The perimeter of a rectangular field is no more than 134 yards. If the length of the field is 39 yards, which number line represents the possible width of the field (in yards)?​

Answer:

0

Step-by-step explanation:

If it lies on the y line then it is horizontal. This means the slope is 0 and so is the x value.

Let x be the number of bags of food Rachel can buy, and let y be the number of toys she can buy.

We can write the linear inequality as follows:

8x + 4y ≤ 46

An inequality is a mathematical statement that shows the relative size of two values.

A linear inequality is an inequality that involves a linear expression, which is an expression that involves variables and constants, but no exponents or other mathematical operations. Linear inequalities are used to represent relationships between variables that are linear in nature.

This inequality can be rewritten as follows:

x + 0.5y ≤ 5.75

This inequality states that the number of bags of food (x) and half the number of toys (0.5y) must be less than or equal to 5.75, which is the amount of money Rachel has available to spend divided by the cost per bag of food.

Therefore, Rachel can buy x bags of food and y toys for her cats as long as the inequality 8x + 4y ≤ 46 (or x + 0.5y ≤ 5.75) is satisfied.

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Let x be the number of bags of food Rachel can buy, and let y be the number of toys she can buy.

We can write the linear inequality as follows:

8x + 4y ≤ 46

What is inequality?

An inequality is a mathematical statement that shows the relative size of two values.

What is linear inequality?

A linear inequality is an inequality that involves a linear expression, which is an expression that involves variables and constants, but no exponents or other mathematical operations. Linear inequalities are used to represent relationships between variables that are linear in nature.

This inequality can be rewritten as follows:

x + 0.5y ≤ 5.75

This inequality states that the number of bags of food (x) and half the number of toys (0.5y) must be less than or equal to 5.75, which is the amount of money Rachel has available to spend divided by the cost per bag of food.

Therefore, Rachel can buy x bags of food and y toys for her cats as long as the inequality 8x + 4y ≤ 46 (or x + 0.5y ≤ 5.75) is satisfied.

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The inequality - 3x - 6 ≤ 12 represents a close circle at x = - 6 and will extend to infinity which is (C) the third line.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

The given inequality is - 3(x + 2) ≤ 12.

- 3x - 6 ≤ 12.

- 3x ≤ 12 + 6.

- 3x ≤ 18.

3x ≥ - 18.

x ≥ - 6.

This will be represented by a close circle at x = - 6 and will extend to infinity.

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So the valid bounding conditions for the sum of the subset problem are:

0 <= x[i] <= 1 (for all i such that 1 <= i <= n)

∑(w[i] * x[i]) <= m (for all i such that 1 <= i <= n)

The valid bounding condition for the sum of the subset problem is:

0 <= x[i] <= 1 (for all i such that 1 <= i <= n)

This means that each item can either be included in the subset (x[i] = 1) or not included in the subset (x[i] = 0).

The sum of the weights of the items in the subset should not exceed the maximum capacity constraint, m. So the bounding condition for the weight of the subset is:

∑(w[i] * x[i]) <= m (for all i such that 1 <= i <= n)

This means that the sum of the weights of the items in the subset should be less than or equal to the maximum capacity constraint.

So the valid bounding conditions for the sum of the subset problem are:

0 <= x[i] <= 1 (for all i such that 1 <= i <= n)

∑(w[i] * x[i]) <= m (for all i such that 1 <= i <= n)

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The unidentified term is 3m.

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, an equation (x-0.2n)² = x-1.2mn+0.04n²

We know that, (a-b)² = a²-2ab+b²

Comparing the given equation with the above identity, we get,

a = x, b = 0.2n and 2ab = 1.2mn

Therefore, 2x×0.2n = 1.2mn

x = 3m

Hence, the unidentified term is 3m

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By looking at the definition of mutually exclusive and independent event, the statement for both events are true.

A statistical term used to describe events that cannot occur concurrently is "mutually exclusive." It is frequently used to refer to circumstances in which the occurrence of one event takes precedence over the other. For instance, it is impossible for war and peace to exist together. They are therefore opposed to one another.

Events classified as independent do not depend on other events for their occurrence. For instance, if we toss a coin in the air and it lands on head, we can toss it again and this time it will land on tail. Both instances include independent occurrences of the two events.

(a) True. The given event is both mutually exclusive as well as independent

(b)True. The given event is both mutually exclusive as well as independent

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Answer: 64/35

Step-by-step explanation:

8/7 and then divide by 5/8 and you get 1 29/35. 35x1= 35 then add the numerator, 29 and you get 64. so the answer would be 64/35

Answer: 5x10^-2, 3x10^-4, 2x10^5, 7x10^5.

Step-by-step explanation: To order the numbers 7x10^5, 5x10^-2, 2x10^5, 3x10^-4 from least to greatest, you need to compare the values of the numbers.

The first step is to compare the base numbers (the numbers before the "x10" part):

7 is greater than 5, which is greater than 2, which is greater than 3.

The second step is to compare the exponent values (the numbers after the "x10" part):

5 is greater than -2, which is greater than 5, which is greater than -4.

Based on these comparisons, the order of the numbers from least to greatest is:

5x10^-2, 3x10^-4, 2x10^5, 7x10^5.

The function, f(x) = -50 and g(x) = -17

A function is a relationship between a set of inputs and a set of potential outputs, where each input is associated to exactly one outcome.

Instance: f(x) = x/2 ("f of x equals x divided by 2")

we are given that f(x) = -3[tex]x^{2}[/tex] -2 and g(x) = 4x - 1

we need to find f(4) and g(-4)

f(4) = -3([tex]4^{2}[/tex]) - 2

f(4) = -3*16 - 2

f(4) = -48-2

f(4) = -50

g(x) = 4x - 1

g(-4) = 4 *-4 -1

g(-4) = -16-1

g(-4) = -17

The function f(x) = -50  and g(x) = -17

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Answer:

d ≈ 8.5 units

Step-by-step explanation:

calculate the distance using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = A (2, - 1 ) and (x₂, y₂ ) = B (- 4, 5 )

d = [tex]\sqrt{(-4-2)^2+(5-(-1))^2}[/tex]

   = [tex]\sqrt{(-6)^2+(5+1)^2}[/tex]

   = [tex]\sqrt{36+6^2}[/tex]

   = [tex]\sqrt{36+36}[/tex]

   = [tex]\sqrt{72}[/tex]

   ≈ 8.5 units ( to 1 decimal place )

Answer: The power 3 times 2=6.0

Step-by-step explanation:multiply the power you get 0 multiply the 2x3

Answer: 16

Step-by-step explanation: [tex]2^{3}[/tex] = 8. This is because when a number is expressed to the power of a #, it means to multiply that # by itself by how many times the number of the exponent is. So, [tex]2^{3}[/tex] =

2 x 2 x 2

4 x 2 = 8

Now, we must remember to multiply the 2 after we get 8. So,

8 x 2 = 16

So, therefore, 2 by the power of 3 times 2 = 16

I hope this helps!

The perimeter of the image is 70 meters and its area is 210 square meters.

The circumference of a shape is known as its perimeter. The lengths of all four sides must be added in order to get a rectangle's or square's perimeter. The sum of the lengths of all the sides in a rectangle is its perimeter, or P. A rectangle's opposite sides are equal, hence it has two equal lengths and two equal widths. The following formula is used to determine a rectangle's perimeter: Diameter is equal to the sum of the following dimensions: length, width, height, and width.

There are numerous practical uses for calculating the perimeter. The size of the fence needed to enclose a yard or garden is known as the calculated perimeter.

Area=(1/2)×base× height

=(1/2)×21×20

=210 square meters

Perimeter=a+ b+ c

=21+20+29

=70meters

Therefore, The perimeter of the image is 70 meters and its area is 210 square meters.

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The x-intercept has an ordered pair (-4, 0) and the y-intercept has an ordered pair(0,16).

In an alternative method, a linear polynomial over a field from which the coefficients are extracted is equalized to zero to produce a linear equation. The values that, when used as placeholders for the unknowns, result in the equality being true are the solutions to this kind of equation.

In this specific situation, where the variable is appropriately referred to as the unknown, the term "linear equation" frequently applies indirectly.

The Cartesian coordinates of a point on the Euclidean plane can be read as each solution in the case of two variables.

Given equation is:

-4x+y=16

For x-intercept, y=0

-4x+0=16

-4x=16

x= -4

The x-intercept has an ordered pair (-4, 0)

For y-intercept, x=0

-4(0)+y=16

y=16

The y-intercept has an ordered pair(0,16)

Therefore, The x-intercept has an ordered pair (-4, 0) and the y-intercept has an ordered pair(0,16).

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x = 3 is the true solution to 2 ln e superscript ln 5 x baseline = 2 ln 15, using the concept of simplification.

Make something simpler by simplifying it. In mathematics, reducing an expression, fraction, or issue to a simpler form is referred to as simplification. With calculations and solutions, the problem is made simple.

In order to achieve consistency in efforts, costs, and time, procedures must be simplified. It gets rid of variation and variety that is superfluous, harmful, and unproductive. It is termed simplification to use and interpret the function in order to make it simpler or easier to grasp.

The equation can be simplified by using the fact,

ln(eˣ) = x

This gives,

2 ln(5x) = 2·ln(15)

Comparing arguments, we see that,

5x = 15

x = 3

Check if it is true or not:

2 ln(e^(ln(5·3))) = 2·ln(15)

2 ln(e^2.70805) = 2·2.70805

2 ln(15) = 5.41610

and,

2·2.70805 = 5.41610

So, it is true.

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Answer: Not a Question

Step-by-step explanation:

No question mark and not a math quiestion

Answer:

2400

Step-by-step explanation:4152 is just 173% of d.

We create an equation d = 4152/1.73

after solving you get 2400.

Answer:

Step-by-step explanation:

Given:

Simple Interest = $50

Principal Amount= $500

Rate of Interest = 9.5%

Find:

Time=?

The formula for Simple Interest is

I=PRT    

{I=Simple Interest

P=Principal amount

R=Rate of Interest

T=Time}

To find out the time for the simple interest to get to $50:

Acc. to the formula T=I/PR

i.e., T=50/(500*9.5/100)

      T=100*50/500*9.5

      T=100/95

      T=1.05 years

Therefore, it will take 1.05 years to get a simple interest of $50 at a rate of 9.5% for a principal amount of $500.

If the radius of the hole is 3 inches than the volume of the resulting solid is 410.29 in³    .

In the question ,

it is given that ,

the manufacturer drills a hole in the metal sphere that has radius of 5 inches ,

the radius of hole in sphere is 3 inches .

the volume of the metal sphere is = (4/3)×π×r³

= (4/3)×π×5³

= 523.33 in³

the volume of the hole of radius 3 inches is = (4/3)×π×3³

= 113.04 in³

So , the volume of the remaining solid is = 523.33 - 113.04

= 410.29 in³  .

Therefore , the Volume of the resulting solid is 410.29 in³    .

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The value of the side AC is 40 if the points  B, D, and F are midpoints of

the sides of ΔACE.

The midpoint theorem states that in order to determine the midpoints of a triangle's sides, "a line segment linking any two of its midpoints is said to be parallel to the triangle's third side and also half the length of the third side."

Divide the distance between the two endpoints by 2, then do it again. The two terminal x coordinates can alternatively be combined, then the result divided by two. Draw a line from a midway to the opposite corner. The centroid of a triangle is the point at where the three medians intersect.

Given,

The points B, D, F are midpoints of the sides of a triangle ACE.

And also given that,

EC =32 and DF=20, AC=?

So, FD=1/2(AC)

AC=2(FD)

AC=2(20)

AC=40

Therefore, the value of the side AC is 40 if the points  B, D, and F are

midpoints of the sides of ΔACE.

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Answer:

y= 3x + 5

Step-by-step explanation:

Some examples

(1,8)

8= 3 (1) + 5

8 = 3 + 5

8= 8

(2,11)

11= 3 (2) + 5

11= 6 + 5

11= 11

Answer:

congruence is compatibility or agreement while equal is the same or equivalent to one another.

It will be 13min until there are 20 grams of the element remaining.

What is exponential decay?

The term "exponential decay" in mathematics refers to the process of a constant percentage rate reduction in an amount over time. It can be written as y=a(1-b)x, where x is the amount of time that has passed, and is the initial amount, b is the decay factor, and y is the final amount.

Here, we have

This is a compound decay problem, which goes by the formula:

F = P(1-r)ˣ

Where

F is the future amount (we want it to be 20)

P is the present amount (240 now)

r is the rate of decay per minute (17.4% = 17.4/100 = 0.174)

x is the time it takes (what we want to find)

Substitute all values in the formula and we get

20 = 240(1-0.174)ˣ

20 = 240(0.826)ˣ

0.0833 = 0.826ˣ

㏑0.0833 = ㏑0.826ˣ

㏑0.0833 = x ㏑0.826

x = ㏑0.0833/㏑0.826

x = 13

Hence, it will be 13min until there are 20 grams of the element remaining.

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Answer:

$1944

Step-by-step explanation:

18x12=216

216x$9=$1944

Answer:

£1944

Step-by-step explanation:

The area of the floor is 216 feet²

18 x 12 = 216

216 x 9 = 1944

The value of the expression, "u + 7" when we are given the equation, 3u + 8 = 2 is determined as: 5.

To evaluate the expression, u + 7, we have to first determine what the value the variable "u" is by solving the equation, 3u + 8 = 2 to find u.

3u + 8 = 2 [given]

Subtract 8 from both sides:

3u + 8 - 8 = 2 - 8 [subtraction property of equality]

3u = -6

Divide both sides by 3

3u/3 = -6/3 [division property of equality]

u = -2

Next, find the value of "u + 7" by plugging in the value of u:

-2 + 7 = 5

Therefore, "u + 7" is equal to 5.

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Answer:

[tex]x^2+9y^2=309[/tex]

[tex](x-3y)^2=177[/tex]

Step-by-step explanation:

Given equations:

[tex]\begin{cases}x+3y=21\\xy=22\end{cases}[/tex]

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

To find the value of x² + 9y²,  first rewrite 9 as 3²:

[tex]\implies x^2+3^2y^2[/tex]

[tex]\implies x^2+(3y)^2[/tex]

[tex]\boxed{\begin{minipage}{5cm}\underline{Sum of two squares}\\\\$a^2+b^2=(a+b)^2-2ab$\\ \end{minipage}}[/tex]

Apply the sum of two squares where:

[tex]\begin{aligned}\implies x^2+(3y)^2&=(x+3y)^2-2x(3y)\\&=(x+3y)^2-6xy\end{aligned}[/tex]

Substitute the given values of (x + 3y) and xy:

[tex]\begin{aligned}\implies (x+3y)^2-6xy&=21^2-6(22)\\&=441-132\\&=309\end{aligned}[/tex]

Therefore:

[tex]\boxed{x^2+9y^2=309}[/tex]

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

To find the value of (x - 3y)², expand:

[tex]\begin{aligned}\implies (x-3y)^2&=x^2-6xy+9y^2\\&=x^2+9y^2-6xy \end{aligned}[/tex]

Rewrite 9 as 3²:

[tex]\begin{aligned}\implies x^2+9y^2-6xy&=x^2+3^2y^2-6xy\\&= x^2+9y^2-6xy\end{aligned}[/tex]

[tex]\boxed{\begin{minipage}{5cm}\underline{Sum of two squares}\\\\$a^2+b^2=(a+b)^2-2ab$\\ \end{minipage}}[/tex]

Apply the sum of two squares  to x² + 9y² where:

[tex]\begin{aligned}\implies x^2+9y^2-6xy&=(x+3y)^2-2x(3y)-6xy\\&=(x+3y)^2-12xy\end{aligned}[/tex]

Substitute the given values of (x + 3y) and xy:

[tex]\begin{aligned}\implies (x+3y)^2-12xy&=21^2-12(22)\\&=441-264\\&=177\end{aligned}[/tex]

Therefore:

[tex]\boxed{(x-3y)^2=177}[/tex]

Answer: C. End of third day

Step-by-step explanation:

The question is asking when there will be 36 pieces left, so you start with the equation:

-6d + 54 = 36

Then, solve this equation:

-6d + 54 = 36

-6d = -18 (subtract 54 from both sides)

d = 3 (divide both sides by -6)

It will take 3 days until there are 36 pieces left, which is the end of the third day.

Answer: [tex](x,y) \to (4x, 4y)[/tex]

Step-by-step explanation:

The rule for dilating a figure by a scale factor of [tex]k[/tex] centered at the origin is [tex](x,y) \to (kx, ky)[/tex].