What is the equation of the exponential function that passes through (0,10) and (3,80) ?

A. y= 80(20)^x
B. y=10(2)^2
C. y=2x+10
D. y=3x+8

The model of for the given relationship is,

R(x) = (200 + 50x)*(10 - x), where R(x) is the revenue of one week

This graph has downward parabola, vertex at (3, 2450) intersects X axis at 10 and Y axis at 40.

Hence the Graph Y.

Given that a candlemaker prices one set of scented candles at $10 and sells an average of 200 sets each week.

If he reduces the price by $1 then the sells increases 50 more per week.

When he will reduce $ x then the sells will increase 50x per week.

Now the price of each set of scented candles = (10 - x)

and sells in a week = (200 + 50x)

So if the candlemaker's weekly revenue is R(x) then

R(x) = (200 + 50x)*(10 - x)

R(x) = 2000 + 500x - 200x - 50x²

R(x) = 2000 + 300x - 50x²

If R(x) = y, then

y = 2000 + 300x - 50x²

50(x² - 6x - 40) = - y

50{(x - 3)² - 49} = - y

50(x - 3)² - 2450 = - y

50(x - 3)² = - (y - 2450)

So, the vertex at (3, 2450) and the parabola is downwards.

when intersect X axis then y = 0

x² - 6x - 40 = 0

x² - 10x + 4x - 40 = 0

(x - 10)(x + 4) = 0

x = -4, 10

and where cuts Y axis then x = 0

y = 40

Hence the correct graph is Graph Y.

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Step-by-step explanation:

slope interception formula is

y-y1=m(x-x1)

where m is m=y-y1/x-x1 in this case m=-2 because the line we are trying to find is parallel to the given one y=-2x-6 where slope k=-2

so the final equation would be

y-1=-2(x-(-4))

y-1=-2x-2*4

y=-2x-8+1=-2x-7

The vertex form of the equation for function g is g(x) = a(x + 1)² - 38, where a is the same as in function f.

A quadratic function is one of the forms f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero.

The vertex form of the equation of a quadratic function is given by:

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex. To find the vertex form of the equation for function g, we need to determine the vertex of function f and then adjust it to 2 units below and 3 units to the left.

To find the vertex of function f, we can use the formula:

h = -b / 2a

where a and b are the coefficients of the quadratic term and the linear term, respectively.

For function f(x) = x² - 4x - 32, we have a = 1 and b = -4, so the vertex has an x-coordinate of:

h = -b / 2a = -(-4) / 2(1) = 2

To find the y-coordinate of the vertex, we can substitute this value of h into the function:

f(2) = 2² - 4(2) - 32 = -36

So the vertex of function f is (2, -36).

To adjust the vertex of the function f 2 units below and 3 units to the left, we need to subtract 2 from the y-coordinate and add 3 to the x-coordinate. Therefore, the vertex of function g is:

(h, k) = (2 - 3, -36 - 2) = (-1, -38)

Therefore, the vertex form of the equation for function g is g(x) = a(x + 1)² - 38, where a is the same as in function f.

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Answer:

y=-4/3x-4

Step-by-step explanation:

y=mx+y intercept    <--- formula i used

Answer:

-m - 4n + 15

Step-by-step explanation:

- (m + 4n - 15)

-m - 4n + 15

This simplifies to:
a² = 12x + 144

This is the equation that results from applying the Secant-Tangent Segment Theorem to the given figure.

Let's first define the terms and state the Secant-Tangent Segment Theorem.

1. Equation: A mathematical statement that shows the equality of two expressions.

2. Secant: A line that intersects a circle at two points.

3. Tangent: A line that touches a circle at only one point, without crossing it.

Secant-Tangent Segment Theorem: If a secant and a tangent are drawn from a point outside a circle, the product of the length of the secant segment and its external part is equal to the square of the length of the tangent segment.

Let's represent the given lengths as follows:
- Length of tangent segment = a
- Length of secant segment (inside the circle) = 12
- Length of the external part of the secant segment (outside the circle) = x

According to the Secant-Tangent Segment Theorem, the equation is:
(a)(a) = (12)(x + 12)

This simplifies to:
a² = 12x + 144

This is the equation that results from applying the Secant-Tangent Segment Theorem to the given figure.

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The cost to rent 1 canoe is $40. We will write equations for both cases and solve for variables.

To determine the cost of renting 1 canoe, let's use the given information and create a system of linear equations.

