Koby did not solve the equation correctly. The correct solution for 4(x - 3) = x + 2 is x = 14/3 or approximately 4.667. The steps include distribution, combining like terms, and isolating the variable.
The student's solution contains errors in the algebraic process. The correct steps to solve the original equation 4(x - 3) = x + 2 are as follows:
Distribute the 4 into the parentheses: 4x - 12 = x + 2.
Subtract x from both sides to get all the x terms on one side: 4x - x - 12 = 2.
Simplify the equation: 3x - 12 = 2.
Add 12 to both sides to isolate the variable term: 3x = 14.
Divide both sides by 3 to solve for x: x = 14/3.
The correct solution is x = 14/3 or approximately 4.667, not x = 2 as Koby had. To check the solution, you substitute the value back into the original equation:
4(14/3 - 3) = 14/3 + 2
which simplifies to:
56/3 - 12 = 14/3 + 2
and further to:
56/3 - 36/3 = 14/3 + 6/3
resulting in an identity:
20/3 = 20/3.
Find the amount of air it would take to fill a basketball if the diameter of the ball is 12 inches
In order to find the amount of air to fill a basketball with a diameter of 12 inches, convert the diameter to a radius and then to metric units. Then, use the formula for the volume of a sphere (4/3 * π * r³) to calculate the volume.
Explanation:This is a problem relating to the volume of a sphere, based in Physics. Given the diameter of the ball (12 inches), we first convert this measure to the radius, which would be half of the diameter (6 inches). This can also be converted to the metric system for ease of calculation, where 1 inch equals roughly 2.54 cm, leading to 6 inches as approximately 15.24 cm.
To find the air required to fill up the ball, we apply the formula for the volume of a sphere (4/3)πr³. Plugging in the value of the radius we get, V = (4/3) * π * (15.24 cm)³. Solving this will get us the volume of air required to fill up the basketball.
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Mario says that the expression 4+3n² has four terms: 4, 3, n, and 2. Is he correct? explain.
_______________________________________________________________________________________________________________________________________
Mario says that the expression [tex]4+3n^2[/tex] has four terms: 4, 3, n, and 2. Mario is incorrect
Solution:
Given that the expression is:
[tex]4+3n^2[/tex]
Given that, Mario says that the above expression has four terms
But Mraio is incorrect
Because the given expression has two terms only
4 is one of the term
[tex]3n^2[/tex] is another term
So there are totally 2 terms only
A term can be a signed number, a variable, or a constant multiplied by a variable or variables
Here 3 is a constant multiplied by [tex]n^2[/tex]
So, [tex]3n^2[/tex] is one term
Each term in an algebraic expression is separated by a + sign or - sign
Thus there are two terms in mario expression
Erica ate 5/8 of a sandwich. Sven ate 2/5 of a sandwich. Micah ate 3/4 of a sandwich. Gabe ate 6/12 of a sandwich. Who ate the most of his sandwich?
The answer is that Micah ate more of a sandwich because he is 1/4 from eating the whole thing.
Answer:
Micah ate the most of their sandwich.
Step-by-step explanation:
If you convert all of the fractions into a percentage,
Erica ate 62.5% of a sandwich
Sven ate 40% of a sandwich
Micah ate 75% of a sandwich
Gabe ate 50% of a sandwich
Micah ate the most of their sandwich.
The function f(x) = 2x + 210 represents the number of calories burned when exercising, where x is the number of hours
spent exercising.
The function g(x) = 2x + 125 represents the calorie deficit that occurs when following a particular diet, where x is the
number of hours spent exercising.
What is (f + g)(2)? Explain.
A. 214 burned just exercise 2 hours
B. 214 burned exercise and
diet 2 hours
C. 343 burned dieting 2 hours
D. 343 burned exercise and diet 2 hours.
The true statement about (f + g)(2) is (D). 343 burned exercise and diet 2 hours.
The functions are given as:
f(x) = 2x+ 210
g(x) =2x + 125
Start by calculating (f + g)(x) using:
(f + g)(x) = f(x) + g(x)
So, we have:
[tex](f + g)(x) = 2x + 210 + 2x + 125[/tex]
This gives
[tex](f + g)(x) = 4x + 335[/tex]
When x = 2, we have:
[tex](f + g)(x) = 4*2 + 335[/tex]
[tex](f + g)(x) = 343[/tex]
This means that 343 calories were burned by exercising and dieting for 2 hours
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Which statement describes the congruent triangles?
Triangles W Z X and Z Y X. Sides W Z and X Y are congruent, sides Z Y and W X are congruent, and sides Z X are congruent.
Triangle W X Z is congruent to triangle Y Z X
Triangle W X Z is congruent to triangle Y X Z
Triangle W X Z is congruent to triangle X Y Z
Triangle W X Z is congruent to triangle Z Y X
Answer:
Triangle W X Z is congruent to triangle Z Y X
Step-by-step explanation:
2 triangles are said to be congruent when all the corresponding sides of the angle and the interior angles are congruent .The two triangle are said to be the mirror image of each other.In the simple case above the two triangles WXZ and ZYX are congruent because every corresponding side has the same length, and every corresponding angle has the same measure.
Answer:
its acctually Triangle W X Z is congruent to triangle Y Z X
Step-by-step explanation:
The theoretical probability of choosing a red grape from a
bag of grapes is 2/9. There are 8 red grapes in the bag. How
many grapes are in the bag?
Answer:36
Step-by-step explanation: if 2 out of 9 or red and there are 8 red that means that divide 8 by to get 4 * 9 + 36
By using the theoretical probability formula, the total number of grapes in the bag is 36
ProbabilityFrom the question, we are to determine how many grapes are in the bag
Let the total number of grapes in the bag be x
From the probability formula,
[tex]P(A) = \frac{Number\ of\ favorable \ outcomes \ to \ A }{Total\ number\ of\ possible\ outcomes}[/tex]
Let R represent red grapes,
Then,
[tex]P(R) = \frac{Number\ of\ favorable \ outcomes \ to \ R }{Total\ number\ of\ possible\ outcomes}[/tex]
From the given information,
P(R) = 2/9
Number of favorable outcomes to R = 8
Therefore,
[tex]\frac{2}{9} = \frac{8}{x}[/tex]
2x = 9 × 8
2x = 72
x = 72 / 2
x = 36
Hence, the total number of grapes in the bag is 36.
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Which line is the graph of y = -2x + 2?
line a
line b
line c
line d
Answer:
The Answer is Line B
Step-by-step explanation:
the points that make up the graph is ( 0,2) and (1,0)
Answer:
Line B
Step-by-step explanation:
Find the value of the expression 21 - 2a if a = 3
Answer:
15
Step-by-step explanation:
Substitute in the values
2 X 3 = 6
21 - 6 =15
To find the value of 21 - 2a when a = 3, substitute 3 for a and simplify to get 21 - 6, which equals 15.
Explanation:The student has asked to find the value of the expression 21 - 2a given that a = 3. To solve for the expression, substitute the value of a into the expression:
21 - 2(3) = 21 - 6 = 15.
Therefore, the value of the expression when a is 3 is 15.
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markdown $20 by [tex][/tex]7%
The final discounted price is $18.6
Step-by-step explanation:
In this problem we have to decrease the value of $20 by 7%.
First of all, we have to calculate the 7% of $20. We can do it as follows:
[tex]d=\frac{7}{100}\cdot 20 = 1.4[/tex]
This means that the 7% of $20 is 1.4$.
Now we want to decrease the original value by 7%, so we calculate the difference:
[tex]f=20 - d = 20-1.4=18.6[/tex]
So, the final discounted price is $18.6
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For the function f(x) = 3(x - 1)2 + 2, identify the vertex, domain, and range. (2 points)
1) The vertex is (1, 2), the domain is all real numbers, and the range is y > 2.
2) The vertex is (1, 2), the domain is all real numbers, and the range is y s 2.
O3) The vertex is (-1, 2), the domain is all real numbers, and the range is y 2 2.
4) The vertex is (-1, 2), the domain is all real numbers, and the range is y s 2.
Answer:
2) The vertex is (1, 2), the domain is all real numbers, and the range is y ≥ 2.
Step-by-step explanation:
Look at the photo below for the graph.
:)
The point P has coordinates (-4,1). In which quadrant does point P lie?
Answer: quadrant 2
Step-by-step explanation:
u first go to the left side because your x axis is a negative than u go up one positive and u are on quadrant 2
what does AE equal?
Answer:
70
Step-by-step explanation:
BD is 1/2 the size of AE which is derived from the property of midpoints and the parallel lines.
Therefore if BD = 35, AE is twice as long.
AE = 70
Omar made $299 for 13 hours of work.
At the same rate, how many hours would he have to work to make $253?
Answer:
The answer is (11 hours)
Step-by-step explanation:
I first divided 299 by 13 hours to find the rate.
I got the dividend of 23.
All you do now is add $23 per hour.
Once you add 11 hours of this rate. You'll get the sum of $253.
