All categories

3 years ago

The perimeter of a rectangular field is 354 yards. If the width of the field is 82 yards, what is its length

Mathematics

2 answers:

Talja [164]3 years ago

8 0

The answer of the length is 95

GenaCL600 [577]3 years ago

4 0

Length is 95 yards.

The perimeter of a rectangle is the sum of four sides. The four sides are either its length or width.

A rectangle has four sides where its angles are all right angles and its opposite sides are congruent or of equal size.

Perimeter = 2length + 2width ==> P = 2L + 2W

354 = 2L + 2(82)
354 = 2L + 164
to get the length. we must transfer all like signs.
2L = 354 - 164
2L = 190
2L / 2 = 190 / 2
L = 95 yards.

You might be interested in

Can someone pls help for brainlest

Sergio039 [100]

Answer:

144

Step-by-step explanation:

5 0

3 years ago

The ___ of a parabola is the line, along with a point not on the line, which is used to generate a parabola.

enot [183]

Answer:

Directrix

Step-by-step explanation:

The <u>directrix</u> of a parabola is the line, along with a point not on the line (which is the <em>focus</em>), which is used to generate a parabola. The <em>directrix</em> is parallel either to the x- or y-axis, and is perpedicular to the parabola's axis of symmetry (at x = h).

Therefore, the correct answer is "<u>directrix</u>."

3 0

2 years ago

Company A: $39.99 per month no installation fee

Svetlanka [38]

Company A represents a proportional relationship, while company B does not.

<h3>Proportional relationship</h3>

The general format of a equation representing a proportional relationship is given as follows:

y = rx.

A proportional relationship is a special case of a linear function, having an intercept of zero.

Then, the output variable y is calculated as the multiplication of the input variable x by the constant of proportionality k.

The costs for each company after x months, in this problem, are represented as follows:

A(x) = 39.99x.

B(x) = 34.99x + 50.

Company B has an intercept different of zero, hence it is not a proportional relationship, while Company A, with an intercept of zero, represents a proportional relationship.

<h3>Missing Information</h3>

The complete problem is:

Two companies offer digital cable television as described below.

Company A: $39.99 per month no installation fee

Company B: $34.99 per month with a $50 installation fee

For each company tell whether the relationship is proportional between months of service and total cost is a proportional relationship. Explain why or why not

More can be learned about proportional relationships at brainly.com/question/10424180

#SPJ1

6 0

1 year ago

Match each vector operation with its resultant vector expressed as a linear combination of the unit vectors i and j.

Cloud [144]

Answer:

3u - 2v + w = 69i + 19j.

8u - 6v = 184i + 60j.

7v - 4w = -128i + 62j.

u - 5w = -9i + 37j.

Step-by-step explanation:

Note that there are multiple ways to denote a vector. For example, vector u can be written either in bold typeface "u" or with an arrow above it $\vec{u}$ . This explanation uses both representations.

$\displaystyle \vec{u} = \langle 11, 12\rangle =\left(\begin{array}{c}11 \\12\end{array}\right)$ .

$\displaystyle \vec{v} = \langle -16, 6\rangle= \left(\begin{array}{c}-16 \\6\end{array}\right)$ .

$\displaystyle \vec{w} = \langle 4, -5\rangle=\left(\begin{array}{c}4 \\-5\end{array}\right)$ .

There are two components in each of the three vectors. For example, in vector u, the first component is 11 and the second is 12. When multiplying a vector with a constant, multiply each component by the constant. For example,

$3\;\vec{v} = 3\;\left(\begin{array}{c}11 \\12\end{array}\right) = \left(\begin{array}{c}3\times 11 \\3 \times 12\end{array}\right) = \left(\begin{array}{c}33 \\36\end{array}\right)$ .

