5. If x= 3 solves the system shown below, what must be the value of a?(1) -4(3) 3y = 5x - 8(2) -1(4) 7y = ax +19

Answer:46

Step-by-step explanation:

The amount of outdoor carpet needed is 40 ft².

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. The area of a plane figure is the area that its perimeter encloses. The quantity of unit squares that cover a closed figure's surface is its area.

Area of a rectangle = length × width.

The amount of square feet of outdoor carpet needed

= area of the largest rectangle in the image - (area of medium rectangle + area of the smallest rectangle)

The amount of square feet of outdoor carpet needed

= 12 × 4 - (3 × 2 + 2 × 1)

= 48 - (6 + 2)

= 40 ft²

Thus, 40 ft² outdoor carpet needed.

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Answer:

1)  695.3 m²

2)  8 ft

3)  172.0 in²

Step-by-step explanation:

To find the area of a regular polygon, we can use the following formula:

\(\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}\)

Given the polygon is an octagon, n = 8.

Given each side measures 12 m, s = 12.

Substitute the values of n and s into the formula for area and solve for A:

\(\implies A=\dfrac{(12)^2 \cdot 8}{4 \tan\left(\dfrac{180^{\circ}}{8}\right)}\)

\(\implies A=\dfrac{144 \cdot 8}{4 \tan\left(22.5^{\circ}\right)}\)

\(\implies A=\dfrac{1152}{4 \tan\left(22.5^{\circ}\right)}\)

\(\implies A=\dfrac{288}{\tan\left(22.5^{\circ}\right)}\)

\(\implies A=695.29350...\)

Therefore, the area of a regular octagon with side length 12 m is 695.3 m² rounded to the nearest tenth.

\(\hrulefill\)

The sum of an interior angle of a regular polygon and its corresponding exterior angle is always 180°.

If the exterior angle of a polygon measures 40°, then its interior angle measures 140°.

To determine the number of sides of the regular polygon given its interior angle, we can use this formula, where n is the number of sides:

\(\boxed{\textsf{Interior angle of a regular polygon} = \dfrac{180^{\circ}(n-2)}{n}}\)

Therefore:

\(\implies 140^{\circ}=\dfrac{180^{\circ}(n-2)}{n}\)

\(\implies 140^{\circ}n=180^{\circ}n - 360^{\circ}\)

\(\implies 40^{\circ}n=360^{\circ}\)

\(\implies n=\dfrac{360^{\circ}}{40^{\circ}}\)

\(\implies n=9\)

Therefore, the regular polygon has 9 sides.

To determine the length of each side, divide the given perimeter by the number of sides:

\(\implies \sf Side\;length=\dfrac{Perimeter}{\textsf{$n$}}\)

\(\implies \sf Side \;length=\dfrac{72}{9}\)

\(\implies \sf Side \;length=8\;ft\)

Therefore, the length of each side of the regular polygon is 8 ft.

\(\hrulefill\)

The area of a regular polygon can be calculated using the following formula:

\(\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}\)

A regular pentagon has 5 sides, so n = 5.

If its perimeter is 50 inches, then the length of one side is 10 inches, so s = 10.

Substitute the values of s and n into the formula and solve for A:

\(\implies A=\dfrac{(10)^2 \cdot 5}{4 \tan\left(\dfrac{180^{\circ}}{5}\right)}\)

\(\implies A=\dfrac{100 \cdot 5}{4 \tan\left(36^{\circ}\right)}\)

\(\implies A=\dfrac{500}{4 \tan\left(36^{\circ}\right)}\)

\(\implies A=\dfrac{125}{\tan\left(36^{\circ}\right)}\)

\(\implies A=172.047740...\)

Therefore, the area of a regular pentagon with perimeter 50 inches is 172.0 in² rounded to the nearest tenth.

Answer:

1.695.29 m^2

2.8 feet

3. 172.0477 in^2

Step-by-step explanation:

1. The area of a regular octagon can be found using the formula:

\(\boxed{\bold{Area = 2a^2(1 + \sqrt{2})}}\)

where a is the length of one side of the octagon.

In this case, a = 12 m, so the area is:

\(\bold{Area = 2(12 m)^2(1 + \sqrt{2}) = 288m^2(1 + \sqrt2)=695.29 m^2}\)

Therefore, the Area of a regular octagon is 695.29 m^2

2.

