The traight line L ha equation 5x2y=31. The point A ha coordinate (0,1). The traight line M i perpendicular to L and pae through A. Line L croe the y-axi at the point B. Line L and M interect at the point C. Work out the area of the triangle ABC

Answers

Answer 1

the area of the triangle ABC is found by using the formula 1/2 * (base * height). Here, the base is 0 and the height is 1. Thus, the area of the triangle ABC = 0.5.

Let x = 0, y = 1 in 5x2y = 31

31 = 0

Thus, the point B is (0, 0).

The area of the triangle ABC = 1/2 * (0 * 1) + (0 * 1) + (1 * 0) = 0.5.

The equation of line L is given as 5x2y = 31. To find the point B, we need to substitute x = 0 in the equation. Doing so, we get 31 = 0, which means that the point B lies on the y-axis at (0, 0).

Next, since the line M is perpendicular to L and passes through A, we can assume that it is a horizontal line passing through (0, 1). Thus, the point C is the point of intersection of L and M, which is (1, 0).

Finally, the area of the triangle ABC is found by using the formula 1/2 * (base * height). Here, the base is 0 and the height is 1. Thus, the area of the triangle ABC = 0.5.

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Related Questions

Sergio poured 4/5 of the soda from a 2 liter bottle for his guests. How much soda in liters is still left in the bottle

Answers

The soda still left in the bottle is given as 4 liters in 2-liter bottle.

As mentioned, Sergio poured 4/5 of the soda from a 2-liter bottle for his guests.

What is the Ratio?

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

Here,
The soda left in the bottle will be the difference of the total quantity and the quality of the soda poured. So,
= 20 - 4/5 × 20
= 20 - 16
= 4

Thus, the soda still left in the bottle is given as 4 liters of a 2-liter bottle.

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What are the first two steps when finding the value of the expression below?
65 (30-24 divided 6× 2)
Use the drop-down menus to explain the first two steps.
The first step us to find the value of ____
The second step is to find the value of ___

Answers

Answer:

The first step is 24 divided by 6 ..... (4)

The second step is 4 x 2 ...... (8)

Step-by-step explanation:

65(30-24 divided by 6 x 2)

65(30- 4 x 2)

65(30 - 8)

65(22)

1,430

Can someone help me with Question 2b of this assignment? I'd deeply appreciate it! :)

Answers

Answer:

x=-6

Step-by-step explanation:

[tex]\frac{1}{2} x[/tex]-6=2x+3

∴2×( [tex]\frac{1}{2} x[/tex]-6)=2×(2x+3)

∴x-12=4x+6

∴3x=-18

∴x=-6

(v³ + 2v² - 21v +21) ÷ (v + 6)

Answers

Answer:

v3+2v2−21v+21/v+6

Step-by-step explanation:

There are no solutions to this equation

how should the decimal point in 52.48be m

Answers

Answer:

5 spaces right

hope this helps

Need Help!!!!!!!!! Solve for side similar triangle

Answers

Answer:

UT=11

Step-by-step explanation:

UV is twice the length of RS. Since UV=11 then RS=22. UT is also twice the length of RS. So if RS=22, then UT=[tex]\frac{1}{2} * 22[/tex]. UT=11

A certain arcade game gives players tickets. The table below shows the number of tickets a player gets for the number of points.

Answers

Answer: Each point appears to give the same number of tickets

9 points give 54 tickets

Step-by-step explanation:

Each point appears to give the same number of tickets

To find the number of tickets, a point gives

divide the number of tickets by the number of points.

18/3 = 6

you get six tickets per point

find the number of points that give 54 tickets by dividing 54 by 6

54/6=9

9 points give 54 tickets

Mio bought x grams of flour. Sol bought 3 8​ more than that. Select ALL of the equations that represent the relationship between the amount of flour that Mio bought, x, and the amount of flour that Sol bought, y.

1) y= 3/8x
2) y= 5/8x
3) y= x+3/8x
4) y= x-3/8x
5) y= 11/8x

Answers

The equation that correctly represents the problem is 3) y = x+ 3/8x

What is a linear equation with two variables?

