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3 years ago

Which ordered pair (a,b) is a solution to the given system of linear equations.

Mathematics

2 answers:

Readme [11.4K]3 years ago

7 0

Answer:

Step-by-step explanation:

egoroff_w [7]3 years ago

6 0

Answer:

A. (-13,-3)

Step-by-step explanation:

Solve the system of two equations:

$\left\{\begin{array}{l}-2a+3b=14\\a-4b=3\end{array}\right.$

From the second equation:

$a=3+4b$

Substitute it into the first equation:

$-2(3+4b)+3b=14\\ \\-6-8b+3b=14\\ \\-8b+3b=14+6\\ \\-5b=20\\ \\5b=-20\\ \\b=-4$

So,

$a=3+4b=3+4\cdot (-4)=3-16=-13$

The solution is (-13,-4)

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Two sets of equatic expressions are shown below in various forms: Line 1: x2 + 3x + 2 (x + 1)(x + 2) (x + 1.5)2 − 0.25 Line 2: x

kherson [118]

Answer: The correct line is

$\textup{Line 1 :}x^2+3x+2=(x+1)(x+2)=(x+1.5)^2-0.25.$

Step-by-step explanation: We are given the following two sets of quadratic expressions in various forms:

$\textup{Line 1: }x^2+3x+2=(x+1)(x+2)=(x+1.5)^2-0.25,\\\\\textup{Line 2 :}x^2+5x+6=(x+2)(x+3)=(x+2.5)^2+6.25.$

We are to select one of the lines from above that represent three equivalent expressions.

We can see that there are three different forms of a quadratic expression in each of the lines:

First one is the simplified form, second is the factorised form and third one is the vertex form.

So, to check which line is correct, we need to calculate the factorised form and the vertex form from the simplified form.

We have

$\textup{Line 1: }\\\\x^2+3x+2\\\\=x^2+2x+x+2\\\\=x(x+2)+1(x+2)\\\\=(x+1)(x+2),$

and

$x^2+3x+2\\\\=x^2+2\times x\times 1.5+(1.5)^2-(1.5)^2+2\\\\=(x+1.5)^2-2.25+2\\\\=(x+1.5)^2-0.25.$

So,

$\textup{Line 1 :}x^2+3x+2=(x+1)(x+2)=(x+1.5)^2-0.25.$

Thus, Line 1 contains three equivalent expressions.

Now,

$\textup{Line 2: }\\\\x^2+5x+6\\\\=x^2+3x+2x+6\\\\=x(x+3)+2(x+3)\\\\=(x+2)(x+3),$

and

$x^2+5x+6\\\\=x^2+2\times x\times 2.5+(2.5)^2-(2.5)^2+6\\\\=(x+2.5)^2-6.25+6\\\\=(x+2.5)^2-0.25\neq (x+2.5)^2+6.25.$

So,

$\textup{Line 2 :}x^2+3x+2=(x+1)(x+2)=(x+1.5)^2+6.25.$

Thus, Line 2 does not contain three equivalent expressions.

Hence, Line 1 is correct.

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3 years ago

Anyone knows the answer?

SIZIF [17.4K]

Asa. angle side angle.

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3 years ago

Which point is located on the x-axis of a coordinate grid?

Leokris [45]

I don't see the grid? did you attach a photo?

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3 years ago

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Natali [406]

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2 years ago

Jordan is cutting a 2 meter by 1 1/4 meter into two pieces by its diagonal line

Airida [17]

Question:

Jordan is cutting a 2 meter by $1\frac{1}{4}$ meter piece of rectangular paper into two pieces along its diagonal. what is the area of each of the pieces?

Answer:

Area of each piece of paper is $1 \frac{1}{4} \ m^2$ .

Solution:

Length of the paper = 2 m

Width of the paper = $1\frac{1}{4}$ m = $\frac{5}{4}$ m

<em>Area of the rectangle = length × width</em>

$$=2\times \frac{5}{4}$

$$= \frac{5}{2} \ m^2$

<em>Diagonal of a rectangle divides it into two equal parts.</em>

Area of each piece = Area of the rectangle ÷ 2

$$=\frac{ \frac{5}{2}}{2}$

$$=\frac{5}{4} \ m^2$

$$=1 \frac{1}{4} \ m^2$

Area of each piece of paper is $1 \frac{1}{4} \ m^2$ .

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3 years ago