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.
Use the figure below to find the measure of angle x.
Answer:
70 degrees
Step-by-step explanation: this is an equilateral triangle. All of its angles are the same.
Mother wants to divide $36 between her daughters Ava and Charlotte in the ratio of their ages. If Ava is 15 years old and Charlotte is 12 years old, find how much Ava and Charlotte will get.
Answer:
Ava's share = $20
Charlotte's share = $16
Step-by-step explanation:
15x + 12x = 36 : multiply each girl's age by same amount and adding gives $36
27x = 36 : add x terms
x = 36 / 27 : divide both sides of equation by 27
x = 4 / 3
Ava's share = 15x = 15 * 4/3 = 20
Charlotte's share = 12x = 12 * 4/3 = 16
In this activity, you will help Darin compare the unit prices, in price per pound, of clementines and navel oranges. Clementines are sold in three-pound bags, and navel oranges are sold by the pound. The table represents the cost of three-pound bags of clementines. Number of Bags Cost 1 $5.00 2 $10.00 3 $15.00 The equation c = $1.49p represents the cost of the navel oranges, where c is the cost and p is the number of pounds. Darin needs to know the price per pound of clementines. What needs to change in the table so that the data on clementines is in units of pounds and cost?
Answer:
The table gives the cost for the number of three-pound bags of clementines. you need to change the number of bags to pounds to be able to get the data for the clementines in units of pounds and cost.
Step-by-step explanation:
each of the bags are three pounds each so 1 bag times 3, 2bags times 3, and then 3bags times 3, hope this answers your question.
The table gives the cost for the number of three pounds bag of clemintines we need to change the number of bags to pounds to get the data or clemintines in units of pounds and cost.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Given that Clementines are sold in three-pound bags, and navel oranges are sold by the pound
The table represents the cost of three-pound bags of clementines.
Number of Bags Cost
1 $5.00
2 $10.00
3 $15.00
The equation c = $1.49p represents the cost of the navel oranges, where c is the cost and p is the number of pounds.
The table gives the cost for the number of three pounds bag of clemintines we need to change the number of bags to pounds to get the data or clemintines in units of pounds and cost.
To learn more on Statistics click:
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Find the distance between points K(−1, −3) and L(0, 0). Round to the nearest tenth.
Answer:
d = √10
Step-by-step explanation:
[tex]K(-1, -3) , L(0, 0).\\\\d=\sqrt{((x_2-x_1)^2+ (y_2-y_1)^2) } \\\\x_1 =-1\\\\y_1 =-3\\\\x_2 =0\\\\y_2 =0 \\\\d = \sqrt{(0-(-1))^2+(0-(-3))^2}\\\\ d = \sqrt{(0+1)^2+(0+3)^2}\\\\ d = \sqrt{(1)^2 + (3)^2}\\\\ d = \sqrt{1 + 9}\\\\ d = \sqrt{10} \\[/tex]
Answer:
[tex]\huge\boxed{|KL|=\sqrt{10}\approx3.2}[/tex]
Step-by-step explanation:
METHOD 1:The formula of a distance between two points (x₁; y₁) and (x₂; y₂):
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We have K(-1; -3) and L(0; 0). Substitute:
[tex]|KL|=\sqrt{(0-(-3))^2+(0-(-1))^2}=\sqrt{3^2+1^2}=\sqrt{9+1}=\sqrt{10}}[/tex]
METHOD 2:Look at the picture.
We have the right triangle with the legs 3 and 1.
Use the Pythagorean theorem:
[tex]leg^2+leg^2=hypotenuse^2[/tex]
substitute:
[tex]3^2+1^2=|KL|^2\\\\|KL|^2=9+1\\\\|KL|^2=10\to|KL|=\sqrt{10}[/tex]
*Do the equations have solutions? x2=x
Answer:
x = 1
Step-by-step explanation:
x² = x
x² / x = 1
x = 1
Check:
1² = 1
Jared hiked a trail that is 12 miles long. He hiked the trail in section that were 1.5
miles each. In how many sections did he complete the hike?
A. 12
B. 8
C. 10
D. 4
3x - y = 0
2x - y = 1
A soma de dois números consecutivos é 11, qual expressão algébrica representa este contexto? * 1 ponto a) X + X + 1 = 11 b) X + X = 11 c) X + X – 1 = 11 d) X + 1 = 11
Answer:
a) X + X + 1 = 11
Step-by-step explanation:
Em matemática, a soma de consecutivos é expressa matematicamente como:
X + (X + 1) + (X + 2) + (X + 3) .............
Na pergunta acima, somos solicitados a encontrar a expressão algébrica que indica que a soma de DOIS inteiros consecutivos é igual a 11
Portanto, esta expressão algébrica é dada como:
X + (X + 1) = 11
X + X + 1 = 11
Portanto, a opção a) X + X + 1 = 11 é a opção correta
Sams building a suspension bridge for the playground at the elementary school I needed some chain-link and some rope he bought a total of 80 feet of materials and The chain-link cost two dollars per foot and the rope cost 1.50 per foot he spent a total of $135 how much of each did he buy
Answer:
Amount of material for chain link = 30 feet
Amount of material for rope = 50 feet
Step-by-step explanation:
Let the amount of chain link = X
The amount of rope be represented by Y
He bought a total of 80 feet of materials
Hence we have:
X + Y = 80 ....... Equation 1
Y = 80 - X
The chain-link cost two dollars per foot and the rope cost 1.50 per foot he spent a total of $135
X × $2 + Y × $1.50 = $135
2X + 1.5Y = 135 ......Equation 2
Substitute 80 - X for Y in Equation 2
2X + 1.5(80 - X) = 135
2X + 120 - 1.5X = 135
Collect like terms
2X - 1.5X = 135 - 120
0.5X = 15
X = 15/0.5
X = 30 feet
Substitute 30 feet for X in Equation 1
X + Y = 80 ....... Equation 1
30 + Y = 80
Y = 80 - 30
Y = 50 feet
Hence the amount of material he used for the chain link = 30 feet and the amount of material he used for the rope was = 50 feet
GIVING BRAINLIEST TO THE FIRST PERSON TO ANSWER!
Three stores have the same tablet computer on sale. The regular price of the tablet is $150. Store A is offering the tablet on sale at 15% off the regular price. Store B is offering a $25 coupon to be deducted from the regular price. Store C is offering a rebate of $20.00 to purchasers. Store D has the tablet on sale for $120.00. Which store is offering the tablet at the lowest cost?
A. Store A
B. Store B
C. Store C
D. Store D
Show ALL work please! <3
Answer: Store D
Step-by-step explanation:
Store A - 15% off:
$150 times 15/100 = 22.5
$150 - $22.50 = $127.50 so the price at store A is $127.50
Store B - $25 coupon
$150 - $25 = $125 so the price at store B is $125
Store C - $20 rebate
$150 - $20 = $130 so the price at store B is $130
Store D - $120
$120 is the lowest so the answer is Store D
Answer:
[tex]\Large \boxed{\mathrm{Store \ D}}[/tex]
Step-by-step explanation:
Store A is offering the tablet on sale at 15% off the regular price.
150 × (1 - 15%) = 127.5
Store B is offering a $25 coupon to be deducted from the regular price.
150 - 25 = 125
Store C is offering a rebate of $20.00 to purchasers.
150 - 20 = 130
Store D has the tablet on sale for $120.00.
Store D is offering the tablet at the lowest cost.
The table shows the number of balls, by sport, in the gym. Select the true statements about the information in the table.
Answer:
Soccer you use the lease amount of balls and in tennis you use the most
Compute
3/10 + 3/5 - 1/5
Answer:
7/10
Step-by-step explanation:
3/10 + 3/5 - 1/5
Combine like terms
3/10 + 2/5
Get a common denominator of 10
3/10 + 2/5 * 2/2
3/10 +4/10
7/10
Answer:
7/10
Step-by-step explanation:
You want to first get all common denominators, in this case that will be 10.
It is now (3/10)+(6/10)-(2/10)
3+6-2=7
7/10
The first few steps in solving the quadratic equation 5x2 + 27x = 14 − 13x by completing the square are shown.
5x2 + 27x = 14 − 13x
5x2 + 40x = 14
5(x2 + 8x) = 14
Which is the best step to do next to solve the equation by completing the square?
Answer:
Step-by-step explanation:
Give the equation 5x² + 27x = 14 − 13x, we are to write the steps needed to solve for x using the completing the square method.
Step 1: Rewrite the equation in a quadratic form by first adding 13x to both sides of the equation.