Solving for the amount of hours by cross multiplication
money/hours=money/hours
$299/13hours=$253/x hours
[tex]\frac{299}{13} =\frac{253}{x} \\\\23=\frac{253}{x} \\\\23x=253\\\\x=253/23\\\\x=11[/tex]
Hope this helps, HAVE A BLESSED AND WONDERFUL DAY! I also hope you had a great Superbowl Weekend! :-)
- Cutiepatutie ☺❀❤
n(17+x)=34x-r solve for x
Answer:
[tex]x=\frac{-17n-r}{(n-34)}[/tex]
Step-by-step explanation:
Given:
[tex]n(17+x)=34x-r[/tex]
Taking the terms of x to one side.
[tex]17n+nx=34x-r\\[/tex]
[tex]nx-34x=-17n-r\\\\x(n-34)=-17n-r\\\\x=\frac{-17n-r}{(n-34)}[/tex]
The value of x is:
[tex]x=\frac{-17n-r}{(n-34)}[/tex]
Solve the equation. Write solutions using integers or simplified fractions. 5−(y−3)=14−4(y+2)
of course the answer is Y=. - 2/3
Answer:
-2/3
Step-by-step explanation:
5 − (y−3)=14− 4 (y+2)
Expand
5 - y + 3 = 14 - 4y - 8
Collect like terms
-y + 4y = 14 - 8 - 5 -3
(-1 + 4)y = - 2
3y = -2
Divide both sides by 3
3y/3 = -2/3
y = -2/3
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chevy have some yarn that he wants to use to make hats and scarves. each hat uses 0.2 kilograms of yarn and each scarf uses 0.1 kilograms of yarn. chevy wants to make a total of 15 items. let h be the number of hats chevy makes and s be number of scarves he makes.
Answer:
[tex]The\ following\ system\ of\ equations\ gives\ number\ of\ hats\ and\ scarves\\\\h+s=15\\\\0.2h+0.1s=k\\\\Where\ k\ is\ total\ yarn\ in\ kg.\\\\If\ k=2\ kg\\\\h=5\ hats,\ s=10\ scarves[/tex]
Step-by-step explanation:
[tex]Number\ of\ hats=h\\\\Number\ of\ scarves=s[/tex]
Total Number of items:
[tex]Total\ items=15\\\\Total\ number\ of\ items=Number\ of\ hats+Number\ of\ scarves\\\\Total\ Number\ of\ items=h+s\\\\h+s=15.......................................eq(1)[/tex]
Total yarn used:
[tex]Yarn\ used\ in\ 1\ hat=0.2\ kg\\\\Yarn\ used\ in 1\ scarf=0.1\ kg\\\\Yarn\ used\ in\ hats=Yarn\ used\ in\ 1\ hat\times Number\ of\ hats\\\\Yarn\ used\ in\ hats=0.2\times h=0.2h\\\\Yarn\ used\ in\ scarves=Yarn\ used\ in\ 1\ scarf\times Number\ of\ scarves\\\\Yarn\ used\ in\ hats=0.1\times s=0.1s\\\\Total\ yarn\ used=0.2h+0.1s\\\\If\ total\ yarn=k\ kg\\\\Solution\ of\ following\ system\ of\ equations\ gives\ number\ of\ hats\ and\ scarves\\\\h+s=15\\\\0.2h+0.1s=k[/tex]
[tex]if\ k=2\\\\h+s=15...............eq(2)\\\\0.2h+0.1s=2.......eq(3)\\\\eq(2)-0.2\times eq(3)\\\\0.1s=1\\\\s=10\\\\From\ eq(2)\\\\h=15-s\\\\h=5\ hats[/tex]
what is y+7= -1/2 (x-6)
Answer:
Step-by-step explanation:
y + 7 = -1/2(x - 6)
y + 7 = -0.5x +3
y = -0.5x - 4
Answer:
y=-1/2x-4
Step-by-step explanation:
first distribute the -1/2 into both terms in the parentheses. next solve for y by subtracting 7 from both sides. combine like terms
Help! Rewrite the expression using the LCD
Answer:
1st one is A
2nd is B
EDGE
Does 5 go into 100 equally
Use the figure. Identify a segment that intersects Ef.
Answer:
[tex]\overline{FG}[/tex]
Step-by-step explanation:
When two line segments intersects, then they have a common point.
From the diagram FG intersects EF
Also HG intersects EF
From the given options, the correct answer is [tex]\overline{FG}[/tex]
Therefore the first choice is correct
A semi-truck can hold 8,500 pounds of cargo. How many tons can it hold?
Answer:4.25 tons
Step-by-step explanation:
is 0.02 greater that 1/50
Answer:
No and yes.
