1. distributive property
2. combine like terms
3. addition property of equality
4. division property of equality
Solution:Given that,
Kelsey solved the following equation:
[tex]7x - \frac{1}{2}(8x+2) = 6[/tex]
Step 1:By distributive property,
a(b + c) = ab + bc
Therefore,
[tex]7x - (\frac{1}{2} \times 8x)+( \frac{-1}{2} \times 2)= 6\\\\7x - 4x - 1 = 6[/tex]
Step 2:Combine the like terms
7x - 4x - 1 = 6
3x - 1 = 6
Step 3:Addition property of equality
The property means that when we add the same number to both sides of an equation, the sides remain equal
3x - 1 = 6
Add 1 on both sides
3x - 1 + 1 = 6 + 1
3x = 7
Step 4:Division property of equality
The Division Property of Equality means that when we divide both sides of an equation by the same non zero number, the sides remain equal
3x = 7
Divide both sides by 3
[tex]\frac{3x}{3} = \frac{7}{3}\\\\x = \frac{7}{3}[/tex]
Thus the correct justifications Kelsey used to solve this equation is:
1. distributive property. 2. combine like terms. 3. addition property of equality. 4. division property of equality
Answer:
I took the test it is 1. Distributive property 2. Combine like terms 3. Addition property of equality 4. Division property of equality
Is 40/48 proportional to 56/42
Answer:
To find if something is proportional you want to reduce them to there simplest form, so we want to reduce each fraction down
40/48= 5/6
56/42= 8/7
Therefore; these two fractions are not proportional because they reduce to different numbers
Hope this helps ;)
Answer:
no
Step-by-step explanation:
Cross multiply:
40 * 42 = 48 * 56
Simplifying
40 * 42 = 48 * 56
Multiply 40 * 42
1680 = 48 * 56
Multiply 48 * 56
1680 = 2688
Solving
1680 = 2688
Tanya went to Robs diner for lunch and received the bill for her meal even though the receipt was ripped she still knew that the sales tax was 6.5%. how much is the total for her meal after the sales tax is added to the subtotal of $8.50?
Answer:
Therefore total for her male after the sales tax is added to the subtotal of $8.50 is = $(8.50+0.55) = $9.05
Step-by-step explanation:
Given the sales tax was 6.5%.
The sales tax for Tanya's meal is [tex]=\$ \frac{6.5}{100}\times 8.50[/tex]
= $0.55
Therefore total for her male after the sales tax is added to the subtotal of $8.50 is = $(8.50+0.55) = $9.05
What is the significance of the point of intersection of a pair of simultaneous equations
Answer:
The point of intersection gives the solution set(s) of the associated system.
Step-by-step explanation:
If we have a pair of simultaneous equations in 2 variables in x and y, then the point of intersection is the ordered pair (x,y).
This could be a unique intersection, only one point or infinitely many intersection.
This gives us the solution of the simultaneous equations.
Therefore the significance of the point of intersection of a pair of simultaneous equations is that, it gives us the solution set(s) of the associated system.
math help
simplify. your awnser should contain only positive exponents with no fractional exponents in the denominator
The solution using laws of exponents is: [tex]y^{\frac{7}{12} } * z^{\frac{1}{2} }[/tex]
How to use laws of exponents?
Some of the laws of exponents are:
- When multiplying by like bases, keep the same bases and add exponents.
- When raising a base to a power of another, keep the same base and multiply by the exponent.
- If dividing by equal bases, keep the same base and subtract the denominator exponent from the numerator exponent.
The expression we want to solve is given as:
[tex]\frac{(x^{-\frac{3}{2} } y^{\frac{5}{3} } z^{-1})^{-1} }{zx^{\frac{3}{2} } y^{-\frac{1}{4} } * y^{-2} z^{\frac{1}{2} } }[/tex]
Using laws of exponents, we have:
[tex]x^{0} * y^{\frac{7}{12} } * z^{\frac{1}{2} }[/tex]
=[tex]y^{\frac{7}{12} } * z^{\frac{1}{2} }[/tex]
what is 1.498 divived by 30. plz show your work.
Answer:
[tex]0.0749[/tex]
Step-by-step explanation:
[tex]1.498/30[/tex]
To divide the form directly in fraction divide the numerator and denominator by a common number to simplify the values.
Simplifying the value
Removing the decimal in the numerator makes 1000 in denominator
[tex]\frac{1498}{30}*\frac{1}{1000}[/tex]
dividing by a common value i.e 2
[tex]\frac{749}{10}*\frac{1}{1000}[/tex]
Now, removing the decimals from denominator puts the decimal in the numerator gives [tex]0.0749[/tex]
Answer:
1.498 divided by 30 equals 749/15000 OR 0.04993
Step-by-step explanation:
Simply divide as you would a whole number, but place the decimal point above in your answer. So, your first step would be to calculate how many times 30 goes into 149. Your answer will go two places AFTER your decimal point. Then you continue to solve, as you would a whole number!
You found an apartment you really
like. The rent is $625 per month. This is 25% of your
monthly income. How much is your monthly income?
Answer:
$2500
Step-by-step explanation:
25% is one fourth of the total monthly income.
If $625 is = x/4 then multiply both sides of the equation with 4
4 × 625 = x/4 × 4 ➡ 2500 = x
PLZ HELP WILL GIVE 10 PTS + BRAINLIEST THX SO SO SO SO SO SO MUCH!!!!
If (6^2)^p = 6^10, what is the value of p?
a. 2
b. 3
c. 4
d. 5
ty! :D
Answer:
d. 5
Step-by-step explanation:
-4h - 3 < 9
h < 12
h > -3
h < -3
h > -12
The solution of the inequality is h > -3 ⇒ 2nd answer
Step-by-step explanation:
Let us revise very important notes about solving inequalities
You can add and subtract both sides of inequality by a number without change the sign of inequalityYou can multiply or divide both sides of inequality by a positive number without change the sign of inequalityYou can multiply or divide both sides of inequality by a negative number with change the sign of inequality (-2x < 4 ⇒ ÷ (-2) makes it x > -2)∵ -4 h - 3 < 9
- Start with adding both sides by 3 to separate the variable
in one side and the numerical term in the other side of the
inequality sign
∴ -4 h - 3 + 3 < 9 + 3
∴ -4 h < 12
- Now divide both sides by -4 and use the last note above
∵ -4 ÷ -4 = 1
∵ 12 ÷ -4 = -3
∵ < must change to > (because we divide both sides by (-) number
∴ h > -3
The solution of the inequality is h > -3
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Answer:
h> -3
Step-by-step explanation:
7 is underlined 0.673 is the place value for 7
x=9y
5x+3y= -48
What does x equal?
What does y equal?
you can plug the x value (9y) into the second equation
5(9y) + 3y = -48
45y + 3y = -48
48y = -48
y = -1
x = 9(-1)
x = -9
Answer:
x = 9
y = -31
Step-by-step explanation:
5x+3y
y = -31
x = 9
plug it in
Which pair of expressions below is equivalent?
A. 9x+2y and 11xy
B. 4x-5y and 5y-4x
C. 5(2x-3y) and 10x-3y
D. X+y+x+y and 2(x+y)
solve y= 2/3x +7 and 3y= 2x -3
Answer:
The system has no solution
Step-by-step explanation:
we have
[tex]y=\frac{2}{3}x+7[/tex] ----> equation A
[tex]3y=2x-3[/tex]
Isolate the variable y
Divide by 3 both sides
[tex]y=\frac{2}{3}x-1[/tex] ------> equation B
Compare equation A and equation B
Both lines have the same slope and different y-intercept
so
Line A and Line B are parallel lines
The lines do not intersect
therefore
The system has no solution, because both lines are parallel
see the attached figure to better understand the problem
How can fishermen save gas
A fishermen can save gas by implementing the strategies Plan Efficient Routes, Maintain Proper Boat Speed, Reduce Idle Time, Optimize Load and Equipment and Regular Maintenance
Fishermen can save gas by implementing the following strategies:
Plan Efficient Routes: By planning their fishing trips in advance and mapping out efficient routes, fishermen can minimize the distance traveled and save on gas consumption.
Maintain Proper Boat Speed: Operating the boat at an appropriate speed can significantly impact fuel efficiency.
Reduce Idle Time: Minimizing idle time while on the water can help save gas.
Optimize Load and Equipment: Carrying excessive weight on the boat can increase fuel consumption.
Regular Maintenance: Keeping the boat and engine properly maintained is essential for fuel efficiency.
Utilize Wind and Tides: When feasible, fishermen can take advantage of wind and tidal currents to reduce reliance on the engine.
Share Resources: Collaborating with other fishermen or joining fishing cooperatives can help share resources and reduce individual fuel consumption.
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The difference of 5 and n cubed
Answer:
6n
Step-by-step explanation:
Final answer:
The difference of 5 and n cubed is calculated by subtracting n cubed from 5. This involves simple algebraic manipulation.
Explanation:
The difference of 5 and n cubed can be represented as 5 - n³. This means subtracting the cube of the variable n from 5.
To illustrate, if n=2, the calculation would be 5 - 2³ = 5 - 8 = -3.
Therefore, the result of the difference between 5 and n cubed is 5 - n³.
Why does 5x2/3 =10x1/3
Explanation of how to simplify expressions with exponents by subtracting exponents. The answer shows the equivalence of 5×2/3 and 10×1/3.
The expression [tex]( \frac{5 \times 2}{3} )[/tex] equals [tex]( \frac{10}{3} )[/tex]. Let's break it down:
[tex]\( \frac{5 \times 2}{3} \)[/tex] means you multiply 5 and 2 first, which gives you 10, then you divide by 3, resulting in [tex]\( \frac{10}{3} \)[/tex].
However, if you're asking why [tex]\( \frac{5 \times 2}{3} \)[/tex] and [tex]\( 10 \times \frac{1}{3} \)[/tex] are equal, it's because multiplication is distributive over division.
In other words, [tex]\( a \times \frac{b}{c} = \frac{a \times b}{c} \)[/tex].
So, [tex]\( 10 \times \frac{1}{3} \)[/tex] can be written as [tex]\( \frac{10 \times 1}{3} \)[/tex], which simplifies to [tex]\( \frac{10}{3} \)[/tex], the same as [tex]\( \frac{5 \times 2}{3} \)[/tex].
Help pls will mark brainlist !! :)
Answer:
144 cubic inches
Step-by-step explanation:
a=lxwxh a=6*6*4
Yo sup??
we should know that the volume of a cuboid is l*b*h
from the given figure we can say that
l=6 inches
b=6 inches
h=4 inches
therefore
V=6*6*4
=144 inches^3
therefore the correct answer is option C
Hope this helps.
On Tuesday James bought seven CDs. On Wednesday half of all the CDs that he had were destroyed. On Thursday he had 12 left. How many did he have on Monday?
Answer:
He have 17 CDs on Monday.
Step-by-step explanation:
Given:
On Tuesday James bought seven CDs. On Wednesday half of all the CDs that he had were destroyed. On Thursday he had 12 left.
Now, to find the CDs he have on Monday.
Let the CDs he have on Monday be [tex]x.[/tex]
So, on Tuesday as James bought 7 CDs:
[tex]x+7.[/tex]
Now, on Wednesday half of all the CDs that he had were destroyed:
[tex]\frac{x+7}{2}[/tex]
As, given on Thursday he had left CDs = 12.
According to question:
[tex]\frac{x+7}{2}[/tex] [tex]=12[/tex]
Multiplying both sides by 2 we get:
[tex]x+7=24[/tex]
Subtracting both sides by 7 we get:
[tex]x=17.[/tex]
Therefore, he have 17 CDs on Monday.
The difference between of two numbers is 9. If the large number is one more than twice the smaller number, find the larger number.
