y=1/20x^2
The directrix of the parabola is:
x=-5
x=5
y=-5

Answer:

A+B+C+D = 13

Step-by-step explanation:

The given expression is:

[tex]\dfrac{1+\sqrt{2}}{2+\sqrt{3}}[/tex]

We have to simply it and express it in the form of:

[tex]A(1+\sqrt{B})-(\sqrt{C}+\sqrt{D})[/tex]

Multiply and divide the given expression with [tex]2-\sqrt 3[/tex]:

[tex]\dfrac{1+\sqrt{2}}{2+\sqrt{3}} \times \dfrac{2-\sqrt 3}{2-\sqrt 3}\\\Rightarrow \dfrac{(1+\sqrt{2}) \times (2-\sqrt 3)}{(2+\sqrt{3})\times (2-\sqrt 3)}\\\Rightarrow \dfrac{2+2\sqrt2-\sqrt3-\sqrt6}{2^2-(\sqrt{3})^2}\\\Rightarrow \dfrac{2+2\sqrt2-\sqrt3-\sqrt6}{4-3}\\\Rightarrow \dfrac{2(1+\sqrt2)-(\sqrt3+\sqrt6)}{1}\\\Rightarrow 2(1+\sqrt2)-(\sqrt3+\sqrt6)[/tex]

It is the simplified form of given expression.

Formula used:

[tex](a+b)(a-b) = a^{2} -b^{2}[/tex]

Comparing the simplified expression with [tex]A(1+\sqrt{B})-(\sqrt{C}+\sqrt{D})[/tex]

[tex]2(1+\sqrt2)-(\sqrt3+\sqrt6)=A(1+\sqrt{B})-(\sqrt{C}+\sqrt{D})\\\Rightarrow A =2, B=2, C=3\ and\ D=6[/tex]

So, value of

[tex]A+B+C+D = 2+2+3+6 = 13[/tex]

[tex]answer \\ 5 \\ solution \\ let \: the \: points \: be \: a \: and \: b \\ a(3 , 8) = > (x1 , y1) \\ b(1 , - 2) = > (x2 , y2) \\ slope = \frac{y2 - y1}{x2 - x1} \\ \: \: \: \: \: = \frac{ - 2 - 8}{1 - 3} \\ \: \: \: \: \: = \frac{ - 10}{ - 2} \\ \: \: \: \: \: \: = 5 \\ hope \: it \: helps[/tex]

To find the slope of the line, I will be showing you the table method.

To find the slope of the line using the table method,

we start by making a table for our ordered pairs.

We will put the x values in the left column

and the y values in the right column.

Our first ordered pair is (3, 8), so we put a

3 in the x column and a 8 in the y column.

Our second ordered pair is (1, -2), so we put a

1 in the x column and a -2 in the y column.

Next, remember that the slope or m, is always equal to

the rate of change or the change in y over the change in x.

Using our table, we can see that the y values

go from 8 to -2 so the change in y is -10.

The x values go from 3 to 1 so the change in x is 2.

Therefore, the rate of change, or the change in y

over the change in x is -10/2 which reduces to 5.

This means that the slope is also equal to 5.

Answer:

9 possible combinations: RGB, RYG, RGB, OYG, OGB, OBP, YGB, YBP, GBP

Step-by-step explanation:

Let's see what are the possible combinations:

3+4= 7 so possible 3rd side is 5

3+5= 8 so possible 3 rd side is 7

3+7= 10 so possible 3rd side is 5 or 9 (5 is repeat of the one above)

3+9= 12 so possible 3rd side is 7, see one above

3+12= 15 so possible 3 rd side is none

4+5=9 so possible 3rd side is 7

4+7= 11 so possible 3rd side is 9

4+9= 13 so possible 3rd side is 12

5+7= 12 so possible 3rd side is 9

5+9= 14 so possible 3rd side is 12

7+9= 16 so possible 3rd side is 12

So the possible 9 combinations are:

Answer:

Y = 2

Step-by-step explanation:

For point (x1,y1) and (x2,y2) on coordinate plane if is divided in ratio of m:n.

Then point of division is given by

(n*x1+m*x2)/ m+n,  (n*y1+m*y2)/ m+n

________________________________

Given point

c = (9,6)

d = (5,1)

ratio = 4:1

using the above formula , point of division is

x= (1*9+4*5)/ 4+1                     y=  (1*6+4*1)/ 4+1

x= (9+20)/ 5                             y=  (6+4)/ 5

x= 29/ 5                                    y=  10/ 5 =2

Thus, answer is y = 2

Answer:

2 is correct

Step-by-step explanation: I got it right on test

Answer:

d

Step-by-step explanation:

2(7)+6=20

14+6=20

20=20

Answer:

2x + 6 = 20

2x = 20 - 6

2x = 14

Divide both sides by 7

x = 7

That's option D.

Hope this helps.

Answer:

See below.

Step-by-step explanation:

It is known that a parallelogram has rotational symmetry, rotated 180 degrees about it's center point. Now by definition a parallelogram is a quadrilateral with two pairs of parallel sides, hence it's name. If you were to take a look at the attachment below, you might see the connection.

Rotational Symmetry will make it so that side AB corresponds to CD, respectively AD and CB. The sides will coincide with one another after a 180 degree rotation, so that AB = CD, and AD = CB. Hence, in the same parallelogram, opposite sides are congruent.

Proved!

Answer:

I think there is an error in the question because

(f-g) = -4

(f-g) (7) = NO SOLUTION

Step-by-step explanation:

[tex]f(x) = -9x + 2 \\g(x) = -9x + 6\\(f - g)(7)\\(f - g) = -9x + 2 - (-9x+6)\\(f - g) = -9x +2 +9x-6\\(f - g) = -9x +9x+2-6\\(f - g) = -4[/tex]

Answer:

15/28

Step-by-step explanation:

3 3/7 ÷ 6 2/5

Change to improper fractions

(7*3+3)/7 ÷ (5*6+2)/5

24/7 ÷32/5

Copy dot flip

24/7 * 5/32

Cancel an 8 from the numerator and denominator

3/7 * 5/4

15/28

Answer: 15/28

Explanation: First write each mixed number as an improper fraction.

As a quick review, to write a mixed number as an improper fraction,

we multiply the denominator times the whole number,

then we add the numerator.

First rewrite 3 and 3/7 as 24/7 and 6 and 2/5 as 32/5.

So we have 24/7 ÷ 32/5.

Dividing by a fraction is the same as multiplying by its reciprocal.

In other words, we can change the division

sign to multiplication and flip the second fraction.

So 24/7 ÷ 32/5 can be rewritten as 24/7 × 5/32.

Before multiplying, noice that the 24 and 32 cross-cancel to 3 and 4.

So we have 3/7 × 5/4 which is 15/28.

Answer:

x= 70

Step-by-step explanation:

This question needs an attachment; see attached

Given

ABD = 55

Required

Find x?

In the figure shown in the attachment, angle b and ABD are alternate interior angles;

From parallel and perpendicular line theorems; alternate interior angles are equal.

This implies that <b = 55

Also; when a rectangle is divided by two diagonals, the resulting triangles are isosceles triangles;

where 2 sides and 2 angles are equal;

This implies that <b = <c = 55

Sum of angles in a triangle  = 180;

So,

<x + <b + <c = 55

x + 55 + 55 = 180

x + 110 = 180

Subtract 110 from both sides

x + 110 - 110 = 180 - 110

x = 180 - 110

x = 70

Answer:

The A) ΔABC ≅ ΔEDC

Step-by-step explanation:

The AAS congruence method requires 2 angles and their un-included side to be congruent. ∠A ≅ ∠E due to the markings, ∠C ≅ ∠C because they are vertical angles, and AB ≅ ED due to the markings. 2 angles and their un-included side are congruent.

As for the congruence statement, A is the correct answer because ∠A ≅ ∠E, ∠B ≅ ∠D, and ∠C ≅ ∠C. The order of the naming of the triangles aligns to the angle's congruence.

Answer:

A) triangle ABC is congruent to triangle EDC

Step-by-step explanation:

The AAS method of proving congruence of triangles uses two angles and a non-included side of the triangle. If two angles and the non-included side of a triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

Let's see what we have in this problem:

<ACB and <ECD are congruent since they are vertical angles.

<A and <E are congruent by given.

Sides AB and ED are non-included sides and are congruent.

Since we have two angles and a non-included side of a triangle and the corresponding parts of another triangle, the triangles are congruent by AAS.

Now we need the statement of congruence.

Angles ACB and ECD are corresponding angles, so the letter C must appear in both triangles in the same position.

Angles A and E are corresponding angles, so the letters A and E must appear in both triangles the same position.

We already have CA and CE. The last angles left are corresponding angles B and D, so we get triangle CAB and triangle CED. Since a triangle may be named using any order of the vertices, we can rename the triangles ABC and EDC and maintain the same corresponding vertices.

Answer: A) triangle ABC is congruent to triangle EDC

Answer:

The equivalent of 5.651 mi is 9945.76  yards

Step-by-step explanation:

Given:

Length of lake = 5.651 mi

Required:

Length of bridge in yards

From table of facts;

1 mile = 1760 yards

This implies that

5.651 miles will be:5.651 * 1760 yards

5.651 * 1760 yards = 9945.76  yards

5.651 * 1760 yards = 9945.8  yards (Aproximated)

Hence, the equivalent of 5.651 mi is 9945.76  yards

Answer:

option b

Step-by-step explanation:

[tex] \sqrt{ \frac{5}{3} } [/tex]

[tex] \frac{ \sqrt{5} }{ \sqrt{3} } [/tex]

the denominator is in the surd form, so it must be rationalized

Answer:

x ≈ 31.3°

Step-by-step explanation:

We can use sin∅ to solve this:

sinx = 13/25

x = [tex]sin^{-1}(13/25)[/tex]

x = 32.3323

Answer:

[tex]g(x) = \frac{1}{9} \,x^2[/tex] which agrees with option A in the list of possible answers

Step-by-step explanation:

A vertical compression by a factor 9 is represented by the transformation:

[tex]\frac{1}{9} \,f(x) = \frac{1}{9} \,x^2[/tex]

Therefore the answer to the problem is:

[tex]g(x) = \frac{1}{9} \,x^2[/tex]

Answer: domain: {2, 3, 4, 6}

range: {–3, –1, 3, 6}

Step-by-step explanation:

DOMAIN: {4}

RANGE: {2,5,7,9}

FUNCTION? NO!

Your domain is always your x-coordinates, which are the first coordinates in a pair.

Your range is always your y-coordinates, which are the second coordinates in a pair.

When listing the points, it's important to remain a relation CANNOT be a function if the x's repeat, so luckily, they do not repeat.

Also, when listing points for your range, remember, if they repeat, you should only count one of the numbers, as you can see from the answer, there were two nines, but instead, I put one.

Answer:

The answer is 3√5 mi.

The formula is: d = √(3h/2)

Wyatt:

h = 120 ft

d = √(3 * 120/2) = √180 = √(36 * 5) = √36 * √5 = 6√5 mi

Shawn:

h = 270 ft

d = √(3 * 270/2) = √405 = √(81 * 5) = √81 * √5 = 9√5 mi

How much farther can Shawn see to the horizon?

Shawn - Wyatt = 9√5 - 6√5 = 3√5 mi

Answer:

its b

Step-by-step explanation:

i just did it

Answer:

x = [tex]-7\frac{2}{3}[/tex]

Step-by-step explanation:

=> 6(2x+11) + 15 = 3x+12

(Expand the brackets)

=> 12x+66+15 = 3x+12

(Adding 66+15)

=> 12x+81 = 3x+12

(Subtracting 81 and 3x to both sides)

=> 12x-3x = 12-81

=> 9x = -69

(Dividing both sides by 9)

=> x = [tex]\frac{-69}{9}[/tex]

(Simplifying)

=> x = [tex]\frac{-23}{3}[/tex]

(Converting it into mixed form)

=> x = [tex]-7\frac{2}{3}[/tex]

So, x = [tex]-7\frac{2}{3}[/tex] will make the equation true.

Answer:hello

The answer is 7

Step-by-step explanation:at first solve this6(2x-11)=12x-66

Then write 12x-66+15

Then we have this 12x-66-15=3x+12

Then we have to write (x) in the left side and number in right side

12x-3x=66-15+129x=63

X=7

Good luck

Answer:

Yes the new method if sample size was less than 20 than that of old method or identical sample numbers of old and new the differences still prove the new operation is better. As 88 patients minus 1% still shows us 76.7475 significance of  old method being low point 67.5 = 30% of 225 and proved a 65.25 low point and 69.75 high point which is also a 20% jump to new methods low point significance.

You cna show this as workings to prove or follow any of the below statements.

