Match the meaning of each of the following expressions.
1. x added to the sum of five and seven
x - (8 + 2)
2. the sum of eight and two, subtracted from x
8 - x
3. eight added to x
x + (5 + 7)
4. eight subtracted from x
x - 8
5. eight minus x
x + 8
6. five subtracted from n
n - 5
7. the sum of x and itself
x + x
8. the difference of eight and two, added to x
5 - n
9. the sum of n and five
x + (8 - 2)
10. five minus n
n + 5

Answer:

Addition and Subtraction of Fractions · 1. Add: (i) 7/ 10 + 2/15 (ii) 2²/₃ + 3¹/₂ · 2. Simplify: (i) 15/16 – 11/12 (ii) 11/15 – 7/20 · 3. Simplify: 4⁵/₆ – 2³/₈ + .

Answer:

7/10 + 2/15= 5/6

2 3/3 + 3 1/2= 6 1/2

15/16 - 11/12= 1/48

11/15 - 7/20= 23/60

Step-by-step explanation:

When adding or subtracting fraction with different denominators, we must find there LCM to be their new denominators. Then divide the new denominator by the old denominator, do for both fractions, then multiply the answer with the numerator, do for both fractions to get their new numerators. Then add or subtract the fractions. Then simplify the answer if needed.

Ex 1:

The LCM of 10 and 15 is 30

7/10 + 2/15

(30 ÷ 10=3, 3 × 7= 21)(30 ÷ 15= 2, 2 × 2=4)

=21/30 + 4/30= 25/30 or 5/6

With whole numbers, add the two whole numbers together. Then n add the fractions. Lastly add both of the answers together.

Ex:

The LCM of 3 and 2 is 6

2 3/3 + 3 1/2

=2 + 3= 5

= 3/3 + 1/2= 9/6 or 1 3/6 or 1 1/2

= 5 + 1 1/2

= 6 1/2

Always remember to simplify if possible or necessary.

I hope this helps! I'm sorry if it's wrong or too complicated.

Answer:

K(3, 5)

Step-by-step explanation:

let K(x, y)

then x + 7 = 5*2 and y + 7 = 6*2 by the midpoint theorem.

solving, x = 3, y = 5

Answer:

40 km/h

Step-by-step explanation:

s = ut where s - Distance

u - Speed

t - Time

when t = 10 min

= 10/60 hours

S1 = 30 * 10/60

= 5km

when t= 20 min

= 20/60 hours

S2 = 45 *20/60

= 15 km

Then total distance = S1 + S2

= 5 + 15

= 20 km

Total time period = (10 + 20 ) / 60 hours

= 1/2 hours

Then average speed = U

S = UT

U = S/ T

= 20/ 0.5 km/ h

= 40 km/ h

Answer:

As the number of files increases, the storage space used increases.

Answer:D

Step-by-step explanation:

2 hours 45 minutes

12h30m - 9h45m =

= (12×60m + 30m) - (9×60m + 45m)

= 750m - 585m

= 165 minutes

= 120m + 45m

= 2 hours 45 minutes

Answer:

You must drink  52 7/12 ounces or 52.58 ounces to reach the goal.

Step-by-step explanation:

Total amount of the water already drank is found by adding the fractions

So

3 1/10 ounces + 2 1/15 ounces + 6 5/20

Converting into improper fractions

31/10 + 31/15+ 125/20

Now finding the lcm of 10,15,20

so  Factors of 10 = 2 x 5

Factors of 15 = 5 x 3

Factors of 20 = 2 x2 x5

LCM= 5x2x2x3= 60

31*6/60 + 31*4/60 + 125*3/60

= 186+124+375/60

= 685/60 = 11.42 ounces

The amount of water already drank is 11.42 ounces

The amount remaining is found by subtracting the amount drank from the total amount

so

64 ounces - 11.42= 52.58

It can be solved in fractions as

64- 11 5/12

Again taking making improper fraction and taking lcm

64- 137/12

= 768-137/12 = 631/12= 52 7/12 ounces

Answer:

A

Step-by-step explanation:

true true true true true true

Answer:

False

Step-by-step explanation:

In order to tell if an inverse is a function, you have to do the horizontal line test. Create an imaginary line going horizontally on the map and if the graphed function goes through more than one line, then the inverse won't be a function. There can only be one point going through the imaginary line. Does that make sense?

hope you understand..................................................................

Answer:

6x³y

Step-by-step explanation:

(2xy) * 3x²

We know that 2 * 3 = 6 and x * x² = x¹ * x² = x⁽¹⁺²) = x³ so the final answer is 6x³y.

Answer:

5,5,15

Step-by-step explanation:

Answer:

1.8 hours.

Step-by-step explanation:

It is important to note that:

Speed = Distance ÷ Time

We have two trains.

Step 1

We have to find the distance that each train travelled.