5x² + 27x +13x= 14 − 13x+13x
5x² + 40x = 14
Step 2: factor out the common constant in the left hand side of the equation.
5(x²+8x) = 14
Step3: The next step to take is to divide through by the the value of 5 to have;
5(x²+8x)/5 = 14/5
x²+8x = 14/5
Step 4: complete the square of the equation at the left hand side by adding the square of half of the coefficient of x to both sides i.e {1/2(8)}² which is 4²
x²+8x +4² = 14/5+4²
x²+8x +16 = 14/5+16
(x+4)² = 94/5
Step 5: Taking the square root of both sides
√(x+4)² = ±√94/5
x+4 = ±√94/5
Step 6: subtract 4 from both sides
x+4-4 = ±√94/5 - 4
x = ±√94/5 - 4
Hence the solution to the equation using completing the square method is x = -4±√94/5
Answer:
5(x2 + 8x + 16) = 94
Step-by-step explanation:
Anyone the answers? Please help
Answer:
1.) 3 shovels/7 buckets
2.)7 buckets/3shovels
ASAP!!!!!!!!! PLEASE help me with this question! This is really urgent! No nonsense answers please.
===============================================
Explanation:
Let's calculate the angle B based off the arcs CDF and GHJ
B = (far arc - near arc)/2
B = (arc CDF - arc GHJ)/2
B = (130 - 40)/2
B = 90/2
B = 45
----------
Now let's change GHJ to 30 degrees, while keeping the other arc the same.
B = (far arc - near arc)/2
B = (arc CDF - arc GHJ)/2
B = (130 - 30)/2
B = 100/2
B = 50
Angle B has increased from 45 degrees to 50 degrees.
subtract c from 7, then divide b by the result
Answer:
[tex]\frac{7-c}{b}[/tex]
Answer:
[tex]\frac{7 -c}{b}[/tex]
Step-by-step explanation:
Subtract c from 7 : 7 - c
Then the result is divide by b : [tex]\frac{7 -c}{b}[/tex]
-4-(3+6²)÷13-1²•(-12)=
Answer:
5
Step-by-step explanation:
-4-(3+6²)÷13-1²•(-12)=
PEMDAS
parrenthesis:
-4-81÷13-1² x (-12)
exponent:
-4-81÷12 x (-12)
multiplication:
-4-81÷ (-144)
divison:
- 4 - (- 9)
subtraction (Actaully addition +):
= 5
-(- makes plus so -4 + 9 makes 5
Hope this helps, have a good day!! :)
Question is in the pic I really suck at this stuff can I get some help plssssss
Answer:
see below
Step-by-step explanation:
The hypotheses is the if part of the statement ( after the if)
hypotheses: it is January
The conclusion is the then part of the statement ( after the then)
conclusion there is snow
shannon is paid £1150 a month after deductions.what is her net annual salary?(a year=12 months )
Answer:
£13800
Step-by-step explanation:
1150*12=£13800
Determine the value of x is
Answer:
x = 5
Step-by-step explanation:
The measure of an arc equals the measure of the central angle that intercepts it.
The measure of an arc intercepted by a diameter is 180 deg.
m(arc)EH = 180
m(arc)EF + m(arc)FG + m(arc)GH = m(arc)EH
10x + 8 + 67 + 11x = 180
21x + 75 = 180
21x = 105
x = 5
PLEASE HELP How can a company use a scatter plot to make future sale decisions
Answer:
From scatter plot companies can predict future sales, and what will happen next. To help with this predictions most companies draw a line through the scattered plot called best-fit line. This line should be close to most of the points on the scattered line. Approximately half the point on the top of the line and half on the bottom.In this case the company will ignore the points tat far away from the line.
Scatter plots are useful to compare two variables to see how they relate to one another (if there is any relationship at all). One example could be comparing the temperature outside versus the sales of ice cream. The general trend is that the warmer it gets, the more sales you'll have. So there's an upward trend. We can also say there's a positive correlation as both variables go up together (or go down together).
Contrast this with negative correlation where one variable goes up and the other goes down (eg: hours spent watching tv versus exam score).
Of course, the ice cream example could be too simple and often overused, so it might be better to use something more specific to the company in question. If you picked a company dealing with health/medicine, then you could look at something like height versus weight and see if there's a correlation going on.
I NEED HELP PLEASE FIRST PERSON TO GET ANSWER RIGHT GETS 5 STARS !
Answer:9/5
Step-by-step explanation:
The school's square parking lot has an
area of 3025 ft2. What is the length of each
side of the parking lot?
Answer:
The answer is 55ftStep-by-step explanation:
Since the school's parking lot is a square,
Area of a square = l²
where l is the length of one side
From the question
Area = 3025ft²
We have
3025 = l²
Find the square root of both sides
l = √3025
l = 55ft
The length of each side of the parking lot is 55ft
Hope this helps you
divide 1725 by 102 show work please
Answer:
16.91176471
Step-by-step explanation:
1725÷102
= 16.91176471
A spinner contains 3 equal sections: one red, one yellow, and one blue. The possible results of two spins are shown in the tree diagram below. What is P(red, then yellow)?
1/9
3 x 3 = 9 (since it is spun twice)
1/9
----------------------------------------------------------------------------
Answer:
1/9
Step-by-step explanation:
Probability of spinning a red = 1/3
Probability of spinning a yellow = 1/3
So Probability of getting red and then yellow = 1/3 x 1/3 = 1/9
the 15 chihuahua puppies ate 63 cups of food last week if each puppy ate the same amount of food how many cups of puppy food did each puppy eat
Answer:4.2 cups
Step-by-step explanation:
Just do 63 cups, divided by the 15 puppies which equals 4.2 cups! pls mark brainliest
Answer:
4.2 cups
Step-by-step explanation:
I am in the assiment and i just got it right on the assiment
PLEASE HELP I WILL GIVE BRAINLIEST Complete the frequency table: Method of Travel to School Walk/Bike Bus Car Row totals Under age 15 60 165 Age 15 and above 65 195 Column totals 152 110 98 360 What percentage of students under age 15 travel to school by car? Round to the nearest whole percent. 11% 18% 41% 80%
Answer:
11%
Step-by-step explanation:
1. Fill out the table with the correct numbers.
2. After you fillout the numbers, you should notice that under the column car and in the first row, there should be the number 18.
3. We know the total number of students under the age of 15 is 165.
4. To find the percent:
18/165 * 100
= 11%
Answer:
41%
Step-by-step explanation:
Look at the column "Age 15 and above".
Notice how the row total for that column is 195.
Also, look at "Bus".
Notice how there is a gap between 60 and 110.
To calculate the answer, you need to fill in the blanks using the surrounding numbers.
60 + 50 = 110, so to the right of "65" on "Age 15 and above", there should be a 50.
The "195" at the end of the row is now on the same row as the numbers: 65, 50, and a blank spot.
Now, all we have to do is simply ask ourselves what 65 + 50 gets us, and what we need to add to that to get 195.
65 + 50 = 115, 115 + 80 = 195.
Although, notice that this does not mean the answer is not 80%.
We need to find what percentage is 80 out of 195.
80 out of 195 = 41.03%.
By rounding, we will get an answer of 41%.
If it is now January, what month will it be 500 months from
now?
(a) January
(b) June
(C) September
(d) December
Find the area of a sector with a central angle of 120° and a diameter of 7.3 cm. Round to the nearest tenth.
Answer:[tex]14cm^{2}[/tex]
Step-by-step explanation:
diameter=7.3cm
radius=[tex]\frac{diameter}{2}[/tex]
=[tex]\frac{7.3}{2}[/tex]
=3.65cm
angle =120°
area=[tex]\frac{angle (tita)}{360}[/tex] × [tex]\frac{\pi r^{2} }{1}[/tex]
=[tex]\frac{120}{360}[/tex] × [tex]\frac{22}{7}[/tex] ×[tex]3.65^{2}[/tex]
=[tex]13.95cm^{2}[/tex]
≅[tex]14cm^{2}[/tex]
-3 = k/12 help please
Answer:
-36 = k
Step-by-step explanation:
-3 = k/12
Multiply each side by 12
-3*12 = k/12 *12
-36 = k
Answer: k= -36
Step-by-step explanation:
[tex]-3=\frac{k}{12}[/tex]
multiply both sides by 12
[tex]\frac{12k}{12}=12\left(-3\right)[/tex]
12*(-3)=-36
[tex]\frac{12k}{12}=12\left(-3\right)[/tex]
k=-36
