1) During the 1990s, the forested area Guatemala decreased at an Average Rate of 1.7%. The forested area on Guatemala was about 34,400 square Kilometers in 1990.
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2) From 1995 to 2005, the tuition at a college increased by about 7% per year. Tuition in 1995 was $12,000n

The solutions of this quadratic inequality are x ≤ -2 and x ≥ 1.

Step 1: Factor the quadratic expression on the left side of the inequality.

X² - 3x + 2 = 0

Step 2: Set the factors equal to zero and solve for x.

(x - 2)(x - 1) = 0

Step 3: Solve the individual equations.

x - 2 = 0

x - 1 = 0

Step 4: Set up the solutions in terms of x.

x ≤ -2

x ≥ 1

The quadratic inequality X² 3x 2 ≤ 0 can be solved by factoring the expression on the left side of the inequality. Setting the factors equal to zero and solving for x will give us the solutions for x. The solutions are x ≤ -2 and x ≥ 1, which can be read as 'x is less than or equal to -2' and 'x is greater than or equal to 1'. In other words, any value of x that is less than or equal to -2 or greater than or equal to 1 will satisfy the inequality.

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So, the midpoint of the line segment joining the points (1,2) and (3,4) lies in the Quadrant 2.

To find the midpoint of a line segment, we need to average the x-coordinates and the y-coordinates of the two given points.

The given points are (1, 2) and (3, 4)

The x-coordinate of the midpoint = (x1 + x2)/2 = (1 + 3)/2 = 2

The y-coordinate of the midpoint = (y1 + y2)/2 = (2 + 4)/2 = 3

So the midpoint of the line segment joining the points (1, 2) and (3, 4) is (2, 3)

The point (2,3) is in Quadrant 2 as x is positive and y is positive.

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Answer:

0.5045

Step-by-step explanation:

9.081 ÷ 18

The axis of symmetry f(x) = x2 is 0 using standard form of axis of symmetry.

Given: y = x2

Using axis of symmetry formula,

x = -b/2a

x = -(0)/2(2)

x = 0

Therefore, axis of symmetry of parabola y = x2 is x = 0.

Formula for Axis of Symmetry

The axis of symmetry formula is used to quadratic equations when the line of symmetry and the equation's standard form are used. The axis of symmetry is a line that splits or bifurcates any object into two equal halves that are mirror images of one another. Any one of the three types of axis—horizontal (x-axis), vertical (y-axis), or inclined line—can be used to divide the objects.

The equation for the axis of symmetry can be shown when the parabola is in one of two forms:

1) standard form

2) Vertex form

1) standard form

Y = ax2 + b x + c is the quadratic equation in standard form.

with real numbers a, b, and c.

The axis of symmetry formula in this instance is x = - b/2a.

2) Vertex form

Y = a (x-h)2 + k is the quadratic equation in vertex form.

where the parabola's vertex is (h, k).

The axis of symmetry equation in this case is x = h.

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The quotient for the given expression  [tex]\frac{2-\sqrt{8} }{4+\sqrt{12} }[/tex]  is ,   1/4

An expression is a sentence with at least two numbers or variables having mathematical operation. Maths operations can be addition, subtraction, multiplication, division.

For example, 2x+3

Given that,

The expression,  [tex]\frac{2-\sqrt{8} }{4+\sqrt{12} }[/tex]

⇒  [tex]\frac{2-\sqrt{8} }{4+\sqrt{12} }[/tex]

⇒  [tex]\frac{2-2\sqrt{2} }{4+2\sqrt{3} }[/tex]

by rationalization of of denominator

⇒   [tex]\frac{2-2\sqrt{2} }{16-12 } \frac{4-2\sqrt{3}}{}}[/tex]

⇒   [tex]\frac{2-\sqrt{3}-2\sqrt{2}+\sqrt{6} }{16-12 }[/tex]

⇒   [tex]\frac{2-\sqrt{3}-2\sqrt{2}+\sqrt{6} }{ 4 }[/tex]

Hence, the quotient is 1/4

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Mathematics is rife with functions, and the sciences depend on them for constructing physical relationships.

