At the beginning of an environmental study a forest cover an area of 1500 km second power since then this area has decreased by 9.8% each year let T be the number of years since the start of the study letter y b the area that the forest covers in km to the second power write an exponential function showing the relationship between Y&T

The function which is created by shifting the graph of function f up 5 units is  [tex]f(x)=4^x-1[/tex]

So, Option A is correct.

Step-by-step explanation:

We are given function: [tex]f(x)=4^x-6[/tex]

We need to determine the function which is created by shifting the graph of function f up 5 units.

The translation is vertical

If g(x)=f(x)+h then the graph is shifted up h units.

So, Applying translation:

[tex]f(x)=4^x-6[/tex]

[tex]g(x)=(4^x-6)+5[/tex]

Simplifying:

[tex]f(x)=4^x-6+5[/tex]

[tex]f(x)=4^x-1[/tex]

The function which is created by shifting the graph of function f up 5 units is  [tex]f(x)=4^x-1[/tex]

So, Option A is correct.

Keywords: Transformation

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Final answer:

Using a system of equations, it's found that Mo's farm stand sold 65 pounds of peaches, with the total sales of apples and peaches being 165 pounds and revenue $337.50.

Explanation:

To determine how many pounds of peaches Mo's farm stand sold, we can set up a system of equations based on the given information about total weight and revenue from apples and peaches. The weight equation can be written as A + P = 165, where A is the weight of apples sold and P is the weight of peaches sold. The revenue equation is 1.75A + 2.50P = 337.50.

Let's solve for A using the weight equation: A = 165 - P. Substitute A in the revenue equation: 1.75(165 - P) + 2.50P = 337.50. Upon solving, we get: 288.75 - 1.75P + 2.50P = 337.50, which simplifies to 0.75P = 48.75. Therefore, P, the weight of peaches sold, is 65 pounds.

56/84 or 2/3

Hope this helped!

Answer:

56/84

Step-by-step explanation:

Adam had 84 questions, and out of 84, he got 56 right.

Out of  just indicates a fraction.

You would then translate:

x/84

If x is how many he got right, you would then substitute in 56:

56/84

:)

Answer:

One notebook costs $2.50

Step-by-step explanation:

The cost of notebook is $2.50.

Algebra is the branch of mathematics that helps in the representation of problems or situations in the form of mathematical expressions.

Given:

let the number of pen be x

let the number of notebooks be y.

So, the equation can be written as

3x + 5y= 13.75....(1)

x - y = 1.25

3x- 3y = 3.75 ....(2)

Solving above 2 equation we get

8y = 10

y= 10/8

y= 5/4

y= 1.25

and, x= 1.25+1.25=2.50

Hence, the notebook costs $2.50.

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Answer:

15 girls

Step-by-step explanation:

Answer:

15 girls

Explanation:

You first set up the ratio of boys to girls (4/5) as a fraction. Then you look. You make another fraction next to the 4/5 fraction to figure out how many girl are in the class.  You know that you are trying figure out how many GIRLS are in the classroom if their are 12 boys. So on the other fraction the DENOMONATER is going to have an x on it because you don't know how many girls their are and girls (according to the fraction boys to girls (4/5) are on the bottom. So, now you cross multiply. 12x5 is 60 and 60/4 is 15. Therefore, you get 15 as your answer.

Answer:

3c-8

Step-by-step explanation:

The expression 13 - (-21) simplifies to 34.

The expression 13 - (-21) can be simplified as follows:

So, the expression 13 - (-21) is equivalent to 34.

To find the equivalent expression for \(13 - (-21)\), you can simplify the subtraction of a negative number, which is the same as adding its positive counterpart. Therefore:

\[ 13 - (-21) \]

is equivalent to:

\[ 13 + 21 \]

Among the given choices, the expression that matches this result is:

\[ \text{(Choice D) } 13 + 21 \]

Final answer:

The expression 13 - (-21) is equivalent to 13 + 21 because we change the subtraction of a negative number to addition. The final result is 34.

Explanation:

The expression 13 - (-21) involves subtracting a negative number from a positive number. According to the rules for subtracting integers, we change the sign of the number being subtracted and then follow the rules for addition as follows:

Therefore, the expression 13 - (-21) is equivalent to 13 + 21, which simplifies to 34.

Hope it helps u............

Answer:

1. See the graph attached

2. 13,400 thousands people will attend the new movie on the 8th day, if the pattern shown in the graph continues.

Explanation:

The table that shows the number of people who attend a new movie ofver teh course of a week is:

Day   Attendance (thousands)

1          12,200

3         12,600

5         13,000

7         13,400

8              x

The graph showing that pattern is attached.

It is a discrete graph because days can take only positive integer values.

You can see that the relation is linear and can calculate the change in the number of people every two days by subracting any two consecutive pairs of data:

Hence, every two days the increase in the number of people is 400 thousands.

For one day the increase is: 400 thousands / 2 days = 200 thousands/day.

Since you know the attendance for the day 7, you can calculate the attendance for the day 8 adding 200 thousands to 13,400:

Answer: 30m - 7

Step-by-step explanation:

combine the two m's (:

Answer:

30m-7

Step-by-step explanation:

18m-7+12m=30m-7

Answer:

$52.5 saved. And he paid $297.50

Step-by-step explanation:

First finding the amount of money of the 15% discount

350.00 × .15 = $52.5

Then the the original price minus the dicount

350.00 - 52.50 = $297.50

Answer:

he saved 52.5$

Step-by-step explanation:

350.00*15/100

=52.5

Answer:

The Population Density is [tex]500\ People/mi^2[/tex].

Step-by-step explanation:

Given,

Total number of People = 900,000

Total Land Area = 1800 sq. mi.

Solution,

For calculating the population density, we have to divide the total number of people by the area of the land.

This can be framed in equation form'

[tex]Population\ Density=\frac{Total\ Number\ of\ People}{Land\ Area}[/tex]

Now putting the given values, we get;

[tex]Population\ Density=\frac{900,000}{1800\ mi^2}=500\ People/mi^2[/tex]

Hence The Population Density is [tex]500\ People/mi^2[/tex].

The expression [tex]\((-4x^2ya^3)^2\)[/tex] written as a monomial in standard form is [tex]\(16x^4y^2a^6\)[/tex].

To write the expression [tex]\((-4x^2ya^3)^2\)[/tex] as a monomial in standard form, you need to apply the exponent to each term inside the parentheses.

Remember that when raising a power to another power, you multiply the exponents.

[tex]\((-4x^2ya^3)^2\)[/tex] means you square each term inside:

[tex]\[ (-4)^2 \cdot (x^2)^2 \cdot (y)^2 \cdot (a^3)^2 \][/tex]

Now, perform the operations:

[tex]\[ 16 \cdot x^{2 \cdot 2} \cdot y^{2 \cdot 1} \cdot a^{3 \cdot 2} \][/tex]

Simplify the exponents:

[tex]\[ 16 \cdot x^4 \cdot y^2 \cdot a^6 \][/tex]

So, [tex]\((-4x^2ya^3)^2\)[/tex] written as a monomial in standard form is [tex]\(16x^4y^2a^6\)[/tex].

for a³, when squared, it becomes [tex]a^(3*2) = a^6.[/tex] Thus, the simplified expression is [tex]16x^4y^2a^6[/tex]

To simplify the expression[tex](-4x^2ya^3)^2[/tex], apply the power rule, squaring each term within the parentheses. First, square the coefficients: (-4)² = 16. Then, square the variables inside the parentheses. For x², when raised to the power of 2, it becomes[tex]x^(2*2) = x^4.[/tex] For y^1, when squared, it becomes [tex]y^(1*2) = y^2[/tex]. Finally, for [tex]a^3,[/tex] when squared, it becomes a^(3*2) = a^6. Thus, the simplified expression is [tex]16x^4y^2a^6[/tex]

To simplify the expression[tex](-4x^2ya^3)^2,[/tex]start by understanding the exponent rule when raising a power to another power. Applying this rule, square the entire expression inside the parentheses:[tex](-4x^2ya^3)^2.[/tex]Begin by squaring the coefficient[tex](-4)^2,[/tex] resulting in 16. Then, square each variable term. For[tex]x^2,[/tex] when squared, it becomes[tex]x^(2*2) = x^4.[/tex]The y term, which is effectively[tex]y^1,[/tex]squared yields[tex]y^(1*2) = y^2.[/tex]Lastly, a^3, when squared, becomes [tex]a^(3*2) = a^6.[/tex]Therefore, combining the simplified coefficients and variables, the final answer is[tex]16x^4y^2a^6.[/tex]

Solving the inequality [tex]7x-25<-39[/tex] we get [tex]x<-2[/tex]

Step-by-step explanation:

We need to solve 25 subtracted from the product of a number and 7 is less than -39

Translating into mathematical form

Let the number be x

[tex]7x-25<-39[/tex]

Solving the inequality to find the value of x

[tex]7x-25<-39[/tex]

Adding 25 on both sides

[tex]7x-25+25<-39+25[/tex]

[tex]7x<-14[/tex]

Divide both sides by 7

[tex]x<-2[/tex]

Solving the inequality [tex]7x-25<-39[/tex] we get [tex]x<-2[/tex]

Keywords: Solving inequalities

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The inequality representing the scenario '25 subtracted from the product of a number and 7 is less than -39' is solved by first setting up the inequality 7x - 25 < -39, then isolating x to find x < -2. Here, x represents the unknown number.

The student's question involves writing an inequality to represent the given scenario: 25 subtracted from the product of a number and 7 is less than -39. To express this in mathematical terms, let's denote the unknown number as x. The product of this number and 7 is written as 7x. Now, according to the question, when you subtract 25 from this product, the result should be less than -39.

So, the inequality becomes: 7x - 25 < -39. To solve this inequality, you would add 25 to both sides, resulting in 7x < -14. Then, dividing both sides by 7 gives us x < -2. This means that for the inequality to be true, the unknown number x must be less than -2.

Answer:

3/10, 3:10

Step-by-step explanation:

3 to 10 : 3/10, 3:10

Answer:

$3.70

Step-by-step explanation:

divide 1.48 by 4 = .37

multiply by 10

The required equations that represent the sum and difference of numbers are: x + y = 77 and [tex]\frac{x}{2} - \frac{y}{3} = 6[/tex]

Solution:

Let the two consecutive numbers be "x" and "y"

Where "x" is the smaller number and "y" is the larger number

Given that sum of two consecutive numbers is 77

Therefore we frame a equation as:

x + y = 77

Also given that The difference of half of the smaller number and one-third of the larger number is 6

Therefore we frame a equation as:

half of the smaller number - one-third of the larger number = 6

half of x - one third of y = 6

[tex]\frac{1}{2}x - \frac{1}{3}y = 6\\\\\frac{x}{2} - \frac{y}{3} = 6[/tex]

Therefore the required equations that represent the sum and difference of numbers are:

x + y = 77

[tex]\frac{x}{2} - \frac{y}{3} = 6[/tex]

Answer:

y=-2x-3

Step-by-step explanation:

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

m=(-5-(-3))/(1-0)

m=(-5+3)/1

m=-2/1

m=-2

y-y1=m(x-x1)

y-(-3)=-2(x-0)

y+3=-2(x)

y+3=-2x

y=-2x-3

Answer:

70

Step-by-step explanation:

We can rewrite the phrase for every '1 red light there are 9 blue lights' as there are 9 blue lights for every red, which may make it slightly clearer.

If there are 7 red lights, and 9 blues for every red, then there are 7*9 blue lights, or 63 blue lights. Now we can add the red and blue lights; 63+7=70, so there are 70 lights in all.

Answer:

70

Step-by-step explanation:

Answer:

The value of a = ±(√3)/(6)

Step-by-step explanation:

Points A and D belong to the x−axis.

All vertices on the parabola y = a (x+1)(x−5) = a (x² - 4x - 5)

So, points A and D represents the x-intercept of the parabola y

To find x-intercept, put y = 0

∴ a (x+1)(x−5) = 0  ⇒ divide both sides by a

∴ (x+1)(x−5) = 0 ⇒ x = -1 or x = 5

so, the x-coordinate of Point A is -1 or 5

And given that: m∠BAD=60°

So, the tangential line of the parabola at point A has a slope of 60°

∴ y' = tan 60° = √3

∴ y' = a (2x-4)

∴ a (2x-4) = √3

∴ a = (√3)/(2x-4)

Substitute with x = -1 ⇒ a = (√3)/(-6)

Substitute with x = 5 ⇒ a = (√3)/(6)

So, The value of a = ±(√3)/(6)

Also, see the attached figure, it represents the problem in case of a = (√3)/(-6)