Where new method of 88 patients -0.01 significance rate stands at 76.7475. This figure has reduced by 11.2525 from 88 patients to 76.7 we compare this to the old method if reversing significance we find  = 62.5 and it's 30% standing value of 67.5  as +1% increase shows us 31% = 69.7  ( 0.31 x 225 = 69.74)

Step-by-step explanation:

88/225  = 0.39111111111 = 39.11%%

P value 01 = 1%  =  225.225 or 5% range of alternative hypotheses.

To graph the P value we take the distance between the sample mean and the null hypothesis value (225 + 1% of sample - x nhv) = y ). We can graph the probability of obtaining a sample mean  (225 +/- ( x +1% of sample) where nhv has a decimal if needed to utilize the 1% added). we would replace nvp in this example with  Ha or H1 which means the alternative hypotheses as the data shows less than or equal to.

We can then show 225.225 -  Ha or H1  then graph the probability of obtaining a sample mean that is at least extreme in both tails  Ha or H1

However it would be the other way round where you take the first set of data and use the sample as the 30% significance of that sample indicates it may be a larger sample or a higher significance. Therefore this would be used in the graphing - 1%

We prove that 30-1 =29  where 29% of 225 = 225 x 0.29 = 65.25

this way we have proved that the new set of data being equal to 88 patients regaining their eyesight is <23 and can be written like this 65.25< x <88

This means that sample mean has taken the 1% to show on the graph we can show 225> 33.11 +1 .

We can prove that both indifference of significance would reduce when 1% is added and close based on being a higher percentage to begin with.

34.11 = 0.3411 x 225 = 76.7475 for second surgeon = 33.11% +1

Where as shown

30 = 0.3 x 225 = 67.5

76.5475 - 67.5 = 9.04 difference when comparing old method = +1%

where new method stands at 76.7475 has reduced by 11.2525 from 88 patients and where old method if reversing = 62.5 and has reduced from 67.5  as +1% and 31% = 69.7  ( 0.31 x 225 = 69.74)

You would therefore graph each higher methods first if comparing both by 0.01 or show 88 on graph and 76.7475 = +1%

NB/ if sample size was 20 more in the old data then 225+20 = 245 x 0.29 = 71.05 and would still be lower than new data. = 2.0 increase level of significance and not relevant unless you are looking for the decrease which means new is greater than 20% success than that of old method findings where 30% = 67.5.

Answer:

64.21

Step-by-step explanation:

After performing some simple mathematical operations, we know that 6.421 x 10 = 64.21.

So, 6.421 x 10 = ?:

Evaluate as follows:

Therefore, after performing some simple mathematical operations, we know that 6.421 x 10 = 64.21.

Know more about mathematical operations here:

https://brainly.com/question/28937023

#SPJ2

The correct question is given below:

Multiply. 6.421 x 10 = _____

A. 0.6421

B. 64.21

C. 642.10

D. 6,421

Answer:

Step-by-step explanation:

hello,

I understand that there are only 4 cards  and then the player draw a card out of the 4 cards, replace it so the second draw is still out of the 4 cards

How many ways can you draw two cards?

as the first card is replaced, this is 4*4=16

so there is 16 possibles ways

hearts hearts

hearts clubs

hearts diamonds

hearts spades

clubs hearts

clubs clubs

clubs diamonds

clubs spades

diamonds hearts

diamonds clubs

diamonds diamonds

diamonds spades

spades hearts

spades clubs

spades diamonds

spades spades

out of these 16 ways, how many have same colour for both cards?

I assume that there are only two colours Red and Black, so we can have

only 8 ways so the first probability is 8/16 = 1/2

out of these 16 ways, how many are red ace first and black ace?

There are 4 ways so the probability is 4/16 = 1/4

hope this helps

Standard deck has aces in four colors

Player draws one from four so the probability of drawing any first card is 1/4 (in the first drawing)

We replace the card so in second drowing its the same

So the probability of drawing two card of one chosen color is 1/4*1/4, and we have four colors

The probability of drawing two card of the same color is:

There are 2 red aces and 2 black aces

(sorry for coments - not reading carefully)

So a probability of drawing red ace in first drawing is 2/4=1/2

a probability of drawing black ace in second drowing is the same ('cause we replace the one drawn first)

So the probability that a red ace is drawn first and then the black ace is:

Answer:

Step-by-step explanation:

$11/ 47 pound = $0.234 for 1 pound

the cost of buying 47 pound for 11 dollars is cheaper than to buy individual 1 pound bag for 0.45.

Answer:

First, let's find the unit price.

