A certain forest covers an area of 4000 km². Suppose that each year this area decreases by 4.25%. What will the area be after 15 years?
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slope-intercept form of an equation for the line perpendicular to y = -2x + 5 is

y = 1/2x -7

The straight line that makes 90 degrees angle with a given line is called the perpendicular to the first line. The indicator of a line perpendicular to other line is the slope that is negative reciprocal to each other.

we know the slope intercept form of an equation of line is y = mx + b

m is the slope of line and b is the y intercept.

given, equation of a line, y = -2x+5

the slope m = -2 and y intercept, b = 5

we need to write an equation in slope-intercept form that perpendicular to the above line and containing the point (8, -3)

The required line of equation will have a slope equal to the negative reciprocal of the given slope.

hence, the slope will be m = 1/2

the equation of straight line will be y = 1/2x + b

as the line passes through the points (8, -3)

so, -3 = 1/2 × 8 + b

   b = -7

y intercept of the new equation = -7

the new equation of line is y = 1/2x -7

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Answer:

Ratios and fractions are connected. A ratio of 3 to 14 is the same thing as 3/14. Multiply 686 by 3/14. You will get 147. That is your amount of zinc. If we simplify 147/686, or 147:686, we get 3:14 confirming our answer.

Answer:

-----------------------------------

Let the amount of zinc be x. Then we have equal ratios:

Solve it for x:

Answer: A scale is a ratio of the size of the representation (such as a drawing) to the size of the real-world object being represented. In this case, Patty's drawing uses a scale of 1 inch = 45 feet, and Jamie's drawing uses a scale of 2 inches = 35 feet.

In order to find the side length of Jamie's drawing of one of the side length we need to use a proportion:

Jamie's side length / Patty's side length = Jamie's scale / Patty's scale

So if we know one of the side length of Patty's drawing we can find the side length of Jamie's drawing. Let's assume that the side length of Patty's drawing is x

x / Jamie's side length = 45 / 35

So we can isolate Jamie's side length by multiplying both sides by Jamie's scale of 35ft/2 inches

Jamie's side length = (x*35)/45

This is the length of one side length in Jamie's drawing using the scale of 2 inches = 35 feet. If you don't have the length of one side in patty's drawing you can't find the side length of Jamie's drawing.

Step-by-step explanation:

Answer:

y=3x+13

2x=y-9

Step-by-step explanation:

i need to know :(

Answer:

Step-by-step explanation:

Substitute 1 in 2 and solve for x.

2x=y-9

2x=3x+13-9

2x = 3x+4

-x = 4

x = -4

Then use equation 1 to solve for x.

y = 3x+13

y = -12+13

y= 1

Using division operation, since Benjamin jogs at a pace of 16 minutes per mile, in 45 minutes he will jog 2.8 miles.

The division operation is one of the basic mathematical operations, including addition, subtraction, and multiplication.

The division operation involves dividing the dividend (the numerator) by the divisor (the denominator) to obtain the quotient (the result).

The distance between Benjamin and Felix = 35 miles

Benjamin's jogging pace or speed = 16 minutes per mile

Felix's jogging pace or speed = 10 minutes per mile

The number of miles that Benjamin can jog in 45 minutes = Time/Speed

= 2.8125 miles (45/16)

Thus, Benjamin will jog 2.8 miles in 45 minutes.

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The price of a seven minute call direct to New York, in the evening, is given as follows:

$5.82.

The cost of the call is obtained considering the information given in the table, for which the proportions are applied.

We have a direct call, meaning that it is a person-to-person call, thus the flat rate is of $3.00 per minute.

Then the minute proportions, considering that the call happens in the evening, are given as follows:

A seven minute call is composed by six additional minutes after the first, hence the total cost is obtained as follows:

0.38 x 3 + 6 x 0.26 x 3 = $5.82.

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The fraction of the original passengers remaining on the bus is 11/21.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, A crowded bus makes several stops along a city street, with no passengers boarding the bus at any stop.

.At the 1st stop 1/3 of the passengers exit.

At the 2nd stop, 3/7 of the remaining passengers exit the bus.

Therefore, The fraction of the original passengers who remain on the bus is,

= [(1 - (1×1/3) - (1)×(1/3)×(3/7)].

= [ 1 - (1/3) - (3/21)].

= [ (2/3) - (3/21)].

= [(14 - 3)/21].

= 11/21.

So, 11/21 remains on the bus.

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Answer:

D

Step-by-step explanation:

explanation on the other response on ur other question

Using mathematical operations, the construction worker requires C. 2 pounds of cement to mix 3 pounds of sand.

The basic mathematical operations are subtraction, addition, division, and multiplication.

These mathematical operations combine numbers, variables, mathematical operands, and the equation symbol to solve mathematical problems.

In this situation, we can apply the mathematical operation of multiplication to determine the quantity of cement required for 5 pounds of gravel.

