a line is perpendicular to y=4x-2 and intersects the point (4,-11). what is the equation of this perpendicular line?

Answers

Answer 1

Answer:

y = -1/4x - 10

Step-by-step explanation:

Hey there!

Well to the slopes of 2 perpendicular lines are reciprocals of each other meaning if the line has a slope of 4 then it’s perpendicular line has a slope of -1/4.

Now to find the y intercept we need to graph,

y = -1/4x and point (4, -11)

Look at the image below.

By looking at the image below we can tell that in order for the perpendicular line to go through point (4,-11) it would be -10.

The equation is y = -1/4x - 10

Hope this helps :)

A Line Is Perpendicular To Y=4x-2 And Intersects The Point (4,-11). What Is The Equation Of This Perpendicular

Related Questions

Find the length of UX

A. 6.03
B. 76.11
C. 7.96
D. 76.53

Answers

Answer:

Answer would be D

Step-by-step explanation:

The measure of the length UX will be 76.53 units. Then the correct option is D.

What is trigonometry?

The connection between the lengths and angles of a triangular shape is the subject of trigonometry.

The measure of the length UX will be given by sine of angle 6°.

  sin 6° = UR / UX

0.1045 = 8 / UX

     UX = 76.53 units

Then the correct option is D.

More about the trigonometry link is given below.

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need help please will give good rating and show work

Answers

Step-by-step explanation:

u just need to imagine it was x^2-17X+16 in the beginning and add square onto the x after u factorise. then solve the x. hope it helps

Please help! Explanation please!​

Answers

Answer:

11 meters.

Step-by-step explanation:

The important thing to note here is that the backyard is a square. Since it's a square, all of its sides all equivalent in length. Thus, let's find the length of the sides. To do this, we use the area formula.

The formula for the area of a square is:

[tex]A=n^2[/tex]

Where n is a side. Since we know the area already, we can find n. Find n:

[tex]121=n^2\\n=11[/tex]

Since every side in a square are equivalent, all sides are 11 meters in length.

Therefore, each section of the fence should be 11 meters long.

You own a farm and have several fields in which your livestock grazes. You need to order barbed-wire fencing for a small pasture that has a length of 5 yards and a width of 3 yards. The barbed wire must be long enough to be placed on all four sides of the outside pasture. How many yards of barbed-wire should you order?

Answers

Answer:

16 yards of barbed wire

Step-by-step explanation:

Length=5 yards

Width=3 yards

Perimeter of the pasture=2(length + width)

=2(5 yards +3 yards)

=2(8 yards)

=16 yards

You should order 16 yards of barbed wire for fencing the pasture

Solve. 4x−y−2z=−8 −2x+4z=−4 x+2y=6 Enter your answer, in the form (x,y,z), in the boxes in simplest terms. x= y= z=

Answers

Answer:

(-2, 4, 2)

Where x = -2, y = 4, and z = 2.

Step-by-step explanation:

We are given the system of three equations:

[tex]\displaystyle \left\{ \begin{array}{l} 4x -y -2z = -8 \\ -2x + 4z = -4 \\ x + 2y = 6 \end{array}[/tex]

And we want to find the value of each variable.

Note that both the second and third equations have an x.

Therefore, we can isolate the variables for the second and third equation and then substitute them into the first equation to make the first equation all one variable.

Solve the second equation for z:

[tex]\displaystyle \begin{aligned} -2x+4z&=-4 \\ x - 2 &= 2z \\ z&= \frac{x-2}{2}\end{aligned}[/tex]

Likewise, solve the third equation for y:

[tex]\displaystyle \begin{aligned} x+2y &= 6\\ 2y &= 6-x \\ y &= \frac{6-x}{2} \end{aligned}[/tex]

Substitute the above equations into the first:

[tex]\displaystyle 4x - \left(\frac{6-x}{2}\right) - 2\left(\frac{x-2}{2}\right)=-8[/tex]

And solve for x:

[tex]\displaystyle \begin{aligned} 4x+\left(\frac{x-6}{2}\right)+(2-x) &= -8 \\ \\ 8x +(x-6) +(4-2x) &= -16 \\ \\ 7x-2 &= -16 \\ \\ 7x &= -14 \\ \\ x &= -2\end{aligned}[/tex]

Hence, x = -2.

