Amira is twice as old as her cousin Pam. Nine years ago, their combined age was 18. What are their present ages?

Answers

Answer 1

Answer:

Amira is currently 24 years old and Pam is currently 12 years old

Step-by-step explanation:

Let Amira's age be [tex]a[/tex] and Pam's age be [tex]p[/tex]. Currently, Amira is twice as old as Pam. Therefore, we can write the equation [tex]a=2p[/tex].

We can write a second equation using the other information given in the question. Nine years ago, Amira and Pam's combined ages was 18. If Amira and Pam are currently [tex]a[/tex] and [tex]p[/tex] years old, respectively, then their respective ages 9 years ago would ben [tex]a-9[/tex] and [tex]p-9[/tex]. Since these add up to 18, we have the equation [tex](a-9)+(p-9)=18[/tex].

Therefore, we have a system of equations:

[tex]\begin{cases}a=2p,\\a-9+p-9=18\end{cases}[/tex]

Substitute the first equation into the second one:

[tex]2p-9+p-9=18[/tex]

Combine like terms:

[tex]3p-18=18[/tex]

Add 18 to both sides:

[tex]3p=36[/tex]

Divide both sides by 3:

[tex]p=\frac{36}{3}=\boxed{12}[/tex]

Now substitute this into any of the equations (I'll choose the first):

[tex]a=2p,\\a=2(12),\\a=\boxed{24}[/tex]

Therefore, Amira is currently 24 years old and Pam is currently 12 years old.


Related Questions

Lem is playing a board game and needs to roll two dice and get a six on both die in order to win the game. What is the probability that Lem will win the game on the next roll? Write your answer as a simplified fraction.

Answers

The probability of getting a 6 on one dice is 1/6

The probability of getting a 6 on both dice would be 1/6 x 1/6 = 1/36

Answer: 1/36

What is the nineteenth term of an arithmetic sequence with first term 9 and common difference 5?

Answers

Answer:

The 19th term is 99.

Step-by-step explanation:

We can write a direct formula and use it to find the 19th term. Recall that the direct formula for an arithmetic sequence is given by:

[tex]x_n = a + d(n-1)[/tex]

Where a is the initial term and d is the common difference.

Since the first term is 9 and the common difference is 5:

[tex]\displaystyle x _ n = 9+5(n-1)[/tex]

To find the 19th term, let n = 19. Thus:

[tex]x_{19} = 9+5(19-1)[/tex]

And evaluate:

[tex]\displaystyle \begin{aligned} x_{19} &= 9+5(18) \\ &= 9+90 \\ &= 99\end{aligned}[/tex]

The 19th term is 99.

Match the word to know with its definition


Expanded form

Product

Place value

Digit


A number that is written as a sum of single digit multiples of powers of 10

Any of the symbols ( 0 to 9 ) that are used to write a number

The result of multiplying two or more numbers together

The value of where a digit is located in a number

Answers

Expanded form
- A number that is written as a sum of single digit multiples of powers of 10.
Consider the number 3,559,761
The expanded form of it is:
3,000,000 + 500,000 + 50,000 + 9,000 + 700 + 60 + 1

Product
- The result of multiplying two or more numbers together.
EXAMPLE:
Multiply 4 x 3 = 12
12 is the product
Product is the answer you get from multiplying two or more numbers together.


Place value
- The value of where a digit is located in a number.
Consider the number “350”
The place value of 3 in 350 is 300
Place value of 5 = 50
Place value of 0 = 0

Digit
- Any of the symbols (0 to 9) that are used to write a number.

I HOPE THIS HELPS!


Can someone quickly answer this please

Answers

Answer:

Step-by-step explanation:

Hello !

(4,4*2,4) + (3,14 * 2,2² )/2 =

10,56 + 7,60 = 18,2 m²

Can someone help me with this answer?

Answers

[tex](4.2 \times {10}^{5}) \times (3.2 \times {10}^{6}) = 15.54 \times {10}^{11} = 1.554 \times {10}^{12} [/tex]

I hope I helped you ^_^

Find the area of each.

Answers

Answer:

14

Step-by-step explanation:

The formula for the area of a triangle is: 1/2 times base times height.

1/2x8x3.5=14

In how many years will the interest of a sum Rs 3600 at the rate of 5.5% per year be Rs 594.8? ​

Answers

Answer:

in 3.04 years the will give required intrest

Find the coordinates of the image of a triangle with vertices A(0, – 3), B(3, 0), and
C(-7, 4) under a rotation of 90° clockwise about the origin.

