solve using completing the square method

Answer:

30th percentile = 105 90th percentile = 176

Step-by-step explanation:

Arrange the data set in order from smallest to largest:

100, 100, 105, 113, 129, 132, 146, 152, 176, 200

30th percentile

r = number of data values = 10

q = percentile = 30

q/100 = 30/100 = 0.3

q/100 × r = 0.3 × 10 = 3

Therefore, count the 3rd number in the ordered set.

⇒ 30th percentile = 105

90th percentile

r = number of data values = 10

q = percentile = 90

q/100 = 90/100 = 0.9

q/100 × r = 0.9 × 10 = 9

Therefore, count the 9th number in the ordered set.

⇒ 90th percentile = 176

30th percentile = 105, 90th percentile = 176

Explanation:

data {129, 113, 200, 100, 105, 132, 100, 176, 146, 152}

arrange in ascending order:

{100, 100, 105, 113, 129, 132, 146, 152, 176, 200}

Answer:

0.04

Step-by-step explanation:

Have a nice day!

Simply just take 4 divided by 100 -> 4 : 100 = 0.04

Answer:

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

a and b are legs, c is the hypotenuse

[tex]9^{2}[/tex] + [tex]11^{2}[/tex] = [tex]c^{2}[/tex]

81   + 121 = [tex]c^{2}[/tex]

202 = [tex]c^{2}[/tex]     ( square root each side  [tex]\sqrt{202}[/tex]

14.2126704036   = c

c = 14.2

The expression that represents the area of the base of the pyramid(right pyramid) is given by: Option A: 3v/h unit²

A right rectangular pyramid is a pyramid, with four slant sides, and a rectagular base, such that all the sides are congruent and the vertex is atop of the midpoint of the base rectangle.

Suppose the base of the pyramid has length = l units, and width = w units.

Suppose that the height of the pyramid is of h units, then:

[tex]v = \dfrac{l \times w \times h}{3} \: \rm unit^3[/tex] is the volume of that pyramid.

The base is a rectangle with length = L units, and width = W units, so its area is:

[tex]b = l \times w\: \rm unit^2[/tex]

Thus, we can express the area of its base in terms of its volume as:

[tex]v = \dfrac{l \times w \times h}{3} \: \rm unit^3 = \dfrac{b\times h}{3}\\\\3v = b\times h\\\\\\b = \dfrac{3v}{h} \: \rm unit^2[/tex]

Thus, the expression that represents the area of the base of the pyramid (right pyramid) is given by: Option A: 3v/h unit²

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Answer:

3V/h units^2

Step-by-step explanation:

Answer:

1) NAME OF CIRCLE : CIRCLE ABDE

2) CHORD : SEGMENT DE

3)DIAMETER: SEG DB

4)TANGENT LINE : RAY E

5) SECANT LINE : SEGMENT AB

HOPE IT HELPS!

MARK AS BRAINLIAST.

Answer:

the answer should be 6.

Step-by-step explanation:

You have to make the fractions have the same denominator, this can be done by converting the 3/4. In this case you multiply both the denominator and the numerator by 2 to get 6/8. Complete the equation 6/8 ÷ 1/8 to get 6 as the full amount. half of this number would be 3 so the final result is 3.

Answer:

B. 2106 pi mm³

Step-by-step explanation:

the solution is attached,

Answer:

B.2106π mm^3

Step-by-step explanation:

here is the volume of a drill

[tex]\pi \: {r}^{2} h \: + \frac{1}{3} \pi \: {r}^{2} h[/tex]

[tex]\pi \times 81 \times 18 + \frac{1}{3} \times \pi \times 81 \times 24[/tex]

[tex] > > > 2106 \pi \: {mm}^{3} [/tex]

Answer:

a. 1710 b. 71.25

Step-by-step explanation:

the formula for simple interest is i=prt

2(9500)(0.09)= 1710

to find the monthly payment, divide by the number of months.

1710/24=71.25

So

Answer:75

Step-by-step explanation:

Answer:

10: 12 units^2 11: 33 units^2

Step-by-step explanation:

10:

Divide into square and 2 triangles (for simplicity)

square=9

one triangle=3/2

both triangles combined=3

9+3=12

11:

divide into 2 triangles

top triangle: height= 4, base=6

bottom triangle: height= 7, base=6

top=12

bottom=21

Add, 33.

Answer:

[tex] \frac{1}{20} [/tex]

or 5%

Step-by-step explanation:

Explanation:

3/4=15/20

1/5=4/20

So, rest of 'em 1/20

Answer:

1/20.