Find z and y using their respective equations:

Second equation:

[tex]\displaystyle \begin{aligned} z&=\frac{x-2}{2} \\ &= \frac{(-2)-2}{2} \\ &= \frac{-4}{2} \\ &= -2\end{aligned}[/tex]

Third equation:

[tex]\displaystyle \begin{aligned} y &= \frac{6-x}{2}\\ &= \frac{6-(-2)}{2}\\ &= \frac{8}{2}\\ &=4\end{aligned}[/tex]

In conclusion, the solution is (-2, 4, -2)

Answer:

x = -2

y =4

z=-2

Step-by-step explanation:

4x−y−2z=−8

−2x+4z=−4

x+2y=6

Solve the second equation for x

x = 6 -2y

Substitute into the first two equations

4x−y−2z=−8

4(6-2y) -y -2 = 8  

24 -8y-y -2z = 8

-9y -2z = -32

−2(6-2y)+4z=−4

-12 +4y +4z = -4

4y+4z = 8

Divide by 4

y+z = 2

z =2-y

Substitute this into -9y -2z = -32

-9y -2(2-y) = -32

-9y -4 +2y = -32

-7y -4 = -32

-7y =-28

y =4

Now find z

z = 2-y

z = 2-4

z = -2

Now find x

x = 6 -2y

x = 6 -2(4)

x =6-8

x = -2

If sin∅+cos∅ = 1 , find sin∅.cos∅.​

Answers

Answer:  0

=============================================

Explanation:

The original equation is in the form a+b = 1, where

a = sin(theta)

b = cos(theta)

Square both sides of a+b = 1 to get

(a+b)^2 = 1^2

a^2+2ab+b^2 = 1

(a^2+b^2)+2ab = 1

From here notice that a^2+b^2 is sin^2+cos^2 = 1, which is the pythagorean trig identity. So we go from (a^2+b^2)+2ab = 1 to 1+2ab = 1 to 2ab = 0 to ab = 0

Therefore,

sin(theta)*cos(theta) = 0

Answer:

sin ∅ cos ∅ = 0.

Step-by-step explanation:

(sin∅+cos∅)^2 = 1^2 = 1

(sin∅+cos∅)^2  = sin^2∅ + cos^2∅ + 2sin ∅ cos ∅ = 1

But  sin^2∅ + cos^2∅ = 1, so:  

2sin ∅ cos ∅ + 1 = 1

2 sin ∅ cos ∅ = 1 - 1 = 0

sin ∅ cos ∅ = 0.

Write 3.6 as a percent.

Answers

Answer:

360%

Step-by-step explanation:

You have to multiply 3.6 by one hundred to get the percentage. When you multiply decimals by numbers that are multiples of ten, you move the decimal place to the right of the number by the number of zeroes that is in your number. Sorry if its confusing.

Examples: 3.76 * 100 = 376. You move the decimal to the right two spaces

46.263 * 1000 = 46263. You move the decimal to the right three spaces. Hope you understand.

Elena drank 3 liters of water yesterday. Jada drank 3/4 times as much water as much water as Elena. Lin drank twice as much water as Jada. Did jada drink more or less water than Elena?

Answers

Answer:

Jada drank less water than Elina.

Step-by-step explanation:

Water drunk by Elina = 3 liters

Jada drank the water [tex]\frac{3}{4}[/tex] times as much as water as Elina.

Therefore, water drunk by Jada = [tex]\frac{3}{4}\times 3[/tex]

                                                     = [tex]\frac{9}{4}[/tex]

                                                     = 2.25 liters

Lin drank water twice as much as Jada.

Therefore, Lin drank the amount of water = 2 × 2.25

                                                                   = 4.5 liters

Since Jada drank 2.25 liters of water and Elina drank 3 liters

Therefore, Jada drank less water than Elina.

3a + 7 b = 2
2a + 9 b = 15

solve this linear equations using elimination method

please show your working ✨✨ THANK YOU

Answers

Answer:

a = -87/13

b = 41/13

Step-by-step explanation:

3a + 7b = 2

2a + 9b = 15

You need to have one of the coefficients have the same number but the opposite sign in both equations.  Multiply the first equation by -2 and the second equation by 3.  You will then be able to cancel out a and solve for b.

-2(3a + 7b) = -2(2)

-6a - 14b = -4

3(2a + 9b) = 3(15)

6a + 27b = 45

-6a - 14b = -4

6a + 27b = 45

0a + 13b = 41

13b = 41

b = 41/13

Plug in the b-value into one of the given equations and solve for a.