$11 ÷ 47 = $0.23 per pound.

$0.45 ÷ 1 = $0.45 per pound.

As you can see here, the 1 pound bag(smaller bag) clearly costs more per pound. The 47 pound bag(larger bag) costs less.

We can also put the values on a number line to compare.

          $0.23               $0.45

      (larger bag)    (smaller bag)

<-|---------o---------------------o---------|------------------------------------------|->

$0                                         $0.50                                           $1

As you can see, the larger bag is closer to zero.

Hope this helped!

-Emma

Answer:

This is true.

Answer:

Reflect the graph of f across the y-axis and then reflect across the x-axis.

Step-by-step explanation:

Reflection rules:

Reflection over x -axis:(x,y)→(x,-y)

Reflection over y-axis : (x,y)→(-x,y)

Graph:[tex]y= f(x)=x^2[/tex]

We are given that the graph of f into the graph of g.

[tex]f(x) = x^2[/tex] and [tex]g(x) = -(-x)^2[/tex]

Reflect over y axis.

Reflected graph [tex]=(-x)^2[/tex]

Reflect the obtained graph over x axis

[tex]g(x)=-(-x)^2[/tex]

So, Option B is true

Hence Reflect the graph of f across the y-axis and then reflect across the x-axis.

Answer:

i reflected it over the x and y axis tho

Step-by-step explanation:

bro trust me

Answer:

Itz B.

Step-by-step explanation:

To form a triangle to two smaller sides have to be able to add up to be greater than the big side

Answer:

5/14

Step-by-step explanation:

Multiply.

(-5 × -1 × 4) / (7 × 8)

20/56

Simplify.

5/14

Answer:

The answer is [tex]\frac{5}{14}[/tex].

Step-by-step explanation:

1. -5 × [tex]\frac{-1}{7}[/tex] =  [tex]\frac{5}{7}[/tex]

2.  [tex]\frac{5}{7}[/tex] · [tex]\frac{4}{8}[/tex] = [tex]\frac{20}{56}[/tex]

3. Simplify:

[tex]\frac{20}{56}[/tex]  = [tex]\frac{5}{14}[/tex]

Answer:

240; 24

Step-by-step explanation:

Given that:

Sum of two numbers = 264

One number ends with '0'

Second number = first number without '0'

Let the first number be 'a'

Since the second number is the first number with '0' erased, then,

Second number = (a ÷ 10)

Therefore, the expression becomes :

a + a/10 = 264

Multiply the equation by 10

10a + a = 2640

11a = 2640

a = 2640/11

a = 240

Therefore ;

a = 240 ;

a/10 = 240/10 = 24

The numbers are 240 and 24

Answer:

[tex]a = 30[/tex]

[tex]b = 40[/tex]

Step-by-step explanation:

Given

The attached triangle

Such that K is parallel to L

Required

Find the value of a and b

From the properties of parallel triangles;

Provided that k is parallel to l, then

[tex]\frac{a}{40} = \frac{a+15}{60}[/tex]

Multiply both sides by (60)(40)

[tex](60)*(40)*\frac{a}{40} = (60)*(40)*\frac{a+15}{60}[/tex]

[tex]60a = 40(a+15)[/tex]

Open Bracket

[tex]60a = 40*a+40*15[/tex]

[tex]60a = 40a+600[/tex]

Subtract 40a from both sides

[tex]60a - 40a = 40a - 40a + 600[/tex]

[tex]20a = 600[/tex]

Divide both sides by 20

[tex]\frac{20a}{20} = \frac{600}{20}[/tex]

[tex]a = \frac{600}{20}[/tex]

[tex]a = 30[/tex]

Similarly;

[tex]\frac{b}{40} = \frac{b+20}{60}[/tex]

Multiply both sides by (60)(40)

[tex](60)*(40)*\frac{b}{40} = (60)*(40)*\frac{b+20}{60}[/tex]

[tex]60b = 40(b+20)[/tex]

Open Bracket

[tex]60b = 40*b+40*20[/tex]

[tex]60b = 40b+800[/tex]

Subtract 40b from both sides

[tex]60b - 40b= 40b - 40b + 800[/tex]

[tex]20b= 800[/tex]

Divide both sides by 20

[tex]\frac{20b}{20} = \frac{800}{20}[/tex]

[tex]b = \frac{800}{20}[/tex]

[tex]b = 40[/tex]