Step-by-step explanation:

1 - 3/4 - 1/5

= 20/20  - 15/20 - 4/20

= 1/20

Answer:

x=4

Step-by-step explanation:

20x-5x=65-5

15x=60

x=60/15

x=4

Answer:

Step-by-step explanation:

In the question we are given with an equation that is 20x + 5 = 5x + 65 . And we are asked to find the value of x.

Solution :

[tex] \longmapsto \: 20x + 5 = 5x +65[/tex]

Step 1 : Subtracting 5 on both sides :

[tex] \longmapsto \: 20x + \bold{ \cancel{5}} - \bold{ \cancel{5}}= 5x + \bold{65 }- \bold{5}[/tex]

On further calculations, we get :

[tex] \longmapsto \: 20x = 5x + 60[/tex]

Step 2 : Subtracting 60 on both sides :

[tex] \longmapsto \:20x - 60 = 5x + \bold{ \cancel{60}}- \bold{ \cancel{60}}[/tex]

On further calculations, we get :

[tex] \longmapsto \:20x - 60 = 5x[/tex]

Step 3 : Transposing 5x to left hand side and -60 to right hand side :

[tex] \longmapsto \:20x - 5x = 60[/tex]

On further calculations , we get :

[tex] \longmapsto \:15x = 60[/tex]

Step 4 : Divide by 15 on both sides :

[tex] \longmapsto \: \frac{ \cancel{15}x}{ \cancel{15} } = \cancel{ \frac{60}{15} }[/tex]

On further calculations, we get :

[tex] \longmapsto \: \red{ \boxed{x = 4}}[/tex]

Now, we are verifying our answer by substituting value of x in given equation :

Therefore , our answer is correct

Answer:

1, -5

Step-by-step explanation:

you can this solve easily

3 - -1 = 4 units down from y = -1

x does not change in this reflection

Matt travelled on a bike and cover a distance of 60 miles . If he had gone 6mph faster, he would have arrived 5 hours. Therefore, the actual rate  is 6 mph.

Rate is the ratio between two related quantities in different units.

He went on a bike ride of 60 miles.

He realized if he had gone 6 miles per hour he would have arrived 5 hours earlier.

The speed he actually ride can be calculated as follows:

let

x = speed he actually ride

y = time he arrived

Therefore,

speed = distance / time

x = 60 / y

On, the other hand his permutation is as follows:

x + 6 = 60 / y - 5

(x + 6)(y - 5) = 60

since, x = 60 / y we can substitute it in the equation

(60 / y + 6)(y - 5) = 60

60 - 300 / y + 6y - 30 = 60

- 300 / y + 6y = 60 - 30

- 300 / y + 6y = 30

6y² - 300 = 30y

6y² - 30y - 300 = 0

y² - 5y - 50 = 0

y² + 5y - 10y - 50 = 0

y(y + 5) -10(y + 5) = 0

(y - 10)(y + 5) = 0

y = 10 or -5

we cannot use negative values.

Therefore,

y = 10

x = 60 / y = 60 / 10 = 6 miles per hour

He actually rode 6 miles per hour.

If he went 6 mph faster that would be 6+6 = 12 mph

If he arrived 5 hrs sooner that would be 10 - 5 = 5 hrs

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Answer:

Amplitude 0.03m, wavelength 2.86m, frequency 0.57Hz, period 1.8s

Step-by-step explanation:

The traveling wave is described with the following equation:

[tex]y=Asin(kx-wt)[/tex]

y=0.03sin(2.2x−3.5t)

A=0.03m

λ=2π/k=2π/2.2≈2.86m

T=1/f≈1.8s

Answer:

See Explanation

Step-by-step explanation:

Given

[tex]\frac{x}{a}= \frac{y}{b} =\frac{z}{c}[/tex]

[tex]Let \: \frac{x}{a}= \frac{y}{b} =\frac{z}{c}=m[/tex]

(where m is any constant)

[tex]\implies[/tex]

[tex]\frac{x}{a}=m\implies x =am[/tex]

[tex]\frac{y}{b}=m\implies y =bm[/tex]

[tex]\frac{z}{c}=m\implies z =cm[/tex]

To Prove:

[tex]\frac{ax-by}{(a+b)(x-y)}+\frac{by-cz}{(b+c)(y-z)}=2[/tex]

LHS [tex]=\frac{ax-by}{(a+b)(x-y)}+\frac{by-cz}{(b+c)(y-z)}[/tex]

(Plug the values of x, y and z in the form of am, bm and cm respectively in the LHS)

[tex]=\frac{a(am)-b(bm)}{(a+b)(am-bm)}+\frac{b(bm)-c(cm)}{(b+c)(bm-cm)}[/tex]

[tex]=\frac{a^2m-b^2m}{(a+b)m(a-b)}+\frac{b^2m-c^2m}{(b+c)m(b-c)}[/tex]

[tex]=\frac{m(a^2-b^2)}{m(a+b)(a-b)}+\frac{m(b^2-c^2)}{m(b+c)(b-c)}[/tex]

[tex]=\frac{\cancel{m(a^2-b^2)}}{\cancel{m(a^2-b^2)}}+\frac{\cancel{m(b^2-c^2)}}{\cancel{m(b^2-c^2)}}[/tex]

= 1 + 1

= 2

= RHS

[tex]\implies \purple{\bold{\frac{ax-by}{(a+b)(x-y)}+\frac{by-cz}{(b+c)(y-z)}}}=\red{\bold{2}}[/tex]

Thus proved

Answer:

Factoring: [tex]x = -\frac{1}{5}, -3[/tex]

Step-by-step explanation:

A) You can factor the expression [tex]5x^2 + 16x + 3[/tex] into [tex](5x+1)(x+3)[/tex].

5x + 1 = 0 and x + 3 = 0

[tex]x = -\frac{1}{5}, -3[/tex]

B) I would use factoring because you can factor this expression, and you don't have to use completing the square

Answer:

  (a)  There are asymptotes at x=3/2 and x=-1/3

Step-by-step explanation:

The denominator zeros can be found by factoring:

  f(x) = (x +1)/((2x -3)(3x +1))

Neither of the denominator factors is cancelled by the numerator factor, so each represents a vertical asyptote, not a function hole.

The asymptotes are at the values of x where the denominator is zero:

  2x -3 = 0   ⇒   x = 3/2

  3x +1 = 0   ⇒   x = -1/3

Answer:A There are asymptotes at x=3/2 and x=-1/3

Step-by-step explanation:

a. i. The parametric equation for the horizontal movement is x = 43.84t

ii. The parametric equation for the vertical movement is y = 50 + 43.84t

b. the location of the football at its maximum height relative to the starting point is (60.1 ft, 60.1 ft)

A parametric equation is an equation that defines a set of quantities a functions of one or more independent variables called parameters.

The parametric equation for the horizontal movement is x = 43.84t

Since

the horizontal component of the velocity is v' = vcosФ.

So, the horizontal distance the football moves in time, t is x = vcosФt

= vtcosФ

= 62tcos45°

= 62t × 0.7071

= 43.84t

So, the parametric equation for the horizontal movement is x = 43.84t

The parametric equation for the vertical movement is y = 50 + 43.84t

Also, since

the vertical component of the velocity is v" = vsinФ.

Since the football is initially at a height of h = 50 feet, the vertical distance the football moves in time, t relative to the ground is y = 50 + vsinФt

= 50 + vtcosФ

= 50 + 62tsin45°

= 50 + 62t × 0.7071

= 50 + 43.84t

The location of the football at its maximum height relative to the starting point is (60.1 ft, 60.1 ft)

Since the football reaches maximum height at t = 1.37 s

The x coordinate of its location at maximum height is gotten by substituting t = 1.37 into x = 48.84t

So, x = 43.84t

x = 43.84 × 1.37

x = 60.0608

x ≅ 60.1 ft

The y coordinate of the football's location at maximum height relative to the ground is y = 50 + 48.84t

The y coordinate of the football's location at maximum height relative to the starting point is y - 50 = 48.84t

So,  y - 50 = 48.84t

y - 50 = 43.84 × 1.37

y - 50 = 60.0608

y - 50 ≅ 60.1 ft

So, the location of the football at its maximum height relative to the starting point is (60.1 ft, 60.1 ft)

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Answer:

$80

Step-by-step explanation

(chart)

             10%         -$10

$140   $126         $130  

$120    $108        $110

$100    $90          $90

$80      $72           $70  

Answer:

70 cubic feel. 3. Abox of oat cereal measures 24 centimeters long by 5 centimeters wide by 25 centimeters high.

Step-by-step explanation:

70 cubic feel. 3. Abox of oat cereal measures 24 centimeters long by 5 centimeters wide by 25 centimeters high.

Answer:

500,000,000,000 + 800,000,000 + 2,000,000 + 9,000 + 600 + 10 + 2

Step-by-step explanation:

To write a standard form number into an expanded form, we must look at the amount of numbers at each 'place' in the number.

Hundred-Billions --> 5            Hundred-Thousands --> 0

Ten-Billions --> 0                     Ten-Thousands --> 0

Billions --> 0                             Thousands --> 9

Hundred Millions --> 8             Hundreds --> 6

Ten Millions --> 0                      Tens --> 1

Millions --> 2                              Ones --> 2

Answer: five hundred billion eight hundred two million nine thousand six hundred twelve.  

