show a quadrilateral ABCD in A is(2,8) and B is (8,6) .the point c lies on the perpendicular bisector of AB and the point D lies on the y- axis. the equation of BC is 3y=4x-14 and angle DAB=90° find
(a) the equation of AD
(b) the coordinates of D
(c) the equation of perpendicular bisector of AB
(d) the coordinates of C
show the area of triangle ABC is 10 units and find the area of the quadrilateral ABCD​

Answers

Answer 1

Answer:

(a) y =  3x + 2; (b) (0,2); (c) y = 3x - 8; (d) (2,-2)

(e) Area of ∆ABC = 30; (f) Area of ABCD = 40

Step-by-step explanation:

(a) Equation of AD

(i) Slope of AB

m₁ = (y₂ - y₁)/(x₂ - x₁) = (6 - 8)/(8 - 2)= -2/6 = -⅓

(ii) Slope of AD

m₂ = 3

(ii) y-intercept

y = 3x + b

8 = 3(2) + b= 6 + b

b = 2

The equation of AD is y = 3x + 2.

(b) Coordinates of D

The coordinates of D are (0,2).

(c) Equation of perpendicular bisector of AB

(i) Mid-points of AB

x = ½(x₂ + x₁) = ½(8 + 2) = ½(14) = 5

y = ½(y₂ + y₁) = ½(6 + 8) = ½(14) = 7

The coordinates of the mid-point are (5,7).

Slope = 3

y = mx + b

7 = 3(5) + b = 15 + b

b = 7 - 15 = -8

The equation of the perpendicular bisector is y = 3x - 8.

(d) Coordinates of C

C is at the intersection of BC and the perpendicular bisector of AD.

 y = 3x -    8

3y = 4x - 14

3y = 9x - 24

 0 = 5x - 10

5x = 10

 x =   2

 y = 3(2) - 8  = 6 - 8 = -2

The coordinates of C are (2,-2).

(e) Area of ∆ABC

A = ½bh = ½ × 10 × 6 = 30

(f) Area of ABCD

Area of ∆ACD = ½bh = ½ × 10 × 2 = 10

Area of ABCD = ∆ACD + ∆ABC =10 + 30 = 40

Show A Quadrilateral ABCD In A Is(2,8) And B Is (8,6) .the Point C Lies On The Perpendicular Bisector

Related Questions

Which inequality is equivalent to absolute value x-4 < 9

Answers

Answer:

–9 < x – 4 < 9

Step-by-step explanation:

The formula for finding the kinetic energy, E, of an object is given below, where m represents the mass and v represents the speed of the object.

Answers

Answer:

v=√E/m or v=√E /√m

Step-by-step explanation:

Complete question below:

The formula for finding the kinetic energy, E, of an object is given below, where m represents the mass and v represents the speed of

the object.

E = mv^2

Solve the formula for v.​

Solution

E=mv^2

Where,

E=kinetic energy

m=mass

v=speed of the object

E=mv^2

Divide both sides by m

E/m=mv^2/m

E/m=v^2

It can be rewritten as

v^2=E/m

Square root both sides

√(v^2)=√E/m

v=√E/m

Or

v=√E/√m

This is to say speed (v)=square root of kinetic energy (E) Over masa(m)

Please answer this now two minutes

Answers

Answer:

s = 8 degrees

Step-by-step explanation:

12s + 42 + 42 = 180

12s + 84 = 180

12s = 96

s = 8 degrees

A soft drink machine can be regulated so that it discharges an average of Mu ounces per cup. If the ounces of fill are Normally distributed with a standard deviation of 0.4 ounces, what value should Mu be set at so that 6-ounce cups will overflow only 2% of the time

Answers

Answer: 5.0693 ounces

Step-by-step explanation:

For a 6 ounce cup to overflow, then the cup content is beyond 6 ounce, at 2%

P(x > 6) = 2% = 0.02; similarly

P(x<6) = 1 - P(x > 6)'.

P(x<6) = 1 - 0.02 = 0.98

The z-score for 0.98 = 2.326

The z - formular for a normally distributed goes thus :

Zscore =(observed score - mean) / standard deviation

Substituting the vamus :

2.326 = (6 - mean) / 0.4

2.326 × 0 4 = 6 - mean

0.9304 = 6 - mean

Mean = 6 - 0.9304

Mean = 5.0693

You make a scale drawing of a garden plot using the scale 2 in. = 17
ft. If the length of a row of vegetables on the drawing is 3 in., how
long is the actual row?
42.5 ft
25.5 ft
17 ft
34 ft

Answers

Answer 158Step-by-step explanation: you have to multiply the fraction by the numerator and divided by itsself and the subtract everything thren get myy642565780

En el mercado del satisfactor X hay 10,000 individuos idénticos, cada uno con una función de demanda definida por Qdx = 12 – Px y 1,000 productores idénticos del satisfactor X, cada uno con una función de oferta dada por Qsx = 20 Px

Answers

Answer:

Px = $4

Step-by-step explanation:

Given that:

En el mercado de satisfacción X hay 10,000 individuos idénticos, cada uno con una función de demanda definida por Qdx = 12 - Px y 1,000 productores idénticos de X satisfactorio, cada uno con una función de oferta dada por Qsx = 20 Px

El precio de equilibrio y la cantidad de equilibrio se pueden determinar de la siguiente manera;

Qdx = 10000(12-Px)

Qdx = 120000 - 10000Px

Qsx = 1000(20 Px)

Qsx = 20000 Px

El punto de equilibrio para completar el enunciado, cuando Qdx = Qsx es:

Qdx = Qsx

120000 - 10000 Px =   20000 Px

120000 =  20000 Px + 10000 Px

120000 =  30000 Px

Px = [tex]\mathbf{ \dfrac{120000}{30000}}[/tex]

Px = $4

Approximate 0.007349 to 3 significant figure​

Answers

Answer:

0.007349 to 3 significant figure=0.00735

Step-by-step explanation:

Approximate 0.007349 to 3 significant figure

Significant figure start from 1 to 9 with the exclusion of 0

From the question above, there are two zeros after the decimal point, so it will be ignored because it is not a significant figure.

0.007349

The first significant number is 7 after 0

The second significant number is 3

The next

The third significant number is 4

The fourth significant number is 9

We want to approximate to three significant figure, so, all figure after 4(third significant figure) will be rounded up or down.

If the numbers are below 5(0, 1,2,3,4) they will be rounded down to 0

If the numbers are above 4(5,6,7,8,9), they will be rounded up to 1

So the number after 4 is 9, therefore it will be rounded up to make 4=5

0.007349 to 3 significant figure=0.00735

PLEASE help me with this question ASAP!!!!

Answers

Step-by-step explanation:

I believe the answer is

The fuction roughly matches the data

Answer:

The function fits very well

Step-by-step explanation:

The equation for the stats is

y=-0.039866x²+3.99375x-0.4785714

Jane wants to estimate the proportion of students on her campus who eat cauliflower. After surveying 24 ​students, she finds 2 who eat cauliflower. Obtain and interpret a 95​% confidence interval for the proportion of students who eat cauliflower on​ Jane's campus using Agresti and​ Coull's method.
Construct and interpret the 95​% confidence interval. Select the correct choice below and fill in the answer boxes within your choice.
​(Round to three decimal places as​ needed.)
A. The proportion of students who eat cauliflower on​ Jane's campus is between___ and __ 95​% of the time.
B.There is a 95​% chance that the proportion of students who eat cauliflower in​ Jane's sample is between __ and __.
C. There is a 95​% chance that the proportion of students who eat cauliflower on​ Jane's campus is between __ and__.
D. One is 95​% confident that the proportion of students who eat cauliflower on​ Jane's campus is between __ and __.

Answers

Answer:

A 95​% confidence interval for the proportion of students who eat cauliflower on​ Jane's campus is [0.012, 0.270].

Step-by-step explanation:

We are given that Jane wants to estimate the proportion of students on her campus who eat cauliflower. After surveying 24 ​students, she finds 2 who eat cauliflower.

Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;

                              P.Q.  =  [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion of students who eat cauliflower

           n = sample of students

           p = population proportion of students who eat cauliflower

Here for constructing a 95% confidence interval we have used a One-sample z-test for proportions.

So, 95% confidence interval for the population proportion, p is ;

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 2.5% level

                                                   of significance are -1.96 & 1.96}  

P(-1.96 < [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < 1.96) = 0.95

P( [tex]-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]{\hat p-p}[/tex] < [tex]1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.95

P( [tex]\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < p < [tex]\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.95

Now, in Agresti and​ Coull's method; the sample size and the sample proportion is calculated as;

[tex]n = n + Z^{2}__(\frac{_\alpha}{2})[/tex]

n = [tex]24 + 1.96^{2}[/tex] = 27.842

[tex]\hat p = \frac{x+\frac{Z^{2}__(\frac{\alpha}{2}_) }{2} }{n}[/tex] = [tex]\hat p = \frac{2+\frac{1.96^{2} }{2} }{27.842}[/tex] = 0.141

95% confidence interval for p = [ [tex]\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] , [tex]\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ]

 = [ [tex]0.141 -1.96 \times {\sqrt{\frac{0.141(1-0.141)}{27.842} } }[/tex] , [tex]0.141 +1.96 \times {\sqrt{\frac{0.141(1-0.141)}{27.842} } }[/tex] ]

 = [0.012, 0.270]

Therefore, a 95​% confidence interval for the proportion of students who eat cauliflower on​ Jane's campus [0.012, 0.270].

The interpretation of the above confidence interval is that we are 95​% confident that the proportion of students who eat cauliflower on​ Jane's campus is between 0.012 and 0.270.

please help i really don't understand

Answers

Answer:

  80 square units

Step-by-step explanation:

The area formula refers to a generic triangle ABC in which side lengths 'a' and 'b' are known and angle C is between those sides.

In the given figure, we have known side lengths of 12 and 14, and the angle between them is 72°.

Putting these numbers into the formula, we find the area to be ...

  A = (1/2)(12)(14)sin(72°) ≈ 79.9 ≈ 80 . . . . square units

The area of the triangle is about 80 square units.

Please answer this in two minutes

Answers

Answer:

tan(X) = 1.05

Step-by-step explanation:

The triangles WXY and VTU are similar using the case AA (angle-angle).

The angle X is equal the angle T, therefore they have the same tangent value.

The tangent value is given by the opposite side to the angle divided by the adjacent side to the angle, so we have that:

[tex]tan(T) = UV / UT[/tex]

[tex]tan(T) = 21 / 20 = 1.05[/tex]

[tex]tan(X) = tan(T) = 1.05[/tex]

solve the equation INCLUDE THE FORMULA x - 5 = 3 - 5x + 3x + 4

Answers

Answer:

x = 4

Step-by-step explanation:

x-5 = 3-5x+3x+4 x = 3-5x+3x+4+5 x = 3-5x+3x+9x = -5x+3x+12x+5x =3x+12 6x =3x+126x-3x = 12 3x = 12x = 12/3x = 4

Consider the two functions. Which statement is true?
A)Function 1 has a greater rate of change by 13/4
B)Function 2 has a greater rate of change by 13/4
C)Function 1 has a greater rate of change by 13/2
D)Function 2 has a greater rate of change by 13/2

Answers

Answer: Function 2 has a greater rate of change by 13/4

Step-by-step explanation:

We must work with linear equations, remember that the general shape is:

y = a*x + b

where a is the slope and b is the y-intercept.

Ok, first we want to find the rate of change (or the slope) of the graphed line:

We know that for a line that passes through the points (x1, y1) and (x2, y2)

The slope is:

a = (y2 - y1)/(x2 - x1)

Then for the graphed function, we can see that it passes through the points:

(0, -2) and (4, 0)

Then the slope is:

a = (0 -(-2))/(4 - 0) = 2/4 = 1/2

Now, the slope of the second line is 15/4.

Let's calculate the difference between the slopes:

15/4 - 1/2 = 15/4 - 2/4 = 13/4

(notice that we are calculating slope2 - slope1)

Then the correct option is:

Function 2 has a greater rate of change by 13/4

Answer:

B) Function 2 has a greater rate of change by 13/4

Step-by-step explanation:

Solve: d |6n+7|=8 can you guys answer me plezzzzzzzz

Answers

Answer: -5/2 or 1/6

Step-by-step explanation:

I6n + 7I = 8

Therefore (6n + 7) = 8 or -8 because modulus means we're only getting it's absolute value, (it's positive value) meaning it could equal 8 or -8 before it's modulus'ed.

Therefore 6n + 7 = 8

or 6n + 7 = -8

Leaving us with:

6n = 1

6n = -15

So n = 1/6

or n = -5/2 (-2.5)

Answer:

n = 1/6                          n = -5/2

Step-by-step explanation:

|6n+7|=8

This has two solutions, one positive and one negative

6n+7 = 8  and 6n+7 = -8

Subtract 7 from each side

6n+7-7 = 8-7         6n+7-7 =-8-7

6n =1                        6n = -15

Divide by 6

6n/6 = 1/6                 6n/6 = -15/6

n = 1/6                          n = -5/2

What is the method of comparing Coefficient ​

Answers

Answer: In mathematics, the method of equating the coefficients is a way of solving a functional equation of two expressions such as polynomials for a number of unknown parameters. It relies on the fact that two expressions are identical precisely when corresponding coefficients are equal for each different type of term.

.

Pls help I need help with 12

Answers

Answer:

B. 14

Step-by-step explanation:

22/x = 11/(21-x)

462 - 22x = 11x

462 = 33x

x = 14

Answer: The value of x is 14, answer choice B

Let y be the other line segment connected to x

Using proportions:

[tex]\dfrac{11}{22}=\dfrac{y}{x}[/tex]

Cross multiply and simplify

[tex]22y=11x[/tex]

[tex]y=\dfrac{1}{2}x[/tex]

We know that x and y add to 21, so we can create the following equation:

[tex]x+y=21[/tex]

Substitute y=(1/2)x

[tex]x+\dfrac{1}{2}x=21[/tex]

Simplify by adding like terms

[tex]\dfrac{3}{2}x=21[/tex]

Divide both sides by 3/2

[tex]x=14[/tex]

Let me know if you need any clarifications, thanks!

Please help with this inequalities problem attached below.

Answers

Answer:

1) A. 5 + 2.75 * S ≤ 21

2) 5

Step-by-step explanation:

Well there is an initial price of $5 and $2.75 per stop, and she can only spend less than or equal to $21 we can make the following inequality,

5 + 2.75 * S ≤ 21,

Meaning, Q.1 is A

Now #2 is 5 stops because if we plug in 5 for s we get 18.75.

Thus, the most amount of stops she can afford is 5.

Hope this helps :)

a supermarket sells 4 brands of detergents a,b,c and d on a particular day 15% of the total boxes sold was brand a and 45% was brand c.Find the ratio of number of boxes of brand a sold to the number of boxes sold. Give your answser in a fraction Search Results Web results

Answers

Answer:

The ratio of number of boxes of brand a sold to the number of boxes sold is 3/20

Step-by-step explanation:

A supermarket sells 4 brands of detergents a, b, c, d.

On this particular day, 15% of the total boxes sold was brand a and 45% was brand c.

ratio of number of boxes of brand a sold to the number of boxes sold = ?

15% of the boxes sold is box a

Total number of boxes sold is 100%,

therefore,

ratio of box a sold to the whole boxes sold will be

15/100 = 3/20   in fraction

Find arc length. (NEED ASAP)

Answers

5.23 m

in cm 523 cm

nearest tenth 520cm

Step-by-step explanation:

60 / 360 × 2 ×22/7 × 5

110/ 21

5.23m

Answer:

5,2(3) meters

Step-by-step explanation:

Find arc length

Formula

arc length = 2π·r (x°/360°)

= 2π·5m(60°/360°)

= 2·3,14·5m·1/6

= 31,4m/6

= 5,2(3) meters

A shop has a sale of 10% off all items in stock. If the original price of a dress is £60 what would be its sale price?

