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3 years ago

Is (1, 4) a solution to this system of equations? 8x + 3y = 20 x + 4y = 17

Mathematics

1 answer:

vampirchik [111]3 years ago

6 0

Answer:

Yes.

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Coordinates (x, y)
Systems of Equations

Step-by-step explanation:

Step 1: Define

Identify

8x + 3y = 20

x + 4y = 17

(1, 4)

Step 2: Check

Plug and verify the coordinates is a solution.

Substitute in point [1st Equation]: 8(1) + 3(4) = 20
Multiply: 8 + 12 = 20
Add: 20 = 20 $\checkmark$
Substitute in point [2nd Equation]: 1 + 4(4) = 17
Multiply: 1 + 16 = 17
Add: 17 = 17 $\checkmark$

∴ Since both equations work out, (1, 4) is a solution to the systems of equations.

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The general term for the sequence 2, 4, 8, 16, 32, . . . is

Nuetrik [128]

We are given

sequence is 2 , 4 , 8 ,16 , 32 , .....

Firstly , we will check whether it is geometric sequence

Checking geometric sequence:

We will find common ratio between successive terms

and then we check whether they are equal

r1=(second term)/(first term)

$r_1=\frac{4}{2}=2$

r2=(third term)/(second term)

$r_2=\frac{8}{4}=2$

r3=(fourth term)/(third term)

$r_3=\frac{16}{8}=2$

r4=(fifth term)/(fourth term)

$r_4=\frac{32}{16}=2$

we can see that all four ratios are same

$r_1=r_2=r_3=r_4=2$

so, this is geometric sequence

Calculation of general term:

We got

common ratio is

$r=2$

Let's assume

number of terms is n

first term is 2

$a_1=2$

now, we can use formula

$a_n=a_1 (r)^{n-1}$

we can plug values

and we get

$a_n=2(2)^{n-1}$

$a_n=2^1(2)^{n-1}$

$a_n=(2)^{n-1+1}$

$a_n=(2)^{n}$ ..................Answer

5 0

2 years ago

The perimeter of a rectangle is 140 feet. The length of the rectangle is 6 more than 2 times the width. What is the length of th

Alja [10]

The equations we get are
l = 6 + 2w (We get this from "The length of the rectangle is 6 more than 2 times the width.")
and
2l + 2w = 140 (We get this from the perimeter. Two times the length plus two times the width equals the perimeter of a quadrilateral.)

The first equation can be written as
l - 2w = 6

So now we have
2l + 2w = 140
l - 2w = 6
____________
Add the two equations.
We get 3l = 146

Divide by 3 on both sides.
l = 48 $\frac{2}{3}$

Your answer is 48 $\frac{2}{3}$ .

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Answer:

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Step-by-step explanation: