A doghouse is to be built in the shape of a right trapezoid, as shown below. What is the area of the doghouse?

A right trapezoid with top side 7 feet and height 7 feet. The bottom side is extended to the right with 5 more feet.


a
45.5 square feet
b
63 square feet
c
66.5 square feet
d
84 square feet

Answer:

a(-2.6) b(5, 0) c(9,5)

Step-by-step explanation:

the rule is x+1 y+2 for each of the vertices

Answer:

D.Z

u see how they have line in between as well, shows that they are going by 5 so 2.0 and then 2.5

and if it was asking for -2.5 which is negative two point five, you would choose A.U

We are given the expression;

To write this as an exponent we shall simolify as follows;

We now have;

To write this without exponents, would mean to multiply it all out in its actual form which is;

Note that

ANSWER:

Answer:

y = -2

Step-by-step explanation:

When you see a horizontal line like this, it will always be " Y = something".

When you see a vertical line, it will always be "X = something".

You can see what that number will be by looking at where it crosses the X or Y axis!

9514 1404 393

Answer:

  $2310

Step-by-step explanation:

The employee will pay 4.2% × $55,000 = $2310.

Answer:

I don't know sorry for your right question ok

Solution

Let the number be represented by x

Now, solve x

The final answer

The number is 3

After answering the presented question, we can conclude that as a function result, the sphere's radius to the closest foot is \(6 feet.\)

In mathematics, a function appears to be a link between two sets of numbers in which each member of the first set (known as the domain) corresponds to a specific member of the second set (called the range). In other words, a function takes input from one collection and creates output from another. The variable x has frequently been used to represent inputs, whereas the variable y has been used to represent outputs. A formula or a graph can be used to represent a function. For example, the formula \(y = 2x + 1\) depicts a functional form in which each value of x generates a unique value of y.

The volume of a sphere is calculated as follows:

\(V = (4/3)\pi r^{3}\)

Where V is the volume of the sphere and r is its radius.

The volume of the sphere is supplied to us as \(904.32 ft^{3}\) and we are requested to find the radius to the closest foot. Hence we can rearrange the equations to find r:

\(r^{3} = (3V/4\pi )\\r= \sqrt[3]{3V/4\pi }\)

When we substitute the provided values, we get:

\(r= \sqrt[3]{3*904.32/4*3.14} \\r= \sqrt[3]{2712.96/12.56} \\r=\sqrt[3]{216}\\ r= 6 ft\)

As a result, the sphere's radius to the closest foot is 6 feet.

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Answer:

\(4x+6\) units

Step-by-step explanation:

Skills needed to solve: Order of Operations, Distributive Property, Perimeter Formula, Like Terms

1) To solve this problem, you need to understand the perimeter formula, and that is:

--> \(P = 2(L+W)\)

P = Perimeter

L = Length

W = Width

2) Based on that, we are given that:

\(L = x\) (since the length is x)

\(W = x+3\) (since the width is x+3)

3) After that, we substitute in the values:

\(P = 2(L+W)\)

\(P = 2(x+(x+3))\)

\(x + (x+3) = x+x+3 = 2x+3\) (with like terms and addition)

so: \(P=2(2x+3)\)

Use distributive property, which is \(a(b+c) = ab+ac\)

get: \(2(2x+3) = 2(2x) + 2(3)\)

\(2(2x) = 4x\)

\(2(3) = 6\)

So: \(P = 4x+6\)

Hope this helps and have a nice day!! :) :]

Answer:

638 in.²

Step-by-step explanation:

Assuming you need to cover just the surface area of the box with no overlaps, and the shape is a rectangular prism, then you need to find the surface area of a rectangular prism.

SA = PH + 2LW

where

P = perimeter of base = 2(L + W),

H = height of prism

L = length of base

W = width of base

SA = 2(16 + 7)(9) + 2(16)(7)

SA = 638

Answer:

Step-by-step explanation:

B=CD-A

By analyzing the graph and evaluating the objective function at each vertex of the feasible region, we can find the optimal solution, which is the vertex that maximizes the objective function z = 3x + y.

To find the optimal solution of the given problem using the graphical method, we need to plot the feasible region determined by the given constraints and then identify the point within that region that maximizes the objective function.

Let's start by graphing the constraints:

1. Plot the line 2x - y = 5. To do this, find two points on the line by setting x = 0 and solving for y, and setting y = 0 and solving for x. Connect the two points to draw the line.

2. Plot the line -x + 3y = 6 using a similar process.

3. The x-axis and y-axis represent the constraints x ≥ 0 and y ≥ 0, respectively.

Next, identify the feasible region, which is the region where all the constraints are satisfied. This region will be the intersection of the shaded regions determined by each constraint.

Finally, we need to identify the point within the feasible region that maximizes the objective function z = 3x + y. The optimal solution will be the vertex of the feasible region that gives the highest value for the objective function. This can be determined by evaluating the objective function at each vertex and comparing the values.

Note: Without a specific graph or additional information, it is not possible to provide the precise coordinates of the optimal solution in this case.

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Solution

8x + 2y = 6

=> 2y = 6 - 8x

Dividing both sides by 2

=> y = 3 - 4x

Hence,

a = -4, b = 3

The figure is indeed symmetric and the number of lines of symmetry the snowflake has is C. Yes; 6 lines of symmetry.

Generally a snowflake is hexagonal and has 6-way radial symmetry. Thus, one can rotate it 60 degrees (the sixth of full rotation) and it still appears the same.

So, overall, this means that a snowflake holds 6 lines of symmetry which divide it into two identical halves reflecting each other. Consequently, it can be rotated in 60-degree increments and still holds identicality. Akin to this final property, the snowflake artifact possesses six uniquely divided

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Answer:

1. -x + y = 3

m=  1

b=  3

2. -4x + 2y = 6

m=  2

b= 3

Step-by-step explanation:

Slope intercept is form to write equation for straight line.

It is represented as  y = mx+ b

where m is the slope of line

B is the y intercept (pint on y axis where the line crosses y axis)

________________________________________________

Given

1. -x + y = 3  

we need to convert this line in form of y = mx+ b

-x + y = 3

to do this we have to move - x from LHS to RHS

it can be done by adding both side +x which will eleminate -x from LHS

-x + y + x = 3 + X

=>y = 3 + x

=> y = x +c

Thus comparing it with slope form line: y = mx+ b

m =1

b = 3

__________________________________________________

Given

1. -4x + 2y = 6  

we need to convert this line in form of y = mx+ b

-4x + 2y = 6

to do this we have to move + 4x from LHS to RHS

it can be done by adding both side +4x which will eleminate -4x from LHS

-4x + 2y + 4x= 6 +4x

=>2y =6 +4x

Now we have to remove 2 from 2y =6 +4x

To do this we divide both side by 2 . now we have equation

=>  2y/2 =(6 +4x)/ 2 = 6/2 + 4x/2

=> y = 3 + 2x

Thus comparing it with slope form line:  y = mx+ b

m = 2

b = 3

__________________________________

Third part has 2x + =3 has y missing

it can be solved similarly.

say in place of y we have my where m is coefficient of y

2x + my =3

to do this we have to move + 2x from LHS to RHS

it can be done by subtracting -2x from both side  which will eleminate 2x from LHS

2x + my -2x =3 -2x

=>my =3 -2x

Now we have to remove m from my =3 -2x

To do this we divide both side by m . now we have equation

=>  my/m =(3 -2x)/ m = 3/m -2x/m

=> y = 3/m - 2x/m

Thus comparing it with slope form line:  y = mx+ b

m = -2/m

b = 3/m

The graph of the given line is attached below.

We are given the line:-

y = (3/5)x - 4

We will find the x and y intercepts of the line to plot in the graph.

As the equation is already in the slope intercept form, we can write,

The y-intercept of the line is -4.

Hence, the coordinates of the point will be (0,-4).

To find the x - intercept of the line we will put y = 0 in the given line.

0 = (3/5)x - 4

4 = 3x/5

x = 20/3

The coordinates of the point will be (20/3,0).

We can plot these points to get the desired graph.

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Answer:

Jemma: 22x + 5

Debra: 20x

Step-by-step explanation:

Answer:

the answer is 3

Step-by-step explanation:

The most appropriate choice of percentage will be given by-

The store have to increase the price of the item by \(11\frac{1}{9}\) %  in order to sell it for the original amount.

What is Percentage?

Percentage is a ratio expressed as a percentage of 100.