An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero. For example, 10x+4y = 3 and -x+5y = 2 are linear equations in two variables.

Given here, mio brought x grams and sol bought 3/8 times more than x hence, sol bought y = x  + 3/8x  

Hence, the correct option is 3) y=x+3/8x

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if x,10,2x-4, and 12 are in proportion find the value of x

Answers

Answer:

x=5

Step-by-step explanation:

To find the value of x, we need to first set up the proportion using the given information. Since the given values are in proportion, we can set up the proportion as follows:

x / 10 = (2x - 4) / 12

Next, we can cross-multiply to solve for the value of x:

12x = 10(2x - 4)

12x = 20x - 40

-8x = -40

x = 5

Thus, the value of x is 5. This means that the other values in the proportion are also 5, 10, 10, and 12, respectively.

The sum of two numbers is 46. The larger number is 16 more than the smaller number.

Answers

Answer:

Smaller number: 15           Larger number: 31

Step-by-step explanation:

Let's call the smaller number x

So, the larger number will be x+16 (it's 16 more)

Then, write an equation:
x (smaller number) + (x+16) (larger number) = 46 (sum)

x+x+16=46
2x+16=46
2x=30
x=15
So, the smaller number is 15
The larger number is x+16, so plug in x:
x+16 = 15+16 = 31
The smaller number is 15, and the larger number is 31

[tex]y = 15 \\ x = 31[/tex]

Step-by-step explanation:

[tex]y + 16 + y = 46 \\ 2y = 30 \\ y = 15 \\ \\ x = 15 + 16 \\ x = 31[/tex]

Which interval contains 11 states? Check all that apply. 0 to 3 3 to 6 6 to 9 9 to 12 12 to 15 15 to 18 18 to 21

Answers

The intervals that contain 11 states, are given as follows:

3 to 6.6 to 9.

What is shown by the bar graph?

The bar graph presented by the image shown at the end of the answer shows the number of states present in each interval.

The features of the graph are given as follows:

Horizontal axis: interval.Vertical axis: number of states in each interval.

Then the number of states for each interval are given as follows:

0 to 3: 16 states.3 to 6: 11 states.6 to 9: 11 states.9 to 12: 3 states.12 to 15: 3 states.15 to 18: 3 states.18 to 21: 4 states.

Hence the intervals 3 to 6 and 6 to 9 are the intervals that contain 11 states, being the correct answers to this problem.

Missing Information

The bar graph is given by the image shown at the end of the answer.

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Write the standard form equation for a hyperbola with center at the origin, vertices at (1, 0) and (-1, 0), and
foci at (5, 0) and (-5, 0).

Answers

Answer:

The answer is the standard form equation for a hyperbola with center at the origin, vertices at (1, 0) and (-1, 0), and foci at (5, 0) and (-5, 0), which is:

x^2 - \frac{y^2}{5} = 1

This equation describes the shape of the hyperbola and allows you to determine the location and size of the hyperbola on a coordinate plane.

Step-by-step explanation:

The standard form equation for a hyperbola with center at the origin, vertices at (1, 0) and (-1, 0), and foci at (5, 0) and (-5, 0) is given by:

$$\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$$

where $a$ and $b$ are the lengths of the semi-major and semi-minor axes, respectively. In this case, the distance between the vertices is 2, so the semi-major axis is 1 and the semi-minor axis is $\sqrt{5}$. Therefore, the equation of the hyperbola is:

$$\frac{x^2}{1^2} - \frac{y^2}{\sqrt{5}^2} = 1$$

which simplifies to:

x^2 - \frac{y^2}{5} = 1

What are the types of triangles based on their sides and angles? How do you classify a triangle as equilateral, isosceles, scalene, acute, right, or obtuse? Give an example of each.

Answers

Based on their sides, the 3 triangles are classified as equilateral triangles, isosceles triangles, and scalene triangles.

A triangle is scalene if all of its three sides and angles are different

Scalene-Triangle-1

In the figure, all three symbols that are given on each side are different, which denotes that all three sides are unequal.

If two of its sides are equal, a triangle is called an isosceles.

