Simplify 2(x + y) + 3(x + y)

Answers

Answer 1

Distribute
2x+2y+3x+3y

Combine like terms
5x+5y

Final answer: 5x+5y

ps Another way to do it is that know the two inner binomials are the same so you can write it as (2+3)(x+y) which simplifies to 5(x+y) and distributes to 5x+5y

Related Questions

8x__=2
10x__= 5
—
2
6x__= 3
—
2
?? Can you fill in the blanks?

Answers

1/4
1/2

1/2
I could only understand 1, 2, & 5

What is the value of x in the equation 2x – 3 = 9 – 4x?

Answers

Add 3 to both sides
2x=12-4x

Add 4x to both sides
6x=12

Divide both sides by 6
x=2

Final answer: x=2

I need help I am trying to find ft

Answers

1 foot = 12 inches

divide 69 by 12

69/12 = 5.75 feet

What is n in a(n-5)+6=bn.(You can use variables in the answer). Please explain, if you can.

Answers

a(n-5)+6=bn
use dis. property for left
an-a5+6=bn
isolate n.
(an-a5+6)/ b= n is the asnwer

How do I solve this equation? I need a refresher on Algebra.

Answers

These equations seem tricky, but aren't as hard as you think. Just solve it like you are regularly adding fractions.

Your common denominator is 9x + 9, so

1/(9x+9) = 36/(9x + 9) - (5x + 5)/9

1 - 36 + 5x + 5 / 9x - 9
30x - 30/9x - 9
10x-10/3x - 3
10(x-1)/3(x-1)
10/3

Hope this helped!

Final answer:

To solve an algebraic equation, identify knowns, find suitable equations, simplify algebraically, substitute known values, solve for the unknown, and check if the answer is reasonable.

Explanation:

To solve an algebraic equation, follow these systematic steps:

Firstly, identify the knowns and make a list of what is given or can be inferred from the problem.

Then, find the appropriate equation or set of equations that contain the unknown you need to solve for.

Simplify the algebra by eliminating terms wherever possible. This might require algebraic rearrangement such as dividing terms or multiplying both sides of the equation to isolate the unknown.

Substitute the known values into the equation.

Solve for the unknown and make sure to include units where necessary.

Finally, always check your answer to see if it is reasonable and makes sense.

These steps should yield a solution that is both accurate and verifiable.

What is 36 divided by 3/4?

Answers

36 divided by 3/4 is 48.

Answer is 48

Explanation: 36 divided by 3/4

36 4 144
____ x ____ = ____ = 48
1 3 3

^
Flip the denominator to numerator
And numerator to denominator

Also divide 144/3

how many integers from 1 to 700 are divisible by 2, 5 and 7

Answers

Final answer:

There are 10 integers from 1 to 700 that are divisible by 2, 5, and 7. This is calculated by finding the least common multiple (LCM) of the numbers, which is 70, and then determining how many multiples of 70 are within the given range.

Explanation:

The question asks to find out how many integers from 1 to 700 are divisible by 2, 5, and 7. An integer divisible by 2, 5, and 7 is also divisible by their least common multiple (LCM). The LCM of 2, 5, and 7 is 70 since 2 x 5 x 7 = 70. So, the task is to find the number of multiples of 70 between 1 and 700.

To find the number of multiples of 70 in that range, you can use the following steps:

Divide the largest number in the range (700) by 70 to find the highest multiple within the range. ∑(700 ÷ 70 = 10).Since we started from 1 and 70 is the first multiple, the total count is the result of the division.

Therefore, there are 10 integers from 1 to 700 that are divisible by 2, 5, and 7.

A family went on vacation and used 5.4 gallons of gasoline to travel 150 miles. How many total gallons of gasoline will they need to travel 200 more miles?

Answers

I would use a ratio
so 5.4 gallons/150 miles = ?gallons/200 miles
so 5.4gallons*200 miles = ?gallons*150 miles
5.4gallons*200miles/150miles = ? gallons
?gallons = 7.2 gallons

7.2 total gallons of gasoline they will need to travel 200 more miles.

What is Distance?

Distance is the total speed of an object. This is regardless of direction. It is also defined as multiplying the speed of an object by the total time taken by the object to travel the length of its path.

Distance = Speed * Time

It's SI unit is metre (m).

It is a scalar quantity which has no direction. It only has magnitude means only value.

For above given example,

For 150 miles 5.4 gallons gas is used

so, for 1 mile 0.036 gallon will be used

So, For more 200 miles= 0.036*200

= 7.2 gallons of gas will be used

Thus, 7.2 total gallons of gasoline they will need to travel 200 more miles.

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pre cal/cal master needed

g(x)={ ax-3, x<-2
{ x^2 -2x, x>-2

What value would the function g(x) have point discon. at x=-2 how to find?

Answers

Hello, I know this is a little late but been busy and noticed you responded on this and my profile.

Ok so we want to find what value of a would the function g(x) have point discontinuity at x=-2.

We find this by subsituting -2 where the x is located in the functions x^2 -2x
x^2 -2x
-2^2 - 2(-2) = 8
Now to find a we use ax - 3 and insert -2 for x like the follow
-2a - 3
Next for the limit to exist both limits have to equal the same so we have
-2a - 3 = 8
Now solve for a
-2a - 3 = 8
-2a - 3 + 3 = 8+3
-2a = 11
-2a / -2 = 11 / -2
a = -5.5

So when a is at -5.5 the function is continuous and anything > or < will make it discontinuous. So when -5.5 < a < -5.5 a will have discontinuity.

The length of a table is 6 feet. On a scale drawing, the length is 2 inches. Write three possible scales for the drawing

Answers

Answer:

The three possible scales for the drawing are 1 inch : 3 feet, 1 inch : 36 inch and 1 inch : 91.44 cm.

Step-by-step explanation:

It is given that the length of a table is 6 feet. On a scale drawing, the length is 2 inches.

The scale for drawing is

[tex]Scale=\frac{\text{Length in drawing}}{\text{Actual length}}=\text{Length in drawing}:\text{Actual length}[/tex]

First possible scale for the drawing is

2 inch : 6 feet

It can be written as

1 inch : 3 feet

We know that 1 feet = 12 in

1 inch : 36 inch

We know that 1 feet = 30.48 cm

1 inch : 91.44 cm

Therefore the three possible scales for the drawing are 1 inch : 3 feet, 1 inch : 36 inch and 1 inch : 91.44 cm.

The three possible scales for the drawing are 1 inch : 3 feet, 1 inch : 36 inch and 1 inch : 91.44 cm.

Here, we have,

It is given that the length of a table is 6 feet. On a scale drawing, the length is 2 inches.

The scale for drawing is

scale = length in drawn/actual length

scale = length in drawn : actual length

First possible scale for the drawing is

2 inch : 6 feet

It can be written as

1 inch : 3 feet

We know that 1 feet = 12 in

1 inch : 36 inch

We know that 1 feet = 30.48 cm

1 inch : 91.44 cm

Therefore the three possible scales for the drawing are 1 inch : 3 feet, 1 inch : 36 inch and 1 inch : 91.44 cm.

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Simplify the equation and write the answer without negative exponents

Answers

[tex] \sqrt{200} - \sqrt{32} = \sqrt{2 \times 100} - \sqrt{2 \times 16} = 10 \sqrt{2} - 4 \sqrt{2} = 6 \sqrt{2} [/tex]

[tex]\bf \sqrt{200}-\sqrt{32}\quad \begin{cases} 200=2\cdot 2\cdot 2\cdot 5\cdot 5\\ \qquad 2^2\cdot 2\cdot 5^2\\ \qquad (2\cdot 5)^2\cdot 2\\ \qquad (10)^2\cdot 2\\ 32=2\cdot 2\cdot 2\cdot 2\cdot 2\\ \qquad 2^2\cdot 2^2\cdot 2\\ \qquad (2\cdot 2)^2\cdot 2\\ \qquad (4)^2\cdot 2 \end{cases}\implies \sqrt{10^2\cdot 2}-\sqrt{4^2\cdot 2} \\\\\\ 10\sqrt{2}-4\sqrt{2}\implies 6\sqrt{2}\implies 6\cdot 2^{\frac{1}{2}}[/tex]