Step-by-step explanation:
Turn both to percentages. Move the decimal point over two spots to the right, making 2%. Multiply the fraction by 2 to get 2/100. PerCENT. A dollar is 100 cents. The fraction as a percentage is 2%. They are equal.
Yes, 0.02 is greater than [tex]\( \frac{1}{50} \)[/tex].
Explanation:
0.02 can be represented as [tex]\( \frac{2}{100} \)[/tex], which simplifies to [tex]\( \frac{1}{50} \)[/tex].
Since [tex]\( \frac{2}{100} \)[/tex] is greater than [tex]\( \frac{1}{50} \)[/tex], it follows that 0.02 is greater than [tex]\( \frac{1}{50} \)[/tex].
Step-by-step explanation:
1. Convert 0.02 to a fraction: [tex]\( 0.02 = \frac{2}{100} \)[/tex].
2. Compare [tex]\( \frac{2}{100} \)[/tex] with [tex]\( \frac{1}{50} \)[/tex].
3. Simplify [tex]\( \frac{2}{100} \) to \( \frac{1}{50} \)[/tex].
4. Since [tex]\( \frac{1}{50} \)[/tex] is smaller than [tex]\( \frac{1}{50} \)[/tex], we conclude that 0.02 is greater than [tex]\( \frac{1}{50} \)[/tex].
The perimeter of the triangular park on the right is 16x-6. What is the missing length? The bottom side length is 5x+4 and the right most side is 2x-5
Answer:
[tex](9x-5)\ units[/tex]
Step-by-step explanation:
The picture of the question in the attached figure
we know that
The perimeter of a triangle is the sum of the length of their three sides
so
[tex]P=a+b+c[/tex]
where
a,b,c are the length sides of the triangle
In this problem we have
[tex]P=(16x-6)\ units\\a=(2x-5)\ units\\b=(5x+4)\ units[/tex]
substitute and solve for the missing length
[tex](16x-6)=(2x-5)+(5x+4)+c\\c=(16x-6)-(2x-5)-(5x+4)\\c=(9x-5)\ units[/tex]
There will be 25 party guests. 8
pieces of pizza dough come in a
package. How many packages do
I need to buy?
36 divided by 6a I’m confused plz help
Answer: 6
Step-by-step explanation:
I'm solving for x, but I'm not confident with my work. I feel like x should be smaller than the other side (121) but I got a result much larger than it. Can someone help?
You have the ratios set up but you need to cross multiply everything:
(5x + 10) x 11 = 121 x 10
55x + 110 = 1210
Subtract 110 from both sides:
55x = 1100
Divide both sides by 55:
X = 1100 / 55
X = 20
Helpp Image attached
The area of new circle is 5625π square inches.
Step-by-step explanation:
Given,
Area of circular plate = 625π square inches
Let,
Radius = r
Area of circular plate = πr²
[tex]\pi r^2=625\pi[/tex]
Dividing both sides by π
[tex]\frac{\pi r^2}{\pi}=\frac{625\pi}{\pi}\\\\r^2=625[/tex]
Taking square root on both sides
[tex]\sqrt{r^2}=\sqrt{625}\\r=25[/tex]
The radius of plate is 25 inches.
When the radius is tripled = 25*3 = 75 inches
New area of circle = πr²
New area of circle = [tex]\pi (75)^2\\[/tex]
New area of circle = [tex]5625\pi[/tex] square inches
The area of new circle is 5625π square inches.
Keywords: circle, area
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On a coordinate plane, is translated 3 units up and 3 units to the right to create Line p is drawn through P and and Line q is drawn through Q and Which statement about Lines p and q is true?
Lines p and q are parallel.
Lines p and q are perpendicular.
Lines p and q have the same x-intercept.
Lines p and q have the same y-intercept.
Answer:
Lines p and q are parallel
Step-by-step explanation:
1) Completing the question:
On a coordinate plane, is translated 3 units up and 3 units to the right to create ′′. Line p is drawn through and ’, and Line is drawn through and ’. Which statement about Lines and is true?
2)
If PQ (x, y) according to that rule then P'Q' (x+3, y+3). So let's plot to answer the question. Setting numbers for,x and y.
3) As you can see below, since we add 3 units to the right and 3 units up then no x-coordinate must be the same, no y-coordinate must remain the same. In addition, p and q won't have the same intercept, neither x nor y.
Please help. There is a file included.
Answer:
0
Step-by-step explanation:
8 + - 4 - 4
(goes in the 2nd box)
0
(goes in the last empty box)
I need help on this:(
Answer:
Not to sure if this is correct but I think it is 6: 1 : 18
pls msg me if you need explanation