A community is building a square garden with a walkway around the perimeter with the design shown at the right. Find the side length of the inner square that would make the area of the inner square equal to 75% of the total area of the garden. Round to the nearest tenth of a foot.

1. What is an expression for the area of the inner square?



2. What is the area of the entire garden?



3. What is 75% of the area of the entire garden?



4. Write an equation for the area of the inner square using the expressions from Steps 1 and 3.



5. Solve the quadratic equation. Round to the nearest tenth of a foot.



6. Which solution to the quadratic equation best describes the side length of the inner square? Explain.

Answer:

The ratio would be 1:2 my guy,if you're trying to triple the size, 1:3 if your trying to quadruple the size, it'd be 1:4, etc, etc

Answer:

Part 1) The measure of angle C is [tex]62\°[/tex]

Part 2) The measure of angle AOB is [tex]56\°[/tex]

Step-by-step explanation:

step 1

Find the measure of angle C

we know that

The inscribed angle measures half that of the arc comprising

so

[tex]m<C=\frac{1}{2}(arc\ AD)[/tex]

we have

[tex]arc\ AD=124\°[/tex]

substitute

[tex]m<C=\frac{1}{2}(124\°)=62\°[/tex]

step 2

Find the measure of angle AOB

we know that

In the isosceles triangle  ODC

∠D=∠C=62°

Remember that

The sum of the internal angles of a triangle must be equal to 180 degrees

so

∠D+∠C+∠DOC=180°

substitute the values

62°+62°+∠DOC=180°

∠DOC=180°-124°=56°

we have that

∠AOB=∠DOC -----> by vertical angles

so

∠AOB=56°

Answer:

a. number of periods over which interest is calculated on the loan

Step-by-step explanation:

A formula should always be accompanied by an explanation of what it calculates and the meaning of each of its variables. This formula calculates P, the periodic payment on a loan of n periods at interest rate i (compounded) per period. The principal amount of the loan is PV.

___

The same formula can also be used to calculate an annuity from which payment P is received at the end of each of n periods. The amount invested is PV and the interest rate per period (compounded per period) is i.

'n' typically represents the number of periods over which interest is calculated in a loan. However, symbols' intended meanings can change depending upon the context.

In most financial and mathematical formulas, the symbol 'n' typically represents the number of periods over which interest is calculated on a loan. It's relevant to note that these periods could be months, years, or any other agreed-upon timeframe. Hence, the correct answer to your question is (a).

However, it's important to state that the representation of variables can change with different contexts. In some scenarios, 'n' could be used to denote the number of years it will take to pay the loan back, but that is not as common as using 'n' for the number of periods.

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To calculate how many cups of flour Genise will need for 2 1/2 batches, multiply the amount of flour for one batch (1 1/2 cups) by the number of batches (2 1/2). This results in 3 3/4 cups of flour needed.

To find how many cups of flour Genise will need, we start by writing an equation that reflects the amount of flour needed for one batch times the number of batches she plans to make. Since she needs 1 1/2 cups of flour for one batch and she wants to make 2 1/2 batches, we set up the multiplication:

flour_needed = (cups of flour per batch) * (number of batches)

So the equation will be:

flour_needed = 1 1/2 * 2 1/2

Converting mixed numbers to improper fractions for easier multiplication, we have:

flour_needed = 3/2 * 5/2 = 15/4 cups

Then, we convert the improper fraction back to a mixed number, which is:

flour_needed = 3 3/4 cups of flour

Answer:

how many cups are needed for the recipe

Step-by-step explanation:

Answer:

ok what is tthe question

Step-by-step explanation:

Answer:

less than

Step-by-step explanation:

The multiplying fraction (5/7) is less than 1 so its product with 6 will be less than 6.

___

5/7·6 = 30/7 = 4 2/7 < 6

The expression 5/7×6 results in a value that is less than 6. This is because the value of 5/7 is less than 1, and multiplying it by 6 gives a result that is consequently less than 6.

To determine whether 5/7×6 is less than, greater than, or equal to 6, we perform the multiplication. Multiplying 5/7 by 6 can be viewed as 5 multiplied by 6, which equals 30, and then that result divided by 7. So the calculation is 30÷7, which equals approximately 4.29. Since 4.29 is less than 6, we can conclude that 5/7×6 is less than 6.

When solving mathematical problems involving multiplication and fractions, it's important to eliminate terms wherever possible to simplify the algebra and to check the answer to see if it is reasonable. Comparing the original fraction to 1 before the multiplication can help us understand whether the result will be greater or less than the number we're multiplying. In this case, since 5/7 is less than 1, multiplying it by 6 will give a result that is less than the original number, which is 6.

Answer:

True, True , False , False , False

Step-by-step explanation:

Let us see the correction for the rest of the three False Statements

3) p→q represent the original conditional statement.

4) ~q → ~p represents the contrapositive of the original conditional statement

5) contrapositive of the original conditional statement will be ~q → ~p

There is one more implication called Converse of the original conditional statement . It is represented as q→p

I think it a but I sorry if it wrong

Answer:

1

Step-by-step explanation:

Add the square of half the x coefficient: (-2/2)^2 = 1.

Answer:

a= 84.83

Step-by-step explanation:

so remember this: my teacher taught me this amazing strategy to remember the formulas

C=πd : cherry pie delicious

a=πr² : apple pie are too

and to find the area of the saded area, we need to find the area of the big circle and subtract that by the smaller circle area.

so, area of the big circle:

fill in the variables for a=πr²

you get: a=π6²

follow the pemdas, the order of operations. now on the state test don't write pemdas as your answer because people are stupid and they dont take that answer

you do the exponent first then multiply by pie.

you get: 6²=36

36xπ=113.09733552923255658465516179806

round that answer to the nearest tenths and get: 113.1

now time to find the area of the smaller circle!!!

fill in a=πr² and get: a=π3²

its not 6 this time because that was the radius for the bigger circle. the smaller circles radius is half the size as the bigger circle so divide that by two and get 3.

now solve:

a=π3²

a=π9

a=28.274333882308139146163790449516

round and get: 28.27

now subtract the the bigger circles area and the smaller circles area:

113.1 is the bigger circles area

28.27 is the smaller circles area.

113.1 - 28.27 = 84.83

a=84.83

plz give me brainliesttt

Answer:

23-5≥3.25n

18≥3.25n

Answer:

How many solution does ++=11

x

+

y

+

z

=

11

have where ,,

x

,

y

,

z

are non-negative integers. In light of the restrictions, its clear that ,,∈{0,1,2,..11}

x

,

y

,

z

∈

{

0

,

1

,

2

,

.

.11

}

. So, at face value I would assign a value for

x

and determine the different combinations that

y

and

z

can hold. For example,

For =0

x

=

0

, we have +=11

y

+

z

=

11

. With writing them out I found that there are 12

12

different assigned combinations for

y

and

z

that satisfy the equation. For =1

x

=

1

, I got 11

11

. Consequently, the pattern becomes clear whereby each one takes a value less by one. Hence, the number of solutions is 1+2+3+4+5+6+7..+12=78

1

+

2

+

3

+

4

+

5

+

6

+

7..

+

12

=

78

. I was wondering if there is an easier method perhaps with combinations equation (,)

C

(

a

,

b

)

..?

Step-by-step explanation:

Answer:

Step-by-step explanation:

The Law of Sines is helpful when you know one side and its opposite angle.

  a/sin(A) = b/sin(B) = c/sin(C)

Rearranging gives you ...

  B = arcsin(b/a·sin(A)) = arcsin(105/109·sin(70°)) ≈ 64.85138°

  C = 180° -B -A = 45.14862°

  c = a·sin(C)/sin(A) ≈ 82.23360

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Comment on the solution method

You can use the Law of Cosines if you like. The formulation would be ...

  a² = b² + c² -2bc·cos(A) . . . . where a, b, and A are known

This gives a quadratic in c, the positive solution being the answer you're looking for. Then, either the law of sines or the law of cosines can be used to find one of the other two angles.

  c = 105·cos[70°] + √[856 + 11025·cos[70°]²]

  c ≈ 82.2336

Answer:

  [-1, 7]

Step-by-step explanation:

If you mean ...

  y = 4sin(2x) +3

then you can substitute the range of the sine function into the equation and evaluate it to find the range of y.

The range of sin( ) is [-1, 1], so the range of y is ...

  4[-1, 1] +3 = [4(-1)+3, 4(1)+3] = [-1, 7]

_____

Comment on the problem statement

The range of y = 4sin²(x)+3 will be different, and the range of 4sin(2x+3) will be different yet. It is usually a good idea to use parentheses around function arguments.

Answer:

-1,7

Step-by-step explanation:

got it right on odessyware

Answer:

see below

Step-by-step explanation:

If the left-side tiles are numbered 1–7 from top to bottom, their order on the right is ...

7 — denominators factored

6 — common factors canceled

5 — make the left side have the same denominator as the right

3 — express the sum over the common denominator

2 — collect numerator terms

Answer:

  C.  0.366

Step-by-step explanation:

In this stemplot, it is apparent that the number on the right is the least-significant digit (thousandths digit) of the batting average. The two most-significant digits are to the left of the vertical line.

Hence the value 0.36 | 6 represents an average that is 36 hundredths plus 6 thousandths: 0.366.

The initial yield of potatoes per acre was 14 tons and after the introduction of the new technology, the yield increased to 18 tons. Therefore, 5600 tons were collected before the technological advances and 7200 tons were collected after.

This problem involves understanding linear equations. Let's denote the initial yield of potatoes per acre as 'x' tons and the yield after the introduction of the new technology as 'y' tons.

It's given that technological advances increase the yield by 4 tons, so we have the equation: y = x + 4. The problem also states that from a 320 acre field 640 more tons were collected than before from a 400-acre field. So, we can write it as: 320y = 400x + 640.

Solve these two equations to find the values of x and y. The initial yield of potatoes per acre (x) was 14 tons while the yield after the introduction of the new technology (y) was 18 tons. Therefore, 5600 tons of potatoes were collected before the technological advances and 7200 tons were collected after.

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Before the new methods were introduced, 640 tons of potatoes were collected. After the introduction of the new technology, 0 tons were collected.

To solve this problem, let's assume x is the number of tons of potatoes collected before the new methods were introduced, and y is the number of tons collected after the introduction of the new technology.

According to the given information, the new technology increased the crop of potatoes from 1 acre by 4 tons, so the increase in yield per acre is 4 tons.

From a field of 320 acres, 640 tons more were collected than before from a field of 400 acres. This means that the increase in yield from the reduced field of 320 acres is twice the increase in yield from the initial field of 400 acres.

Setting up the equation, we have:

(y - x) = 2(4)(320 - 400)

(y - x) = 2(4)(-80)

(y - x) = -640

We also know that the total increase in yield is 640 tons, so we have:

x + y = 640

To solve these equations, we can use substitution or elimination method. Solving for x in the second equation, we get:

x = 640 - y

Substituting x in the first equation, we have:

(y - (640 - y)) = -640

2y - 640 = -640

2y = 0

y = 0

Substituting y in the equation x + y = 640, we get:

x + 0 = 640

x = 640

Therefore, before the new methods were introduced, 640 tons of potatoes were collected, and after the introduction of the new technology, 0 tons were collected.

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Answer:

  c). a reflection across the x-axis followed by a translation of 1 unit right and 1 unit down

Step-by-step explanation:

You want to know the transformations that map ΔABC onto ΔDEF.

The answer choices would ask us to consider some combination of the following transformations:

We can apply these relations to the answer choices to see if they provide the desired mapping ...

a) Reflection across the y-axis, translation (1, 2)

  A(-4, 1) ⇒ A'(4, 1) . . . reflection

  A'(4, 1) ⇒ D(4+1, 1+2) = D(5, 3) . . . . not the correct point

b) Rotation CW 90°, translation (4, 4)

  A(-4, 1) ⇒ A'(1, 4) . . . rotation 90° CW

  A'(1, 4) ⇒ D(1+4, 4+4) = D(5, 8) . . . . not the correct point

c) Reflection across the x-axis, translation (1, -1)

  A(-4, 1) ⇒ A'(-4, -1) . . . reflection

  A'(-4, -1) ⇒ D(-4+1, -1+(-1)) = D(-3, -2) . . . . the correct location of D

d) Reflection across y=x, rotation CCW 270°

  A(-4, 1) ⇒ A'(1, -4) . . . reflection

  A'(1, -4) ⇒ D(-4, -1) . . . . not the correct point

The correct series of transformations is reflection across the x-axis followed by translation 1 right and 1 down.

Answer:

(x, y, z) = (-2, -1, 2)

Step-by-step explanation:

Your graphing calculator can usually solve systems of linear equations easily.

Answer:

y =  [4(x-3)]/3

Step-by-step explanation:

4x = 12+3y

3y = 4x-12

y =  [4(x-3)]/3

Best regards

The truck cannot drive under the archway since it is taller than the highest point of the archway.

To determine if a truck can drive under the semielliptic archway without going into the other lane, we need to compare the height and width of the truck to the height and width of the archway. The truck has a height of 12 feet and a width of 14 feet. The highest point of the archway is at its center, which is 15 feet high. So, the truck will not fit under the archway since it is taller than the highest point of the archway.

Step-by-step explanation:

Look at the picture.

A' - The complement of a set is the set of all elements in the given universal set U that are not in A.

B - A - The set difference of sets A and B is the set of all elements in A that are not in B.

A ∩ B - The intersection of sets A and B is the set of all distinct elements that are in both A and B.

16. The first attachment shows a table of the given values and the function evaluated at those points.

___

17. The cost function for this problem is an expression of the total cost as a function of number of days open:

  c(x, y) = 40x + 50y

The system of inequalities expresses the constraints on delivery of glass and aluminum in terms of the number of days open:

To minimize costs, Center 1 should be open 6 15/16 days; Center 2 should be open 5 11/16 days. The cost function is minimized when it goes through the vertex of the feasible region that puts it closest to the origin.

___

18. (a) Jane can use the revenue function ...

  r(x, y) = 120x +70y

(b) The constraints on hours and numbers of visits are ...

(c) For the given vertices, Jane's best choice is (4, 7), which will produce $970 in revenue for the office.

As is sometimes the case, the integer vertex closest to the corner of the feasible region is not the one that maximizes revenue. Jane's best choice is not on the problem's list. It is (5, 6), which will produce $1020 in revenue.

See the second attachment for the graph related to the problem.

_____

Apology

The graphs are out of order because my first attempt at 17 had an error. The corrected graph was added as the last attachment.

_____

Steps

In all of these linear programming problems, the "objective function" is the function of the problem variables that you want to maximize or minimize. In order to write it, you need to understand what the problem variables are and how they relate to the objective. In each of these problems, you are told what x and y stand for and their relation to the objective.

When considering the constraints, you must consider how the problem variables relate to any limits imposed. As in problem 17, sometimes the limits are minima (must deliver at least ...). In problem 18, the limits are maxima (8 hours in a day; no more than 7 follow-ups).

So, first read and understand the problem statement and the relationships it is telling you. Then, do what the problem asks you to do. Sometimes that will involve finding a solution; sometimes not.

Often, you can use logic to help you understand whether your solution is reasonable. In the doctor problem (18), the doctor makes more money per hour doing follow-ups, so would probably want to maximize those (4, 7). However, doing that leaves a half-hour with zero revenue. That last hour is better spent seeing a new patient ($120) than seeing only one follow-up patient ($70).

Answer:

B

Step-by-step explanation:

Theta is found using the sin-1 function. Start off with the sin of theta.

sin(theta) = opposite over hypotenuse.

sin(theta) = 3/8 = 0.375

Theta = Sin-1 (0.375)

Theta = 22.02 degrees.

Answer: B

Answer:

The equation of the perpendicular bisector is  2x + 3y - 3 = 0

Step-by-step explanation:

* How to find the equation of a line from two points (x1 , y1)

 and (x2 , y2) lie on it

- Find the slope of the line using the rule

 The slope (m) = (y2 - y1)/(x2 - x1)

- Use the rule of the equation y - y1 = m (x - x1), where m is

 the slope of the line and (x1 , y1) is a point on the line

* Remember if two line are perpendicular, then the product of

 their slopes = -1, that means one of them is an additive inverse

 and multiplicative inverse to the other

 # Ex: if the slope of a line is a/b, then the slope of the

   perpendicular to it is -b/a

* Now lets read the problem, we need the equation of the

 perpendicular bisector to the line that passes through the

 points (2 , 4) and (-2 , -2)

- Find the slope of the line in the graph by using the given points

 # m = (-2 - 4)/(-2 - 2) = -6/-4 = 3/2

∴ The slope of the perpendicular line = -2/3 ⇒ multiplicative

   inverse and additive inverse of it

* Bisector means intersect it in the mid-point of the given line

- The rule of the mid-point is [(x1 + x2)/2 , (y1 + y2)/2]

∴ The mid-point of the line is [(2 + -2)/2 , (4 + -2)/2] = (0 , 1)

* Now we have the slope and a point on the line, to find the

 equation of the perpendicular bisector its slope is -2/3 and

 a point (0 , 1)

∴ The equation: y - 1 = -2/3 (x - 0)

  The equation : y - 1 = -2/3 x ⇒ Multiply both sides by 3

  The equation : 3y - 3 = -2x ⇒ collect x , y in the same side

  The equation : 2x + 3y - 3 = 0

* The equation of the perpendicular bisector is  2x + 3y - 3 = 0

Answer:3/2

Step-by-step explanation:

Answer:

  56 photos per page

Step-by-step explanation:

1344 photos/(24 pages) = 1344/24 photos/page = 56 photos per page

Answer:

i need points to ask my question

Step-by-step explanation:

Answer:  [tex]\bold{\dfrac{1}{5}}[/tex]

Step-by-step explanation:

[tex]\dfrac{DF}{AK}=\dfrac{4}{20}=\large\boxed{\dfrac{1}{5}}[/tex]

The surface area of a cylinder is given by

[tex]A_A = 2\pi rh[/tex]

which is the surface area of cylinder A.

To compute the surface area of cylinder B, we have to map [tex](r,h)\mapsto (2r, 2h)[/tex] and we have the following formula

[tex]A_B = 2\pi(2r)(2h)[/tex]

If we manipulate the second expression, we have

[tex] A_B = 8\pi rh[/tex]

Which implies

[tex]\dfrac{A_B}{A_A} = \dfrac{8\pi rh}{2\pi rh} = 4 [/tex]

Answer:

  (x^(11/4))(y^(5/9))

Step-by-step explanation:

The applicable rules of exponents are ...

  (x^a)(x^b) = x^(a+b)

  (x^a)/(x^b) = x^(a-b) . . . . . no surprise, since 1/x^b = x^-b

_____

Your expression simplifies to ...

  x^((5/4) -(-5/4) -(-1/4)) · y^((1/18) -(-1/2))

  = x^(5/4 +5/4 +1/4) · y^(1/18 +1/2)

  = x^(11/4) · y^(1/18 +9/18)

  = x^(11/4) · y^(5/9)