20 POINTS ASAP

What are the next two terms in the sequence 16, 13, 10, __, __?
7, 4
3, -6
8, 5
5, 2

The composite result function ( g o f )(x) in the functions f(x) = x² - 3 and g(x) = 2x - 1 is 2x² - 7.

A function is simply a relationship that maps one input to one output.

Given the data in the question;

First, set up the composite result function (g o f)(x).

(g o f)(x) = g( f(x) )

g( x )  = 2x - 1

g( f(x) ) = 2( f(x) ) - 1

g( f(x) ) = 2( x² - 3 ) - 1

Now, simplify the function by applying distributive property.

g( f(x) ) = 2( x² - 3 ) - 1

g( f(x) ) = 2 × x² - 2 × 3 - 1

g( f(x) ) = 2x² - 6 - 1

Add -6 and -1

g( f(x) ) = 2x² - 7

Therefore, the function operation ( g  o f ) is 2x² - 7.

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Answer:

x-2

Step-by-step explanation:

If you start of with X, you don't know what the value of X is, so you take away two from what we label as X

The approximate area of Central Park is about 450 square blocks.

The given dimensions of the park stated in the question are

Length of Central Park = 50 blocks

Width of Central Park = 9 blocks

The approximate area of Central Park is the product of its length and width:

So, we have

Area of Central Park = Length x Width

When the given values are substituted into the the equation mentioned above, we obtain the subsequent expression

Area = 50 * 9

Evaluate

Area = 450

Hence, the approximate area is about 450 square blocks.

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Answer:

<HDG = 39°

Step-by-step explanation:

Red square is a right angle which mean its a 90°

Those two angle <CDG and <HDG are complementary angle which mean they both add up to 90°

<CDG + <HDG = 90°

51° + (3t+15)° = 90°

Solve for t.

3t + 51 + 15 = 90°

3t + 66 = 90°

3t = 24

t = 8

Plug t = 8 into <HDG to find the measurement.

<HDG = 3t + 15

<HDG = 3*8 + 15

<HDG = 24 + 15

<HDG = 39°

Answer:

We can simplify this expression by using the formula (a + b)(a - b) = a^2 - b^2:

(1 + √10)(1 - √10) = 1^2 - (√10)^2 = 1 - 10 = -9

Therefore,

(1 + √10)(1 - √10) = -9

Now we can multiply by 2:

2(1 + √10)(1 - √10) = 2(-9)

2(1 - 10) = -18

So the final result is -18.

The expression when simplified is (d)

From the question, we have the following representation that can be used in our computation:

Using the above as a guide, we have the following:

The given expression is

3 * Black triangle + 2 * White triangle + 2 * Black square + 1 * White square

This gives

-3x + 2x - 2 + 1

Evaluate the like terms

-x - 1

This means

1 Black triangle and 1 Black square

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a.  The new interest rate for the loan of $250,000 with 2 points is 5.9%, and the cost of points is $5,000.

b.

The new interest rate for the loan of $260,000 with 3 points is 2.8%, and the cost of points is $7,800.

c.

The new interest rate for the loan of $230,000 with 1 point is 5.09%, and the cost of points is $2,300.

An interest rate is described as the amount of interest due per period, as a proportion of the amount lent, deposited, or borrowed.

For part a.

Loan amount = $250,000

Original APR = 6.1%

2 points with a .2% discount per point

Cost of one point = 1% of loan amount = 0.01 x $250,000 = $2,500

Discount per point = 0.2% of loan amount = 0.002 x $250,000 = $500

Total cost of 2 points = 2 x $2,500 = $5,000

Effective interest rate after discount = Original APR - Discount per point = 6.1% - 0.2%

= 5.9%

for part b.