The formula for the exterior angle of a regular polygon is:

\(\boxed{\bold{Exterior \:angle = \frac{360^o}{n}}}\)

where n is the number of sides in the polygon.

In this case, the exterior angle is 40°, so we can set up the following equation:

\(\bold{40^o=\frac{ 360^0 }{n}}\)

\(n=\frac{360}{40}=9\)

Therefore, the polygon has n=9 sides.

Perimeter=72ft.

We have

\(\boxed{\bold{Perimeter = n*s}}\)

where n is the number of sides in the polygon and s is the length of one side.

Substituting Value.

72 feet = 9*s

\(\bold{s =\frac{ 72 \:feet }{ 9}}\)

s = 8 feet

Therefore, the length of each side of the polygon is 8 feet.

3.

Solution:

A regular pentagon has five sides of equal length. If the perimeter of the pentagon is 50 in, then each side has a length = \(\bold{\frac{perimeter}{n}=\frac{50}{5 }= 10 in.}\)

The area of a regular pentagon can be found using the following formula:

\(\boxed{\bold{Area = \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *s^2}}\)

where s is the length of one side of the Pentagon.

In this case, s = 10 in, so the area is:

\(\bold{Area= \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *10^2=172.0477 in^2}\)

Drawing: Attachment

Consider the expression 4(8x + 5)

Complete 2 descriptions of the parts of the expression.

1. The entire expression is the product of 2 factors.

2. On its own, (8x + 5) is a sum with 2 terms.

The area covered by the signal is 181.37 m²

Here we can see that the area covered by the signal is the fourth of a circle of radius R = 15.2m

The area of a circle of radius R is given by:

A = 3.14*R²

Then the area of a fourth of a circle is:

A = (3.14/4)*R²

Replacing the value of the radius in the formula we will get:

A =  (3.14/4)*(15.2m)² = 181.37 m²

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Answer:

the square root of -1 is i

Step-by-step explanation:

Well, actually, the square root of -1 (or any negative number at that) is not a real number. What I mean by that is that there is no way to square a real number to get a negative number (ie \(2^{2} = 4, -2^{2} =4\), there is no way to square a real number to get -4).

To solve this, mathematicians came up with the "imaginary number" i which, when squared, equals to -1. This allows us to get the square root of negative numbers (\(\sqrt{-4} = 2i\)) or get negative numbers through squaring (\(2i^{2} = -4\)).

The required value of the square root of -1 is i. The correct answer is option B.

As we know that complex number is made up of real and imaginary values. It is represented by the equation z = a + ib, where a, b, and i are real values and i is an imaginary number.

The square root of -1 is denoted as "i" in mathematics, where "i" represents the imaginary unit.

The imaginary unit is defined as the square root of -1. It is important to note that the square root of a negative number is not a real number, but an imaginary number.

⇒ √(-1)

⇒ √(i²)

⇒ i

So, the correct answer is "i."

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Answer:

30 lb bag is cheaper by about $2.40

Step-by-step explanation:

to find per pound we divide

19.49/4= 4.8725

$4.87per pound

$73.99/30=2.46633

$2.47 per pound

30 lb bag is cheaper per pound

4.87-2.47=2.40

hopes this helps please mark brainliest

Answer:

52.5 inch square

Step-by-step explanation:

Area of pentagon: A = 1/2 × p × a;

where 'p' is the perimeter of the pentagon and 'a' is the apothem of the pentagon.

A = 1/2 x (6 x 5) x 3.5 = 1/2 x 30 x 3.5 = 15 x 3.5 = 52.5

The area of the regular pentagon with apothem 3.5 and side 6 is 52.5

In Mathematics, a pentagon is a polygon with 5 sides. A pentagon can be classified as a regular pentagon and irregular pentagon. When all the sides and the angles of a pentagon are of equal measure, then it is called a regular pentagon.

Given the question, we need to find the area of the regular pentagon with apothem 3.5 and side 6.

