All categories

1 year ago

The quotient of two numbers is 3 and their sum is 8 what are he two numbers

Mathematics

1 answer:

Nezavi [6.7K]1 year ago

4 0

<h2>Translating Word Equations into Numerical Equations</h2>

To change words into equations, we can recognize keywords that translate into operations and/or numbers:

quotient = divide
a number/the number/two numbers = variables
sum = add

<h2>Solving the Question</h2>

Let the two numbers be a and b.

We're given:

quotient of a and b is 3
⇒ $\dfrac{a}{b}=3$
sum of a and b is 8
⇒ $a+b=8$

First, isolate a in the first equation and substitute it in the second equation to solve for b:

$\dfrac{a}{b}=3\\\\a=3b$

$a+b=8\\3b+b=8\\4b=8\\b=2$

Therefore, one of the numbers is 2. Substitute this into one of our equations to solve for a:

$a+b=8\\a+2=8\\a=6$

Therefore, the other number is 6.

<h2>Answer</h2>

The two numbers are 2 and 6.

You might be interested in

A group of four friends went out for dinner. Their bill came to $50.95. They also need to pay 8% sales tax, and want to tip thei

bija089 [108]

Answer:

Enter cost and tip percent to get a tip amount and total dinner amount. Also split the total amount; divide among any number of people. ... Money, Pay, Taxes. > Tip ... Enter your meal or dinner cost along with the tip percentage. ... To calculate a gratuity or tip on any calculator it is a simple multiplication. ... All rights reserved

Step-by-step explanation:

After eating at your favorite restaurant, you know that the bill before tax is $52.60 and that the sales tax rate is 8%. You decide to leave a 20% tip for the waiter based on the pre-tax amount. How much ... To figure out the tip, you need to find 20% of $52.60. 0.2 \times 52.6

3 0

2 years ago

The answer and how you got it

mart [117]

The answer is 12
12-(5+3)=4
4+8=12

8 0

3 years ago

Find the area of the largest rectangle (with sides parallel to the coordinate axes) that can be inscribed in the region enclosed

garik1379 [7]

F(x) = 18-x^2 is a parabola having vertex at (0, 18) and opening downwards.
g(x) = 2x^2-9 is a parabola having vertex at (0, -9) and opening upwards.
By symmetry, let the x-coordinates of the vertices of rectangle be x and -x => its width is 2x.
Height of the rectangle is y1 + y2, where y1 is the y-coordinate of the vertex on the parabola f and y2 is that of g.
=> Area, A
= 2x (y1 - y2)
= 2x (18 - x^2 - 2x^2 + 9)
= 2x (27 - 3x^2)
= 54x - 6x^3
For area to be maximum, dA/dx = 0 and d²A/dx² < 0
=> 54 - 18x^2 = 0
=> x = √3 (note: x = - √3 gives the x-coordinate of vertex in second and third quadrants)

d²A/dx² = - 36x < 0 for x = √3
=> maximum area
= 54(√3) - 6(√3)^3
= 54√3 - 18√3
= 36√3.

4 0

2 years ago

Amelia launched her science fair rocket, and then backed away. The path of the rocket is given by the equation below, where y is

Mamont248 [21]

Answer:

1)The rocket hit the ground at $x = \frac{5}{4}$

2)The maximum height of the rocket = 12.468 feet

Step-by-step explanation:

Step(i):-

Given equation

y = -2 x² + 5 x + 7 ...(i)

Differentiating equation (i) with respective to 'x' , we get

$\frac{dy}{dx} = -2( 2x) +5(1) = -4x +5$

Equating zero

$\frac{dy}{dx} = 0$

⇒ -4 x +5 =0

⇒ -4 x = -5

⇒ $x = \frac{5}{4}$

The rocket hit the ground at $x = \frac{5}{4}$

Step(ii):-

$\frac{dy}{dx} = -4x +5$ ...(ii)

Again differentiating equation (ii) with respective to 'x' , we get

$\frac{d^{2} y}{dx^{2} } = - 4(1)$

The maximum height at x = $\frac{-5}{4}$

y = -2 x² + 5 x + 7

$y = -2 (\frac{5}{4})^{2} + 5 (\frac{5}{4} ) + 7$

$y = \frac{-2(25)+ 25 (16)+7(64)}{64}$

$y = \frac{798}{64} = 12.468 feet$

The maximum height of the rocket = 12.468 feet

4 0

2 years ago

Show all work. PLEASE HELP!!!!

34kurt

(a) Using the table, give the values fo rthe inverse

1) original table of values:

x      1     2     3    4    5

f(x)   0     1     1    5    3

2) The inverse of the function is obtained by exchanging x and f(x), this is:

                   ( x, f(x) ) → ( f(x), x)

3) So, the table of values of the inverse of the given function is:

x          0    1     1      5     3

f⁻¹ (x)   0     1     2     3     4

(b) Is the inverse a function?

No, the inverse is not a function, since the table of the inverse shows that the x -value 1 has two different images.

This ambigüity is opposite to the definition of a function, which requires that any input value has only one output. For that reason, the inverse is not a function. You cannot tell whether the image of 1 is 1 or 2, because both are images of the same value.

7 0

3 years ago