Loan amount = $260,000

Original APR = 3.4%

3 points with a .6% discount per point

Cost of one point = 1% of loan amount = 0.01 x $260,000 = $2,600

Discount per point = 0.6% of loan amount = 0.006 x $260,000 = $1,560

Total cost of 3 points = 3 x $2,600 = $7,800

Effective interest rate after discount = Original APR - Discount per point = 3.4% - 0.6%

= 2.8%

for part c.

c. Loan amount = $230,000

Original APR = 5.6%

1 point with a .51% discount per point

Cost of one point = 1% of loan amount = 0.01 x $230,000 = $2,300

Discount per point = 0.51% of loan amount = 0.0051 x $230,000 = $1,173

Total cost of 1 point = 1 x $2,300 = $2,300

Effective interest rate after discount = Original APR - Discount per point = 5.6% - 0.51%

= 5.09%

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If F(-9,-4), E(-7, a) G(-2,5), and H(-6,-1) then the value of a is equal to -1, then EF is parallel to GH.

What are the parallel lines?

Parallel lines are lines in a plane that are always the same distance apart. Parallel lines never intersect.

To determine if EF is parallel to GH, we need to compare the slopes of the two lines.

The slope of line EF can be found using the coordinates of points E and F:

slope of EF = (y2 - y1)/(x2 - x1) = (a - (-4))/(-7 - (-9)) = (a + 4)/2

The slope of line GH can be found using the coordinates of points G and H:

slope of GH = (y2 - y1)/(x2 - x1) = (5 - (-1))/(-2 - (-6)) = 6/4 = 3/2

For EF to be parallel to GH, their slopes must be equal. Therefore, we can set the slope of EF equal to the slope of GH and solve for a:

(a + 4)/2 = 3/2

Multiplying both sides by 2, we get:

a + 4 = 3

Subtracting 4 from both sides, we get:

a = -1

Therefore, if a is equal to -1, then EF is parallel to GH.

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The volume of the cone is approximately 94.25π cubic cm.

To find the volume of a cone, we use the formula V = 1/3πr²h, where V is the volume, r is the radius of the base, and h is the height or depth of the cone. In this case, we know that the depth of the cone is 14 cm and the base radius is 9/2 cm.

First, we need to calculate the radius of the base in terms of cm, since the formula requires it. We are given that the base radius is 9/2 cm, so we can substitute this value for r:

r = 9/2 cm

Next, we need to calculate the volume of the cone using the formula. We know that the depth of the cone is 14 cm, so we can substitute this value for h:

V = 1/3πr²h

V = 1/3π(9/2)²(14)

V = 1/3π(81/4)(14)

V = 1/3π(1134/4)

V = 1/3π(283.5)

V = 94.25π

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Starting with a $500 investment, you would have approximately $6,795.70 after 40 years if the investment increases exponentially by about 15% every 2 years.

Algebraic expression can be defined as combination of variables and constants.

To find the future amount of the investment after 40 years, we can use the formula for compound interest:

Future Amount = Present Value x (1 + Interest Rate/Compounding Frequency)^(Compounding Frequency x Time)

In this case, the present value (PV) is $500, the interest rate (r) is 15%,

the compounding frequency (n) is 1 (since the interest is compounded every 2 years).

The time (t) is 40 years.

Plugging in the values, we get:

Future Amount = [tex]500 \times (1 + 0.15/1)^{(1 \times 40/2)}[/tex]

Future Amount = [tex]500 \times (1.15)^{20}[/tex]

Future Amount = [tex]500 \times 13.591409[/tex]

Future Amount = $6,795.70 (rounded to the nearest cent)

Therefore, starting with a $500 investment, you would have approximately $6,795.70 after 40 years if the investment increases exponentially by about 15% every 2 years.

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The marginal profit at a production level of 40 items is 2064.

To find the marginal profit at a production level of 40 items, we need to first find the marginal cost and marginal revenue at this production level. The marginal cost and marginal revenue are the derivatives of the cost and revenue functions, respectively.

The marginal cost function is:
C'(q) = 3q^2 - 22q + 56

The marginal revenue function is:
R'(q) = -6q + 2600

At a production level of 40 items, the marginal cost is:
C'(40) = 3(40)^2 - 22(40) + 56 = 296

The marginal revenue at this production level is:
R'(40) = -6(40) + 2600 = 2360

The marginal profit is the difference between the marginal revenue and marginal cost:
Marginal profit = 2360 - 296 = 2064

Therefore, the marginal profit at a production level of 40 items is 2064.

Answer :[tex]\boxed{2064}[/tex].

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In the following question, Jordan needs 2200 square centimetres of carpet to cover the surface of the post, including the bottom.

To find the surface area of the scratching post, we need to add up the surface areas of all the sides.

The scratching post has a rectangular prism shape with dimensions of 10 cm x 10 cm x 90 cm. The bottom is also a 10 cm x 10 cm square.

So the surface area of the post, including the bottom, is:

2(10 cm x 10 cm) + 2(10 cm x 90 cm) + 2(10 cm x 10 cm) = 200 cm^2 + 1800 cm^2 + 200 cm^2 = 2200 cm^2

Therefore, Jordan needs 2200 square centimetres of carpet to cover the surface of the post, including the bottom.

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Answer:

x = 8

Step-by-step explanation:

4(x + 3) = 44 ( divide both sides by 4 )

x + 3 = 11 ( subtract 3 from both sides )

x = 8

Answer:

Step-by-step explanation:

As before, I'll put slope-intercept first:

5. y = 1/4x + 1 ; y-2 = 1/4(x-4)

6. y = -1/2x + 2 ; y-1 = -1/2(x-2)

7. y = 1/3x + 1 ; y-2 = 1/3(x-3)

8. y = -x ; y-1 = 1(-x+1)

9. y = 2/3x -1 ; y-1 = 2/3(x-3)

Hope this helps!

The answer is Start Fractiοn 2 οver 7 End Fractiοn.

Algebraic expressiοn can be defined as cοmbinatiοn οf variables and cοnstants.

Kyle's handful οf trail mix cοntains a tοtal οf 2 + 4 + 3 + 5 = 14 items.

The prοbability οf picking a peanut is the number οf peanuts in the handful divided by the tοtal number οf items in the handful:

prοbability οf picking a peanut = number οf peanuts / tοtal number οf items

prοbability οf picking a peanut = 4 / 14

Simplifying the fractiοn by dividing bοth the numeratοr and denοminatοr by 2, we get:

prοbability οf picking a peanut = 2 / 7

Therefοre, the answer is StartFractiοn 2 οver 7 EndFractiοn.

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The equation of the line shown is y = 2x.

In Mathematics, a proportional relationship can be defined as a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Next, we would determine the constant of proportionality (k) as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 2/1 = 4/2

Constant of proportionality, k = 2.

Therefore, the required equation is given by:

y = kx

y = 2x

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Answer:

Now, This number is neither a perfect square nor a perfect cube

So, 34 can be evaluated as, 34 = (30 + 4) (15 + 15 + 4)

Here is the evaluated form of 34.

Step-by-step explanation:

is of goggle btw so just change some of the words

These two numbers are -4, 2. The smallest possible product is -8.

To find a pair of numbers that satisfy the given conditions, we can use algebra. Let x be the first number and y be the second number. According to the problem, one number is 8 less than twice a second number. This can be written as:
x = 2y - 8
We need to find the product of these two numbers, which is x*y. Substituting the value of x from the equation above, we get:
x*y = (2y - 8)*y
= 2y^2 - 8y
To find the smallest possible product, we need to minimize this expression. We can do this by finding the vertex of the parabola represented by this equation. The vertex of a parabola in the form ax^2 + bx + c is given by (-b/2a, f(-b/2a)). In this case, a = 2, b = -8, and c = 0. So, the vertex is:
(-b/2a, f(-b/2a)) = (-(-8)/(2*2), f(-(-8)/(2*2)))
= (2, f(2))
Substituting y = 2 into the equation for the product, we get:
x*y = 2(2)^2 - 8(2)
= 8 - 16
= -8
So, the smallest possible product is -8. To find the pair of numbers that give this product, we can substitute y = 2 into the equation for x:
x = 2y - 8
= 2(2) - 8
= -4
Therefore, the pair of numbers are -4 and 2.