In order to find the area, the formula to calculate the area of the regular pentagon is given by:

\(\text{Area of pentagon} =\sf \huge \text(\dfrac{5}{2}\huge \text) \times s \times a\)

Now,

\(\text{Area of pentagon} =\sf \huge \text(\dfrac{5}{2}\huge \text) \times s \times a\)

\(\text{Area of pentagon} =\sf \huge \text(\dfrac{5}{2}\huge \text) \times 6 \times 3.5\)

\(\text{Area of pentagon} =52.5\)

Therefore, the area of the regular pentagon with apothem 3.5 and side 6 is 52.5

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Option (A) is the correct option and on simplifying the expression by combining like terms we get,

24 - 3p.

Given, the expression 6(4 - 2p) + 9p

On simplifying, we get

24 - 12p + 9p

24 - 3p

So, on simplifying the given expression, we get

24 - 3p

Hence, Option (A) is the correct option and on simplifying the expression by combining like terms we get,

24 - 3p

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For the given expression, the variable is p, coefficient is 17 and the exponent is 5.

Expression:

Expression refer the algebraic expression that consists of variables, numbers and math operators.

Given,

Here we have the expression 17p⁵

Now, we have to find the exponent, coefficient and variable.

As per the definition of exponent, the term exponent refers the power value of the expression.

So, the exponent is 5.

And the definition of coefficient is an integer that is written along with a variable or it is multiplied by the variable.

So, the coefficient is 17.

And the variable of this expression is p.

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Answer:

Incremental cost is the total cost incurred due to an additional unit of product being produced. Incremental cost is calculated by analyzing the additional expenses involved in the production process, such as raw materials, for one additional unit of production.

Step-by-step explanation:

The incremental manufacturing cost Martinez incurs, if it increases production from 10,000 to 10,001 units, is $21.5.

We have,

Average cost = Sum of cost of all the units / Number of units

From the table given,

The average cost per unit when it produces 10,000 units.

= 6 + 3.5 + 1.5 + 4 + 3 + 2 + 1 + 0.5

= 21.5

Now,

Substituting the values here,

Average cost = Sum of cost of all the units / Number of units

21.5 = Sum of the cost of 10,000 units / 10,000

The sum of the cost of 10,000 units

= 21.5 x 10,000

= 215000

Now,

The incremental cost is the cost of one unit.

= 21.5

Thus,

The incremental manufacturing cost Martinez incurs, if it increases production from 10,000 to 10,001 units, is $21.5.

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Given:

To find the test statistics, t:

The formula for the test statistics is,

On substitution we get,

Hence, the answer is, t = 2.705 (rounded to 3 decimal places).

Answer:

Step-by-step explanation:

The type of savings is the saving of uniform amount with interest applied to the sum of the amount in the account.

Reasons:

The amount saved per month = $150

Amount saved per year, A = 12 × $150 = $1,800

The interest rate on the account, i = 5%

The amount, F, in the account after 15 years is given as follows;

The uniform series compound amount factor formula is presented as follows;

\(\displaystyle F = \mathbf{\frac{A \cdot \left[ \left(1 + i \right)^n - 1 \right]}{i}}\)

Therefore;

\(\displaystyle F = \frac{1,800 \times \left[ \left(1 + 0.05 \right)^{15} - 1 \right]}{0.05} \approx \mathbf{38,841.4}\)

The amount the account is worth after 15 years to the nearest cent is approximately $38,841.4.

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Answer:

Step-by-step explanation:

X=3 or x=-3

Answer:

Answer:

When the maker of a promissory note fails to pay, the note is said to be dishonored.

Step-by-step explanation:

A six-digit number is a number whose number of digits is 6

The six-digit number is 401956, and the square root of the six-digit number is 634

The number is given as:

4abcd6

Since the number ends with 6, it means that:

The square root of the number ends with 6 or 4

Also, the square root of the six-digit number is a three-digit number

Using trial by error, the six-digit number is 401956

The square root of 401956 is 634

Hence, the six-digit number is 401956, and its square root is 634

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Answer:

5/3 (I think)

Step-by-step explanation:

The third side of the triangle 12.5

A triangle is a polygon with three edges and three vertices. The important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees. This property is called angle sum property of triangle.

we the measurements of given two sides of the triangle 16.5 and 29

In a triangle, the sum of any two sides should be greater than the third side and the difference between any two sides should be lesser than that of the third side.

