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3 years ago

Which Lines Are Parallel if M<4 = m<5? Justify Your Answer.

Mathematics

2 answers:

Taya2010 [7]3 years ago

6 0

Answer:

The other person is correct!

Step-by-step explanation:

( I wanted to give them credit because if I put close to what they put I would be reported for Plagiarism so I Just wanted to say they are correct!) :)

Keith_Richards [23]3 years ago

5 0

Answer:

Opposite angles formed by two intersecting lines are equal, so angle 1 is the same as angle 4. That means angle 1 = angle 5 as well.

When a line intersects two parallel lines, the corresponding angles are equal. That is, if r and s are parallel, then the angles formed when l intersects r are the same s the angles formed when l intersects s. Angle 1 = Angle 5, Angle 2 = Angle 6, and so forth. Since we know angle 1 = angle 5, we can conclude that r and s are parallel.

You might be interested in

The length of a rectangle is 1 more than 3 times the width . If the perimeter of the rectangle is 18 units , what’s it’s area?

nika2105 [10]

Answer:

14 square units

Step-by-step explanation:

You need to know the formulas for the perimeter of a rectangle and the area of a rectangle, which are

2L + 2W - P where L is the length, W is the width, and P is the perimeter

and

A = LW

So we need to find the length and width to find the area

Step 1: Write equations out of the given information

"The length of a rectangle is 1 more than 3 times the width" can be rewritten as

L = 3W + 1

"the perimeter of the rectangle is 18 units" can be rewritten as

2L + 2W = 18

Step 2: Plug the first formula into the second one and solve

2(3W + 1) + 2W = 18

Simplify...

6W + 2 + 2W = 18

Combine like terms and subtract 2 from both sides

8W = 16

Divide both sides by 8 to isolate the W

W = 2

Step 3:

Plug W = 2 into the formula for L and solve for L

L = 3(2) + 1

L = 6 + 1

L = 7

Step 4: Use the length and width to calculate the area

A = LW

A = (7)(2)

A = 14 units squared

6 0

4 years ago

Select the correct answer1 - quadratic, linear, exponential2 - 1.5, 18, 16, 123 - 16, 12, 20, 184 - 18, 6, 20, 12

Alexxandr [17]

1 - The equation is:

$p(x)=-0.5x^2+6x$

Since it has no variable on exponents and it has a term with x to the second power, this is a quadratic function.

2 - x represents the length of the tomato patch, so if we want the area of the bell pepper patch, we can input x = 8 into the function:

$\begin{gathered} p(8)=-0.5\cdot8^2+6\cdot8 \\ p(8)=-0.5\cdot64+48 \\ p(8)=-32+48 \\ p(8)=16 \end{gathered}$

Thus, the area is 16 square feet.

3 - Since the leading coefficient is negative, the vertex of the parabola gives the maximum value for the function.

The x value of the vertex is:

$\begin{gathered} ax^2+bx+c \\ x_v=-\frac{b}{2a} \end{gathered}$

So, in this case:

$x_v=-\frac{6}{2\cdot(-0.5)}=-\frac{6}{-1}=6$

And to find the value for the area, we need to input that into the function:

$\begin{gathered} p(6)=-0.5\cdot6^2+6\cdot6 \\ p(6)=-0.5\cdot36+36 \\ p(6)=-18+36 \\ p(6)=18 \end{gathered}$

Thus, the maximum area is 18 square feet.

4 - The value for the length of the tomato patch is just the corresponding x for this maximum, which we calculated as the vertex x:

$x_v=6$

Thus, the length of the tomato patch for this maximum value is 6 feet.

3 0

2 years ago

I need help with this question

slamgirl [31]

Answer:

ummmm

Step-by-step explanation:

I cant help sorry :C

4 0

3 years ago

Write the rule for finding a point translated vertically k units up. 2. Use this rule to find the coordinates for (−3, −6) when

Alex17521 [72]

Answer:

Rule is (x, y+k)

New point is (-3,9)

Step-by-step explanation:

A point translated vertically k units up means the x coordinate remains the same in the translation but the y coordinate is increased by k units

This can be represented mathematically as;

Let;s assume the point to be A with coordinates (x,y) then to get the image of the point under a vertical translation k units up you add k to the y coordinate value.

Given ;

$A=(\frac{x}{y} )\\\\T=(0,k)\\\\A'=(\frac{x}{y} )+(\frac{0}{k} )=(\frac{0+x}{y+k} )\\\\A'=\frac{x}{y+k} =(x,y+k)$

where T is the translation

In the question

Given (-3,-6) and T is (0,5) the new coordinate will be

$=(\frac{-3}{4}) +(\frac{0}{5} )=\frac{-3}{9} =(-3,9)$

8 0

3 years ago

The measure of the first angle in a right triangle is 10 less than the measure of the second angle.The third angle is the right

prohojiy [21]

Triangle angles add up to a total of 180 degrees.

X will substitute for the second angle.

(X - 10) will substitute for the first angle, which is 10 less than the second angle (x).

The third angle is a right angle which is 90 degrees.

The equation therefore, the summation of the angles:
90 + x + (x - 10) = 180

Join like terms:
80 + 2x = 180

Solve for x:
2x = 100
x = 50

This means that:
The second angle is 50.
The first angle is 50 - 10 which is 40.

We can double check by adding the angles 50, 40, and 90 together to get 180.

5 0

3 years ago