S varies inversely as G. If S is 9 when G is 2.4​, find S when G is 6. ​a) Write the variation. ​b) Find S when G is 6

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Explanation:

Use the two given angle measures (Y and Z) to find angle X.

X+Y+Z = 180

X+141+25 = 180

X+166 = 180

X = 180-166

X = 14

Angle X is 14 degrees.

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Now use the law of sines to determine side length z.

Make sure your calculator is in degree mode.

z/sin(Z) = x/sin(X)

z/sin(25) = 830/sin(14)

z = sin(25)*830/sin(14)

z = 1449.9438

z = 1449.9 cm is the final answer.

The solution is : the length of z, to the nearest 10th of a centimeter is, 1449.9 cm.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

here, we have,

Explanation:

Use the two given angle measures (Y and Z) to find angle X.

X+Y+Z = 180

X+141+25 = 180

X+166 = 180

X = 180-166

X = 14

Angle X is 14 degrees.

Now use the law of sines to determine side length z.

z/sin(Z) = x/sin(X)

z/sin(25) = 830/sin(14)

z = sin(25)*830/sin(14)

z = 1449.9438

z = 1449.9 cm is the final answer.

Hence, The solution is : the length of z, to the nearest 10th of a centimeter is, 1449.9 cm.

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Answer:

A consistent of equations has at least one solution,and an inconsistent system has no solution, watch an example of analyzing a system to see if its consistent or inconsistent.

Answer:  see below

Step-by-step explanation:

Consider the standard form of a linear equation in Slope-Intercept form:

        y = mx + b    where

A CONSISTENT system of equations is where the equations have different slopes OR the same slope and y-intercept.

This results in the lines crossing so they have at least one solution.

An INCONSISTENT system of equations is where the equations have the same slope but different y-intercepts.

This results in parallel lines so they have no solutions.

Answer:

$5073.37

Step-by-step explanation:

We can use the simple interest rate (appreciation) formula: A = P(1 + r)^t

Because it gives us 3 months, we need to put it in terms of years. That will give us 1/4 of a year:

A = 5000(1 + 0.06)^0.25

When you plug that into the calc, you should get 5073.37 as your final answer!

Answer:

-15

Step-by-step explanation:

-16 -|-6| +7

-16 - 6 + 7

= - 15

Absolute value is just taking the positive value of a number.

Step-by-step explanation:

-16-(-2-4)+7=

-16-(-6)+7=

-16+6+7=

-16+13=

-3

The measure of the variable 'b' from the line is 11

Collinear points are points that lies on the same straight line. From the given diagram:

XY = YZ  (since Y is the midpoint of XZ)

where:

XY = 2b + 7

YZ = 3b - 4

Substitute the given parameters to have:

2b + 7 = 3b - 4

2b - 3b = -4 - 7

-b = -11

b = 11

Hence the measure of the value of b from the line is 11

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The zeros with each multiplicity are given as follows:

The factor theorem is used to define the functions, which states that the function is defined as a product of it's linear factors, if x = a is a root, then x - a is a linear factor of the function.

Considering the linear factors of the function in this problem, the zeros are given as follows:

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Answer:

106 ft 2

Step-by-step explanation:

Answer:

323 in

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

Answer:

Step-by-step explanation:

slope intercept: y = mx + b

where m is the slope and b is the y-intercept

Equation: y = -3x + 4

Since y-intercept is given, then we have the first point of the line as (0,4)

Let's find the value of x when y is 0

y = -3x + 4

0 = -3x + 4

3x = 4

x = 4/3

(4/3,0) ---second point

Since there are two points/coordinates already then we can now plot/graph.

Answer:

Three different ways (to : / )

Step-by-step explanation:

Examples:

3 to 5

3:5

3/5

Account Compounding Interest after 6 years

1 quarterly

A1 = -$1798.42

2 monthly $

A2 = -$1798.01

3 daily $

A3 =  -$1797.96

1) An account with quarterly compounding: After 6 years, the formula to calculate the interest is:

Interest = Principal \(\times\)(1 + (rate / \(n))^{(n * t)}\) - Principal

Substituting the given values:

Principal = $2200

Rate = 3% = 0.03

n = 4 (quarterly compounding)

t = 6 years

Interest = $2200 \(\times\) (1 + (0.03 / \(4))^{(4 \times 6)}\) - $2200

Interest = $2200 \(\times\)\((1.0075)^{(24)}\) - $2200

Interest ≈ $401.58 - $2200

Interest ≈ -$1798.42 (rounded to two decimal places).

2) An account with monthly compounding: After 6 years, the formula remains the same, but the compounding frequency changes:

   Principal = $2200

   Rate = 3% = 0.03

   n = 12 (monthly compounding)

   t = 6 years

Interest = $2200 \(\times\)(1 + (0.03 / \(12))^{(12 \times 6)}\) - $2200

Interest = $2200 \(\times\)\((1.0025)^{(72)}\) - $2200

Interest ≈ $401.99 - $2200

Interest ≈ -$1798.01 (rounded to two decimal places)

3) An account with daily compounding: Using the same formula with the compounding frequency:

   Principal = $2200

   Rate = 3% = 0.03

   n = 365 (daily compounding)

   t = 6 years

Interest = $2200 \(\times\)(1 + (0.03 / \(365))^{(365 \times 6)}\) - $2200

Interest = $2200 \(\times\)\((1.000082)^{(2190)}\) - $2200

Interest ≈ $402.04 - $2200

Interest ≈ -$1797.96 (rounded to two decimal places)

In all three cases, the interest earned is negative, indicating that the accounts would have lost money rather than gained interest.

This suggests that there might be an error in the calculations or the provided interest rates. It's important to verify the given information to ensure accurate calculations and resolve any discrepancies.

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Answer:

The probability to have both = 0.06

Step-by-step explanation:

Given:

Security system home = 20% = 0.2

Manpower for security calls = 30% = 0.3

Find:

The probability to have both

Computation:

The probability to have both = P(Security system home) × P(Manpower for security calls)

The probability to have both = (0.2)(0.3)

The probability to have both = 0.06

Step-by-step explanation:

For intersecting chords ....the products of each set of segments is equal

8 * 6  = x *   x+8

48 = x^2 + 8x

x^2 + 8x -48 = 0    

( x +12)(x-4) = 0        shows the value of x = 4   ( -12 will not work)

Liam divided his blueberries into 3 equal portions.

What are the portions?

Let's denote by x the number of equal portions that Liam divided his blueberries into. Since Norah divided her blueberries into 6 equal portions and gave away 3 of them, she gave away 3/6 = 1/2 of her blueberries.

Therefore, Liam gave away 3/4 - 1/2 = 1/4 of the total blueberries.

Since Liam gave away 1 portion of his blueberries, this means that the total number of portions of blueberries is x+1.

Therefore, the fraction of blueberries that Liam gave away is 1/(x+1), and we know that this is equal to 1/4. We can write this as an equation:

1/(x+1) = 1/4

Multiplying both sides by 4(x+1), we get:

4 = x+1

Subtracting 1 from both sides, we get:

x = 3

Therefore, Liam divided his blueberries into 3 equal portions.

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Complete question is:

• Norah divided her blueberries into 6 equal portions and gave away 3 of the portions

• Liam divided his blueberries into equal portions and gave away 1 of the portion

• Together, Norah and Liam gave away 3/4 kilogram of blueberries. tow many equal portions did Liam divide his blueberries into 3 equal portions.

The rectangular form of the complex number z = 2.5(cos(3.6) + isin(3.6)) is given as follows:

B. z = -2.25 - 1.1i.

A complex number is a number that is composed by a real part and an imaginary part, as follows:

z = a + bi.

In which:

The number for this problem is given as follows:

z = 2.5(cos(3.6) + isin(3.6))

Hence the real and the imaginary part are given as follows:

Hence the rectangular form of the number is:

B. z = -2.25 - 1.1i.

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Answer:

Step-by-step explanation:

Given the system of equation

3x1 − 2x2 + x3 = −10 ............. 1

2x1 + 6x2 − 4x3 = −10 ............ 2

−8x1 − 2x2 + 5x3 = −26  ............... 3

Reduce the system of equations:

multiply equation 1 by 3 and add to 2

Eqn 1 * 3 gives;

9x1 − 6x2 + 3x3 = −30

Add to equation 2:

9x1+2x1 +(3x3-4x3) = -30-10

11x1 - x3 = -40 ........... 4

multiply eqn 3 by 3 and add to eqn 2

eqn 3 * 3 gives

−24x1 − 6x2 + 15x3 = − 78

Add to eqn 2:

-24x1+2x1)+15x3-4x3 = -78-10

-22x1 + 11x3 = -88 ......... 5

solve 4 and 5:

11x1 - x3 = -40 ........... 4 * 2

-22x1 + 11x3 = -88 ......... 5 * 1

.....................................................

22x1 - 2x3 = -80

-22x1 + 11x3 = -88

Add together:

-2x3 + 11x3 = -80-88

9x3 = -168

x3 = -168/9

x3 = 18.7

subtitute x3 = 18.7 into 4

11x1 - 18.7 = -40

11x1 = -40+18.7

11x1 = -21.3

x1 = -21.3/11

x1 = -1.93

Substitute x1 and x3 into 1

3(-1.93)− 2x2 + 18.7 = −10

- 5.79-2x2 = -28.7

-2x2 = -18.7 +5.79

-2x2 = -22.91

x2 = 11.455

At a price of $3, the total revenue will be the greatest, and the company will sell 3 units at that price.

To find the total revenue at each price, we can multiply the price by the corresponding quantity.

Price        Quantity          Total Revenue

$6                0                      $0

$5                 1                       $5

$4                 2                       $8

$3                 3                        $9

$2                 4                         $8

$1                  5                          $5

To find the price at which total revenue is the greatest, we look for the highest value in the Total Revenue column.

In this case, the highest total revenue is $9, which occurs when the price is $3.

At a price of $3, the company will sell 3 units (as indicated in the Quantity column).

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Answer:

Step-by-step explanation:

The two marked angles are supplementary, so they add up to 180°.

The equation is solved in following steps:

Answer: y = -2x

Step-by-step explanation:

For a line to be perpendicular to another, it must have the opposite reciprocal slope.  In this case, that means 1/2 becomes -2/1 or -2.  For the line to pass through 0,0 the y intercept must be 0.  Thus the line is y = -2x + 0, or y = -2x

Answer:

\(Area = 279ft^2\)

Step-by-step explanation:

Given

See attachment for tent

Required

The material needed

This implies that we calculate the surface area of the tent.

This is calculated as:

Area = 2 * Area of Congruent triangles + 2 * Area of Congruent Rectangles + Area of Base Rectangle

So, we have:

\(Area = 2 * \frac{1}{2} * 6 * 8 + 2 * 10.5 * 7 + 10.5 * 8\)

\(Area = 48 + 147 + 84\)

\(Area = 279ft^2\)

Answer:

0.339

Step-by-step explanation:

Hope it helped!

Hii!

___________________________________________________________

Answer: 0.339

Explanation:

There are two rounding rules that will help us whenever we need to round a number! These are the rules.

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Now that we know the rules, let's get down to solving our problem! ^^

The nearest thousandth is 3 decimal places.

_._ _ _ <==== Nearest thousandth

The third number after the decimal point is 9. After it is a digit that is less than 5. According to the rounding rules, we should round down.

\(\boldsymbol{0.3391=== > 0.339}\)

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Hope that this helped! Best wishes.

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Answer:

day 4: 16000
day 5: 32000
day 6: 64000
day 7: 128000
day 8: 256000
day 9: 512000
day 10: 1024000

Step-by-step explanation:

just fill in the day number as x and solve the equation.    

I attached a sketch of the graph. My paper isn't big enough to draw in all points, but you should get the idea on how to draw this. On the y axis, you use the number of people infected, on the x axis, the number of days.
Then you draw in each point, just as the exercise is asking for.
Then you also can read on the graph how many people are infected on day 6 and a half and day 11. You read this by checking what y value there is approximately for x = 6.5 and x = 11.
(hint: should be about 90500 for 6.5 days and 2048000 for 11 days)

Answer:

This relation does not represent a function because the domain 1 repeats.

Answer:

A) 8x - 4   ||   B) 6x + 29

Step-by-step explanation:

A) -2x + 5 + 10x - 9

→ -2x+10x+5-9

→ -2x+10x-4

→ 8x - 4

B) 3(x + 7) + 2(-x + 4) + 5x

→ 3x + 21 - 2x + 8 + 5x

→ 6x + 29

Answer:

A) 8x - 4

B) 6x + 29

Step-by-step explanation:

A) -2x + 5 + 10x - 9 : given

= (10x - 2x) + (5 - 9) : put like terms together

= 8x - 4 : group

B) 3(x + 7) + 2(-x + 4) + 5x : given

= 3x + 21 - 2x + 8 + 5x : expand

= (3x - 2x + 5x) + (21 + 8) : put like terms together

= 6x + 29 : group

Thanks! Have a great day studying!

Answered by : ms115

Answer:

1500

Step-by-step explanation:

x=number

x/5 is 50 more than x/6

x/5=50+x/6

6x/30=50+5x/30

minus 5x/30 from both sides

x/30=50

times 30 both sides

x=1500

Answer:

Step-by-step explanation:

Let the number is n.

Set up equation according to problem:

Proof:

Answer:

The correct answer is 80, 190

Answer:

13

Step-by-step explanation:

You simply apply the distance formula:

\(d=\sqrt{(\Delta x)^2+(\Delta y)^2} =\sqrt{(5-0)^2+(-12-0)^2} = \sqrt{25+144}=\sqrt{169}=13\)

Answer:

If the angle between two unit vectors u and v is 3.14/3, then using the law of cosines, ||u + v||^2 = 2 + 2cos(3.14/3) = 2 + 2(0.5) = 3. Hence ||u + v|| = sqrt(3).

To find the value of k such that the system has a unique solution, no solution, or an infinite number of solutions, we can use the determinant of the coefficient matrix. If the determinant is nonzero, then the system has a unique solution. If the determinant is zero and the system of equations is inconsistent, then the system has no solution. If the determinant is zero and the system of equations is consistent, then the system has an infinite number of solutions. In this case, the determinant of the coefficient matrix is zero, which implies that the system has an infinite number of solutions.

The eigen values and eigen vectors of the matrix can be found by solving the characteristic equation, which is obtained by det(A - λI) = 0, where A is the matrix and I is the identity matrix.

For the matrix

2 1 -1

3 2 -3

3 1 -2

the characteristic equation is

(2 - λ)(3 - λ) - 3 = 0

which gives us λ = 1 and λ = 3 as the eigen values.

The corresponding eigen vectors can be found by solving the system of equations (A - λI)x = 0, where x is the eigen vector.

For λ = 1, the eigen vector is (1, -1, 1).

For λ = 3, the eigen vector is (-1, 2, 1).

If f(x) is a polynomial of degree 4 with roots 1, 2, 3, 4 and leading coefficient 1, and g(x) is a polynomial of degree 4 with roots 1, 1/2, 1/3, 1/4 and leading coefficient 1, then the limit of 1/f(x)/g(x) as x approaches infinity does not exist. This can be seen by noting that f(x) and g(x) both grow without bound as x grows without bound, so the ratio of the two polynomials also grows without bound.

The length AC in the kite is 8.7 cm.

A kite is a quadrilateral that has two pairs of consecutive equal sides and

perpendicular diagonals. Therefore, let's find the length AC in the kite.

Hence, using Pythagoras's theorem, let's find CE.

Therefore,

7² - 4² = CE²

CE = √49 - 16

CE = √33

CE = √33

Let's find AE as follows:

5²- 4² = AE²

AE = √25 - 16

AE = √9

AE = 3 units

Therefore,

AC = √33 + 3

AC = 5.74456264654 + 3

AC = 8.74456264654

AC = 8.7 units

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