1, we can have x = 10,000-y

let’s substitute this into equation ii

5(10,000-y) + 6y = 57500

50,000-5y + 6y = 57500

50,000 + y = 57500

y = 57500-50,000

y = 7,500

Recall;

x = 10,000-y

so we have;

x = 10,000-7500 = 2,500

Answer:

[tex]\boxed{x = 251.4 cm}[/tex]

Step-by-step explanation:

Part 1: Sketching the triangle

We are given the angle of elevation, 70°, and the distance along the ground, 86 centimeters. Our unknown is a ladder leaning against the building. Buildings are erected vertically, so the unknown side length is the hypotenuse of the triangle.

We can then sketch this triangle out to visualize it (attachment).

Part 2: Determining what trigonometric ratio can solve the problem

Now, we need to refer to our three trigonometric ratios:

[tex]sin = \frac{opposite}{hypotenuse}[/tex]

[tex]cos = \frac{adjacent}{hypotenuse}[/tex]

[tex]tan = \frac{opposite}{adjacent}[/tex]

Visualizing the sketched triangle, we can assign the three sides their terms in correspondence to the known angle -- this angle cannot be the right angle because the hypotenuse is opposite of it.

Therefore, we know our unknown side length is the hypotenuse of the triangle and because the other side is bordering the 70° angle, it is the adjacent side.

By assigning the sides, we can see that we need to use the trigonometric function that utilizes both the hypotenuse and the adjacent side to find the angle. This is the cosine function.

Part 3: Solving for the unknown variable

Now that we have determined what side we need to solve for and what trigonometric function we are going to use to do so, we just need to plug it all into the equation.

The cosine function is provided: [tex]cos( \alpha) = \frac{adjacent}{hypotenuse}[/tex], where [tex]\alpha[/tex] is the angle. We just need to plug in our values and solve for our unknown side; the hypotenuse.

[tex]cos (70) = \frac{86 cm}{x}[/tex], where x is the unknown side/the hypotenuse.

[tex]x * cos (70) = \frac{86 cm}{x} * x[/tex] Multiply by x on both sides of the equation to eliminate the denominator and make the unknown easier to solve for.

[tex]\frac{xcos (70)}{cos(70)} = \frac{86 cm}{cos(70)}[/tex], Evaluate the second fraction because the first one cancels down to just the unknown, x.

[tex]\frac{86}{cos(70)} = 251.4[/tex], round to one decimal place.

Your final answer is [tex]\boxed{x=251.4cm}[/tex].

Answer:

If the number is x, we can write the following equation:

2 + 10x = 2

10x = 0 so therefore, x must be 0. There is no other number that satisfies this property.

~ ANSWER=1/2 ~

Simple probability is found by counting all the results which fit requirements and dividing by all possible results.

To find probability of two results in a row, multiply chance of first result by chance of second result.

Since you are replacing the marble before the second draw, we don’t have to figure out the various changes in odds for the different possible first draws. It’s just that simple.

There are 5 white marbles

There are 4 red marbles

There are always 20 marbles in all

5/20*4/20=1/4*1/5=1/20 or 1/2

By coincidence, the same as the chance of drawing the white marble in one draw.

Answer:

5/18

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

I took the test and that's the answer.

Answer:

16

Step-by-step explanation:

CHECK THE ATTACHMENT FOR THE FIQURE OF THE QUESTION;

✓The given figure is a special right triangle and it's a 30° 60° 90° angle.

The length of its side have the ratio of

1: √3: 2 i.e adjacent, opposite, Hypotenuse

✓ it has an Hypotenuse which is double in value to the adjacent.

✓ the adjacent ( shortest sides) = 8 unit,

Then the Hypotenuse= ( 2×8)= 16 units

Answer:

[tex]\large \boxed{\sf \ \ \ a+b+c=3 \ \ \ }[/tex]

Step-by-step explanation:

Hello,

[tex]4x^2+2x-1=4(x^2+\dfrac{2}{4}x)-1=4[(x+\dfrac{1}{4})^2-\dfrac{1}{4^2}]-1[/tex]

As

[tex](x+\dfrac{1}{4})^2=x^2+\dfrac{2}{4}x+\dfrac{1^2}{4^2}=x^2+\dfrac{2}{4}x+\dfrac{1}{4^2} \ \ So \\\\x^2+\dfrac{2}{4}x=(x+\dfrac{1}{4})^2-\dfrac{1}{4^2}[/tex]

Let 's go back to the first equation

[tex]4x^2+2x-1=4[(x+\dfrac{1}{4})^2-\dfrac{1}{4^2}]-1=4(x+\dfrac{1}{4})^2-\dfrac{1}{4}-1\\\\=4(x+\dfrac{1}{4})^2-\dfrac{1+4}{4}=\boxed{4(x+\dfrac{1}{4})^2-\dfrac{5}{4}}[/tex]

a = 4

[tex]b=\dfrac{1}{4}\\\\c=-\dfrac{5}{4}[/tex]

[tex]a+b+c=4+\dfrac{1}{4}-\dfrac{5}{4}=\dfrac{4*4+1-5}{4}=\dfrac{12}{4}=3[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

To show that triangle ABC is congruent to triangle XYZ by side-angle-side congruency theorem, BC must be equal to YZ (BC ≅ YZ).

Two triangles are said to be similar if they have the same shape and the corresponding sides are congruent to each other. Also, corresponding angles are congruent.

To show that triangle ABC is congruent to triangle XYZ by side-angle-side congruency theorem, BC must be equal to YZ (BC ≅ YZ).

Find out more on similar triangles at: https://brainly.com/question/2644832

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Answer:

[tex] y = A_o (b)^t[/tex]

With [tex] A_o = 82.6[/tex] the initial amount and t the time on hours and t the time in hours. since the half life is 12 hours we can find the parameter of decay like this:

[tex] 41.3= 82.6(b)^{12}[/tex]

And solving for b we got:

[tex] \frac{1}{2}= b^{12}[/tex]

And then we have:

[tex] b= (\frac{1}{2})^{\frac{1}{12}}[/tex]

And the model would be given by:

[tex] y(t) = 82.6 (\frac{1}{2})^{\frac{1}{12}}[/tex]

Step-by-step explanation:

Assuming this complete question: "A specific radioactive substance follows a continuous exponential decay model. It has a half-life of 12 hours. At the start of the experiment, 82.6g is present. "

For this case we can create a model like this one:

[tex] y = A_o (b)^t[/tex]

With [tex] A_o = 82.6[/tex] the initial amount and t the time on hours and t the time in hours. since the half life is 12 hours we can find the parameter of decay like this:

[tex] 41.3= 82.6(b)^{12}[/tex]

And solving for b we got:

[tex] \frac{1}{2}= b^{12}[/tex]

And then we have:

[tex] b= (\frac{1}{2})^{\frac{1}{12}}[/tex]

And the model would be given by:

[tex] y(t) = 82.6 (\frac{1}{2})^{\frac{1}{12}}[/tex]

Answer:

  88

Step-by-step explanation:

2.75 ft = (2.75 ft)(12 in/ft) = 33 in

At 0.375 inches per plate, there will be ...

  (33 in)/(0.375 in/plate) = 88 plates

There are 88 steel plates in the pile.

Step-by-step explanation:

If the line is parallel to y=2/3x+4 then,

m=m

slope of eqn y=2/3x+4

m=2/3(On comparing with y= mx + c)

the passing point is (3,7) then,

y-y1 = m(x-x1)

y-7=2/3(x-3)

y-7=2/3x -2

y-7= -4x/3

3y-7= -4x

4x + 3y - 7=0

So, The reqd eqn is 4x + 3y - 7 = 0

Answer:  The level of the dose be after 3 hours=  0.03125 mg.

Step-by-step explanation:

General exponential decay equation : [tex]y=A(1-r)^x[/tex] , where A = initial value , r= rate of decay , x =Time period.

Here, drug’s effectiveness  is decreasing exponentially.

AS per given , we have

A= 250 mg

x=3

r= 95% = 0.95

Then, [tex]y=250(1-0.95)^3 = 250(0.05)^3=250*0.000125=0.03125[/tex]

Hence, the level of the dose be after 3 hours = 0.03125 mg.

Answer:

214.34 about (213.75 on calculator)

Step-by-step explanation:

95% of 250=237.5

95% of 237=225.15

95% of 225=213.75

Answer:

y = -7

Step-by-step explanation:

-3x – 2y = -25

Let x = 13

-3 * 13 -2y = -25

-39 -2y = -25

Add 39 to each side

-39+39 -2y = -25+39

-2y =14

Divide by -2

-2y/-2 = 14/-2

y = -7

Answer:

y = -7

Step-by-step explanation:

-3x - 2y = -25

Plug x as 13.

-3(13) - 2y = -25

-39 - 2y = -25

Add 39 on both sides,

- 2y = 14

Divide both sides by -2.

y = -7

Answer:

260

Step-by-step explanation:

By PEMDAS, we know multiplican comes first. 53*5=265. Then, subtract 5 to get 260.

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Answer:

260

Step-by-step explanation:

the rule is to start with multiplication first 53*5=265 then subtract 5

53 × 5-5= 265-5=260