Which system of inequalities is shown in the graph?

36 > (x + 3)2 + (y – 2)2 and 16 > (x – 4)2 + y2
36 > (x – 2)2 + (y + 3)2 and 16 > (x – 4)2 + y2
36 < (x + 3)2 + (y – 2)2 and 16 > (x – 4)2 + y2
36 < (x – 2)2 + (y + 3)2 and 16 > (x – 4)2 + y2

Answer: If order does not matter then we can use following formula to find different combinations of 6 numbers out of 46 numbers

Step-by-step explanation: Use following Combination formula

nCr = n! / r!(n-r)!

n=46

r=6

=46!/6!(46-6)!

=46!/[6!(40)!]

=(46*45*44*43*42*41*40!)/(6*5*4*3*2*1)(40!)

Cancel out 40!

=46*45*44*43*42*41/(6*5*4*3*2*1)

=6744109680/720

=9366819

Answer:

[tex] - 3(x + 4) {}^{2} - 4[/tex]

Step-by-step explanation:

Vertex form is

[tex]a(x - h) {}^{2} + k = f(x)[/tex]

We know that h and k are both -4. Let x be -2 and y be -16.

[tex]a( - 2 + 4) {}^{2} - 4 = - 16[/tex]

[tex]a(2) {}^{2} - 4 = - 16[/tex]

[tex]4a - 4 = - 16[/tex]

[tex]4a = - 12[/tex]

[tex]a = - 3[/tex]

So the equation in vertex form is

[tex] - 3(x + 4) {}^{2} - 4[/tex]

I don't know what methods are available to you, so I'll just use one that I'm comfortable with: generating functions. It's a bit tedious, but it works! If you don't know it, there's no harm in learning about it.

Let U(x) be the generating function for the sequence u(n), i.e.

[tex]\displaystyle U(x) = \sum_{n=0}^\infty u(n)x^n[/tex]

In the recurrence equation, we multiply both sides by xⁿ (where |x| < 1, which will come into play later), then take the sums on both sides from n = 0 to ∞, thus recasting the equation as

[tex]\displaystyle \sum_{n=0}^\infty u(n+2) x^n = 8 \sum_{n=0}^\infty u(n+1) x^n - 16 \sum_{n=0}^\infty u(n) x^n[/tex]

Next, we rewrite each sum in terms of U(x). For instance,

[tex]\displaystyle \sum_{n=0}^\infty u(n+2) x^n = \frac1{x^2} \sum_{n=0}^\infty u(n+2) x^{n+2} \\\\ \sum_{n=0}^\infty u(n+2) x^n = \frac1{x^2} \bigg(u(2)x^2 + u(3)x^3 + u(4)x^4 + \cdots \bigg) \\\\ \sum_{n=0}^\infty u(n+2) x^n = \frac1{x^2} \sum_{n=2}^\infty u(n) x^n \\\\ \sum_{n=0}^\infty u(n+2) x^n = \frac1{x^2} \left(\sum_{n=0}^\infty u(n) x^n - u(1)x - u(0)\right) \\\\ \sum_{n=0}^\infty u(n+2) x^n = \frac1{x^2}(U(x) - 16x - 1) \\\\ \sum_{n=0}^\infty u(n+2) x^n = \frac1{x^2}U(x) - \frac{16}x - \frac1{x^2}[/tex]

After rewriting each sum in a similar way, we end up with a linear equation in U(x),

[tex]\displaystyle \frac1{x^2}U(x) - \frac{16}x - \frac1{x^2} = \frac8x U(x) - \frac8x - 16 U(x)[/tex]

Solve for U(x) :

[tex]\displaystyle \left(\frac1{x^2}-\frac8x+16\right) U(x) = \frac1{x^2} + \frac8x \\\\ \left(1-8x+16x^2\right) U(x) = 1 + 8x \\\\ (1-4x)^2 U(x) = 1 + 8x \\\\ U(x) = \dfrac{1+8x}{(1-4x)^2}[/tex]

The next step is to get the power series expansion of U(x) so that we can easily identity u(n) as the coefficient of the n-th term in the expansion.

