1/2(12n- 4) =14-10n
First, apply the distributive property to solve the parenthesis
1/2 (12n)+1/2 (-4) = 14-10n
6n-2 =14-10n
Combine like terms
6n+10n = 14+2
16n=16
Divide both sides of the equation by 16
16n/16 =16/16
n= 1
The cost per student of a ski trip varies inversely as the number of students who attend. It will cost each student $250 if 24 students attend. How many students would have to attend to get the cost down to $200?
ANSWER
30 students
EXPLANATION
The cost per student varies inversely as the number of students.
Inverse proportion is written as:
[tex]\begin{gathered} y\propto\frac{1}{x} \\ y=\frac{k}{x} \\ \text{where k = constant of proportionality} \end{gathered}[/tex]Let the cost per student be y.
Let the number of students be x.
It will cost each student $250 if 24 students attend. This means that:
[tex]\begin{gathered} 250=\frac{k}{24} \\ \Rightarrow k=250\cdot24 \\ k=6000 \end{gathered}[/tex]If the cost is down to $200, it means that y is now $200.
That is:
[tex]\begin{gathered} 200=\frac{6000}{x} \\ \Rightarrow x=\frac{6000}{200} \\ x=30\text{ students} \end{gathered}[/tex]Therefore, 30 students could attend.
Find the angle between the following pair of vectors: Around your answers to nearest tenths.p = < -8 , 1 > r = < -4 , 0 >
Angle = 7.1°
John's bank account was overdrawn. The status of his account was − $162. He did not realize the problem and wrote another check for $78. The bank charged him a $24 fee for being overdrawn.What was the new status of John's account at this point?
The initial status of John's bank account was -$162.
After he wrote a check for $78 and being charged in $24 for being overdrawn, the new status is - 162 - 78 - 24 = -$264
A planner at Barnes and Noble originally cost $10. During the weekend, the planner went on sale for $9. What is the price markdown (percent of change)?
new cost = $9
original cost = $10
Substitute the value into the formula;
[tex]\text{percentage change =}\frac{10-9}{10}\times100^{}[/tex]
= 1/10 x 100%
= 10%
√45 + √20 = 5√5
———————————————
Answer:
and the fact that she got to the shoe store and bought it for her if she was a kid she would have a lot of gumball toys
Step-by-step explanation:
perpendicular
Consider the following pair of points.
(-3, -3) and (2, 9)
Step 1 of 2: determine the distance between the two points.
Step 2 of 2: determine the midpoint of the line segment joining the pair of points.
Answer:
.
Step-by-step explanation:
URGENT PLEASE HELL SOLVE FOR X . idc if you don’t show work
Select all points from the list below that lie in the solution set of the system of inequalities graphed below?
Question 3 options:
(7, 0)
(3, 0)
(0, 7)
(-3, -5)
(9, -3)
(0, -1)
The points that lie in the solution set of the system of inequalities graphed are: (7, 0), (3, 0), (9, -3)
In this question, we have been given a graph system of inequalities.
We need to select all points from the given list that lie in the solution set of the system of inequalities.
The solution set for given inequalities is the set of all points which satisfy inequalities.
The solution set is represented by the common region shaded between two inequalities.
From graph, we can see that the points (7, 0), (3, 0), (9, -3) lie in the solution set of the system of inequalities graphed.
Therefore, the points that lie in the solution set of the system of inequalities graphed are: (7, 0), (3, 0), (9, -3)
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Find the square of each number. (Do not add extra spaces in your response.)
1.) 7 =
2.) 21 =
3.) -3 =
4.) 45 =
5.) 2.7 =
6.) −14=
7.) -5.7 =
8.) 25=
700 tickets were sold for a game for a total of $900.00 If adult tickets sold for $2.00 and children's tickets sold for $1.00 how many of each kind of ticket were sold?
Let x be the number of adult tickets and let y be the number of children.
We know that in total there were sold 700 tickets, that means:
[tex]x+y=700[/tex]Now we know that each adult ticket was $2 and the children's tickets was $1, and that the total was $900, this means that:
[tex]2x+y=900[/tex]Then we have the following system of equations:
[tex]\begin{gathered} x+y=700 \\ 2x+y=900 \end{gathered}[/tex]To solve it we substract the second equation from the first one, then we have:
[tex]\begin{gathered} x+y-2x-y=700-900 \\ -x=-200 \\ x=200 \end{gathered}[/tex]Now that we have the value of x we plug it in the first equation to find y:
[tex]\begin{gathered} 200+y=700 \\ y=700-200 \\ y=500 \end{gathered}[/tex]Therefore, there were 200 adult's tickets and 500 children's tickets sold.
calculate the cost of manufacturing a standard cereal box if cardboard costs $0.05 per square inchsurface area 290inches^2 volume is 264in^2cost would be?
We will have that the cost of manufacturing would be:
[tex]C=(0.05)(290)\Rightarrow C=14.5[/tex]So, the cost per box is $14.5.
