Sammy was playing Games with Alex. The ratio of games Sammy won was to the number of games Alex won was 9 to 5. If Sammy won 36 games, how many games did Alex win?

Try this suggested option, answers are marked with colour.

[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{5}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{1}}} \implies \cfrac{5 +1}{3 -1}\implies \cfrac{6}{2}\implies 3[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{3}(x-\stackrel{x_1}{1}) \\\\\\ y+1=3x-3\implies y=3x-4[/tex]

Answer:

I got 5-20

Step-by-step explanation:

Answer:

[tex]\textsf{a)} \quad P=-20(x-2)^2+3380[/tex]

b)  cost of ticket = $13

    max profit = $3380

    number of tickets sold = 260

Step-by-step explanation:

Profit equation:   [tex]P=20(15-x)(11+x)[/tex]

Vertex form of quadratic equation:  [tex]y=a(x-h)^2+k[/tex]

(where (h, k) is the vertex and [tex]a[/tex] is some constant)

First, write the given profit equation in standard form [tex]ax^2+bx+c[/tex]:

[tex]\begin{aligned}\implies P&=20(15-x)(11+x)\\& = 20(165+4x-x^2)\\& = -20x^2+80x+3300\end{aligned}[/tex]

Factor -20 from the first two terms:

[tex]\implies P=-20(x^2-4x)+3300[/tex]

Complete the square:

[tex]\implies P=-20(x^2-4x+4)+80+3300[/tex]

[tex]\implies P=-20(x-2)^2+3380[/tex]

The vertex of the profit equation is (2, 3380).

Therefore, the cost of the ticket is when x = 2 ⇒ $11 + 2 = $13

The maximum profit is the y-value of the vertex:  $3380

The number of tickets sold at this price is:

⇒ max profit ÷ ticket price

= 3380 ÷ 13

= 260

Answer:

19 minutes.

Step-by-step explanation:

49  - 30

= 19 minutes.

Answer:

x = 48

Step-by-step explanation:

(x - 6)⁰ + ( 2x + 42)⁰ = 180⁰

x - 6⁰ + 2x + 42⁰ = 180⁰

x + 2x - 6⁰ + 42⁰ = 180⁰

3x + 36⁰ = 180⁰

3x + 36⁰ - 36⁰ = 180⁰ - 36⁰

3x = 144⁰

3x / 3 = 144⁰ / 3

x = 48

Hope this helps, thank you :) !!

Answer:

A=28.95502437A=28.95502437B=104.47751218B=104.47751218C=46.56746344C=46.56746344a=4a=4b=8b=8c=6

Answer:

72+30=102

Step-by-step explanation:

0+2=2

7+3=10 so the answer

10

+002

102

Answer:

-9 degrees.

Subtract 20 from 11 to get -9.

Answer:

5/33

Step-by-step explanation:

Probability of first caller (comedy) = 5/(3+4+5) = 5/12

Probability of second caller (action) = 4/(3+4+4) = 4/11

Probability of both = 5/12 * 4/11 = 5/33

Answer:

( 0 , -7 ) , (5 , -7 ) , (1 , -5 )

The number of tourists that only visited the Universal Studios is: 367.

Universal set W of 1007 tourists

Subsets

M of 266 tourists;

L of 282 tourists;

Their in-pairs intersections

ML of 50 tourists;

MU of 59 tourists

LU of 89 tourists

Their triple intersection

MLU of 17 tourists.

Number of tourists who visited only Universal studio

n(M U L U U) = m(M) + n(L) + n(U) - n(M ∩ L) - n(M ∩ U) - n(L ∩ U) + n(M ∩ L ∩ U)

n(M U L U U)= 266 + 282 - 50 - 59 - 89+ 17

n(M U L U U)= 367

Therefore the number of tourists that only visited the Universal Studios is: 367.

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Answer: [tex]x=4[/tex]

Step-by-step explanation:

[tex]2x-7+x=5[/tex]

Group like terms:

[tex]\left(2x+x\right)-7=5[/tex]

Simplify the arithmetic:

[tex]3x-7=5[/tex]

Add 7 to both sides:

[tex]3x-7+7=5+7[/tex]

Simplify the arithmetic:

[tex]3x=5+7[/tex]

Simplify the arithmetic:

[tex]3x=12[/tex]

Divide both sides by 3:

[tex]\frac{3x}{3}=\frac{12}{3}[/tex]

Simplify the fraction:

[tex]x=\frac{12}{3}[/tex]

Find the greatest common factor of the numerator and denominator:

[tex]x=\frac{4\cdot 3}{1\cdot 3}[/tex]

Factor out and cancel the greatest common factor and the answer will be:

[tex]x=4[/tex]

Answer:

29 center (3,-5) radius=2

30 center (0,0) radius=2/3

The exponential growth is 1.95% and after 35.72 years the population will double.

It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent [tex]\rm y = a^x[/tex]

where a is a constant and a>1

Let's suppose the exponential growth function is:

[tex]\rm y = Ae^{rt}[/tex]

A = 163,000

y = 1,686,000

t = 2020 – 1900 = 120 years

Plug all the values in the function:

[tex]\rm 1686000 = 163000e^{120r}[/tex]

[tex]\rm e^{120r} = 10.343[/tex]

Taking ln both side and solving:

r = 0.0194

r = 1.946 ≈ 1.95%

[tex]\rm 2A = Ae^{0.0194t}[/tex]  (the population to double)

After solving:

t = 35.72 years

Thus, the exponential growth is 1.95% and after 35.72 years the population will double.

