Simplify the expression.
(5x + 1/2) + (3x - 7 1/2)

Answer:

12

Step-by-step explanation:

Answer:

Bro? wheres the question ?

Answer:  240 liters

=======================================================

Work Shown:

x = capacity of barrel in liters

This value of x is some positive real number. It represents the most amount of water the barrel can hold.

The problem states that the barrel is 2/3 full to start with. This means, we start off with (2/3)x liters of water. Then we subtract off 60 of them to get to 5/12 full, meaning we have (5/12)x liters left.

We can form this equation

(2/3)x - 60 = (5/12)x

Multiply both sides by 12 to clear out the fractions

(2/3)x - 60 = (5/12)x

12*( (2/3)x - 60 ) = 12*(5/12)x

12*(2/3)x - 12*60 = 12*(5/12)x

8x - 720 = 5x

From here we solve for x

8x - 5x = 720

3x = 720

x = 720/3

x = 240

The barrel's full capacity is 240 liters

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

Check:

2/3 of 240 = (2/3)*240 = 160

The barrel starts off with 160 liters of water inside.

We then use 60 of them to be left with 160-60 = 100 liters

Note how 100/240 = (5*20)/(12*20) = 5/12, showing that 100 liters out of 240 total reduces to the fraction 5/12. In other words, when we say "5/12 full" we mean 100 liters full. This helps confirm we have the right answer.

Answer:

silas

Step-by-step explanation:

Answer:

25%

Step-by-step explanation:

Given that,

Initial cost of a t-shirt = $30

Final cost of a t-shirt = $37.50

We need to find percent of change. The percentage change in any value is given by :

[tex]\%=\dfrac{\text{final value-initial value}}{\text{initial value}}\times 100\\\\=\dfrac{37.5-30}{30}\times 100\\\\=25\%[/tex]

Hence, the percentage error is 25%.

Answer:

66 pounds of tomatoes

Step-by-step explanation:

A recipe code lasagna calls for 3 pounds of tomatoes to serve 5 people. A caterer wants to make enough lasagna to serve 110 people. How many pounds of tomatoes does he neeed

From the above question:

5 people = 3 pounds of tomatoes

110 people = x pounds of tomatoes

Cross Multiply

5 people × x pounds = 110 people × 3 pounds

x pounds = 110 people × 3 pounds/5 people

x pounds = 66 pounds of tomatoes

Answer:↓↓↓

Step-by-step explanation:

We are given that side AB is congruent to BD. We are also given that side AC is congruent to CD.

We know that side BC and side CB are congruent because of the Reflexive property.

Therefore, ΔABC and ΔDBC are congruent because of SSS Postulate.

Hope this helped!

Answer:

x = 12

Step-by-step explanation:

Answer:

120

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Answer:

(x+1)^2+7

Step-by-step explanation:

khan academy

Answer:

s = 9 cm

p = 8s

p = 72 cm

Step-by-step explanation:

s = p ÷ 8

Where,

s = length of a side

p = perimeter of a regular octagon

find s when p = 72 cm

s = p ÷ 8

= 72 cm ÷ 8

= 9 cm

s = 9 cm

Formula for p in terms of a

s = p ÷ 8

Equivalent to

s = p/8

Cross product

s * 8 = p

p = 8s

Find p when s = 9 cm

p = 8s

p = 8 * 9 cm

= 72 cm

p = 72 cm

Answer:

d

Step-by-step explanation:

take out of parenthesis so its 8-6r+2 and the 8 and to to get 10 and the -6r stays the same

Answer:

A

Step-by-step explanation:

The only one with nothing else in front of the X, which means you can't divide, which means it stays the same.

Answer:

what is the question you didn't put one up

Answer:

Where is the question?

Step-by-step explanation:

?

Answer:

a = 44 is correct

Step-by-step explanation:

a + 4 = 48

plug in the #'s 1 at a time

43 + 4 = 48

47 = 48  FALSE

51 + 4 = 48

55 = 48  FALSE

44 + 4 = 48  TRUE

52 + 4 = 48  FALSE

Hope this Helps!!!

Answer:

Your answer would be a= 44

Step-by-step explanation:

44+4=48

To check: 48-4=44

Therefore, your answer is 44

Answer:[tex]313^{\circ}[/tex]

Step-by-step explanation:

Given

[tex]\angle {EFG}=133^{\circ }[/tex]

When rotated 180 degree clockwise gives E'F'G' which measures

[tex]\angle E'F'G'=180^{\circ}+133^{\circ}=313^{\circ}[/tex]

This can be explained by the below-given digram  

Rotation is a rigid transformation.

The measure of angle E'F'G' is 133 degrees

Because rotation is a rigid transformation, it does not change the side lengths and the angle measures.

This means that the measure of angle EFG will remain unchanged after rotation.

i.e.

[tex]\mathbf{\angle E'F'G' = \angle EFG}[/tex]

Hence, the measure of angle E'F'G' is 133 degrees

Read more about rotation at:

https://brainly.com/question/1571997

Answer:

length= 710 width= 420

Step-by-step explanation:

As we consider a rectangle we can replace "length" with l and "width" with w so that the perimeter will be:

2l+2w= 2260

With the length as:

l= w+290

The length, substituted into the perimeter is:

2(w+290)+2w=2260

Distribute:

4w+580=2260

Subtract:

4w=1680

Divide:

w=420

To find the length, take the width and add 290:

420+290=710

l=710

Answer:

x plus 1

Step-by-step explanation:

Answer:

x+1

Step-by-step explanation:

if you simplify the equation, you will get x+1

first, you take the parentheses away.  The equation becomes

3x-2x-4+5

then you combine like terms

x+1

Answer: $12.87

Step-by-step explanation:

You need to set up your equation. We are trying to find x.

Step 1:  [tex]\frac{x}{39} = \frac{33}{100}[/tex]

Step 2: Multiply across: 39 x 33 divided by 100.

39 x 33 = 1287

1287 divided by 100 = $12.87

Answer: $12.87

Answer:

[tex]2abcosC = 37[/tex]

Step-by-step explanation:

Given

[tex]a^2 + b^2 - 2abcosC = c^2[/tex]

Required

[tex]2abcosC[/tex]

[tex]a^2 + b^2 - 2abcosC = c^2[/tex]

Add [tex]2abcosC[/tex] to both sides

[tex]a^2 + b^2 - 2abcosC+2abcosC = c^2+2abcosC[/tex]

[tex]a^2 + b^2 = c^2+2abcosC[/tex]

Subtract [tex]c^2[/tex] from both sides

[tex]a^2 + b^2 -c^2= c^2 -c^2+2abcosC[/tex]

[tex]a^2 + b^2 -c^2= 2abcosC[/tex]

From the attachment:

[tex]a = 4[/tex] [tex]b = 5[/tex] and [tex]c = 2[/tex]

So, we have:

[tex]4^2 + 5^2 -2^2= 2abcosC[/tex]

[tex]16 + 25 -4= 2abcosC[/tex]

[tex]37= 2abcosC[/tex]

i.e.

[tex]2abcosC = 37[/tex]

Answer:

A. 37

Step-by-step explanation:

Step-by-step explanation:

Marta put $4.89 in her coin bank.

Each day she added 1 quarter, 1 nickel, and 6 pennies.

We know that,

1 quarter = 25 cents

1 nickel = 5 cents

1 penny = 1 cent

⇒ 6 pennies = 6 cent

Total amount added in 6 days,

= 25 cents + 5 cents + 6 cent

= 36 cents

We know that,

1$ = 100 cents

36 cents = $0.36

Total money in her bank,

= $4.89 + $0.36

= $5.25

Hence, this is the required solution.

Answer:

The answer is D.

Step-by-step explanation:

Answer:

2/5+1/10

Step-by-step explanation:

2/5 ×2/2= 4/10

4/10+1/10=

5/10=1/2

Answer:

Step-by-step explanation:

It will be 129

Answer:

LCM of both polynomials=[tex]\mathbf{5m^3}[/tex]

Step-by-step explanation:

Least Common Multiple

We are given the polynomials

[tex]5m^7+ 35m^6+50m^5[/tex]

[tex]-20m^5-80m^4+100m^3[/tex]

Find the common factors of each polynomial, first the coefficients:

5 = 5

35 = 5*7

50 = 5*5*2

The common factor with the least exponent; 5

Now for the variables:

[tex]m^7, m^6, m^5[/tex]

The common factor with the least exponent; m^5

LCM of [tex]5m^7+ 35m^6+50m^5: 5m^5[/tex]

Similarly:

20 = 2*2*5

80=2*2*2*2*5

100 = 2*2*5*5

Common factor of the coefficients: 2*2*5=20

Common factor of variables: [tex]m^3[/tex]

LCM of [tex]-20m^5-80m^4+100m^3 = 20m^3[/tex]

LCM of both polynomials=[tex]\mathbf{5m^3}[/tex]

Given:

The function is

[tex]f(x)=\left(\dfrac{1}{3}\right)^x[/tex]

To find:

The missing values for a, b, and c in the given table.

Solution:

We have,

[tex]f(x)=\left(\dfrac{1}{3}\right)^x[/tex]

At x=-2,

[tex]f(-2)=\left(\dfrac{1}{3}\right)^{-2}[/tex]

[tex]a=\left(3\right)^{2}[/tex]         [tex]\left[\because \left(\dfrac{a}{b}\right)^{-n}=\left(\dfrac{b}{a}\right)^{n}\right][/tex]

[tex]a=9[/tex]

At x=-1,

[tex]f(-1)=\left(\dfrac{1}{3}\right)^{-1}[/tex]

[tex]b=\left(3\right)^{1}[/tex]         [tex]\left[\because \left(\dfrac{a}{b}\right)^{-n}=\left(\dfrac{b}{a}\right)^{n}\right][/tex]

[tex]b=3[/tex]

At x=0,

[tex]f(0)=\left(\dfrac{1}{3}\right)^{0}[/tex]

[tex]c=1[/tex]         [tex]\left[\because a^0=1, a\neq 0\right][/tex]

Therefore, the missing values of a,b and c are 9, 3, and 1 respectively.

Answer: below

Step-by-step explanation:

Answer:

angleWTR + angleWTU = 180°

Thus they are supplementary.

Option B.

Answer:

Part A: 1.2 minutes

Part B: 0.83

Part C: 25.2

Answer:

a. 1.2 minutes

b. one lap per 1.2 minutes

c. 25.20 minutes

Step-by-step explanation:

a. do 6 mins/5 laps which gives you 1.2, so 1.2 minutes or 1 minute and 20 seconds

b. uh one lap per 1.2 minutes

c. 25.2 minutes which is approx. 25 minutes and 20 seconds. I reallly hope this helps!