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3 years ago

Given: rectangle ABCD is similar to rectangle ZBXY. If ZY = 5, XC = 3, DC = 4, then XY =

Mathematics

2 answers:

soldier1979 [14.2K]3 years ago

7 0

Answer:

The length of XY is either 10 or 2.5.

Step-by-step explanation:

Given information: ZY = 5, XC = 3 and DC = 4.

Case 1: Rectangle ABCD is smaller than ZBXY.

The opposite sides of the rectangle are same.

$ZY=BC+XC$

$5=BC+3$

$2=BC$

The length of ABCD is 4 and width of ABCD is 2. The width of ZBXY is 5. The corresponding sides of the similar rectangles are is in the same proportion.

$\frac{4}{XY}=\frac{2}{5}$

$\frac{4\times 5}{2}=XY$

$10=XY$

Therefore the value of XY is 10.

Case 2: Rectangle ABCD is larger than ZBXY.

$ZY=BC-XC$

$5=BC-3$

$8=BC$

The length of ABCD is 4 and width of ABCD is 8. The width of ZBXY is 5. The corresponding sides of the similar rectangles are is in the same proportion.

$\frac{4}{XY}=\frac{8}{5}$

$\frac{4\times 5}{8}=XY$

$2.5=XY$

Therefore the value of XY is 2.5.

Semenov [28]3 years ago

4 0

Answer:

The answer is 2 1/2 I just did the assignment and that was the answer.

Step-by-step explanation:

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What is the simplified form of the following expression? 6m² + 7.2n - 4n+2m2-n

Nimfa-mama [501]

Answer:

6m² + 2.2n + 4m

Step-by-step explanation:

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3 years ago

“a railroad bridge spans a gorge 40 feet wide and connects two cliffs at heights of 98 and 158 feet above the bottom of the gorg

VMariaS [17]

Answer:

Height above the bottom gorge is 113 feet

Step-by-step explanation:

The width of the gorge = 40 feet

The height of the higher cliff = 158 feet

The height of the lower cliff = 98 feet

The length of the bridge = √((158-98)² + 40²) = 72.11 feet

The slope of the bridge = (158-98)/40 = 1.5

The length of 1/4 of the bridge from the lower cliff =72.11 - 3/4×72.11 = 18.03 feet

The angle of inclination of the bridge = tan⁻¹(1.5) = 56.31°

The height above the bottom at 3/4 from the higher cliff = The height above the bottom at 1/4 from the lower cliff = 98+ 18.03×sin(56.31 ) = 113 feet

Which can also be found directly from the heights of the two cliffs knowing that 3/4 from the higher cliff = 1/4 from the lower cliff giving;

Height above the bottom gorge = 98 + 1/4×(158 - 98) = 113 feet.

8 0

3 years ago

Write the equation of the line in fully simplified slope-intercept form.

Bad White [126]

Answer:

$y = -\frac{2}{5} x-6$

Step-by-step explanation:

1) First, find the slope of the line. Use the slope formula $m =\frac{y_2-y_1}{x_2-x_1}$ . Pick two points on the line and substitute their x and y values into the formula, then solve. I used the points (-5,-4) and (0,-6):

$m = \frac{(-6)-(-4)}{(0)-(-5)} \\m = \frac{-6+4}{0+5} \\m = \frac{-2}{5} \\$

So, the slope of the line is $-\frac{2}{5}$ .

2) Next, use the point-slope formula $y-y_1 = m (x-x_1)$ to write the equation of the line in point-slope form. (From there, we can convert it to slope-intercept form.) Substitute values for the $m$ , $x_1$ and $y_1$ into the formula.

Since $m$ represents the slope, substitute $-\frac{2}{5}$ in its place. Since $x_1$ and $y_1$ represent the x and y values of one point on the line, pick any point on the line (any one is fine, it will equal the same thing at the end) and substitute its x and y values in those places. (I chose (0,-6), as seen below.) Then, with the resulting equation, isolate y to put the equation in slope-intercept form:

$y-(-6) = -\frac{2}{5} (x-(0))\\y + 6 = -\frac{2}{5} x\\y = -\frac{2}{5} x-6$