One example of the angles of an isosceles acute triangle is 50°, 50°, and 80°.

A triangle with all three equal sides is called equilateral.

The sum of all three angles of an equilateral triangle is equal to 180 degrees.  60° + 60° + 60° = 180°

Acute angles measure less than 90 degrees.

the examples of acute angles are 25°, 36°, 47°, 64°, 55°, 72°, 80° and so on

Right angles measure 90 degrees.

Examples of right angles are all around us. We can see right angles in the corners of a room, book, cube, windows, and at several other places.

Obtuse angles measure more than 90 degrees

Examples of obtuse angles include 166°, 121°, 110°, 117°, and 91°.

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PLEASE HURRY! Gianna has 23 feet of leftover wood to use to build a bookshelf. The design calls for two side pieces that are each 4 feet in length, plus a top piece, a bottom piece, and three shelves that are equal in length.

How long is each shelf?

___ feet

Answers

Why do you want an answer immediately. Just know, don't ever cheat by using 'Brainly'

Which equation has infinitely many solutions? 5(2x 4) = 10x – 12 5(2x 4) = 10(x 2) 5(2x 4) = 12x 5(2x 10) = 20(x 1)

Answers

The equation that has infinitely many solutions is 5(2x + 4) = 10(x + 2).

An equation can have infinitely many solutions when both sides of the equation satisfy the same conditions. The system of an equation has infinitely many solutions when the lines are coincident, and they have the same y-intercept. If the two lines have the same y-intercept and the slope, they are actually in the same exact line. For the given equations it can determine if the equation has infinitely many solutions by simplifying the equation and see if both sides are equal. Hence,

5(2x + 4) = 10x – 12

10x + 20 ≠ 10x - 12

5(2x + 4) = 10(x + 2)

10x + 20 = 10x + 20

5(2x + 4) = 12x

10x + 20 ≠ 12x

5(2x + 10) = 20(x + 1)

10x + 50 ≠ 20x + 20

Hence, 5(2x + 4) = 10(x + 2) has infinitely many solutions.

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At Sparky' Candy World, Mile pent a total of $13. 75 on gummy bear and jelly bean. He bought 2. 5 pound of gummy bear at $3. 40 per pound. If jelly bean cot $1. 50 per pound, how many pound of jelly bean did he buy?

Answers

By solving this question of algebra we can calculate that Mile bought 3.5 pounds of jelly bean.

What is algebra?

Algebra is the study of using variables to denote some quantity, and then solving equations to calculate the value of the quantity based on some conditions given.

How to solve questions of algebra?

Let x be the amount of gummy bear bought and y be the amount of jelly bean bought. Then, 3.40x + 1.5y = 13.75 (total amount of money)

x = 2.5 (given in question)

then,

3.40 (2.5) + 1.5y = 13.75

y = 3.5 pounds

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Ethan buy a video game on ale. If the video game ueully cot $39. 99 and it wa on ale for 20% off how much did ethan pay?

Answers

Answer:

$31.99

Step-by-step explanation:

I have no idea what to put here

Given that is it ever possible to have
Explain.

Answers

The answer is yes, it is possible to have the sum of square roots equal the square root of the sum of the radicands.

What are square roots?

A square root of a number is a value that, when multiplied by itself, gives the number.

Given that, is it possible √a+√b = √a+b

Yes, it is possible to have the sum of square roots equal the square root of the sum of the radicands.

If either a or b equals zero, then the sums would be the same.

Since the square root of 0 is ±0, adding it to a given radical would not change the radical. Also, adding zero to the radicand would not change its value.

Hence, it is possible to have the sum of square roots equal the square root of the sum of the radicands.

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what is the difference between 6x2 and 6²

Answers

Answer:

6x2 is multiplying 6 by 2 while 6² is said as '6 squared' meaning 6x6.

Step-by-step explanation:

6x2 is basic multiplication of 6x2 while 6² means we should completed 6x6.

in a factorial anova, compared to a design with only one independent variable, a major modification of using anova to analyze variability is that the sources of

Answers

A t-test cannot cover more than one group. This has to do with the underlying method used to calculate the test value.

