The point A (1,1) and the point B(5,-1) lie on the line L. Find the equation of the line L

The measure of angle MAC is 90°.

What is means of isosceles triangle?

An isosceles triangle is a type of triangle where two of its sides are congruent, or have the same length. This means that if you draw a line down the center of an isosceles triangle, it will split the triangle in half and both halves will have the same side lengths.

In an isosceles triangle, the angles opposite the congruent sides are congruent. Therefore, in triangle ABC, m∠BAM = m∠CAB = m∠NAC.

Since angle BAM and angle NAC are congruent, and they are both supplementary to angle MAC, it follows that angle MAC is congruent to itself.

Therefore, m∠MAC = m∠MAC = 180 - m∠BAM = 180 - m∠NAC.

Since m∠BAM = m∠NAC, we can conclude that

m∠MAC = 180 - m∠NAC = 90°

Hence, the measure of angle MAC is 90°.

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The Law of Cosines can be used to calculate the angles of an isosceles triangle given three side lengths. Two of the angles are equal, while the third can be found by subtracting the two known angles from 180°.

Since you are given three sides of an isosceles triangle, you can use the Law of Cosines to calculate the angles of the triangle. The Law of Cosines states that for a triangle with side lengths a, b, and c and angle C opposite side c, the following equation holds:

c² = a² + b² - 2abcosC

Therefore, you can rearrange the equation to solve for angle C:

C = arccos((a² + b² - c²) / (2ab))

For an isosceles triangle, two of the angles will be equal, so you can calculate those two angles using the equation above, and the third angle can be found by subtracting the two known angles from 180°.

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Answer:

The lines are perpendicular

Step-by-step explanation:

Answer:

perpendicular

Step-by-step explanation:

Answer:

A = (6,6)

Hope this helps!

Answer:

sure, the answer is 50

Step-by-step explanation: Because this is a right triangle, you can use the pythagorean theorem, which is a^2 + b^2 =c^2 so you square 48 and add it to 14 squared and then take the square roo t to get the value of the hypotenuse, note that c will always represent the hypotenuse or longest side, and that pythagorean theorem can only be used on right triangles

Answer:

You will need to eaither choose 2 odd numbers and 1 even number or choose  2 even numbers and 1 odd number

Step-by-step explanation:

In both cases we will be choosing two from 5 and 1 from 4

Answer:

480

Step-by-step explanation:

Find the difference between 2400 and 40 by dividing:

2400 / 40 = 60

Multiply each value by 60:

12 x 60 = 720 chocolate

15 x 60 = 900 caramel

5 x 60 = 300 banana

8 x 60 = 480 marshmallow

Answer:

7.5433234e+12 is your answer

Step-by-step explanation:

Answer:

7.5433234e+12

Step-by-step explanation:

Point (-12 , 8) is on the line that passes through (0, 6) and is parallel to the given line.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Since, We know that;

Parallel lines have same slopes and different y-intercepts

The formula of the slope of a line which passes through points (x₁ , y₁) and (x₂, y₂) is,

⇒  m = (y₂ - y₁) / (x₂ - x₁)

Since, The given line passes through points (-12 , -2) and (0 , -4)

Hence, Use the formula of the slope above to find the slope of the given line as;

⇒ m = (y₂ - y₁) / (x₂ - x₁)

⇒ m = (-4 - (-2)) / (0 - (-12))

⇒ m = (-2) / 12

⇒ m = - 1/6

Since, The two lines are parallel.

Hence, Their slopes are equal

So, The slope of the parallel line = - 1/6

Here, The parallel line passes through point (0 , 6)

Since, The form of the linear equation is y = mx + b, where m is the slope and b is the y-intercept.

⇒ m = -1/6 and b = 6

Hence, The equation of the parallel line is,

⇒ y =  x + 6

Now, Let us check which point is on the line by substitute the x in the equation by the x-coordinate of each point to find y, if y is equal the y-coordinate of the point, then the point is on the line as;

Point (-12 , 8)

Substitute x = -12 and y = 8

⇒ y =  (-12) + 6

⇒ y = 2 + 6 = 8

Clearly, The value of y is equal the y-coordinate of the point.

So, Point (-12 , 8) is on the line.

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Answer:

55 feet

Step-by-step explanation:

If you draw it out, the diagnonal along wiht 2 sides of the rectangle make a rigth angles traingle.

Using pythagoras theoreom, [tex]c^{2} =a^{2} +b^{2}[/tex], c is the length of the diagonal and a and b are 2 sides of rectangle.