Let's assign variables to the unknowns: let x be the cost to rent 1 canoe, and y be the cost to rent 1 inner tube. We can now create two equations based on the information provided:
1) 4x + 2y = $190 (ladies' rentals)
2) 3x + 5y = $195 (guys' rentals)
To solve this system of equations, we can use the substitution or elimination method. Let's use the elimination method by first multiplying equation 1 by 5 and equation 2 by 2. This will allow us to eliminate the y variable:
1) 20x + 10y = $950
2) 6x + 10y = $390
Now, subtract equation 2 from equation 1:
(20x + 10y) - (6x + 10y) = $950 - $390
14x = $560
Now, divide both sides by 14 to find the cost of renting 1 canoe:
x = $40
So, the cost to rent 1 canoe is $40.

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Answer:

12

Step-by-step explanation:

6/9 tells you that you need 2/3 of matirial per drape

so 12 x 2/3 gets you 8

12 yards of matirial for 8 drapes

When solving this equation you would need 12 drapes for 8 pairs

Steps for solving this equation:

Step One: 9÷6=1.5

1.5 for each pair of drapes, so if we have eight drapes we need to multiply 1.5 by 8.

Step Two: 1.5*8=12

ANSWER: 12 drapes

Using the properties of rational exponents, the value of y is 7/3.

Solve the equation using the properties of rational exponents. We are given the equation: (x^(4/3))^2 / x^(1/3) = x^y, and we need to find the value of y.

Step 1: Apply the power rule of exponents to (x^(4/3))^2.
The power rule states that (a^m)^n = a^(m*n).

So, in our case, (x^(4/3))^2 = x^((4/3)*2) = x^(8/3).

Step 2: Rewrite the equation with the result from step 1.
Now, our equation is x^(8/3) / x^(1/3) = x^y.

Step 3: Apply the quotient rule of exponents.
The quotient rule states that a^m / a^n = a^(m-n).

In our case, x^(8/3) / x^(1/3) = x^((8/3) - (1/3)) = x^(7/3).

Step 4: Compare the resulting expression to x^y.
Now our equation is x^(7/3) = x^y.

Since the bases (x) are the same, we can conclude that the exponents must be equal. Therefore, y = 7/3.

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Answer:c

Step-by-step explanation:

The pivot elements are utilised to eliminate variables one at a time until a unique solution.

If there is a pivot in each column of the coefficient matrix for a linear system of three equations in three variables, the matrix is row equivalent to the identity matrix. This shows that there is only one possible solution to the set of equations.

If you think about how row operations are used to solve a system of linear equations, you can see why this is the case. In the system of equations, the leading coefficients are corresponding to the pivotal elements in the matrix. The pivot elements are utilised to eliminate variables one at a time until a unique solution is produced during the row-reducing procedure of the matrix to row echelon form or reduced row echelon form.

With a pivot in each column, the coefficient matrix.

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Answer:

It was rotated D. -180 degrees

Step-by-step explanation:

the reason that it was -180 degrees is because when you look at the points, points A and B were perfectly flipped around and on the other side of (0,0)

To find g(-2), we'll substitute -2 for x in the equation g(x) = -4x² - 5x + 9. So,g(-2) = -4(-2)² - 5(-2) + 9g(-2). The value of g(-2) is -6.

To find g(-2), substitute -2 for x in the equation

g(x) = -4x² - 5x + 9 to get

g(-2) = -6 + 9g(-2)

We are given three functions as follows:

f(x) = (1/3)x - 5, g(x)

= -4x² - 5x + 9, and

h(x) = 1/(x - 8) + 3.

We are asked to find g(-2), which is the value of g(x) when x = -2.

Substituting -2 for x in the equation g(x) = -4x² - 5x + 9, we get

g(-2) = -4(-2)² - 5(-2) + 9.

This simplifies to g(-2) = -16 + 10 + 9 = -6.

Hence, g(-2) = -6.

The value of g(-2) is -6.

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tan(41π/36) can be written in terms of the tangent of a positive acute angle as (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

To express tan(41π/36) in terms of the tangent of a positive acute angle, we need to find an angle within the range of 0 to π/2 that has the same tangent value.

First, let's simplify 41π/36 to its equivalent angle within one full revolution (2π):

41π/36 = 40π/36 + π/36 = (10/9)π + (1/36)π

Now, we can rewrite the angle as:

tan(41π/36) = tan((10/9)π + (1/36)π)

Next, we'll use the tangent addition formula, which states that:

tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))

In this case, A = (10/9)π and B = (1/36)π.

tan(41π/36) = tan((10/9)π + (1/36)π) = (tan((10/9)π) + tan((1/36)π)) / (1 - tan((10/9)π)tan((1/36)π))

Now, we need to find the tangent values of (10/9)π and (1/36)π. Since tangent has a periodicity of π, we can subtract or add multiples of π to get equivalent angles within the range of 0 to π/2.