Simplity 24 ÷ (-2)(3) + 7
Nashia, this is the solution:
24 ÷ (-2)(3) + 7
• We use ,PEMDAS, for the order of operations, as follows:
Step 1: Solve the parenthesis
24 ÷ -6 + 7
Step 2: We solve the division
-4 + 7
Step 3: We solve the addition
3
The result is 3
For a right triangle ABC, you are told that cos A=X and sun A=y. Which option gives an expression that is equivalent to tan A? X/ x2+y2. X/y. Y/X. Y/x2+y2
For a right triangle ABC, the expression that is equivalent to tan A is y/x.
What is defined as the trigonometric functions?Trigonometric functions, also recognized as circular functions, are simply functions of a triangle's angle. These trig functions define the relationship between both the angles as well as sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions. The sine, cosine, as well as tangent angles are the primary categorization of trigonometric functions. The primary functions can be used to derive the three functions cotangent, secant, and cosecant.For the given question,
In a right triangle ABC.
The cosine and sin functions are defined as;
cos A=X and sin A=y.
Then, we know that tan A function can be written in the form in the form of cos A and sin A as,
tan A = sin A/ cos A
Put the values,
tan A = y/x
Thus, the expression that is equivalent to tan A is y/x.
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help me pleasee!!
thank you
The equation of the line is [tex]f(x) =- \frac{1}{3}x -4[/tex]
How is the equation of the line calculated?
The line passes through the following points,
[tex](x_1,y_1)=(-6, -2)\\\\(x_2,y_2)=(-9,-1)[/tex]
The slope- intercept form of the equation,
y = mx +c ----(1)
(a)What is the slope (m) ?
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{-1+2}{-9+6} \\\\m= \frac{1}{-3} \\\\m= -\frac{1}{3}[/tex]
(b) What is the constant ( c) ?
Substituting [tex](x_1,y_1)[/tex] and m in (1)
[tex]y = mx+c\\\\-2 = -\frac{1}{3} (-6)+c\\\\-2 = +2 +c\\\\c = -4[/tex]
Substituting m and c in (1)
y = mx +c
[tex]y =- \frac{1}{3}x -4[/tex]
Using function notation, y = f(x)
The equation of the line is,
[tex]f(x) =- \frac{1}{3}x -4[/tex]
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Our school district is sending two teachers to a 3-day training session on innovative teaching
strategies. Expenses per person: registration, $275; supplies, $40; breakfast, $8; lunch $15;
and dinner $20. Total transportation cost for the two people is $120. If our district has
budgeted $1,500 for the 2 to attend the training session, what is the most they can each pay
for their hotel per person per night?
Answer: Approximately $117.33
Step-by-step explanation:
1. Add all the Expenses per person to get $338
2. Multiply these expenses by 2 for each person to get $676
3. Add $120 for Transportation to get $796
4. Multiply the people going by the amount of days they are staying to get 6
5. Subtract the total expenses by the budget to get $704
7. Divide the answer of step 4 by the remaking budget to get the final answer of approximately $117.33
Factors of 12: 1. 2. 3. 4. 6. 12 Factors of 20: 1, 2, 4, 5, 10, 20 • Which numbers are common factors of 12 and 20? Choose ALL that apply. 1 2 3 6 10 12 20
The common factors are; 1,2,4
Lisa started a busines 8 years ago with an intial investment of $250,000. It is now worth 6 times that amout. How much is the company worth now?
Answer:
1,500,000 is the answer
Answer:
Step-by-step explanation:
1,500,000 million, enjoy
What is the equation for a line transforming from y= x with a slope 5/6?
The equation of the transformed function is y' = 5/6x
How to determine the equation of the transformed function?From the question, we have the following equation that can be used in our computation:
y = x
Also, we have the slope of the linear function to be
Slope = 5/6
This can be rewritten as:
m = 5/6
When the function is transformed, we have the following representation:
y' = m * y
Substitute the known values in the above equation
y' = 5/6 * x
Evaluate
y' = 5/6x
Hence, the equation is y' = 5/6x
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Determine whether the point (2,0) is a solution to the system of equations.
From the given graph of the system of equations
[tex]\begin{gathered} f(x)=|x-1|+1 \\ g(x)=3x+2 \end{gathered}[/tex]It is the point (2,0) is not on any of the graphs of f(x) and g(x). Also,
[tex]\begin{gathered} f(2)=|2-1|+1 \\ =2 \\ \ne0 \\ g(2)=8 \\ \ne0 \end{gathered}[/tex]Since (2,0) doesn't satisfy given equations, therefore, (2,0) is not a solution of the given system.
It can be noted that the solution of the system is (0,2) as it lies on the intersection of f(x) and g(x)
this question is just 4 people to get their status up. <333
Answer:
ok
Step-by-step explanation:
ok.............................
A store purchased an item for $90 and planned to sell it for $162.00 so that their profitwould be 40% of their cost. If they were unable to sell it for this amount, what minimumselling price would allow them to break even?$
Given that a store purchased an item for $90.
They want a profit of 40% of their costs.
So, 40% of their costs = 40% of $90
= 40/100 * 90
= $36
Let y be the minimum selling price
So, from the question we c an say thst:
y = $(90 + 36)
y = $126
Therefore the minimum selling price of $126 would give the profit of 40% of their cost.
find the following and trophs velties. Foeliconicagate axis enda ontsuchsympotes 28-12-22graph item 1
vertices: (3, 2) and (-1, 2)
foci: (1+√13, 2) and (1-√13, 2)
conjugate axis endpoints: (1, 5) and (1, -1)
asymptotes: y = 2 + 3/2(x - 1) and y = 2 - 3/2(x - 1)
Fill in the missing statement and reason in the proof of the corresponding angles theorem.
It is given that AB is parallel to CD and the points E, G, H and F are collinear.
The measure of angle EGF is 180 degrees.
Now,
Angle AGE+angle AGF=180 degrees.
So, it happends using the addition property of equality.
Now, angle AGF and CHF are the same side interior angle.
Therefore, the correct option is (D)
Find the length of the leg of a triangle with a hypotenuse of 16 and a side of 12
c= 4√7
1) Given that we have a leg of 12 and a hypotenuse of 16 units. Let's use the Pythagorean Theorem to find the missing leg.
2) a² =b²+c²
hypotenuse² = leg² +leg²
16² =12² +c²
256= 144 + c²
256 -144 = c²
112=c²
√c²=√112
c=4√7 (approximately 10.58 units)
3) Hence, we can state that the missing leg has the size of 4√7 units
If D = t +9t2 and C = t - t - 8, find an expression that equals D - 3C in standard form?
we have
[tex]\begin{gathered} D-3C=t+9t^2-3(t-t-8)=t+9t^2-3(-8) \\ =t+9t^2+24 \end{gathered}[/tex]in standard form
[tex]9t^2+t+24[/tex]hello I need on this hw question please thank you
Given:
The given equation is,
[tex]3x-19+(?)x=-5x-19[/tex]Required:
To find the missing value.
Answer:
The given equation is,
[tex]\begin{gathered} 3x-19+(?)x=-5x-19 \\ \end{gathered}[/tex]By putting (-8) in place of (?) in the given equation, we get,
[tex]\begin{gathered} 3x-19+(-8)x=-5x-19 \\ \Rightarrow3x-19-8x=-5x-19 \\ \Rightarrow-5x-19=-5x-19 \\ \Rightarrow-19=-19 \end{gathered}[/tex]This shows that the given equation has infinitely many solutions.
Final Answer:
The missing value is -8.
|5а + 10| = |6a - 8|
i don’t understand how to do this pls help
Answer:
Step-by-step explanation:
|5a+10|=|6a-8|
5a+10=±(6a-8)
5a+10=6a-8
10+8=6a-5a
a=18
or
5a+10=-(6a-8)
5a+10=-6a+8
5a+6a=8-10
11a=-2
a=-2/11
someone help me thanks! it's on pythagoras theorem btw
Answer:
y = 3
Step-by-step explanation:
Pythag theorem : ( only applies to RIGHT triangles)
Hypotenuse ^2 = leg1 ^2 + leg 2^2
(7y-1)^2 = (5y-3)^2 + (5y+1)^2
49 y^2 - 14y +1 = 25y^2 -30 y + 9 + 25y^2 + 10y + 1
-y^2 + 6y -9 = 0
or y^2 -6y + 9 = 0 solve by factoring or using Quadratic Formula
( y -3)(y-3) = 0 shows y = 3
I WILL GIVE BRAINLIEST
Which equation represents a line that passes through (–9, –3) and has a slope of –6?
Explain How You got the answer
y – 9 = –6(x – 3)
y + 9 = –6(x + 3)
y – 3 = –6(x – 9)
y + 3 = –6(x + 9)
Answer:
y – 9 = –6(x – 3)
y – 3 = –6(x – 9)
i think im not quit sure if this is correct but i hope this helps :)
write the equations of all the circles in the design from smallest to biggest .( please help me )
The equation of a circle is given by the formula;
(x-h)² + (y-k)² = r²
r is the radius of the circle
(h,k) is the center of the circle
Smallest circle (Red circle)
r = 1
(h,k)= (0, 7)
substitute the values into the formular
(x - 0)² + (y-7)² = 1²
x²+ (y-7)² =1
Bigger circle (Blue circle)
r= 3 h=0 K=3
substitute the values into the formula
(x -0)² + (y-3)²= 3²
x² + (y-3)² = 9
Biggest circle ( Orange Circle)
r=5 h=0 K=-5
substitute the values into the formula and evaluate
(x-0)² + (y+5)² = 5²
x² +(y+5)² = 25
