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Rufina [12.5K]
3 years ago
6

Which statement could be used to conclude that this parallelogram is a rhombus?

Mathematics
2 answers:
cricket20 [7]3 years ago
8 0

Answer

its just A, he explained to much

BaLLatris [955]3 years ago
7 0
A parallelogram is a quadrilateral with two opposite sides equal in lengths while a rhombus is a parallelogram with the two sets of opposite sides equal to each other. A rhombus forms perpendicular bisectors when <span>diagonals are intersected with each other. Answer then is A</span>
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5x15 is 75 and 7x6 is 42
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Write a linear equation with a slope of 14 and y-intercept -12.
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Answer:

y=14x-12

Step-by-step explanation:

in the standard format y=mx+b, m is the slope and b is the y-intercept, so this equation would be y=14x-12 since the slope is 14 and the y-intercept is -12.

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Tell whether the two ratios are proportional or not proportional 3/7=6/9
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A line passes through the points (-7, 2) and (1, 6).A second line passes through the points (-3, -5) and (2, 5).Will these two l
BlackZzzverrR [31]

Answer:

Yes, the lines intersect at (3,7). The solution is (3,7).

Explanation:

Step 1. The first line passes through the points:

(-7,2) and (1,6)

and the second line passes through the points:

(-3,-5) and (2,5)

Required: State if the lines intersect, and if so, find the solution.

Step 2. We need to find the slope of the lines.

Let m1 be the slope of the first line and m2 be the slope of the second line.

The formula to find a slope when given two points (x1,y1) and (x2,y2) is:

m=\frac{y_2-y_1}{x_2-x_1}

Using our two points for each line, their slopes are:

\begin{gathered} m_1=\frac{6-2}{1-(-7)} \\  \\ m_2=\frac{5-(-5)}{2-(-3)} \end{gathered}

The results are:

\begin{gathered} m_1=\frac{6-2}{1-(-7)}=\frac{4}{1+7}=\frac{4}{8}=\frac{1}{2} \\  \\  \end{gathered}m_2=\frac{5+5}{2+3}=\frac{10}{5}=2

The slopes are not equal, this means that the lines are NOT parallel, and they will intersect at some point.

Step 3. To find the intersection point (the solution), we need to find the equation for the two lines.

Using the slope-point equation:

y=m(x-x_1)+y_1

Where m is the slope, and (x1,y1) is a point on the line.

For the first line m=1/2, and (x1,y1) is (-7,2). The equation is:

y=\frac{1}{2}(x-(-7))+2

Solving the operations:

\begin{gathered} y=\frac{1}{2}(x+7)+2 \\ \downarrow\downarrow \\ y=\frac{1}{2}x+7/2+2 \\ \downarrow\downarrow \\ y=\frac{1}{2}x+5.5 \end{gathered}

Step 4. We do the same for the second line. The slope is 2. and the point (x1,y1) is (-3, -5). The equation is:

\begin{gathered} y=2(x-(-3))-5 \\ \downarrow\downarrow \\ y=2x+6-5 \\ \downarrow\downarrow \\ y=2x+1 \end{gathered}

Step 5. The two equations are:

\begin{gathered} y=\frac{1}{2}x+5.5 \\ y=2x+1 \end{gathered}

Now we need to solve for x and y.

Step 6. Equal the two equations to each other:

\frac{1}{2}x+5.5=2x+1

And solve for x:

\begin{gathered} \frac{1}{2}x+5.5=2x+1 \\ \downarrow\downarrow \\ 5.5-1=2x-\frac{1}{2}x \\ \downarrow\downarrow \\ 4.5=1.5x \\ \downarrow\downarrow \\ \frac{4.5}{1.5}=x \\ \downarrow\downarrow \\ \boxed{3=x} \end{gathered}

Step 7. Use the second equation:

y=2x+1

and substitute the value of x to find the value of y:

\begin{gathered} y=2(3)+1 \\ \downarrow\downarrow \\ y=6+1 \\ \downarrow\downarrow \\ \boxed{y=7} \end{gathered}

The solution is x=3 and y=7, in the form (x,y) the solution is (3,7).

Answer:

Yes, the lines intersect at (3,7). The solution is (3,7).

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