3a + 7b = 2

3a + 7(41/13) = 2

3a + 287/13 = 2

3a = -261/13

a = -87/13

Alonso went to the market with \$55$55dollar sign, 55 to buy eggs and sugar. He knows he needs a package of 121212 eggs that costs \$2.75$2.75dollar sign, 2, point, 75. After getting the eggs, he wants to buy as much sugar as he can with his remaining money. The sugar he likes comes in boxes that each cost \$11.50$11.50dollar sign, 11, point, 50.

Answers

Answer:

2.75+11.50S[tex]\leq[/tex]55

4

Step-by-step explanation:

The Total amount of money Alonso went to the market with is: = $55

Items to be bought includes:

eggssugar

Alonso knows that:

A pack of 12 eggs costs = $2.75 Now, he wants to use the remaining amount to purchase as much sugar as possible

Requirement for his taste for sugar:

a box of sugar he likes = $11.50

From this information, the objective would be to determine the number of sugar he can purchase with the money left after he has already bought the eggs.

To start with, the amount of money left after buying the eggs is:

= $55 - $2.75

= $52.25

Now, if a box of sugar he likes cost = $11.50

Then he will be able to purchase (x( bost of sugar with = $52.50

Now, to determine the number of boxes of sugar he can purchase, we have:

1 box of sugar = $11.50

x(box) of sugar = $52.25

[tex]\mathbf{x (box) of sugar = \dfrac{\$52.25 \times 1 box of sugar }{\$11.50}}[/tex]

x = 4.5 box of sugar

Therefore, after buying a pack of 12 eggs for = $2.75, Alonso will be able to buy [tex]\mathbf{ 4\dfrac{1}{2}}[/tex]  or 4.5 boxes of sugar.

Learn more about word problems here:

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Match each expression with its greatest common factor. 4a + 8 2a2 + 8a 12a2 − 8a 4 − 6a Greatest Common Factor Expression 4 : 2 : 2a : 4a :

Answers

Answer:

see explanation

Step-by-step explanation:

4a + 8               4

2a² + 8a            2a

12a² - 8a           4a

4 - 6a                2

Match each expression with its greatest common factor as follows;

4a + 8               4

2a² + 8a            2a

12a² - 8a           4a

4 - 6a                2

What is the greatest common factor?

The largest number that is found in the common factors is called the greatest common factor.

The given expression are;

4a + 8              

2a² + 8a            

12a² - 8a      

4 - 6a              

The greatest common factor of the expression are as follows;

4a + 8  = 4(a+2) = common factor = 4    

2a² + 8a = 2a(a+4a) = common factor = 2a

12a² - 8a = 4a(3a-2) = common factor = 4a

4 - 6a = 2(2-3a) = common factor = 2

Learn more about the greatest common factor here;

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The digits of a two-digit number differ by 3. If the digits are interchanged, and the resulting number is added to the original number, we get 143. What can be the original number?

Answers

Answer:

The original number could be 85.

Step-by-step explanation:

Let the 2 digits be x and y.

Let the number be xy then, assuming that x is the larger digit:

x - y = 3.

x = y + 3

Also

10y + x + 10x + y = 143

Substituting for x:

10y + y + 3 + 10(y + 3) + y = 143

22y + 33 = 143

22y = 110

y = 5.

So x = y + 3 = 8.

Answer:

Let the unit digit be x and tens digit be x + 3

Therefore, the original number = 10(x + 3) + x

On interchanging, the number formed = 10x + x + 3

❍ According to Question now,

➥ 10(x + 3) + x + 10x + x + 3 = 143

➥ 10x + 30 + 12x + 3 = 143

➥ 22x + 33 = 143

➥ 22x = 143 - 33

➥ 22x = 110

➥ x = 110/22

x = 5

__________________...

Therefore,

The unit digit number = x = 5

The tens digit number = x + 3 = 5 + 3 = 8

__________________...

The original number = 10(x + 3) + x

The original number = 10(5 + 3) + 5

The original number = 50 + 30 + 5

The original number = 85

Hence,the original number is 85.

Before 8 A.M., there were 64 trucks and 24 cars in a parking lot. Between 8 A.M. and 9 A.M., more cars entered the parking lot and no trucks entered or exited the lot. At 9:00 A.M., the number of trucks represented 1/5 of the parking lot's vehicles. How many cars entered between 8 A.M. and 9 A.M? A. 56 B. 112 C. 148 D. 192 PLZ EXPLAIN

Answers

Answer:

232 cars

Step-by-step explanation:

Let's say the number of cars that entered is c.

