Luke is going to plant 54 cucumber plants and 72 carrot plants. Luke would like to plant the plants in rows where each row has the same number of cucumber plants and each row has the same number of carrot plants. What is the greatest number of rows Luke can plant?

The formula for the arithmetic sequence is aₙ = 2 + (n - 1)(-4)

An equation is an expression composed of variables and numbers linked together by mathematical operations.

The arithmetic sequence is a sequence in which the difference between successive numbers is constant. It is given by:

aₙ = a₁ + (n - 1)d

where a₁ is the first term and d is the common difference

Given the sequence:

2,-2,-6,-10

The first term (a₁) = 2, the common difference (d) = -2 - 2 = -4

The formula is:

aₙ = 2 + (n - 1)(-4)

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The fraction of Polygon P's area, that is Polygon Q's area, given the scale factor, is 1 / 4.

The fact that Polygon Q is a scaled copy of Polygon P using 1 / 2 as a scale factor means that Polygon Q is half the size of Polygon P.

This means that in terms of area, Polygon Q in relation to Polygon P would be :

= 1 /2 x 1 / 2

= 1 / 4

For example, a square with sides 6 would have an area of :

= 6 x 6

= 36 units ²

The scaled shape would have sides of 3 because of the scale factor of 1 / 2 :

= 3 x 3

= 9 units ²

The fraction of the smaller shape's area is:

= 9 / 36

= 1 / 4

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By function composition, f(x) and g(x) are inverse functions

A function is a relationship between inputs where each input is related to exactly one output.

f(x)= ∛(x-1) and g(x)=x³+1

To confirm the inverse relationship using composition.

If f(g(x)) = g(f(x)) then they are inverse functions

Let's confirm:

f(g(x)) = f(∛(x³+1))

         = ( ∛((x³+1)-1 )

        = ∛(x³)

       = x

g(x)=x³+1

g(f(x)) = g(∛(x-1) )

        = (∛(x-1))³ + 1

        = x-1+1

        = x

Since  f(g(x)) = g(f(x)) then they are inverse functions

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There are approximately 13.38 ounces of chips in the bag.

What is division?

Division is one of the four basic mathematical operations of arithmetic, along with addition, subtraction, and multiplication. It is the inverse operation of multiplication, and it is used to find out how many times one number is contained within another number.

To find out how many ounces of chips are in the bag, you can use the formula:

cost of bag / cost per ounce = number of ounces

In this case, you know that the cost of the bag is $3.91 and the cost per ounce of chips is 29.5 cents per ounce.

First, you need to convert the cost per ounce from cents to dollars. 29.5 cents is equal to 0.295 dollars (29.5 cents / 100 cents = 0.295 dollars)

So, you can substitute these values into the formula:

3.91 / 0.295 = 13.38

Hence, there are approximately 13.38 ounces of chips in the bag.

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Answer:

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Identify two points on the line:

Find the slope using these two points:

The answer is NO.

Therefore , When the side lengths are (2x-1) and (4x + 5), the smartboard's perimeter is expression is  as 12x2 - 8.

In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted.

Here,

Given :

smartboard of side length is ( 2x-1) and ( 4x + 5 )

perimeter of small board = 2( l+ b)

2( 2x-1 + 4x + 5  )

2( 6x - 4)

When the side lengths are (2x-1) and (4x + 5), the smartboard's perimeter is expressed as 12x2 - 8.

The diagram can be imagined as a big whiteboard of shape of rectangle.

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The correct expression to represent this situation through inequality is "p + n ≥ 17"

In mathematics, inequalities are mathematical expressions that compare two values without using the symbol = (equal). Instead, in inequalities, one value is greater than, less than, etc. Due to this, the most common symbols used to write an inequality are:

< = This means less than

> = This means greater than

≥ = This means equal or greater than

≤ = This means equal or less than

Considering, the amoung of pennies and nickels is minimum 17, the correct symbol to use is ≥, which means the amoung of coins is either 17 or more than 70. Moreover, the letters p and n can be used to represent the pennies and nickels. Based on this, the correct expression is:

p + n ≥ 17

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The integral of f(x) on the interval [0, 6] is equal to 8.

Here we have the graph of f(x), and we want to find the integral:

[tex]\int\limits^6_0 {f(x)} \, dx[/tex]

Remember that the integral is the area under the curve, so we only need to find the areas of the "blocks" on the image.