Answer:

Step-by-step explanation:

[tex]a=+(3+9\sqrt{3})/52\\ a=-(3+9\sqrt{3})/52\\[/tex]

Answer:

-5x - 6x ≤ 8 - 8x - x

-11x ≤ 8 - 9x

-2x ≤ 8

x ≥ -4

Answer:

1:2

Step-by-step explanation:

Find the ratio of the ratio of the number of minutes he lifted weights to the total number of minutes of his entire workout and simplify it

25:10+25+15

25:50

1:2

Answer:

1 to 2

1:2

1/2

Step-by-step explanation:

Ratios can be written in three forms:

A to B

A:B

A/B

Ratios are also simplified by reducing to lowest terms like fractions are.

This problem's ratio is:

minutes lifted weights to total minutes workout

The number of minutes lifting weights is in the question: 25.

To find the total minutes of his workout, add the number of minutes he spent for all of the activities:

Total minutes = warm-up + lifting weights + treadmill

Total minutes = 10 + 25 + 15

Total minutes = 50

The ratio before simplifying is 25/50.

This ratio can be reduced to lowest terms. Both sides are divisible by 25.

25/25 = 1

50/25 = 2

The ratio in lowest terms is 1/2.

It can also be written as 1 to 2 or 1:2.

HOPE IT HELPS U.............

Answer:

x = y

Step-by-step explanation:

7x = 5y + 2x

Subtract 2x from both sides

5x = 5y

x = y

Lets turn E into x and F into y.

We already know that x is 0.8. And if y/x = 0.6, we have to figure that out.

y/x = 0.6

y/0.8 = 0.6

Multiply by 8 to get y = 0.48.

So we have to find P(xy)

So if we know that x = 0.8 and y = 0.48 then all we have to do is multiply 0.48 and 0.8.

0.48 * 0.8 = 0.384

P(E and F) is 0.384.

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Answer:

x = 25

y = 60

Step-by-step explanation:

Angles with meauseres 80° and 4x° are the same-side interior angles when two parallel lines are cut by transversal. This means the sum of the measures of these angles is equal to 180°.

[tex]80^{\circ}+4x^{\circ}=180^{\circ}\\ \\4x=180-80\\ \\4x=100\\ \\x=25[/tex]

Angles with measures 4x° and (2y - 20)° are vertical angles, so they are congruent:

[tex]4x^{\circ }=(2y-20)^{\circ}\\ \\4\cdot 25=2y-20\\ \\2y-20=100\\ \\2y=100+20\\ \\2y=120\\ \\y=60[/tex]

Final answer:

The solution to the algebraic equation 6x = 322 is found by dividing both sides by 6, which results in x ≈ 53.67.

Explanation:

The value of x that makes the equation 6x = 322 true can be found by performing simple algebra. In order to solve for x, you need to isolate it on one side of the equation.

Here are the steps:

Therefore, the value of x that satisfies the equation is approximately 53.67.

Answer:

4x/9

Step-by-step explanation:

The quotient of four times a number and nine in an algebraic expression can be represented as (4x/9).

The quotient of four times a number and nine in an algebraic expression can be represented as (4x/9). Here, 'x' represents the unknown number. To calculate the value of this expression, you would multiply 4 with 'x' and then divide the result by 9. For example, if the unknown number is 6, the expression would evaluate to (4 * 6)/9 = 24/9 = 2.67.

In the realm of algebraic expressions, the quotient derived from four times an unspecified number divided by nine takes on the simple yet versatile form of (4x/9), with 'x' standing in as the variable denoting the unknown quantity. The computation entails a straightforward process wherein you multiply the value of 'x' by 4 and subsequently divide the outcome by 9. For instance, if 'x' were to represent the value 6, the expression's evaluation would unfold as follows: (4 * 6)/9 = 24/9 = 2.67. This straightforward algebraic framework empowers us to efficiently compute the result based on the specific value attributed to 'x,' facilitating various calculations and problem-solving endeavors.

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Answer:

Angle M = 98 degrees

Step-by-step explanation:

All triangle angles add up to 180.

Set up equation like this:

(x+6)+(3x-16)+(x)=180

Combine like terms.

5x-10=180

Add on both sides.

5x=190

Divide 5 both sides.

x=38

Solve for angle M.

3(38)-16=98