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4 years ago

Multiply (3x – 5y)(2x + 3y)

Mathematics

1 answer:

Ghella [55]4 years ago

8 0

Answer:

6x² - xy - 15y²

Step-by-step explanation:

To multiply these two binomials together, we can use FOIL. FOIL stands for:

First: Multiply the first terms of the binomials together.

Outer: Multiply the first term of the first binomial by the second term of the second binomial.

Inner: Multiply the second term of the first binomial by the first term of the second binomial.

Last: Multiply the second (last) terms of the two binomials together.

(3x - 5y)(2x + 3y) = (3x)(2x) + (3x)(3y) + (-5y)(2x) + (-5y)(3y)

= 6x² + 9xy - 10xy - 15y²

= 6x² - xy - 15y²

I hope you find my answer helpful.

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What is the equation of the circle shown?

Mkey [24]

Answer:

(x + 4)² + (y - 2)² = 8

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

Here (h, k ) = (- 4, 2 ) , then

(x - (- 4))² + (y - 2)² = r²

(x + 4)² + (y - 2)² = r²

CA is the radius of the circle

To find r use the distance formula

r = $\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }$

with (x₁, y₁ ) = C(- 4, 2) and (x₂, y₂ ) = A(- 2, 4)

r = $\sqrt{(-2+4)^2+(4 -2)^2}$

= $\sqrt{2^2+2^2}$

= $\sqrt{8}$ , then r² = ( $\sqrt{8}$ )² = 8

Then

(x + 4)² + (y - 2)² = 8 ← equation of circle

5 0

3 years ago

The function f(x) = x is translated using the rule (x, y) - (x - 6, y + 9) to create A(x).

anyanavicka [17]

It seems the correct function you need to mention is f(x) = sqrt x

so, I am assuming $f(x) = \sqrt{x}$ and will solve the question based on it.

Answer:

Check the explanation

Step-by-step explanation:

Given the function

$f(x) = \sqrt{x}$

As the function is translated according to the rule

(x, y) → (x - 6, y + 9)

Translation of the function $f(x) = \sqrt{x}$ 6 units to the left will bring the function

$g(x) = \sqrt{x+6}$

Translation of the function $g(x) = \sqrt{x+6}$ 9 units up will bring the function

$A\left(x\right)=\sqrt{x+6}+9$

Determining the range of $A\left(x\right)=\sqrt{x+6}+9$

As we know that the range is the set of dependent values for which the function is defined.

$\mathrm{The\:range\:of\:an\:radical\:function\:of\:the\:form}\:c\sqrt{ax+b}+k\:\mathrm{is}\:\:f\left(x\right)\ge \:k$

$k=9$

$f\left(x\right)\ge \:9$

$\mathrm{Range\:of\:}\sqrt{x+6}+9:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)\ge \:9\:\\ \:\mathrm{Interval\:Notation:}&\:[9,\:\infty \:)\end{bmatrix}$

Therefore, the expression describes the range of A(x) will be:

$f\left(x\right)\ge \:\:9\:or\:y\:\ge \:\:\:9$

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Find the gradient of the line Joining the points p(-2,6) and Q(3,-2)

Rudiy27

Answer:

$- \frac{8}{5}$

Step-by-step explanation:

$\boxed{gradient = \frac{y1 - y2}{x1 - x2} }$

(x₁, y₁) is the 1st coordinate while (x₂, y₂) is the 2nd coordinate.

Gradient of the line

$= \frac{6 - ( - 2)}{ - 2 - 3}$

$= \frac{6 + 2}{ - 5}$

$= - \frac{8}{5}$

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The percent of the discount is 28 percent off

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