A classroom board is 23 inches wide and 17 inches tall. Juan

What is the slope of –3x + 5y = 10? A. m = B. m = 5 C. m = – D. m = –3

nika2105 [10]

Answer:

The slope is 3/5

Step-by-step explanation:

–3x + 5y = 10

Rewrite the equation in slope intercept form y = mx+b where m is the slope and b is the y intercept

Add 3x to each side

5y = 3x+10

Divide by 5

y = 3/5 x + 10/2

The slope is 3/5

7 0

2 years ago

Determine the coordinates of the point p on the line y=-x+6 such that p is equidistant from the points a(10,-10) and o(0,0) (tha

Katena32 [7]

Solution,

Let P = ( x, -x + 6) = (x, 6 - x)

We want to solve this

( Distance from P to (0,0) )^2 = (Distance from P to (10, -10) )^2

x^2 + (6 - x)^2 = [ ( x - 10)^2 + ( 6 - x + 10)^2

x^2 + x^2 - 12x + 36 = x^2 - 20x + 100 + x^2 - 32x + 256 simplify

-12x + 36 = -52x + 356

40x = 320

x = 8

And y = -(8) + 6 = -2

So...P = ( 8, -2)

In mathematics, an equation is an equation that expresses two equations by joining them with an equal sign =. Equations in other languages and the word their relatives can have slightly different meanings; for example, in French, an equation is defined as containing one or more variables, but in English, it is an equal sign.

A well-formed expression consisting of two combined equations is an equation, and a variable makes the equation true. The variable for which the equation must be solved is also called the unknown, and the value of the unknown that satisfies the equation is called the solution of the equation. There are two types of equations: identities and constraint equations. The ID applies to all values of the variable. Constraint equations apply only to specific values of variables

Learn more about Equations here: brainly.com/question/2972832

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6 0

2 years ago

Can you help me please.

Snezhnost [94]

Answer:

-86

Step-by-step explanation:

-102-

98 so the answer is -86

5 0

2 years ago

The ratio of men to women working for a company is 8 to 5. If there are 234 employees total, how many women work for the company

Dimas [21]

Answer:

144

Step-by-step explanation:

The ratio of men to women working for a company is 8 to 5.

Total men and women working as per the ratio is 8+5 = 13

So the ratio of men to total is

the ratio of women to total is

there are 234 employees total

To find the number of men works , we make a proportion

Cross multiply it

8 * 234 = 13x

1872 = 13x

Divide by 13 on both sides

x= 144

3 0

2 years ago

Read 2 more answers

A homeowner plans to enclose a 200 square foot rectangular playground in his garden, with one side along the boundary of his pro

Anestetic [448]

Answer:

Therefore the length and width of the playground are 15.5 feet and 12.9 feet respectively.

Step-by-step explanation:

Given that, a homeowner plans to enclose a 200 square foot rectangle playground.

Let the width of the playground be y and the length of the playground be x which is the side along the boundary.

The perimeter of the playground is = 2(length +width)

=2(x+y) foot

The material costs $1 per foot.

Therefore total cost to give boundary of the play ground

=$[ 2(x+y)×1]

=$[2(x+y)]

But the neighbor will play one third of the side x foot.

So the neighbor will play $=\$(\frac13x)$

Now homeowner's total cost for the material is

$=\$[ 2(x+y)-\frac13x]$

$=\$[2x+2y-\frac13x]$

$=\$[2y+x+x-\frac13x]$

$=\$[2y+x+\frac{3x-x}{3}]$

$=\$[2y+x+\frac{2}{3}x]$

$=\$[2y+\frac53x]$

$\therefore C(x)=2y+\frac53x$

where C(x) is total cost of material in $.

Given that the area of the playground is 200.

We know that,

The area of a rectangle is =length×width

=xy square foot

∴xy=200

$\Rightarrow y=\frac{200}{x}$

Putting the value of y in C(x)

$\therefore C(x)=2(\frac{200}{x})+\frac53x$

The domain of C is $(0,\infty )$ .

$\therefore C(x)=2(\frac{200}{x})+\frac53x$

Differentiating with respect to x

$C'(x)= - \frac{400}{x^2}+\frac53$

Again differentiating with respect to x

$C''(x) = \frac{800}{x^3}$

To find the critical point set C'(x)=0

$\therefore 0= - \frac{400}{x^2}+\frac53$

$\Rightarrow \frac{400}{x^2}=\frac{5}{3}$

$\Rightarrow x^2 =\frac{400\times 3}{5}$

$\Rightarrow x=\sqrt{240}$

$\Rightarrow x=15.49 \approx15.5$

Therefore

$\left C''(x) \right|_{x=15.5}=\frac{800}{15.5^3}>0$

Therefore at x= 15.5 , C(x) is minimum.

Putting the value of x in $y=\frac{200}{x}$ we get

$\therefore y=\frac{200}{15.5}$

=12.9

Therefore the length and width of the playground are 15.5 feet and 12.9 feet respectively.

6 0

3 years ago