Recall that for |x| < 1, we have

[tex]\displaystyle \frac1{1-x} = \sum_{n=0}^\infty x^n[/tex]

By differentiating both sides, we get

[tex]\displaystyle \frac1{(1-x)^2} = \sum_{n=0}^\infty nx^{n-1} = \sum_{n=1}^\infty nx^{n-1} = \sum_{n=0}^\infty (n+1)x^n[/tex]

It follows that

[tex]\displaystyle \frac1{(1-4x)^2} = \sum_{n=0}^\infty (n+1)(4x)^n[/tex]

and so

[tex]\displaystyle \frac{1+8x}{(1-4x)^2} = \sum_{n=0}^\infty (n+1)(4x)^n + 8x\sum_{n=0}^\infty (n+1)(4x)^n \\\\ \frac{1+8x}{(1-4x)^2} = \sum_{n=0}^\infty 4^n(n+1)x^n + 2\sum_{n=0}^\infty 4^{n+1}(n+1)x^{n+1} \\\\ \frac{1+8x}{(1-4x)^2} = \sum_{n=0}^\infty 4^n(n+1)x^n + 2\sum_{n=1}^\infty 4^nnx^n \\\\ \frac{1+8x}{(1-4x)^2} = \sum_{n=0}^\infty 4^n(n+1)x^n + 2\sum_{n=0}^\infty 4^nnx^n \\\\ \frac{1+8x}{(1-4x)^2} = \sum_{n=0}^\infty 4^n(3n+1)x^n[/tex]

which means

[tex]u(n) = \boxed{4^n(3n+1)}[/tex]

[tex] \Large \mathbb{SOLUTION:} [/tex]

[tex] \begin{array}{l} \text{Let }r\text{ be the rate of the boat in still water and} \\ c\text{ be the rate of the current.} \\ \\ \text{So } \\ \begin{aligned} \quad&\bullet\:\text{Rate Upstream}= r - c \\ &\bullet\:\text{Rate Downstream}= r - c\end{aligned} \\ \\ \text{We know that }\text{Rate} = \dfrac{\text{Distance}}{\text{Time}}. \end{array} [/tex]

[tex] \begin{array}{l} \bold{Equations:} \\ \\ \begin{aligned} &\quad\quad \quad r - c = \dfrac{104}{4} = 26\quad (1) \\ \\ & \quad \quad \quad r + c = \dfrac{200}{4} = 50\quad (2)\\ \\ & \text{Adding (1) and (2), we get} \\ \\ &\quad\quad 2r = 76 \implies \boxed{r = 38\ \text{kph}} \\ \\ &\text{Using (2), it follows that} \\ \\ & \quad \quad c = 50 - r \implies \boxed{c = 12\ \text{kph}} \end{aligned} \end{array} [/tex]

Answer:

k=4

Step-by-step explanation:

remove x:

10x.(-3) + ky.(-3)=-8.(-3)         (1)

-15x.2 - 6y.2 = 12.2               (2)

(1) - (2)  => -3ky+12y = 0

<=> (12-3k)y = 0

so that y has infinitely many solutions then

12-3k = 0 => k=4

Answer:

10417 cubic units (to nearest unit)

Step-by-step explanation:

A formula for the volume of pyramids (and cones--"pointy" things) is one-third times the area of the base times the height.

[tex]V=\frac{1}{3}Bh[/tex]  where  B  is the area of the base.

[tex]V=\frac{1}{3}(625)(50) \approx 10417[/tex] cubic units (rounded)

9514 1404 393

Answer:

  A.

Step-by-step explanation:

If you can find the given points (pounds, dollars) = (2, 3.50), (3, 5.25), and (4, 7.00) on the graph, then it is an appropriate graph. If the graph label matches the value it shows for 1 pound, then that graph and label are the one you want.

Graph A meets these requirements. It shows the cost of 1 lb to be $1.75, as the label says.

Answer:

∠3z = 108 degrees

∠2z = 72 degrees

Step-by-step explanation:

First, we need to create an equation.

3z + 2z = 180

5z = 180

Divide both sides by 5:

z = 36

Now, substitute z for five for both angles.

3 x 36 = 108 degrees

2 x 36 = 72 degrees

Hope this helps!

If there is something wrong, please let me know.