At 9:00 am, there are a total of 24 + c cars and 64 trucks. We know that this value of 64 represents 1/5 of the total number of vehicles. The total number of vehicles is (24 + c) + 64 = 88 + c. So, we have:

64/(88 + c) = 1/5

Cross-multiply:

88 + c = 64 * 5 = 320

c = 320 - 88 = 232

Thus, the answer is 232 cars.

Note: as 232 doesn't show up in the answer choices, it's possible that the problem was copied correctly.

~ an aesthetics lover

Answer:

232 cars entered between 8 and 9

Step-by-step explanation:

at 9 am there are 64 x 5 vehicles total = 320

320 - 64 - 24 = 232

Find the difference of functions s and r shown
below.
r(x) = -x2 + 3x
s(x) = 2x + 1
(s - r)(x) =

Answers

Answer:

[tex]\displaystyle (s-r)(x) = x^2 - x + 1[/tex]

Step-by-step explanation:

We are given the two functions:

[tex]\displaystyle r(x) = -x^2 + 3x \text{ and } s(x) = 2x + 1[/tex]

And we want to find:

[tex]\displaystyle (s-r)(x)[/tex]

This is equivalent to:

[tex]\displaystyle (s-r)(x) = s(x) - r(x)[/tex]

Substitute and simplify:

[tex]\displaystyle \begin{aligned}(s-r)(x) & = s(x) - r(x) \\ \\ & = (2x+1)-(-x^2+3x) \\ \\ & = (2x+1)+(x^2-3x) \\ \\ & = x^2 +(2x-3x) + 1 \\ \\ & = x^2 - x + 1 \end{aligned}[/tex]

In conclusion:

[tex]\displaystyle (s-r)(x) = x^2 - x + 1[/tex]

The line plot below displays the fraction of incoming calls answered before the second ring by a group of employees. What fraction of employees answered less than of their incoming calls before the second ring?

Answers

Answer:

1/6

Step-by-step explanation:

People who answered less than 1/2 were:  2 +  1 + 3 = 6 people.

There are a total of 36 people.

People who answered their calls before the second ring were only 6/36.

When we simplify the fraction, we get 1/6.

So, the answer is 1/6

At the Olympic games, many events have several rounds of competition. One of these events is the men's 100 100100-meter backstroke. The upper dot plot shows the times (in seconds) of the top 8 88 finishers in the final round of the 2012 20122012 Olympics. The lower dot plot shows the times of the same 8 88 swimmers, but in the semifinal round. Which pieces of information can be gathered from these dot plots? (Remember that lower swim times are faster.) Choose all answers that apply: Choose all answers that apply:

Answers

Answer:

The center of the semifinal round distribution is greater than the center of final round distribution.

The variability in the semifinal round distribution is less than variability in the final round distribution.

Step-by-step explanation:

The mean value of each distribution set is not calculates as the center of semifinal round distribution is greater than the final round distribution. MAD Mean Absolute Deviation is calculated from the dotted graph plot, the distribution of semifinal round is less spread out than the final round distribution.

Answer:

correct answer is None of the above i understood nothing the other person was trying to say...

Step-by-step explanation:

mark me brainliest please...

If an arrow is shot upward on Mars with a speed of 62 m/s, its height in meters t seconds later is given by y = 62t − 1.86t². (Round your answers to two decimal places.) Estimate the speed when t = 1. Can you please show me the steps to solve this?

Answers

Answer:

Approximately [tex]58.28\; \rm m \cdot s^{-1}[/tex].

Step-by-step explanation:

The velocity of an object is the rate at which its position changes. In other words, the velocity of an object is equal to the first derivative of its position, with respect to time.

Note that the arrow here is launched upwards. (Assume that the effect of wind on Mars is negligible.) There would be motion in the horizontal direction. The horizontal position of this arrow will stays the same. On the other hand, the vertical position of this arrow is the same as its height: [tex]y = 62\, t - 1.86\, t^2[/tex].

Apply the power rule to find the first derivative of this [tex]y[/tex] with respect to time [tex]t[/tex].