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[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ P(\stackrel{x_1}{2}~,~\stackrel{y_1}{2})\qquad Q(\stackrel{x_2}{-3}~,~\stackrel{y_2}{-6})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ PQ=\sqrt{[-3 - 2]^2 + [-6 - 2]^2}\implies PQ=\sqrt{(-5)^2+(-8)^2} \\\\\\ PQ=\sqrt{25+64}\implies PQ=\sqrt{89}\implies \boxed{PQ\approx 9.4}[/tex]

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ P(\stackrel{x_1}{2}~,~\stackrel{y_1}{2})\qquad Q(\stackrel{x_2}{-3}~,~\stackrel{y_2}{-6}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ -3 + 2}{2}~~~ ,~~~ \cfrac{ -6 + 2}{2} \right)\implies \left(\cfrac{-1}{2}~~,~~\cfrac{-4}{2} \right)\implies \left( -\cfrac{1}{2}~~,~~-2 \right)[/tex]

Answer:

85°

Step-by-step explanation:

The two angles are known as vertical angles, which are always congruent

Answer:

∠DEB = 85°

Step-by-step explanation:

Vertical Angle Theorem

When two straight lines intersect, they form two pairs of angles.  The vertically opposite (non-adjacent) angles are congruent.

Angles AEC and DEB are vertically opposite angles, therefore:

∠AEC = ∠DEB

As ∠AEC = 85° then ∠DEB = 85° also.

Step-by-step explanation:

the scale factor of similar objects apply to every line and side length.

we see here the ratio of small side length to large side length is 3/9 = 1/3.

so the small side length is 1/3 if the large side length.

a surface is airways the multiplication of 2 dimensions. so, the scale factor is to be used twice in this multiplication and therefore squares.

so, small surface to large surface is 1/3 × 1/3 = 1/9.

and a volume is airways the result of a multiplication of 3 dimensions. so, the scale factor is then 3 times in that multiplication and is therefore cubed.

so, small volume to large volume is 1/3 × 1/3 × 1/3 = 1/27

The approximate space required to store the bales is 4.6 cubic meters if the bale has a diameter of 1.5 m and a height of 2.6 m.

In geometry, it is defined as the three-dimensional shape having two circular shapes at a distance called the height of the cylinder.

We know the volume of the cylinder is given by:

[tex]\rm V = \pi r^2 h[/tex]

We know the radius will be half of the diameter:

r = 1.5/2 = 0.75 m

h = 2.6 m

V = π(0.75)²(2.6)

V = 4.59 ≈ 4.6 cubic meters

Thus, the approximate space required to store the bales is 4.6 cubic meters if the bale has a diameter of 1.5 m and a height of 2.6 m.

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Answer:

the answer is 67 square inches.

Answer:

Area = 67 sq in

Step-by-step explanation:

To solve this is quite easy, we'll first divide the shape into 3 separate shapes, that being 2 rectangles and a triangle.

Triangle:

A=AB/2

A=6*4/2

A=12

Large Rectangle:

(please note that by looking at the size of other shapes we can use their size to justify this shapes size!)

A=AB

A=5*9

A=45

Small Rectangle:

A=AB

A=2*5

A=10

Now we simply add all of our areas together which gives us a total of 67!

Hope this helps! -SC

(Let me know if the answer is wrong so I can change my response and help others!)

Answer:

16.8 is the answer to this question.

Answer:

33.6

Step-by-step explanation:

Its area = base * height = 8 * 4.2 = 33.6

Answer:

  $47,039

Step-by-step explanation:

The time-value-of-money (TVM) functions of a calculator or spreadsheet can be used to find the present value of a series of $600 payments, discounted at 5.2% compounded monthly. (See the attachment for an example.) The present value is found to be about $47,039.

The owner can afford to borrow up to $47,039.

__

This can be figured "by hand" using the amortization formula.

  A = P(r/12)/(1 -(1 +r/12)^(-12·t))

A is the payment on a loan of principal P at annual rate r for t years, compounded monthly.

Solving for P, we have ...

  P = 12A(1 -(1 +r/12)^(-12t))/r = 12·600(1 -(1 +0.052/12)^-96)/0.052

  P ≈ 47039.0653

The owner can borrow up to $47,039.

Answer: 19

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

(40.50 + 56.95) + 25.75 ; 25.75 + (40.50 + 56.95) correctly represent the situation using the commutative property.

Answer:

8.062257748

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The sum of the angles in the triangle must be equals to 180 degrees for it to be the angle measure of a triangle.

The sum of angles in a triangle is equals to 180 degrees.

Therefore, adding up the three angles in a triangle must be equals to 180 degrees.

Hence,

42 + 34 + 56 = 132 degrees

This does not form a triangle.

35 + 80 + 65 = 180 degrees

This can be the angle measure of a triangle.

15 + 51 + 24 = 90 degrees

This cannot be the angle measure of a triangle.

18 + 42 + 120  = 180

This can be the angle measure of a triangle.

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Answer:

3.74 mph

Step-by-step explanation:

412÷110=3.74