Answers

Answer:

A'(-3,0), B'(0,-3) and C'(4,7)

Step-by-step explanation:

We are given that the vertices of triangle are A(0,-3), B(3,0) and C(-7,4).

We have to find the coordinates of the image of triangle under a rotation of 90° clockwise about the origin.

90° clockwise about the origin

Rule:[tex](x,y)\rightarrow (y,-x)[/tex]

Using the rule

The coordinates of A'

[tex]A(0,-3)\rightarrow A'(-3,0)[/tex]

The coordinates of B'

[tex]B(3,0)\rightarrow B'(0,-3)[/tex]

The coordinates of C'

[tex]C(-7,4)\rightarrow C'(4,7)[/tex]

Hence, the vertices of image of triangle is given by

A'(-3,0), B'(0,-3) and C'(4,7)

An expression is shown below: \sqrt(50)+\sqrt(2) is it irrational or rational

Answers

Answer:

Irrational

Step-by-step explanation:

It's an irrational number since both of them are irrational

please help! Similarity transformations!! I’ll mark brainliest later on :)

Answers

1. 1/2

2. Y

3. 1 left 3 ups. (-1, 3)

Question 1 of 10
Identify the domain of the function shown in the graph.
10
O A.-1sxs 0
OB. x is all real numbers.
PREVIOUS

Answers

Answer:

The answer would be B. x is all real numbers.

Step-by-step explanation:

It can't be A since the squiggling line is going beyond x = -1 and x = 0. That would've been a vertical line.

Well, good luck on the other 9 problems!

Rebecca can paint a room in 12 hours Guadalupe can paint the same room in 16 hours how long does it take for both Rebecca and Guadalupe to paint the room if they are working together

Answers

Rebecca can paint in 12 hrs (Let Rebecca be R.)
Guadalupe can paint in 16hrs (and Guadalupe G)
How long ? = (RxG) x 24 divided by 2
(12x16)24/2
2304/60
38.4hrs.

Can u help solve this

Answers

Answer:

2

Step-by-step explanation:

slope = rise/run

rise = difference in y

run = difference in x

slope = (8 - 2)/(3 - 0)

slope = 6/3

slope = 2

Answer:

Slope = 2

Step-by-step explanation:

Use the Slope-Formula to find the slope

m = slope

m = change in y/change in x

m = (y2 - y1)/(x2 - x1)

Points: (0, 2) (3, 8) where the first point is x1 & y1 and the second point is x2 & y2.

m = (8 - 2)/(3 - 0)

m = 6/3

m = 2

The slope will be 2

using trig to solve for the missing angle

Answers

Step-by-step explanation:

Since there is a 45 and 90 degree angle, this is a 45-45-90 triangle. The legs are equal in a 45-45-90 ttiangle. The hypotenuse sqr root of 2 times more than the legs. So this means the hypotenuse measure is

[tex]18 \sqrt{2} [/tex]

So we can set up a equation.

[tex] {18}^{2} + {x}^{2} = ({18 \sqrt{2}) }^{2} [/tex]

[tex]x = 18[/tex]

So the missing side is 18

The midpoint of a segment is ( 6, -6) and one endpoint is (13,-1). Find the coordinates of the other endpoint

Answers

So, the formula for finding the midpoint of a segment given the coordinates of its endpoints is:

((x1+ x2)/2, (y1 + y2)/2 {Average of the x coordinates, average of the y coordinates}.

For this problem we know the coordinates of the midpoint along with one of the endpoints.

So the x coordinate of the midpoint (9) must equal (12 + x2)/2.

That is: 9 = (12 + x2)/2 Solve for x2. Follow a similar pattern to find the y coordinate of the unknown endpoint.

5.3.8 Higher / Lower 2.0

Answers

Answer:

Higher...

Step-by-step explanation:

5.3.8 isn't really a legal number... if you meant 5.38 then it would be higher than 2. If you really meant 5.3.8 then I don't know.

Or is this code?

Say you have this: (sorry there's no indentation)

my_float = round(3.3312, 2)

while True:

guess = float(input("Guess my number: "))

if guess > round(my_float, 2):

print ("Too high!")

elif guess < round(my_float, 2):

print ("Too low!")

elif round(guess,2) == round(my_float, 2):

print("Correct!")

break

print("Great job guessing my number!")

You should be able to use the round function just like you do in the if statement. This can be done on a separate line between taking input and the if or it can be done on the same like.

guess = round(guess, 2)

Or:

guess = round(float(input(“Guess my number: “)), 2)

Hope this helped! Have a nice day!

the difference of 8 and 3 is multiplied by one quarter of the sum of 7 and 5​

Answers

Answer:

15

Step-by-step explanation:

the difference of 8 and 3 : 8-3 = 5

sum of 7 and 5 : 7+5 = 12

a quarter of that sum : 12/4 = 3

the difference from before is now multiplied by that quarter : 5 × 3 = 15

I know, you are a beginner, but you don't know basic arithmetic calculation of +, -, × , / ? really ?

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. The solution of the difference of 8 and 3 is multiplied by one-quarter of the sum of 7 and 5 is 15.

What is multiplication?

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

The statement can be solved as shown below,

1.   The difference between 8 and 3,

     8 - 3 = 5

2.   The difference between 8 and 3 is multiplied by one-quarter of the    sum of 7 and 5,

    ​[tex](8-3) \times \dfrac{(7+5)}{4}\\\\= 5 \times \dfrac{12}{4}\\\\= 15[/tex]

Hence, the solution of the difference of 8 and 3 is multiplied by one-quarter of the sum of 7 and 5 is 15.

Learn more about Multiplication:

https://brainly.com/question/14059007

#SPJ2

For what value of k does the linear system below have infinite solutions?
2x - 6y = k
6x - 18y = 30

Answers

Answer:

10

Step-by-step explanation:

The first equation should be the same with the second one, then we will have an infinite number of solutions of this system.

So if I multiply the first equation by 3, it'll be

6x-18y=3k

So if they should be the same, 30=3k

K=10

Find the greatest common factor

Answers

Answer:

3x^2y^2

Step-by-step explanation:

I think:

3*2*x*x*x*y*y*y*y

3*3*x*x*y*y

3*6*x*x*x*y*y

They all have 3x^2y^2 in common.

If the triangle on the grid below is translated three units left and nine units down, what are the coordinates of C"?​

Answers

Answer: (-4,-7)
Explanation: if you just pay attention to the c when you move three units to the left then the x-axis becomes -4, and when you move the y-axis 9 units down it then becomes -7.

[tex]5x- \dfrac{ \sqrt{ 9 { x }^{ 2 } -6x+1 \phantom{\tiny{!}}} }{ 1-3x }[/tex]

Answers

Answer:

[tex]=5x+1[/tex]          or          [tex]=5x-1[/tex]

Step-by-step explanation:

One is given the following equation:

[tex]5x-\frac{\sqrt{9x^2-6x+1}}{1-3x}[/tex]

The problem asks one to simplify the expression, the first step in solving this equation is to factor the equation.  Rewrite the numerator and denominator of the fraction as the product of two expressions. Remember the factoring patterns:

[tex](a-b)^2=a^2-2ab+b^2[/tex]

[tex]=5x-\frac{\sqrt{9x^2-6x+1}}{1-3x}[/tex]

[tex]=5x-\frac{\sqrt{(3x-1)^2}}{-(3x-1)}[/tex]

Now simplify the numerator. Remember, taking the square root of a squared value is the same as taking the absolute value of the expression,

[tex]=5x-\frac{\sqrt{(3x-1)^2}}{1-3x}[/tex]

[tex]=5x-\frac{|3x-1|}{-(3x-1)}[/tex]

Rewrite the expression without the absolute value sign in the numerator. Remember the general rule for removing the absolute value sign:

[tex]|a-b|\\=a -b[/tex]           or           [tex](-a-b) = b-a[/tex]

[tex]=5x-\frac{|3x-1|}{-(3x-1)}[/tex]

[tex]=5x-\frac{3x-1}{-(3x-1)}[/tex]          or          [tex]=5x-\frac{-(3x-1)}{-(3x-1)}[/tex]

Simplify both expressions, reduce by canceling out common terms in both the numerator and the denominator,

[tex]=5x-\frac{3x-1}{-(3x-1)}[/tex]          or          [tex]=5x-\frac{-(3x-1)}{-(3x-1)}[/tex]

[tex]=5x-(-1)[/tex]          or          [tex]=5x-(1)[/tex]

Simplify further by rewriting the expression without the parenthesis, remember to distribute the sign outside the parenthesis by the terms inside of the parenthesis; note that negative times negative equals positive.

[tex]=5x-(-1)[/tex]          or          [tex]=5x-(1)[/tex]

[tex]=5x+1[/tex]          or          [tex]=5x-1[/tex]

2. Use factoring to determine the x-intercepts and vertex of the quadratic function
y = 2x2 + 5x -3
(answer plsss)

Answers

Step-by-step explanation:

I solved for the x hope it's correct

Which expressions are equivalent to 5+(-3)(6x-5)5+(−3)(6x−5)5, plus, left parenthesis, minus, 3, right parenthesis, left parenthesis, 6, x, minus, 5, right parenthesis ? Choose all answers that apply: Choose all answers that apply: (Choice A) A 18x-2018x−2018, x, minus, 20 (Choice B) B 3x-33x−33, x, minus, 3 (Choice C) C None of the above

Answers

5+(-18x+15)5 + (-18x +15)5

5+ (-90x +75) + (-90x + 75)

-180x +155

let's see the alternatives:

a) -2000x - 2018 -> -200x - 201,8

b) -30x - 33 -> -180x -198

c) none of the above

so, c is the right one

hope it helps :)

Answer:

ITS C

Step-by-step explanation:

Which three lengths could be the lengths of the sides of a triangle? 21 cm, 7 cm, 11 cm 7 cm, 23 cm, 11 cm, 12 cm, 7 cm, 19 cm 10 cm, 15 cm, 23 cm

Answers

Answer:

  (d) 10 cm, 15 cm, 23 cm

Step-by-step explanation:

21 cm, 7 cm, 11 cm — 7+11 < 21 . . . not a triangle

7 cm, 23 cm, 11 cm — 7+11 < 23 . . . not a triangle

12 cm, 7 cm, 19 cm — 7+12 = 19 . . . not a triangle

10 cm, 15 cm, 23 cm — 10+15 > 23 . . . can form a triangle

__

The sum of the two shortest sides must exceed the length of the longest.

of (3, -2) reflected across the line x = 1 is?

Answers

Answer:  (-1, -2)

===========================================================

Explanation:

Plot (3,-2) on the xy grid. Then draw a vertical line through 1 on the x axis.

Note that the horizontal distance from the point to the line is exactly 2 units. We move 2 units to the left to go from (3,-2) to (1,-2). Then we move another 2 units to the left to arrive at the final destination of (-1, -2)

In short, (3,-2) reflects over the vertical line x = 1 to get to (-1, -2)

See the diagram below.


Matching the Meaning of Key Features of a Graph

Match the key aspect of a function's graph with its meaning.

Answers

Answer:

a goes to 3

b goes to 4

c goes to 1

d goes to 2

Step-by-step explanation:

just did it right on edge

An iceberg weighs 450,000 pounds if it loss 0.2% of its weight in a day, what is its new weight at the end of the day

Answers

Answer:

449 100

Step-by-step explanation:

0.2% × 450000÷ 100=900

450000-900= 449 100

Answer:

Step-by-step explanation:

The answer is 449100 pounds .

-6>t-(-13)
slove for the inequality

Answers

Answer:

-19>t

Step-by-step explanation:

-6>t-(-13)

-6>t +(13)

Subtract 13 from each side

-6-13 > t+13-13

-19>t

Do you think mathematics is used when collecting and reporting your data ? Give your reasons.

Answers

yes because everyone needs mathematics

mathematics are everywhere even if u said u dont like math u still cant get away with math

PPPPPlease HHHHHelp, see the picture!

Answers

Answer:  Choice D)  5.2 * 10^7

This value is 52 million.

===================================================

Explanation:

During the first year, the well produced 50,000 quarts of water per week. Since there are 52 weeks in a year, the well produced 52*50,000 = 2,600,000 quarts in total for that first year alone. This is the initial value 'a'.

The common ratio is r = 1 - 0.05 = 0.95

So we have a geometric sequence with starting term a = 2,600,000 and common ratio r = 0.95

Since -1 < r < 1 is true, we can use the infinite geometric series formula as shown below.

S = a/(1 - r)

S = (2,600,000)/(1-0.95)

S = 52,000,000

S = 5.2 * 10^7 which is choice D

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