Betwen 0 and 2 we can see that f(x) = 2, there the area is:

A = 2*(2 - 0) = 4

Between 2 and 4 we have f(x) = -3, then:

A' = -3*(4 - 2) = -3*2 = -6

And between 4 and 6 we have f(x) = 5, then:

A'' = 5*(6 -4) = 5*2 = 10

Then the integral is:

[tex]\int\limits^6_0 {f(x)} \, dx = 4 - 6 + 10 = 8[/tex]

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The time required for the baseball to reach the given height is 2 and 5/3 units respectively.

The general form of a quadratic equation is given as ax^2 + bx + c = 0.

Here, a ≠ 0 and b and c are integers.

The degree of a quadratic equation is 2.

The equation for the height of baseball can be written as,

h(t) = -12t² + 44t + 6

It is a quadratic equation.

At h = 46 ft, the value of t can be found as,

Plug h(t) = 46 in  h(t) = -12t² + 44t + 6 as,

⇒ -12t² + 44t + 6 = 46

⇒ -12t² + 44t - 40 = 0

⇒ t = 2, 5/3

Hence, the time at which the height is 46 ft are given as 2 and 5/3 units respectively.

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Answer: 8

Step-by-step explanation: make it x = 1/3 times 24.

Also, try inserting 8 in the blank.

The line 5 = 3X - Y or3X minus Y equals five is the same line of  Y equals 3X -5. The correct option is A.

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

Given line:

Y equals 3X -5

Simplifying,

Y = 3X - 5

This is a linear equation.

To find the same line:

Y = 3X - 5

Taking constant to one side and variable to one side,

That means,

5 = 3X - Y

3X minus Y equals five

Therefore, 3X minus Y equals five or 5 = 3X - Y is the required line.

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Answer:

1,449

Step-by-step explanation:

Answer:

1449

Step-by-step explanation:

when you multiply equations like this you have to cross multiply. you go from right to left.

7x7=49

you would carry your 4 over the 0.

7x0=0 plus the 4 you carried so 4.

last you would do 7x2=14

your answer is 1,449

[tex]A=e^2[/tex], where e is the side length of the square and A is the area of the square.

Answer:

3π/2 radians

Step-by-step explanation:

Its 3 quadrants. That's 3/4 of 2π radians, or 3π/2 radians.

The graph that shows the solution set of the inequality t > 4 or t < -1 is given by the image presented at the end of the answer.

The inequality for this problem is defined as follows:

t > 4 or t < -1.

It is a compound inequality, as it has two conditions.

The first condition is given as follows:

t > 4.

Which means that numbers to the right of t = 4 are graphed, with an open circle representing an open interval.

The second condition is given as follows:

t < -1.

Which means that numbers to the left of t = -1 are graphed, with an open circle also representing an open interval.

The open intervals are because none of the conditions contain the equal symbol.

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The line with slope 1 passing through the point (5, 3) is y = x - 2.

A number that describes a line's direction and steepness is known as the slope or gradient of a line in mathematics.

The letter m is frequently used to represent slope; the reason for this is unclear, but it is first used in English by O'Brien in 1844, who wrote the equation for a straight line as "y = mx + b," and by Todhunter in 1888,

who wrote it as

                                             y = mx + c

To Graph the line with slope 1 passing through the point (5, 3) we need to find the slope intercept form

The slope formula =  y - y₁ = m(x -x₁)

⇒  y - 3 = 1(x -5)

⇒  y = x -5 + 3

⇒  y = x - 2

Now putting the value on graph we get [See attachment]

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Answer: yes

Step-by-step explanation: yesterday

According to this postulate, two triangles are congruent if their two angles and included sides are congruent with each other.

If the sides and angles of one triangle are the same as the sides and angles of another triangle, then two or more triangles are said to be congruent. Three postulates—ASA (angle-side-angle), SAS (side-angle-side), and SSS—that are demonstrated in the lesson can also be used to assess for congruency.

If, for example, triangle ABC has a hypotenuse of 5 cm and a leg of 4 cm and triangle PQR has a hypotenuse of 5 cm and a leg of 4 cm, then these two triangles have the same dimensions and, according to the HL theorem, are congruent to one another.

Triangle congruence can be implied in some situations by SSA, but not always. It differs from the other triangle congruence postulates/criteria because of this.

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98,329.16 is the Growing Ordinary Annuity's Future Value (FV). Given a predetermined rate of return or discount rate, the present value of an annuity is the entire cash worth of all of your future annuity payments.