The quantity of gravel per pound of sand = 1²/₃ = 1.667 pounds

For 3 pounds of sand, the quantity of gravel required = 5 pounds (1²/₃ x 3)

The quantity of cement per pound of gravel = ²/₅ pounds or 0.4

For 3 pounds of sand and 5 pounds of gravel, the quantity of cement required = 2 (5 x 0.4) or (5 x ²/₅)

Thus, 2 pounds of cement are needed to mix with 3 pounds of sand and 5 pounds of gravel.

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Answer: x = 9

Step-by-step explanation: To find the value of x, we must understand a few things:

- whatever is in lines like | 2x + 4 | means it's the absolute value or positive value of the number.

Now, with that out of the way, I have one more thing to explain.

- whenever trying to find the value of a variable, you need to do inverse operations, so the opposite of adding is subtracting, and the opposite of multiplication is division. Now, let's solve:

22 - 4 = ?

? = 18

18 / 2 = ?

?(x) = 9

Therefore, x = 9

We can check our answer by doing:

| 2(9) + 4 | = 22

2 x 9 = 18

18 + 4 = 22

22 = 22

So, both answers add up, so x = 9

I hope this helps!

Answer: To translate the given sentence into an equation, we can start by replacing the words "five times the sum" with the mathematical expression "5(x + 9)". Then, we can replace the word "number" with the variable y, to get:

5(y + 9) = 3

Next, we can distribute the 5 to obtain:

5y + 45 = 3

Finally, we can subtract 45 from both sides to solve for y:

5y = -42

y = -42/5

y = -8.4

Therefore, the equation that represents the given sentence is y = -8.4.

Step-by-step explanation:

Answer:

light

Step-by-step explanation:

it has kinetic energy

Answer:

Step-by-step explanation: Kinetic energy is made because of movement. So Motion would be the correct answer

Answer:

Step-by-step explanation:

-1 +2=1

2+2=4

5+1=6

The sugar required to make each batch of brownies is 3/26 cups

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

Brownies = 4 1/3 batches

Sugar = 1/2 cups

The amount of sugar required to make each batch of brownies is then calculated as

Sugar needed = Sugar/Brownies

Substitute the known values in the above equation, so, we have the following representation

Sugar needed = (1/2)/(4 1/3)

Evaluate

Sugar needed = 3/26

Hence, the amount is 3/26 cups

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Using Continuous compounding in 15.07 months, the bike's value will be less than £1200.

Continuous compounding refers to the process of compounding interest at an infinitely frequent rate. It is a way to figure out how much an asset will depreciate over time or how much an investment will increase.

[tex]A=Pe^{rt}[/tex]

where:

A is the asset's final value

P is its initial value

r is the interest rate (or rate of depreciation in the case of a depreciating asset)

t is the time periods (months, years, etc.)

A= 1200

P= 2550

r= -0.05

We want to find t, so we can rearrange the formula to solve for t:

[tex]t=\frac{log\frac{A}{P}}{r}\\\\t=\frac{log\frac{1200}{2550} }{-0.05} \\ \\t=15.07months[/tex]

In 15.07 month motorbike value will depreciate to less than £1200

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The notation of the limit as a definite integral is given as follows:

[tex]\lim_{n \rightarrow \infty} \sum_{k = 1}^{n} \sqrt{k} \times n^{-\frac{3}{2}} = \int_0^{n^{-\frac{1}{2}}} \sqrt{x} dx[/tex]

The limit for this problem is defined as follows:

[tex]\lim_{n \rightarrow \infty} \sum_{k = 1}^{n} \sqrt{k} \times n^{-\frac{3}{2}}[/tex]

This is a limit of a Riemann sum, hence it can be written as a definite integral according to the rule presented as follows:

[tex]\int_a^b f(x) dx = \lim_{n \rightarrow \infty} \sum_{i = 1}^{n} f(a + \Delta_x i) \Delta_x[/tex]

As the second term is only a factor of n, the Delta is given as follows:

[tex]\Delta_x = n^{-\frac{3}{2}}[/tex]

As the a term does not appear in the function, the value of the coefficient a is given as follows:

a = 0.

The parent function dependent on k is given as follows:

[tex]f(x) = \sqrt{x}[/tex]

The parameter b is obtained as follows:

[tex]\Delta_x = \frac{b - a}{n}[/tex]

[tex]n^{-\frac{3}{2}} = \frac{b}{n}[/tex]

[tex]b = n^{-\frac{1}{2}}[/tex]

(the parameter n is not given).

Hence the definite integral is obtained as follows:

[tex]\int_0^{n^{-\frac{1}{2}}} \sqrt{x} dx[/tex]

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Her class of 30 pupils can be divided into 10 groups using 5 groups of 2 students and 5 groups of 4 students each.