A) f (0)

Substituting the value of x = 0

f (0) = 6(0) -3

      = 0 - 3

      = -3

B) f (2)

Substituting the value of x =2

f (2) = 6(2) -3

      = 12 - 3

      = 9

C) f (-2)

Substituting the value of x = -2

f (2) = 6(-2) -3

      = -12 - 3

      = -15

D) f (1)

Substituting the value of x =1

f (1) = 6(1) -3

      = 6 - 3

      = 3

E ) f (-3)

Substituting the value of x =2

f (2) = 6(-3) -3

      = -18 - 3

      = -21

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Natalie would have $136 more in her account than Tamika

The formula for compound interest is given by:

A = P (1 + r/n)^(nt)

Where:

A = the final amount (principal + interest)

P = the initial principal or starting amount

r = the annual interest rate (expressed as a decimal)

n = the number of times the interest is compounded per year

t = the number of years for which the interest is calculated.

For Natalie:

P =  $470, r = 8 7/8% = 0.08875, n = 365 and t = 14

A = P (1 + r/n)^(nt)

A = 470 (1 + 0.08875/365)^(365×14)

A = $1628

The formula for compound interest compounded continuously is:

A = P e^(rt)

For Tamika:

P =  $470, r = 8 1/4% = 0.0825, and t = 14

A = 470× e^(0.0825×14)

A = $1492

Difference = $1628 - $1492 = $136

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A line graph, sometimes referred to as a line chart or a line plot, is frequently used to display data that varies over time. Several points connected by straight lines can be used to plot it.

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The distance between the two points (-5, 7) and (-1, 3) is 4√2 units.

Distance is the sum of an object's movements, regardless of direction.

The distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

Learn how to apply the Pythagorean theorem to find the distance between two points using the distance formula.

The Pythagorean theorem can be rewritten as d=(((x 2-x 1)2+(y 2-y 1)2) to calculate the separation between any two locations.

So, the distance formula:

d=(((x 2-x 1)2+(y 2-y 1)2)

The points we have are: (-5, 7) and (-1, 3)

d=(((x 2-x 1)2+(y 2-y 1)2)

d= (−5−(−1))2 +(7−3)2

d= 16+16

d= 32

d= 4√2

​

Therefore, the distance between the two points (-5, 7) and (-1, 3) is 4√2 units.

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Answer:

ang tanga mo naman para di malaman ang sagot

When multiplying a number by a sum, you can apply the distributive property of multiplication over addition. Say you want to multiply 3 by the sum of 10 plus 2, for instance: 3(10 + 2) =? This attribute allows you to add the integers and then multiply the result by three.

The distributive property of multiplication is used when multiplying each integer by the sum of two or more addends. The subtraction and addition of two or more numbers are both subject to the distributive property of multiplication.

Boost the equation's size. Divide (multiply) the initial number in each set, the outer number in each set, the inner number in each set, and the last number in each set. Join similar phrases. If necessary, simplify the equation after solving it.

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The probability that the three new numbers still sum to 100 is 0.9.

The three positive real numbers that sum to 100 can be any combination of numbers that add up to 100. If we round them to the nearest tenth, we will lose some precision, and it is possible that the new numbers will not sum up to 100.

We can think of this problem in two steps: first, we pick any three positive real numbers that add up to 100, then we round them to the nearest tenth.

The total number of possible sets of three positive real numbers that add up to 100 is infinite, but we are only interested in the sets that will round to 100 after the transcription.

To find the probability of this happening, we can think of the rounding as a rounding error. There is a probability of 0.05 that the rounding error will make the sum greater than 100 and a probability of 0.05 that the rounding error will make the sum less than 100.

So the probability that the three new numbers still sum to 100 = 100-0.05-0.05 = 0.9

Therefore, the probability that the three new numbers still sum to 100 is 0.9.