By the power rule:

the first derivative of [tex]t[/tex] (same as the first derivative of [tex]t^2[/tex] (same as [tex]t[/tex] to the second power) with respect to

Therefore:

[tex]\begin{aligned}\frac{dy}{d t} &= \frac{d}{d t}\left[62 \, t - 1.86\, t^2\right] \\ &= 62\,\left(\frac{d}{d t}\left[t\right]\right) - 1.86\, \left(\frac{d}{d t}\left[t^2\right]\right) \\ &= 62 \times 1 - 1.86\times\left(2\, t) = 62 - 3.72\, t\end{aligned}[/tex].

In other words, the (vertical) velocity of this arrow at time [tex]t[/tex] would be [tex](62 - 3.72\, t)[/tex] meters per second.

Evaluate this expression for [tex]t = 1[/tex] to find the (vertical) velocity of this arrow at that moment: [tex]62 - 3.72 \times 1 =58.28[/tex].

Answer:

58.28 m/s

Step-by-step explanation:

y = 62t - 1.86t²

Speed, S = dy/dt = 62 - 2(1.86)t

S = 62 - 3.72t

When t = 1

S = 62 - 3.72 = 58.28 m/s

need help on this one

Answers

The correct answer is (B)

hey help me with this question plzzzz

Answers

Two Answers: choice C, choice D

Look at where we don't have repeating x values. This happens with function C and function D. All the x values are unique for each choice mentioned.

In choices A, B, and E, the value x = -3 repeats itself. So we don't have a function for either of these. A function is only possible if any input (x) leads to exactly one output (y).

Please answer this question now

Answers

Answer:

V = 60 m³

Step-by-step explanation:

Volume of Triangular Pyramid: V = 1/3bh

Area of Triangle: A = 1/2bh

b = area of bottom triangle (base)

h = height of triangular pyramid

Step 1: Find area of base triangle

A = 1/2(8)(5)

A = 4(5)

A = 20

Step 2: Plug in known variables into volume formula

V = 1/3(20)(9)

V = 1/3(180)

V = 60

Evaluate the expression for x= 3 and y= 6.
51x² + y + 3​

Answers

Answer:

468

Step-by-step explanation:

The equation is: 51x² + y + 3​

Let's first find x.  It says x= 3, so let's subsitute that in.

51(3)² + y + 3​

3² is 9 because 3 times 3 is 9, which means:

51(9) + y + 3​.  

It is 51 times 9 and not 519 because x was supposed to be squared by itself and 51 was next to it.  When a number is close to another number, especially with parentheses, it wants you to multiply the two together.  

For example: 3(3) is 9 and 4(5) is 20.

Now that we found x, let's get y.  The problem states that y= 6...let's subsitute that in.  

51(9) + 6 + 3​.  

Now that we got all the variables out of the way, we can simplify!

51 times 9= 459

459+6+3 is the same thing as 459+9, since 6+3= 9.

459+15= 468  :)

How do the number line graphs of the solutions sets of Negative 23 greater-than x and x greater-than-or-equal-to negative 23 differ?

Answers

Answer:

For "Negative 23 greater-than x" , highlight the left half of the number line starting at -23 and use a parenthesis ) on -23.

For "x greater-than-or-equal-to negative 23", highlight the right half of the number line starting at -23, and use a square bracket [ on -23.

Step-by-step explanation:

Start by locating the number -23 on the number line. Please see attached image to accompany the explanation.

In the first case:  "Negative 23 greater-than x" , which is expressed mathematically as:

[tex]-23 >x[/tex]

notice that "x" has to be strictly smaller than the number -23, therefore those sought x values must reside to the left of the number -23, so we have to highlight that half of the number line. Apart from that, we need to include a symbol on top of the number -23, that indicates that -23 itself shouldn't be considered as part of the set, that symbol is by convention a parenthesis ).

In the second case: "x greater-than-or-equal-to negative 23", which is expressed mathematically as:

[tex]x\geq -23[/tex]

notice that "x" has to be greater than or equal to the number -23, therefore those sought x values must reside to the right of the number -23, so we have to highlight that half of the number line. Apart from that, we need to include a symbol on top of the number -23, that indicates that -23 itself should be considered as part of the set, that symbol is by convention a square bracket [.

Answer:

the answer is A

Step-by-step explanation:

Chantal is driving on a highway at a steady speed. She drives 55 miles every hour. Let d be the total distance in miles and let h be the number of hours.

Write an equation that represents the situation. ​I'll give out the brainliest if you get it right.

Answers

Answer:

[tex] d = 55h [/tex]

Step-by-step explanation:

We are given that Chantal drives at a constant speed of 55 miles per hour.

