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3 years ago

Find the slope of the line. A: -2/3 B: 2/3 C: 3:2 D: -3/2

Mathematics

1 answer:

tia_tia [17]3 years ago

3 0

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points (look at the picture) (0, 1) and (-2, -2). Substitute:

$m=\dfrac{-2-1}{-2-0}=\dfrac{-3}{-2}=\boxed{\dfrac{3}{2}}\to\boxed{D}$

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3 years ago

Which products result in a perfect square trinomial? Select three options.

Kazeer [188]

Answer:

Second option: $(xy+x)(xy+x)$

Third option: $(2x-3)(-3+2x)$

Fifth option: $(4y^2+25)(25+4y^2)$

Step-by-step explanation:

By definition, a perfect square trinomial can be obtained by squaring binomials.

Then:

$(a+b)^2=(a+b)(a+b)=a^2+2ab+b^2\\\\(a-b)^2=(a-b)(a-b)=a^2-2ab+b^2$

Knowing this, to obtain a perfect square trinomial, the binomials that you multiply must be equals.

Therefore, the products result in a perfect square trinomial are:

$(xy+x)(xy+x)=(xy+x)^2=(xy)^2+2(xy)(x)+x^2=x^2y^2+2x^2y+x^2$

$(2x-3)(-3+2x)=(2x-3)^2=(2x)^2-2(2x)(3)+3^2=4x^2-12x+9$

$(4y^2+25)(25+4y^2)=(4y^2+25)^2=(4y^2)^2+2(4y^2)(25)+25^2=16y^4+200y^2+625$

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3 years ago

Read 2 more answers

Which expressions are equivalent to 10a - 25 + 5b

sergey [27]

Answer:

Step-by-step explanation:

$10a-25+5b\\\\-2(-5a-25+5b)=(-2)(-5a)+(-2)(-25)+(-2)(5b)\\=10a+50-10b\qquad NOT\\\\(2a-5+b)(5)=(2a)(5)+(-5)(5)+(b)(5)=10a-25+5b\qquad YES\\\\10(a-2.5+0.5b)=(10)(a)+(10)(-2.5)+(10)(0.5b)\\=10a-25+5b\qquad YES\\\\(-2a+5-b)(-5)=(-2a)(-5)+(5)(-5)+(-b)(-5)\\=10a-25+5b\qquad YES\\\\-10(-a-2.5-0.5b)=(-10)(-a)+(-10)(-2.5)+(-10)(-0.5b)\\=10a+25+5b\qquad NOT$

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3 years ago

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Ilia_Sergeevich [38]

Solve for p by simplifying both sides of the equation, then isolating the variable.
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