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Anna [14]
2 years ago
8

Series of math questions

Mathematics
1 answer:
nordsb [41]2 years ago
8 0

\huge\fbox{Answer ☘}

<h2>1 ) </h2>

when x = 3 ; y = 2

\bold\blue{✯\:\:\:2x + y}

substitue x = 3 and y = 2 in the given equation !

\bold{2(3) + 2 = 6 + 2 } \\  \bold{ =  > 8}

<h2>—————————————</h2>

<h2>2 ) </h2>

We've to divide 328 in the ratio of 1 : 3

let the respective distribution be x and 3x.

Then ,

\bold{x + 3x = 328} \\\bold{ 4x = 328 }\\ \bold{x =  \cancel\frac{328}{4} } \\  \\ \bold{x = 82}

the respective shares are :

x = $82

3x = $246

<h2>—————————————</h2>

<h2>3 ) </h2>

6 pens cost $90

therefore ,

cost of 1 pen =

\cancel \frac{90}{6}  = 15 \\

further ,

cost of 9 such pens = $15 × 9 = $135

<h2>—————————————</h2>

<h2>4 )</h2>

0.5 of a pound = 113.398 grams

<h2>—————————————</h2>

hope helpful~

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Which operation can you perform to both sides of the equation below in order to isolate x? X+1=12
Leviafan [203]

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Step-by-step explanation:

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Two functions are shown in the table below. Function 1 2 3 4 5 6 f(x) = −x2 + 4x + 12 g(x) = −x + 6 Complete the table on your o
Kruka [31]

For \fbox{\begin \\\math{x}=6\\\end{minispace}} the function f(x)=-x^{2} +4x+12 and g(x)=-x+6 has same value.

Step by step explanation:  

The given functions are,

f(x)=-x^{2}+4x+12

g(x)=-x+6

Step 1:  

Substitute x=1 in f(x)=-x^{2} +4x+12 to obtain the value of f(1).

f(1)=-1^{2} +4(1)+12\\f(1)=-1+4+12\\f(1)=15

Substitute x=1 in g(x)=-x+6 to obtain the value of g(1) .

g(1)=-1+6\\g(1)=5

Step 2:

Substitute x=2 in f(x)=-x^{2} +4x+12 to obtain the value of f(2).

f(2)=-2^{2} +4(2)+12\\f(2)=-4+8+12\\f(2)=16

Substitute x=2 in g(x)=-x+6 to obtain the value of g(2) .

g(2)=-2+6\\g(2)=4

Step 3:

Substitute x=3 in f(x)=-x^{2} +4x+12 to obtain the value of f(3).

f(3)=-3^{2} +4(3)+12\\f(3)=-9+12+12\\f(3)=15

Substitute x=3 in g(x)=-x+6 to obtain the value of g(3) .

g(3)=-3+6\\g(3)=3

Step 4:

Substitute x=4 in f(x)=-x^{2} +4x+12 to obtain the value of f(4).

f(4)=-4^{2} +4(4)+12\\f(4)=-16+16+12\\f(4)=12

Substitute x=4 in g(x)=-x+6 to obtain the value of g(4) .

g(4)=-4+6\\g(4)=2

Step 5:

Substitute x=5 in f(x)=-x^{2} +4x+12 to obtain the value of f(5).

f(5)=-5^{2} +4(5)+12\\f(5)=-25+20+12\\f(5)=7

Substitute x=5 in g(x)=-x+6 to obtain the value of g(5) .

g(5)=-5+6\\g(5)=1

Step 6:

Substitute x=6 in f(x)=-x^{2} +4x+12 to obtain the value of f(6).

f(6)=-6^{2} +4(6)+12\\f(6)=-36+24+12\\f(6)=0

Substitute x=6 in g(x)=-x+6 to obtain the value of g(6) .

g(6)=-6+6\\g(6)=0

Step 7:

As per the given condition f(x)=g(x).

(a). Substitute f(x)=-x^{2} +4x+12 and g(x)=-x+6 in above equation.

-x^{2} +4x+12=-x+6

(b). Multiply with -1 on both sides.

x^{2} -4x-12=x-6

(c). Shift the term x-6 to left hand side.

x^{2} -4x-12-x+6=0\\x^{2} -5x-6=0

(d). Split the middle term in such a way that its sum is 5 and multiplication is 6.

x^{2} -(6-1)x-6=0\\x^{2} -6x+x-6=0\\x(x-6)+1(x-6)=0\\(x+1)(x-6)=0\\x=-1 ,6

It is observed from the above solution that for x=6 both the functions f(x) and g(x) has same value.

Direct method:

f(x)=g(x)\\\Leftrightarrow-x^{2} +4x+12=-x+6\\\Leftrightarrow-x^{2} +4x+12+x-6=0\\\Leftrightarrow-x^{2} +5x+6=0\\\Leftrightarrow-x^{2} +6x-x+6=0\\\Leftrightarrow x^{2} -6x+x-6=0\\\Leftrightarrow x(x-6)+1(x-6)=0\\\Leftrightarrow(x+1)(x-6)=0\\\Leftrightarrow x=6,-1

The table for the function f(x)=-x^{2} +4x+12 and g(x)=-x+6 is attached below.

Learn more:  

1. what is the y-intercept of the quadratic function f(x) = (x – 6)(x – 2)? (0,–6) (0,12) (–8,0) (2,0) brainly.com/question/1332667

2. which is the graph of f(x) = (x – 1)(x + 4)?  brainly.com/question/2334270  

Answer details:  

Grade: Middle school.  

Subjects: Mathematics.  

Chapter: Function.

Keywords: Function, Middle term split method, Binomial,Quadratic, Polynomial, Factorized, Perfect square, Zeros, Zeros of a function, Expression, Equation, x, x^2, x^3, -x^2+4x+12, -x+6, roots of equation.

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3 years ago
5. Ricky invested $1000 in an account at 8% interest compounded quarterly. How much money will he have earned on the account aft
Ipatiy [6.2K]

Answer:

1,741.02

Step-by-step explanation:

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3 years ago
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