Answers

Answer:

£ 54

Step-by-step explanation:

Given,

Discount percent = 10%

Marked price ( MP ) = £ 60

Selling price ( SP ) = ?

Now, finding the discount amount:

Discount amount = discount percent of MP

= 10% of 60

= £ 6

Selling price = Marked price - Discount amount

=£ 60 - £ 6

= £ 54

hope this helps...

Good luck on your assignment..

MP= £60
Discount= 10%

SP= 60-(10/100*60)
= 60-6
= £54

Hope it helps
Please mark my answer as BRAINLIEST

Please answer this in two minutes

Answers

Answer:

Hey there!

S would be 2 times 7, or 14.

Hope this helps :)

Answer:

14

Step-by-step explanation:

This is a 30-60-90 triangle, so the sides corresponding are x, 2x, and xsqrt3. the side, s, that we want is the 2x, and the x is 7. So, s is 14.

1.
How can you count following distance?

Answers

At a MINIMUM, during dry weather conditions, you should have at least 2 seconds of space between you and the vehicle in front of you (3 seconds is better). Do this by using a fixed object such as a bridge, tree, or even a crack or shadow in the roadway.

Calculate the gap between you and the car in front of you by selecting an inanimate object along the lane. If the other car goes past the target, then "1000 one, 1000 two ..." count. You are three seconds behind this car when you get to "one thousand three" before you go through the piece.

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

Hope this helps!

Brainliest would be great!

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

With all care,

Forbidden

How do I know that the following equation is true:

Answers

Answer:

Half angle Identity for cosine:

[tex]$\cos \left(\frac{\theta}{2} \right)=\pm \sqrt{\frac{1+\cos(\theta)}{2} } $[/tex]

[tex]\text{Note that it is} \pm \text{because we don't know which Quadrant the half-angle is, }[/tex][tex]\text{the information of}\cos(\theta) \text{is not enough to conclude the angle}[/tex]

[tex]$\frac{\pi}{8} \text{ is a Quadrant I angle, therefore, positive}$[/tex]

[tex]$\cos \left(\frac{\pi}{8} \right)=\sqrt{\frac{1+\cos(\frac{\pi}{4} )}{2} } $[/tex]

The equation is true.

The polygon below is a regular pentagon.
Calculate the size of the angle

X

Y

Z

Answers

Answers:

x = 108

y = 36

z = 72

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

Explanation:

Check out the diagram below. I have added letters of x, y and z in places to help find the values of y and z. Note the triangle on top is isosceles (since a regular polygon has all sides equal; therefore the triangle on top has the top diagonal sides equal).

Before we find either y or z, let's find x.

For any regular polygon, the interior angles are all the same measure. They sum to 180(n-2). In this case, n = 5, so the angles sum to 180(5-2) = 540. Each individual interior angle is 540/n = 540/5 = 108 degrees

x = 108

Another way to find this interior angle is to first find the exterior angle. For any convex polygon (regular or not), the exterior angles always add to 360. When we talk about regular polygons, each individual exterior angle is 360/n. So in this case, we have 360/5 = 72 as one exterior angle. The adjacent interior angle is therefore x = 180-72 = 108. So there are two ways to find the measure of an interior angle.

--------

Referring to the diagram, specifically the isosceles triangle on top, we can see that it has angles of x, y and y. They add to x+y+y = x+2y. Set this equal to 180, plug in x = 108 and solve for y

x+2y = 180

108+2y = 180

2y = 180-108

2y = 72

y = 72/2

y = 36

--------

The bottom most triangle is a congruent copy of the triangle on top. We have another isosceles triangle with the same side lengths as before. This triangle also has x, y and y as mentioned above.

Notice the adjacent angles of y and z in the bottom left corner. They must add to 108 as this was the measure of the interior angle of a regular pentagon. So,

y+z = x

36+z = 108

z = 108-36

z = 72

I need your help with this question please explain why and show work.

Answers

Answer:

1

Step-by-step explanation:

y=2x+3, 2x represents the slope of the line and 3 represents the y-intercept

3 ) is correct. 1/2 is the slope and 3 is the y intercept

what does the variable k represent in the following equation : k/2 +1/2=3

Answers

the variable k equals 5

A magazine provided results from a poll of adults who were asked to identify their favorite pie. Among the ​respondents, ​% chose chocolate​ pie, and the margin of error was given as percentage points. Describe what is meant by the statement that​ "the margin of error was given as percentage​ points.
Which one would be a true statement?
A. The statement indicates that the study is 100%−3​%=97​% confident that the true population percentage of people that prefer chocolate pie is 11​%
B. The statement indicates that the interval 11​%+3​% is likely to contain the true population percentage of people that prefer chocolate pie.
C. The statement indicates that the true population percentage of people that prefer chocolate pie is in the interval 11​%±3​%.
D. The statement indicates that the study is only 3​% confident that the true population percentage of people that prefer chocolate pie is exactly 11​%.

Answers

Answer:

C. The statement indicates that the true population percentage of people that prefer chocolate pie is in the interval 11​%±3​%.

Step-by-step explanation:

Data provided in the questions

Number of respondents = 1,000

Choose chocolate pie = 11%

margin of error = ±3 percentage points

Based on the above information,

The lower limit is

= 0.11 - 0.03

= 0.08

And, the upper limit is

= 0.11 + 0.03

= 0.14

So based on the above computation, the option c is correct as it represents the true population percentage of people with respect to the chocolate pie preference

find the rules for these sequence ​

Answers

Answer:

start with -29, multiply each term by 4

start with 60, multiply each term by 0.1

start with 97 and multiply each term by 0.5

3.03 cells

Step-by-step explanation:

1. The first sequence begins with -29. -116 ÷ -29 = 4, -464 ÷ -116 = 4, etc. Each value is multiplied by 4 to get the next value.

2. The second sequence begins with 60. 6 ÷ 60 = 0.1, 0.6 ÷ 6 = 0.1, etc. Each value is multiplied by 0.1 to get the next value.

3. The colony starts with 97 cells. Splitting into two is the same as multiplying by 0.5.

4. Multiply 97 by 0.5, 5 times for 5 minutes.

97 · 0.5 · 0.5 · 0.5 · 0.5 · 0.5 = 3.03

Lucy is tiling her bathroom. She buys white and blue tiles in the
ratio 13:2.Blue tiles cost £2.80 while white tiles cost £2.35.If she
buys 16 blue tiles how much does Lucy spend on tiles in total?

Answers

Answer:

£289.20

Step-by-step explanation:

13:2 = x:16 or 13/2 = x/16

cross multiply: 208 = 2x

simplify: x = 104

16 blue tiles x £2.80 each = £44.80

104 white tiles x £2.35 each = £244.40

44.80 + 244.40 = £289.20

how to do this question plz ​

Answers

Answer:

148 cm ^2

Step-by-step explanation:

Hey there!

Well is the area of the base is 30 then we can conclude that the side lengths are 5 and 6.

Then if the volume is 120 we can do,

120 ÷ 30 = 4

So the height is 4 cm.

Now we already have the area of the base we just need to find the area of the rest of the rectangles.

If the bottom base is 30 then the top base is also 30.

30 + 30 = 60cm^2

Now we can do the two rectangles on the side that have side lengths of 5 and 4.

5*4 = 20

20+20 = 40 cm^2

Now we can do the two final rectangles that have side lengths of 6 and 4.

6*4=24

24 + 24 = 48 cm^2

Now we can add all the areas up,

48 + 40 + 60

= 148 cm^2

Hope this helps :)

Other Questions
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