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3 years ago

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Mathematics

1 answer:

Aleks04 [339]3 years ago

7 0

The line is parallel to y = 6/7 x - 5

The slope will be same .So equation of the line will be of the form:

$y = \frac{6}{7} x + k \\$

It passes through C(1,5)

$5 = \frac{6}{7} \times 1 + k \\ \\5 = \frac{6}{7} + k \\ \\ k = 5 - \frac{6}{7} \\ \\ k = \frac{7 \times 5 - 6}{7} = \frac{29}{7}$

$line : \red{y = \frac{6}{7} x + \frac{29}{7} } \\$

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The line containing the median of the trapezoid whose vertices are R(-1, 5) , S(1, 8), T(7, -2), and U(2, 0).

bearhunter [10]

Answer:

$y=-\dfrac{5}{3}x+6.5$

Step-by-step explanation:

Given: trapezoid RSTU with vertices R(-1, 5), S(1, 8), T(7, -2), and U(2, 0).

Plot these points on the coordinate plane. As you can see, lines RU and ST are parallel lines and segments ST and RU are bases of the trapezoid.

The median of the trapezoid (the middle line) passes through the midpoints of the sides RS and TU. Find these midpoints:

$M\left(\dfrac{x_S+x_R}{2},\dfrac{y_S+y_R}{2}\right)\Rightarrow M(0,6.5)\\ \\N\left(\dfrac{x_T+x_U}{2},\dfrac{y_T+y_U}{2}\right)\Rightarrow N(4.5,-1)$

The equation of the line MN is

$\dfrac{x-0}{4.5-0}=\dfrac{y-6.5}{-1-6.5}\\ \\\dfrac{x}{4.5}=\dfrac{y-6.5}{-7.5}\\ \\y=-\dfrac{5}{3}x+6.5$

4 0

4 years ago

I need help plz NO FILES no files helpppp it do at 2

Romashka-Z-Leto [24]

Answer:

Step-by-step explanation:

325/5= 65

2 numbers are over 65

4 0

3 years ago

Which line is the same as cd in the figure below

shtirl [24]

Answer: A.

Step-by-step explanation: if you look close enough, you can see exactly how long it is, and see that it does also have the two arrows along with it, but it’s the exact same just tilted a little bit but trust me I believe he correct answer is A.

8 0

2 years ago

65% of what number is 78?<br> A. 120<br> B. 143<br> C. 785<br> D. 5,070

RideAnS [48]

Answer:

Step-by-step explanation:

65% × 78 =

(65 ÷ 100) × 78 =

(65 × 78) ÷ 100 =

5,070 ÷ 100 =

50.7;

6 0

4 years ago

Read 2 more answers

Postal regulations specify that a parcel sent by priority mail may have a combined length and girth of no more than 126 in. Find

Zarrin [17]

Answer:

The package of maximum dimensions has:

Width and height = 21 in each , and length = 42 in

Step-by-step explanation:

A package of square cross section has a girth equal to the perimeter of the square ("4 x" if we consider "x" as the side of the square). This quantity, added to the package's length "L" has to be no more than 126 in.

The maximum allowed for priority mail is therefore: $4x+L=126 \,in$

At the same time, we want the volume of the package to be a maximum. The volume of this parcel is defined as the product of all three dimensions of the package:

$V=width\,*\,height\,*\,length\\V=x\,*\,x\,*\,L\\V=x^2\,L$

We can now use the first formula for the priority mail maximum dimensions, to write L in terms of "x" and replace it in the volume formula:

$4x+L=126 \,in\\L=126-4x$

So now the volume expression becomes:

$V=x^2\,(126-4x)=126x^2-4\,x^3$

If the student doesn't know calculus, a graphing tool can be used to find the maximum.

With calculus derivatives the maximum can be easily found:

We can request the derivative of the volume to satisfy the conditions for derivative = 0 and the function concave down to locate the function's "maximum".

$V'(x)=252\,x-12\,x^2\\0=252\,x-12\,x^2\\0=12\,x\,(21-x)$

This tells us that there are two solutions to the derivative equal zero:

$x=0\,\,and\,\,x=21$

The first solution is clearly a minimum since it would render a package of zero volume. the second solution ( $x=21$ ) is the one that corresponds to the maximum of the volume function.

Therefore, the dimensions of the package of largest volume are: width and height: 21 in each, and length L= 126 - 4*21 = 42 in

8 0

3 years ago