Let the original price be x

Percentage decrease in price due to sale = 10%

Decrease in price due to sale = \(\frac{10}{100} \times x\)

                                                  = \(\frac{x}{10}\)

New price = (\(x - \frac{x}{10}\))

                 = \(\frac{10x-x} {10}\)

                 = \(\frac{9x}{10}\)

Now,

Increase in price from \(\frac{9x}{10}\) to \(x\) = \(\frac{x}{10}\)

Percentage by which the store have to increase the price of the item in order to sell it for the original amount =

                                                                  \(\frac{\frac{x}{10} }{\frac{9x}{10} } \times 100\)

                                                              =\(\frac{x}{10} \times \frac{10}{9x} \times 100\)

                                                              = \(\frac{100}{9}\)

                                                              = \(11\frac{1}{9}\) %

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Both g(x) = 5 - x² and h(x) = \(5 - e^(6-^x^)\)have the same range as f(x) = -2√(x) - 3 + 8, which is (-∞, 5].

To determine which function has the same range as f(x) = -2√(x) - 3 + 8, we need to first find the range of f(x).

The square root function √(x) takes non-negative values as input and gives non-negative outputs, so the expression -2√(x) will always be non-positive. Therefore, the range of f(x) will be all real numbers less than or equal to -3 + 8, which is 5.

In other words, the range of f(x) is (-∞, 5].

So, we need to find a function whose range is also (-∞, 5]. One possible function is g(x) = 5 - x². We can see that when x is zero, g(x) is at its maximum value of 5, and as we increase or decrease x, g(x) will decrease, eventually approaching negative infinity.

Another possible function is h(x) = 5 - e^(-x). When x is negative infinity, e^(-x) is approaching positive infinity, so h(x) is approaching 0. As we increase x, e^(-x) is approaching zero, so h(x) is approaching 5.

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Answer:

$215.92

Step-by-step explanation:

Answer:

correct order=

Step-by-step explanation:

The degree of the polynomial is 14

The polynomial is given as:

y^2+7x^14-10x^2

Here, we assume that the variable of the polynomial is x

The highest power of x in the polynomial y^2+7x^14-10x^2 is 14

Hence, the degree of the polynomial is 14

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Answer:

The problem is clearly solved in the attachment

Answer:

a. Group 1 and 2

b. 6 people

Step-by-step explanation:

(a) So the "fishing adventures" company rents max. 1200lbs boats for 150lbs people. 10lbs gear for everyone, 200 for the boat.

1. 150+10=160 (everyone will in total be 160lbs)

2. 1200-200=1000 (for the gear)

3. 1000/160=6.25 (6 people can rent a boat---don't cut anybody and 7 people would cause overload!)
4. Group 1 and 2 can rent because they all have less than 6 people!

(b)

It's already been answered! (see above underlined portion).

6 people max can rent a boat!

I hope this helps <3

Whatever I am, I'm not a genius XD

~CR~

The equivalent ratio of 1.25 : 3.75 : 7.5 is 5 : 15 : 30.

To calculate the equivalent ratio of 1.25 : 3.75 : 7.5, we need to find a common multiplier that can be applied to all the numbers in the ratio to make them whole numbers. In this case, the common multiplier is 4 because it can be multiplied to each number to eliminate the decimals.

By multiplying each number in the ratio by 4, we get:

1.25 * 4 = 5

3.75 * 4 = 15

7.5 * 4 = 30

So the equivalent ratio of 1.25 : 3.75 : 7.5 is 5 : 15 : 30.

This means that the relative sizes or quantities represented by the original ratio are maintained in the equivalent ratio. For example, if we had 1.25 units of something, it would be equivalent to 5 units in the new ratio, and if we had 7.5 units, it would be equivalent to 30 units in the new ratio.

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Answer: k=3

Step-by-step explanation:

To solve for k, you want to isolate k.

\(\frac{2}{5} (5k+35)-8=12\)            [add both sides by 8]

\(\frac{2}{5} (5k+35)=20\)                  [multiply both sides by 5/2]

\(5k+35=50\)                       [subtract both sides by 35]

\(5k=15\)                               [divide both sides by 5]

\(k=3\)

Now, we know that k=3.

Answer:

1808.64 IN^3

Step-by-step explanation:

Helium needed = volume of spherical shaped ice cream + volume of cone

Volume of a sphere = 4/3 x pi x r^3

4/3 x 3.14 x 6^3 = 904.32 ft^3

Volume of a cone 1/3 x (nr^2h)

n = 22/7

r = radius  = 12/2 = 6

the diameter is the straight line that passes through the centre of a circle and touches the two edges of the circle.

h = height

1/3 x 3.14 x 6^2 x 24 = 904.32

helium needed = 2 x 904.32 = 1808.64 in^3