For (10/9)π, we can subtract π to get an equivalent angle within the range:

(10/9)π - π = (1/9)π

Similarly, for (1/36)π, we can add π to get an equivalent angle:

(1/36)π + π = (37/36)π

Now, we can rewrite the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Since we are looking for an angle within the range of 0 to π/2, we can further simplify the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Therefore, tan(41π/36) can be written in terms of the tangent of a positive acute angle as the expression given above.

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Answer:

D) \(1 < x\leq 4\)

Step-by-step explanation:

1 is not included, but 4 is included, so we can say \(1 < x\leq 4\)

The longest piece of wood we need is the bottom left piece, which requires a board of at least 15 inches in length

Based on the dimensions provided in the image, we can see that Yeidalis needs a board that is at least as long as the longest piece of wood required.

The longest piece of wood required is the diagonal of the rectangle with dimensions 12 inches and 9 inches.

Using the Pythagorean theorem, we can calculate the length of this diagonal as:

sqrt(12^2 + 9^2) = sqrt(144 + 81) = sqrt(225) = 15 inches

So Yeidalis needs a board that is at least 15 inches long to create her artwork.

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We need to add the first 4 terms of the series in order to find the sum to the indicated accuracy of 0.00005.

The series ∑n=1[infinity]​(−1)n−1n49​ is an alternating series, which means that the terms alternate in sign and decrease in size.

This type of series converges,and the error   in approximating the sum with the first n terms is less than or equal to the absolute value of the (n+1)th term.

In this case, we are given that the desired accuracy is 0.00005.

The (n+1)th   term of the series is (-1)^n / n⁴⁹, so we need to find the smallest n such that (-1)^n / n⁴⁹ <0.00005.

Using a calculator, we can find that n = 4   satisfies this condition. Therefore, we need to add the first 4 terms of the series in order to find the sum to the indicated accuracy.

The first 4 terms of the series are -

1/1⁴⁹ = 1

-1/2⁴⁹ = -1/1610612736

1/3⁹ = -1/29859862048

-1/4⁴⁹ = 1/209227898880

The sum of these 4 terms is 0.12345, which is accurate to within 0.00005

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The domain and range of the function f(x) = 4/x-3 are ( -∞,3 ) U ( 3,∞ ) and ( -∞,0 ) U ( 8,∞ ) respectively.

The domain is simplify the portion of the x-axis that a graph covers while range is the portion of the y-axis that the graph covers.

Given the function in the question;

f(x) = 4/x-3

To find the domain, set the denominator in the function equal to zero and find where the expression is undefined.

x - 3 = 0

Add 3 to both sides

x - 3 + 3 = 0 + 3

x = 0 + 3

x = 3

Hence, the domain is all values of x that makes the expression defined.

{ x|x ≠ 3 }

( -∞,3 ) U ( 3,∞ )

Range is the set of all valid y values, from the graph.

{ y|y ≠ 0 }

( -∞,0 ) U ( 8,∞ ).

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fourty four percent hope this helps !

Average Auction Price is 0.9925the noncompetitive bidders will receive $750 million at a price of $0.9925 per $1 of par value.

To determine who will receive T-bills, what quantity, and at what price, we need to rank the bidders based on the bid prices and allocate the T-bills in descending order of bid prices until the entire $2.5 billion par value has been allocated. The bid prices listed are quoted as a percentage of par value, so we need to calculate the dollar amount bid for each bidder as follows:

Bid Amount = Bid Price × Par Value

For Bidder A:

Bid Amount = 0.9940 × 500 million

Bid Amount = $497 million

For Bidder B:

Bid Amount = 0.9901 × 750 million

Bid Amount = $742.6 million

For Bidder C:

Bid Amount = 0.9925 × 1.5 billion

Bid Amount = $1.48875 billion

For Bidder D:

Bid Amount = 0.9936 × 1 billion

Bid Amount = $993.6 million

For Bidder E:

Bid Amount = 0.9939 × 600 million

Bid Amount = $596.34 million

Total Bid Amount = $3.31874 billion

Since the total bid amount exceeds the $2.5 billion par value of the T-bills being auctioned, we need to allocate the T-bills to the highest bidders until the entire $2.5 billion has been allocated.

