A quadrilateral has vertices at (0,1), (3,4), (4,3) and (3,0). Its perimeter can be expressed in the form a\sqrt2+b\sqrt{10} with A and B integers. What is the sum of A and B?

Answers

Answer 1

Answer:

The sum is 6

Step-by-step explanation:

Given

[tex]Vertices: (0,1), (3,4), (4,3), (3,0)[/tex]

[tex]Perimeter: a\sqrt{2} + b\sqrt{10}[/tex]

Required

[tex]a + b[/tex]

The first step is to name each points, as follows

[tex]A: (0,1)\\B: (3,4)\\C: (4,3)\\D: (3,0)[/tex]

Next is to calculate the distance between each consecutive point

We'll calculate the distance AB, BC, CD and DA

Distance between points is calculated as thus;

[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]

Calculating distance AB

[tex]A: (0,1)\\B: (3,4)[/tex]

Here,

[tex]x_1 = 0; x_2 = 3[/tex]

[tex]y_1 = 1; y_2 = 4[/tex]

[tex]AB = \sqrt{(0 - 3)^2 + (1 - 4)^2}[/tex]

[tex]AB = \sqrt{(- 3)^2 + (-3)^2}[/tex]

[tex]AB = \sqrt{9+9}[/tex]

[tex]AB = \sqrt{18}[/tex]

Expand 18 as 9 * 2

[tex]AB = \sqrt{9 * 2}[/tex]

Split surds

[tex]AB = \sqrt{9} * \sqrt{2}[/tex]

Take square root of 9

[tex]AB = 3 * \sqrt{2}[/tex]

[tex]AB = 3 \sqrt{2}[/tex]

Calculating distance BC

[tex]B: (3,4)\\C: (4,3)[/tex]

Here,

[tex]x_1 = 3; x_2 = 4[/tex]

[tex]y_1 = 4; y_2 = 3[/tex]

[tex]BC = \sqrt{(3 - 4)^2 + (4 - 3)^2}[/tex]

[tex]BC = \sqrt{(-1)^2 + (1)^2}[/tex]

[tex]BC = \sqrt{1 + 1}[/tex]

[tex]BC = \sqrt{2}[/tex]

Calculating distance CD

[tex]C: (4,3)\\D: (3,0)[/tex]

Here,

[tex]x_1 = 4; x_2 = 3[/tex]

[tex]y_1 = 3; y_2 = 0[/tex]

[tex]CD = \sqrt{(4 - 3)^2 + (3 - 0)^2}[/tex]

[tex]CD = \sqrt{(1)^2 + (3 )^2}[/tex]

[tex]CD = \sqrt{1 + 9}[/tex]

[tex]CD = \sqrt{10}[/tex]

Calculating distance CD

[tex]D: (3,0)\\A: (0,1)[/tex]

Here,

[tex]x_1 = 3; x_2 = 0[/tex]

[tex]y_1 = 0; y_2 = 1[/tex]

[tex]DA = \sqrt{(3 - 0)^2 + (0 - 1)^2}[/tex]

[tex]DA = \sqrt{(3)^2 + (- 1)^2}[/tex]

[tex]DA = \sqrt{9 + 1}[/tex]

[tex]DA = \sqrt{10}[/tex]

At this point, the perimeter can then be calculated

[tex]Perimeter = AB + BC + CD + DA[/tex]

[tex]Perimeter = 3 \sqrt{2} + \sqrt{2}\ + \sqrt{10} + \sqrt{10}[/tex]

[tex]Perimeter = 4 \sqrt{2} + 2\sqrt{10}[/tex]

From the given parameters;

[tex]Perimeter: a\sqrt{2} + b\sqrt{10}[/tex]

This implies that;

[tex]a\sqrt{2} + b\sqrt{10} = 4 \sqrt{2} + 2\sqrt{10}[/tex]

By comparison;

a = 4 and b = 2

Hence;

[tex]a + b = 4 + 2[/tex]

[tex]a +b = 6[/tex]


Related Questions

Calculate the mean of this data set: 12, 35, 44, 74, 23, 49, 45, 18, 90, 56, 84,
38, 7. What is the sample proportion of numbers that are within +10 of
the mean? (Round off the mean to the nearest integer for your calculations.)

Answers

Well, here is the mean of ur data collected 48.181818...

Answer: 0.38

Step-by-step explanation:

The mean is the sum of all the observations divided by the number of observations. It is 44.2 (rounded off to 44) Next is fraction observations that lie between 34-35 (just answered this and it is correct)

Determine the measure of ∠A. ANSWWER: 1) 192° 2) 88° 3) 84° 4) 168°

Answers

Answer:

3) 84°

Step-by-step explanation:

The angle formed by a chord and a tangent measures half of the intercepted arc.

m<A = (1/2)m(arc) = (1/2) * (168 deg) = 84 deg

Answer:

84 degrees

Step-by-step explanation:

Tim explained a function in words and Paul wrote an equation. Tim: The amount of money in a savings account increases at a rate of $225 per month. After eight months, the bank account has $4,580 in it. Paul: y−1,400=56(x+26)
Whose function has the smaller y-intercept?
A. Tim’s with a y-intercept of $2,700
B. Paul’s with a y-intercept of $2,856
C. Paul’s with a y-intercept of $2,800
D. Tim’s with a y-intercept of $2,780

Answers

Answer:

D. Tim’s with a y-intercept of $2,780

Step-by-step explanation:

The function with the smaller y-intercept is Tim’s with a y-intercept of $2,780

The equation of Paul's savings is given as:

y-1400=56(x+26)

Set x to 0, to calculate the y-intercept

y-1400=56(0+26)

Evaluate the sum

y-1400=56(26)

Evaluate the product

y-1400=1456

Add 1400 to both sides

y = 2856

For Tim, we have the following equation

y = 225x + c

Where c represents the y-intercept

After eight months, the bank account has $4,580

So, we have:

4580 = 225*8 + c

Evaluate the product

4580 = 1800 + c

Subtract 1800 from both sides

c = 2780

2780 is less than 2856

Hence, the function with the smaller y-intercept is Tim’s with a y-intercept of $2,780

Read more about y-intercepts at:

https://brainly.com/question/1884491

Help please, Topic: Arrangments

Answers

Answer: B: 120

Step-by-step explanation:

You multiply these choices together to get your result: 5 x 4 x 3 x 2 (x 1) = 120.

Since there are 5 choices to choose from.

For f(x) = 2x +1 and g(x) = x^2-7, find (f/g) (x)

Answers

Answer:

 (2x  +  1)/(x^2 - 7),    x  ≠ ±√7

Step-by-step explanation:

I'm not sure if this is what your looking for.

20 poinst plzzzzzz help me

Answers

Answer:

Step-by-step explanation:

Jason saw a shoes tat cost 41 dollars, he already ave 19 dollars in his saving account, his neighbor asked him to walk the dog for 4 dollars an hour, how many hours Jason need to walk the dog so e will be able to buy the shoes?

4x+19≥41

second one: A sign on abridge says that max. weight is 41 ton, a truck weighs 19 ton without any loads, the driver needs to pass by the bridge loading 3 boxes, how much the boxes should weigh so he will be able to pass the bridge.

3x+19≤ 41

third riddle: A cellphone company charges 19 dollars , and charge 0.05 cents for every text message. what limit of text message jason needs to keep his bill under 41 dollars.

19+0.05≤41

pls help i give brainliest

Answers

Answer: B no

Step-by-step explanation:

Plot in the x and y coordinates into the equation to solve it.

The x coordinate is  4 and the y coordinate is 1  

-4(4) +3(1)= 2

-16 + 3 = 2

-13 ≠2

-13 does not equal 2 so (4,1) is not a solution.

Answer: NO

Step-by-step explanation:

[tex]Substitute \\\\-4(4)+3(1)=2\\\\Multiply\\\\-16+3=2\\\\Combine \\like \\terms\\-13=2[/tex]

-13 does NOT equal 2, so it is not a solution

Hope it helps <3

Please Help Soon! A 4-foot by 8-foot rectangular piece of plywood will be cut into 4 congruent rectangles with no wood left over and no wood lost due to the cuts. What is the positive difference, in feet, between the greatest possible perimeter of a single piece and the least possible perimeter of a single piece?

Answers

Answer: 6 feet

Step-by-step explanation:

Given that a 4-foot by 8-foot rectangular piece of plywood will be cut into 4 congruent rectangles with no wood left over and no wood lost due to the cuts

Let assume that the 4 rectangles will be of the same area since they are congruent.

The area of the big rectangle will be

Area = 4 × 8 = 32

Divide 32 by 4

32/4 = 8

Suggest the two possible numbers in which their product will be equal to 8

4 and 2 or 8 and 1

If 4 and 2

The perimeter = 2L + 2B

Substitute the 4 and 2 into the formula

Perimeter = 2(4) + 2(2)

Perimeter = 8 + 4

Perimeter = 12

If 8 and 1

Perimeter = 2(8) + 2(1)

Perimeter = 16 + 2 = 18

The positive difference, in feet, between the greatest possible perimeter of a single piece and the least possible perimeter of a single piece will be:

18 - 12 = 6 feet

For which value of b can the expression x^2+bx+18 be factored?

Answers

Answer:

b=9

Step-by-step explanation:

You bought a magazine for $5 and four erasers. You spent a total of $25. How much did each eraser cost? Include a let statement in your answer.

Answers

Answer:

5$??.

Step-by-step explanation:

If a magazine was 5$, 25-5= 20. So then, 20÷4= 5. There fore an eraser costs 5$.

Answer:

5 dollars

Step-by-step explanation:

Let x be the price of each eraser

We bought a magazine and 4 erasers with 25 dollars

so : 5+4x = 25⇒ 4x= 20⇒x= 20/4⇒ x=5

The eraser costs 5 dollars

Which inequality is shown in this graph?

Answers

Answer:

B.

Step-by-step explanation:

y- int. = - 2

Slope is negative because the line is going down. So, it is  B. or C.

The shaded area is under the line, so it is ≤. The answer is B.

The answer is letter B.

Find the slope of the line on the graph.

Answers

Answer:

m = -3/4

Step-by-step explanation:

Slope Formula: [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]

Simply plug in 2 coordinates into the formula:

(0, 1) y-int

(4, -2) random

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

m = -3/4

Answer: 3/4

Explanation:

rise/run = 3/4

work out the length of AB. give your answer to 3 significant figures.

Answers

Answer:

Distance formula = √(x₂ - x₁)² + (y₂ - y₁)²

(x₁, y₁) = (1, 7) and (x₂, y₂) = (10, 3)

AB = √(10 - 1)² + (7 - 3)²

= √9² + 4²

= √81 + 16

= √97

= 9.85

Find the area of ΔDEF to the nearest tenth. ANSWERS: A) 127.8 square units B) 46.5 square units C) 63.9 square units D) 23.3 square units

Answers

Answer:

C) 63.9 square units

Step-by-step explanation:

From the above diagram, we can see that the triangle has 2 sides and and angle

The formula for the area of a triangle that has 2 sides and an angle = 1/2absinθ

θ = 70°

a = DE = 8 units

b = EF = 17 units

Area of ΔDEF = 1/2 × 8 × 17 × sin 70°

Area of ΔDEF = 63.9 square units.

Answer:

63.9 square units

Step-by-step explanation:I took the test

In how many different ways can 5 people be seated at a round table?

Answers

Answer:

120

Step-by-step explanation:

there is a simple way to solve these

the equation is

1 x 2 x 3 x 4 x 5

up to whatever number of objects

Answer:

There are 120 ways that 5 people can b seated if they are at a round table.

Step-by-step explanation:

What you do to find this out in a simple way is to multiply.

1 x 2 x 3 x 4 x 5 = 120

Write a direct variation equation that relates x-miles and y- kilometers.

Answers

Answer:

Step-by-step explanation:

is this the whole question or is there answers i will edit this once i know

Is this the whole question?

I NEED HELP CAN SOMEONE PLEASE ANSWER THIS ASAP PLEASE!!!​

Answers

Answer:

y = 5x - 3

Step-by-step explanation:

ok so perpendicular just means the opposite reciprocal of the slope of the normal equation. It just means that they form a 90 degree angel when they intersect.

Answer all please number 2

Answers

Answer:

(a) 26.43%

(b) 189 seconds

Step-by-step explanation:

(a) Data

mean: 3 minutes and 48 seconds = 3*60 + 48 = 228 s standard deviation, sd: 19 svalue of interest, x: 4 minutes = 4*60 = 240 s

Z-score is calculated as follows:

z = (x - mean)/sd

z = (240 - 228)/19

z = 0.63

We want to find the next probability P(Z>0.63), which is equivalent to 1 - P(Z≤0.63)

From table, 1 - P(Z≤0.63) = 1 - 0.7357 = 0.2643 or 0.2643*100 = 26.43%

(b) We want to find z1 at which P(Z≤z1) = 0.2. From the second table, z1 is between -2.05 and -2.06.

z = (x - mean)/sd

-2.055 = (x - 228)/19

(-2.055)*19 + 228 = x

x = 189 s

(b) In the DBE 122 class, there are 350 possible points. These points come from 5 homework sets that are worth 10 points each and 3 exams that are worth 100 points each. A student has received homework scores of 7, 8, 7, 5, and 8 and the first two exam scores are 81 and 80. Assuming that grades are assigned according to the standard scale, where if the grade percentage is 0.9 or higher the student will get an A, and if the grade percentage is between 0.8 and 0.9 the student will get a B, and there are no weights assigned to any of the grades, is it possible for the student to receive an A in the class? What is the minimum score on the third exam that will give an A? What about a B? [8 marks]
(c) Factorize completely [2 marks]
(d) (i) The cost of six hens and one duck at the university poultry farm is GH₵40. While four hens and three ducks cost GH₵36. What is the cost of each type of bird? [13 marks]
(ii) A circular coffee table has a diameter of 5 m. What will it cost to have the top refinished if the company charges GH₵3 per square metre for the refinishing? [take ] [7 marks]

Answers

Answer:

Step-by-step explanation:

ii) circumference of the circular coffee table= πd= 3.14× 5=15.7m

Therefore the cost of the refinishing a circular coffee table = 15.7 × GH¢3=GH¢47.10

In the diagram of circle A, what is m?

Answers

Answer:

upload ur diagram so we can solve it for u

Which statement is true about the given function?
fx) > 0 over the interval (-0,3).
f(x) > 0 over the interval (-:-).
f(x) <0 over the interval (-0,3).
f(x) <0 over the interval (- : -).

Answers

Answer:

Option C.

Step-by-step explanation:

If the graph of a function f(x) lies above the x-axis, then f(x) > 0.

If the graph of a function f(x) lies below the x-axis, then f(x) < 0.

From the given graph it is clear that the graph of f(x) intersect the x-axis at x=3.

Before x=3 the graph lies below the x-axis. So,

[tex]f(x) < 0[/tex] over the interval [tex](-\infty,3)[/tex].

After x=3 the graph lies above the x-axis. So,

[tex]f(x) > 0[/tex] over the interval [tex](3,\infty)[/tex].

Therefore, the correct option is C.

Which of the following is equivalent to: -5 - 4?*

Answers

Answer:

-9

Step-by-step explanation:

-5 - 4 = -5 + (4)

You are adding two negative numbers, so add the absolute values of the numbers, and the sign of the answer is negative.

-5 - 4 = -(|-5| + |4|) = -(5 + 4) = -9

Find the equation of the line: With an x intercept of 4 and a y intercept of 1. PLEASE HELP I ONLY HAVE 15 MINUTES LEFT

Answers

Answer:

y = -1/4x + 1

Step-by-step explanation:

that is (0,1) and (4,0)

gradient

can be -1/4

c can be y = mx + c

we'll take anyone of the equation

1 = 0 + c

c = 1

Hi can someone plz help me with this question

Answers

Answer: n/4-1

Step-by-step explanation:

n/4 means how much each friend would have eaten if the pizza was equally divided and - 1 references to the one slice less he ate.