Explain about t-test?

The t-test is designed to compare the means of two populations based on the means of the two samples. (any sample from either population).

The most important observation is that the t-test computes the difference between two sample means.

If you have trouble understanding 'variance', you can use the word standard deviation from the previous text to get your points.

In other words, there is more than one difference between the groups, but we want one measure of Total Difference Between Groups. The t-test cannot do that.

So the procedure for groups of three or more is: Run ANOVA first. As a second step, if you have reason to believe that differences exist (based on this test), you can use the t-test to determine where those differences lie.

A t-test cannot cover more than one group. This has to do with the underlying method used to calculate the test value.

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Let's solve. 3x a) 3X 8 10. d) { + 14/= 1/1/2 ¼ 4 / = 7 3 8) ²³² + ³ = 5 X​

Answers

Answer: hmmmm who knows?

Step-by-step explanation: but you got it good luck!

jay designed 4 t-shirts. sal designed 5 times as many t-shirts. which equation shows how many more t-shirts sal designed?

Answers

The equation which shows that how many more t- shirts sal designed is x^{y} .....

If jay designed 4 t-shirts and sal designed 5 times as many t-shirts. So the equation which shows how more t- shirts sal designed is....

Firstly we make the data to simplify the peoblem:

Suppose:

T-shirts designed by jay =  x

T-shirts designed by sal = y

As t-shirts designed by jay are 4 so

x=4

and t-shirts designed by sal are 5 times as many t- shirts so

y= 5times = 4×4×4×4×4 = 1,024

So the equation which shows how many more t-shirts sal designed will be:

Required equation = x^{y}

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If Hugo has 4 times as many quarters as nickels and they have a combined value of 840 cents, how many of each coin does he have?

Answers

Let Q be the number of quarters and N be the number of nickels that Hugo has. We are given that Hugo has 4 * N quarters and that the total number of quarters and nickels is worth 840 cents. Since each quarter is worth 25 cents and each nickel is worth 5 cents, the total number of quarters is worth 25 * Q cents and the total number of nickels is worth 5 * N cents. Therefore, the total number of quarters and nickels is worth 25 * Q + 5 * N cents. Since the total number of quarters and nickels is worth 840 cents, we can set up the following equation to represent this information:

25 * Q + 5 * N = 840

We are also given that Hugo has 4 * N quarters, so we can set up the following equation to represent this information:

Q = 4 * N

We can solve this system of equations to find the number of quarters and nickels that Hugo has. Substituting the value of Q in the second equation into the first equation, we get the following:

25 * (4 * N) + 5 * N = 840

Distributing the 25 on the left side of the equation, we get the following:

100 * N + 5 * N = 840

Combining like terms, we get the following:

105 * N = 840

Dividing both sides of the equation by 105, we get the following:

N = 8

Substituting the value of N into the second equation, we get the following:

Q = 4 * 8

Solving for Q, we get the following:

Q = 32

Therefore, Hugo has 8 nickels and 32 quarters.

Answer:

32 quarters

8 nickels

Step-by-step explanation:

Information:

1 quarter = 25 cents1 nickel = 5 cents

Define the variables:

Let x be the number of quarters.Let y be the number of nickels.

If Hugo has 4 times as many quarters as nickels:

[tex]\implies x=4y[/tex]

If the combined value of quarters and nickels is 840 cents:

[tex]\implies 25x+5y=840[/tex]

Substitute the first equation into the second equation and solve for y:

[tex]\implies 25(4y)+5y=840[/tex]

[tex]\implies100y+5y=840[/tex]

[tex]\implies 105y=840[/tex]

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

Substitute the found value of y into the first equation and solve for x:

[tex]\implies x=4(8)[/tex]

[tex]\implies x=32[/tex]

Therefore, Hugo has:

32 quarters8 nickels

You might need:
Nizhoni adds water at a constant rate to a 2 L reservoir in a water filtering pitcher until it is full.
At the same time, water goes through the filter and out of the reservoir, into the pitcher. It takes
5/11 minutes to fill the reservoir, then another 3 minutes for the reservoir to empty.
3 1/3 minutes for it to empty. at what rate does nizhoni add water to the reservoir?