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The LCM of the given polynomials is \[ (x+6y)(x+2y)(x-6y) \].

The LCM (Least Common Multiple) of two polynomials is the smallest polynomial that is a multiple of both of the given polynomials. To find the LCM, we need to factor the given polynomials and then take the product of the highest power of each factor.

Factoring the first polynomial: \[ x^{2}+8 x y+12 y^{2} = (x+6y)(x+2y) \]
Factoring the second polynomial: \[ x^{2}-36 y^{2} = (x+6y)(x-6y) \]

Now, we can take the product of the highest power of each factor to find the LCM:

\[ LCM = (x+6y)(x+2y)(x-6y) \]

So, the LCM of the given polynomials in factored form is \[ (x+6y)(x+2y)(x-6y) \].

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We can conclude that -

The exponential function is of the form -

f(x) = eˣ

Given is to write the exponential growth and exponential decay equation.

{ 1 } -

The general exponential growth equation is -

[tex]$f(x)=a(1+r)^{x}[/tex]

{ 2 } -

The general exponential decay equation is -

[tex]$\frac {dN}{dt}= -\lambda N[/tex]

Option {A} and option {E} represent the exponential decay. Option {B}, {E} and {D} represent exponential growth.

Therefore, we can conclude that -

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According to Descartes' Rule of Signs, the possible number of positive real zeros for a polynomial function is determined by the number of sign changes in the coefficients of the terms in the function.

Similarly, the possible number of negative real zeros is determined by the number of sign changes in the coefficients of the terms in the function when x is replaced with -x.

For the polynomial function P(x)=6x^(4)-x^(3)+5x^(2)-x+9, there are 2 sign changes in the coefficients of the terms: from 6 to -1, and from 5 to -1. Therefore, the possible number of positive real zeros is 2 or 0.

For the polynomial function P(-x)=6(-x)^(4)-(-x)^(3)+5(-x)^(2)-(-x)+9, there are 0 sign changes in the coefficients of the terms. Therefore, the possible number of negative real zeros is 0.

In conclusion, the possible number of positive real zeros for the polynomial function P(x)=6x^(4)-x^(3)+5x^(2)-x+9 is 2 or 0, and the possible number of negative real zeros is 0.

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Prism:
- Minimum number of faces: 5 (2 bases and 3 lateral faces)
- Minimum number of edges: 9 (3 edges on each base and 3 lateral edges)

Pyramid:
- Minimum number of faces: 4 (1 base and 3 lateral faces)
- Minimum number of edges: 6 (3 edges on the base and 3 lateral edges)

Polyhedron:
- Minimum number of faces: 4 (a tetrahedron)
- Minimum number of edges: 6 (a tetrahedron)

a. A prism is a polyhedron with two parallel congruent bases and rectangular faces connecting the bases. The minimum number of faces for a prism is 5: two bases and three rectangular faces. The minimum number of edges for a prism is 9: three edges connecting each vertex of one base to the corresponding vertex of the other base, and six edges connecting the vertices of the rectangular faces to the vertices of the bases.

b. A pyramid is a polyhedron with a polygonal base and triangular faces connecting the base to a common vertex. The minimum number of faces for a pyramid is 4: one polygonal base and three triangular faces. The minimum number of edges for a pyramid is 6: one edge for each side of the polygonal base, and three edges connecting each vertex of the base to the common vertex.

c. A polyhedron is a three-dimensional shape with flat faces and straight edges. The minimum number of faces and edges for a polyhedron depends on the specific shape, and there is no general formula to determine the minimum values. For example, a tetrahedron has 4 triangular faces and 6 edges, while a cube has 6 square faces and 12 edges. The minimum number of faces and edges for a polyhedron can be calculated by examining the shape and its properties, such as symmetry and number of vertices.

