The backyard of a new home is shaped like a trapezoid with a height of 46 ft and bases of 78 ft and 111 ft. What is the cost of putting sod on the​ yard, if the landscaper charges ​$0.21 per square foot for​ sod?

The sod will cost ​$

Answer:

20.5 and 21.5

Step-by-step explanation:

It says 2 significant figures so the least it can possibly be is 0.5 less and the most it can be is 0.5 more as if it was, lets say 20.4 it would round down to 20 not 21.

Answer:

f(x + 2) = - 3x - 1

Step-by-step explanation:

substitute x = x + 2 into f(x) , that is

f(x + 2)

= 5 - 3(x + 2)

= 5 - 3x - 6

= - 3x - 1

Let S be the amount of money the salesperson needs to sell in a week to earn the same amount with the two options. The salesperson earns 40 * $18 = $<<40*18=720>>720 with Option A.

We can set up the following equation to represent the amount of money the salesperson earns with Option B:

0.04S = $720

Solving for S, we find that the salesperson needs to sell $720 / 0.04 = $<<720/0.04=18000>>18,000 to earn the same amount with Option B.

The closest estimate of x when the functions satisfy the condition f(x) = g(x) is 1.65

What is a function?

Function is a mathematical law that establishes the relationship between an independent variable and a dependent variable.

Given,

[tex]f(x) =[/tex] [tex]\log\x_{3} (2x)[/tex]

[tex]g(x) = -4x^{2} + 3x +7[/tex]

Now plotting both the graphs in Desmos, we got the result as in the below figures.

Given f(x) = g(x)

So from the graphs, we can find an intersecting point. This intersecting point is common to both f(x) and g(x)

Therefore from the graph, the closest estimate of x is 1.65.

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As per the following graph, if y = 0,then it makes the horizontal line on graph.

The term graph in math is defined as the visual representation of data or equation.

Here we have given that the value of y = 0.

Here we know that the slope of a horizontal line is zero while the slope of a vertical line is undefined.

Here the following Slopes represent a line's ratio of vertical change to horizontal change.

Whereas horizontal and vertical lines remain constant and never increase or decrease, they're merely straight lines.

Here we have also know that the Horizontal lines have no steepness at all.

Therefore if y=0 is the linear equation to denote the x - axis, then all the points on the x- axis, have their y co-ordinate as 0.

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Answer:

5

Step-by-step explanation:

0-6x will be -6x if we divide that six then we will get -30/-6 since minus gets cancelled we will be left with 5

9514 1404 393

Answer:

  Any of ...

Step-by-step explanation:

The question is asking you what combinations of rotation, reflection, translation, and dilation will make the W have the position, orientation, and size of the M.

The image (M) is the same size as the preimage (W), so no dilation is involved.

The up-down orientation of the image is opposite that of the preimage, so reflection across a horizontal line, or rotation 180° will be involved. Depending on the line of reflection or the center of rotation, translation to the final image position may be required.

The preimage is symmetrical about a vertical centerline, so translation left or right can also be accomplished by reflection about a suitable vertical line.

_____

If you have trouble visualizing this, it can help to cut the letter from a piece of paper and manipulate it to model rotation, reflection, or translation.

The area of a square playground which has a side measures 40metres would be 100[tex]m^2[/tex].

step1

Perimeter of square = 40m

We have given that perimeter of square is 40m. To find its area, we have to calculate its side first.

Perimeter of square = 4× side

Substituting values in formula

Area of square = 4 × side

=> 40 = 4 × side

=> side = 40÷4

=> side = 10m

Side of square is 10m.

step 2

Calculating area of square :

We found that side of square is 10m. To find it area, required formula is:

Area of square = (side)²

To find area, substitute values in formula :-

Substituting values in formula :-

Area of square = (side)²

=> Area of square = (10)²

=> Area of square = 10 × 10

=> Area of square = 100m

so if the perimeter of square is 40m then the area is 100m.

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Answer:

x - 6 = 12 is the answer

im 100% sure

Answer:

x-6=12

Step-by-step explanation:

X=12+6

X=18

substitute for X in the equation

18-6=12

Answer:

12.32 units

Step-by-step explanation:

Use the distance formula to find the lengths between two points:

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

the distance between (-2, -1) and (-5,-1) is

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

=[tex]\sqrt{3^2+0^2}[/tex]

=[tex]\sqrt{9}[/tex]

=3

the distance between (-2, -1) and (-3, -4) is

[tex]\sqrt{(-2-(-3))^2+(-1-(-4))^2}[/tex]

=[tex]\sqrt{1^2+3^2}[/tex]

=[tex]\sqrt{10}[/tex]

≈3.16

the distance between (-6, -4) and (-3, -4) is

[tex]\sqrt{(-6-(-3))^2+(-4-(-4))^2}[/tex]

=[tex]\sqrt{(-3)^2+0^2}[/tex]

=[tex]\sqrt{9}[/tex]

=3

the distance between (-6, -4) and (-5, -1) is

[tex]\sqrt{(-6-(-5))^2+(-4-(-1)^2}[/tex]

=[tex]\sqrt{(-1)^2+3^2}[/tex]

=[tex]\sqrt{10}[/tex]

≈3.16

Now, add all the sides:

3+3.16+3+3.16=12.32 units

Note: A property of a parallelogram is that it has two pairs of congruent sides, so for this problem, you could solve for 2 different sides, double them, then add and you will get the same thing.

