Answer:
1. You can divide both sides of an equation by any number except zero. If dividing both sides simplifies the equation, then it's better to do than than to distribute.
2. A fraction can be thought of as a ratio. To keep the value of the fraction the same, you must multiply or divide the numerator and denominator by the same number. If you multiply only the denominator by a number, the value of the fraction changes.
Step-by-step explanation:
1.
6(3x + 4) = 12
Since the goal in solving this equation is to isolate x, meaning you want x alone on the left side, you need to do whatever legal operations that will accomplish that. Since 6 is a factor and (3x + 4) is a factor in a multiplication, you can divide both sides by 6 simplifying the left side. It is also correct to distribute on the left side, but it will make the solution longer.
Method 1: start by dividing both sides by 6
6(3x + 4) = 12
Step 1: Divide both sides by 6
3x + 4 = 2
Step 2: Subtract 4 from both sides
3x = -2
Step 3: Divide both sides by 3
x = -2/3
Method 2: start by distributing on the left side
6(3x + 4) = 12
Step 1: distribute the 6 on the left side
18x + 24 = 12
Step 2: subtract 24 from both sides
18x = -12
Step 3: divide both sides by 18
x = -12/18
Step 4: reduce the fraction
x = -2/3
As you can see, the solution is the same. The only difference is one extra step with the reduction of the fraction in the case of distributing the 6.
2.
This has to do with the meaning of fractions.
For example, take the fraction 1/2.
This fraction means that you divided the unit into 2 equal parts, shown by the denominator of 2. Then you are taking 1 of those parts, shown by the numerator of 1. 1/2 means 1 out of 2. You can also think of 1/2 as the ratio of 1 to 2.
To add and subtract two factions, we need a common denominator. That means we must rewrite one or both fractions being added or subtracted in a way that they both have the same denominator. We need the fractions to represent the same amounts they did originally. If you changed only the denominator, you'd be changing the actual value of the fraction.
You need to add 1/2 and 3/10.
The least common denominator of 2 and 10 is 10, so we need to have both fractions with a denominator of 10. 3/10 already has a denominator of 10, so we just need to change 1/2 to a fraction with 10 in the denominator. By multiplying 2 by 5 we get 10, so we need to multiply the denominator of 1/2 by 5 to end up with a denominator of 10.
1/2 + 3/10
If you only changed the denominator of 1/2 to 10 by multiplying 2 * 5 = 10, you'd end up with
1/10 + 3/10,
but now think of the fraction 1/10 and compare it to 1/2.
1/2 means divide the unit into 2 equal parts and take 1 part.
1/10 means divide the unit into 10 equal arts and take 1 part.
1/2 is not the same as 1/10, so rewriting the addition
1/2 + 3/10 as 1/10 + 3/10 is actually changing the problem.
Now see what happens when we multiply both the numerator and denominator by the same number, in this case 5.
We change 1/2 to (1 * 5)/(2 * 5) = 5/10. 1/2 equals 5/10. If you divide a unit into 10 equal parts and you take 5 parts, you have taken the same number of parts as if you had divided the unit into 2 parts and taken 1 part.
In other words, 1/2 is exactly the same amount as 5/10. The only difference between 1/2 and 5/10 is the way they are written.
Now we can correctly continue with the addition:
1/2 + 3/10 = 5/10 + 3/10 = 8/10
Finally we reduce 8/10 to 4/5 by dividing both the numerator and denominator by 4.
Geometry, please answer question ASAP
Answer:
D
Step-by-step explanation:
The perimeter is the sum of the 3 sides of the triangle, that is
perimeter = 20 + 13 + 21 = 54 → D
Help anyone can help me do the question,I will mark brainlest.
Answer:
Step-by-step explanation:
14.
by pythagoras,s theorem
[tex]x=\sqrt{2^2+2^2} =\sqrt{8} =\sqrt{4 \times 2} =2\sqrt{2} \\y^2=x^2+2^2=(2\sqrt{2} )^2+2^2=8+4=12=4 \times 3\\y=2\sqrt{3}[/tex]
15.
first perpendicular=y(say)
and second perpendicular=z (say)
y²=9²+7²=81+49=130
z²=y²+5²=130+25=155
x²=z²+4²=155+16=171
x=√(171)
What is the volume of the cone below?
A. 432 units 3
B. 1447 units 3
C. 1087 units 3
D. 2167 units 3
Answer:
[tex]144\pi[/tex]
Step-by-step explanation:
To find the volume of a cone use the formula [tex]v = \pi r^2\frac{h}{3}[/tex]
When you substitute that into an equation it will be [tex]v = \pi 4^2\frac{27}{3}[/tex]
First you should evaluate the exponent making it 16
Next divide 27 and 3 which is 9
Since you don't have to multiply by 3.14 ([tex]\pi[/tex]) the equation should be ...
[tex]144\pi[/tex]
Answer:
144
Step-by-step explanation:
Andrew rents rooms in his hotel for an average of $97 per night. The variable cost per rented room is $36. His fixed costs are $52,000 per month. How many rooms does he have to rent per month in order to break even?
Answer:
853 rooms
Step-by-step explanation:
If someone just opens the door with the intent to stay, Andrew has variable costs to pay which come off the 97 dollars. So his actual profit is 97 - 36 = 61 dollars. So how many rooms in total does he have to rent?
52000 / 61 = 853 rounded.
Is this realistic? The average month has 30 days
853 / 30 = 29 rooms rounded
Each room of 29 would have to be rented every night. I would say he better sell the hotel and go into something else.
Find the term of each sequence.
32, 80, 200, ...5th term
Answer:
t5 = 1250
Step-by-step explanation:
Each term is derived by multiplying the previous term by 2.5
t2 = t1 * 2.5
t2 = 32 * 2.5
t2 = 80
===========
tn = a*b^(n - 1)
t3 = 32*2.5^2
t3 = 200
That's just to test the formula. It does work.
===============
t5 = 32*2.5^(5 -1)
t5 = 32*2.5^4
t5 = 1250
why is gravitational force between two object usually unnoticeable
Answer:
gravitational attraction is based upon mass.More the mass more the force.When the object is as big as a moon it has a very less gravity.When we are talking about small objects like 2 pencils the force exists but is so weak that no noticabke movement takes place
Answer:
To notice that force, the objects have to have a big mass and be close to each others.
Generally in eveydays life, you don't notice this force since it is weak but that doesn't mean it does't exist.
If you go the space, you can notice this force since planets have big mass. If you get close to the gravitational field of a planet, you will feel a force that is pulling you toward the planet.
A family club keeps a small amount of money on hand for members to borrow for short periods of time. The simple interest charged is 7.5%. Stephen borrowed $5,000 for 3 months. How much, to the nearest dollar, was he required to pay back at the end of 3 months?
Answer:
$6125
Step-by-step explanation:
5000 x 3 x .075 = 1,125
5000 + 1125 = 6125
Which statement is true about the function represented by this graph?
Answer: Choice D)
The function has a range of all real numbers less than or equal to 2.
=======================================================
Explanation:
Let's go through the answer choices to see which are true, and which are false.
A) This is false because (0,-2) is a y intercept, and not an x intercept. A zero of a function is always an x intercept.B) This is false. The curve peaks at the vertex (2,2) showing we have a max point, and not a min point.C) This is false. A function can have at most one y intercept. If it had more than one y intercept, then it wouldn't be a function (since the input x = 0 leads to more than one output).D) This is true. The range is the set of possible y outputs. We see that y = 2 is the largest output, which occurs at the vertex. We can get anything smaller than this y value. Therefore, the range is the set of y values such that [tex]y \le 2[/tex]Answer:
option D
Step-by-step explanation:
THE FUNCTION HAS A RANGE OF ALL REAL NUMBERS LESS THAN OR EQUAL TO 2
Me ajudem
1- a) 5 ( x – 1) = 30
b) 3 (x + 10 ) – 2 ( x – 5 ) = 0
Answer:
a)7, b)-40
Step-by-step explanation:
a) 5(x-1)=30
=>5x -5=30
=>5x=30+5
=>5x=35
=>x=35/5
so, x=7
b)3(x+10)-2(x-5)=0
=>3x+30-2x+10=0
=>x+40=0
so,x=-40
WILL MARK BRAINLIEST HELP ASAP The student's in Roberto's school are painting a mural that will be 8 feet by 15 feet. First they make a scale drawing of the mural with a scale of 2 feet:5 feet. What are the length and width of the scale drawing in feet?
Answer:
4ft and 3ft
Step-by-step explanation:
Real mural: 8ft by 15ft
Scale: 2ft by 5ft
Length and width of scale drawing> 8t / 2ft= 4ft (length
>15ft/ 5ft= 3ft(width)
ANSWER 4FT BY 3FT
What is the range of the given data set? OA) 30 OB) 32 OC) 37 OD) 40
Answer:
Range = maximum number - minimum number
maximum number = 99minimum number = 62Range = 99 - 62 = 37
Answer:
37
Step-by-step explanation:
The range is the difference between the highest number and the smallest number.
Looking at the stem and leaf plot we can identify the largest and smallest number
Largest number: 99
Smallest number: 62
If range = largest number - smallest number then range = 99 - 62 = 37
Amazon is sold at rupees 99000 after 10% discount and 10% bat on the Marked price find the discount amount and vat amount
Answer:
Here,
SP with VAT = Rs. 99000
Discount = 10%
VAT = 10%
Discount Amount =?
VAT Amount = ?
We know,
SP = "100" /"100 + v% " × SP with VAT
= "100" /"100 + 10 " × 99000
= "100" /"110 " × 99000
= Rs. 90000 ∴ VAT Amount = SP with VAT – SP
= Rs. 99000 – 90000
= Rs. 9000 Again, MP = "100" /"100 – d% " × SP
= "100" /"100 – 10 " × 90000
= "100" /"90" × 90000
= Rs. 100000
∴ Discount Amount = MP – SP
= Rs. 100000 – 90000
= Rs. 10000
Step-by-step explanation:
Here is the list of all formulas on MP, Discount, SP, and VAT.
1. Discount Amount = Discount % of MP
2. Discount % = (Discount Amount)/MP ×100%
3. SP = MP – Discount Amount
4. SP = (100 - d%)/(100 ) × MP
5. MP = 100/(100 - d% ) × SP
6. VAT amount = VAT percent of SP
7. VAT percent = (VAT Amount)/SP ×100%
8. SP with VAT = SP + VAT amount
9. SP with VAT = (100 + v%)/(100 ) × SP
10. SP = 100/(100 + v% ) × SP with VAT
11. MP = (100 × 100)/((100 - d%)(100 + v%)) × SP with VAT
12. SP with VAT = ((100 - d%)(100 + v%))/(100 × 100) × MP
PLEASE HELP ASAP.....
Answer:
3√3
Step-by-step explanation:
to get x, we divide 6 by 2 and get 3
therefore, we multiply the short leg by √3
the answer finally equals to 3√3
Answer:
[tex]\boxed {\boxed {\sf y=3}}[/tex]
Step-by-step explanation:
We are asked to find y, a missing side in a triangle.
1. Special Triangle RulesThis triangle is special. There is a 30-degree angle and a right angle or 90 degree angle, the unlabeled angle is 60 degrees. This is a 30-60-90 triangle so the sides are always in a specific relationship.
The side across from the 30-degree angle is a, the hypotenuse is 2a, and the side across from the 60-degree angle is √3 a.
y is across from the 30 degree angle, so it is equal to a. However, we have to find a. We are given one side that measures 6. It is the hypotenuse because it is across from the right angle. Therefore, it is equal to 2a.
2a= 6a is being multiplied by 2. Divide both sides by 2 to solve for a.
2a/2= 6/2 a= 6/2 a=3y is across from the 30-degree angle, so it is equal to a or 3.
2. Trigonometric Functions
We can also solve using the 3 main trigonometric functions.
sinθ= opposite/hypotenuse cosθ= adjacent/hypotenuse tanθ= opposite/adjacenty is opposite the 30-degree angle and 6 is the hypotenuse, and we will use sine.
[tex]sin \theta= \frac{opposite}{hypotenuse}[/tex]
[tex]sin (30)= \frac{y}{6}[/tex]
y is being divided by 6. The inverse operation of division is multiplication. Multiply both sides by 6 to solve for y.
[tex]6 * sin(30)= \frac{y}{6} *6[/tex]
[tex]6 * 0.5 = y[/tex]
[tex]3= y[/tex]
The missing side, y , is equal to 3.
Halla el valor de x :
•27/x = x/3
A timeline. 27 B C E to 180 C E PAX ROMANA. 44 B C E The Roman Empire was founded. 80 C E The Colosseum was built. 121 C E Hadrian's Wall was built in England to keep out enemies. 306 C E Constantine became emperor.
How many years passed between the building of the Colosseum and the building of Hadrian’s Wall?
201
121
41
36
Answer:
the answer is 41
Step-by-step explanation:
C. 41
Step-by-step explanation:
Would someone plz help me out with this
Answer:
$25,500
Step-by-step explanation:
Its an increase of $1,500 each year
What is the image of the point (4,7) after a reflection about the line y = 4.?
Answer:
(4, 1)
Step-by-step explanation:
See attachment courtesy of Desmos.
Quadrilateral ABCD is inscribed in circle P as shown. Which statement is necessarily true?
Answer:
B. m∠A + m∠C = m∠B + m∠D
Step-by-step explanation:
To inscribe a quadrilateral in a circle, the sums of its opposite angles must be equal (each sum of its opposite angles equals 180 °)
What is the square root of 100?
Answer:
10
Step-by-step explanation:
Square root of 100 is 10
Answer:
10
Step-by-step explanation:
The square root of 100 is written as 2√100=√100=±10.
So it is 10. Also, 10 times 10 equals 100, so it checks out.
A square root is just two of the same numbers added together to equal a specific number.
Help me please and thank you
Answer:
Below
Step-by-step explanation:
The domain tells you if there are any restrictions on the x's
The -5 in the function tells us that it has moved 5 units RIGHT from the original parent function. Because of this, any x coordinates have to be bigger or equal to 5!
So, the domain of this function is x >/ 5
Hope this helps!
2c+17.6 =6 / 4 SOLVE give your answer as a decimal get brainly
Answer:
-8.05
Step-by-step explanation:
In order to solve for C you first have to subtract 17.6 from both sides.
2c=(6/4)-17.6
6/4 is 1.5
1.5-17.6=-16.1
2c=-16.1
c=-8.05
Answer:
1.5
Step-by-step explanation:
2c+17.6=6/4
2c+176/10=6/4
2c+88/5=6/4
2c=6/4-88/5
2c=30-352/20
2c=-322/20
2c=-161/10
c=-8.05
Proof:
2c+17.6=6/4
2(-8.05)+17.6=6/4
-16.1+17.6=6/4
1.5=1.5
Hope this helps ;) ❤❤❤
hey guys i need help again with this plzz help me
Answer: A) -4
================================================
Explanation:
The 3^0 in the denominator is equal to 1. Any nonzero number raised to an exponent of 0 is always 1. So this equation x^0 = 1 is true when x is nonzero.
This allows us to simplify to the equation 3^x = 1/81
Note how 81 = 3^4. Taking the reciprocal of 81 means the exponent goes from positive to negative. So 3^(-4) = 1/81. The rule is x^(-k) = 1/( x^k ). We could use logarithms to solve 3^x = 1/81.