If, d represents the total distance in miles, and

h represents number of hours, the following equation can be used to express the given situation:

[tex] d = 55h [/tex]

For every hour, a distance of 55 miles is covered.

Thus, if h = 1, [tex] d = 55(1) = 55 miles [/tex]

If h = 2, [tex] d = 55(2) = 110 miles [/tex].

Therefore, [tex] d = 55h [/tex] , is an ideal equation that represents the situation given in the question above.

which of the following best describes the effect of replacing the graph of y = f(x) with the graph of y= f(x) - 9? a. the graph of y = f(x) will shift up 9 units b. the graph of y = f(x) will shift down 9 units c. the graph of y = f(x) will shift left 9 units d. the graph of y = f(x) will shift right 9 units

Answers

Answer:

B

Step-by-step explanation:

If you were to have an equation y = x.

Then, x - 9 shifts it down 9.

If you were to have an equation y = 2x.

Then, 2x - 9 shifts it down 9.

Using this pattern, we deduce that  f(x) - 9, shifts the graph down 9 units.

So, our answer is B>

What is the volume of the composite figure?

Answers:
192ft^3
96ft^3
76ft^3
152ft^3

Answers

Answer:

68 ft³

Step-by-step explanation:

Take the above figure to be 2 rectangular prism. A smaller prism on top, and a bigger one under.

Volume of the smaller rectangular prism on top:

[tex] Volume = whl [/tex]

Where,

w = 2 ft

h = 4 ft

l = 4 ft

[tex] Volume = 2*4*4 = 32 ft^3 [/tex]

Volume of bigger Rectangle prism under:

w = 2 ft

h = 3 ft

l = 6 ft

[tex] Volume = 2*3*6 = 36 ft^3 [/tex]

Volume of composite figure = 32 + 36 = 68 ft³

Answer:

Step-by-step explanation:

The correct answer is 76

Big prism: 4x8x2=64

What's Left: (6-4)x2x3=12

64+12=76

Ahmad has some files.
زرا
He gave
of the files and had 14 files left.
5
How many files did he have at first?​

Answers

Step-by-step explanation:

why did u add the 5 in the question?.

4 3/4 - 2 3/8 thanks

Answers

Answer:

2 3/8

Step-by-step explanation:

First get the LCM (Least Common Multiple) for the denominators so we can subtract them.  The denominators would both be 8 because it is the lowest number that they can have to be able to subtract.  (The LCM).  So is 4 3/4 has a denominator of 8 it'll become:

4 3/4= 4 6/8 because if 4 turned into 8, that means it multiplied by 2.  So, you need to multiply 3 by 2 as well which equals 6.  This is it as a ratio:

3:4 into x:8    

So 4 times 2, which means you need to do 3 times 2 as well.  It equals 6.

So now that we know 4 3/4 is 4 6/8, it is time to subtract.  2 3/8 already has a denominator of 8 so we don't need to do anything with that.  Subtract.

4 6/8-2 3/8= 2 3/8.  4-2=2, so the whole number is 2.  6-3= 3, so the numerator (the top number) is 3.  The denominator (the bottom number) always stays the same so it is the same, which is 8.

find the value of 3m-2, if m =7.

Answers

Answer:

37-2=35 or 3^7-2=2185

thing
Fill in the blank with the correct response.
The slope of the graph of y= 5x is
ao

Answers

Answer:

slope is 5

Step-by-step explanation:

y = 5x

This is in the form

y = mx+b where m is the slope and b is the y intercept

The slope is 5 and the y intercept is 0

The slope is 5.

In slope intercept form, y=mx+b, m is the slope. You can see that 5 is in the place of m, so the slope is 5

. In an extra-curricular club with 15 members,7 people played rugby, 6 people played soccer and 4 people neither play rugby nor soccer. How many people played both rugby and soccer?

Answers

Answer:

2

Step-by-step explanation:

In the above question, we are given the following information:

Total member in the club = 15

Rugby = n(R) = 7

Soccer = n(S) = 6

Neither Rugby nor Soccer = 4

Rugby and soccer = n( R ∩ S) = (Unknown)

Total number of club members = n(R) + n(S) - n( R ∩ S) + Neither Rugby nor soccer

15 = 7 + 6 - n( R ∩ S) + 4

15 = 17 - n( R ∩ S)

15 - 17 = - n( R ∩ S)

-2 = - n( R ∩ S)

n( R ∩ S) = 2

Therefore, the number of people that played both rugby and soccer is 2

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