Answer:

all of the above

Step-by-step explanation:

the ratio between the flour, the baking soda, and the salt would = 1:1:2 (disregarding tsp or cup measurements, since all the units stay the same in the choices)

so really, all the answers are correct

hope this helps!

Answer:

B. 1/2 teaspoon of salt per 1 teaspoon of baking soda.

Step-by-step explanation:

The ratio of cups of flour to tsp. of baking soda to tsp. of salt shown above is:

1/2 : 1/2 : 1/4

An equivalent rate to the ratio of tsp. of salt to tsp. of baking soda is 1/2 : 1 because:

Ratio of tsp. of salt to tsp. of baking soda is:

1/4 : 1/2

If we were to find an equivalent rate to this, it would be 1/2 teaspoon of salt per 1 teaspoon of baking soda for:

Multiply 2 to both terms in the ratio 1/4 : 1/2:

1/4 x 2 = 1/2 (simplified)

1/2 x 2 = 1 (simplified)

The new ratio is 1/2 : 1, which also represents the rate 1/2 teaspoon of salt per 1 teaspoon of baking soda.

Hope this helps!

Please comment back if this was correct.

Answer:

There are three basic trigonometric ratios: sine , cosine , and tangent .

Step-by-step explanation:

Answer:

3c^2

Step-by-step explanation:

Answer:

x =7/ 3

Step-by-step explanation:

5x+  22=  2x+  29

⇔5x - 2x= 29 - 22

⇔3x = 7

⇔x = 7/3

Answer:

A) 3

Pippa kept 3 stickers for herself

Answer to question 2:

The misconception of if a student selects D) 27 is that instead of dividing to find out how many stickers Pippa kept for herself, the student subtracted. They subtracted instead of dividing.

Step-by-step explanation:

It said that Pippa gave each of her friends an EQUAL number of stickers and AS MANY STICKERS AS POSSIBLE. This tells us that to find our answer we need to divide and what ever the remainder is, is how many stickers Pippa kept for herself.

(You will kind of need to do long division for this)

35 ÷ 8 = 4

8 x 4 = 32

35 - 32 = 3

Pippa will give each of her friends 4 stickers and will keep 3 for herself.

Step-by-step explanation for question 2:

35 stickers - 8 friends = 27

D) 27 is the wrong answer to question 1/part 1

I hope this helped! c:

Answer:

14 and 21 and 28

Step-by-step explanation:

2:3:4.

The shortest side is 14

14/2 = 7

Multiply each side by 7

2*7:3*7:4*7

14 : 21 : 28

Answer:

"D"

Step-by-step explanation:

just add the two functions

5x^2 - 8x^2 = -3x^2 etc

Answer:

B

Step-by-step explanation:

9514 1404 393

Answer:

  B.  (21, 6)

Step-by-step explanation:

The preimage coordinates are multiplied by the dilation factor to obtain the image coordinates. If P is the preimage point and the dilation factor is 1/3, you have ...

  (1/3)P = (7, 2)

  P = 3(7, 2) = (3·7, 3·2)

  P = (21, 6)

The preimage point is (21, 6).

Answer:

Answer:

The 99% confidence interval for the true population mean turtle weight is between 77.76 and 82.24 ounces.

Step-by-step explanation:

We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.99}{2} = 0.005[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a p-value of [tex]1 - 0.005 = 0.995[/tex], so Z = 2.575.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 2.575\frac{6.1}{\sqrt{49}} = 2.24[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 80 - 2.24 = 77.76 ounces.

The upper end of the interval is the sample mean added to M. So it is 80 + 2.24 = 82.24 ounces.

The 99% confidence interval for the true population mean turtle weight is between 77.76 and 82.24 ounces.

