3. the product of 33 and j
write an algebraic expression ​

Answer: Isabella has 4 more photos than the other photo albums. So, Isabella has more pages than the number on one page in the example problem.

Step-by-step explanation: 3 divided by 36 equals 12. 12 times 3 = 36

The number of photos on one of these pages is more than the number on one page in the example problem because Isabella's photo album contains 4 more photos.

Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.

* Multiplication operation: Multiplies values on either side of the operator

For example 4*2 = 8

/ Division operation: Divides left-hand operand by right-hand operand

For example 4/2 = 2

We have been given that Isabella filled 3 more pages with 36 photos which she evenly divided between the pages.

As per the given condition,

36 divided by 3

⇒ 36 / 3 = 12

Here 12 times 3 is equal to 36

Therefore, Isabella's photo album contains 4 more photos. The number of pages in Isabella is greater than the number on one page in the example problem.

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Answer:

f(x) = x³ - 6x² + 10x - 8

Step-by-step explanation:

Complex zeros occur as conjugate pairs, thus

Given x = 1 - i is a zero then x = 1 + i is also a zero

Given the zeros are

x = 4, x = 1 - i, x = 1 + i then the corresponding factors are

(x - 4), (x - (1 - i) ), (x - (1 + i ) ), that is

(x + 4), ( x - 1 + i), (x - 1 - i)

f(x) is then the product of the factors, that is

f(x) = (x - 4)((x - 1) + i)((x - 1) - i ) ← distribute the complex factors

     = (x - 4)((x - 1)²  - i² ) → i² = - 1

     = (x - 4)(x² - 2x + 1 + 1)

     = (x - 4)(x² - 2x + 2) ← distribute

     = x³ - 2x² + 2x - 4x² + 8x - 8 ← collect like term

f(x) = x³ - 6x² + 10x - 8

The required polynomial is f(x) = x³ - 6x² + 10x - 8 which has a degree is 3 with real coefficients.

A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers.

The required polynomial F(x) of degree 3 with real coefficients and the following zeros. 4, 1-i

This means i.e.

x = 4, x = 1 - i, and x = 1 + i

As per the fundamental of algebra, the corresponding factors are (x - 4), (x - (1 - i) ), (x - (1 + i ) ),

The factors are (x + 4), ( x - 1 + i), and (x - 1 - i)

If the above corresponding factors are multiplied then we can find f(x)

f(x) = (x - 4)((x - 1) + i)((x - 1) - i )

f(x) = (x - 4)((x - 1)²  - i² ) → i² = - 1

f(x) =  (x - 4)(x² - 2x + 1 + 1)

f(x) = (x - 4)(x² - 2x + 2)

f(x) = x³ - 2x² + 2x - 4x² + 8x - 8

f(x) = x³ - 6x² + 10x - 8

Thus, the required polynomial is f(x) = x³ - 6x² + 10x - 8.

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Answer -rational numbers and irrational numbers

Using number sets, it is found that the set of dense numbers is composed of rational and irrational numbers. Therefore, option C is the correct answer.

From options, we need to check which answer describes the type of numbers that are dense.

Numbers are an integral part of our everyday lives, right from the number of hours we sleep at night to the number of rounds we run around the racing track and much more. In math, numbers can be even and odd numbers, prime and composite numbers, decimals, fractions, rational and irrational numbers, natural numbers, integers, real numbers, rational numbers, irrational numbers, and whole numbers.

Numbers can be classified as:

Whole numbers: All positive numbers and 0, so: {0,1,2,...}

Integer numbers: Positive or negative, not decimal so: {...,-2,-1,0,1,2,....}

Rational numbers: Integer plus decimals that can be represented by fractions, that is, they either have a pattern or have a finite number of decimal digits, for example, 0, 2, 0,45(finite number of decimal digits), 0.3333(3 repeating is the pattern), 0.32344594459 (4459 repeating is the pattern).

Irrational numbers: Decimal numbers that are not represented by patterns, that is, for example, 0.1033430290339, which can be approximated to the rational 0.1.

Real numbers: Rational plus irrational.

A subset is dense of the rational numbers if all numbers can be approximated to rational numbers, and thus, rational and irrational numbers are dense.

Therefore, option C is the correct answer.

