a. The table below shows some ordered pairs for an exponential function f. 2 3 0 1 2 f(x) 21.6 3.6 0.6 0.1 i. Determine the 1-unit growth factor for f. ii. Determine the 1-unit percent change for f h. iii. Determine the initial value for f (the output value when the input is 0. iv. Write a function formula for f.

Answer:

4.52 inches

Step-by-step explanation:

Hope this help:) 5 star please:))))

Step-by-step explanation:

The triangle is an Isosceles Right.

The total cost of materials and labor for the office space, considering a tile unit cost of P300 and labor cost equal to the materials cost, amounts to P63,000.

To calculate the total cost of materials and labor, we first need to determine the cost of the tiles. Given that the unit cost of a certain tile is P300, we can multiply this by the area of the office space to find the total cost of the tiles. The office space has an area of 63 sqm, so the total cost of the tiles is P300 * 63 = P18,900.

Next, we need to calculate the labor cost, which is 100% of the materials cost. Since the materials cost is P18,900, the labor cost will be equal to P18,900. Therefore, the total cost of labor is also P18,900.

To find the total cost of materials and labor, we add the cost of the tiles (P18,900) and the labor cost (P18,900): P18,900 + P18,900 = P37,800.

Therefore, the total cost of materials and labor for the office space is P37,800.

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Answer:

8.8

Step-by-step explanation:

The length of AB is 8.8

Strains that intersect each other forming a right angle are referred to as perpendicular traces. example: the steps of a straight ladder; the alternative facets of a rectangle.

The perpendicular symbol is ⊥. it's far used between the two traces to reveal that they're perpendicular to every other. what's the difference between perpendicular strains and parallel traces? Perpendicular traces intersect at proper angles (ninety°) even as parallel traces are parallel to every different and in no way intersect.

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Answer:8/25

Step-by-step explanation:

Answer:

Step-by-step explanation:

32/100 = 16/50 = 8/25

Answer:

28 students

Step-by-step explanation:

7 times 4 = 28

there are are seven students in 4 teams, so that means there are 4 groups of seven, and you multiply them together to get how many students in the class

Answer:

28

Keyword(s):

divided, four, 7, per team, how many

Step-by-step explanation:

7 × 4 = 28

Answer:

angle 2 = 37

Step-by-step explanation:

180-143=37

Answer:

where is it?

Step-by-step explanation:

Answer:

C. All of the above

Step-by-step explanation:

Step-by-step explanation:

we know that midpoint of a segment is found from formula

x=(x1+x2)/2

and y=(y1+y2)/2

in this case x=3 and y=4 x2=-1 and y2=2

so x1=2x-x2 =2*3-(-1)=6+1=7

y1=2y-y2=2*4-2=8-2=6

the other endpoint is (7,6)

The center of a dilation is a fixed point in the plane about which all points are expanded or contractedAnswer:

Step-by-step explanation:

Answer:

1.\(8m-2n\)
2.\(-2b+5\)
3.\(-8c+46\)

Step-by-step explanation:

Given the following questions:

\(3m-2n+5m\)
\(-b-b+5\)
\(50-9-8c+5\)

To simplify the following we are going to have to regroup and combine like terms which means we are going to use inverse of operations on terms with similar variables.

Question one:
\(3m-2n+5m\)
\(3m-2n+5m=3m+5m-2n\)
\(3m+5m-2n\)
\(3m+5m=8m\)
\(=8m-2n\)

Question two:
\(-b-b+5\)
\(-b-b=-b+-b=-2b\)
\(=-2b+5\)

Question three:
\(50-9-8c+5\)
\(50-9-8c+5=-8c+50-9+5\)
\(-8c+50-9+5\)
\(50-9=41\)
\(-8c+41+5\)
\(41+5=46\)
\(=-8c+46\)

Which means your answers are "8m - 2n, -2b + 5, and -8c + 46."

Hope this helps.

Therefore, the probability that the red team wins is 60%, and the probability that the blue team wins is 55%, based on this we can conclude for a 180-game season:

The fan expect the red team wins 108 games

For the blue team:

As compared to the blue team, the red team:

Will win 7 games more than the blue team

Statements are False: 1. interchanging rows changes determinant. 2. determinant zero not implies specific rows. 3. determinant not product of diagonal entries. 4. determinant is scalar not matrix.

What is matrix ?

A matrix is a rectangular array of numbers or other mathematical objects, typically arranged in rows and columns. Matrices are often denoted using capital letters, such as A, B, and C. Each element of a matrix is identified by its row and column indices,

1) False, If two row interchanges are made in succession, the determinant of the new matrix is the negative of the determinant of the original matrix.

2) False, If the determinant of a matrix is zero, it does not necessarily mean that two rows or two columns are the same or a row or column is zero, it only means that the matrix is singular, i.e. non-invertible and it also can mean that the matrix is linearly dependent.

3) False, The determinant of a matrix is not always equal to the product of the diagonal entries, it is a scalar value calculated through a specific method called matrix expansion which is based on the entries of the matrix and it depends on the size of the matrix.

4) False, The determinant of a matrix is a scalar value, it cannot be equal to another matrix.

Statements are False: 1. interchanging rows changes determinant. 2. determinant zero not implies specific rows. 3. determinant not product of diagonal entries. 4. determinant is scalar not matrix.

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Answer:

2.75 x 10^11

Step-by-step explanation:

Not sure about the mantissa part.  

Answer:

the length of the minute hand is 36/100 . 150 = 54 (mm)

y is the distance between the minute hand and the hour hand now

x is the angle beween the minute hand and the hour hand, so we have:

cos x = 36/54 = 2/3 => sin x = \(\sqrt{1-(\frac{2}{3})^{2} }=\frac{\sqrt{5} }{3}=\frac{y}{54}\)  => y = 18√5 (mm)

a) see in the ques, u can see that in 45', the minute hand will move a distance equal to 2 times its length and a distance = 2.18√5 (mm)

=> the distance which the minute hand will move is 54.2 + 2.18√5 = 188,50 (mm)

b) the distance which the minute hand will move in 1h is 54.4 - 18√5 = 175,75(mm)

the distance which the hour hand will move in 1h is 36.4 = 144 (mm)

=> the minute hand will move: 175,75 - 144 = 31,75(mm) further than the hour hand

Step-by-step explanation:

The graph (A) in the picture represents the solution to the inequality, option (A) is correct.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

The options are missing.

The graph is in the picture, please refer to the picture.

We have an inequality:

y − 2x ≤ 1

The above inequality represents a straight line with a positive slope.

The right side region of the line is representing the solution to the inequality.

Graph (A) represents the inequality.

Thus, the graph (A) in the picture represents the solution to the inequality, option (A) is correct.

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The future value of an annuity is  $351,135. The correct option is B.

To calculate the future value of an annuity, we can use the formula:

FV = Pmt x [(1 + r)^n - 1] / r

where:

Pmt is the amount of the periodic payment

r is the interest rate per period

n is the number of periods

In this case, Pedro is investing $17,000 at the beginning of each year for 11 years, so:

Pmt = 17,000

n = 11

The interest rate is given as 12 percent, but we need to convert it to a periodic interest rate. Since Pedro is making annual payments, the periodic interest rate is also annual. So:

r = 12% per year

Now we can calculate the future value using Appendix C to find the FV factor for 12% and 11 periods:

FV factor = 3.784

FV = 17,000 x [(1 + 0.12)^11 - 1] / 0.12

FV = 17,000 x 3.784

FV = $64,328

So the future value of Pedro's investments is $64,328.

However, this is only the future value of his first investment of $17,000. To find the total future value of all his investments, we need to add up the future value of each individual investment. We can use the formula we just calculated to find the future value of each investment, and then add them up:

Total FV = $17,000 x 3.784 + $17,000 x 3.784^2 + ... + $17,000 x 3.784^11

Using a financial calculator or spreadsheet software, we can calculate this sum to be approximately $351,135.

Therefore, the answer is B. $351,135.

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Answer:45 ish

Step-by-step explanation:

Answer:

28

Step-by-step explanation:

4 cubed means 4 x 4 x 4, which is 64.

6 squared means 6 x 6, which is 36.

So,

4 cubed - 6 squared = 64 - 36 = 28.

Answer:

WHOS THAT?

Step-by-step explanation:

EDUCATE ME:)

The slope of the line segment is 3/5. Your answer is A) 3/5.

To find the slope of the line segment given by the parametric equations, we need to find the slope of the line passing through the two endpoints of the segment.

When t = -3, x = 5(-3) + 2 = -13 and y = 3(-3) = -9. So the first endpoint is (-13, -9).

When t = 3, x = 5(3) + 2 = 17 and y = 3(3) = 9. So the second endpoint is (17, 9).

The slope of the line passing through these two points is:

slope = (y2 - y1)/(x2 - x1) = (9 - (-9))/(17 - (-13)) = 18/30 = 3/5


So, the slope of the line segment is 3/5. Your answer is A) 3/5.

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The final coordinates of the figure, following the reflection and translation are;

A''(-2, -1)

B''(-3, 1)

C''(2, 2)

A translation transformation is a geometric transformation that moves every point of a shape or object by the same distance in the same direction.

The coordinates of the vertices of the triangle are;

(-5, -1), (-6, -3), and (-1, -4)

1) The first transformation is a reflection across the x-axis

The coordinate of the point (x, y) following a reflection across the x-axis =  The point (x, -y)

Therefore, the coordinate of the image of the triangle following the reflection across the x-axis are the points;

(-5, -1) ⇒ (-5, 1)

(-6, -3) ⇒ (-6, 3)

(-1, -4) ⇒ (-1, 4)

The coordinates of the image following the reflection are therefore;

A'(-5, 1), B'(-6, 3), C'(-1, 4)

b. The coordinates of the image of the reflected triangle following a translation of <3, -2> are;

A'(-5, 1) ⇒ A''(-5 + 3, 1 - 2) = A''(-2, -1)

B'(-6, 3) ⇒ B''(-6 + 3, 3 - 2) = B''(-3, 1)

C'(-1, 4) ⇒ C''(-1 + 3, 4 - 2) = C''(2, 2)

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The relative price is a useful measure for comparing the prices of different products or services, especially in the context of consumer preferences and demand.

Relative price refers to the price of a particular product or service in relation to other goods or services in the market.

It is calculated as the ratio of the price of a given product or service to the price of a reference product or service, commonly referred to as a base good or service.

Let the price of a pair of shoes be $5 and the price of a box of tea be $3.

Then the relative price of a pair of shoes is given by:

Relative price of shoes = Price of shoes / Price of tea

= $5 / $3

= 1.67

Thus, the relative price of a pair of shoes is 1.67.

Similarly,

The relative price of a box of tea can be calculated as follows:

Relative price of tea = Price of tea / Price of shoes

= $3 / $5

= 0.6

Therefore, the relative price of a box of tea is 0.6.

This means that the price of tea is relatively cheaper than that of shoes, as its relative price is less than one.

The relative price of shoes is greater than one, which indicates that shoes are relatively more expensive than tea.

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The value of the car in 2000 is expected to be $3800, given a starting value of $7700 in 1990 and a decrease of $390 per year for 10 years.

To find the value of the car in each subsequent year, we can subtract $390 from the previous year's value. Let's calculate the value of the car for each year from 1990 to 2000.

Year 1990: $7700

Year 1991: $7700 - $390 = $7310

Year 1992: $7310 - $390 = $6920

Year 1993: $6920 - $390 = $6530

Year 1994: $6530 - $390 = $6140

Year 1995: $6140 - $390 = $5750

Year 1996: $5750 - $390 = $5360

Year 1997: $5360 - $390 = $4970

Year 1998: $4970 - $390 = $4580

Year 1999: $4580 - $390 = $4190

Year 2000: $4190 - $390 = $3800

Therefore, the value of the car is expected to be $3800 in the year 2000.

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Answer:

The answer is 82,472

Step-by-step explanation:

The nearest estimate of 208.4=208.

The nearest estimate of 396.51 is 396.5

So the product is 82,472

4. f(x,y) is homogeneous of degree 2.

5. a) f(x,y) is homothetic with h(x,y) = xy and g(x) = x-1

4. Show that f(x,y)=\(x^2\)y is homogeneous, and find its degree of homogeneity:

A function is said to be homogeneous of degree k, if it satisfies the condition:

f(tx,ty) = \(t^k\)f(x,y)

We have f(x,y) = \(x^2\)y. Let’s check if it satisfies the above condition:

f(tx,ty) = \((tx)^2(ty) = t^3x^2y = t^2(x^2y\)) = \(t^2\)f(x,y)

Hence f(x,y) is homogeneous of degree 2.

5. Which of the following functions f(x,y) are homothetic? Explain.

(a) f(x,y)=\((xy)^2\)+1

(b) f(x,y)=\(x^2+y^3\)

Let us first understand the meaning of homothetic transformation.

A homothetic transformation is a non-rigid transformation of the Euclidean plane that preserves the direction of the straight lines but not their length. It stretches or shrinks the plane by a constant factor called the dilation.

Let’s now find out whether the given functions are homothetic or not.

(a) f(x,y)=\((xy)^2\)+1

In order to check if f(x,y) is homothetic or not, we need to check if the function satisfies the following condition:

f(x,y) = g(h(x,y))

where g is a strictly monotonic function and h is a homogeneous function with degree 1

We have

f(x,y) = \((xy)^2\)+1

Let’s assume g(x) = x - 1, then g(x+1) = x

Similarly, let’s assume h(x,y) = (xy), then h(tx,ty) = \(t^2\)h(x,y)

Now, we have

g(h(x,y)) = h(x,y) - 1 = (xy) - 1

Thus f(x,y) is homothetic with h(x,y) = xy and g(x) = x-1

(b) f(x,y)=\(x^2+y^3\)

We can’t write this function in the form f(x,y) = g(h(x,y)) where h(x,y) is a homogeneous function with degree 1. Hence this function is not homothetic.

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To show that w = u × v and v = w × u, we need to demonstrate that the cross product of vectors u and v yields the same result as the cross product of vectors w and u.

Given that u = v × w, let's calculate the cross product of w and u:

w × u = (u × v) × u

Since the cross product is not associative, we need to use the vector triple product identity:

w × u = u × (v × u) - (u · u) v

Since u is orthogonal to v, the dot product (u · v) is zero. Therefore, we can simplify the equation:

w × u = u × (v × u)

Next, let's calculate the cross product of v and u:

v × u = (u × v) × v

Using the vector triple product identity:

v × u = v × (u × v) + (v · v) u

Again, since u is orthogonal to v, the dot product (v · v) is zero:

v × u = v × (u × v)

Thus, we have shown that w = u × v and v = w × u, indicating that the cross products are equivalent in both directions.

In summary, when u, v, and w are orthogonal unit vectors, the cross product of u and v yields the same result as the cross product of w and u, as well as the cross product of v and w.

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