The sum of two sides rule

\(x + 16.5 > 29\\ x > 29 - 16.5\\ x > 12.5\\\)

The difference between the two sides rule

\(29 - 16.5 < x \\ 12.5 < x\)

Therefore, the value of x is 12.5

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Answer:

if the relationship between two quantities is a proportional relationship, this relationship can be represented by the graph of a straight line through the origin with a slope equal to the unit rate. For each point (x, y) on the graph, ž is equal to k, where k is the unit rate. The point (1, k) is a point on the graph.

Step-by-step explanation:

The first debt that Alice would have to pay based on the Stack method would be the third debt. Option C

From the stack method, the debt that Alice would have to pay off first would be the debt that has the highest interest rate.

The amount of 150 dollars would then be added to the debt that has the second highest rate.

Hence the amount of debt that would be paid off first would be the first debt based on the stack method.

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Answer:

7

Step-by-step explanation:

collect like terms

o+7

when adding or subtracting 0, the quantity does not change

7

so 7 is your solution

1. The estimated price of vest is $30.

The amount of discount is $10.

1) 25% of $40 is $10.

2) The discount percent is 25%.

What is discount?

A discount is a reduction in the regular selling price of a good or service, either in terms of money or as a percentage.

To estimate the sale price of a vest, we can round the original price of $42 to a convenient value, such as $40.

The amount of the discount can be calculated as 25% of the rounded price -

Discount = 0.25 x $40 = $10

Subtracting the discount from the rounded price gives us the sale price -

Sale price = $40 - $10 = $30

Therefore, the estimated sale price of a vest is $30.

25% of $40 = 0.25 x $40 = $10

Subtracting the discount of $10 from the rounded price of $40 gives us the sale price -

Sale price = $40 - $10 = $30

Therefore, the estimated sale price of a vest is $30.

The discount percent is 25%.

This is the percentage by which the original price is reduced to obtain the sale price.

Since the sale price is 75% of the original price, the discount is 25% of the original price.

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The amount of dry ingredients used in the cake recipe is approximately 7 cups.

We have,

3 ½ cups of flour, 2 ⅔ cups of sugar, and 1 ¾ cups of cocoa.

Now, first convert all quantity in same unit.

3 ½ cups of flour

= 3 cups + 0.5 cups

= 3 cups and 8 ounces.

and, 2 ⅔ cups of sugar

= 2 cups + 0.67 cups,

= 2 cups and 10.72 ounces.

and, 1 ¾ cups of cocoa

=1 cup + 0.75 cups

= 1 cup and 12 ounces.

So, the total amount

= 3 cups and 8 ounces + 2 cups and 10.72 ounces + 1 cup and 12 ounces = 6 cups and 14.72 ounces

= 7 cups

Therefore, the amount of dry ingredients used in the cake recipe is approximately 7 cups.

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The gas bill exceeded $87 from last month to this month.

We know simple interest (SI) is given by SI = (p×r×t)/100, where

p = principle, r = rate in percentage, and t = time in years.

Given, The Haddad expected the automatic withdrawal of their gas bill to

be more than last month's bill of $215.85 but did not know by how much.

Their account showed a previous balance of $417.80, $350.00 in deposited checks, and an automatic deposit of $150.00.

∴ Their current balance is (417.80 + 250 + 150) = $817.8 and $5.25 in interest which is (105/100)×$817.7 = $858.69.

Haddads' present balance is $555.82,

∴ The gas bill is $(858.69 - 555.82) = $302.87.

So the gas bill s exceeded by $(302.87 - 215.85) = $87.

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Answer:

1

Step-by-step explanation:

There is only one K listed, meaning the coeffiecent would have to be 1.

If it was 30, you would see 30K

if it was zero, it wouldn't be there.

The perimeter of the equilateral triangle is 45 meters.

An equilateral triangle is a polygon that has three sides that are of equal length. The sum of angles in an equilateral triangle is 180 degrees. The perimeter of an equilateral triangle  is the distance round the triangle. It can be determined by adding the length of the three sides of the triangle together.

The first step is to determine the side length of the triangle. The base can be determined from the area.

Area of a triangle = 1/2 x base x height

97.5 = 1/2 x 13 x b

b = (97.5 x 2) / 13

b = 15 meters

Perimeter = 15 x 3 = 45 meters

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Answer:

C

Step-by-step explanation:

Answer:

A

number is correct answer