In trapezoid ABCD(AB ∥CD), point M∈AD, so that AM:MD=3:5. Line l ∥ AB and passes through point M to intersect diagonal AC and leg BC at points P and N ,respectively. Find AC:PC.

please answer soon will give brainiest if correct.

Based on the triangle midsegment theorem, the length of CZ is calculated as: 7.2 m.

The triangle midsegment theorem states that when two sides of a triangle are joined together by a line segment at their midpoint, the line segment is called the midsegment, and it is parallel to the third side whose measure is twice its length.

This implies that, AB is a midsegment in the image shown for triangle XYZ. It is parallel to YZ.

Therefore:

AB = 1/2(the length of YZ)

Substitute the value of AB into the equation:

7.2 = 1/2(YZ)

2(7.2) = YZ

YZ = 14.4 m.

The length of CZ = 1/2(the length of YZ) [this is because YC = CZ]

CZ = 1/2(14.4)

CZ = 7.2 m.

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The solution to the system of equations is x = −7 and y = −1.

To solve the given system of equations using an inverse matrix, we can represent the system in matrix form, Ax=B, then find the inverse of matrix A to solve for 'x'.

Given matrix:

[tex]\left\{\begin{array}{ccc}x-6y=-1\\-2x+9y=5\end{array}\right[/tex]

[tex]\hrulefill[/tex]

First, we rewrite the system of equations in matrix for, Ax=B:

[tex]A = \left[\begin{array}{cc}1&-6\\-2&9\\\end{array}\right], \ x = \left[\begin{array}{cc}x\\y\\\end{array}\right], \ B = \left[\begin{array}{cc}-1\\5\\\end{array}\right][/tex]

So, Ax=B can be written as:

[tex]\Longrightarrow \left[\begin{array}{cc}1&-6\\-2&9\\\end{array}\right] \left[\begin{array}{cc}x\\y\\\end{array}\right] = \left[\begin{array}{cc}-1\\5\\\end{array}\right][/tex]

[tex]\hrulefill[/tex]

[tex]\boxed{\left\begin{array}{ccc}\text{The inverse of a 2x2 matrix,} \ \left(\begin{array}{ccc}a&b\\c&d\end{array}\right), \ \text{is given by:}\\\\\\A^{-1}= \dfrac{1}{ad-bc}\left(\begin{array}{ccc}d&-b\\-c&a\end{array}\right)\end{array}\right}[/tex]

Here,

[tex]\Longrightarrow A = \left[\begin{array}{cc}1&-6\\-2&9\\\end{array}\right][/tex]

The determinant ∣A∣ is:

[tex]\Longrightarrow |A|=(1)(9)-(-6)(-2)=9-12\\\\\\\\\therefore |A|=-3[/tex]

Since the determinant is not zero, A has an inverse, which can be calculated as:

[tex]\Longrightarrow A^{-1}= \dfrac{1}{-3}\left(\begin{array}{ccc}9&6\\2&1\end{array}\right)\\\\\\\\\therefore A^{-1}=\left(\begin{array}{ccc}-3&-2\\-2/3&-1/3\end{array}\right)[/tex]

[tex]\hrulefill[/tex]

We can solve for 'x' using x=A⁻¹B:

[tex]\Longrightarrow x = \left(\begin{array}{ccc}-3&-2\\-2/3&-1/3\end{array}\right)\left(\begin{array}{cc}-1\\5\\\end{array}\right)[/tex]

Upon multiplication, we get:

[tex]\Longrightarrow x = \left(\begin{array}{cc}(-3)(-1)+(-2)(5)\\(-2/3)(-1)+(-1/3)(5)\\\end{array}\right)\\\\\\\\\Longrightarrow x = \left(\begin{array}{cc}3-10\\2/3-5/3\\\end{array}\right)\\\\\\\\\Longrightarrow x = \left(\begin{array}{cc}-7\\-3/3\\\end{array}\right)\\\\\\\\\therefore \boxed{\boxed{x=\left(\begin{array}{cc}-7\\-1\\\end{array}\right)}}[/tex]

Thus, the solution to the system of equations is x = −7 and y = −1.

The outside temperature t when Josefina ate breakfast was 55F.

What are equations?

An equation is a mathematical statement that shows that two mathematical expressions are equal.

According to the given question:

Let the temperature outside at the time of breakfast be t.

Temperature dropped by 20F by the time for dinner.

So the temperature at the time of breakfast was t - 20

Now, when she ate dinner the temperature was 35F

So the equation for outside temperature t when Josefina ate breakfast is

t - 20 = 35

Solving to get t that is temperature in the morning

t = 35 + 20

t = 55F

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Answer:

C

Step-by-step explanation:

4x + 3y = 24

3y = -4x + 24

y = -3/4x + 8

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Answer:

Y= -4/3x + 8

Step-by-step explanation:

4x + 3y = 24

-4x             -4x

3y = -4x + 24

/3      /3     /3

Y = -4/3x + 8

Answer:

3,4

Step-by-step explanation:

use section formula,as it divides in 1 :1

7+x/2 =5 so x is 3

Answer:

y = 2/3x - 2

Step-by-step explanation:

To Literally Solve for y, we must first isolate it. This means putting it and its coefficient on the own side of the equation.

If you add, multiply, divide, subtract, put something to the power/root both sides of an equation, the final result will stay the same.

4x - 6y = 12

Subtract 4x on both sides.

4x - 4x -6y = 12 - 4x

Simplify.

-6y = 12 - 4x

Divide both sides by -6.

y = -2 + 2/3x

Adjusted the equation for clarity.

y = 2/3x - 2

The pound as a unit of mass , 14 x (1ounce)= 14 ounce.

The British imperial and American customary systems of measurement both utilize the pound as a unit of mass. The international avoirdupois pound, which is legally defined as exactly 0.45359237 kilograms and is divided into 16 avoirdupois ounces, is the definition that is currently most frequently used.

The avoirdupois pound is represented by the worldwide standard symbol, lbm (for the majority of pound definitions), (mostly in the U.S.),  and  (particularly for the apothecaries' pound).

The currency came from the Roman libra (hence the abbreviation "lb"). The Dutch term pond, the Swedish word pund, and the German word pfund are all cognates of the English word pound.

Older and no longer in use, these units (replaced by the metric system).

Hence, 14 x (1ounce)= 14 ounce.

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Answer:

The top left table.

Step-by-step explanation:

An initial value is the y-intercept, which is where the function touches the y-axis. If the initial value is 3, the coordinate must be (0,3). This rules out the both tables on the right.

The rate of change is how much the function's y values increase or decrease. If the rate change is 4, the y values increase by 4 each unit, which matches the top left table.

Answer:

The graph of x - y = 4 is D.

Step-by-step explanation:

substituting a random value for either x or y will give you a value for the other unknown

that's to say,if x is 2 ,then y will be -2

More pairs of coordinates then are got using the same method

these are plotted and a graph similar to the one in D is got.

Based on the definition of an equilateral triangle, the measure of angle KML is: d 60.

An equilateral triangle can be described as a triangle that has three sides that are equal and also equal interior angles that measures 60 degrees each.

The image shows that the three sides of triangle KML are marked equally by three strokes. This shows that the three sides of triangle KML are congruent to each other. Since they are congruent, they have equal length.

Therefore, triangle KML is an equilateral triangle that has interior angles that measures 60 degrees.

Angle KML is an interior angle of the equilateral triangle, therefore:

The measure of angle KML is: d. 60 degrees.

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Answer:

? = 180

Step-by-step explanation:

Answer:

16.5

Step-by-step explanation:

8.25+8.25=16.5

Answer:

yes

Step-by-step explanation:

With a total pay last week of $4720 and a 2.5% commission on sales, she made 275 in sales.

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100). Rather than being expressed as a fraction, a percentage is a piece of a whole expressed as a number between 0 and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. You divide the part of the whole by the whole and multiply the result by 100 to get the percentage.

Here,

The money earned by sales=2.5%*600

=$15

Let the total sales be x,

600+15x=4720

15x=4720-600

15x=4120

x=274.67

x=275 sales

Her last week sales was 275 as her total salary last week was $4720 and she receives 2.5% commission on sales.

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For the given similar triangle the value of x will be 9 inches.

It is defined as the law to prove that two triangles have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.

Since the two triangles are similar,

Suppose the unknown side is x,

Since the ratio of the sides of the similar triangles is equal the obtained expression is,

8/6=12/x

x=12×6 / 8

x=9 inches

Thus, for the given similar triangle the value of x will be 9 inches.

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The required length of AE will be 14 units on the given rhombus.

We know that all sides of a rhombus are equal, then note that AD equals DC, that is;

4x + 2 = 7x - 13

2 + 13 = 7x - 4x

15 = 3x

Divide both sides of the equation by 3

5 = x

If AD = 4x + 2, then when x  = 5

AD = 4(5) + 2

AD = 20 + 2

AD = 22

So, triangle ADE may now be separated, with AD measuring 22 units and ED measuring 17 units (midpoint between points B and D). Line AE may be determined using Pythagoras' theorem, which states:

AC² = AB² + BC²

Where AC is the hypotenuse, and AB and BC are the two other sides

Substituting for values as given in the question, we now have;

AD² = ED² + AE²

22² = 17² + AE²

484 = 289 + AE²

484 - 289 = AE²

195 = AE²

√195 = AE

13.96 = AE

So, length AE ≈ 14 units (to the nearest whole number)

Thus, the required length of AE will be 14 units on the given rhombus.

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The standard deviation of a binomial distribution is C. 3.46

Standard deviation is the measure of spread of a set of data.

Since a binomial trial has a probability of success of 0.2, and 75 trials are performed. To find the standard deviation, we use the formula for standard deviation of a binomial distribution.

The standard deviation of a binomial distribution is given by σ = √(npq) where

Given that for our binomial trial

So, substituting the values of the variables into the equation, we have that

σ = √(npq)

σ = √(75 × 0.2 × 0.8)

σ = √(75 × 0.16)

σ = √12

σ = 3.464

σ ≅ 3.46

So, the standard deviation is C. 3.46

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Answer:

x = 0 and y = 2

Step-by-step explanation:

5x + 3y = 6

-5x - 3y = -6

Adding the equations gives 0 = 0, so the equations are equivalent.

x = 0 and y = 2

After fitting a bookcase with a height of 2.5 feet into a space with a width of 3.25 feet, 0.375 feet will be left on each side.

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

Here,

Width of bookshelf=2.5 feet

Space to keep the bookshelf=3.25 feet

Total difference for the remaining space near bookshelf,

=3.25-2.5

=0.75 feet

Space remaining on either side of bookshelf,

=0.75/2

=0.375 feet

A space of 0.375 feet will be remaining on each side after keeping a bookshelf of size 2.5 feet in a space of 3.25 feet.

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Answer: 80

Step-by-step explanation:

The owners will need 80 racks to hold all 7,200 comic books. (7,200 / 90 = 80)

Answer:

Step-by-step explanation:

No it is not

y = 13x ,y = x - 2 and y = 2x + 11 represents a straight line which is proportional to x i.e. a linear function .

The proportional relation equation is y = kx .

The letters y and x are the variables, which can change, and the letter k is the constant of proportionality.

According to the question ,

Given: y = 13x

since y ∝ x,

Therefore the equation is said to be proportional .

Given: y = x²

Since the term y is proportional to the square of square ,so we can't say say that the equation is proportional .

Given: y = x - 2

Since ,y is in the form of the equation y = mx + c and y is proportional to x as well ,therefore we say that x is proportional to x .

Given : y = 2x + 11

Since y is in the form of y = mx + c and y is proportional to x

As the given expression represents a straight line , so its proportional to x .

Hence, all the given expressions are proportional to x except the second option which is proportional to square of x and is not forming a linear equation that is a straight line.

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Answer:

15

Step-by-step explanation:

Answer:

Approximately 2.6% of the total number of parking spots are designated as accessible.

Step-by-step explanation:

If the ratio of accessible parking spots to general parking spots is 2:75, this means that for every 2 accessible parking spots, there are 75 general parking spots. This can also be written as a fraction: 2/(2+75) = 2/77.

The fraction represents the proportion of the total number of parking spots that are designated as accessible. In this case, 2/(2+75) = 2/77 = approximately 0.026, or 2.6%. This means that approximately 2.6% of the total number of parking spots are designated as accessible.

It's important to note that the number of accessible parking spots should be determined based on the needs of the community and should meet or exceed the minimum requirements set by law. In the United States, the Americans with Disabilities Act (ADA) sets minimum requirements for the number of accessible parking spaces that must be provided in public parking lots. The exact number of spaces required depends on the size and type of the parking lot.

The letters of the points that satisfy the inequalities are  points A, D, E, I

An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

The given parameters are:

y<-[tex]\frac{1}{2}x +2[/tex]   and

2x+y≤8

If we plot the graphs of the first inequality,

we notice that the coordinates of the origin are (0,0) then we have

Rearrange the inequality

[tex]y > -\frac{1}{2} x=2[/tex]

At origin y=0, x=0

[tex]0+\frac{1}{2}(0) > 2[/tex]

⇒ 0+0<2                (false)

Therefore the origin is not included

In the second inequality

2x+y≤8

Coordinates of the origin are (0,0)

2(0)+(0)≤8

0+0≤8             (False)

Therefore the origin is not included.

In conclusion the points that satisfy the inequalities are points A,D,E,I

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Entonces, la distancia entre los puntos A y B es de aproximadamente 15.

Generalmente, Para encontrar la distancia entre los puntos A y B, puedes utilizar la fórmula de la distancia euclidiana:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

En este caso, la distancia sería:

d = √((3 - (-6))² + (-7 - 5)²)

The square root of ((3 - (-6))² + (-7 - 5)²) is equal to:

=√((3 - (-6))² + (-7 - 5)²)

= √((9)² + (-7 - 5)²)

= √(81 + 144)

= √225

d ≈15

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Encontró la pregunta completa

El punto A está en (-6,5) y el punto B está en (3,-7). ¿Cuál es la distancia entre los puntos

The KN is 21.4 rounded to the nearest tenth.

The orthocenter of a triangle is the place where the perpendicular drawn from the vertices to the opposing sides of the triangle intersect each other. The orthocenter for a triangle with an acute angle is located within the triangle. The orthocenter for a triangle with an acute angle is outside the triangle.

Now we need to find the slope of JL.

From that we have to find the slope of the perpendicular line through B.

Slope of JL=  (y₂ - y₁) / (x₂ - x₁)

J (7, 8) and L (5, 2)

here x₁=  7,y₁  = 8, x₂ = 5 and y₂ = 2

=  -6 / -2

= 3

Slope of the altitude KM  =  -1/ slope of JL = -1/3

Equation of the altitude KM : (y - y₁)  =  m (x -x₁)

Here K(1,2);

(y - 2)  =  -1/3 (x -1)

(y - 2)  =  -x/3 +1/3

Now we need to find the slope of JK.

From that we have to find the slope of the perpendicular line through D.

Slope of KL=  (y₂ - y₁) / (x₂ - x₁)

J(7,8) and K(1,2)

here x₁=  7,y₁  = 8, x₂ = 1 and y₂ = 2

 = 1

Slope of the altitude JO  =  -1/ slope of JL

                                         = -1

Equation of the altitude JO : (y - y₁)  =  m (x -x₁):

 (y - 8)  =  -1 (x - 7)

Solving the equation, x = 21 and y = -6

So the orthocenter N is (21 , -6)

Now the distance of KN is = √(21 - 1)² + (-6 -2)²

                                             =√464

                                             = 21.5

Therefore, the KN is 21.5 rounded to the nearest tenth.

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Answer:6.3

Step-by-step explanation:

I got it correct on my test

Answer:

Step-by-step explanation:

o.67891

can you send a picture of the question?