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KengaRu [80]
1 year ago
6

Which shows the phrase "the product of a number and 3" as a variable expression?

Mathematics
1 answer:
JulijaS [17]1 year ago
3 0

The algebraic expression for the word phrase "the product of a number and 3" as a variable expression is 3z

<h3>How to write an algebraic expression for the word phrase "the product of a number and 3" as a variable expression?</h3>

The word phrase is given as:

"the product of a number and 3"

Represent the number with z

So, the word phrase can be rewritten as:

"the product of a number z and 3"

The product of a number z and 3 is represented as:

z * 3

When evaluated,, the expression becomes

z * 3 = 3z

Hence, the algebraic expression for the word phrase "the product of a number and 3" as a variable expression is 3z

Read more about algebraic expression at

brainly.com/question/4344214

#SPJ1

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Answer:

2x + 3y + 5z = 9

Step-by-step explanation:

The normal defines all the planes perpendicular to that vector. To isolate to a single plane, just apply the known point.

ax + by + cz = d

2x + 3y + 5z = d

2(1) + 3(-1) + 5(2) = 9

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Recall the equation for a circle with center (h, k) and radius r. At what point in the first quadrant does the line with equatio
lina2011 [118]

Answer:

The point of intersection is:

\displaystyle \left(\frac{6\sqrt{5}}{5}, \frac{3\sqrt{5}}{5}+5\right)\approx \left(2.68, 6.34)

Step-by-step explanation:

We want to find the point in QI at which the line with the equation:

y=0.5x+5

Intersect a circle with a radius of 3 and a center of (0, 5).

First, write the equation of a circle. The equation for a circle is given by:

(x-h)^2+(y-k)^2=r^2

Where (<em>h, k</em>) is the center and <em>r</em> is the radius.

Since our center is (0, 5), <em>h</em> = 0 and <em>k</em> = 5. The radius is 3. So, <em>r</em> = 3. Substitute:

(x-0)^2+(y-5)^2=(3)^2

Simplify:

x^2+(y-5)^2=9

At the point where the two equations intersect, its <em>x-</em>coordinate and <em>y-</em>coordinate will be the same. Therefore, we can substitute the equation of the line into the equation of the circle and solve for <em>x</em>. So:

x^2+((0.5x+5)-5)^2=9

Simplify:

x^2+(0.5x)^2=9

Square:

x^2+0.25x^2=9

Combine like terms:

\displaystyle 1.25x^2=\frac{5}{4}x^2=9

Solve for <em>x: </em>

<em />\displaystyle \begin{aligned} x^2&=\frac{36}{5} \\ x&=\pm\sqrt{\frac{36}{5}} \\ x&\Rightarrow \frac{6}{\sqrt{5}}=\frac{6\sqrt{5}}{5}\approx2.68\end{aligned}<em />

Note that since we are looking for the point of intersection in QI, <em>x</em> should be positive. So, we can ignore the negative answer.

To find the <em>y-</em>coordinate, substitute the <em>x-</em>value back into either equation. Using the linear equation:

\displaystyle y=0.5\left(\frac{6\sqrt{5}}{5}\right)+5=\frac{3\sqrt{5}}{5}+5\approx 6.34

So, the point of intersection in QI is:

\displaystyle \left(\frac{6\sqrt{5}}{5}, \frac{3\sqrt{5}}{5}+5\right)\approx \left(2.68, 6.34)

6 0
2 years ago
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