How would I simplify these expressions? (Pre-Calculus) I know that you are supposed to multiply all of these to do so, but every time I do that, I still get the wrong answer. My textbook says that these are the answers:
19: -15 + 8i
21: 8 + 6i
23: 34
25: 85
Could anyone explain how they got these answers? Mine are way off. Is the book just wrong? In #21, how would 3 times 3 equal 8 in the answer? Am I missing something?

Step-by-step explanation:

The area of a parallelogram is just base x height, same as a rectangle.

[tex]a=b*h\\a=ir*r[/tex]

If ir is 2 separate variables rather than just 1, that can be simplified to this:

[tex]a=ir^2[/tex]

Length of larger piece be x

x=12m

[tex]\\ \sf\longmapsto 4x+5=4(12)+5=60+5=65m[/tex]

Total length=65+12=77m

The length of the bigger piece is 1.75 meters and the total length of the carpet is 13.75 meters.

Given that length of the smaller piece is 12 meters.

The length of the smaller piece is 5 meters greater than 4 times the length of the larger piece.

Let's represent the length of the larger piece as "x."

Length of the smaller piece = 4 times the length of the larger piece + 5

12 = 4x + 5

Subtracting 5 from both sides:

12 - 5 = 4x

7 = 4x

Dividing both sides by 4:

7/4 = x

1.75 = x

So, the length of the bigger piece is 1.75 meters.

To calculate the total length of the carpet, we add the length of the smaller piece and the length of the bigger piece:

Total length of the carpet = Length of the smaller piece + Length of the bigger piece

Total length of the carpet = 12 + 1.75

Total length of the carpet is approximately 13.75 meters.

Therefore, the length of the bigger piece is 1.75 meters and the total length of the carpet is 13.75 meters.

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Answer:

6 months

Step-by-step explanation:

We can think of Natalie as 100 + 10x and her sister as 25 + 25x. If we put them together, we will get 100 + 10x < 25 + 25x, We can simplify it by moving the 25 to the left side and 10x to the right side. Then we will get 75 < 15x, and the smallest solution is 6 because 5 * 15 is equal to 75

Answer:

Definitely rational because 576 and 684 are both natural numbers

Step-by-step explanation:

Answer:

(8x^9 x y^4) : (1/2x^3)=16x^6y^4

Step-by-step explanation:

8 : 1/2 = 16

x^9 : x^3 = x^6

Equation - [tex]8x^3y^4[/tex] divided by (1/2x^3)=16x^6y^4.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign. A mathematical equation is a formula that uses the equals sign to express the equality of two expressions. The meanings of the word equation as well as its cognates in other languages can vary slightly. For instance, in French, an equation is defined as having one or more variables, whereas in English, an equation is any well-formed formula that consists of two expressions linked by the equals sign.

Finding the values of the variables that result in the equality is the first step in solving an equation with variables. The unknown variables are also known as the variables for which the equation must be solved, and the unknown variable values that satisfy the equality are known as the equation's solutions.

Let the required term be z.

[tex]z/ (1/2x^3)=16x^6y^4[/tex]

[tex]z=(16x^6y^4) }{(1/2x^3)}[/tex]

[tex]z = 8x^3y^4[/tex]

Hence, [tex]8x^3y^4[/tex]

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Answer:

5 ⋅ 37

Step-by-step explanation:

185 has factors of 5 and 37.

Answer:

Step-by-step explanation:

All Factors of 185: 1, 5, 37 and 185.

Negative Factors of 185: -1, -5, -37 and -185.

Prime Factors of 185: 5, 37.

Prime Factorization of 185: 5^1× 37^1

Sum of Factors of 185: 228.

Answer:both involving 6 and 7. (-6,-7) would be in quadrant 3 while point (-6,7) would be on top of it in quadrant 2.

Step-by-step explanation:

Answer:

25-10  (25 - A and 10 - B)

Step-by-step explanation:

25 - 10 equals the 15 point margin

25 plus 10 equals the 35 point score combined

Hope it helps

Answer:

  x = 9 cm

  y = 4 cm

Step-by-step explanation:

The angle markings tell you the three angles of one triangle are equal to the three angles of the other triangle. That means the triangles are "similar", and the lengths of corresponding sides have the same ratio.

The bottom sides, between the angles with 1 mark and 3 marks, are shown as 3 cm in the green triangle and 6 cm in the blue triangle. This tells you all of the the green triangle dimensions are half those of the corresponding dimensions in the blue triangle:

  x = (18 cm)/2 = 9 cm

It also tells you the blue triangle dimensions are 2 times those of the green triangle:

  y = 2(2 cm) = 4 cm

_____

Additional comments

Corresponding sides having the same ratio means they are proportional (and vice versa). This can be expressed in equation form as ...

  y/(2 cm) = (18 cm)/x = (6 cm)/(3 cm)

__

You may want to discuss this problem with your teacher. The side lengths shown in the figure do not form a triangle. The two short sides are too short to connect to the ends of the long side. The figure is impossible.

Answer:

The negatives are at the bottom and the positives are at the top, if you need help with the (x,y) let me know!!!

Step-by-step explanation:

Answer:

right and above side of graph are positive

and

left and bottom side of graph are negative

Answer:

$2695

Step-by-step explanation:

$265 + $0.90p=C

To find out the value of C (cost), we must solve the equation by replacing P (number of keychains) with the given value, 2700.

265 + 0.90(2700) = C

Now, we use order of operations. (PEMDAS)

In this case, the parentheses stand for multiplication. Since multiplication comes first, we multiply 0.90 by 2700.

The product of 0.90(2700) is 2430.

Our new equation should look like this

265 + 2430=C

Adding those together you get 2695, to finish this off, C=$2695

(Side note: be sure to identify what the value is, for example 2695 is the cost of producing 2700 key chains, meaning it's $)

I hope this made sense and helped lol

Answer:

0.6 cm

Step-by-step explanation:

15/25=0.6

Answer:

0.6 Is the answer

Step-by-step explanation:

Hope this helped ¬∪ω∪¬

Answer:

5 seconds

Step-by-step explanation:

hope it helps

correct me if i'm wrong

Answer:

5 7/12 feet left

Step-by-step explanation:  

Step 1:  8 5/6 - 3 1/4

Step 2:  = 67/12 (Put into proper fraction)

Step 3:  = 5 7/12

Hope that helps :)

Answer:

5 7/12

Step-by-step explanation:

Given that the board is 8 5/6 feet long.

Cuts off 3 1/4 feet.

8 5/6- 3 1/4

Change fractions into improper fractions.

8 5/6=53/6

3 1/4=13/4

-------------------------------------------------------------

53/6x2/2=106/12

13/4x3/3=39/12

106/12-39/12=67/12

=5 7/12

Hope this helps :)

9414 1404 393

Answer:

  $1.80, 2.90, 4.00, 10.90

  not proportional

Step-by-step explanation:

For some distance d, we have a charge f(d) that is ...

  [tex]f(d)=\begin{cases}1.00&0\le d\le0.1\\1.00+0.10\cdot\dfrac{(d-0.1)}{0.10}&0.1<d\end{cases}[/tex]

for d > 0.1, this simplifies to d +0.9.

Then the charges are ...

  [tex]\begin{array}{cc}\underline{\text{miles}}&\underline{\text{charge}}\\9/10&1.80\\2&2.90\\3\ 1/10&4.00\\10&10.90\end{array}[/tex]

The different relation for the first 1/10 mile indicates ...

  the relationship is not proportional.

Answer:

8 hours

Step-by-step explanation:

23 + 3x = 5x + 7

     - 3x   -3x

23 = 2x + 7

-7          - 7

16 = 2x

16/2 = 2x/2

x = 8

Answer:

BillyBob got it right, well explained..

Step-by-step explanation:

Answer:

19

Step-by-step explanation:

Note that

[tex]\dfrac{10a}{b+c} + \dfrac{10b}{a+c} + \dfrac{10c}{a+b} = 10\left(\dfrac{a}{b+c} + \dfrac{b}{a+c} + \dfrac{c}{a+b} \right)[/tex]

and

[tex]\dfrac{7-b-c}{b+c}+\dfrac{7-a-c}{a+c}+\dfrac{7-a-b}{a+b}=\dfrac{a}{b+c} + \dfrac{b}{a+c} + \dfrac{c}{a+b}[/tex]

from [tex]a+b+c=7 \implies a=7-bc; b = 7-a-c; c = 7-a-b[/tex]

and

[tex]\dfrac{7-b-c}{b+c}+\dfrac{7-a-c}{a+c}+\dfrac{7-a-b}{a+b} = 7\left(\dfrac{1}{a+b}+\dfrac{1}{b+c}+\dfrac{1}{a+c}\right)-3[/tex]

because it is not difficult to note that

[tex]$\sum \dfrac a{b+c}=\dfrac a{b+c}+\dfrac b{c+a}+\dfrac c{a+b}$[/tex]

Therefore,

[tex]7\left(\dfrac{7}{10}\right)-3 = \dfrac{49}{10}-3 =\boxed{ \dfrac{19}{10}} = \dfrac{a}{b+c} + \dfrac{b}{a+c} + \dfrac{c}{a+b}[/tex]

Finally,

[tex]10\left(\dfrac{a}{b+c} + \dfrac{b}{a+c} + \dfrac{c}{a+b} \right) = 10 \cdot \dfrac{19}{10} = 19[/tex]

Answer:

the part where it's 25 and 183 should be 5400 if you are rounding to the nearest 10 and then multiplying

Answer:

You made a wrong answer in 183 and 25.

It should be 5,400

Step-by-step explanation:

183 round to the nearest ten = 180

25 round to the nearest ten = 30

180 * 30 = 5,400

Answer:

Step-by-step explanation:

I will ASSUME that your equation is

s(t) = 3t⁴ - 40t³ + 126t² - 9

1) velocity is the derivative of position

v(t) = s'(t) = 12t³ - 120t² + 252t

2) changing what? position? velocity? acceleration? gender? color?

position No   the plot is continuous

velocity Yes  both magnitude and direction. Zeros at t = 0, 3, and 7 s

acceleration Yes, both magnitude and direction. Zeros at approx. t = 1.306 and 5.361 s

gender? who knows

color? probably.

3) velocity is positive (moving to the right on a standard number line) for

0 < t < 3 and t > 7

Moves to the left for

t < 0 and 3 < t < 7

1. the velocity of the object at any time "t" is v(t) = 12t³ - 120t² + 252t.

2. the object stops changing at t = 6 and t = 3.5.

3. the object is moving to the right in the interval 0 < t < 3.5 and moving to the left in the interval t > 6.

To determine the velocity of the object at any time "t," we need to find the derivative of the position function "s(t)" with respect to "t."

1. Velocity of the object at any time "t":

The velocity is the rate of change of position with respect to time, which is given by the derivative of the position function, s(t).

s(t) = 3t⁴ - 40t³ + 126t² - 9

To find the velocity function, we take the derivative of s(t) with respect to t:

v(t) = d/dt (3t⁴ - 40t³ + 126t²- 9)

v(t) = 12t³ - 120t² + 252t

So, the velocity of the object at any time "t" is v(t) = 12t³ - 120t² + 252t.

2. Does the object ever stop changing?

The object stops changing when its velocity becomes zero. To find when the velocity is zero, we need to solve the equation v(t) = 0.

12t³ - 120t² + 252t = 0

Now, we can factor out common terms:

t(12t² - 120t + 252) = 0

Now, set each factor equal to zero and solve for "t":

1st factor: t = 0

2nd factor: 12t² - 120t + 252 = 0

To solve the quadratic equation, we can either factor it further or use the quadratic formula. Factoring the quadratic equation gives us:

(t - 6)(12t - 42) = 0

Setting each factor to zero:

1. t - 6 = 0

t = 6

2. 12t - 42 = 0

12t = 42

t = 3.5

So, the object stops changing at t = 6 and t = 3.5.

3. When is the object moving to the right and when is the object moving to the left?

The object is moving to the right when its velocity (v(t)) is positive, and it is moving to the left when its velocity (v(t)) is negative.

Let's analyze the velocity function

v(t) = 12t³ - 120t² + 252t

To find the intervals where the object is moving to the right or left, we need to determine when v(t) is positive or negative.

1. Find critical points by setting v(t) = 0 and solving for "t":

12t³ - 120t² + 252t = 0

As we already found earlier, the critical points are t = 6 and t = 3.5.

2. Test each interval created by these critical points using test points to determine the sign of v(t) in those intervals.

Pick a value of "t" in each of these intervals:

- When t < 3.5 (e.g., t = 0),

- When 3.5 < t < 6 (e.g., t = 4),

- When t > 6 (e.g., t = 7).

Now, substitute these test values into the velocity function v(t):

- v(0) = 12(0)³ - 120(0)² + 252(0) = 0

- v(4) = 12(4)³ - 120(4)² + 252(4) = 192

- v(7) = 12(7)³ - 120(7)² + 252(7) = -588

Based on the test points, we can conclude:

- The object is moving to the right when 0 < t < 3.5 (positive velocity).

- The object is moving to the left when t > 6 (negative velocity).

Therefore, the object is moving to the right in the interval 0 < t < 3.5 and moving to the left in the interval t > 6.

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Answer:

3000×0.07=210 tins

Step-by-step explanation:

210 tins

Step-by-step explanation:

3000÷100×0.07

=2.1

Answer:

D

Step-by-step explanation:

Commutative switchs the numbers but not with subtraction or divion

Answer:

it is D I know because it is the opposite

Answer:

y = 2x + 1

Step-by-step explanation:

Pls mark as brainliest

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

The equation of the line with slope m = 2 and point (8, 19) is

y = 2x + 3

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

Slope:

m = 2

Point = (8, 19) = (x, y) _____(A)

Now,

The equation of a line is given as,

y = mx + c ______(B)

Substitute (A) into (B)

From (A) we get,

19 = 2 x 8 + c

19 = 16 + c

c = 19 - 16

c = 3

Now,

The equation of the line with slope m = 2 and point (8, 19) is

y = 2x + 3

Thus,

The equation of the line with slope m = 2 and point (8, 19) is

y = 2x + 3

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Answer:

similar by angle angle similarity property.

Step-by-step explanation:

they have the right angles, and then the two vertical angles.

:))

I think is the B, tell me if it's correct OK i'm trying to help

Answer:

5√7-5x√7

Step-by-step explanation:

[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{0}}}\implies \cfrac{4+3}{3}\implies \cfrac{7}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{\cfrac{7}{3}}(x-\stackrel{x_1}{0})[/tex]

we can always find the y-intercept by simply setting x = 0, or namely

[tex]y-(-3)=\cfrac{7}{3}(0-0)\implies y+3=\cfrac{7}{3}(0)\implies y+3=0\implies y=-3 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{\textit{y-intercept at}}{(0~~,~-3)}~\hfill[/tex]

Answer:

first one is 7/3

second one is -3

third one is g(x) = 7/3x-3

Step-by-step explanation:

I got it right