If there are 7 frankfurters to the pound, how
many pounds of frankfurters are needed for a
picnic to supply 19 pupils with 2 frankfurters
each?​

Answers

Answer:

6lbs

Step-by-step explanation:

Total # of Frankfurters needed.

[tex]19*2=38[/tex]

Divide the total needed by the amount in a lb, to find out how many lbs we need.

[tex]\frac{38}{7}=5.4[/tex]

Therefore, we need 6 full lbs in order to create at least 38 Frankfurters.

If we only have 5lbs, we can only create 35 Frankfurters.

5.4 pounds of frankfurters are needed for a picnic.

there are 7 frankfurters to the pound

let x pounds of frankfurters needed for a picnic. to supply 19 pupils with 2 frankfurters each.

What is the Ratio?

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

since there are 19 pupil and each of has 2 frankfurters.

total frankfurters = 19 x 2
= 38
required pound,
x =38/7
x = 5.4  

Thus, 5.4 pounds of frankfurters are needed for a picnic to supply 19 pupils with 2 frankfurters each.

Learn more about Ratio here:

brainly.com/question/13419413

#SPJ2

which side of the quadrilateral abcd
has a length equal to 10?​

Answers

Answer:

AD

Step-by-step explanation:

You must measure the difference between A and D. To get to this answer you should try all available combinations.

If it takes 13 cup of flour to make 14 of a cake, how many cups of flour are needed to make a whole cake? i need help plz

Answers

Answer:

1-1/3 if its 14

1/52 if its 1/4

Step-by-step explanation:

what is the volume of a right triangle with the dimesions 24 20 12

Answers

Answer:

Assuming you mean area the answer is 120

Step-by-step explanation:

a right triangle has too shorter sides who are perpendicular and one longer side that you can't use. the longer side is 24 since 24>20>12

so 24 is the hypontenuse (longer side)

the two perpendicular sides are 20 and 12

the area for a triangle is b*h*1/2

the base (20) times the height (12) is 240. 240 times 1/2 is 120.

Volume is half the base times height multiplied by the lateral height.
Meaning
V=(1/2(24)(20))*(12)
The base is 240.
You multiply the base times the material height which is 12
Therefore, the answer is 2880

PLEASE MARK BRAINLIEST

PLSSS HELP!!! I really need help with this i have tried everything! Please provide instructions so I could learn how to do it! You are interested in finding a 98% confidence interval for the average number of days of class that college students miss each year. The data below show the number of missed days for 11 randomly selected college students. Round answers to 3 decimal places where possible. 9, 1, 2, 2, 9, 10, 1, 3, 7, 4, 2 a. To compute the confidence interval use a ? distribution. b. With 98% confidence the population mean number of days of class that college students miss is between ? and ? days. c. If many groups of 11 randomly selected non-residential college students are surveyed, then a different confidence interval would be produced from each group. About ? percent of these confidence intervals will contain the true population mean number of missed class days and about ? percent will not contain the true population mean number of missed class days.

Answers

Step-by-step explanation:

a. When the sample size is below 30 or the population standard deviation is not known, use a t distribution rather than a normal distribution.

b. The confidence interval is:

CI = x ± CV × SE

where x is the sample mean,

CV is the critical value (in this case, t).

and SE is the standard error (the sample standard deviation).

For the data given, the mean is x = 4.545, and the standard deviation is SE = 3.503.

There are 11−1 = 10 degrees of freedom, and the confidence level is 98%.  For a t-table, the critical value is CV = 2.764.

So the confidence interval is:

CI = 4.545 ± 2.764 × 3.503

CI = (-5.1, 14.2)

c.  The confidence level is 98%, so 98% of these confidence intervals will contain the true population mean, and 2% will not.

What is the value of q?

Answers

Answer:

14

Step-by-step explanation:

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