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2 years ago

What is the area of the triangle shown below?

Mathematics

2 answers:

Nimfa-mama [501]2 years ago

7 0

Answer:

300 mm squared

Step-by-step explanation:

mojhsa [17]2 years ago

3 0

Answer:

The answer is 150 mm squared.

Step-by-step explanation:

Area of Triangle = 1/2bh

Base = 15 mm

Height = 20 mm

= 1/2 (15)(20)

= 1/2 (300)

= 150 mm squared

Area = 150 mm squared

Hope I helped ya.

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According to the Rational Root Theorem, Negative seven-eighths is a potential rational root of which function?

viktelen [127]

Answer A should be correct

8 0

3 years ago

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Consider the following initial-value problem. (x + y)2 dx + (2xy + x2 − 2) dy = 0, y(1) = 1 Let ∂f ∂x = (x + y)2 = x2 + 2xy + y2

IRISSAK [1]

$(x+y)^2\,\mathrm dx+(2xy+x^2-2)\,\mathrm dy=0$

Suppose the ODE has a solution of the form $F(x,y)=C$ , with total differential

$\dfrac{\partial F}{\partial x}\,\mathrm dx+\dfrac{\partial F}{\partial y}\,\mathrm dy=0$

This ODE is exact if the mixed partial derivatives are equal, i.e.

$\dfrac{\partial^2F}{\partial y\partial x}=\dfrac{\partial^2F}{\partial x\partial y}$

We have

$\dfrac{\partial F}{\partial x}=(x+y)^2\implies\dfrac{\partial^2F}{\partial y\partial x}=2(x+y)$

$\dfrac{\partial F}{\partial y}=2xy+x^2-2\implies\dfrac{\partial^2F}{\partial x\partial y}=2y+2x=2(x+y)$

so the ODE is indeed exact.

Integrating both sides of

$\dfrac{\partial F}{\partial x}=(x+y)^2$

with respect to $x$ gives

$F(x,y)=\dfrac{(x+y)^3}3+g(y)$

Differentiating both sides with respect to $y$ gives

$\dfrac{\partial F}{\partial y}=2xy+x^2-2=(x+y)^2+\dfrac{\mathrm dg}{\mathrm dy}$

$\implies x^2+2xy-2=x^2+2xy+y^2+\dfrac{\mathrm dg}{\mathrm dy}$

$\implies\dfrac{\mathrm dg}{\mathrm dy}=-y^2-2$

$\implies g(y)=-\dfrac{y^3}3-2y+C$

$\implies F(x,y)=\dfrac{(x+y)^3}3-\dfrac{y^3}3-2y+C$

so the general solution to the ODE is

$F(x,y)=\dfrac{(x+y)^3}3-\dfrac{y^3}3-2y=C$

Given that $y(1)=1$ , we find

$\dfrac{(1+1)^3}3-\dfrac{1^3}3-2=C\implies C=\dfrac13$

so that the solution to the IVP is

$F(x,y)=\dfrac{(x+y)^3}3-\dfrac{y^3}3-2y=\dfrac13$

$\implies\boxed{(x+y)^3-y^3-6y=1}$

5 0

2 years ago

(SELECT ALL THAT APPLY)

steposvetlana [31]

The sequences of transformations that could be applied to the parent function will be:

reflect over the y-axis, vertically stretch by a factor of 3, and then shift down 1 unit
shift right 1 unit, reflect over the y-axis, and then vertically stretch by a factor of 3.
reflect over the x-axis, vertically stretch by a factor of 3, and then shift down 1 unit.

<h3>What is transformation?</h3>

A transformation of a function is a function that turns one function or graph into another, usually related function or graph.

In this case, the sequences of transformations could be applied to the parent function f(x) = x to obtain the graph of g.

Learn more about transformation on:

brainly.com/question/4289712

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1 year ago

What scale factor was applied to the first rectangle to get the resulting image? Enter your answer as a decimal in the box. A re

kicyunya [14]

Answer:

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