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3 years ago

I need help with this

Mathematics

2 answers:

masya89 [10]3 years ago

8 0

Hello there! With finding the area of the rectangle in this scenario, we have to multiply binomials by doing distribution or in this case, the FOIL method. This means, multiply the terms by the first terms of each parenthesis, the outer terms of the parenthesis, inner terms of the parenthesis, and the last terms in both parenthesis. It's a bit like regular distribution. Set it up like this:

(4x - 7)(x + 3)

Now, multiply the terms. 4x * x is 4x². 4x * 3 is 12x. -7 * x is -7x. -7 * 3 is -21. Combine like terms in order to get 4x² + 5x - 21. The answer is D.

Note: If there is a negative in front of the number you are multiplying, you incorporate the negative in that number. x² is there, because two x's are being multiplied together. Be sure to incorporate these steps and solve the right way and be aware of the symbols. Otherwise, you might make a mistake.

rodikova [14]3 years ago

5 0

You need to expand (4x-7)(x+3), multiplying each term in the first bracket by each term in the second bracket, in order to get 4x^2+5x-21. Hope that helps!

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Bogdan [553]

Answer:

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Step-by-step explanation:

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4 years ago

Find the standard form of the equation for the conic section represented by x^2 + 10x + 6y = 47.

Levart [38]

Answer:

The standard form of the equation for the conic section represented by $x^2\:+\:10x\:+\:6y\:=\:47$ is:

$4\left(-\frac{3}{2}\right)\left(y-12\right)=\left(x-\left(-5\right)\right)^2$

Step-by-step explanation:

We know that:

$4p\left(y-k\right)=\left(x-h\right)^2$ is the standard equation for an up-down facing Parabola with vertex at (h, k), and focal length |p|.

Given the equation

$x^2\:+\:10x\:+\:6y\:=\:47$

Rewriting the equation in the standard form

$4\left(-\frac{3}{2}\right)\left(y-12\right)=\left(x-\left(-5\right)\right)^2$

Thus,

The vertex (h, k) = (-5, 12)

Please also check the attached graph.

Therefore, the standard form of the equation for the conic section represented by $x^2\:+\:10x\:+\:6y\:=\:47$ is:

$4\left(-\frac{3}{2}\right)\left(y-12\right)=\left(x-\left(-5\right)\right)^2$

where

vertex (h, k) = (-5, 12)

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3 years ago

The general form of the equation of a circle is x2+y2−4x−8y−5=0.

valentina_108 [34]

Answer:

centre = (2, 4)

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Given

x² + y² - 4x - 8y - 5 = 0

Rearrange the x/y terms together and add 5 to both sides

x² - 4x + y² - 8y = 5

Use the method of completing the square on both the x/y terms

add ( half the coefficient of the x/y terms )² to both sides

x² + 2(- 2)x + 4 + y² + 2(- 4)y + 16 = 5 + 4 + 16

(x - 2)² + (y - 4)² = 25 ← in standard form

with centre (2, 4) and r = $\sqrt{25}$ = 5

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4 years ago

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2 years ago