The area of square abcd is 36 square units and the area of triangle ebf is 20 square units. if line eb is perpindicular to line bf and line ae is equal to 2 find the length of line cf

The method of simultaneous equations is a mathematical technique used to solve systems of equations with two or more unknowns. It involves solving a set of equations simultaneously, that is, finding values for all the unknowns in the equations at the same time.

The method of simultaneous equations is a mathematical technique used to solve systems of equations with two or more unknowns. It involves solving a set of equations simultaneously, that is, finding values for all the unknowns in the equations at the same time. This method is also known as elimination, substitution, or the linear system technique. The method of simultaneous equations involves manipulating the equations to express one of the variables in terms of the others. This can be done by either adding or subtracting the equations from each other, or by multiplying or dividing them by a common factor. Once one of the variables is expressed in terms of the others, the remaining equations can be solved, and the solutions can be substituted into the original equation to find the value of the other variables. The method of simultaneous equations is particularly useful for solving linear systems, which involve equations with linear coefficients, as the equations can be manipulated relatively easily. It is also useful for solving systems of non-linear equations, although it is more difficult to manipulate the equations in this case.

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The minimum number of hours Hiroto can tutor to make at least $180 is 2 hours.

From the information, Hiroto tutors Japanese for $15 an hour and works at a dairy for $10 an hour. He wants to work 15 hours this week and we want to calculate the minimum number of hours Hiroto can tutor to make at least $180.

Hiroto wants to earn at least $180 this week. If he works 15 hours at the dairy, he will earn 15 * $10 = $150.

To earn at least $180, he needs to earn an additional $180 - $150 = $30.

At $15/hour for tutoring, Hiroto needs to work 30 / 15 = 2 hours tutoring.

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The point (2,0), which is (-3,2), is √29 units away from the origin.

A pair of numbers called coordinates are used to locate a point or a shape in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane. The term "ordinate" refers to a point's separation from the x-axis when scaled with the y-axis. Coords are the collective noun for the abscissa and ordinate. The study of algebraic equations on graphs is known as coordinate geometry. The plotting of points, lines, and curves on an x and y axis is an illustration of coordinate geometry.

Here,

distance=√(y2-y1)²+(x2-x1)²

=√(2-0)²+(-3-2)²

=√2²+-5²

=√4+25

=√29

The distance of the point (-3,2) from the origin that is (2,0) is √29 units.

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If runners in the half marathon entered in 3 waves and 7 out of eight runners finished the race, runners that did  not finish is 119 runners.

First step is to find the total runners in the 3 waves

Total runners = 341 runners + 295 runners + 316 runners

Total runners = 952 runners

Second step is to find runners that finished the race

Runners (Finished) = 7/8 ×  952 runners

Runners (Finished) = 833 runners

Now let find runners that did not finished

Runners (Unfinished) = 952 runners - 833 runners

Runners (Unfinished) =119 runners

Therefore 119 runners did not finish.

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The area, in square meters is 121π m²

The formula for calculating the area of a circle is expressed as;

A = πr²

Where;

Also, the circumference of the circle is expressed as;

Circumference = 2πr

Now, substitute the value of the circumference, we have;

22π = 2πr

Make 'r' the subject of formula, we get;

r = 11

Now, subsitiute into the formula for area;

Area = π(11)²

Find the square

Area = 121π m²

Hence, the value is 121π m²

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The area of the circle in terms of π is 121π metres square.

The circumference of the circle is 22π metres. The circumference of a circle is the perimeter of the circle.

Therefore,

circumference of a circle = 2πr

where

Hence,

circumference of the circle = 22π metres

22π = 2πr

r = 22π / 2π

r = 11 metres

Let's find the area of the circle.

Therefore,

area of the circle = πr²

where

Therefore,

area of the circle = 11² × π

area of the circle = 121π metres²

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Answer:

Millions

Step-by-step explanation:

A 7 digit number is called "Millions"

1,000,000=Millions

and then the rest all the way till 9 is a seven digit million.

The error in the measurement is 3.5%.

Percentage error is a measurement of the discrepancy between an observed (measured) and a true (expected, accepted, known etc.) value. Mathematically, we can write -

[tex]$\delta = \left| \frac{v_A - v_E}{v_E} \right| \cdot 100\%[/tex]

Given is that James tries to cut a wooden board 20 inches long. The wooden board ends up being 20.7 inches long.

We can write the percentage error as -

p% = |20.7 - 20|/20 x 100

p% = 0.7 x 5

p% = 3.5%

Therefore, the error in the measurement is 3.5%.

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When the graphs of a system of linear equations are parallel, there is no solution. There are infinite solutions. When the graphs are the same line, a system of linear equations has infinite solutions.

An inconsistent pair of linear equations is a system of linear equations that has no solution.

Furthermore, a linear equation with two variables has an unlimited number of solutions. Every linear equation in two variables has a straight line as its graph, and each point on the graph (straight line) indicates a solution to the linear equation.

The majority of linear systems have precisely one solution. It is feasible, however, that there are no answers or that there are infinitely many. (It is impossible for there to be exactly two answers.) In this case, the word unique denotes that there is a solution, and it is the only one.

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The probability that he draws a pair of tens is  1/2652 or approximately 0.000378 which is approx 0.04%

The probability of drawing a pair of tens from a standard deck of cards is (number of ways to get a pair of tens) / (total number of possible outcomes).

In this case there are 4 tens (2 of hearts, 2 of diamonds, 2 of spades, 2 of clubs) and he is drawing 2 cards from the deck, so there is only 1 way to get a pair of tens. There are 52 cards in a standard deck, so the total number of possible outcomes is 52 * 51 = 2652.

So the probability of drawing a pair of tens is 1/2652 or approximately 0.000378 which is approx 0.04%

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Answer:

you are right bro keep up

Answer:

A

Step-by-step explanation:

9 x 2 = 18

9 x 5m = 45m

y=1. A straight line in slope (m) and intercept (c) form is: y=mx+c. In this example, y is a straight line of slope 0 and y− intercept of 1.

To see the graph of y = 1

Now, According to the question:

What is called graph?

In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The points on the graph often represent the relationship between two or more things.

Hence, y=1. A straight line in slope (m) and intercept (c) form is: y=mx+c. In this example, y is a straight line of slope 0 and y− intercept of 1.

Now, To see the representation of graph  y = 1

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Applying the definition of a midpoint, the length of SA is: C. 4 m.

The midpoint of a line segment or a side of a triangle is the point where the segment or side is divided into two equal segments.

Based on the information given, we can say that triangles QRS and ASB are similar triangles, therefore, their corresponding sides are proportional to each other.

Thus, let SA = x. We will have the following:

SA/SQ = BA/RQ

x/(x + 4) = 3/6

Cross multiply:

6x = 3(x + 4)

6x = 3x + 12

6x - 3x = 12

3x = 12

3x/3 = 12/3

x = 4

Length of SA is: C. 4 m.

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Answer:b 81/256

Step-by-step explanation:

Answer: Jacinta

Step-by-step explanation: But the fraction still can be simplified to 1/7

Answer: j is correct

Step-by-step explanation:

The value of x and y in the angles of a triangle in the given diagram is x = 70°, y = 60°.

In ΔABC, we have

∠A = x

∠B = 50°

∠ACB = y

∠ACD = 120°

We know that,

If the exterior angle of a triangle is θ and the two opposite interior angles are θ₁ and θ₂, then the sum of θ₁ and θ₂ will be equal to the θ.

⇒θ = θ₁ + θ₂

⇒∠ACD = ∠A + ∠B

⇒120° = x + 50°

⇒x = 120° - 50°

⇒x = 70°

We know that,

If the angles of a triangle are θ₁, θ₂ and θ₃, respectively. Then the sum of θ₁, θ₂ and θ₃ is equal to 180°.

⇒θ₁ + θ₂ + θ₃ = 180°

⇒∠A + ∠B +  ∠ACD = 180°

⇒x + 50° + y = 180°

⇒70° + 50° + y = 180°

⇒120° + y = 180°

⇒y = 180° - 120°

⇒y = 60°

Hence, x = 70°, y = 60°

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The ratio of correct answers to total questions will not remain the same.

From the information, in the trivia game, Levi answered 8 questions correctly out of 10 turns in the game. In this case, the ratio will be:

= 8 / 10

= 4/5

= 4: 5

He then answered the next three questions correctly. The new ratio will be:

= (8 + 3) / (10 + 3)

= 11 / 13

The ratio of correct answers to total questions will not remained the same. In this case, 4/5 is different from 11/13.

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The solution of the given equation is 3+i or 3-i.

What is Quadratic Equation ?

Quadratic Equation can be defined as the equation in which it is in the form of ax^2+bx+c = 0

where a, b , c are constants.

Given,

equation x^2-6x+10 = 0

So for solving the roots , here she used quadratic formula

so,

x = (-b + [tex]\sqrt{b^2 - 4ac}[/tex] )/ 2a  or (-b - [tex]\sqrt{b^2 - 4ac}[/tex] )/ 2a

here a = 1 b = -6 and  c = 10

x =( 6 + [tex]\sqrt{6*6 - 4 * 1*10}[/tex] )/ 2 or ( 6 - [tex]\sqrt{6*6 - 4 * 1*10}[/tex] )/ 2

x = (6 + [tex]\sqrt{36-40}[/tex] ) / 2 or (6 - [tex]\sqrt{36-40}[/tex] ) / 2

[tex]\sqrt{36-40}[/tex] = 2i

so,

x = 6+2i / 2  or 6-2i / 2

x = 3+i or 3-i

Hence, The solution of the given equation is 3+i or 3-i.

