A charity gala is held in a hotel ballroom each year. The cost is $150 for the ballroom and an additional $22.50 for each attendee. Write an equation showing how the cost of the gala, y, depends on the number of attendees, x. Do not include dollar signs in the equation. y=

Answer: 290

Step-by-step explanation:

[tex]First\ integer\ on\ line\ n\ is:\ \dfrac{n^2}{2}-\dfrac{n}{2}+1 \\\\For \ line\ 17\ : \dfrac{17^2}{2}-\dfrac{17}{2}+1 =137\\\\\\Last \ integer\ on\ line\ n\ is:\ \dfrac{n*(n+1)}{2} \\\\For\ line\ 17:\ \dfrac{17*(17+1)}{2} =153\\\\Sum=137+153=290[/tex]

I have not say the equation in u(n+3) for the recurrence,

the resolution of the equation caracteristic and the resolution of a system of 3 equations with 3 variables.

6.18000 x 10 5

This is the standard form of 618,000

Thanks , Please mark me brainliest

TyrantMC

Answer:

[tex]\frac{1}{10} * \frac{1}{100} = \frac{1}{1000}[/tex]

1000 times

Step-by-step explanation:

Answer:

0.1% = 1 spin then

100% = ( 100×1) ÷0.1 = 1000

we are using 100% because its a sure bet it will happen but not logically

the answer is 1000

Answer:

x = 2, -4

Step-by-step explanation:

4x^2 + 8x – 32 = 0

Divide by 4

x^2 + 2x – 8 = 0

Add 8 to each side

x^2 + 2x  = 8

Take the coefficient of x

2

Divide by 2

2/2 =1

Square it

1^2=1

Add it to each side

x^2+2x+1 = 8+1

(x+1)^2 = 9

Take the square root of each side

sqrt((x+1)^2) = ±sqrt(9)

x+1 = ±3

Subtract 1 from each side

x = -1±3

x = -1+3, -1-3

x = 2, -4

Answer:

B

Step-by-step explanation:

Given

4x² + 8x - 32 = 0 ( divide through by 4 )

x² + 2x - 8 = 0 ( add 8 to both sides )

x² + 2x = 8

To complete the square

add ( half the coefficient of the x- term)² to both sides

x² + 2(1)x + 1 = 8 + 1

(x + 1)² = 9 ( take the square root of both sides )

x + 1 = ± [tex]\sqrt{9}[/tex] = ± 3 ( subtract 1 from both sides )

x = - 1 ± 3

Then

x = - 1 + 3 = 2

x = - 1 - 3 = - 4

Answer:

5*2 +2*2 = s*2

s = 5.38

s = 5.4

Answer:

100000 = 8 (4) ^t

Step-by-step explanation:

We are multiplying by 4 each time

y = a (4)^t

The initial amount is 8

y = 8 (4)^t

We want to get to 100000

100000 = 8 (4) ^t

Answer:

B

8 ⋅ 4^t  = 100,000

Step-by-step explanation:

Answer:

11341-5=11336

-122+42=-80, when you have different signs always keep in mind that you have to subtract and then get the sign of the big number.

for the third one you firstly have to work with the two negative signs,you have to multiply them, take note that when you multiply a negative by a negative you get a positive, a positive by a positive you get a positive and a negative by a positive you get a negative.

-0.35-(-0.25)

-0.35+0.25

=-0.1

I hope this helps

Answer:

(1, 3)

Step-by-step explanation:

Since up and down are opposites, the point didn't move at all.

I hope this helps!

pls ❤ and mark brainliest pls!

Use the Pythagorean theorem

? = sqrt(52^2 + 19^2)

? = sqrt(2704 + 361)

? = sqrt(3065)

Answer: sqrt(3065)

Answer:

Step-by-step explanation:

Let's try all of them one by one.

Our equation is 4x + 2y + 3 = 19.

A:

20 + 6 + 3 = 19

Not quite!

B:

16 + 10 + 3 = 19

Still not it!

C:

12 + 4 + 3 = 19

We got it!

But still, we check D.

8 + 10 + 3 = 21

Nope.

C (or the 3rd option) is our answer.

I hope this helped.

Answer: x=-3

Step-by-step explanation:

2(x)-39=5(x+2x)

2x-39=5(3x)

2x-39=15x

-39=13x

-39/13=-3

Answer:

The slope of AB is - 2,

Slope of BC is \frac{1}{2}

2

1

Slope of CD is -\frac{3}{4}−

4

3

Slope of AD is \frac{1}{2}

2

1

,

ABCD is trapezoid because one pair of opposite sides is parallel.

Step-by-step explanation:

Given vertices of quadrilateral ABCD,

A(−1, −1) , B(−3, 3) , C(1, 5) , and D(5, 2),

∵ Slope of a line passes through two points (x_1, y_1)(x

1

,y

1

) and (x_2, y_2)(x

2

,y

2

) is,

m=\frac{y_2-y_1}{xc_2-x_1}m=

xc

2

−x

1

y

2

−y

1

Thus, the slope of AB = \frac{3+1}{-3+1}=\frac{4}{-2}=-2

−3+1

3+1

=

−2

4

=−2

Slope of BC = \frac{5-3}{1+3}=\frac{2}{4}=\frac{1}{2}

1+3

5−3

=

4

2

=

2

1

Slope of CD = \frac{2-5}{5-1}=-\frac{3}{4}

5−1

2−5

=−

4

3

Slope of DA = \frac{-1-2}{-1-5}=\frac{-3}{-6}=\frac{1}{2}

−1−5

−1−2

=

−6

−3

=

2

1

Since, when two line segment having the same slope then they are parallel to each other.

∴ BC ║ DA

A quadrilateral only having two parallel sides is called trapezoid,

Hence, ABCD is a trapezoid.

Given the graph of quadrilateral ABCD, the coordinates of A, B, C and D are (-3,-4), (1,4), (4,0) and (1,-4) respectively. The length of DA using distance formula is 4 units.

The coordinates of the points in the graph is given in the form of (x,y) where x is the abscissa and y is the ordinate.

The distance formula is used to find the length of the line given the endpoints of the line.

Given endpoints as [tex](x_1, y_1) \ and \ (x_2, y_2)[/tex],

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

The coordinates of vertices are given by:

A = (-3,-4)

B = (1,4)

C = (4,0)

D = (1,-4)

The length of DA can be found by distance formula :

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

Learn more about distance formula here

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Answer:

m=4

Step-by-step explanation:

m = y2 - y1/x2 - x1

(y2=8, y1=0, x2= 2, x1=0)

m = y2 -y1/x2 - x1

= 8 - 0/2 - 0

= 8/2

=4

The order of Rotational symmetry is 2 (option B) for the given figure.

It is basically the number of times we obtain the initial(or same) figure in a single rotation of 360°.

The rotational symmetry of a shape demonstrates that when an object is rotated on its axis, the form of the object examines the same. Many geometrical shapes emerge to be symmetrical when they exist rotated 180 degrees or with some angles, clockwise or anticlockwise. Some of the examples exist as squares, circles, hexagons, etc.

If we rotate the picture by 90°or 270°, then it wont match the initial figure.

If we rotate the picture by 180° from initial, it will match the figure.

If we further rotate it by 180°( full 360° completed) , it will again match.

Hence, it matches 2 times in a single rotation.

Therefore it has rotational symmetry of order 2.

To solve more questions about rotational symmetry refer:

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Answer:

Y = 8 + 2d

Step-by-step explanation:

Y = 8 + 2d where d is miles traveled

Answer:

y = 2d + 8

Brainliest, please!

Step-by-step explanation:

y = mx + b

m = slope, b = y-intercept

The flat rate of $8 is the y-intercept, and the slope is $2.

y = 2x + 8

We can change x to d to match the context of this problem.

y = 2d + 8

Answer: D

Step-by-step explanation:

To get rid of denominator in x, multiply everything by 3

3y=2x+21

Move the variables to the left

-2x+3y=21

Answer:

impossible

Step-by-step explanation:

The sum of the internal angles of the regular polygon and the theorem n-sided polygon is equal to: (n-2)×180° (n is greater than or equal to 3 and n is an integer)

when n=3，The internal angle sum is 180°

Answer:

126

Step-by-step explanation:

Answer:

126°

Step-by-step explanation:

x = (87+165)/2

x = 252/2

x = 126

Answered by GAUTHMATH

Answer:

0 is the answer . The explanation is in the attachment .

It needs [tex]140\ \text {pounds}[/tex] of the spirulina to get in order to make the blend.

Used the concept of a system of linear equations that states,

Linear equations are equations of the first order. The linear equations are defined for lines in the coordinate system.

Example; ax + by = 0

Given that,

The cost of protein per pound = [tex]\$10.25[/tex]

The cost of powdered spirulina per pound = [tex]\$22.45[/tex]

And, the blend ends up costing [tex]\$16.35[/tex] per pound.

Let us assume that,

There are x pounds of protein and y pounds of spirulina in the mixture.

Hence, by given conditions the equation is,

[tex]10.25x + 22.45y = 16.35 (x + y)[/tex]

[tex]10.25x + 22.45y = 16.35x +16.35 y[/tex]

Combine like terms,

[tex]22.45y - 16.35 y= 16.35x - 10.25x[/tex]

[tex]6.1 y = 6.1x[/tex]

[tex]y = x[/tex]

Since the company has 140 pounds of whey protein on hand.

So, the amount of spirulina it needs to get in order to make the blend is,

[tex]y = 140\ \text {pounds}[/tex]

Learn more about systems of equations at:

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Answer:

122

Step-by-step explanation:

The exterior angle of a triangle is the sum of the opposite interior agnles

32+90 =x

122 =x

An exterior angle of a triangle is equal to the sum of its interior opposite angles.

[tex] \bf \large \hookrightarrow \: \: x \: = \: 32 \degree \: + \: 90 \degree [/tex]

[tex]\bf \large \hookrightarrow \: \: x \: = \: 122 \degree[/tex]

Answer:

1 / 5

Step-by-step explanation:

Given the outcome of number cube spin : 2, 5, 3, 5, 1, 2, 3, 3, 4, 6

The experimental probability of an event, A is given as :

P(A) = number of times A occurs / total number of trials

Therefore, the experimental probability of getting 2 ;

P(getting 2) = Number of times 2 occurs / total number of trials

P(getting 2) = 2 / 10 = 1/5

Answer:

the answer is a and ik because I just had the test

Answer:

see image

Step-by-step explanation:

[tex]\\ \sf\longmapsto 41sin\Theta=40[/tex]

[tex]\\ \sf\longmapsto sin\Theta=\dfrac{40}{41}[/tex]

Now

[tex]\boxed{\sf cos\Theta=\sqrt{1-sin^2\Theta}}[/tex]

[tex]\\ \sf\longmapsto cos\Theta=\sqrt{1-\left(\dfrac{40}{41}\right)^2}[/tex]

[tex]\\ \sf\longmapsto cos\Theta=\sqrt{1-\dfrac{1600}{1682}}[/tex]

[tex]\\ \sf\longmapsto cos\Theta=\sqrt{\dfrac{1681-1600}{1681}}[/tex]

[tex]\\ \sf\longmapsto cos\Theta=\sqrt{\dfrac{81}{1681}}[/tex]

[tex]\\ \sf\longmapsto cos\Theta=\dfrac{9}{41}[/tex]

We know

[tex]\boxed{\sf tan\Theta=\dfrac{Sin\theta}{Cos\Theta}}[/tex]

[tex]\\ \sf\longmapsto \dfrac{tan\Theta}{1-tan^2\Theta}[/tex]

[tex]\\ \sf\longmapsto \dfrac{\dfrac{sin\Theta}{cos\Theta}}{1-\dfrac{sin^2\Theta}{cos^2\Theta}}[/tex]

[tex]\\ \sf\longmapsto \dfrac{\dfrac{\left(\dfrac{40}{41}\right)}{\left(\dfrac{9}{41}\right)}}{1-\dfrac{\left(\dfrac{40}{41}\right)^2}{\left(\dfrac{9}{41}\right)^2}}[/tex]

[tex]\\ \sf\longmapsto \dfrac{\dfrac{{40}}{{9}}}{1-\dfrac{{40}^2}{{9}^2}}[/tex]

[tex]\\ \sf\longmapsto \dfrac{\dfrac{40}{9}}{\dfrac{9^2-40^2}{9^2}}[/tex]

[tex]\\ \sf\longmapsto \dfrac{\dfrac{40}{9}}{\dfrac{81-1600}{81}}[/tex]