Supposed to angles are supplementary and one of them measures 31° what is the measure of the other angle

Answers

the answer is 149 because it is 180-31

i need help 7th grade 13 + p + - 4 3

Answers

13 + -30 = -43 I think that's it

you first combine like terms.
13+p-43=
-30+p

Which Rate Does Not Belong With The Other Three. Explain

60 mi/h
88 ft/s
500 ft/min
1,440 mi/day

Answers

88ft/s

hop this helps

use properties to find 4 times 23 times 25

Answers

The answer to the problem is 2300

Answer:

2300

Step-by-step explanation:

How are the values of the eights in 880 relared

Answers

The 8 next to the zero is the tens of the number (80) while the leftmost 8 is the hundreds of the number (800)
the number 880 can be written as:
880 = 800 + 80 + 0

what is 28.5 divided by 5

Answers

38383833333333333333333333

28.5 divided by 5 is 5.7

PLEASE ASAP
Trapezoid W ′ X ′ Y ′ Z ′ is the image of trapezoid WXYZ under a dilation through point C. What scale factor was used in the dilation?
− 7/3
− 3/7
3/7
7/3

Answers

you need a picture to be able to answer the question

You are building a new house on a cartesian plane whose units are measured in miles.

Your house is to be located at the point (6,0). Unfortunately, the

existing gas line follows the curve y=√16x^(2)+6x+19.

It costs 300 dollars per mile to install new pipe connecting your house to the existing line.

What is the least amount of money you could pay to get hooked up to the system?

Answers

so.. we'll use the distance formula for it, keeping in mind that, where the line touches the parabola is at ( x , f(x) ), check the picture below on the left-hand-side

[tex]\bf y=\sqrt{16x^2+6x+19}\\\\ -------------------------------\\\\ L(x)=\left[(6-x)^2+(0-\sqrt{16x^2+6x+19})^2 \right]^{\frac{1}{2}} \\\\\\ L(x)=[36-12x+x^2+16x^2+6x+19]^{\frac{1}{2}} \\\\\\ L(x)=(17x^2-6x+55)^{\frac{1}{2}}\\\\ [/tex]

so, that's L(x) equation for the line, simplified, now, let's check its derivative.

[tex]\bf \cfrac{dL}{dx}=\cfrac{1}{2}(17x^2-6x+55)^{-\frac{1}{2}}(34x-6) \\\\\\ \cfrac{dL}{dx}=\cfrac{1}{2}(17x^2-6x+55)^{-\frac{1}{2}}2(17x-3) \\\\\\ \cfrac{dL}{dx}=\cfrac{17x-3}{\sqrt{17x^2-6x+55}}\\\\[/tex]

now, we get critical points when the derivative is 0, or when the denominator is 0, however (usually cusps or asymptotes), but in this case, we won't check the denominator, because it doesn't yield any, so, we'll just zero out the derivative and see what critical points we get.

[tex]\bf 0=17x-3\implies 3=17x\implies \cfrac{3}{17}=x[/tex]

easy enough, so we only got one point... well, is it a minimum though?

well, running a first-derivative test on the left-region and the right-region of 3/17, we get a negative value on the left and a positive value on the right, that means the original function drops and then goes up, check the picture on the right-hand-side.

So, it's a minimum, those numbers in red in the picture are the ones I used to check it, but any value on the region will work, even -1,000,000, anyway.

so, at 3/17 is at a minimum... now how many miles, and how much is that?

[tex]\bf f\left( \frac{3}{17} \right)\approx 4.53\qquad \qquad \stackrel{miles}{4.53}\cdot \stackrel{\textit{\$ per mile}}{300}\approx 1360.2[/tex]

Irrigation improves the yield of strawberries per acre according to the function S=-(w-2)^2 +50 where S is the number of pints of strawberries grown per acre and w is the acre-feet of water used. Strawberries sell for $3 per pint and water costs $5 per acre-foot. Graph the yield function.

Answers

Given:
The yield of strawberries per acre is
S = -(w - 2)² + 50
where
S = number of pints of strawberries per acre
w = acre-feet of water

Strawberries sell for $3 per pint
Water costs $5 per acre-feet.

The yield function is the revenue minus the expenses. It is
Y = (S pints)*($3 per pint) - (w acre-ft)*($5 per acre-ft)
Y = -3(w - 2)² -5w + 150 dollars

A graph of the yield function is shown below.
It indicates that
a) the yield is maximum when the acre-feet is about 1.5;
b) the yield increases between zero and 1.5 acre-feet;
c) the yield decreases quickly when the acre-feet exceed 1.5;
d) the yield vanishes when the acre-feet exceed 8.

How do you write 7/20 as a percentage??

Answers

can either be 0.35 or 35%

7/20
In decimal form would be 0.35 .
To get the percentage move the decimal to the right 2 times .
:)

The slope of a line is 2/3. What is the slope of a line that is perpendicular to this line? Type a numerical answer in the space provided. Do not include spaces in your answer. If necessary, use the / key to represent a fraction bar and only type improper fractions (no mixed numbers).2/3

Answers

The slope perpendicular to 2/3, would be -3/2

we know that

If two lines are perpendicular, then the product of their slopes is equal to minus one

[tex]m1*m2=-1[/tex]

In this problem we have

[tex]m1=\frac{2}{3}[/tex]

Substitute in the formula and solve for m2

[tex]\frac{2}{3}*m2=-1[/tex]

[tex]m2=-\frac{3}{2}[/tex]

therefore

the answer is

The slope is equal to [tex]-\frac{3}{2}[/tex]

The second side of a triangular deck is 6 feet longer than the shortest side and a third side that is 6 feet shorter than twice the length of the shortest side. If the perimeter of the deck is 68 feet, what are the lengths of the three sides?

Answers

you have x, x + 6, and 2x - 6. Together, they equal 68 feet, meaning that 4x = 68. therefore x = 17 feet. The lengths would then be 17 ft, 23 ft, and 28 ft.

Answer: The required lengths of the three sides of the deck are 17 feet, 23 feet and 28 feet.

Step-by-step explanation: Given that the second side of a triangular deck is 6 feet longer than the shortest side and a third side that is 6 feet shorter than twice the length of the shortest side.

The perimeter of the deck is 68 feet.

We are to find the lengths of the three sides of the deck.

Let x feet be the length of the shortest side.

Then, according to the given information,

the length of the second side = (x+6) feet

and

the length of the third side = (2x-6) feet.

Since the perimeter of the deck is 68 feet, so we must have

[tex]x+x+6+2x-6=68\\\\\Rightarrow 4x=68x=\dfrac{68}{4}\\\\\Rightarrow x=17.[/tex]

Therefore the lengths of the three sides are

17 feet, (17+6) feet and (2×17-6) feet

= 17 feet, 23 feet and 28 feet.

Thus, the required lengths of the three sides of the deck are 17 feet, 23 feet and 28 feet.

Give A={a,b,c},how many subsets does A have including 0?

Answers

Answer: 8 subsets

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

There are n = 3 elements in the given set, so there are 2^n = 2^3 = 2*2*2 = 8 subsets. Those 8 subsets are listed below

{a,b,c}
{a,b}, {a,c}, {b, c}
{a}, {b}, {c}
{ }

The first row is the original set. Any set is a subset of itself.
The second row represents subsets with exactly 2 elements.
The third row represents subsets with exactly 1 element
The fourth row is the empty set which can be written as [tex]\varnothing[/tex]

2x+5=10
Solve for x

Answers

2x+5=10

Subtract 5 from both sides.
2x + 5 - 5 = 10 - 5
2x = 5

Divide both sides by 2.
2/2x = 5/2
x = 5/2

5/2 can be simplified to 2 1/2 or 2.5.

Work: 2x+5=10
-5 both sides
2x=5
÷2 both sides
X=5/2
Answer: x=5/2
Check your work:
2 (5/2)+5=10
5+5=10
10=10

Answer is correct

Hope that helps you :)
Let me know if you need any more help :)

what is 25.6 divided by 0.5 =

Answers

51.2 it says on my calculator.

I hope this helps you alot. God Bless you.

It is 51.2 because yeah that’s is what I got in my calculator hope it helps (:

The graph below represents the running schedule of a distance runner, who is increasing the distance she runs each week. What is the distance she will run in the ninth week?