Step-by-step explanation:

500,000,000,000=five hundred billion

800,000,000=eight hundred million

2,000,000=two million

9,000=nine thousand

600=six hundred

10=ten

2=two

Answer:

x = 1/4

Step-by-step explanation:

To solve, we need to find the constant of proportionality (k) which is defined by the equation:

yx = k

[tex](68)(1/17) = k\\k = 4[/tex]

Therefore when y= 16,

[tex]16x = 4\\x= \frac{1}{4}[/tex]

When y varies inversely with x that means mathematically

  [tex]y = \frac{k}{x}[/tex]

We know for one, that when y = 68 and x = 1/17, that means

  [tex]68 = \frac{k}{\frac{1}{17} } \\68 = 17k\\k = 4[/tex]

Therefore we get the equation of the relationship between y and x as

  ⇒ [tex]y = \frac{4}{x}[/tex]

So when y = 16, then

 [tex]16 = \frac{4}{x} \\4 = 16x\\x = \frac{1}{4}[/tex]

Thus the value of x when y = 16 is 1/4 or the third choice.

Hope that helps!

Answer:

C = 14[tex]\pi[/tex], A = 49[tex]\pi \\[/tex].

Step-by-step explanation:

C = Circumference, A = Area

So, the Circumference is 14[tex]\pi[/tex] and the area is 49[tex]\pi \\[/tex].

Hope this helps :)

Answer:

Step-by-step explanation:

x is the adjacent side of 30°

Hypotenuse = 22

[tex]Cos \ 30^ \circ = \dfrac{adjacent \ side}{hypotenuse}\\\\\\0.866 = \dfrac{x}{22}\\\\\\0.866*22 = x\\[/tex]

x = 19.1

Answer:

cosθ=Adjacent/ hypotenuse

[tex] \cos(30) = \frac{x}{22} \\ \\ \frac{ \sqrt{3} }{2} = \frac{x}{22} \\ \\ 2x = 22 \sqrt{3} \\ \\ x = \frac{22 \sqrt{3} }{2} \\ \\ x = 11 \sqrt{3} = 19.05 = 19.1[/tex]

Answer:

3 7/12

Step-by-step explanation:

First find the common denominator.

8,16,24

3,6,9,12,15,18,24

Once you find the common denominator. You have to fix the numerator.

7 2/8 would become 7 6/24

Whole numbers stay the same.

8 x 3 = 24

2 x 3 = 6

Now we repeat it on the other mixed number.

3 2/3 would become 3 16/24

Again whole numbers stay the same.

3 x 8 = 24

2 x 8 = 16

Once you convert the fractions to having the same denominator you subtract like normal.

7 6/24 - 3 16/24 = 3 14/24

3 14/24 can be simplified to 3 7/12

Answer:

[tex]\boxed{3 \dfrac{7}{12}}[/tex]

Step-by-step explanation:

The first step in simplifying the expression is to convert both the fractions into improper fractions [a/b (a > b)].

⇒ [tex]7\dfrac{2}{8} - 3\dfrac{2}{3}[/tex]

⇒ [tex]\dfrac{7 \times 8 + 2}{8} - \dfrac{3 \times 3 + 2}{3}[/tex]

⇒ [tex]\dfrac{56 + 2}{8} - \dfrac{9 + 2}{3}[/tex]

⇒ [tex]\dfrac{58}{8} - \dfrac{11}{3}[/tex]

The next step in simplifying the expression is to make the denominators of both fractions equivalent.

⇒ [tex]\dfrac{58}{8} - \dfrac{11}{3}[/tex]

⇒ [tex]\dfrac{58 \times 3}{8 \times 3} - \dfrac{11 \times 8}{3 \times 8}[/tex]

⇒ [tex]\dfrac{174}{24} - \dfrac{88}{24}[/tex]

The third step in simplifying the expression is to subtract the fractions.

⇒ [tex]\dfrac{174}{24} - \dfrac{88}{24}[/tex]

⇒ [tex]\dfrac{86}{24}[/tex]

The fourth step in simplifying the expression is to simplify the difference of the two fractions.

⇒ [tex]\dfrac{86}{24}[/tex]

⇒ [tex]\dfrac{86 \div 2}{24 \div 2}[/tex]

⇒ [tex]{\dfrac{43}{12}}[/tex]

The fifth step in simplifying the expression is to convert the improper fraction into mixed fraction.

⇒ [tex]{\dfrac{43}{12}}[/tex]

⇒ [tex]{\dfrac{36}{12}} + \dfrac{7}{12}[/tex]

⇒ [tex]3 + \dfrac{7}{12}[/tex]

⇒ [tex]\boxed{3 \dfrac{7}{12}}[/tex]