Since Speed = Distance ÷ Time

Distance = Speed × Time

First train

It travels at 105 miles per hour

Distance travelled by first train =

105 × x hours

= 105x miles

Second Train

It travels at 85 miles per hour

Distance travelled by the second train = 85 miles × x hours

= 85x miles

We are told that: the two trains leave stations 342 miles apart at the same time and travel toward each other

Hence, the time it would take each train to meet each other is calculated as:

105x + 85x = 342 miles

190x = 342 miles

x = 342/190

x = 1.8 hours.

Answer: c).

Both options are true. You can see that the whiskers of data set 2 (The lines extending on either side of the box plots) represent a much larger range of data than data set 1, and that the median in data set 2 (the line down the middle of the boxes) is greater than data set 1.

Hope this helps!

Answer:

0.8208 ; 0.8448

Step-by-step explanation:

Given the following :

Number of tosses = 4

Probability of head on any toss :

P(head) = 0.4

Therefore ;

(1 - p(head)) = (1 - 0.4) = 0.6

Binomial probability :

P(X) = nCx * P^x * (1 - P) ^(n-x)

Where:

n = number of trials ; x = number of success ; P = probability of success.

P(X≤2) = P(0) + P(1) + p(2)

using binomial probability calculator to ensure faster computation:

P(X≤2) = 0.1296 + 0.3456 + 0. 3456

= 0.8208

B)

P(1 ≤ X ≤ 3) = P(1) + P(2) + P(3)

P(1 ≤ X ≤ 3) = 0.3456 + 0.3456 + 0.1536

= 0.8448

Answer:

Think of the double angle formula for

sin

2

x

Explanation:

sin

2

x

=

sin

x

2

sin

x

cos

x

=

sin

x

2

sin

x

cos

x

−

sin

x

=

0

sin

x

(

2

cos

x

−

1

)

=

0

Solution A:

sin

x

=

0

⇒

x

=

k

π

,

k

∈

Z

Solution B:

2

cos

x

=

1

⇒

cos

x

=

1

2

,

x

=

±

π

3

+

2

k

π

=

π

3

(

6

k

±

1

)

,

k

∈

Z

∴

x

=

k

π

or

x

=

π

3

(

6

k

±

1

)

,

k

∈

Z

Step-by-step explanation:

Answer:

       [tex]\bold{x=\frac\pi3+2k\pi\quad \vee\quad x=\frac{5\pi}3+2k\pi\quad \vee\quad x=k\pi\ ,\quad k\in\mathbb Z}[/tex]

Step-by-step explanation:

[tex]\sin 2x=\sin x\\\\\sin2x - \sin x=0\\\\2\sin x\cos x-\sin x=0\\\\(2\cos x-1)\sin x=0\\\\2\cos x-1=0\qquad\qquad\qquad\qquad or\qquad \sin x=0\\\\2\cos x=1\quad\qquad\qquad\qquad\qquad\ or\qquad \sin x=0\\\\\cos x=\frac12\qquad\qquad\qquad\qquad\qquad or\qquad \sin x=0\\\\x=\frac\pi3+2k\pi\quad \vee\ \ x=\frac{5\pi}3+2k\pi\quad\ \ \vee\ \ x=0+k\pi\ ,\quad k\in\mathbb Z[/tex]

Answer:

x^1/4

Step-by-step explanation:

[tex]\frac{x^{\frac{1}{2}}}{x^{\frac{1}{4}}}\\\\\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}\\\\\frac{x^{\frac{1}{2}}}{x^{\frac{1}{4}}}=x^{\frac{1}{2}-\frac{1}{4}}\\\\\mathrm{Simplify}\:x^{\frac{1}{2}-\frac{1}{4}}:\\\\\quad x^{\frac{1}{4}}[/tex]

Answer:

Step-by-step explanation:

finding the first term by putting n=1

t(1)=4.[tex](1)^{2}[/tex] +2 = 4.1 +2 = 4+2 = 6

finding the second term by putting n=2

t(2)=4.[tex](2)^{2}[/tex] +2 = 4.4 +2 = 16+2 = 18

finding the third term by putting n=3

t(3)=4.[tex](3)^{2}[/tex] +2 = 4.9 +2 = 36+2 = 38

hence first three terms are:

               6,18,38,......,4[tex]n^{2}[/tex] +2

Answer:

f(2) = 16

or

y = 16

Step-by-step explanation:

Step 1: Write out function

y = 6x + 4

Step 2: Define variable for problem

x = 2

Step 3: Plug into function f(x)

f(2) = 6(2) + 4

f(2) = 12 + 4

f(2) = 16

Step 4: Change f(2) to y

y = 16

Answer:

49

Step-by-step explanation:

(-7)² = (-7)(-7) = 49

Answer:

z = -1

Step-by-step explanation:

0 = 8z + 8

-8 = 8z

-8/8 = z

z = -1

check:

0 = 8*-1  +  8

0 = -8 + 8

Step-by-step explanation:

In the plane geometry Abeka, second edition, it is given :

Principle 2 states that between any two points, only one straight line can be drawn.