Answers

At the rate of 4 2/5 L of water is added into the reservoir per minute.

What is Unitary Method?

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

As  It takes 5/11 minutes to fill the reservoir.

So, the rate at which Nizhoni adds water to the reservoir.

Rate=  Volume/ Time taken

Rate = 2 L/ (5/ 11)

        = 2 x 11/5

        = 22/5 L/ min

         = 4 2/5 L/ min.

Hence, at the rate of 4 2/5 L of water is added into the reservoir in one minute.

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Answer: 5

Step-by-step explanation: I answered this question.

Work out the circumference of this circle. Give your answer in terms of pi.

Answers

Answer:

[tex]12\pi[/tex]

Step-by-step explanation:

Circumference Formula: [tex]2\pi r[/tex]

Our radius is 6, plug that in.

[tex]2\pi 6[/tex]

12[tex]\pi[/tex]

Leave in terms of pi, so do not simplify further.

Twice w is at most 30

Answers

Answer:

2w [tex]\leq[/tex] 30

Step-by-step explanation:

Two times the value of w must be less than or equal to 30

Answer:  w < = 15

Step-by-step explanation:

Our equation is

2w < = 30

Divided by 2 both sides

w < = 15

Using the "split" string method from the preceding lesson, complete the get_word function to return the {n}th word from a passed sentence. For example, get_word("this is a lesson about lists", 4) should return "lesson", which is the 4th word in this sentence. Hint: remember that list indexes start at 0, not 1.

Answers

The function to return the nth word of the sentence will be given as -

def get_word(sentence, n):

# Only proceed if n is positive

if n > 0 :

words = sentence.split()

# Only proceed if n is not more than the number of words

if n <= len(words) :

return words[n-1]

return("")

According to the data given in the question we can see that the method to obtain the string will be the split string method,

According to the split string method, we separate distinct parts of the strings based on the delimiter using signs such as comma(,), hyphen(-), whitespace), etc.

To extract the 4th word in the sentence, we will assume position 3 for the 4th word.

#The function to print lesson counting from 0,

print(get_word("This is a lesson about lists", 4))

print(get_word("This is a lesson about lists", -4))

#No printing as the first condition is not met

print(get_word("Now we are cooking!", 5))

#No printing occurs as it also does not meet the condition of the second statement.

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if two sides of a triangle are 22 in and 13 in, what is the smallest whole number value for the 3rd side?

Answers

If two sides of a triangle are 22 in and 13 in, then is the smallest whole number value for the 3rd side will be 10

According to the rule of triangle the sum of first angle and second angle should be greater than the third angle.

first angle+ second angle > third angle

Here

22-13 = 9

so to became a triangle the minimum value of the third side will be 10(9+1).

Therefore, If two sides of a triangle are 22 in and 13 in, then is the smallest whole number value for the 3rd side will be 10

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Write an equation of the line that passes through (4, 8) and is perpendicular to the line y = x-5.
An equation of the perpendicular line is

Answers

The slope of a line that is perpendicular to the line y = x - 5 is the negative reciprocal of the slope of y = x - 5. The slope of y = x - 5 is 1, so the slope of the line that passes through (4, 8) and is perpendicular to y = x - 5 is -1.

We can use the point-slope form of a line to write the equation of the line that passes through (4, 8) and has a slope of -1. The point-slope form of a line is given by the equation y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. In this case, (x1, y1) is (4, 8) and m is -1, so the equation of the line is y - 8 = -1(x - 4). Simplifying this equation, we get y - 8 = -x + 4. Adding 8 to both sides of the equation, we get y = -x + 12. This is the equation of the line that passes through (4, 8) and is perpendicular to y = x - 5.

The distance between (-7, a) and
(5, 1) is 13 units.
Find two possible values for a.

Answers

Answer:

1

Step-by-step explanation:

you will be required to find a magnitude of the two points that is (5,1) -(-7,a) =(12,1-a)

then find square root using the formula √x^2+y^2

thus (√12^2+a^2)=13 thus 12+a= 13 hence a=13-12

a=1

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