The larger number is 17
Solution:
Let "x" be the larger number
Let "y" be the smaller number
The difference between of two numbers is 9
Therefore,
larger number - smaller number = 9
x - y = 9 -------- eqn 1
The large number is one more than twice the smaller number
Larger number = 1 + 2(smaller number)
x = 1 + 2y ------ eqn 2
Let us solve eqn 1 and eqn 2
Substitute eqn 2 in eqn 1
1 + 2y - y = 9
1 + y = 9
y = 9 - 1
y = 8
Substitute y = 8 in eqn 1
x - 8 = 9
x = 8 + 9
x = 17
Thus the larger number is 17
Which situation described relates to the graph?
A)A small pizza cost $2, and each topping costs an additional $6.
B)A small pizza cost $4, and each topping costs an additional $2.
C)A small pizza cost $6, and each topping costs an additional $2.
D)A small pizza cost $6 and each topping costs an additional $4.
Answer:
C) A small pizza cost $4, and each topping costs and additional $2.
Step-by-step explanation:
Answer:
A small pizza cost $6, and each topping costs an additional $2.
find the lateral area of the figure
Answer:
you just have to add or divide
Please answerrrr I need it desperately please EXPLAIN. I WILL PUT YOU AS A BRANLIEST ANSWER IF YOU EXPLAIN AND TRY YOUR BEST!!!!! Good luck and remember to EXPALIN.
Answer:
Option B
see the attached figure
Step-by-step explanation:
we know that
Opposite number or additive inverse of any number (n) is a number which, if added to n, results in 0
so
In this problem
The opposite of -1/2 is 1/2
so
point M is 1/2 ----> point M is located in the interval (0,1)
The opposite of 5/2 is -5/2
so
point N is -5/2 ----> point M is located in the interval (-3,-2)
therefore
The correct answer is the option B
If y = 2x - 1 and (3, 5) and (4.7) are part of the pattern then what is the y coordinate of (5, _ )?
Answer:
y = 9
Step-by-step explanation:
Substitute the x- coordinate of the point into the equation and solve for y, that is
y = 2(5) - 1 = 10 - 1 = 9
Thus point is (5, 9 )
Veronica tried to solve an equation step by step. \begin{aligned} 8&=y-4.6\\\\ 8+4.6&=y-4.6+4.6&\green{\text{Step } 1}\\\\ 12.6&=y&\blue{\text{Step } 2} \end{aligned} 8 8+4.6 12.6 =y−4.6 =y−4.6+4.6 =y Step 1 Step 2 Find Veronica's mistake.
Answer:
she did not make a mistake
Step-by-step explanation:
Answer:
veronica didn't make a mistake.
Step-by-step explanation:
Unemployment is the ratio of
A. unemployed workers to employed workers
B. unemployed workers to total workers
C. workers to total population
D. workers to nonworkers
Answer:
C. Workers to total population.
Unemployment is defined as the condition of people who are able to work but cannot find jobs. The unemployment ratio is most accurately described by option B: 'unemployed workers to total workers'. This does not include people who are not part of the labor force.
Explanation:Unemployment is defined as the condition in which people who are able and willing to work cannot find jobs. In terms of the provided options, unemployment is best defined by option B: 'unemployed workers to total workers'. This is because the unemployment rate is calculated by dividing the number of unemployed individuals by the total number of individuals in the labor force (which includes both the employed and the unemployed) and then multiplying by 100 to get a percentage.
This measure gives a good representation of the number of people who are jobless compared to the overall amount of people who are either working or actively seeking work. It's important to keep in mind that it doesn't include people who are not part of the labor force, like children, retirees, and others who are not looking for work.
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House prices in a certain area went
up by 150% between 1995 and 2005.
The price of a house in the area was
£180 000 in 2005.
What was its price in 1995?
Answer:
£60000
Step-by-step explanation:
Sheila mixed 3 ounces of blue paint with
2 ounces of yellow paint. She decided to
create 20 ounces of the same mixture. How
many ounces of yellow paint does Sheila
need for the new mixture?
Answer:
she needs 6 ouonces of yellow paint
Step-by-step explanation:
she has 5oz, 3 blue: 2 red, she needs 20oz. which means she needs 15oz more. 15/5=3. 3*2=6
Briana has been offered a sales job in another city. The offer was for $42,500 plus 8% of her total sales. In order to make it worth the move, Briana needs to have an annual salary of at least $66,500. What would her total sales need to be for her to move?
Answer:
[tex]Total\ sales\ should\ be=\$ 300000[/tex]
Step-by-step explanation:
[tex]Let\ her\ total\ sale=x[/tex]
Total Earning:
[tex]The\ offer=\$ 42500\\\\Income\ from\ the\ sales=8\%\ of\ total\ sale\\\\Income\ from\ the\ sales=8\%\ of\ x\\\\Income\ from\ the\ sales=\frac{8}{100}\times x\\\\Income\ from\ the\ sales==0.08x\\\\Total\ earning=Offer+Income\ from\ the\ sales\\\\Total\ earning=42500+0.08x[/tex]
Required Earning=$66500
[tex]To\ move\ that\ city\\\\Total\ earning=required\ earning\\\\42500+0.08x=66500\\\\0.08x=66500-42500\\\\0.08x=24000\\\\x=\frac{24500}{0.08}\\\\x=300000\\\\Total\ sales\ should\ be=\$ 300000[/tex]
Her total sales would need to be at least $300,000 for her to move
Step-by-step explanation:
Briana has been offered a sales job in another city
The offer was for $42,500 plus 8% of her total salesBriana needs to have an annual salary of at least $66,500We need to find what would her total sales need to be for her to move
Assume that her total sales is x
∵ The offer was for $42,500 plus 8% of her total sales
∵ Her total sales = x
- To find her annual salary multiply x by 8% and add the
product to $42,500
∴ Her annual salary = 8% × x + 42,500
∵ 8% × x = [tex]\frac{8}{100}[/tex] × x = 0.08 x
∴ Her annual salary = 0.08 x + 42,500
∵ Briana needs to have an annual salary of at least $66,500
- At least means ≥
∴ Her annual salary ≥ 66,500
- Substitute her annual salary by the expression above
∴ 0.08 x + 42,500 ≥ 66,500
- Subtract 42,500 from both sides of inequality
∴ 0.08 x ≥ 24,000
- Divide both sides by 0.08
∴ x ≥ 300,000
∴ Her total sales ≥ $300,000
Her total sales would need to be at least $300,000 for her to move
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Break 42 into 7 equal fractions
Answer:
42/7 = 6.00
6.00 x 7 = 42
6.00 is fraction for 42.
Step-by-step explanation:
42 divided b 7 is 6.
What is ×7 9/27 reduced to lowest term
Answer:
[tex]2 \frac{1}{3} [/tex]
Step-by-step explanation:
Assuming the question is
[tex]7 \times \frac{9}{27} [/tex]
reduced to the lowest term.
We proceed as follows:
[tex]7 \times \frac{9}{3 \times 9} [/tex]
We cancel the common factors to get:
[tex]7 \times \frac{1}{3} [/tex]
This simplifies to
[tex] \frac{7}{3} = 2 \frac{1}{3} [/tex]
Natasha has a red and a white sweater. She can wear with a blue skirt, yellow skirt and a black skirt. How many different combinations can she make
Natasha can make 6 different combinations by pairing 2 sweaters with 3 skirts. She can pair each of her red and white sweaters with each of her blue, yellow, and black skirts.
Explanation:Natasha has a red sweater and a white sweater that she wants to pair with a blue skirt, yellow skirt, and a black skirt. To determine the number of different combinations she can make, we use basic combinatorics. Each sweater can be paired with any of the skirts, so we multiply the number of sweaters by the number of skirts.
Here is the calculation:
Number of sweaters: 2 (red and white)Number of skirts: 3 (blue, yellow, and black)Thus, Natasha can make 2 sweaters imes 3 skirts = 6 combinations.
These combinations are:
Red sweater with blue skirtRed sweater with yellow skirtRed sweater with black skirtWhite sweater with blue skirtWhite sweater with yellow skirtWhite sweater with black skirt