A circle is created in the plane by each point that is a specific distance from another point (center). Thus, it is a curve made up of points that are separated from one another by a defined distance in the plane. Every pair of points in a circle's closed, two-dimensional plane are evenly spaced apart from the "center." A circular symmetry line is made by drawing a line through the circle.

given

10 groups of 3 students = 30 students :

5 groups of 2 students + 5 groups of 4 students = 30 students : 7 groups of 3 students + 3 groups of 3 students = 30 students

so Her class of 30 pupils can be divided into 10 groups using 5 groups of 2 students and 5 groups of 4 students each.

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The first five multiples of 5 is 5, 10, 15, 20, 15 and the multiple equation is

5×1, 5×2, 5×3, 5×4, 5×5.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, Find the first five multiples of the number.

Let, The number be 5.

Therefore, The first five multiples of 5 is,

5, 10, 15, 20, 25.

And, the multiple equation is,

5×1, 5×2, 5×3, 5×4, 5×5.

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The numeric value of the expression ((2.1)² + 5.2 - 7.2) x 7.1 is given as follows:

17.1.

The expression for this problem is defined as follows:

((2.1)² + 5.2 - 7.2) x 7.1

The precedence of operators follows the PEMDAS acronym, as follows:

Hence the parenthesis takes precedence, thus:

(2.1)² + 5.2 - 7.2.

Then the power takes precedence, thus:

(2.1)² + 5.2 - 7.2 = 4.41 + 5.2 - 7.2

Addition and subtraction can be done in any order, hence:

4.41 + 5.2 - 7.2 = 2.41.

Then the multiplication is given as follows:

2.41 x 7.1 = 17.1.

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Step-by-step explanation:

note that 7⁰ is always 1.

[tex] \frac{ {7}^{ - 10} }{ {7}^{4} } \\ \\ \frac{1}{ {7}^{14} } \\ \\ {7}^{ - 14} [/tex]

the answer is shown above

Answer:

Last option, [tex]\frac{1}{7^{14} }[/tex]

Step-by-step explanation:

[tex]\frac{7^{-10} }{(7^{4} )(7^{0} )}[/tex]=>[tex]\frac{7^{-10} }{7^{4+0}}[/tex]=>[tex]\frac{7^{-10} }{7^{4}}[/tex]=>[tex]7^{-10-4}[/tex]=>[tex]7^{-14}[/tex]=>[tex]\frac{1}{7^{14} }[/tex]

Answer:

-5/4

Step-by-step explanation:

slope(m)= y2-y1/x2-x1

from the graph 5-0/-2-2

=5/-4

answer = -5/4

Step-by-step explanation:

as the description says, the higher the ratio the better.

9/10 = 0.9

12/15 = 4/5 = 0.8

so, Tasha has the better batting average, as she has the higher ratio.

9/10 = 27/30

12/15 = 24/30

27/30 is higher than 24/30.

The equation will be  [tex]y=40000+16000*x[/tex]

Solve one of the equations for a particular variable. After that, insert that into the other equation and find the variable there. To find the value for the other variable, enter that value into either equation.

Equations come in two varieties: identities and conditional equations. All possible values of the variables result in an identity. Only certain combinations of the variables' values make a conditional equation true. Two expressions joined by the equals symbol ("=") form an equation.

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Answer:

the k is 7

Step-by-step explanation:

12×2=24

12×3=36

12×4=48

12×5=60

12×6=72

12×7=84

Answer:

k = 7

Step-by-step explanation:

The product of 12 and k is 84 [tex]\rightarrow 12k=84[/tex].

[tex]12k = 84 \\ k = \dfrac{84}{12} \\ \boxed{k = 7}[/tex]

The best price for her to purchase ice cream is given as follows:

D. $49.60 / five gallon tub.

The best price is obtained applying the proportions in this problem, dividing the price by the volume of the cartoon/tub, in ounces.

For item a, the price per ounce is calculated as follows:

3.99/24 = $0.16625 per ounce.

The ratios for the remaining items are given as follows:

Hence the prices for items b, c and d are given as follows:

Due to the lower cost per ounce, the option D represents the best option for her to purchase ice cream.

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Therefore the predicted full rear repair cost would be $1211.576 if y=2060-0.186x is the line of regression of a table of values comparing for front crash repair cost.

When modeling the connection between a scalar answer and one or more explanatory variables in statistics, linear regression is a linear method. Simple linear regression is used when there is only one explanatory variable, while multiple linear regression is used when there are numerous variables.

Physical values known as scalars are unaffected by modifications to the vector space basis. Scalars frequently include units of measurement, such as "10 cm." Scalar quantities include things like mass, space, charge, volume, time, speed, and the overall size of physical vectors.

To predict the full rear repair cost from a full front repair cost of $4594, you would substitute 4594 for x in the equation y = 2060 - 0.186x and solve for y.

y = 2060 - 0.186(4594)

y = 2060 - 848.424

y = 1211.576

So the predicted full rear repair cost would be $1211.576

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Answer:

$1,206

Step-by-step explanation:

Answer:

$10.80

Step-by-step explanation:

9 times 0.20 equals 1.80

9 + 1.80 = $10.80