And according to principle 3 two straight lines interacts at one point only.

Thus this can be well illustrated by two straight lines which are represented by the streets of a city and these two streets intersects at a point.

Answer:

A square root of a number is a value that, when multiplied by itself, gives the number.

Example: 4 × 4 = 16, so a square root of 16 is 4.

The symbol for a square root is √ which always means the positive square root.

Example: √36 = 6 (because 6 x 6 = 36)

Answer:

Hi there!

Step-by-step explanation:

In my opinion, the answer should be 1 (and maybe 4)

We can tell 1)has no width is the answer because the lines the one dimensional.

So the answer has to be number 1.

And...

Number 4 might also be correct because that would be a line segment (which goes on in both directions)

********************************************

So your answer should be letter 1 (also it might be letter 4 too, but I am not that sure)

Hope this helps!

~Have a great day!~

If you have any questions feel free to ask! :)

Find the number in the tenth place  1  and look one place to the right for the rounding digit  9 . Round up if this number is greater than or equal to  5  and round down if it is less than  5 .

5.2

Answer:

It can always be written as a fraction.

Step-by-step explanation:

The importance of this question is to differentiate rational and irrational numbers.

Rational numbers can be written as a ratio, hence a fraction, or a repeating or terminating decimal.

Irrational numbers cannot be written as a ratio and will not have a terminating or repeating decimal.

So the first statement is true since the sum of two rational numbers will be rational.

The second statement is false since the sum of two rational numbers can absolutely be represented by a fractional ratio.

The third statement is false since the sum of two rational numbers is not always a repeating decimal.

The fourth statement is false since the sum of two rational numbers could be written as a terminating decimal.

Cheers.

I agree with the other person's response. The sum is always rational (it can always be written as a fraction of integers)

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

Here's a proof:

Let x and y be two rational numbers. This means

x = a/b

y = c/d

where a,b,c,d are integers. The denominators b and d cannot be 0.

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

Let's add x and y, then simplify

x+y = (a/b) + (c/d)

x+y = (ad/bd) + (bc/bd)

x+y = (ad+bc)/(bd)

This last expression is in the form p/q

p = ad+bc is an integer

q = bd is also an integer

we have a ratio or fraction of integers, therefore x+y is also rational

Answer:

P(spades) = 7/10

Step-by-step explanation:

there are 10 different cards that can be picked, out of which what we want to pick is spades which are 7. and so there are 7 chances that we will get to pick spades out of all the 10 possibilities. hope it is easy to understand

Answer:

0.08(50h)

Step-by-step explanation:

The amount of tax payable over a particular object or goods is always represented as a particular percentage of the total cost of buying or repairing an object.

From the above question we are given the expression,

0.08(50h) + 50h = Total amount Deborah is paying to repair her computer

Note that: Total amount payable by Deborah = Cost (Price or amount) of fixing the computer + Tax

h = number of hours required to repair the computer.

Hence, the Cost (amount) to repair the computer = 50 × h = 50h

In the expression, we have

0.08(50h) = 8% of 50h

Tax is always represented as percentage of the cost of fixing the computer

Hence, 0.08 or 8% of 50 h equal to = 0.08(50h) = The tax Deborah is paying.

Therefore, the expression repesents the amount of tax Deborah has to pay is 0.08(50h)

Answer:

a) The perimeter of a rectangle is written as:

P = 2*L + 2*W

where L is the length amd W is the width (broad in this case).

here we have:

L = 8cm and W = b

then the perimeter is:

P = 2*8cm + 2*b

And we know that:

18cm ≤ P ≤ 50cm

where ≤ is used because there is written "not more" and "not less", so the equalities are allowed

now we can replace P by the above equation:

18cm ≤ 16cm + 2*b ≤ 50cm

now we can subtract 16cm in each side and get:

18cm - 16cm ≤ 2*b ≤ 50cm - 16cm

2cm ≤ 2*b ≤ 34cm

Now we can divide each side by 2.

1cm ≤ b ≤ 34cm/2 = 17cm

1cm ≤ b ≤ 17cm.

b) Here we have missing information, so this can not be answered.

(only knowing that one side length is x, and another side length is x + 3cm, we can know that x > 0cm, so the minimum value of x is really close to 0cm)

Answer:

Monday, at 12:15 AM

Step-by-step explanation:

Do this question in parts. First, add 2 days to Friday to get Sunday at 5:45 PM. Then, add 6 hours to 5:45 to get 11:45 PM. Finally, add 30 minutes to 11:45 PM. That takes you to 12:15, and since you passed midnight, Sunday is now Monday. That means the bus arrives Monday, at 12:15 AM.

Answer:

Reflection, Translation, and possibly Rotation