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Answer:

line segment

Step-by-step explanation:

the answer is above

The base of the triangle x, with an area of 5 units square is equal to 2 units.

For any triangle, the area is calculated as half the base multiplied by the height of the triangle, that is;

Area of triangle = 1/2 × base × height

we have the area as 5 units square and the height as 5 units, so we solve for the base x as follows:

1/2 × x × 5 units = 5 units²

divide through by 5 units;

1/2 × x = 1 unit

multiply both sides by 2;

x = 2 units

Therefore, the base of the triangle x, with an area of 5 units square is equal to 2 units.

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Possible question:

The triangle with an area of 5 units square and height 5 units has the length of its base as x. Solve for x.

A function is a relation in which each element of the domain is paired with exactly one element of the range.

Determine whether each relation is a function. Find the domain and range?

(-2,2) (0,0) (2,-2)

This is a function because it is a many to one relation(-2 map to 2,0 map to 0,2 map to -2

Domain( -2,0,2)

Range(-2,2)

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The value of the composite function are as follows:

(f - g)(x) = 2x² - x - 1

(f + g) = 2x² + x + 1

(f .g)(-2) = 2

A composite function is a function that depends on another function. In other words, a composite function is a function that is within another function.

Therefore, let's solve the function as follows:

f(x) = 2x²

g(x) = x + 1

Therefore,

(f - g)(x) = f(x) - g(x) = 2x² - (x + 1) = 2x² - x - 1

(f + g) =  f(x) + g(x) = 2x² + (x + 1) = 2x² + x + 1

(f .g)(-2) = f(g(-2))

g(-2) = -2 + 1 = -1

Hence,

(f .g)(-2) = 2(-1)² = 2

Therefore,

(f - g)(x) = 2x² - x - 1

(f + g) = 2x² + x + 1

(f .g)(-2) = 2

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Answer: -8

Step-by-step explanation: 1/4 + 1/4 = 1/2, -8 1/2 + 1/2 = -8

The newer pump will take 6.25 hours to drain the pool working alone

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

According to the data we can state:

x = time new pump to drain the pool alone

4x = time older pump

Together they drain the pool in 5 hours, therefore:

1/x + 1/4x = 1/5

Multiply everything by x:

1 + 1/4 = 1/5 x

(4+1)/4 = 1/5x

5/4 = 1/5x

5/4 * 5 = x

25/4 = x

x = 6.25 hours

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The length of each scarf is given by the equation A = 4.9 feet

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the length of each scarf be represented as A

Now , the equation will be

The total length of all the scarves = 470.4 inches

The total number of scarves = 8 scarves

So , the length of each scarves = total length of all the scarves / total number of scarves

Substituting the values in the equation , we get

The length of each scarf A = 470.4 / 8

The length of each scarf A = 58.8 inches

Now , 12 inches = 1 foot

So , 1 inch = ( 1/12 ) foot

The length of each scarves A = 58.8 ( 1/12 ) feet

On simplifying the equation , we get

The length of each scarf A = 4.9 feet

Hence , the length of each scarf is 4.9 feet

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The ratio of the edge lengths of the large and small cubes is 6:1

The ratio that compares the edge lengths of the large and small cubes is the ratio of the length of the edge of the large cube to the length of the edge of the small cube.

The edge length of the large cube is 12 cm and the edge length of the small cube is 2 cm. To find the ratio, we divide the length of the large cube by the length of the small cube.

So the ratio of the edge length of the large cube to the small cube is:

12cm/2cm = 6

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A customer earns 1 free night per 10 nights stayed.

A hotel offers a reward program based on the number of nights stayed. The function f(x) represents the number of free nights earned as a function of x, the number of nights stayed.

f(x)=x/10

When we put x=10, we get f(1)=10/10=1

Here f(1)  represents the number of free nights earned by the customer is 1 per 10 nights stayed.

When we put x=20, we get f(2)=20/10=2

Here f(2)  represents the number of free nights earned by the customer is 2 per 20 nights stayed.

When we put x=30, we get f(3)=30/10=3

Here f(3)  represents the number of free nights earned by the customer is 3 per 30 nights stayed.

When we put x=40, we get f(4)=40/10=4

Here f(4)  represents the number of free nights earned by the customer is 4 per 40 nights stayed.

Then, the pattern permits you to conclude that a customer earns 1 free night for every 10 nights stayed.

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Answer:

No, they not equal

Step-by-step explanation:

23+37+9=60+97

It not equal

69 ≠ 157

The angle at which the ladder is leaning according to the base and length of the ladder is 62°.

The angle formed between ladder and house is right angled triangle. Thus, the trigonometric formula to be used for calculation is -

cos theta = base ÷ hypotenuse

Keeping the values in formula to find the value of theta which represents angle of leaning of ladder

cos theta = 7/15

Performing division on Right Hand Side of the equation to find the value of theta

cos theta = 0.47

theta = [tex] { \cos }^{ - 1} [/tex] 0.47

theta = 61.97

Thus, the angle is 61.97 or 62°.

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The functions f(x) and 9(x) are not inverse functions because their graphs are not reflected across the line y=x. is not true.

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The average speed of the car is 50 km/hour.

To find the average speed of a car, you can use the formula:

Speed = Distance / Time

In this case, the distance is 100 km and the time is 2 hours. So, to find the average speed of the car:

Speed = 100 km / 2 hours = 50 km/hour

So the average speed of the car is 50 km/hour.

In mathematics, distance refers to the measurement of the difference between two points in a space or a geometric figure. It can be represented by a numerical value, and is often used to determine the shortest path between two points. The most common distance formula used in Euclidean geometry is the distance between two points (x1, y1) and (x2, y2) is the square root of ((x2 - x1)^2 + (y2 - y1)^2). This is known as the Euclidean distance.

Therefore, the average speed of the car is 50 km/hour.

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The greatest possible perimeter  26  the least possible perimeter of the parallelogram 20

[ -1 + 2 , 0 + 4 ]  - [ 2 , -4 ]  =  [  [ 1 , 4] - [2 , - 4 ] =   ( -1, 8  )

The perimeter of this parallelogram =

2  [  sqrt  [ (-1-2)^2 + (8-4)^2]  + 8  ]  =

2 [ sqrt [ 9 + 16 ] +  8 ]  =

2 [ 5  + 8 ] =

26

Another possible  point is

[ 2 + 2, 4 - 4]  - [-1,0] =  [ 4, 0]  - [ -1,0]  = (5,0)

The perimeter of this parallelogram =

2 [ sqrt [ (5-2)^2  + (0 - 4)^2]  + sqrt [ (2- -1)^2 + (4 - 0)^2) ] ] =

2 [ sqrt (3^2 + 4*2)  + sqrt (3^2 + 4^2) ]  =

2 sqrt (25)  + sqrt (25) ] =

2 [ 5 + 5 ] = 20

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Answer: 2 [tex]\sqrt{170}[/tex]

Step-by-step explanation:

Using the Pythagorean theorem, 14^2 + 22^2 = x^2

196 + 484 = x^2

680 = x^2

x = [tex]\sqrt{680}[/tex]

   [tex]2\sqrt{170}[/tex]

Answer:

sqrt317

Step-by-step explanation:

Using the Pythagorean theorem, we know that a^2+b^2=c^2.

So, (14)^2+(11)^2=x^2

We multiply it out, giving us 196+121=x^2
This means that 317=x^2

We square root both sides, giving us x=sqrt317

The absolute value of the inequality |2x -1| >3  will have a union type of solution set.

By using the absolute rule that states:

An inequality equation's absolute value can be solved.

where the "or" functionality symbolizes the union between the solution sets.

Given that:

|2x - 1| > 3

Applying the absolute rule, we have:

2x - 1 < - 3 or 2x - 1 > 3

2x < -4 or 2x > 4

x < -4/2 or x > 4/2

x< -1 or x > 2    

This denotes the union of between the solution sets.

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