So is the case when the constant is negative:

$-2\;\vec{v} = (-2)\; \left(\begin{array}{c}-16 \\6\end{array}\right) =\left(\begin{array}{c}(-2) \times (-16) \\(-2)\times(-6)\end{array}\right) = \left(\begin{array}{c}32 \\12\end{array}\right)$ .

When adding two vectors, add the corresponding components (this phrase comes from Wolfram Mathworld) of each vector. In other words, add the number on the same row to each other. For example, when adding 3u to (-2)v,

$3\;\vec{u} + (-2)\;\vec{v} = \left(\begin{array}{c}33 \\36\end{array}\right) + \left(\begin{array}{c}32 \\12\end{array}\right) = \left(\begin{array}{c}33 + 32 \\36+12\end{array}\right) = \left(\begin{array}{c}65\\48\end{array}\right)$ .

Apply the two rules for the four vector operations.

$\displaystyle \begin{aligned}3\;\vec{u} - 2\;\vec{v} + \vec{w} &= 3\;\left(\begin{array}{c}11 \\12\end{array}\right) + (-2)\;\left(\begin{array}{c}-16 \\6\end{array}\right) + \left(\begin{array}{c}4 \\-5\end{array}\right)\\&= \left(\begin{array}{c}3\times 11 + (-2)\times (-16) + 4\\ 3\times 12 + (-2)\times 6 + (-5) \end{array}\right)\\&=\left(\begin{array}{c}69\\19\end{array}\right) = \langle 69, 19\rangle\end{aligned}$

Rewrite this vector as a linear combination of two unit vectors. The first component 69 will be the coefficient in front of the first unit vector, i. The second component 19 will be the coefficient in front of the second unit vector, j.

$\displaystyle \left(\begin{array}{c}69\\19\end{array}\right) = \langle 69, 19\rangle = 69\;\vec{i} + 19\;\vec{j}$ .

$\displaystyle \begin{aligned}8\;\vec{u} - 6\;\vec{v} &= 8\;\left(\begin{array}{c}11\\12\end{array}\right) + (-6) \;\left(\begin{array}{c}-16\\6\end{array}\right)\\&=\left(\begin{array}{c}88+96\\96 - 36\end{array}\right)\\&= \left(\begin{array}{c}184\\60\end{array}\right)= \langle 184, 60\rangle\\&=184\;\vec{i} + 60\;\vec{j} \end{aligned}$ .

$\displaystyle \begin{aligned}7\;\vec{v} - 4\;\vec{w} &= 7\;\left(\begin{array}{c}-16\\6\end{array}\right) + (-4) \;\left(\begin{array}{c}4\\-5\end{array}\right)\\&=\left(\begin{array}{c}-112 - 16\\42+20\end{array}\right)\\&= \left(\begin{array}{c}-128\\62\end{array}\right)= \langle -128, 62\rangle\\&=-128\;\vec{i} + 62\;\vec{j} \end{aligned}$ .

$\displaystyle \begin{aligned}\;\vec{u} - 5\;\vec{w} &= \left(\begin{array}{c}11\\12\end{array}\right) + (-5) \;\left(\begin{array}{c}4\\-5\end{array}\right)\\&=\left(\begin{array}{c}11-20\\12+25\end{array}\right)\\&= \left(\begin{array}{c}-9\\37\end{array}\right)= \langle -9, 37\rangle\\&=-9\;\vec{i} + 37\;\vec{j} \end{aligned}$ .

7 0

3 years ago

Find the slope and y-intercept of the line 6x−7y=2

Allisa [31]

To easily find the slope and y intercept of the line, put it in slope intercept form by rearranging the variables around.

6x-7y = 2
6x - 7y + 7y = 2 + 7y
6x = 7y + 2
6x - 2 = 7y + 2 - 2
7y = 6x - 2
7y/7 = 6x/7 - 2/7
Y = 6/7(X) - 2/7

Y = 6/7x - 2/7
Slope = m = 6/7
Y intercept = b = -2/7
(0, -2/7).

3 0

3 years ago