All categories

3 years ago

When three times the sum of a number and seven is increased by ten, the result is four. What is the number ?

Mathematics

1 answer:

densk [106]3 years ago

4 0

Answer:

x=9 :))

Step-by-step explanation:

First set up your equation.

"3 times" is multiplication

"THE SUM of A NUMBER and seven" that is parenthesis because of the multiplication before it

"is increased by ten" that is an addition at the end

Now we have 3(x+7)+10=4

Solve your equation!

Distribute the 3 now we have 3x+21+10=4

Add like terms

now it should look like this... 3x+31=4

Subtract 31 from both sides and it looks like...

3x=27

Divide by the x-value

x=9

You might be interested in

Geometry helppp please ;c

nignag [31]

What’s the question?

4 0

3 years ago

Read 2 more answers

Given the quadratic equation <img src="https://tex.z-dn.net/?f=y%20%3D%202%28x%20-1%29%5E%7B2%7D%20%2B%208" id="TexFormula1" tit

Sunny_sXe [5.5K]

Answer:

Part 1) "a" value is $2$

Part 2) The vertex is the point $(1,8)$

Part 3) The equation of the axis of symmetry is $x=1$

Part 4) The vertex is a minimum

Part 5) The quadratic equation in standard form is $y=2x^{2}-4x+10$

Step-by-step explanation:

we know that

The equation of a vertical parabola into vertex form is equal to

$y=a(x-h)^{2}+k$

where

(h,k) is the vertex of the parabola

if a > 0 then the parabola open upward (vertex is a minimum)

if a < 0 then the parabola open downward (vertex is a maximum)

The equation of the axis of symmetry of a vertical parabola is equal to the x-coordinate of the vertex

$x=h$

In this problem we have

$y=2(x-1)^{2}+8$ -----> this is the equation in vertex form of a vertical parabola

The value of $a=2$

a>0 then the parabola open upward (vertex is a minimum)

The vertex is the point $(1,8)$

$(h,k)=(1,8)$

The equation of the axis of symmetry is $x=1$

The equation of a vertical parabola in standard form is equal to

$y=ax^{2}+bx+c$

Convert vertex form in standard form

$y=2(x-1)^{2}+8$

$y=2(x^{2}-2x+1)+8$

$y=2x^{2}-4x+2+8$

$y=2x^{2}-4x+10$

see the attached figure to better understand the problem

7 0

3 years ago

An artificial lake is in the shape of a rectangle and has an area of 9/20 square mile the width of the lake is 1/5 the length of

DIA [1.3K]

Answer: The dimensions are:   " 1.5 mi.  × ³⁄₁₀ mi. " .
_______________________________________________
{ length = 1.5 mi. ; width = ³⁄₁₀  mi. } .
________________________________________________
Explanation:
___________________________________________
Area of a rectangle:

A = L * w ;

in which: A = Area = (9/20) mi.² ,
L = Length = ?
w = width = (1/5)*L = (L/5) = ?
________________________________________
A = L * w ; we want to find the dimensions; that is, the values for
"Length (L)" and "width (w)" ;
_______________________________________
Plug in our given values:
_______________________________________
(9/20) mi.² = L * (L/5) ; in which: "w = L/5" ;

→ (9/20) = (L/1) * (L/5) = (L*L)/(1*5) = L² / 5 ;

   ↔ L² / 5 = 9/20 ;

  → (L² * ? / 5 * ?) = 9/20 ?

→ 20÷5 = 4 ; so; L² *4 = 9 ;

    ↔ 4 L² = 9 ;

→ Divide EACH side of the equation by "4" ;

→ (4 L²) / 4 = 9/4 ;
______________________________________
to get: → L² = 9/4 ;
Take the POSITIVE square root of each side of the equation; to isolate "L" on one side of the equation; and to solve for "L" ;
___________________________________________

→   ⁺√(L²) = ⁺√(9/4) ;

→   L = (√9) / (√4) ;

→ L = 3/2 ;

→ w = L/5 = (3/2) ÷ 5 = 3/2 ÷ (5/1) = (3/2) * (1/5) = (3*1)/(2*5) = 3/10;
________________________________________________________
Let us check our answers:
_______________________________________
(3/2 mi.) * (3/10 mi.) =? (9/20) mi.² ??

→ (3/2)mi. * (3/10)mi. = (3*3)/(2*10) mi.² = 9/20 mi.² ! Yes!
______________________________________________________
So the dimensions are:

Length = (3/2) mi. ; write as: 1.5 mi.

width = ³⁄₁₀ mi.
___________________________________________________
or; write as: " 1.5 mi. × ³⁄₁₀ mi. " .
___________________________________________________

7 0

3 years ago

Write an absolute value equation with-1 and 5 as the solution.

Dvinal [7]

Answer:

it is detailed solution. please mark brainlest.

Thank you have a nice day