1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
seropon [69]
3 years ago
13

Simplify this expression. 20.25 – 9 + 11 о 1 4 0 18.75 0 21? 0 40.75

Mathematics
1 answer:
Greeley [361]3 years ago
8 0

Answer:

21\frac{3}{4}

Step-by-step explanation:

Step 1: Add the numbers.

20.25 can also be expressed as 20\frac{1}{4}, because \frac{2025}{100} = \frac{81}{4} = 20\frac{1}{4}. So if we add 20\frac{1}{4} and 11, we would get 31\frac{1}{4}

Step 2: Solve

31\frac{1}{4} -9\frac{1}{2}

  • Subtract the whole numbers

31-9=21

  • Combine the fractions

This means addition. Also, since our denominators are not the same value, we have to find the LCM (Least Common Denominator): What do 2 and 4 have in common that they can divide themselves by? 4. We know this because 2 divided by 4 is 2, and 4 divided by 4 is 1, so they can both divide themselves by 4.

\frac{5}{4}-\frac{1}{2}

LCM

\frac{5}{4}-\frac{2}{4} =\frac{3}{4}

Therefore, the simplified expression to this is 21\frac{3}{4}.

Learn more: brainly.com/question/403991

You might be interested in
Evaluate the expression when x = 1/2 and y = -2/5. Show all work.<br>1. -x + y<br>2. x +2y
NISA [10]
I am old, so I like to use paper & pencil

4 0
3 years ago
You decide to enter in a rowing competition. To train, you go to the boat house and begin rolling down stream. You row for the s
fredd [130]

Answer:

Time spent rowing down stream =100\ seconds

Speed of boat in still water =14\ ms^{-1}

Step-by-step explanation:

Let speed of boat in still water be = x\ ms^{-1}

Speed of current = 10\ ms^{-1}

Speed of boat down stream = \textrm{Speed of boat in still water +Speed of current}= (x+10)\ ms^{-1}

Distance rowed down stream = 2400 m

Time spent rowing down stream = \frac{Distance}{Speed}=\frac{2400}{x+10}\ s = \frac{Distance}{Speed}=\frac{2400}{x+10}\ s

Speed of boat up stream = \textrm{Speed of boat in still water -Speed of current}= (x-10)\ ms^{-1}

Distance rowed up stream = \frac{1}{6} \textrm{ of distance rowed downstream}=\frac{1}{6}\times 2400 = 400\ m

Time spent rowing up stream = \frac{Distance}{Speed}=\frac{400}{x-10}\ s

We know that,

\textrm{Time spent rowing down stream =Time spent rowing up stream}

So,

\frac{2400}{x+10}=\frac{400}{x-10}

Cross multiplying

2400(x-10)=400(x+10)

Dividing both sides by 400

\frac{2400(x-10)}{400}=\frac{400(x+10)}{400}

6(x-10)=x+10

6x-60=x+10

Adding 60 to both sides.

6x-60+60=x+10+60

6x=x+70

Subtracting both sides by x

6x-x=x+70-x

5x=70

Dividing both sides by 5.

\frac{5x}{5}=\frac{70}{5}

∴ x=14

Speed of boat in still water =14\ ms^-1

Time spent rowing down stream =\frac{2400}{14+10}=\frac{2400}{24}=100\ s

3 0
3 years ago
II. Word Problem:
Leona [35]
I don’t know understand
5 0
2 years ago
Find the partial fraction decomposition of the rational expression with prime quadratic factors in the denominator
SpyIntel [72]
\dfrac{5x^4-7x^3-12x^2+6x+21}{(x-3)(x^2-2)^2}=\dfrac{a_1}{x-3}+\dfrac{a_2x+a_3}{x^2-2}+\dfrac{a_4x+a_5}{(x^2-2)^2}
\implies 5x^4-7x^3-12x^2+6x+21=a_1(x^2-2)^2+(a_2x+a_3)(x-3)(x^2-2)+(a_4x+a_5)(x-3)

When x=3, you're left with

147=49a_1\implies a_1=\dfrac{147}{49}=3

When x=\sqrt2 or x=-\sqrt2, you're left with

\begin{cases}17-8\sqrt2=(\sqrt2a_4+a_5)(\sqrt2-3)&\text{for }x=\sqrt2\\17+8\sqrt2=(-\sqrt2a_4+a_5)(-\sqrt2-3)\end{cases}\implies\begin{cases}-5+\sqrt2=\sqrt2a_4+a_5\\-5-\sqrt2=-\sqrt2a_4+a_5\end{cases}

Adding the two equations together gives -10=2a_5, or a_5=-5. Subtracting them gives 2\sqrt2=2\sqrt2a_4, a_4=1.

Now, you have

5x^4-7x^3-12x^2+6x+21=3(x^2-2)^2+(a_2x+a_3)(x-3)(x^2-2)+(x-5)(x-3)
5x^4-7x^3-12x^2+6x+21=3x^4-11x^2-8x+27+(a_2x+a_3)(x-3)(x^2-2)
2x^4-7x^3-x^2+14x-6=(a_2x+a_3)(x-3)(x^2-2)

By just examining the leading and lagging (first and last) terms that would be obtained by expanding the right side, and matching these with the terms on the left side, you would see that a_2x^4=2x^4 and a_3(-3)(-2)=6a_3=-6. These alone tell you that you must have a_2=2 and a_3=-1.

So the partial fraction decomposition is

\dfrac3{x-3}+\dfrac{2x-1}{x^2-2}+\dfrac{x-5}{(x^2-2)^2}
7 0
3 years ago
Find the original price of a pair of shoes if the sale price is $20 after a 50% discount.
MrMuchimi
The Original Price is $40

Explanation:
50 1 20
—- = — Which means ——
100 2 40

7 0
3 years ago
Other questions:
  • A website uses the formula above to calculate a seller’s rating, R, based on the number of favorable reviews, F, and unfavorable
    15·1 answer
  • PRECALCULUS HELP IM BEGGING YOU
    7·1 answer
  • How does a translations 6 units up and 1 unit left change the coordinates of a shape?
    5·1 answer
  • the foundation of a building is in the shape of a rectangle WITH THE LENGTH OF 20 METERS AND A WIDTH OF 18 METERS. TO THE NEARES
    5·1 answer
  • Each side of a square is lengthened by 1 inch. The area of this new, larger square is 9 square inches. Find the length of a side
    14·1 answer
  • How do I solve equations with a variable to the power of something (give steps please)
    7·2 answers
  • I really need help with this TvT
    8·2 answers
  • Priscilla is on her school’s swim team. Her coach has noted the number of laps Priscilla and five of her teammates can swim with
    9·1 answer
  • I need help fast please
    14·1 answer
  • Simplify, will give brainliest plus 50 points
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!