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Answer:

Step-by-step explanation:

the percentage error: P

Approximate value=a 1.41

Exact = e(1.41421356 or √2)

p=[(e-a)/e]×100

p=[√2-1.41)/√2]×100

p=0.29794385 ≅0.30 or 30 percent when rounded to the nearest hundredth

b: p=[(π-3.14)/π]×100=0.05069573≅0.05 =5 percent when rounded to the nearest hundredth. in the pi case the percentage of error is small 5 % but in the case of square roots the percentage id higher(30%). in this case it is better to round the answer at the end of calculation( math problem)

c) sometimes when rounding square roots or irrational number like pi it is useful to use decimal approximate, in the case of pi the percentage rate was 5 percent which is very low comparing to the square root which is 30 %.

Answer:

For #21, x = 35, y = 85

Step-by-step explanation:

For these types of problems, you will simply use to facts.  The sum of the measure of a line is 180 degrees, and alternate angles of crossing lines are equivalent.  With that being said, let's work #21.

We can see that there are two lines, and we are given 2 values to find with 3 possible equations.

[1] ( 2x + 25 ) + y = 180

[2] y + ( 3x - 10 ) = 180

[3] 2x + 25 = 3x - 10

Using any of these equations, we can solve for the variables.  Let's use the 1st and 3rd equations to find x and y.

2x + 25 = 3x - 10

2x + -2x + 25 + 10 = 3x + -2x + -10 + 10

35 = x

Now plug in the value of x to find y:

( 2x + 25 ) + y = 180

( 2(35) + 25 ) + y = 180

( 70 + 25 ) + y = 180

95 + y = 180

y = 85

We can check these values by plugging into the 2nd equation

x = 35 ; y = 85

y + ( 3x - 10 ) = 180

(85) + (3(35) - 10) = 180

85 + ( 105 - 10) = 180

85 + 95 = 180

180 = 180

Thus, we have validated our results and found the values of x and y.

Cheers.

Answer:

h,  negative,  negative

Step-by-step explanation:

Answer:

He invested approximately $2,215

Step-by-step explanation:

Mr Y invested $2000 in two accounts.

One pays 7%, and the other pays 5%.

At the end of one year, Mr Y earned $155 in interest. We want to know how much Mr Y invested in the account paying 7%.

Let the amount he invested be X, then

7% of X = 155

(7/100)X = 155

0.07X = 155

X = 155/0.07

= 2,215

He invested approximately $2,215

Answer:

d

Step-by-step explanation:

add the dashes up =10

Answer:

10

Step-by-step explanation:

AC is the difference between the position of A and C, that is

AC = | - 8 - 2 | = | - 10 | = 10 or

AC = |  2 - (- 8) | = | 2 + 8 | = | 10 | = 10

Answer:

[tex] \huge{ \fbox{ \sf{x = 5}}}[/tex]

Step-by-step explanation:

[tex] \star{ \sf \: - 8 = 12 - 4x}[/tex]

[tex] \text{Step \: 1 \: : Swap \: the \: sides \: of \: the \: equation}: [/tex]

[tex] \mapsto{ \sf{12 - 4x = - 8}}[/tex]

[tex] \text{Step \: 2 \: : Move \: 12 \: to \: right \: hand \: side \: and \: change \: its \: sign}[/tex]

[tex] \mapsto{ \sf{ - 4x = - 8 - 12}}[/tex]

[tex] \text{Step \: 3 \: : Calculate}[/tex]

[tex] \text{ \underline{Remember ! }} : \sf{ \: The \: negative \: integers \: are \: always \: added \: but \: posses \: the \: negative \: ( - ) \: sign.}[/tex]

[tex] \mapsto{ \sf{ - 4x = - 20}}[/tex]

[tex] \text{Step \: 4 \: : Divide \: \: both \: sides \: by \: 4}[/tex]

[tex] \mapsto{ \sf{ \frac{ - 4x}{ - 4} = \frac{ - 20}{ - 4}}} [/tex]

[tex] \text{Step \: 5 \: : Calculate}[/tex]

[tex] \mapsto{ \sf{x = 5}}[/tex]

Hope I helped!

Best regards! :D

~[tex] \sf{TheAnimeGirl}[/tex]

Answer:

D -3/2

Step-by-step explanation:

The solutions are x = -3 and x = 3/2, however, you can solve this as well by looking at part of the quadratic formula:

[tex]x_1+x_2 = \frac{-b + \sqrt{b^2-4ac}}{2a} + \frac{-b - \sqrt{b^2-4ac}}{2a} = \frac{-b}{a}[/tex]

the formula implodes when you add the roots!

Answer/Step-by-step explanation:

Line segment AB consists of segment AC and segment CB.

AC = 7 cm

CB = 21 cm

The entire segment, AB = 21 + 7 = 28cm

The ratio of the segments partitions can be stated as follows:

Ratio of AC to CB = AC:CB = 7:21 = 1:3 = [tex] \frac{1}{3} [/tex]

AC is ¼ of AB [tex] (\frac{1}{1 + 3} = \frac{1}{4}) [/tex]

CB is ¾ of AB [tex] (\frac{3}{1 + 3} = \frac{3}{4}) [/tex]

Answer:

-8x+56

Step-by-step explanation:

we have to multiply 8 by x and -7

-8 times x is -8x. However -8 times -7 is POSTIVE 56

Answer:

So the answer to this problem would be -8x+56

Step-by-step explanation:

The reason for this is -8 multiply by x and multiply by -7 so if you multiply -7 and -8 together u will get 56 and -8 multiplied with x is = -8x

Hope that helps

Answer:

You can make 6 batches of cookies.

Step-by-step explanation:

3/4 + 3/4 = 1 1/2 (2)

1 1/2 + 1 1/2 = 3 (4)

3 + 1 1/2 = 4 1/2 (6)

Answer:

6 batches

Step-by-step explanation:

4 1/2 divided by 3/4

is 6

4 1/2  /  3/4 = 6

so you can make six

is how many batches

you can make.

(i checked my answer with a calculator)

Answer:

the curved area would be 396cm^2

Answer:

The false statement is ∠1 ≅ ∠2.

Answer:

26 coaches and 143 players

Step-by-step explanation:

11/2=5.5

22/4=5.5

143/26=5.5

Answer:

26 coaches and 143 players

Step-by-step explanation:

Answer:

Quotient = 5

Step-by-step explanation:

Step 1

Round each mixed number to the nearest whole number

a) 24 16/17 = 424/17

= 24.941176471

Approximately to the nearest whole number ≈ 25

b) 4 8/9 = 44/9

= 4.8888888889

Approximately to the nearest whole number ≈ 5

Next step we estimate the quotient

Quotient = Dividend ÷ Divisor

Dividend = 25

Divisor = 5

Quotient = 25 ÷ 5

= 5

Therefore, the quotient is 5

Answer:

2<x>16

Step-by-step explanation:

Answer:

The base length of the triangle is 34.5 mm.

34.5×2+5=74.

Step-by-step explanation:

Subtract 5 from 74 then divide 2 from 69 and you will get 34.5.

Answer:

The first answer is 74=2b+5

And the second answer is 34.5

Step-by-step explanation:

Answer:

The first one is greater in value

Step-by-step explanation:

3 x 2 + x − 2 VS 4 x − 1

Answer:

384

Step-by-step explanation:

Triangle sides: 12x10/2. Then multiply by four to get all four sides.

Bottom: 12x12.

Add together, get 384.

Answer:

7/4

Step-by-step explanation:

1x3+3/4

then will get you to

4+3/4

and the solution is

7/4

Answer:

5.4 * 10^6 in.

Step-by-step explanation:

3000 * 1800 in. = 5,400,000 in. = 5.4 * 10^6 in.

Answer:

  P'(-9, 3)

Step-by-step explanation:

The transformation for rotation counterclockwise about the origin by some angle α will be ...

  (x, y) ⇒ (x·cos(α) -y·sin(α), x·sin(α) +y·cos(α))

When the angle is α = 90°, this reduces to ...

  (x, y) ⇒ (-y, x)

You have (x, y) = (3, 9), so the image point is P'(-9, 3).

__

Additional comment

The "work" is applying the right sign and choosing the right coordinate to fill in the values (-y, x). I find it easier to look up the transformations for ±90° and 180°, rather than try to derive them from first principles every time. Your text may have a list: