The sum of two numbers is twenty. Three times the smaller is equal to twotimes the larger. Find the two numbers.

Answers

Answer 1

Answer:

the smaller number is 8, and the larger number is 12, and they indeed add up to 20, and three times the smaller number (3 * 8) is equal to two times the larger number (2 * 12).

Let's call the two numbers x and y, with x being the smaller number and y being the larger number.

We have two pieces of information from the problem:

1. The sum of the two numbers is twenty:

x + y = 20

2. Three times the smaller number is equal to two times the larger number:

3x = 2y

Now, we can solve this system of linear equations.

First, we can solve equation (1) for x:

x = 20 - y

Now, substitute this expression for x into equation (2):

3(20 - y) = 2y

Now, distribute the 3 on the left side:

60 - 3y = 2y

Now, isolate the variables on one side of the equation and constants on the other side:

60 = 2y + 3y

Combine like terms:

60 = 5y

Now, divide by 5 to solve for y:

y = 60 / 5

y = 12

Now that we have found the value of y, we can substitute it back into equation (1) to find x:

x + 12 = 20

Subtract 12 from both sides:

x = 20 - 12

x = 8

So, the two numbers are:

x = 8 (smaller number)

y = 12 (larger number)

Therefore, the smaller number is 8, and the larger number is 12, and they indeed add up to 20, and three times the smaller number (3 * 8) is equal to two times the larger number (2 * 12).

To know more about number:

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Answer 2

Answer:

Answer:

The smaller number is 8

The larger number is 12

Step-by-step explanation:

Let the smaller number be x

Let the larger number be y

Translate the question and solve ;

$x +y = 20\n3(x) =2(y) \n\n\begin{bmatrix}x+y=20\n 3x=2y\end{bmatrix}\n\n\mathrm{Isolate}\:x\:\mathrm{for}\:x+y=20:\quad x=20-y\n\n\mathrm{Subsititute\:}x=20-y\n\n\begin{bmatrix}3\left(20-y\right)=2y\end{bmatrix}\n\n\mathrm{Isolate}\:y\:\mathrm{for}\:3\left(20-y\right)=2y:\quad y=12\n\n\mathrm{For\:}x=20-y\n\n\mathrm{Subsititute\:}y=12\n\nx=20-12\n\nSimplify\n\nx =8\n\nx=8,\:y=12$

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Solve using elimination, 2x+5y=2 3x-5y=53

Answers

2x + 5y =2
(+) 3x - 5y =53
-------------------------
5x + 0 = 55

Then finish it.

5x = 55
x = 11

Substitute x = 11,

2(11) + 5y = 2
22 - 2 + 5y = 0
20 + 5y = 0
5y = -20
y= -4

2x+5y=2
3x-5y=53
---------------
+
2x+3x=2+53
5x=55 / : 5
x=11

x=11
3x-5y=53

x=11
3*11-5y=53

x=11
33-5y=53

x=11
-5y=53-33

x=11
-5y=20 / : (-5)

x=11
y=-4

Debra and Ian shared in $1,000,000 estate. If Ian received $125,000 and debra the rest, what fraction of the estate did Debra receive?

Answers

Answer: Fraction of the estate Debra will received is $(7)/(8)$

Step-by-step explanation:

Since we have given that

Amount shared by Debra and Lan = $1000,000

Amount received by Lan = $125,000

According to question, Debra received the rest.

So, Amount received by Debra is given by

$\$1000000-\$125000\n\n=\$875000$

Fraction of the estate Debra will receive is given by

$(875000)/(1000000)\n\n=(875)/(1000)\n\n=(35)/(40)\n\n=(7)/(8)$

Hence, Fraction of the estate Debra will received is $(7)/(8)$

Debra received 7/8
if you divide 1,000,000 by 125,000 you get 8. which means Ian got 1/8 of the money. leaving 7/8 for Debra

How many sixths are there in 3 1/3

Answers

convert the mixed number into an improper fraction 10/3 now turn the denominator into 6 10/3× 2/2 = 20/6 there are 20 sixths in 3 1/3

Solve the equation
1/2log(x-2) = 3log2-3/2log(x-2)
all logs are in base 5

Answers

no clue sorry i tried my best

1. Which of the following represents a function? x -2 -1 0 -1 -2
y 2 3 4 5 6

x 1 1 0 2 2
y 1 2 3 4 5

x 1 2 3 4 5
y 2 2 3 3 4

x 1 1 1 1 1
y 2 3 4 5 6

2. What is the domain of the function: {(2, 1); (4, 2); (6, 3); (8, 4)}?
{1, 2, 3, 4}
{1, 2, 3, 4, 6, 8}
{2, 4, 6, 8}
{6, 8}

3. What is the range of the function: {(2, 1); (4, 2); (6, 3); (8, 4)}?
{1, 2, 3, 4}
{1, 2, 3, 4, 6, 8}
{2, 4, 6, 8}
{6, 8}

4. Suppose p varies directly with d, and p = 7 when d = 3. What is the value of d when p = 28?
4/3
12
16
140/3

5. Given the function T(z) = 7 − z, find T(−4).
−11
11
−3
3
6. What is the equation of the graph?

f(x) = − |x| + 2
f(x) = − |x| − 2
f(x) = − |x + 2|
f(x) = − |x − 2|
7. The number of calories burned, C, varies directly with the time spent exercising, t. When Dennis walks for 4 hours, he burns 800 calories. Which of the following equations shows this direct linear variation?
C = t
C = 800t
C = 4t
C = 200t

Answers

$1.\n\#1\ not\ because\ for\ x=-2\to y=2\ and\ y=6\n\#2\ not\ because\ for\ x=1\to y=1\ and\ y=2\n\#3\ \boxed{IT'S\ OK}\leftarrow answer\n\#4\ not\ because\ for\ x=1\to y=2\ and\ y=3\ and...$

$2.\ (x;\ y)\to x\in D-domain\n\ntherefore:\n\n\{(2;1);\ (4;2);\ (6;\ 3);\ (8;\ 4)\}\n\n\boxed{The\ domain\ D=\{2;\ 4;\ 6;\ 8\}}$

$3.\ (x;\ y)\to y\in Range\n\n\{(2;\ 1);\ (4;\ 2);\ (6;\ 3);\ (8;\ 4)\}\n\n\boxed{the\ range:\{1;\ 2;\ 3;\ 4\}}$

$4.\n(p)/(d)=constans\n\n(28)/(d)=(7)/(3)\ \ \ \ |cross\ multiply\n\n7\cdot d=3\cdot28\ \ \ \ |divide\ both\ sides\ by\ 7\n\nd=(84)/(7)\n\n\boxed{d=12}$

$5.\ T(z)=7-z\n\nT(-4)\to z=-4\n\nput\ the\ value\ of\ z\ to\ (7-z):\n\nT(-4)=7-(-4)=7+4=\boxed{11}$

$6.\ny=|x|\to\ the\ axis\ of\ symmetry\ is\ OY\ (S_(OY))\n\ny=-|x|\to\ the\ axis\ of\ symmetry\ is\ OX\ (S_(OX))\n\nso....\ the\ y-intercept\ is\ (0;\ 2),\ therefore\ answer\ is\ \boxed{f(x)=-|x|+2}$

$7.\n\begin{array}{ccc}C&-&t\n800&-&4\end{array}\ \ \ \ |cross\ multiply\n\n4C=800t\ \ \ \ \ |divide\ both\ sides\ by\ 4\n\n\boxed{C=200t}$

1. 3rd one, because for each x there's only one y.

2. The domain are x's, so it's {2, 4, 6, 8}

3. The range are y's, so it's {1, 2, 3, 4}

4.
$p=kd\n7=3k\nk=(7)/(3)\np=(7)/(3)d\nd=(3)/(7)p\nd=(3)/(7)\cdot28=12$

5. $T(-4)=7-(-4)=7+4=11$

6. $f(x) = - |x| + 2$

7.
$C=kt\n800=4k\nk=200\nC=200t$

Which of the following is x⁴ + y⁴ identically equal to?(A) (x² + y²)(x + y)(x - y)
(B) (x² + xy + y²)(x² - xy + y²)
(C) (x² + √2xy + y²)(x² - √2xy + y²)
(D) (x² + √3xy + y²)(x² - √3xy + y²)
(E) (x + y)²(x-y)²
Can someone explain me how to make it step by step?

Answers

$x^4+y^4 \n \nx^4= (x^2)^2, y^4 = (y^2)^2 \n \nx^4- y^4= (x^2)^2 - (y^2)^2 = (x^2 + y^2)(x^2 - y^2 )\n \nnow \ you \ can \ factor \ the \ second \ again \n \n(hopefully \ you \ see \ that \ it's \ a \ difference \ of \ squares): \n \nx^4 - y^4= (x^2 + y^2)(x + y)(x - y) \n \nAnswer : \ (A) \ (x^2 + y^2)(x + y)(x - y) \n \n \n a^2-b^2 =(a-b)(a+b)$

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