Answer:

Step-by-step explanation:

new length=15+x

width=19+x

then area=(15+x)×(19+x)=285+15x+19x+x²=x²+34x+285 ft²

original area=15×19=285 ft²

then 285+98=x²+34x+285

or

x²+34x-98=0

x²+34x+17²=98+17²

(x+17)²=98+289=387

x+17=√387=3√43

x=3√43-17 ft

Answer:

Focus is at the origin, so (0,0)

directrix at x=1/34

the equation of the parabola is,

[tex]x = \frac{1}{68} - 17 {y}^{2} [/tex]

Answer:I have the same problem

Step-by-step explanation

Complete Question

Complete Question is attached below

Answer:

[tex]M=160[/tex]

Step-by-step explanation:

From the question we are told that:

Standard models contribute $20

Deluxe  models contribute $30

Availability Average :

Stamping machine S= 30 minutes per hour

Motor installation Production M=60 minutes

Wiring is W=90 minutes per hour

Generally the formulation of the linear program is given as

[tex]Maximium (M)=20x + 30 y[/tex]

Where

For Stamping machine

[tex]S= 3x + 6y \leq 30.....Equ 1[/tex]

For Motor installation Production

[tex]10x + 10y \leq 60....Equ 2[/tex]

For Wiring

[tex]10x + 15y \leq 90....Equ3[/tex]

Therefore

Solving Equ...(1,2,3) simultaneously we have

[tex]x=2\\\\y=4[/tex]

Therefore

[tex]Maximium\ (M)=20x + 30 y[/tex]

[tex]M=20(2)+30(4)[/tex]

[tex]M=160[/tex]

everything seems to be correctly filled.

if you wanted confidence by confirmation: here, take some

It is an exponentially decaying function.

An exponential function is where the independent variable is in the exponent. Generally the the independent variable is in the power of a constant term e.

Exponential functions are of two types one is exponentially growing function and exponentially decaying function.

when the we have a positive exponent the function is exponentially growing and when we have a negative exponent the function is exponentially decaying.

In the given question f(x) = 8e⁻ˣ

when, x = 0 f(x) = 8

f(x) = 8e⁻ˣ

f(0) = 8e⁰

f(0) = 8

Learn more about Exponential functions here :

https://brainly.com/question/15352175

#SPJ5

Answer:

c.

Step-by-step explanation:

Answer:

D. When the purchase is greater than $350.

Step-by-step explanation:

Stores prefer to use credit card for customer whose purchase are worth high. The Barnes store manager prefer that customers use credit card for most purchases. When customers buy more than worth of $350, the store manager will prefer to use credit card.

Answer:

B

Step-by-step explanation:

(a) You can parameterize C by the vector function

r(t) = (x(t), y(t) ) = P (1 - t ) + Q t = (2 - 2t, 7t )

where 0 ≤ t ≤ 1.

(b) From the above parameterization, we have

r'(t) = (-2, 7)   ==>   ||r'(t)|| = √((-2)² + 7²) = √53

Then

ds = √53 dt

and the line integral is

[tex]\displaystyle\int_C(9x(t)+5y(t))\,\mathrm ds = \boxed{\sqrt{53}\int_0^1(17t+18)\,\mathrm dt}[/tex]

(c) The remaining integral is pretty simple,

[tex]\displaystyle\sqrt{53}\int_0^1(17t+18)\,\mathrm dt = \sqrt{53}\left(\frac{17}2t^2+18t\right)\bigg|_{t=0}^{t=1} = \boxed{\frac{53^{3/2}}2}[/tex]

Answer: Choice C. [tex]\frac{1}{x^{2}y^{5} }[/tex]and Choice E. [tex]x^{-2} y^{-5}[/tex]

Step-by-step explanation:

Algebraic exponents.

(y^-8)(y^3)(x^0)(x^-2)

(y^-8)(y^3)(x^-2)

(y^-5)(x^-2)

(1) / (y^5)(x^2)

Options 3 and 5 are correct

Hope this helps!

Answer:

4=x y=325

Step-by-step explanation:

60x + 20 = 65x

group the variables

20=5x

because you subtracted 60x from both

4=x

because you divided 5 from both

now substitute 5 for x

65×5 is 325

y=325

Based on the information, the triangles share two sides but have one different side. one included angle is bigger than the other.

This means that the triangle with side 2x-4 must be smaller than the triangle with the side 10.

Let first, find it minimum amount. A triangle side must be greater than zero so

[tex]2x - 4 > 0[/tex]

[tex]2x > 4[/tex]

[tex]x > 2[/tex]

The triangle side must be smaller than 10.

[tex]2x - 4 < 10[/tex]

[tex]2x < 14[/tex]

[tex]x < 7[/tex]

So x must be greater than 2 but must be smaller than 7.