Answer & Step-by-step explanation:
[tex]1)\\(3x+9)+(2x+4)\qquad\text{combine like terms}\\\\=(3x+2x)+(9+4)\\\\=\boxed{5x+13}\\\\===========================[/tex]
[tex]2)\\(2n+6)+(6n-2)\qquad\text{combine like terms}\\\\=(2n+6n)+(6-2)\\\\=\boxed{8n+4}\\\\===========================[/tex]
[tex]3)\\(-3x+9)+(6x-12)\qquad\text{combine like terms}\\\\=(-3x+6x)+(9-12)\\\\=\boxed{3x-3}\\\\===========================[/tex]
[tex]4)\\\left(\dfrac{1}{4}x+10\right)+\left(\dfrac{1}{2}x-7\right)\qquad\text{combine like terms}\\\\=\left(\dfrac{1}{4}x+\dfrac{1}{2}x\right)+(10-7)\\\\=\left(\dfrac{1}{4}x+\dfrac{1\cdot2}{2\cdot2}x\right)+3\\\\=\left(\dfrac{1}{4}x+\dfrac{2}{4}x\right)+3\\\\=\boxed{\dfrac{3}{4}x+3}\\\\===========================[/tex]
[tex]5)\\(3x+5)-(2x+2)\\\\=3x+5-2x-2\qquad\text{combine like terms}\\\\=(3x+2x)+(5-2)\\\\=\boxed{5x+3}\\\\===========================[/tex]
[tex]6)\\10-8=\boxed{2}\\\\===========================[/tex]
[tex]7)\\7.8x-2.5x=\boxed{6.3x}\\\\===========================[/tex]
[tex]8)\\(5.8x+10)-(3.4x+8)\\\\=5.8x+10-3.4x-8\qquad\text{combine like terms}\\\\=(5.8x-3.4x)+(10-8)\\\\=\boxed{2.4x+2}\\\\===========================[/tex]
[tex]9)\\(8x-2)-(2x+8)\\\\=8x-2-2x-8\qquad\text{combine like terms}\\\\=(8x-2x)+(-2-8)\\\\=\boxed{6x-10}\\\\===========================[/tex]
[tex]10)\\(-4x-3)-(-4x-3)\\\\=-4x-3-(-4x)-(-3)\\\\=-4x-3+4x+3\qquad\text{combine like terms}\\\\=(-4x+4x)+(-3+3)\\\\=0+0\\\\=\boxed{0}\\\\\text{You could do it shorter.}\\\text{The result will be 0 because we subtract}\\\text{ the same expressions from each other.}[/tex]
To add or subtract linear expressions, combine like terms. For example, to add 3x + 9 and 2x + 4, you combine the x terms and the constant terms separately to get 5x + 13. The same method is applied to the rest of the problems, resulting in simplified linear expressions.
Adding and Subtracting Linear Expressions:
To add or subtract linear expressions, you combine like terms, which are terms that have the same variables raised to the same power. Let's go through the problems one by one:
Sum of 3x + 9 and 2x + 4: (3x + 2x) + (9 + 4) = 5x + 13.
Add 2n + 6 and 6n - 2: (2n + 6n) + (6 - 2) = 8n + 4.
Add -3x + 9 and 6x - 12: (-3x + 6x) + (9 - 12) = 3x - 3.
Add 1/4x + 10 and 1/2x - 7: (1/4x + 1/2x) + (10 - 7) = 3/4x + 3.
Find the difference: (3x + 5) - (2x +2) = (3x - 2x) + (5 - 2) = x + 3.
Subtract 8 from 10: 10 - 8 = 2.
Subtract 2.5x from 7.8x: 7.8x - 2.5x = 5.3x.
Subtract (3.4x + 8) from (5.8x + 10): (5.8x - 3.4x) + (10 - 8) = 2.4x + 2.
Find the difference: (8x + 5) - (2x + 8) = (8x - 2x) + (5 - 8) = 6x - 3.
Evaluate (-4x -3) - (-4x -3): (-4x + 4x) - (-3 + 3) = 0x + 0 = 0.
These are the simplified forms of the linear expressions after combining like terms.
Movies are on sale for 1/4 the original price. If the original price is $20, which expression gives the sale price?
Write an expression in simplest form to represent the area of the shaded region
3x+2 2x 3x 4x
d - 10 - 2d + 7 = 8 + d - 10 - 30
Answer:
[tex]d=14.5[/tex]
Step-by-step explanation:
Given equation:
[tex]d - 10 - 2d + 7 = 8 + d - 10 - 30[/tex]
To solve the equation for 'd', take the terms of 'd' to one side and the constants to the other side.
[tex]d - 2d - d = 8 - 10 - 30- 7+10[/tex]
[tex]-2d=8-30-7\\-2d=1-30\\-2d=-29\\ d=\frac{29}{2}\\ d=14.5[/tex]
On, solving the equation the value of 'd' is [tex]d=14.5[/tex]
a. 8% of ? = 20
b. 75% of ? = 30
c. 20% of ? = 45
d. 150% of ? = 36
Answer:
A. 250
B.40
C.225
D.24
Step-by-step explanation:
20/0.08 = 250
30/0.75 = 40
45/0.2 = 225
36/1.5 = 24
Answer:
a. 8% of 250 = 20
b. 75% of 40 = 30
c. 20% of 225 = 45
d. 150% of 24 = 36
Step-by-step explanation:
20×100÷8
=250
30×100÷75
=40
45×100÷20
=225
36×100÷150
=24
I had 20 dollars and earned 15, leaving me with 35. What is the percent that it increased in pay?
Answer:
42.8%
Step-by-step explanation:
I asked Alexa lol
Answer:
The answer is 40%
Step By Step Explanation:
The reason why is because if you do 10 divided by 25 you get 0.40 and then if you multiply it you get 40 = 40%
Find the missing side length of S
Answer:
s=12
Step-by-step explanation:
Since we know that triangle ABC is similar to XYZ, we know that the side lengths will be proportional to one another. As such, we should take a ratio to determine the side length of s.
[tex]\frac{XY}{AB}=\frac{XZ}{AC}\\\\\frac{9}{6} =\frac{s}{8}\\\frac{8*9}{6} =s\\s=72/6=12\\s=12[/tex]
For what value of x is the rational expression below equal to zero?
X-4/x-6
Answer:
Step-by-step explanation:
When x equals to 4
4-4 = 0
-------------
4-6 = -2
0/-2 = 0
The rational expression X-4/x-6 equals zero when X equals 4, as long as the denominator is not zero, which avoids division by zero.
The question asks: For what value of x is the rational expression below equal to zero? The expression given is X-4/x-6. To find when this expression is equal to zero, we need to understand that a rational expression equals zero when its numerator is zero (and the denominator is not zero, to avoid division by zero).
To solve X-4 = 0, we simply add 4 to both sides of the equation, getting X = 4. This means that the rational expression is equal to zero when X equals 4, given that X is not equal to 6 to avoid making the denominator zero, which would be undefined. Hence, the value of X that satisfies the condition is 4.
Solve the equation for y plz -1.2y-4.2y=-3.78
Answer:
y=0.7
Step-by-step explanation:
-1.2y-4.2y=-3.78
Simplify:
-5.4y=-3.78
5.4y=3.78
3.78/5.4=0.7
y=0.7
Substitute x+3y=4
2x-6y=8
Answer:
x=4, y=0. (4, 0).
Step-by-step explanation:
x+3y=4
2x-6y=8
------------
x=4-3y
2(4-3y)-6y=8
8-6y-6y=8
8-12y=8
12y=8-8
12y=0
y=0/12
y=0
x+3(0)=4
x+0=4
x=4-0
x=4
At midnight the temperature is -6°C. At midday the temperature is 9°C. By how much did the temperature rise?
Answer:
15 degrees
Step-by-step explanation:
It went from -6 to 0 which is 6 degrees of change then from 0 to 9 degrees which is 9 degrees of change 9+6=15
The amount of temperature that has been increased from midnight to midday is 15°C.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Midnight temperature = -6°C
Midday temperature = 9°C
The difference between the temperature.
= 9 - (-6)
= 9 + 6
= 15°C.
Thus,
The temperature is raised by 15°C.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ2
Solve for y.
2(-4y + x) = 4
Answer:
Step-by-step explanation:
-4y + X = 2
-4y = 2 - x
y = 2 - x/ -4
hope this helps!!
The value of y in terms of x is -1/2 + x/4.
To solve for y, we start with the equation 2(-4y + x) = 4.
Distribute the 2 inside the parentheses: -8y + 2x = 4.
Move the term with x over to the other side by subtracting 2x from both sides: -8y = 4 - 2x.
Isolate the y by dividing both sides by -8: y = (4 - 2x) / -8.
Simplify the right side by dividing both terms by -8: y = -1/2 + x/4.
use the completing the square method to solve the equation x^2 + 16x + 2.
x = - 0.12 or - 15.87
Step-by-step explanation:
Step 1: Divide the equation with the coefficient of [tex]x^{2}[/tex]. In this case, coefficient of Step 2: Move the number term to the right hand side of the equation. Now, the equation becomes [tex]x^{2} + 16x = -2[/tex]Step 3: Complete the square in the left hand side of the equation and then add the same number to the right hand side to balance the equation. Now, equation becomes [tex]x^{2} +16x+64 = -2+64[/tex] So, [tex]x^{2} +16x+64 = 62[/tex] [tex]ie, (x+8)^{2} = 62[/tex] Step 4: Take the square root of both sides. Therefore, [tex]x+8 = \sqrt{62}[/tex] So, [tex]x =[/tex] ± [tex]7.87 - 8[/tex]Therefore, [tex]x = -0.12, -15.87[/tex]
The high temperature on Monday was -14 F.on Tuesday the high temperature was 24 F. What is the difference in high temperatures on theses 2 days
What is the scale factor on the map (10 points
Answer:
2785
Step-by-step explanation:
What is the answer to 4•4+4(5-2)+7
Answer:
35
Step-by-step explanation:
4 x 4+4(5-2)+7
4 x 4+4(3)+7
16+12+7
28+7
35
A principle of $20,000 is invested at $6.25 and earns $10,000 simple interest how long has the money been invested
Answer:
1600
Step-by-step explanation:
Assuming $6.25 is the interest earned annually,
Let n be the no. of years
Then,
6.25 × n = 10000
n = 10000/6.25
n = 1600
Eden spent half of her weekly allowance on candy. To earn more money her parents let her weed the garden for $5. What is her weekly allowance if she ended with 12?
Answer:
her weekly allowance would be 7
Step-by-step explanation:
Answer:
$24
Step-by-step explanation:
12 is 1/2 of 24.
So, when she weeds the garden, she will have $17.
If she gets her weekly allowance and the $5, she will have $41, assuming she doesn't spend any of the money she already has.
What is wrong with this solution?
-5m - 16 = 19
5m - 16 + 16 = 19 + 16
Step One:
Step Two:
Solution:
m = 7
Final answer:
The solution shown is incorrect because the equation is not simplified before performing operations.
Explanation:
The solution shown is incorrect. Let's go step by step to find the error:
Step One: -5m - 16 = 19
Step Two: 5m - 16 + 16 = 19 + 16
Step Three: 5m = 35
Step Four: Divide both sides by 5: m = 7
The mistake in the solution occurs in Step Two. The previous equation should be simplified to 5m = 35 before dividing by 5. The addition of 16 on both sides should be taken care of first by canceling it out, resulting in 5m = 35 instead of 5m + 0 = 35.
Therefore, the correct solution is m = 7.
Final answer:
The solution to the equation -5m - 16 = 19 is m = -7, not m = 7. The student initially misplaced the sign after dividing by -5.
Explanation:
The student has made a mistake in the initial steps of solving the equation -5m - 16 = 19. The correction process involves isolating the variable m on one side of the equation to find its value.
Step One
Add 16 to both sides of the equation to eliminate the -16:
-5m - 16 + 16 = 19 + 16
-5m = 35
Step Two
Divide both sides by -5 to solve for m:
-5m / -5 = 35 / -5
m = -7
The correct solution is m = -7, not m = 7. It is important to follow the addition rules and subtraction rules carefully and to remember to divide by the coefficient of m, which in this case is -5, resulting in changing the sign of the solution.
Chang drove 315 miles in 5 hours.
At the same rate, how long would it take him to drive 567 miles?
I hours
Answer:
AROUND 6-7 HOURS
Step-by-step explanation:
The length of a rectangle is 2 units more than the width. The area is 63 units. What is the width, in units, of the rectangle?
Answer:
the width is 7. i just did this in deltamath
Step-by-step explanation:
-2 square root 20- square root 125
Answer:-5.93958251....
Step-by-step explanation:
To simplify the expression -2√20 - √125, we first factored the square roots, realizing that √20 equals 2√5 and √125 equals 5√5. Plugging these back into the equation, we then combined like terms to get the final answer of -9√5.
The question asks to simplify the expression -2√20 - √125.
First, let's simplify the square roots by factoring out squares from under the radical:
√20 = √(4×5) = √4√5 = 2√5√125 = √(25×5) = √25√5 = 5√5Now let's substitute these simplified forms back into the original equation and simplify:
-2(2√5) - 5√5 = -4√5 - 5√5
Combine like terms to get the final simplified result:
-9√5
complete question given below:
simplify -2 square root 20- square root 125
The green dots must make up a triangle 1/3 of the original picture PLZ HELP
Consider Point P to be (0,0) count the grid lines to find the location of points A, B and C
A=. (-6,-3)
B = (-9,6)
C =(3,9)
Now the scale is 1/3. So divide all the points by 3 to get the new location and place the green dots on them:
A’=(-2,-1)
B’ =(-3,2)
C’ =(1,3)
3. You want to leave a tip for a meal that
costs $17.95. If all you have is $3.00, what
percentage tip will you be able to leave?
Answer:
17%
Step-by-step explanation:
3/17.95 = 0.167
0.167 × 100 = 16.7 *rounding to 17
12.95 × 0.17 = 3.0515
What is 4/9 as a decimal
Answer:
0.4 and alot of other 4's
Step-by-step explanation:
Answer:
.44444444 repeating
Any number less than 9 over 9 will be itself forever after a decimal point
Step-by-step explanation:
the sum of 7 times a number and 9 is 4
Michael is organizing a game of chance for his class. He asks each student to pick a ribbon from a bag and then put it back into the bag. The bag has 12 yellow ribbons, 7 red ribbons, and 3 blue ribbons. If Jane picks a ribbon, what is the probability that the ribbon will be yellow and what is the likelihood of this event?
A.
The probability is 1, and the event is certain.
B.
The probability is 3/11 , and the event is likely.
C.
The probability is 6/11, and the event is unlikely.
D.
The probability is 6/11 , and the event is neither likely nor unlikely.
Answer:
D. The probability is 6/11, and the event is neither likely nor unlikely
Step-by-step explanation:
54% = 6/11
Answer:
D
Step-by-step explanation:
If a circle has a radius of 12 feet, whats its circumference most nearly?
Answer:24π feets
Step-by-step explanation:
Since the circumference C= 2πr and r=12
C= 2x12xπ
C=24π
Which of the following equations would result in destructive interference with the wave y= -2sin(2pi/3 x)?
A.) y= -2sin(2pi/3 x)
B.) y=2sin(2pi/3 x)
C.) y= -2sin 3pi/2 x)
D.) y=2sin (3pi/2 x)
Answer:
B: 0.449 secs
A, C, and D: y=2sin(pi/5x), y=2sin(pi/10x), y=2sin(10pi x)
B: y=2sin(2pi/3x)
Answer:
B. y=2sin(2pi/3x)
Step-by-step explanation:
What is 4 equal expressions to 4(2x^2+16)
Answer:
8x^2+64
Step-by-step explanation:
You received an order for a 28-day supply for Propranolol HCI 120mg tablets po q.i.d. to prevent post M I reinfection How many tablets will be dispensed for the 28-day supply?
112 tablets will be dispensed for the 28-day supply.
Step-by-step explanation:
Given:
Received an order of 120 mg tablet po q.i.d. for a 28-day supply.
Here in medical prescription, the term 'po' and 'q.i.d' means a lot to understand the question.
In medical prescription, the term 'po' refers the treatment that should be taken orally. i.e. by opening mouth or the way of openingIn medical prescription, the term 'q.i.d' refers four times in a day.Therefore, to find the number of tablets need to be dispensed for 28- day supply is given by,
[tex]number\ of\ the\ tablet\ for\ 28- day \times number of tablets taken in a day =28 \times 4[/tex]
tablets to be dispensed for the 28-day supply = 112 tablets.