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By answering the above question, we may state that Shade the region to line the left of the open circle, since x is less than 4.

A line is a geometric object that is infinitely long and has no width, depth, or curvature. A line, which can also exist in two-, three-, and more-dimensional spaces, is therefore a one-dimensional object. A line is often used to refer to a line segment with two points as its endpoints. A line is a flat, one-dimensional object that may extend indefinitely in both directions and has no thickness. The terms "straight line" or "old correct line" are sometimes used to describe a line that has no "wobble" anywhere along its length.

plot the inequality 4x-22<-6 on a number line,

4x - 22 + 22 < -6 + 22

4x < 16

4x/4 < 16/4

x < 4

Plot an open circle at 4 on the number line to indicate that x is not included in the solution set.

Shade the region to the left of the open circle, since x is less than 4.

The resulting graph should look like this:

     ○----------------->

     |  |  |  |  |  |  |

   -∞  -5  -4  -3  -2  -1  0  1  2  3  4  5  6

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Answer:

Step-by-step explanation:

The rank of At is the number of linearly independent rows or columns in the matrix. Since At has an inverse for all values of t, the rank of At is 3 for all values of t.

In order to determine the values of t for which At has an inverse, we need to find the determinant of At. If the determinant of At is not equal to 0, then At has an inverse. The determinant of At is given by:

|At| = (1)(5)(-6) + (3)(t)(4) + (2)(2)(7-t) - (4)(5)(2) - (7-t)(t)(1) - (-6)(2)(3)

Simplifying the above expression, we get:

|At| = -30 + 12t + 28 - 14t - 40 - 5t2 + 12

Combining like terms, we get:

|At| = -5t2 - 2t - 30

Setting the determinant equal to 0, we get:

-5t2 - 2t - 30 = 0

Using the quadratic formula, we can find the values of t for which the determinant is equal to 0:

t = (-(-2) ± √((-2)2 - 4(-5)(-30)))/(2(-5))

t = (2 ± √(4 - 600))/(-10)

t = (2 ± √(-596))/(-10)

Since the square root of a negative number is not a real number, there are no real values of t for which the determinant of At is equal to 0. Therefore, At has an inverse for all values of t.

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The Rational Roots Theorem states that the possible rational roots of a polynomial equation are the factors of the constant term divided by the factors of the leading coefficient. Therefore, the possible rational roots of P(x) are ±1, ±2, ±4, and ±4.

To find the exact roots of P(x), we can use synthetic division. Synthetic division is an efficient way of dividing a polynomial by a number. Using this method, we can determine that there are three roots for P(x): 1, -2, and -3. To verify this, we can evaluate P(x) for each of the three roots and confirm that the result is zero.

We can also use the quadratic formula to find the remaining two roots. Since P(x) is a 5th degree polynomial, the two remaining roots are complex and can be found using the quadratic formula. The complex roots of P(x) are -0.5 ± 0.5i.

In conclusion, the roots of P(x) are 1, -2, -3, -0.5 ± 0.5i. All of these results can be verified by evaluating P(x) and confirming that the result is zero.

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Answer: 126

Step-by-step explanation: I belive that is the answer

The given equation (5)/(x - 5) = 5 + (x)/(x - 5) is a conditional equation.

We can simplify the equation as follows:

(5)/(x - 5) - (x)/(x - 5) = 5

(5 - x)/(x - 5) = 5

Now, we can cross-multiply to get rid of the fraction:

5 - x = 5(x - 5)

Distributing the 5 on the right side of the equation gives us:

5 - x = 5x - 25

Adding x to both sides and adding 25 to both sides gives us:

30 = 6x

Dividing both sides by 6 gives us:

x = 5

Since the equation has a solution, it is a conditional equation. Therefore, the answer is a conditional equation.

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Answer:$7.49

Step-by-step explanation:

just subtract 42.50 from 49.99
49.99-42.50=7.49