Ranking the bidders in descending order of bid prices, we have:

Bidder B with a bid price of $0.9901

Bidder C with a bid price of $0.9925

Bidder D with a bid price of $0.9936

Bidder E with a bid price of $0.9939

Bidder A with a bid price of $0.9940

Allocating T-bills to the highest bidders until the entire $2.5 billion par value has been allocated, we have:

Bidder B will receive $750 million at a price of $0.9901 per $1 of par value.

Bidder C will receive $750 million at a price of $0.9925 per $1 of par value.

Bidder D will receive $500 million at a price of $0.9936 per $1 of par value.

Bidder E will receive $250 million at a price of $0.9939 per $1 of par value.

The noncompetitive bids of $750 million will be allocated at the average auction price, which is calculated as the simple average of the four highest accepted bid prices:

Average Auction Price = (0.9901 + 0.9925 + 0.9936 + 0.9939) / 4

Average Auction Price = 0.9925

Therefore, the noncompetitive bidders will receive $750 million at a price of $0.9925 per $1 of par value.

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The tangent vector  → \(r(t)=〈4cos(2t),4sin(2t),5t〉\), normal vector at t=0 is given by →N(0) = 〈-1,0,0〉, and binormal vector at t=0 is given by →\(B(0) = 〈0, -0.441, -0.898〉\)

The tangent vector, normal vector, and binormal vector of the given curve are as follows:

Given curve:

→ \(r(t)=〈4cos(2t),4sin(2t),5t〉\) at the point t=0

To find: Tangent vector, the Normal vector, and the Binormal vector (→T, →N and →B) at the point t=0

Tangent vector: To find the tangent vector of the given curve

→\(r(t)=〈4cos(2t),4sin(2t),5t〉\) at the point t=0,

we need to differentiate the equation of the curve with respect to t.t = 0, we have:

→\(r(t) = 〈4cos(2t),4sin(2t),5t〉→r(0) = 〈4cos(0),4sin(0),5(0)〉= 〈4,0,0〉\)

Differentiating w.r.t t:→\(r(t) = 〈4cos(2t),4sin(2t),5t〉 → r'(t) = 〈-8sin(2t),8cos(2t),5〉t = 0\),

we have:

→\(r'(0) = 〈-8sin(0),8cos(0),5〉= 〈0,8,5〉\)

Therefore, the tangent vector at t = 0 is given by

→\(T(0) = r'(0) / |r'(0)|= 〈0,8,5〉 / sqrt(89)≈〈0.000,0.898,0.441〉\)

Normal vector:To find the normal vector of the given curve

→\(r(t)=〈4cos(2t),4sin(2t),5t〉\)

at the point t=0, we need to differentiate the equation of the tangent vector with respect to t.t = 0, we have:

→\(T(0) = 〈0.000,0.898,0.441〉\)

Differentiating w.r.t t:

→\(T'(t) = 〈-16cos(2t),-16sin(2t),0〉t = 0\),

we have:

→\(T'(0) = 〈-16cos(0),-16sin(0),0〉= 〈-16,0,0〉\)

Therefore, the normal vector at t = 0 is given by

→\(N(0) = T'(0) / |T'(0)|= 〈-16,0,0〉 / 16= 〈-1,0,0〉\)

Binormal vector: To find the binormal vector of the given curve

→\(r(t)=〈4cos(2t),4sin(2t),5t〉\)

at the point t=0, we need to cross-product the equation of the tangent vector and normal vector of the curve.t = 0, we have:

→\(T(0) = 〈0.000,0.898,0.441〉→N(0) = 〈-1,0,0〉\)

The cross product of two vectors:

→\(B(0) = →T(0) × →N(0)= 〈0.000,0.898,0.441〉 × 〈-1,0,0〉= 〈0, -0.441, -0.898〉\)

Therefore, the binormal vector at t = 0 is given by→B(0) = 〈0, -0.441, -0.898〉

Hence, the tangent vector, normal vector, and binormal vector of the given curve at t=0 are as follows:

→\(T(0) = 〈0.000,0.898,0.441〉→N(0) = 〈-1,0,0〉→B(0) = 〈0, -0.441, -0.898〉\)

The given curve is

→\(r(t)=〈4cos(2t),4sin(2t),5t〉 at the point t=0.\)

We are asked to find the tangent vector, the normal vector, and the binormal vector of the given curve at t=0.

the tangent vector at t=0. To find the tangent vector, we need to differentiate the equation of the curve with respect to t. Then, we can substitute t=0 to find the tangent vector at that point. the equation of the curve Is:

→\(r(t) = 〈4cos(2t),4sin(2t),5t〉\)

At t = 0, we have:

→\(r(0) = 〈4cos(0),4sin(0),5(0)〉= 〈4,0,0〉\)

We can differentiate this equation with respect to t to get the tangent vector as:

→\(r'(t) = 〈-8sin(2t),8cos(2t),5〉\)

At t=0, the tangent vector is:

→\(T(0) = r'(0) / |r'(0)|= 〈0,8,5〉 / sqrt(89)≈〈0.000,0.898,0.441〉\)

Next, we find the normal vector. To find the normal vector, we need to differentiate the equation of the tangent vector with respect to t. Then, we can substitute t=0 to find the normal vector at that point.

At t=0, the tangent vector is:

→\(T(0) = 〈0.000,0.898,0.441〉\)

Differentiating this equation with respect to t, we get the normal vector as:

→\(T'(t) = 〈-16cos(2t),-16sin(2t),0〉\)

At t=0, the normal vector is:

→\(N(0) = T'(0) / |T'(0)|= 〈-16,0,0〉 / 16= 〈-1,0,0〉\)

Finally, we find the binormal vector. To find the binormal vector, we need to cross-product the equation of the tangent vector and the normal vector of the curve.

At t=0, we can cross product →T(0) and →N(0) to find the binormal vector.

At t=0, the tangent vector is:

→\(T(0) = 〈0.000,0.898,0.441〉\)

The normal vector is:

→N(0) = 〈-1,0,0〉Cross product of two vectors →T(0) and →N(0) is given as:

→\(B(0) = →T(0) × →N(0)= 〈0.000,0.898,0.441〉 × 〈-1,0,0〉= 〈0, -0.441, -0.898〉\)

Therefore, the tangent vector, normal vector, and binormal vector of the given curve at t=0 are:

→\(T(0) = 〈0.000,0.898,0.441〉→N(0) = 〈-1,0,0〉→B(0) = 〈0, -0.441, -0.898〉\)

The tangent vector of the given curve

→\(r(t)=〈4cos(2t),4sin(2t),5t〉\)

at the point t=0 is given by →\(T(0) = 〈0.000,0.898,0.441〉.\)

The normal vector at t=0 is given by →N(0) = 〈-1,0,0〉.

The binormal vector at t=0 is given by →B(0) = 〈0, -0.441, -0.898〉.

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The volume of the tetrahedron with vertices (0,0,0), (2,0,0), (0,4,0), and (0,0,6) is 8 cubic units. To find the volume of a tetrahedron with vertices (0,0,0), (2,0,0), (0,4,0), and (0,0,6), we can use the formula for the volume of a tetrahedron in terms of its vertices.

The volume of a tetrahedron can be calculated as one-sixth of the absolute value of the scalar triple product of three edges.

The three edges of the tetrahedron can be determined from its vertices as follows:

Edge 1: (2,0,0) - (0,0,0) = (2,0,0)

Edge 2: (0,4,0) - (0,0,0) = (0,4,0)

Edge 3: (0,0,6) - (0,0,0) = (0,0,6)

The scalar triple product of these three edges is calculated as follows:

|(2,0,0) ⋅ (0,4,0) × (0,0,6)| = |(0,8,0) × (0,0,6)| = |(48,0,0)| = 48

Finally, we take one-sixth of the absolute value of the scalar triple product:

V = (1/6) * |48| = 8

Therefore, the volume of the tetrahedron with vertices (0,0,0), (2,0,0), (0,4,0), and (0,0,6) is 8 cubic units.

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Answer:

3/5

Step-by-step explanation:

the chance of landing on an even number (2 or 4) is 2/5

the chance of landing on the unshaded section (3) is 1/5

add the 2 together since the problem said "or" to get 3/5

Step-by-step explanation:

Answer:

Total number of students= 5

Each ate = 2/3

Total amount eaten=?

Then,

2/3×5

=10/3

Hence 10/3 is the total amount eaten.

A) C(7) represents the cost of an Uber for 7 miles. Since 'm' is the cost for m miles, '7' is the cost for 7 miles.

B) If Todd's total bill was $30, that means the cost (C) is 30. Replace C with 30.

30 = 1.5m+4.5

Now solve this equation.

30-4.5 = 1.5m+4.5-4.5

25.5 = 1.5m

m = 17

If Todd's total bill was $30, his Uber ride was 17 miles.

Answer:

lets get started

Step-by-step explanation: