Convert to rectangular form.

All are rational.

Any number you can write exactly and completely, or any repeating decimal is a rational number. Any number that can only be written exactly using a symbol, such as π or √2, is an irrational number. Something like √6.25 is rational, because it can be written exactly as 2.5, without the symbol.

The idea of "rational" means the number can be expressed as the ratio of two integers. Any integer can be expressed as the ratio of itself and 1.

All of your numbers can be expressed as the ratio of integers:

... -0.45 = -45/100 . . . . any terminating decimal can be expressed as a ratio of integers by making use of the place value multipliers

... 5/12 . . . . is the ratio of integers

... 0 = 0/1

... 247 = 247/1

The reasoning is correct. The ratio of number of bulbs tested to defective bulbs is always 14 to 1.

We generally expect industrial processes to produce defects at about the same rate, meaning the proportion of defective product is generally considered to be a constant. Here, the proportion of defective bulbs is ...

... 1/14 = 2/28 = 6/84

so we expect it will be also 24/336. That is, the ratio of the number of bulbs tested to defective bulbs is expected to remain constant at about 14.

Answer:

A. The reasoning is correct. The ratio of number of bulbs tested to defective bulbs is always 14 to 1.

Step-by-step explanation:

Look at the prime factorization. If all the factors have powers that are multiples of 6, then the number is a square and a cube. If they are multiples of 3, then a cube; if multiples of 2, then a square.

1000 = 2³·5³ . . . . a perfect cube

4 = 2² . . . . a perfect square

120 = 2³·3·5 . . . . none of the above (not a square or a cube)

36 = 2²·3² . . . . a perfect square

100 = 2²·5² . . . . a perfect square

49 = 7² . . . . a perfect square

125 = 5³ . . . . a perfect cube

25 = 5² . . . . a perfect square

Answer:

[tex]\dfrac{2}{3x^5y}[/tex]

Step-by-step explanation:

A negative exponent in the numerator is the same as a positive exponent in the denominator, and vice versa.

... a^-b = 1/a^b . . . . . for any value of b, positive or negative

The exponent of a product is the sum of the exponents:

... (a^b)(a^c) = a^(b+c)

___

Applying these rules, you have

... = 2/(3x^4·x·y) = 2/(3x^(4+1)·y) = 2/(3x^5·y)

1–4: The interior angle of an n-sided regular polygon is (n-2)/n times 180°. For n ∈ {5, 6, 11, 4}, this is {3/5, 4/6, 9/11, 2/4} · 180°, or {108°, 120°, 147.3°, 90°}

5–8: The exterior angle of an n-sided regular polygon is 360°/n. For n ∈ {5, 9, 7, 4}, this is 360°/{5, 9, 7, 4}, or {72°, 40°, 51.4°, 90°}

Answer:

x=-7+8ı ,-7-8ı

Step-by-step explanation:

Move all terms to one side

x²+14x+17+96=0

Simplify x²+14x+17+96 to x²+14x+113

x²+14x+113=0

Use the quadratic Formula

x= -14+16/2 ,  -14-16ı/2

Simplify Solutions

x=-7+8ı ,-7-8ı

5.3

The mnemoic SOH CAH TOA reminds you that ...

... Tan = Opposite/Adjacent

... tan(24°) = x/12

Then multiplying by 12 gives ...

... 12·tan(24°) = x = 5.34274 ≈ 5.3

Answer:

The attachment shows ΔBAC ~ ΔBDA

Step-by-step explanation:

You want segment AB to be part of two similar, but not congruent, triangles. One way to do that is to make AB the hypotenuse of one triangle and the leg of another.

It is convenient to construct these triangles using point M as the arbitrary midpoint of the hypotenuse of the larger triangle. (We don't know the coordinates of M—we just know it is on the perpendicular bisector of AB.) BC is a diameter of circle M, and AD is the altitude of ΔABC.

Answer:

77°

Step-by-step explanation:

Angles B and C are adjacent angles of a parallelogram, so are supplementary.

... ∠C = 180° -∠B = 180° -103° = 77°

The measure of ∠BCD in a parallelogram with ∠B given as 103° is also 103° because opposite angles in a parallelogram are equal.

The measure of ∠BCD in a parallelogram can be found by using the property that opposite angles in a parallelogram are equal.

To find the measure of angle BCD, we can use the fact that angles in a quadrilateral sum up to 360 degrees.

We know that angle B is 103 degrees.

Since quadrilateral ABCD has sides AB and DC parallel, as well as sides AD and BC parallel, it is a parallelogram.

Given that ∠B is 103°, the measure of ∠BCD is also 103° because it is the angle opposite ∠B.

Answer:

2y^14

Step-by-step explanation:

= (-1/2)^3 · (y^4)^3 · (-16) · y^2

= (-1/8)·(-16) · (y^(4·3) · y^2) . . . . . simplify some

= 2 · y^(12 +2) . . . . . simplify more

= 2y^14

Answer:

$12.47

Step-by-step explanation:

The total charge was ...

... $13.28 +14.25 = $27.53

The change from 2 $20 bills is ...

... 2 × $20 - 27.53 = $40.00 -27.53 = $12.47

The total cost of lunch is $27.53. Ana paid with two $20 bills, which equals $40.00. After Ana gave the two $20 bills, she received $12.47 in change.

The subject area of this question is mathematics, specifically arithmetic involving decimal numbers. To solve this, we first add together the costs of the two lunches, which are $14.25 and $13.28, that result in $27.53. Ana initially pays with two $20 bills, which sums up to $40.00. Now, we subtract the total cost of the lunches from the amount Ana paid with. So, $40.00 - $27.53 gives us $12.47. This tells us that Ana received $12.47 in change back after paying for lunch.

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Answer:

r = -0.9997  

Step-by-step explanation:

A statistics calculator gives the value

r = -0.9997

You can see in the graph below that it represents an excellent negative correlation between x and y.

Every point appears to be exactly on the regression line .

It represents a linear positive correlation between x and y −0. 999.

Given

The table shows Britney's distance, in miles, from her destination after different time intervals in hours:

Time (hours) (x) 2 4 1 3 6 5 7

Distance from destination (miles) (y) 1,000 880 1,060 940 760 820 690

A number between +1 and −1 is calculated so as to represent the linear interdependence of two variables or sets of data.

Then,

The correlation coefficient for the data, and what does it represent is;

It represents no correlation between x and y.

Hence, it represents a linear positive correlation between x and y −0. 999.

To know more about the correlation coefficient click the link given below.

brainly.com/question/12400903

Answer:

30 units ^2

Step-by-step explanation:

To find the area of the shaded region, we find find the area of the large triangle and subtract the area of the unshaded triangle.

A of large triangle = 1/2 b*h

height = (6+3) = 9

The base is found by using the pythagorean theorem c^2 = a^2 + b^2

We need to  find b^2  

c^2 -a^2 = b^2

taking the square root on each side

sqrt(c^2 -a^2) = sqrt(b^2)

                           the base = sqrt(c^2 -a^2)

                                            = sqrt( 15^2 - 9^2)

                                            = sqrt(225-81)

                                             = sqrt(144)

                                              =12

Now that we know the base and the height, we can find the area

A of large triangle = 1/2 b*h

                               = 1/2 * 12 * 9

                              = 6*9 = 54

Using the rule of similar triangles

9               6

----  =  ----------

12           base

We can use cross products to find the base of the smaller triangle

9* base = 12*6

9* base = 72

Divide by 9 on each side

base = 72/9 = 8

Now we can find the area of the smaller triangle

base = 8 and height = 6

A of smaller triangle = 1/2 b*h

                                   = 1/2 *8 * 6

                                   = 4*6 = 24

Area of the shaded region = Area large triangle - Area of small triangle

                                              = 54-24

                                                = 30

Answer:

[tex]\dfrac{-x+5}{6x^2-x-12}[/tex]

Step-by-step explanation:

The denominators are the same. You can add the numerators without any extra work.

[tex]=\dfrac{(4x+5)-(5x)}{6x^2-x-12}=\dfrac{-x+5}{6x^2-x-12}[/tex]

The denominator factors as (2x-3)(3x+4), so there are no factors that will cancel with the numerator.

The notation f(x) means you have a function that has been given the name f, and it makes use of the variable x. The variable in the parentheses is called the "argument" of the function f.

(a) To find f(q), you put q everywhere x is in the function equation. This is called evaluating the function for an argument of "q". In the following, note that we have simply changed x to q. (It's really that simple.)

... f(q) = q² -2q +3

(b) As in the previous case, we replace x with (x+h) everywhere.

... f(x+h) = (x+h)² -2(x+h) +3

You can multiply it out, but there appears to be no need to do so for this part of the question.

(c) The intent here is that f(x+h) and f(x) will be replaced by their values and the whole thing simplified. This requires you  expand the expression you see in part (b), subtract f(x), collect terms, and divide the whole thing by h. You have to make use of what you know about multiplying binomials.

We can do it in parts:

... f(x+h) = (x+h)² -2(x+h) +3

... = (x² +2xh +h²) + (-2x -2h) +3

Separating the h terms, this looks like ...

... = (x² -2x +3) + (2xh -2h +h²)

Now, we can finish the numerator part of the expression by subtracting f(x):

... f(x+h) -f(x) = (x² -2x +3) +(2xh -2h +h²) -(x² -2x +3)

You can see that the stuff in the first parentheses matches that in the last parentheses, so when we subtract the latter from the former, we get zero. We are left with only the terms containing h.

... f(x+h) -f(x) = 2xh -2h +h²

To finish up this problem, we need to divide this numerator value by the denominator h.

... (f(x+h) -f(x))/h = (2xh -2h +h²)/h

... = (2xh)/h -(2h)/h +h²/h

... = 2x -2 +h . . . . . this is the value of the expression

... (f(x+h) -f(x))/h = 2x -2 +h

Answer:

8√2

Step-by-step explanation:

4√2 + 7√2 - 3√2 = (√2)(4 + 7 - 3) = 8√2

Recognize that √2 is a common factor and simply add its coefficients.

[tex]4\sqrt2+7\sqrt2-3\sqrt2=(4+7-3)\sqrt2=\boxed{8\sqrt2}\\\\Answer:\ \boxed{\text{8\ square root of 2}}[/tex]

Answer:

60% increase

Step-by-step explanation:

Percentage increase = (new - old)/ old * 100

We know the new = 4.00

old = 2.50

Lets substitute the values in

Percentage increase = (4-2.5)/2.5 *100

                                   = 1.5/2.5 * 100

                                     =.6*100

                                    =60%

Answer: First prism has the greatest volume.

Step-by-step explanation:

Since we have given that

Volume of prism = Length × Breadth × Height

So, we need to find the greatest volume, for which we find volumes of all figures:

1) Volume of prism would be

[tex]5\times 7\times 5\\\\=175\ cm^3[/tex]

2) Volume of prism would be

[tex]10\times 3\times 4\\\\=120\ cm^3[/tex]

3) volume of prism would be

[tex]7\times 7\times 3\\\\=147\ cm^3[/tex]

4) Volume of prism would be

[tex]5\times 3\times 7\\\\=105\ cm^3[/tex]

Hence, first prism has the greatest volume.

The volume of the prism with the Greatest volume is 250cm³

The volume of a prism is calculated by multiplying the prism's base area by its height. Mathematically expressed as

V = Base Area×Height

, it represents the space enclosed within the prism.

Since the prism is a cuboid, then

V = l × w × h

Where h is the height , l is the length and w is the width.

V = 5 × 5 × 10

V = 250 cm³

The volume of the prism is 250cm³

Answer:

(3, 8)

Step-by-step explanation:

For x = 3,

. . . y = 2^x

. . . y = 2^3 = 2·2·2 = 8

This is represented by the ordered pair (x, y) = (3, 8).

Answer:

(3,8)

Step-by-step explanation:

Since the answer choices are given we can plug the "x" value and see if it returns the y-value given in the ordered pair (x,y) and so:

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

Let's use the ordered pair (3,8) meaning that when x=3 y =8 and so:

[tex]y=2^3=2\times2\times2=8[/tex]

[tex]y=8[/tex]

This is correct and so this is a solution, since the solution is unique when x=3 y is always going to return an 8.

$450

Each year, the amount of interest earned is ...

... 4.5% × $5000 = $225

After 2 years, a total of ...

... $225 × 2 = $450

has been transferred.

_____

Comment on percentages

Of course, you know that 4.5% = 4.5/100 = 45/1000 = 0.045.

You can think of the % symbol as a fancy (shorthand) way to write /100. (Likewise, the ‰ symbol means /1000.)

Answer:

$3,659.82

Step-by-step explanation:

Adding to the checkbook those debits and credits not already there brings its balance to ...

... $3045.58 +651.84 -37.60 = $3659.82

Adjusting the bank's balance by the deposits and checks not already there brings its balance to ...

... $4262.92 +220.05 -325.50 -497.65 = $3659.82

Thus, the reconciled accounts will agree on the balance $3659.82.

The reconciled balance for Gregory Co. was $3,659.82 after accounting for all transactions including deposits, outstanding checks, credited note, and bank charges.

The question involves reconciling the checkbook balance with the bank statement balance for Gregory Co. To reconcile the bank balance with the checkbook balance, we need to account for any transactions that have not been reflected in one or the other. We start with the bank statement balance and adjust it for outstanding checks and deposits not reflected on the statement.

Answer:

(5, 3)

Step-by-step explanation:

The given coordinates define a right triangle with (9, 8) as the vertex where the right angle is located. Then the other two coordinates define a diameter of the circumcircle. Its midpoint is the center.

... center = ((1, 8) +(9, -2))/2 = (5, 3)

For this case, we have that by definition:

Let "x" be an angle of any vertex of a right triangle.

[tex]Sin (x) = \frac {Cathet \ opposite} {hypotenuse}[/tex]

So, if we want to find the sine of angle A:

[tex]Sin (A) = \frac {3} {5}[/tex]

Thus, the sine of angle "A" is[tex]\frac {3} {5}[/tex]

Answer:

[tex]\frac {3} {5}[/tex]

Option A

Answer:

63 tons

Step-by-step explanation:

The problem statement asks for the tons of hay removed from the first pit. It is convenient to let a variable (x) represent that amount. This is said to be 3 times the amount removed from the second pit, so that amount must be x/3.

The amount remaining in the first pit is 90-x.

The amount remaining in the second pit is 75 -x/3.

Since the first pit remaining amount is half the second pit remaining amount, we can write the equation ...

... 90 -x = (1/2)(75 -x/3)

... 180 -2x = 75 -x/3 . . . . multiply by 2

... 105 - 2x = -x/3 . . . . . . subtract 75

... 315 -6x = -x . . . . . . . . multiply by 3

... 315 = 5x . . . . . . . . . . . add 6x

... 63 = x . . . . . . . . . . . . . divide by 5

63 tons of hay were taken from the first pit.

_____

Check

After removing 63 tons from the first pit, there are 27 tons remaining. After removing 63/3 = 21 tons from the second pit, there are 54 tons remaining. 27 is half of 54, so the answer checks OK.

Answer:

A. 49°

Step-by-step explanation:

∠O is the other base angle (along with ∠Q) of the isosceles triangle OPQ. Base angles of an isosceles triangle have the same measure.

Answer:

See the attached

Step-by-step explanation:

A graph of almost any exponential function quickly goes off-scale. The attachment shows a short table of values.

Answer:

D. The inequality has an equal sign it

Step-by-step explanation:

We use solid lines whenever the inequality contains [tex]\leq[/tex] or [tex]\geq[/tex]. That means it contains an equal sign which means the boundary line is inclusive.

On the other hand when the inequality does not have an equal sign in it we use a dashed line to indicate that all values on the boundary line are not inclusive.

That is we use a dashed or broken line for the boundary line of an inequality whenever it contains [tex]\:<\: or \:>\:[/tex].

The correct answer is D

9. AM ≅ AT

10. x=3, y=5

AH being the perpendicular bisector of MT means MH ≅ TH. Then ΔAHM ≅ ΔAHT by SAS, and by CPCTC.

... SAS — side-angle-side: if two adjacent sides and the included angle of a triangle are congruent to their corresponding sides and angles in another triangle, the two triangles are congruent.

... CPCTC — Corresponding Parts of Congruent Triangles are Congruent

___

Using the result of problem 9 as a guide, you can say that ...

... 2x = x+3 ⇒ . . . . (subtract x from both sides)

... y +4 = 2y -1 ⇒ . . . . (add 1-y to both sides)