A sequence of equal-spaced payments constitutes an annuity. There are a lot of real-world examples of financial transactions involving annuities, including. • an automobile loan with a set repayment schedule of equal monthly payments.

Calculating the present value of an annuity is done by multiplying the dollar amount of each payment by the following formula:[tex]P = PMT \times [1- [ (1 / 1+r)^n] / r][/tex]  where P is the present value of your annuity stream. PMT is short for payment method type.

A set of periodic payments that will be received in the future at the start of each period or at its conclusion is referred to as a "annuity." The formula used to determine annuity payments and annuities due is based on the PV of annuities due, the effective interest rate, and the number of periods.

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Answer:

Each student would get 25 sheets of paper.

Step-by-step explanation:

Mr. Perez starts out with 500 sheet.  He puts 1/4 in the printer.  That leaves 3/4 that he did not put in the printer.

3/4 x 500 = 375.

He take 2/3 of the 375 sheets and stores them.  This leaves 1/3 of 375 sheet to hand out to students.

1/3 x 375 = 125

He has 125 sheets to share among 25 students.

125/5 = 25

Answer: 1/7^3

Step-by-step explanation:

When dealing with negative integers, you divide instead of multiplying and you write it as a fraction. Therefore, 1/7 to the 3rd power is the same as 3 to the power of -7. Hope this helps!

Answer:

Sure, here is a more casual and friendly way to explain how to calculate the weighted dollar amount of the savings account:

"Hey there! To find out the weighted dollar amount of the savings account, you just need to do a little math. First, multiply the amount invested in the savings account by the return on investment (ROR). Then, divide that number by the total ROR for all investments.

So, if you have $2,700 invested in the savings account and it has an ROR of 3.6%, the weighted dollar amount of the savings account would be:

($2,700 * 3.6%) / (3.6% + 1.8% + 13.6% - 1.2%) = $104.04

Easy peasy! Let me know if you have any other questions!

Brad needs to rent the scaffolding for 6 hours for the cost to be the same from each rental company.

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.

Handy Rentals

C = $15 + $12.50h ---------- 1

EZ Rental Company

$7.50 + $13.75h ------------ 2

where h is number of hours

Equating both equations

$15 + $12.50h = $7.50 + $13.75h

$15 - $7.50 = $13.75h - $12.50h

$7.5 = $1.25h

h = $7.5/$1.25

h = 6 hours

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Answer: LCM(6,8)

Step-by-step explanation: Each of six slices of the first pasta has the area 1%2F6 of the entire pan.

Each of eight slices of the second pasta has the area 1%2F8 of the original pan.

David will cut each 1%2F6 in 4 equal pieces to get 1%2F24.

he also will cut each 1%2F8 in 3 equal pieces to get 1%2F24.

Then he will meet his goal.

Notice that the number 24 is the Less Common Multiple of the numbers 6 and 8: 24 = LCM(6,8).

Answer:

There would be six pieces in each pan.

Step-by-step explanation:

1. To make the number of pieces in each pan equal, the total number must be the same.

2. 8 pieces from the first pan + 6 pieces from the second pan = 14 pieces.

3. Divide 14 by 2 to get the same number of pieces in each pan:

14/2 = 7

4. Round down 7 to get six pieces in each pan.

Answer:

4

Step-by-step explanation:

To find f(-1), we can plug -1 into the equation in place of x and simplify:

f(-1) = 4(-1)² + 9(-1) + 9

f(-1) = 4 + (-9) + 9

f(-1) = 4 - 9 + 9

f(-1) = 4 - 0

f(-1) = 4

Therefore, f(-1) = 4.

Answer:

The answer is D, y=0.25t + 9.5

Step-by-step explanation:

Since the crew has been painting at a rate of 0.25 per hour continuosly, it will be 0.25 times the number of hours (t), plus the already completed road, which is 9.5.

Answer:

(A)

Step-by-step explanation:

SOS: Here is The correct answer, Brainly would not allow me to type it, so I took a screenshot instead. Hope this helps!! :D

The coefficient of friction between the ring and the rod is approximately 0.408.

friction = (force parallel to the surface) ÷ (force perpendicular to the surface)

       F_horizontal = friction

       F_horizontal = µ × F_perpendicular

       8 N = µ × m × g

      where m is the mass of the ring and g is the acceleration due to gravity.

       8 N = µ × 0.2 kg × 9.8 m/s²

           µ = 8 N ÷ (0.2 kg * 9.8 m/s²)

            µ = 0.408

So the coefficient of friction between the ring and the rod is approximately 0.408.

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