A. 22 miles

B. 21 miles

C. 20 miles

D. 19 miles (My answer???)

Answers

check the picture below.

Answer: The answer is (D) 19 miles.

Step-by-step explanation: We are given a graph that represents the running schedule of a distance runner, who is increasing the distance she runs each week. We are to find the distance she will run in the ninth week.

In the graph, the number of week are represented by the X-axis and the distance run is represented by the Y-axis.

Since we are to find the distance run in the ninth week, so we will have to find the value of y when the value of x is 9.

We can see from the graph that when x = 9, then y = 19, as (9, 19) is a point on the graph. So, the distance run in the ninth week is 19 miles.

Thus, (D) is the correct option.

What is the vertex of the graph of y+2x+3 = -(x+2)^2 + 1?
A. (-3,-33)
B. (-3,3)
C. (3,-24)
D. (3,21)

Answers

the vertex is (-3,3)
The graph opens downward too

your answer is B. ) -3,3

py+7=6y+q solve for y

Answers

We know that we are solving for y.

This is a step by step procedure to get the value of y.

First: Move all terms to the left side and set equal to zero.

Second: Then set each factor equal to zero.

The application is:

Given: py+7=6y+q

-6y -7 -6y -7 = 0

(p-6)y = q-7

divide both sides by p-6
y=(q-7)/(p-6)

Answer is y = (q – 7) / (p – 6)

The solution of expression for y as,

⇒ y = (q - 7) / (p - 6)

We have to given that,

An expression is,

⇒ py + 7 = 6y + q

Now, We can simplify the expression for y as,

⇒ py + 7 = 6y + q

Subtract 6y both side,

⇒ py - 6y + 7 = 6y + q - 6y

Subtract 7 both side,

⇒ py - 6y = q - 7

⇒ y (p - 6) = (q - 7)

Divide both side by (p - 6);

⇒ y = (q - 7) / (p - 6)

Therefore, The solution of expression for y as,

⇒ y = (q - 7) / (p - 6)

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A factory makes an oil mixture by mixing oils of grades A and B as follows. For every 2.3 liters of grade A oil, 1.2 liters of grade B oil are mixed in. How many liters of grade A oil and grade B oil will the factory need to make 1000 liters of their oil mixture? Explain your solution.

Answers

The ratio is 2.3:1.2 for A:B. Ratios will remain the same but can be scaled up or down by some factor/multiple. Like if you had a food recipe that you needed to double, the scaling factor would be 2 and all ingredients in the recipe would be doubled.

Since we don't know the scaling factor, we assign that multiple "x". Then the amounts of each ingredient oil would be:

amount of A = 2.3x
amount of B = 1.2x

add them together to get the required mixture amount.

1000 = 2.3x + 1.2x
1000 = 3.5x
1000/3.5 = x
285.7 = x
this is the scaling factor.

plug x in to find the amounts of each oil type.

A = 2.3(285.7)
A = 657.1 L

B = 1.2(285.7)
B = 342.9 L

To produce 1000L of mixture the factory will need 657 liters of grade A and 343 liters of grade B. To determine this you have to figure out the percentage of each grade in the mixture. The ratio is 2.3 liters to 1.2 liters. Therefor in this scenario the unit equaling 100% is 3.5 liters. To find the percentage of grade A you divide the amount used by the total amount of the unit 100%: 2.3 divided by 3.5 = .657 (multiply the answer by 100 to get 65.7%). To find the percentage of grade B you divide the amount used by the total amount of the unit 100%: 1.2 divided by 3.5 = .343 (multiply the answer by 100 to get 34.3%) To test your answer make sure both percentages add up to 100%: 65.75 plus 34.35 = 100% To determine how much of grade A and grade B is needed for a set amount of liters you multiply the percentage by the liters needed. For this situation you multiply 65.7% (when multiplying percentages you need to multiply in decimal form). For grade A you multiply .657 (65.7%) by 1000 liters = 657 liters For grade B you multiply .343 (34.3%) by 1000 liters = 343 liters To test your answer you can use the same addition as you did to test the percentages: 657 liters plus 343 liters = 1000 liters

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