HELPP


You want to enclose a rectangular region with an area of
1200 square feet and a length of 40 feet, 50 feet, or 60 feet.
Find the perimeter for each possible region. Explain why
you might rewrite the area formula to find the solutions.

This relationship is not true.

[tex]1 + \sec^2(x) = 1 + (1 - \tan^2(x)) = 2 - \tan^2(x)[/tex]

and

[tex]\cot^2(x) = \dfrac1{\tan^2(x)}[/tex]

Rewrite the equation in terms of only tangent.

[tex]2 - \tan^2(x) = \dfrac1{\tan^2(x)} \iff \tan^4(x) - 2\tan^2(x) + 1 = 0[/tex]

Factorize the left side.

[tex]\left(\tan^2(x) - 1\right)^2 = 0[/tex]

Solve for [tex]\tan(x)[/tex].

[tex]\tan^2(x) - 1 = 0[/tex]

[tex]\tan^2(x) = 1[/tex]

[tex]\tan(x) = \pm 1[/tex]

[tex]x = \pm\tan^{-1}(1) + n\pi = \pm\dfrac\pi4 + n\pi[/tex]

where [tex]n[/tex] is an integer. That is, the equation only holds for certain values of [tex]x[/tex], as opposed to all [tex]x[/tex], so it's not an identity.

The minuend and the subtrahend of 696 - 275 can be decomposed to give;

600 + 90 + 6

-

200 + 70 + 5

400 + 20 + 1

The decomposition into place values is chosen because of ease of reinforcing knowledge.

The decomposition method of subtraction involves decomposing the subtrahend, which is the smaller number and the place value of the numbers can be simply subtracted from the minuend.

In the subtraction, 696 - 275, the minuend is 696, while the subtrahend is 275.

Decomposing the subtrahend, gives;

275 = 200 + 70 + 5

Decomposing the minuend, gives;

696 = 600 + 90 + 6

The subtraction expression in the question, 696 - 275 gives;

696

-275

The above can therefore be decomposed as follows;

600 + 90 + 6

-

200 + 70 + 5

400 + 20 + 1

400 + 20 + 1 = 421

Therefore;

696 - 275 = 421

The reason the decomposition into place values of each digit is chosen is so as to make use of the easier understanding of subtracting numbers that are multiples of 10.

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Answer: 53.44

Step-by-step explanation:

Answer:

53.4 repeating

Step-by-step explanation:

Step 1:Start by setting it up with the divisor 9 on the left side and the dividend 481 on the right side like this:         9⟌481

Step 2:The divisor (9) goes into the first digit of the dividend (4), 0 time(s). Therefore, put 0 on top:    0    9⟌481

Step 3:Multiply the divisor by the result in the previous step (9 x 0 = 0) and write that answer below the dividend.     0    9⟌481   0  

Step 4:Subtract the result in the previous step from the first digit of the dividend (4 - 0 = 4) and write the answer below.     0    9⟌481   -0      4  

Step 5:Move down the 2nd digit of the dividend (8) like this:    0    9⟌481   -0      48 

Step 6:The divisor (9) goes into the bottom number (48), 5 time(s). Therefore, put 5 on top:    05   9⟌481   -0      48 

Step 7:Multiply the divisor by the result in the previous step (9 x 5 = 45) and write that answer at the bottom:    05   9⟌481   -0      48     45 

Step 8:Subtract the result in the previous step from the number written above it. (48 - 45 = 3) and write the answer at the bottom.    05   9⟌481   -0      48    -45      3 

Step 9:Move down the last digit of the dividend (1) like this:    05   9⟌481   -0      48    -45      31

Step 10:The divisor (9) goes into the bottom number (31), 3 time(s). Therefore put 3 on top:    053  9⟌481   -0      48    -45      31

Step 11:Multiply the divisor by the result in the previous step (9 x 3 = 27) and write the answer at the bottom:    053  9⟌481   -0      48    -45      31     27

Step 12:Subtract the result in the previous step from the number written above it. (31 - 27 = 4) and write the answer at the bottom.    053  9⟌481   -0      48    -45      31   - 27      4

You are done, because there are no more digits to move down from the dividend.The answer is the top number and the remainder is the bottom number.Therefore, the answer to 481 divided by 9 calculated using Long Division is: 53 4 Remainder

Answer:

∠ EBF = 47°

Step-by-step explanation:

since BE bisects ∠ ABF , then

∠ ABE = ∠ EBF = 2(w + 11) = 2w + 22

∠ ABF = ∠ ABE + ∠ EBF ( substitute values )

8w - 6 = 2w + 22 + 2w + 22

8w - 6 = 4w + 44 ( subtract 4w from both sides )

4w - 6 = 44 ( add 6 to both sides )

4w = 50 ( divide both sides by 4 )

w = 12.5

Then

∠ EBF = 2w + 22 = 2(12.5) + 22 = 25 + 22 = 47°

The equation will be,

→ 5/10 = 12/24

Is 5/10 equivalent to 12/24?

→ 5/10 = 12/24

→ 24 × 5 = 12 × 10

→ 120 = 120

→ [ LHS = RHS ]

Hence, they are equivalent.

Answer: 8 1/2 cups of flour

Step-by-step explanation:

You can look at this solution as x being the number of batches of biscuits.

1x = 1 batch of biscuits

1x = 3 2/5 cups of flour, or 17/5 cups of flour

We need to make 2 1/2 batches, restated as 5/2 batches.

This can be restated as 5/2x.

To determine our answer, we multiply x by 5/2.

5/2*(1x) = 5/2*(17/5)

5/2x = 85/10

Simplify.

85/10 = 8 5/10 or 8 1/2 cups

8 1/2 cups of flour are needed to make 2 1/2 batches of biscuits.

Answer:

  17 bars

Step-by-step explanation:

Peter wants to compute the maximum number of bars he can load safely if the load limit of 1200 kg and the bar weight of 60 kg are each rounded to the number of significant digits those numbers have.

The error in a rounded number is assumed to be as much as half of the least significant digit of the number.

Peter's load limit may actually be as low as ...

  1200 kg - (1/2)(100 kg) = 1150 kg . . . . . . . 1200 is rounded to nearest 100

Peter's bar weight might be as high as ...

  60 kg + (1/2)(10 kg) = 65 kg . . . . . . . . . . . 60 is rounded to nearest 10

If Peter has maximum-weight bars and does not want to exceed the minimum his load limit might be, the number of bars he can load is ...

  (1150 kg) / (65 kg/bar) ≈ 17.7 bars

The greatest number of bars Peter can load safely is 17.

Answer: A.   {3, 4, 5}

Explanation:

Write out the whole numbers from 2 to 6 to get 2,3,4,5,6

But we erase the first and last values since we aren't including those endpoints. So we end up with 3,4,5

Domain: (−∞,∞) , {x|x ∈ R}

Range: [0,∞) , {y|y ≥ 0}

Continuity: y=3x^2 is a parabola opening upwards, the vertex is at (0,0) and the focus is (0,1/12)

Max's and Min's: the minimum and maximum x value goes to infinity while for the y value the minimum is 0 and goes up to infinity.

Intervals: both x and y start to increase from the origin

Symmetry: the axis of symmetry is x=0 so therefore there the parabola is symmetrical

Answer:

Step-by-step explanation:

Given function:

[tex]y=3x^2[/tex]

The domain is the set of all possible input values (x-values).

The domain of the given function is unrestricted.

Therefore, the domain is (-∞, ∞).

The range is the set of all possible output values (y-values).

As x² ≥ 0, the range of the given function is [0, ∞).

A function f(x) is continuous when, for every value [tex]c[/tex] in its domain:

[tex]\text{$f(c)$ is de\:\!fined \quad and \quad $\displaystyle \lim_{x \to c} f(x) = f(c)$}[/tex]

Therefore, the function is continuous on its domain (-∞, ∞).

Stationary points occur when the gradient of a graph is zero.

Therefore, to find the x-coordinate(s) of the stationary points of a function, differentiate the function, set it to zero and solve for x.

[tex]\begin{aligned}y & = 3x^2\\\implies \dfrac{\text{d}y}{\text{d}x} & = 6x\\\\\dfrac{\text{d}y}{\text{d}x} & = 0\\\implies 6x & = 0\\x & = 0\end{aligned}[/tex]

[tex]\textsf{When} \:x = 0 \implies y=3(0)^2=0[/tex]

Therefore, the stationary point of the given function is (0, 0).

To determine if a stationary point is minimum or maximum, differentiate the function again and substitute the x-value of the stationary point:

[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & = 6x\\\implies \dfrac{\text{d}^2y}{\text{d}x^2} & = 6 \end{aligned}[/tex]

As the second derivative is positive regardless of the x-value of the stationary point, the stationary point is a minimum.

[tex]\textsf{A function is \textbf{increasing} when the \underline{gradient is positive}} \implies \dfrac{\text{d}y}{\text{d}x} > 0[/tex]

[tex]\textsf{A function is \textbf{decreasing} when the \underline{gradient is negative}} \implies \dfrac{\text{d}y}{\text{d}x} < 0[/tex]

Increasing

[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & > 0 \\ \implies 6x & > 0 \\ x & > 0\end{aligned}[/tex]

Decreasing

[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & < 0 \\ \implies 6x & < 0 \\ x & < 0\end{aligned}[/tex]

Therefore:

[tex]\textsf{A function is \underline{even} when $f(x) = f(-x)$ for all $x$.}[/tex]

[tex]\textsf{A function is \underline{odd} when $-f(x) = f(-x)$ for all $x$.}[/tex]

As x² ≥ 0 and there is symmetry about the y-axis,

[tex]\textsf{then $f(x)=f-x)$ for all $x$,}[/tex]
so the function is even.

Answer:

56 degrees

22 minutes

48 seconds

Answer:

$623.50

Step-by-step explanation:

(100 - 29)% = 71%

71% = 71 / 100 = 0.71

Original price:
442.69 / 0.71 = 623.50

Hope this helps

Answer:

$675.00

Step-by-step explanation: The chart says it all

The classification within the real number system that describes all numbers in the set -1, 1, 0, 14/2, square root 25 is; Rational Numbers

Real numbers can be defined as the union of both rational and irrational numbers.

Rational numbers are numbers that can be represented by fractions, such as exact roots and repeating decimals.

Irrational numbers cannot be represented by fractions, such as non-repeating decimals and non-exact roots.

Now;

-1 is a rational number

1 is a rational number

14/2 is a rational number

The square root of 25 is equal to 5 as 25 is a perfect square of 5. Hence, as 5 is an integer and can be expressed in the form of p/q root, then we say that 25 is rational number

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Answer:

equation: x + 50 = 180

solution x = 130

Step-by-step explanation:

supplementary: angles that add to 180

50 +  x = 180

180 - 50 = 130

x = 130

Answer:

the equation is x+50=180

solution is 130

Step-by-step explanation:

A straight line is 180 degrees so 180-50=130

So the equation is x+50=180

solution is 130

Group C ran more miles than Group D

the central value of a set of data is expressed by the average of a list of data. It is defined mathematically as the ratio of the total number of data points to the number of units in the list. In terms of statistics, the term "mean" also refers to the average of a certain set of numerical data. The average of 2, 3, and 4 is, for instance, (2+3+4)/3 = 9/3 = 3. The center value of 2, 3, and 4 in this instance is 3, thus. Finding the mean value of a bunch of numbers is the definition of average.

Average = Total Values / Total Values

Group C = 27/4 = 6.75

Group D = 39 /6 = 6.5

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Answer:

Omar can ride the roller coaster 4 times and will have 4 tickets leftover.

Step-by-step explanation:

For a more simple problem like this, long division is not necessary.

You may have learned the technique of finding how many times a divisor can "go in" to the dividend.

In this case, 5 (the cost of riding the coaster) can go into 24 (the amount Omar has) 4 times, because 5, 10, 15, 20. However, going in one more time puts us at 25, which Omar does not have, so 5 can only go into 24 5 times.

Since there is still 4 tickets leftover, Omar can ride the coaster 4 times, and will have 4 tickets left.

(A∩B)∪(A∩C) using roster method is as follows:

(A∩B)∪(A∩C)  = {a, e, f}

Sets are an organized collection of objects that can be represented in set-builder form or roster form.

Therefore,

The universal sets is as follows:

U = {a, b, c, d, e, f, g, h}

The subsets are as follows:

A = {c, e, f}

B = {a, e, f}

C = {a, b, d, g, h}

Therefore, let's find (A∩B)∪(A∩C) using roster method.

The roster method is defined as a way to show the elements of a set by listing the elements inside of brackets.

Hence,

(A∩B) = {e, f}

(A∩C) = {a}

Finally,

(A∩B)∪(A∩C) = {a, e, f}

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The number of apples Maria has after giving 1 apple to Lillian at the end is is 5 apples.

Given data:

The expressions representing the change in values of the apples are:

Lilian starts with 12 apples, and she gives half (6 apples) to Sebastian. She now has 12 - 6 = 6 apples.

Sebastian starts with 6 apples and gives 2 apples to Jose. He now has 6 - 2 = 4 apples.

On simplifying the expressions:

Maria starts with 6 apples and gives 2 apples to Jose. She now has 6 - 2 = 4 apples.

Sebastian gives half of his remaining apples (4 / 2 = 2 apples) to Maria. Maria now has 4 + 2 = 6 apples.

Maria gives 1 apple to Lilian. She now has 6 - 1 = 5 apples.

Hence, at the end of the given actions, Maria has 5 apples.

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a) "how many quarters you have is a function of how many times you paid for the parking meter."

b) y = 10 - x

domain: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

range: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

c) table:

x: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

y: 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0

Here we know that you have a total of 10 quarters, and the parking meter costs 1 quarter.

Then, each time if we define two variables:

y = how many quarters you have.

x = how many times you paid for the parking meter.

We can write:

"y is a function of x"

Or:

"how many quarters you have is a function of how many times you paid for the parking meter."

b) The rule is really simple, it would be a linear relation:

y = 10 - x

The domain (the set of possible values of x) is:

{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

You can't use less than 0 quarters and you can't use more than 10.

c) The range is also:

{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Which represents the possible numbers of quarters that you can have.

And the table will be:

x: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

y: 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0

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Answer: 697

Step-by-step explanation:

17 * 41=

17 * (40+1)=

17 * 40 + 17 * 1=

17 * 10 * 4 + 17=

170 * 4 + 17=

680+17=697

The number in each of the set of blank boxes is 10

From the first number set of stamps, we see that the sum of each row is;

5 + 5 + 5 + 5 = 20

There are four rows. Thus;

Total sum of set of stamps = 20 + 20 + 20 + 20

Total sum of set of stamps = 80

Now, for the blank set of stamps, we see that there are 8 boxes which are al equal. Now, for this 8 boxes t have same sum as that of the initial set of stamps, it means they must sum up to 80.

If the number in each box is x, then;

8x = 80

x = 80/8

x = 10

Thus, the number in each of the set of blank boxes is 10

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The 17th term of the sequence is 289

The nth term is given as

Sn = n^2

The 17th term of the sequence implies that

n = 17

So, we have

S17 = 17^2

Evaluate

S17 = 289

Hence, the 17th term of the sequence is 289

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In linear equation , length of each car =.375 feet.

What in mathematics is a linear equation?

Rack of the cars on the train were the same length = 8

train was 3 feet long.

length of each car = 3/8 = .375 feet

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let DF become y

y = x + 9

to find x let y = 0

0 = x + 9

transpose 9

-9 = x

therefore DF = -9 as an integer

Answer: y=1

Step-by-step explanation:

Slope formula: m=(y2-y1)/(x2-x1)

m=(1-1)/(0-8)

m=0/(-8)

m=0

y=mx+b

1=0(0)+b

b=1

y=0x+1

y=1

Answer:

bca

Step-by-step explanation:

5x5=25 5 to the power of 2 is 25 plus the power of x on all of them

The total number of students who graduated from the Cincinnati universities and colleges are 15382.

We are given that 6.76 % of Cincinnati college and university graduates majored in Registered Nursing.

The number of the Cincinnati college and university graduates who majored in Registered Nursing = 1026.

We need to find the total number of students that graduated from the Cincinnati universities and colleges altogether in 2016.

Let the total number of students be x.

ATQ:

6.67 % x = 1026

6.67 x = 102600

667 x = 10260000

x = 10260000 / 667

x = 15382.309

Rounding off to the nearest whole number is:

x = 15382.

Therefore, we get that the total number of students who graduated from the Cincinnati universities and colleges are 15382.

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The proportional relation that tells us how many hours she practices basketball in D days is:

H = 2*D

We know that Shermika practices basketball for two hours each day, then in one day she will practice 2 hours, in 2 days she will practice 4 hours, and so on.

We want to find an expression that relates the number of hours practiced, H, in D days.

If she practices 2 hours per day, then in D days she will practice a total of:

H = 2*D

This is just a proportional relation that tells us how many hours she practices basketball in D days.

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Based on the fact that the shape of the given square is dilated with a scale factor, the result would be the first square with a dimension of 3.

The Dilation is to be with a scale factor of 1/3.

This means that the dimensions on the new shape will be:

= Dimensions on original shape x scale factor

= 9 x 1/3

= 9/3

= 3

Dilation does not change the shape of an object so the result of the Dilation would be the first square with a side measurement of 3.

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