So c=[tex]\sqrt{a^{2} +b^{2} }[/tex]

=[tex]\sqrt{33^{2} +44^{2} }[/tex]

put in alculator and get:

55

=55 feet

The measure of the diagonal of the rectangle plot which has the measure of 33 feet by 44 feet is 55 feet.

The diagonal of the rectangle is the distance from opposite vertices of it. There are two diagonals in a rectangle which are equal in measure.

To find the diagonal of the rectangle, the following formula is used.

[tex]d=\sqrt{l^2+w^2}[/tex]

Here, (l) is the length of the rectangle and (w) is the width of it.

The width of the rectangular plot measures 33 feet and length measure 44 feet. Plug in these values in the above formula to find the diagonal of the plot.

[tex]d=\sqrt{(44)^2+(33)^2}\\d=\sqrt{1936+1089}\\d=\sqrt{325}\\d=55\rm\; ft[/tex]

Hence, the measure of the diagonal of the rectangle plot which has measure of 33 feet by 44 feet is 55 ft.

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Answer:

37.5 and 82.5

Step-by-step explanation:

Answer:

I am against testing on animals.

Step-by-step explanation:

Personally based on my faith humans are told to make the earth their dominion. To dominate doesn't only mean to use to one's advantage but to also take care of and replenish any loss caused by unintentioned damage. Animals do have feelings, both emotional and physical, and though those feelings may not be quite as developed as those of humans, they are undoubtedly existent. With how far technology has come when it comes to predictability and how calculated and concise science experiments have become, if as the most advanced species on earth we are still unable to determine how long a deodorant or lipstick or eyeliner would last without torturing other species, then what exactly have we achieved, and are we truly any more advanced than we were 10000 years ago? And for things that quite necessarily do need testing like vaccines and medicines it is to some extent understandable, but then again if the death sentence still exists for offenders of heinous crimes , why don't we instead of killing those criminals dedicate them to science and research for testing of vaccines and medicines. That way we all benefit from it. They don't have to die and neither do the animals and neither do we. It's a far stretch of a solution but alternatives can be made. Where there's a will there's a way.

Answer:

165 centimeters

Step-by-step explanation:

An example of calculating BMI using the formula: Height = 165 cm (1.65 m), Weight = 68 kg One centimeter is equal to 0.01 meter: 1cm = 0.01m. You are 65 inches tall. 65 * (2.54) = 165.1 cm.

Answer:

165 cm

Step-by-step explanation:

1.65 meters = 1.65 × 100 = 165 centimeters

Exponential graph is identified by its curve.

An exponential graph is a graph that shows a rapid increase or decrease of a value over time, where the rate of change is proportional to the current value. It is usually represented by a curve that bends upward or downward.

The key characteristic of an exponential graph is that the Y-axis is on a logarithmic scale, and the curve of the graph is a steep curve going either up or down. The equation of an exponential graph is usually of the form y = ab^x, where a is the initial value, b is the growth or decay factor, and x is the independent variable.

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To solve for x, bring the variable to one side, and bring all the remaining values to the other side by applying arithmetic operations on both sides of the equation. Simplify the values to find the result.

Let's begin with a straightforward equation: x + 2 = 7.

How do you obtain X on your own?

Take away two from both sides.

⇒ x + 2 - 2 = 7 - 2\s⇒ x = 5

Check the solution, x = 5, by reentering it into the equation. We get 5 + 2= 7.

R.H.S. L.H.S.

Utilizing triangle properties or the Pythagorean theorem, we can get a solution for the unknown side or angle of a triangle.

With the aid of an example, let's clarify how to solve for x in a triangle.

Two of ABC's legs, which measure 7 units and 24 units respectively, are right-angled at B. Look for the hypotenuse X.

By using the Pythagorean theorem to ABC,

We obtain AC2 = AB2 + BC2, where x2 = 72 + 242, 49 + 576, and 625 where x2 = 625.

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Yes it is divisible by 3. A number is fully divisible by three if its digit sum is also divisible by three, according to the rule of divisibility test for three.

The divisibility rule is a concise and practical approach to check, often by looking at the integer's digits, whether a given integer is divisible by a given set divisor without actually executing division. Without actually doing the division procedure, you may quickly discover if a given number can be divided by a defined divisor using the divisibility test. When dividing two numbers exactly, the quotient must be an integer and the remainder must be zero.

add all number

9+9+0 = 18

and 18/3 = 6

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On solving the provided question, we can say that in this triangle 2x-6 = 3 => 2x = 9 => x = 9/2 and 2z = 4 => z = 2

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

here,

in this triangle

2x-6 = 3

2x = 9

x = 9/2

2z = 4

z = 2

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The two lines intersect at (-3,-5) and thus a common solution.

The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.

Given here, the system of linear equations as  Y=4x+7 and 2=x-y

On solving these two equations we get that the two lines intersect at (-3,-5) and thus a common solution.

The two equations are plotted in the attachment below.

Hence, The two lines intersect at (-3,-5) and thus a common solution.

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Answer:

$540

Step-by-step explanation:

Interest = Principal x Rate x Time

I = 3000(.045)(4)

I = 540

The y-intercept represents the loan amount initially. And the rate of change of the function will be negative The equation of Mr. Allen's plan will be y = - 80x + 560 and Mr. Jessup's plan will be y = - 40x + 400.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

From the graph, the y-intercept of the line represents the value of the loan initially.

From the graph, the slope of both lines is negative, then the rate of change of the function will be negative.

Let 'x' be the number of months and 'y' be the amount owed.

The two points are (0, 560) and (1, 480). Then the equation of the line is given as,

(y - 560) = [(560 - 480) / (0 - 1)](x - 0)

y - 560 = - 80x

y = - 80x + 560

And the equation of the line for Mr. Jessup's plan will be given as,

y = - 40x + 400

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Answer:

aboout 1268 students

Step-by-step explanation:

Answer

0.975 is the probability value

Step-by-step explanation:

We start by getting the z score of 86

z-score = (x - mean)/SD

z-score = (86-98)/6 = -12/6 = -2

So we want to find the probability of z greater than or equal to 2

We shall be using the standard normal distribution table here

We have the answer as;

0.975

Answer:

x = 2

Step-by-step explanation:

(7x + 19) + 90 + 57 = 180

(7x + 19) + 147 = 180

7x + 19 = 33

7x = 14

x = 2

Have a nice day!

Answer:

The answer is 11

Step-by-step explanation:

The answer is 11 because you need to add the sides up that the points are on point P is 5 Point Q is 3 and point R is 3 5+3 is 8 8+3 is 11

Answer:

19.56

Step-by-step explanation:

PR = [tex]\sqrt{3^{2} + 3^{2} }[/tex] = [tex]\sqrt{18}[/tex] = 3[tex]\sqrt{2}[/tex]

RQ = [tex]\sqrt{5^{2} +5^{2} }[/tex] = [tex]\sqrt{50}[/tex] = 5[tex]\sqrt{2}[/tex]

QP = [tex]\sqrt{8^{2} +2^{2} }[/tex] = [tex]\sqrt{68}[/tex] = 2[tex]\sqrt{17}[/tex]

Perimeter = sum of the sides = 3[tex]\sqrt{2}[/tex] +  5[tex]\sqrt{2}[/tex] +  2[tex]\sqrt{17}[/tex] = 19.56

Break the triangle PQR into 3 right triangles, with each leg being a hypotenuse.  Then you can use the Pythagorean theorem to find the length of each leg.  Add them all together to get the perimeter.

Answer:

the radius found on the letter c

Answer:

the radius found on the letter c

The new dimensions of the rectangle will be 4.8 x 4.4.

To find the new dimensions, we need to find the area of the original rectangle (2.4 x 2.2 = 5.28), and then multiply it by 16 to find the desired new area (5.28 x 16 = 84.48).

Since the area of a rectangle is determined by the product of its length and width, we can find the new dimensions by taking the square root of the new area and dividing it by the original length.

These are the new dimensions of the rectangle.

We have to make sure that the new dimensions are in the same proportion as the original one, we can use the same factor of multiplying to get the new length and width.

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Note that the resultant expression after simplifying simplify square root of 3y² if y<0 is: y√3

Note that we need to take a factor out of the square root:  √(3y²) , where y<0.

The given expression is  √(3y²)

Recall that to take out a factor out of the square root that factor must have a degree in multiple of 2 such as x², x⁴, (x-2)⁴, thus,

√(3y²)  = √3y²

⇒ √3 √y²

⇒  √3 (y²)[tex]^\frac{1}{2}[/tex]

⇒ √3 (y)[tex]^\frac{2}{2}[/tex]

= y √3

Thus, having simplified the expression √(3y²), the result is:  y √3.

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Answer:

y=1/2x-3

Step-by-step explanation:

y=mx+b

y=1/2x-3

We can find the x-intercept by writing the equation in intercept form which  is also known as factored form, y= (x-p) (x-q) where p, q are the x-intercepts.

To find the vertex of the quadratic function we can write the function  in standard form , the vertex is located at the point where y=f (x).

A function which has a degree of two is known as a quadratic function.

Example, 3x² + 2 , here the maximum degree is 2 , hence the given function is quadratic. The general form of a quadratic equation is given as ,

f(x) = ax2 + bx + c .

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