[tex]\\ \sf\longmapsto \dfrac{\dfrac{40}{9}}{\dfrac{-1519}{81}}[/tex]

[tex]\\ \sf\longmapsto {\dfrac{40}{\cancel{9}}}\times \dfrac{\cancel{81}}{(-1519)}[/tex]

[tex]\\ \sf\longmapsto \dfrac{40\times 9}{(-1519)}[/tex]

[tex]\\ \sf\longmapsto - \dfrac{360}{1519}[/tex]

Answer:

a) The horizontal asymptote is y = 0

The y-intercept is (0, 9)

b) The horizontal asymptote is y = 0

The y-intercept is (0, 5)

c) The horizontal asymptote is y = 3

The y-intercept is (0, 4)

d) The horizontal asymptote is y = 3

The y-intercept is (0, 4)

e) The horizontal asymptote is y = -1

The y-intercept is (0, 7)

The x-intercept is (-3, 0)

f) The asymptote is y = 2

The y-intercept is (0, 6)

Step-by-step explanation:

a) f(x) = [tex]3^{x + 2}[/tex]

The asymptote is given as x → -∞, f(x) = [tex]3^{x + 2}[/tex] → 0

∴ The horizontal asymptote is f(x) = y = 0

The y-intercept is given when x = 0, we get;

f(x) = [tex]3^{0 + 2}[/tex] = 9

The y-intercept is f(x) = (0, 9)

b) f(x) = [tex]5^{1 - x}[/tex]

The asymptote is fx) = 0 as x → ∞

The asymptote is y = 0

Similar to question (1) above, the y-intercept is f(x) = [tex]5^{1 - 0}[/tex] = 5

The y-intercept is (0, 5)

c) f(x) = 3ˣ + 3

The asymptote is 3ˣ → 0 and f(x) → 3 as x → ∞

The asymptote is y = 3

The y-intercept is f(x) = 3⁰ + 3= 4

The y-intercept is (0, 4)

d) f(x) = 6⁻ˣ + 3

The asymptote is 6⁻ˣ → 0 and f(x) → 3 as x → ∞

The horizontal asymptote is y = 3

The y-intercept is f(x) = 6⁻⁰ + 3 = 4

The y-intercept is (0, 4)

e) f(x) = [tex]2^{x + 3}[/tex] - 1

The asymptote is [tex]2^{x + 3}[/tex]  → 0 and f(x) → -1 as x → -∞

The horizontal asymptote is y = -1

The y-intercept is f(x) =  [tex]2^{0 + 3}[/tex] - 1 = 7

The y-intercept is (0, 7)

When f(x) = 0, [tex]2^{x + 3}[/tex] - 1 = 0

[tex]2^{x + 3}[/tex] = 1

x + 3 = 0, x = -3

The x-intercept is (-3, 0)

f) [tex]f(x) = \left (\dfrac{1}{2} \right)^{x - 2} + 2[/tex]

The asymptote is [tex]\left (\dfrac{1}{2} \right)^{x - 2}[/tex] → 0 and f(x) → 2 as x → ∞

The asymptote is y = 2

The y-intercept is f(x) = [tex]f(0) = \left (\dfrac{1}{2} \right)^{0 - 2} + 2 = 6[/tex]

The y-intercept is (0, 6)

Answer:

see below

Step-by-step explanation:

y = x^2 +2x - 8

Factor

y = ( x+4)(x-2)

The zeros are

x+4 = 0  x-2 = 0    

x= -4    x= 2

(-4,0)  (2,0)

The axis of symmetry is 1/2 way between the zeros

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

x = -1

The x coordinate of the vertex is at the axis of symmetry

The y value is found by substituting x=-1

y = (-1+4) (-1-2)= 3*-3 = -9

Vertex ( -1,-9)

The domain is all real numbers

The range is from -9 up

y≥ -9  since it opens upward

Answer:

(2, 0) and (0, 4) are coordinates in the form of (x, y)

(2, 0) -> x = 2, y = 0

(0, 4) -> x = 0, y = 4

Answer:

- 190

Step-by-step explanation:

-10x (4x - 12 - 3)

-40x - 120x - 30x

- 190

Answer:

-20x³ + 30x^4 + 15x²

Step-by-step explanation:

−5x²(4x − 6x² − 3)

-20x³ + 30x^4 + 15x²