3-2(x-1)=2+4x
How do you solve
Answer:
x = 1/2
Step-by-step explanation:
3 - 2(x - 1) = 2 + 4x
3 - 2x + 2 = 2 + 4x
-2x + 5 = 2 + 4x
-2x - 4x = 2 - 5
-6x = -3
x = -3/-6
x = 1/2
3x2 − y3 − y3 − z if x = 3, y = −2, and z = −5.
Answer:
35
Step-by-step explanation:
3x2=6
or if x is variable :18
2x3=6
2x3=6
+5
add them all up:
18+6+6+5=35
let me know if something is confusing.
Solve. 2x−y+3z=6 2x+y=3 2y−4z=−4 Enter your answer, in the form (x,y,z), in the boxes in simplest terms. x= y= z=
Answer:
(3/2, 0, 1)
Step-by-step explanation:
From 2x+y=3 we have => y=3-2x
From 2y-4z=-4 we have -4z=-2y-4 => z=1/2y+1 => z=1/2 (3-2x) +1 => z=5/2-x
Plug in y & z to find x
2x−y+3z=6 => 2x+(3-2x)+3(5/2-x)=6 => 2x+3-2x+15/2-3x=6 => 21/2-3x =6 => x=3/2
plug in x to find y
2x+y=3 => 2(1.5) + y =3 => y=0
plug in y to find z
2y -4z =-4 => 2(0)-4z=-4 => -4z=-4 => z=1
A number y satisfies y 24th power - 256 = 0. What equation does the number x =y to the 4th power satisfy?
We conclude that the equation x = y^4 satisfies x = 256.
What does the equation x = y^4 satisfy?
First, we know that:
y^4 - 256 = 0
With this equation, we can find the value of y, it will give:
y^4 = 256
Then:
y = 256^(1/4) = 4
Now if we have the equation x = y^4, we can write:
x = y^4 = 256
x = 256
We conclude that the equation x = y^4 satisfies x = 256.
If you want to learn more about equations:
https://brainly.com/question/13763238
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what is the method or solution to this question (3)x-1=81x
[tex]3x-1=81x\\78x=-1\\x=-\dfrac{1}{78}[/tex]
Answer:
[tex]\large \boxed{\displaystyle x=- \frac{1}{78}}[/tex]
Step-by-step explanation:
[tex]3x-1=81x[/tex]
Subtract 3x from both sides of the equation.
[tex]-1=78x[/tex]
Divide both sides of the equation by 78.
[tex]\displaystyle \frac{-1}{78} =x[/tex]
At a tanning salon, customers are charged \$10 for their first visit in a calendar month and \$6 for each visit after that in the same calendar month. In the last calendar month, 100 customers visited the salon, of which 30 made a second visit, and 10 made a third visit. All other customers made only one visit. If those visits were the only source of revenue for the salon, what was the revenue for the last calendar month at the salon
Answer:
The salon would've made $1,240.
Step-by-step explanation:
Think of the customers as the numbers and the visits as variables. Then the equation would look something like this:
Revenue = 100(first visit) + 30(second visit) + 10(third visit)
And now, we just solve:
r = 100(10) + 30(6) + 10(6)
r = 1,000 + 180 + 60
r = $1,240
The mean of 14 numbers is 49. Removing one of the numbers causes the mean to decrease to 43. What number was removed?
Answer:
126 was removed.
Step-by-step explanation:
The total before division took place was
Total = mean * 14
mean = 49
Total = 49 * 14
Total = 685
Now you subtract x from the total
685 - x
And divide by 13 [one number is missing]
(685 - x)/13
and the result = 43
(685 - x ) / 13 = 43 Multiply both sides by 13
685 - x = 43 * 13
685 - x = 559 Subtract 685 from both sides
- x = - 126 Multiply by - 1
x = 126
Can someone help me with this
Answer:
Does the answer help you?