Ask question

Ask question

All categories

3 years ago

11

The length of a rectangular picture frame is 4 inches less than three times the width. The perimeter is 136 inches. Find the len

gth and the width.

1 answer:

natulia [17]3 years ago

6 0

Answer:

The width of the rectangle is 18 inches, and the length is 50 inches

Step-by-step explanation:

We can designate a variable, x, to represent the width of the rectangle. To represent the length and widths of the rectangle, we can say that the length is 3x-4 and the width is just x. We can then write an equation for the perimeter and solve:

2(3x-4) + 2x = 136

6x - 8 + 2x = 136

8x - 8 = 136

8x = 144

x = 18

To calculate the length

(3x - 4)

3(18) - 4 = 50 in

You might be interested in

Classify the variable as discrete or continuous. weights of backpacks of first graders on a school bus

kondor19780726 [428]

The weights of their backpacks would be discrete

4 0

3 years ago

Evaluate the expression when y=6 and x = 35.<br> x-3y

vredina [299]

Answer:

17

Step-by-step explanation:

Given: y = 6; x + 35

Step 1: Equation

x - 3y

Step 2: Substitution

35 - 3(6)

Step 3: Solving

35 - 18 = 17

Answer:

17

Hope This Helps :)

4 0

3 years ago

Read 2 more answers

Milan fills an aquarium to a depth of 3/8 meters in 6 minutes.

Nadya [2.5K]

Answer:

1/16m per minute

Step-by-step explanation:

If Milan fills the aquarium to a depth of 3/8 in 6 minutes then just divide 3/8 by 6 to find how much she fills in 1 minute

5 0

3 years ago

P(x) = x + 1x² – 34x + 343<br> d(x)= x + 9

Feliz [49]

Answer:

$x=\frac{9}{d-1},\:P=\frac{-297d+378}{\left(d-1\right)^2}+343$

Step-by-step explanation:

Let us start by isolating x for dx = x + 9.

dx - x = x + 9 - x > dx - x = 9.

Factor out the common term of x > x(d - 1) = 9.

Now divide both sides by d - 1 > $\frac{x\left(d-1\right)}{d-1}=\frac{9}{d-1};\quad \:d\ne \:1$ . Go ahead and simplify.

$x=\frac{9}{d-1};\quad \:d\ne \:1$ .

Now, $\mathrm{For\:}P=x+1x^2-34x+343, \mathrm{Subsititute\:}x=\frac{9}{d-1}$ .

$P=\frac{9}{d-1}+1\cdot \left(\frac{9}{d-1}\right)^2-34\cdot \frac{9}{d-1}+343$ .

Group the like terms... $1\cdot \left(\frac{9}{d-1}\right)^2+\frac{9}{d-1}-34\cdot \frac{9}{d-1}+343$ .

$\mathrm{Add\:similar\:elements:}\:\frac{9}{d-1}-34\cdot \frac{9}{d-1}=-33\cdot \frac{9}{d-1}$ > $1\cdot \left(\frac{9}{d-1}\right)^2-33\cdot \frac{9}{d-1}+343$ .

Now for $1\cdot \left(\frac{9}{d-1}\right)^2 > \mathrm{Apply\:exponent\:rule}: \left(\frac{a}{b}\right)^c=\frac{a^c}{b^c} > \frac{9^2}{\left(d-1\right)^2} = 1\cdot \frac{9^2}{\left(d-1\right)^2}$ .

$\mathrm{Multiply:}\:1\cdot \frac{9^2}{\left(d-1\right)^2}=\frac{9^2}{\left(d-1\right)^2}$ .

Now for $33\cdot \frac{9}{d-1} > \mathrm{Multiply\:fractions}: \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c} > \frac{9\cdot \:33}{d-1} > \frac{297}{d-1}$ .

Thus we then get $\frac{9^2}{\left(d-1\right)^2}-\frac{297}{d-1}+343$ .

Now we want to combine fractions. $\frac{9^2}{\left(d-1\right)^2}-\frac{297}{d-1}$ .

$\mathrm{Compute\:an\:expression\:comprised\:of\:factors\:that\:appear\:either\:in\:}\left(d-1\right)^2\mathrm{\:or\:}d-1 > This\: is \:the\:LCM > \left(d-1\right)^2$

$\mathrm{For}\:\frac{297}{d-1}:\:\mathrm{multiply\:the\:denominator\:and\:numerator\:by\:}\:d-1 > \frac{297}{d-1}=\frac{297\left(d-1\right)}{\left(d-1\right)\left(d-1\right)}=\frac{297\left(d-1\right)}{\left(d-1\right)^2}$

$\frac{9^2}{\left(d-1\right)^2}-\frac{297\left(d-1\right)}{\left(d-1\right)^2} > \mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}> \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}$

$\frac{9^2-297\left(d-1\right)}{\left(d-1\right)^2} > 9^2=81 > \frac{81-297\left(d-1\right)}{\left(d-1\right)^2}$ .

Expand $81-297\left(d-1\right) > -297\left(d-1\right) > \mathrm{Apply\:the\:distributive\:law}: \:a\left(b-c\right)=ab-ac$ .

$-297d-\left(-297\right)\cdot \:1 > \mathrm{Apply\:minus-plus\:rules} > -\left(-a\right)=a > -297d+297\cdot \:1$ .

$\mathrm{Multiply\:the\:numbers:}\:297\cdot \:1=297 > -297d+297 > 81-297d+297 > \mathrm{Add\:the\:numbers:}\:81+297=378 > -297d+378 > \frac{-297d+378}{\left(d-1\right)^2}$

Therefore $P=\frac{-297d+378}{\left(d-1\right)^2}+343$ .

Hope this helps!

5 0

3 years ago

The slope of (17,2) and (18,-17)

Ahat [919]

<u>m= -19/1</u>

We need to use the slope equation

$\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

We are working with the points,

(17, 2) and (18, -17)

x1 y1 x2 y2

$\frac{-17-2}{18-17}$

<u>m= -19/1</u>

4 0

3 years ago