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2 years ago

Solve by the substitution method. 6x + 8y = 0 -7x + y = 31

Mathematics

1 answer:

jekas [21]2 years ago

7 0

Answer:

(-4, 3)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Algebra I

Solving systems of equations using substitution/elimination

Step-by-step explanation:

Step 1: Define Systems

6x + 8y = 0

-7x + y = 31

Step 2: Rewrite Systems

-7x + y = 31

Add 7x to both sides: y = 7x + 31

Step 3: Redefine Systems

6x + 8y = 0

y = 7x + 31

Step 4: Solve for x

Substitution

Substitute in y: 6x + 8(7x + 31) = 0
Distribute 8: 6x + 56x + 248 = 0
Combine like terms: 62x + 248 = 0
Isolate x term: 62x = -248
Isolate x: x = -4

Step 4: Solve for y

Define equation: -7x + y = 31
Substitute in x: -7(-4) + y = 31
Multiply: 28 + y = 31
Isolate y: y = 3

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Answer:

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Step-by-step explanation:

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2 years ago

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Which represents a quadratic function ?

mars1129 [50]

Answer:

$\boxed{\boxed{B.\ f(x)=\dfrac{3}{4}x^2+2x-5}}$

Step-by-step explanation:

Quadratic function-

It is a function that can be represented by an equation of the form $f = ax^2 + bx + c$ , where $a\neq 0$

In a quadratic function, the greatest power of the variable is 2.

As in the first option the highest power is 3, so it is not a quadratic function.

Even though the power of x is 2 in the third option, but as it is in the denominator, so the overall power of x becomes -2. Hence it is not a quadratic function.

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3 years ago

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Determine whether or not the vector field is conservative. if it is, find a function f such that f = ∇f. if the vector field is

amm1812

$\dfrac{\partial f}{\partial x}=3y^2z^3\implies f(x,y,z)=3xy^2z^3+g(y,z)$

$\dfrac{\partial f}{\partial y}=6xyz^3+\dfrac{\partial g}{\partial y}=6xyz^3$
$\implies\dfrac{\partial g}{\partial y}=0\implies g(y,z)=h(z)$

$\dfrac{\partial f}{\partial z}=9xy^2z^2+\dfrac{\mathrm dh}{\mathrm dz}=9xy^2z^2$
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3 years ago

What steps should be taken to calculate the volume of the prism? Select three options. A rectangular prism with a length of 9 an

fgiga [73]

The steps to be taken to determine the volume of the rectangular prism are:

Use A = bh to find the area of the base.

Use V = Bh to find the volume of the prism.

Volume of the prism, V = (228)(6) = 1,368 feet cubed.

<h3>How to Find the Volume of a Rectangular Prism?</h3>

A rectangular prism has a height, base, and width. The volume of the rectangular prism can be found by using the following steps:

Find the base area of the rectangular prism using the formula, A = bh, where b is the base length and h is the height of the base.
Then, find the Volume using the formula, V = Bh, where B is the base area and h is the height of the prism.

Parameters are:

Length of prism = 9 and one-half feet,

Width of prism = 24 feet,

Height of prism = 6 feet

Given the dimensions of the rectangular prism above, do the following:

Find the area of the base of the rectangular prism:

Area of base = (9 1/2)(24) = 228 cm²

Find the Volume of the prism using V = Bh :

Volume of the prism = (228)(6) = 1,368 feet cubed.

Therefore, the steps to be taken to determine the volume of the rectangular prism are:

Use A = bh to find the area of the base.
Use V = Bh to find the volume of the prism.
Volume of the prism, V = (228)(6) = 1,368 feet cubed.

Learn more about volume of the rectangular prism on:

brainly.com/question/12917973

#SPJ1

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1 year ago

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Sergio [31]

Step-by-step explanation:

Set A is a subset of set B if all the elements of A are also the elements of Set B.. (common element)

The above set have 0 common elements so.. if there is no common element and are subsets then it means that there arent any elements in both the sets

so, the answer for the question would be "both the Sets A and B are the empty sets"

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1 year ago