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A vertical line's equation is provided by the expressions x = an or x = -a, where x denotes any point on the line's x coordinate and a denotes the point at which the line intersects the x-intercept.

The vertical line is either another line that is regarded as the base or a line that is perpendicular to the surface. The vertical lines in coordinate geometry are typically perpendicular to the horizontal lines and parallel to the y-axis. Whether it is going from top to bottom or bottom to top, a vertical line is always a straight line. The standing lines refer to the vertical lines.

A vertical line is a line on the coordinate plane with the same x-coordinate at each point. We discover that when the coordinates are joined when plotting the points for the function x = a on a coordinate plane, a vertical line results.

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The value of x is 3/7 because the angles of the two intersecting lines at point c, a c e and e c b, have specific values that can be used to solve for x.

Step 1: Calculate the angle of intersection between lines de and ab at point c.

Step 2: Calculate the angle of intersection between lines de and ab at point c.

Step 3: Subtract the angle of intersection between lines de and ab from the angle of intersection between lines d e and a b.

Step 4: Divide the difference in angles by 7 to get the value of x.

To calculate the value of x, first calculate the angle of intersection between lines de and ab at point c. This angle is (2x +2) degrees. Then calculate the angle of intersection between lines d e and a b at point c, which is (5x +3) degrees. Subtract the angle of intersection between lines de and ab from the angle of intersection between lines d e and a b, which is

(5x + 3) - (2x + 2) = 3x + 1

Divide the difference in angles by 7 to get the value of x, which is

x = (3x + 1)/7 = 3/7.

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Answer: Explain to them the game. Explain to them that you'll be giving them multiple numbers of elephants, and they need to try to figure out how many elephants there ...

Missing.

The cable company that has the best rate per channel is given as follows:

Tel-EVision.

The rate per channel is obtained applying the proportions in the context of this problem, dividing the total price by the number of channels.

Hence the rates for each company are given as follows:

The best rate is the lower rate, which is the justification for the answer given at the beginning of the problem.

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If two lines intersect at a 90-degree angle, we can say those lines are perpendicular.

Perpendicular lines are lines that intersect at right angles.

This produces a measurement of 90 degrees for each of the four angles created by the intersection of the line.

As the measurement of a straight line is 180 degrees, creating an angle of 90 degrees by one line intersection the other necessitates that the adjacent angle must also be 90 degrees because

180−90=90

When lines intersect, they form four different angles. The measurement of those angles will depend on how the lines intersect. Opposite angles will always be congruent, while adjacent angles will always have a sum of 180 degrees.

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The formula for a 30-60-90 triangle is as follows: the hypotenuse is always twice the length of the shorter leg, and the longer leg is the square root of 3 times the length of the shorter leg.

To calculate the sides of a 30-60-90 triangle, first determine the length of one of the shorter legs. Let's call this length "x". Then, the length of the hypotenuse is twice x (2x). The length of the other short leg is the square root of 3 times x (√3x). Finally, the length of the long leg is the square root of 2 times x (√2x). In summary, the formula for a 30-60-90 triangle is x, 2x, √3x, and √2x, where x is the length of one of the shorter legs. To calculate the angles in a 30-60-90 triangle, the angles are 30°, 60° and 90°, respectively. These angles are always the same in a 30-60-90 triangle regardless of the side lengths.

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Answer: -0.0555555.....

Step-by-step explanation:

Divide: -1 ÷18

= -0.05555555.....

Answer:

1/18 as a decimal is 0.0555555555555555555555555555555555555555555555555555555555555555...

Step-by-step explanation:

Answer: (-4,2)

Step-by-step explanation:

To solve the system using the elimination method, you first need to adjust the equations a bit so that you can add or subtract to eliminate either x or y.

Eliminating x seems more convenient in this situation, so let's try.

We can multiply 3 to the second equation so that we end up with this:

3x+5y=-2

-3x+6y=24

Now, all we need to do is add up the two equations to get:

11y=22

y=2

Since we now know the value of y, let's plug it in to get x.

3x+10=-2

3x=-12

x=-4

Therefore, the answer is x=-4, y=2 or(-4,2)

Answer:

(-4, 2)

Step-by-step explanation:

Answer:

17.a)  See below.

17.b)  x = 34.3 cm, y = 34.3 cm

18.a)  See below.

18.b)  r = 8 m

Step-by-step explanation:

Given information (see attachment 1):

According to the Similar Triangles Side Splitter Theorem, if a line parallel to one side of a triangle intersects the other two sides, then this line divides those two sides proportionally.  Therefore, triangles ABC and ADE are similar (refer to attachment 1).

As corresponding sides of similar triangles are always in the same ratio, the ratio of the base to height of the smallest triangle is equal to the ratio of the base to height  of the largest triangle:

[tex]\implies \sf DE:AD=BC:AB[/tex]

[tex]\implies y:80-x=60:80[/tex]

[tex]\implies \dfrac{y}{80-x}=\dfrac{60}{80}[/tex]

[tex]\implies 80y=60(80-x)[/tex]

[tex]\implies y=\dfrac{60(80-x)}{80}[/tex]

[tex]\implies y=\dfrac{3(80-x)}{4}[/tex]

The maximum area of a rectangle is when the length and height are equal:

[tex]\implies x=y[/tex]

Therefore, to find the value of x when the area of the rectangle is at its maximum, substitute x = y into the equation from part (a) and solve for x:

[tex]\implies x=\dfrac{3(80-x)}{4}[/tex]

[tex]\implies 4x=3(80-x)[/tex]

[tex]\implies 4x=240-3x[/tex]

[tex]\implies 7x=240[/tex]

[tex]\implies x=\dfrac{240}{7}[/tex]

[tex]\implies x=34.3\; \sf cm\;\;(nearest\;tenth)[/tex]

Therefore, the dimensions of the rectangle of maximum area to the nearest tenth are:

--------------------------------------------------------------------------------------------

Given information:

The formula for the volume of a cone is:

[tex]V=\dfrac{\pi r^2 h}{3}[/tex]

If the sum of the base radius r and the height h is 12 metres then:

[tex]\implies r + h = 12[/tex]

[tex]\implies h=12-r[/tex]

Substitute the expression for h into the volume of a cone formula to create an equation for V in terms of r:

[tex]\implies V=\dfrac{\pi r^2 (12-r)}{3}[/tex]

[tex]\implies V=\dfrac{12\pi r^2-\pi r^3}{3}[/tex]

[tex]\implies V=\dfrac{12\pi r^2}{3}-\dfrac{\pi r^3}{3}[/tex]

[tex]\implies V=4\pi r^2-\dfrac{1}{3}\pi r^3[/tex]

To find the radius of the cone that yields the maximum volume, differentiate V with respect to x:

[tex]\implies \dfrac{\text{d}V}{\text{d}x}=2 \cdot 4\pi r^{2-1}-3 \cdot \dfrac{1}{3}\pi r^{3-1}[/tex]

[tex]\implies \dfrac{\text{d}V}{\text{d}x}=8\pi r-\pi r^2[/tex]

[tex]\implies \dfrac{\text{d}V}{\text{d}x}=\pi r(8-r)[/tex]

Set the differentiated equation equal to zero and solve for x:

[tex]\implies \pi r(8-r)=0[/tex]

[tex]\implies 8-r=0[/tex]

[tex]\implies r=8[/tex]

(Note: r is also equal to zero, but we can discard that solution since the radius has to be more than zero).

Therefore, the radius of the cone that yields the maximum volume is 8 m.

The quotient is 2x^2 + 4x +6.

The given polynomial is 2x^3 - 2x -12. As we can see that the given polynomial is a three-degree polynomial but the second degree term is missing, we can write the polynomial as 2x^3 + 0x^2 - 2x -12.

The divisor is (x-2).

First we choose a term to multiply with the first term of the divisor such that we get the first term of the polynomial:

(x) (2x^2) = 2x^3

Thus, we multiply the divisor (x-2) by 2x^2 which gives 2x^3 - 4x^2

Now we subtract this from the polynomial which gives 4x^2 -2x -12.

Repeating the same we multiply the divisor by 4x which gives 4x^2 - 8x. Subtracting the same from 4x^2 -2x -12, we get 6x - 12.

Now we multiply the divisor with 6 to get 6x - 12. Subtracting it from the remaining polynomial 6x -12 leaves the remainder 0.

Thus, we get the quotient as  2x^2 + 4x +6.

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when the value of x=1 the value of y will be 0.

What is a function?

A function is a special form of relation where every input has exactly one output. In other words, for every input value, the function returns exactly one value. Given that one is mapped to two separate values, the graph above depicts a relation rather than a function. But if one were instead mapped to a single value, the relation above would change into a function. In addition, output values could match input values exactly.

The function machine receives the x-value input. The function machine then executes its operations and produces the y-values. Any function may be the function within.

If y varies directly as x, and y=2 when x=3

f(x)=y=x+c

So 2 = 3+c

c=-1

So function is y = x-1

y = 1-1

y=0

Hence, when the value of x=1 the value of y will be 0.

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Area a + b + c = Area of Semi-circle on BC (radius 5). = Area c + d ... Shaded area = Sum of semi-circles on AC and AB – Semi-circle on BC + Triangle Area.

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