The radius of a semicircle is 9.1 centimeters. What is the semicircle's perimeter?

The solution to the system of equations is (45, –30)

The equations are given as:

y =-4/5x + 6

y = –30

Substitute y = –30  in y =-4/5x + 6

-30 =-4/5x + 6

Subtract 6 from both sides

-36 = -4/5x

Divide both sides by -4

9 = 1/5x

Multiply both sides by 5

x = 45

So, we have:

(x,y) = (45, –30)

Hence, the solution to the system of equations is (45, –30)

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Answer:

(45, –30)

Step-by-step explanation:

Answer:

Soln;

From the given question, We know that:

x= -2

So,

y= 5x+6

= 5*(-2)+6

= -4 Ans

Answer:  4x - 3y (choice B)

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Explanation:

The letter x is a variable, and a placeholder for a number. Which number? We don't know. It's basically a box where a number goes inside.

x represents having 1 box

2x is two boxes, and so on

If we add 3x and 1x, then we'll have four boxes and 3x+1x = 4x

We can only add the x terms together, which we consider to be called "like terms".

The y terms -5y and 2y are the other pair of like terms, which combine to -3y

If you want, you can draw a vertical number line. Start at -5 which is five units below zero. Then move up two spaces to arrive at -3. This is a visual way to demonstrate that -5+2 = -3, and by extension, -5y+2y = -3y

Answer:

sqrt (65) = 8.062 units  =  x

Step-by-step explanation:

use Pythagorean theorem for a right triangle

a ^2 + b^2 = c^2     where a   and  b   are the legs and c is the hypotenuse

4^2   + x^2   = 9^2

x^2 = 9^2 - 4^2

x^2 = 65

x = sqrt 65

Answer:

c

Step-by-step explanation:

[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &12250\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ t=years\dotfill &6\\ \end{cases} \\\\\\ A=12250(1 - 0.06)^{6}\implies A=12250(0.94)^6\implies A\approx 8450.90[/tex]

The true statement about the circle with center P is that triangles QRP and STP are congruent, and the length of the minor arc is 11/20π

Given that the circle has a center P

It means that lengths PQ, PR, PS and PT

From the question, we understand that QR = ST.

This implies that triangles QRP and STP are congruent.

i.e.  △QRP ≅ △STP is true

The given parameters are:

Angle, Ф = 99

Radius, r = 1

The length of the arc is:

L = Ф/360 * 2πr

So, we have:

L = 99/360 * 2π * 1

Evaluate

L = 198/360π

Divide

L = 11/20π

Hence, the length of the minor arc is 11/20π

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The equivalent equation using the completing the square method is (x+5)² = -2

Quadratic equations are equation that has a degree of 2. Given the equations expressed as:

x^2+10x+27 = 0

Subtract 27 from both sides

x^2+10x = -27

Complete the squares

x^2+10x = -27
x^2+10x + 5^2= -27 + 25
(x+5)² = -2

Hence the equivalent equation using the completing the square method is (x+5)² = -2

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Answer:

The equation is 3x²-6x+5

[tex]12\sqrt{23 x^{13}}+14\sqrt{23 x^{13}}\\\\=(12+14)\left(\sqrt{23 x^{13}}\right)\\\\=26\left(\sqrt{23 x^{13} }\right)\\\\=26\sqrt{23} \sqrt{x^{13}}\\\\=26\cdot 23^{\tfrac 12} \cdot x^{\tfrac {13}2}[/tex]

The function that can be used to model the graphed geometric sequence is y = 1555.2(5/6)^x

The standard exponential function is expressed as y = ab^x

Using the coordinates (3, 900) and (4, 750)

Create the equations

900 = ab^3 ............. 1

750 = ab^4 ................. 2

Divide

900/750 = 1/b
b = 75/90
b = 5/6

Determine the value of "a"

900 = a(5/6)^3

900 = (125/216)a

a = 1555.2

Determine the required equation

y = 1555.2(5/6)^x

Hence the function that can be used to model the graphed geometric sequence is y = 1555.2(5/6)^x

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Answer:

a

Step-by-step explanation:

Answer:

Step-by-step explanation:

How many solutions are in 18+6x=20+6x

18+6x=20+6x

take away 6x from both side

18 = 20

the equation has no solution, 18 is not 20.

Answer:

8

Step-by-step explanation:

To get a fraction of a number, we will simply multiply this fraction by the number.

The closest integer value of x where both functions are equal is 1

The equations are given as:

y = 12x + 12

y  = (14)^x

Next, we plot the graph of both equations.

From the attached graph, both functions intersect at:

x = 1.249

Approximate this value

x = 1

Hence, the closest integer value of x where both functions are equal is 1

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Answer:

44

Step-by-step explanation:

The mode will be a as it is the most in frequency.

Calculating 'a' by taking the mean

Step-by-step explanation:

there are 13 out of 52 diamond cards.

and there are 26 out of 52 black cards.

so, for the first card to be diamond the probability is

13/52 = 1/4 = 0.25

but now, he does not put the card back.

he pulls the second card out of 51 possible cards.

the desired cases are still 26.

so, the probability to pull a black card as the second card under the restriction that the first card was a diamond is

26/51 = 0.509803922...

the probability for that combined event is then

1/4 × 26/51 = 26/204 = 13/102 = 0.12745098...

so, c. is the right answer.