Answer: 12 units

Step-by-step explanation:

∴ Area of Square = side length × side length

⇒144 = lengt²

⇒length = √144

⇒length = 12 units ANSWER

hope that helps...

The height of the tree to the nearest hundredth of metres is 2.03 metres.

Emily is 1.65 metres tall. At 3 pm she measure the length of a tree's shadow to be 28.15 metres . She stands 22.9 metres away from the tree, so that the tip of her shadow meet the tip of the tree shadow.

Therefore, the height of the tree to the nearest hundredth of metres can be calculated as follows:

using proportion,

let

x = height of the tree

Therefore,

1.65 / 22.9 = x / 28.15

cross multiply

28.15 × 1.65 = 22.9 × x

22.9x = 46.4475

divide both sides by 22.9

x = 46.4475 / 22.9

x = 2.02827510917

x = 2.03 metres

Therefore,

height of tree = 2.03 metres

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Answer:

258.39 m^2

Step-by-step explanation:

Solve for the rectangle:

18 • 12= 216

Now solve for the 3 semi circles:

A = 3.14(3)^2= 28.26/2 = 14.13 •3 = 42.39

Add up the areas:

216 + 42.39 = 258.39

Answer:

4.472135955

Step-by-step explanation:

Answer:

slope = 2

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (1, 4) ← 2 points on the line

m = [tex]\frac{4-0}{1-(-1)}[/tex] = [tex]\frac{4}{1+1}[/tex] = [tex]\frac{4}{2}[/tex] = 2

Answer: The slope is 2.

Step-by-step explanation: To find the slope of a line, we first need to pick two points on a line. To solve this, I picked points (-2, -2) and (1, 4). The slope is rise over run, so you need to find the rise and run and divide.

We need to go 6 spaces up from (-2, -2) to get to (1, 4). This is our rise. Then, we go 3 spaces to the right. That is our run. 6 / 3 is 2, so that's your slope. Notice that if you cannot divide the rise and run into a whole number, keep it as a fraction instead.

Let me know if this is right! :)

Answer:

minimum value : -1

Step-by-step explanation:

y= 2x^2- |0x+1|

y=2x^2-1

0x has no value they're just putting that in there to trip you up. Also you can view the graph on Desmos graphing calc online to see the minimum value of this function.

x is positive so parabola opens up: meaning minimum value

y-intercept is (0, - 1) so minimum value = -1

Answer:

A) All positive real numbers.

Step-by-step explanation:

Money can only be real numbers/decimals

And because your adding it can't be negative.

Answer:

D

Step-by-step explanation:

This is a real world situation, meaning that there will be no negative amount if weeks, This rules out B and C. As all the numbers are whole, there is no reason for the answer to be all positive real numbers making the answer D.

Answer:

The first two

Step-by-step explanation:

The first two

The bottom equation of the second set is the

bottom equation of the first set multipied by -2

Answer: C

x = Grace's collection

3x = Maci's collection

4 = Kendra's collection

52 = Total collection

Because the total is 52, the equation would be x + 3x + 4 = 52. Add the like terms to get 4x+4=52. Subtract 4 on both sides to get 4x=48. Divide 4 on both sides to get x = 12. Because Maci's collection is 3x, she should have 36 earrings.

0.01 is not the way of expressing the relationship because it does not represent the correct ratio between 10 square and 100 square

A ratio tells the relationship between two or more quantities by comparing their relative sizes.It is typically written as two or more numbers separated by a colon (:), such as 2:4, or expressed as a fraction, such as 2/4. The numbers in a ratio represent the relative amounts of the quantities being compared. A ratio can be used to compare any type of quantity, such as length, weight, or time.

A) 10 square is 1/10th of the area of 100 square. It can be represented as a fraction, where the numerator is the area of the smaller square (10) and the denominator is the area of the larger square (100). The fraction would be 1/10.

B) Another way of expressing the relationship is as a percentage, where the smaller area (10) is divided by the larger area (100), and the result is multiplied by 100 to get the percentage. So 10 square is 10% of 100 square.

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The correct answer is option A. For P= -1/2 0 1/2 1/2 0 -1/2 0 0 1 D= 0 4 0 0 0 4 -1 0 0. The matrix can be diagonalized using the eigenvectors.

To diagonalize the matrix, the eigenvectors must be found first. The eigenvectors can be found by solving the characteristic equation and finding the eigenvalues. The eigenvalues of the matrix are 2 and -1. The eigenvectors associated with each eigenvalue are determined by solving the eigenvalue equation.

The eigenvectors for the matrix are [1, -2], [1, 2], [1, 0], and [0, 1]. After the eigenvectors are found, the matrix can be diagonalized by constructing the transformation matrix P. The transformation matrix P is composed of the normalized eigenvectors. The transformation matrix P is: P=[-1/2, 0, 1/2, 1/2, 0, -1/2, 0, 0, 1], and the diagonal matrix D is composed of the eigenvalues.

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Answer:

Discounted price= $16.1

Step-by-step explanation:

Giving the following information:

Discount rate (d)= 30%

Regular price= $23

To calculate the discounted price, we need to use the following formula:

Discounted price= regular price*(1 - discount rate)

Discounted price= 23*0.7

Discounted price= $16.1

The speed of the object is 9.14 cm per day.

A unit conversion expresses the same property as a different unit of measurement. For instance, time can be expressed in minutes instead of hours, while distance can be converted from miles to kilometers, or feet, or any other measure of length.

Given that, An object is moving at a speed of 3 yards per month. we are asked to express this speed in centimeters per day.

For this, we will have to convert the units,

1 yard = 91.44 cm

3 yards = 91.44 × 3 = 274.32 cm

Therefore, we can say the object is moving 274.32 cm per month

Now,

If it moves 274.32 cm in one month,

Therefore, in day, it will move = 274.32 / 30    [1 month = 30 days]

= 9.144

Hence, the speed of the object is 9.14 cm per day.

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The polynomial 5x³ 4x² 7x has three terms, with the highest degree being 3, which makes the degree of the polynomial 3. The polynomial can be written as 5x³ + 4x² + 7x.

1. Identify the polynomial: 5x³ + 4x² + 7x

2. Count the number of terms: 3

3. Find the highest degree (the largest exponent): 3

4. The degree of the polynomial is 3.

The degree of a polynomial is the highest degree of its terms. A polynomial is a mathematical expression consisting of one or more terms with coefficients and exponents. In this case, the polynomial is 5x³ + 4x² + 7x. This polynomial has three terms, and the highest degree is 3, which makes the degree of the polynomial 3. This means that the largest exponent of the terms is 3. To calculate the degree of a polynomial, simply count the number of terms and identify the highest degree, which is the largest exponent. If the polynomial has only one term, then the degree is the exponent of that term

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The two examples of the solution are sugar water, and soda water.

The term solution is defined as a homogeneous mixture of two or more components in which the particle size is smaller than 1 nm.

Here according to the definition of solution, here we know that Common examples of solutions are sugar in water and salt in water solutions, soda water, etc.

As we all know that the solutions have two components, one is solvent and the other is solute.

Here the components, that is the component that dissolves the other component is called the solvent where as the component(s) that is/are dissolved in the solvent is/are called solute(s).

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The answer is 4cd/3b

hope it's correct

For adults, there were 40 tickets sold, and for kids, there were 60 tickets sold.

There are several laws that regulate the sequence in which you should do the operations in math and algebra. The Commutative, Associative, and Distributive Laws are the three that are most frequently discussed.

Let x be the total number of adult tickets sold.

6.50 × x + 2.50 × (100 - x) = 410

6.50 × x + 250 - 2.50x = 410

4x = 410 - 250

x = 40

Hence,

a) 40 tickets were sold by adults, according to item

and

b) 100-40=60 tickets were sold to children.

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The multiplicative inverse of 7/5 is 5/7 using the formula of multiplicative inverse like (x)^-1 which equals to 1/x.

let's try to learn what is multiplicative inverse.

1/N or [tex]N^-1[/tex] is used to denote a number's multiplicative inverse, such as the number N. From the Latin word "reciprocus," it is also known as reciprocal. Inverse refers to something that is the opposite. The acquired reciprocal of a number is such that its value equals identity 1 when multiplied by the original number. In other terms, it is a technique for producing identity 1 by diluting a number by itself, as in N/N = 1.

One is obtained when a number is multiplied by its own multiplicative inverse.

When a number is multiplied by its original number, the multiplicative inverse of that number, or x^-1, produces a value equal to 1. The multiplicative inverse of 2, for instance, is 2^-1 since it fulfils the formula: 2 x (2^-1) = 2 x (1/2) = 1.It is also known as a number's reciprocal.

Multiplicative inverse of 7/5 is (7/5)^-1 = 1/(7/5) = 5/7.

Given question is incomplete complete question here:

What is the multiplicative inverse of 7/5?

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Check the picture below.

[tex]\sin(30^o)=\cfrac{\stackrel{opposite}{PQ}}{\underset{hypotenuse}{4}}\implies 4\sin(30^o)=PQ\implies 4\left( \cfrac{1}{2} \right)=PQ\implies 2=PQ[/tex]