Step-by-step explanation:

Let the number be X

3×X=3X

Increased by 2

3X+2>0≤-3

Answer:

3/5

Step-by-step explanation:

Concepts + Application + Solution

We can write the probability of this event happening like this:

For recap, a prime number is a number that's greater than 1 whose only factors are 1 and itself. Take the number 7 for example; its factors are only 7 and 1.

Given this information above, let's find the prime numbers in the spinner.

As you can see, we have 3/5 numbers that are prime, making the probability of landing on a prime number 3/5.

Answer:

11

Step-by-step explanation:

3(2) - (3(3) + 2) + 16

6 - (9 + 2) + 16

6 - 11 + 16

11

good luck, hope this helps :)

Answer:

4-20(6x-5x)^2+11

(6-5x)^2=11+(-16)

6^2-10x+25=-5

6^2-10x+20

Answer:

-6, -4

Step-by-step explanation:

I got it right

Answer:

6

Step-by-step explanation:

Find the predicted y value when x=1:

[tex]\hat{y}=1.25x-6.25\\\hat{y}=1.25(1)-6.25\\\hat{y}=1.25-6.25\\\hat{y}=-5[/tex]

Find the residual:

[tex]\text{Residual}=\text{Actual Value}-\text{Predicted Value}\\\text{Residual}=y-\hat{y}\\\text{Residual}=1-(-5)\\\text{Residual}=1+5\\\text{Residual}=6[/tex]

Because our residual is positive, this is an indicator that our predicted y value is too low.

Answer:

D. [tex](x - 5)^{2} = 36[/tex]

Step-by-step explanation:

given equation: [tex]x^{2} - 10x - 11 = 0[/tex]

Answer:

Carolyn

Step-by-step explanation:

Carolyn:

45% = 0.45

We multiply the orignal price with 0.45 to see how much it increased.

[tex]20(0.45) = 9[/tex]

We then add it to the original price

[tex]20+9 =29[/tex]

Emily:

31% = 0.31

We multiply the orignal price with 0.31 to see how much it increased.

[tex]20(0.31) = 6.2[/tex]

We then add it to the original price

[tex]20+6.2=26.2[/tex]

That means that Carolyn is correct.

The area of square x will be one-fourth of the area of square y. Then the correct option is C.

It is a polygon with four sides. The total interior angle is 360 degrees. A square's opposite sides are parallel and all sides are equal, and each angle is 90 degrees. Its diagonals are all the same length and intersect in the center.

There are two squares.

The perimeter of square x is half the perimeter of square y.

Let the side of the square x be a and the side length of the square y be b. Then we have

Perimeter x = Perimeter y / 2

              4a = 2b

              2a = b

Then the area of the square x will be

Area of square x = (2a)²

Area of square x = 4a²

Then the area of the square y will be

Area of square x = (b)²

Area of square x = b²

Then the area of square x will be one-fourth of the area of square y.

Thus, the correct option is C.

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Answer:

6

Step-by-step explanation:

Using the monthly payment formula, it is found that the amount he will have to pay is given as follows:

a. $151.73.

It is given by:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

In which:

In this problem, the parameters are given as follows:

P = 2513.77, r = 0.1066, n = 1.5 x 12 = 18.

Hence:

r/12 = 0.1066/12 = 0.008883.

[tex]A = 2513.77\frac{0.008883(1 + 0.008883)^{18}}{(1 + 0.008883)^{18} - 1} = 151.73[/tex]

Hence option A is correct.

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Based on the probability that each gear will fail and the fact that the gears are not linked, the probability that both will fail is 0.4%.

Because the gears are not linked together, the probability that both will fail can be found as:

= Probability that gear fails after 5 years x Probability that gear fails after 10 years

Solving gives:

= 5% x 8%

= 0.4%

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Answer: 40x^4 + 56x^3 − 16x − 14

Step-by-step explanation:

1. For any two functions, the derivative of the product of two functions is the first function times the derivative of the second plus the second function times the derivative of the first.

2. The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0.

3. Simplify

4. Multiply 4x^2 + 7x^1 times 6x^2

5. Multiply 2x^3 - 2 times 8x^1 + 7x^0

6. To multiply powers of the same base, add their exponents.

7. Simplify

8. Combine like terms

9. For any term t, t^1 = t

10. For any term t except 0, t^0 = 1

Answer: Choice D

y-4 = -3(x+1)

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Explanation:

Let's first find the slope of the line through (-1,4) and (1,-2)

[tex](x_1,y_1) = (-1,4) \text{ and } (x_2,y_2) = (1,-2)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-2 - 4}{1 - (-1)}\\\\m = \frac{-2 - 4}{1 + 1}\\\\m = \frac{-6}{2}\\\\m = -3\\\\[/tex]

The slope is -3, which tells us that the answer must be choice D.

Choices A,B, & C can be eliminated because choices A and B have a slope of -13, while choice C has a slope of 3.

Refer to the point-slope format [tex]y-y_1 = m(x - x_1)[/tex] where m is the slope and [tex](x_1,y_1)[/tex] is a point the line goes through.