Avoidable costs are costs that can be eliminated if the activity that caused them is discontinued. The examples are listed.
What are list of avoidable costs?Direct materials: Direct materials are the materials that go into a product and can be easily traced to it. For example, the wood used to make a table is a direct material. If a company decides to stop making tables, it can avoid the cost of buying wood.
Direct labor: Direct labor is the labor that is directly involved in making a product. For example, the wages paid to the workers who assemble a car are direct labor. If a company decides to stop making cars, it can avoid the cost of paying direct labor.
Variable overhead: Variable overhead is the overhead costs that vary with the number of units produced. For example, the cost of electricity used to power a factory is a variable overhead cost. If a company decides to stop producing a product, it can avoid the variable overhead costs associated with that product.
Sunk costs: Sunk costs are costs that have already been incurred and cannot be recovered. For example, the cost of research and development for a new product is a sunk cost. If the company decides not to launch the product, it cannot recover the cost of research and development.
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Darvin furniture marks up the price of a dining room set 40%. What will be the selling price of a dining room set that Darvin buys for 1500?
Answer:
$2100
Step-by-step explanation:
40% of 1500 is 600
1500 + 600 = 2100
The selling price will be $2100
100 Points! Geometry question. Determine whether each pair of triangles is similar. If so, write a similarity statement. If not, what would be sufficient to prove the triangles similar? Explain your reasoning. Photo attached. Thank you!
Answer:
Δ ABC [tex]\bold{\sim}[/tex] ΔPQR is similar.
Step-by-step explanation:
Similar triangles are two or more triangles that have the same shape, but their sides are in proportion.
For Question:
In Δ ABC and ΔPQR
AB:PQ =8:6=4:3
BC: QR=12:9=4:3
AC: PR=12:9=4:3
Since the length of any side of one triangle is by the corresponding side of another triangle, you will get the same number.
Therefore,
Δ ABC [tex]\bold{\sim}[/tex] ΔPQR is similar.
Hence Proved:
Answer:
ΔABC ~ ΔPQR
Step-by-step explanation:
In similar triangles, corresponding sides are always in the same ratio.
Therefore, if triangle ABC is similar to triangle PQR then:
[tex]AB : PQ = BC : QR = AC : PR[/tex]
Substitute the side lengths into the ratio equation:
[tex]AB : PQ = BC : QR = AC : PR[/tex]
[tex]8 : 6 \;\;\;\:= \;\;12 : 9 \;\;\;\:= \;\;12 : 9[/tex]
Simplify each ratio by dividing all parts of the ratio by their highest common factor:
[tex]\dfrac{8}{2}:\dfrac{6}{2}=\dfrac{12}{3}:\dfrac{9}{3}=\dfrac{12}{3}:\dfrac{9}{3}[/tex]
[tex]4:3=4:3=4:3[/tex]
As the corresponding sides of triangles ABC and PQR are in the same ratio, this proves that the two triangles are similar.
Valerie practiced the viola for 15 minutes. Chuck practiced the cello for hour.
Floyd practiced the flute for 10 minutes longer than Chuck practiced. How long did
the three friends practice together?
The three friends practiced together for 1 hour and 25 minutes.
Valerie practiced the viola for 15 minutes, while Chuck practiced the cello for an hour. Floyd practiced the flute for 10 minutes longer than Chuck.
So, Floyd practiced the flute for 1 hour + 10 minutes.
To find the total practice time, we add the individual practice times together: 15 minutes + 1 hour + 10 minutes = 1 hour and 25 minutes.
In summary, Valerie, Chuck, and Floyd practiced their instruments for a total of 1 hour and 25 minutes.
Valerie contributed 15 minutes, Chuck practiced for 1 hour, and Floyd practiced for 1 hour and 10 minutes.
Adding these times together gives us a total practice time of 1 hour and 25 minutes.
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Algebraic expression for 4less then 3x
When 'x' is 5, the Algebraic expression 3x - 4 evaluates to 11.
To find the algebraic expression for "4 less than the product of 3 and some number," let's break it down step by step.
First, let's define the unknown number as 'x.' Since the problem states "the product of 3 and some number," we can express this as 3 * x or simply 3x.
Next, we want to subtract 4 from this product. The phrase "4 less than" indicates subtraction, so we subtract 4 from 3x. This can be represented as 3x - 4.
In summary, the algebraic expression for "4 less than the product of 3 and some number" is 3x - 4, where 'x' represents the unknown number.
To calculate the value of this expression for a specific value of 'x,' you substitute that value into the expression and simplify. For example, if 'x' is 5, you would substitute 5 into the expression:
3(5) - 4
This simplifies to:
15 - 4 = 11
So, when 'x' is 5, the expression 3x - 4 evaluates to 11.
In general, the algebraic expression allows us to represent a mathematical relationship between quantities using symbols and operations. By substituting specific values into the expression, we can calculate the corresponding results.
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Note the complete question:
Algebraic expression for 4 less than the product of 3 and some number
What is the algebraic expression for "4 less than the product of 3 and some number?
Please help me understand the meaning of how to calculate.
7. Here are two dot plots that represent the ages of the five children in each of two
Families
Dot plots are graphical displays of data that use dots to represent the frequency or count of a specific value in a data set. The ages of five children in each of two families are represented in the dot plots above.
Both dot plots have a similar range of ages, but family A has a higher median age and a smaller spread of ages than family B.
For family A, the median age is 10 years old because the middle dot in the plot is located at 10. Family A has a small range of ages because all the dots are concentrated in the 8-12 age range.
In contrast, family B has a wider range of ages, from 6 to 15 years old, and a larger spread because the dots are scattered across the plot.
The median age for family B is approximately 11 years old.
In conclusion, dot plots are useful for comparing data sets and analyzing their characteristics such as median age and spread.
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Please awnser asap I will brainlist
PLEASE HELP ASAP WOULD APPRECITAE IT
The values of w, x, y, z are 120°, 60°, 120° , 60° respectively.
What are angles on parallel lines?Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.
lines PQ and RS are parallel to each other and AB and CD are also parallel to each other. A pair of parallel line will serve as transversal.
Angles on parallel lines can be ;
Vertically opposite, alternate, corresponding and in each case the angles are equal.
w = 120°( vertically opposite angles)
x = 180-120 = 60( corresponding angles)
x = z = 60° ( corresponding angles)
y = 180-60 = 120°( angles on a straight line)
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A delivery driver makes $78 each day that he works and makes approximately $10 in tips for each delivery that he makes. If he wants to make at least $238 in one day, at least how many deliveries does he need to make?
Answer:
16 deliveries
Step-by-step explanation:
We can model the situation using a linear inequality. Since we're told that the driver makes $10 in tips for each delivery.Thus, this is the slope.Since he makes $78 each day, this number is a constant and he makes it even when no deliveries are made. Thus, this is the y-interceptSince he wants to make at least #238, we want to find a value of d (number of deliveries) which would cause his wages to equal #238. Thus, we can use the following equation to find:238 ≤ 10d + 78
160 ≤ 10d
16 ≤ d
Thus, he needs to make at least 16 deliveries to make at least $238 in one day. Any less than 16 deliveries will cause him to fall short of his goal and any more than 16 deliveries will cause him to exceed his goal.
(Exponents)
what is the meaning of the expression? 3v^4
Answer: The expression, 3v^4, means that the variable, v, is multiplied by itself 4 times (v * v * v * v) and then is multiplied after by the coefficient 3.
Step-by-step explanation:
Exponent indicates the number of times a number needs to be multiplied by itself.
For example if your given x^2
that simply means that the variable, x, is being multiplied by itself twice:
x * x
if your given 2z^9
that means that the variable, z, is first multiplied by itself nine times and after that it is multiplied by the coefficient, two.
NO LINKS!! URGENT HELP PLEASE!!!
11. Write the equation for the graph
This is the same as writing y = sqrt(4(x+5)) - 1
===============================================
Explanation:
The given graph appears to be a square root function.
The marked points on the curve are:
(-4,1)(-1,3)(4,5)Reflect those points over the line y = x. This will have us swap the x and y coordinates.
(-4,1) becomes (1,-4)(-1,3) becomes (3,-1)(4,5) becomes (5,4)Recall the process of reflecting over y = x means we're looking at the inverse. The inverse of a square root function is a quadratic.
----------
Let's find the quadratic curve that passes through (1,-4), (3,-1) and (5,4).
Plug the coordinates of each point into the template y = ax^2+bx+c.
For instance, plug in x = 1 and y = -4 to get...
y = ax^2+bx+c
-4 = a*1^2+b*1+c
-4 = a+b+c
Do the same for (3,-1) and you should get the equation -1 = 9a+3b+c
Repeat for (5,4) and you should get 4 = 25a+5b+c
We have this system of equations
-4 = a+b+c-1 = 9a+3b+c4 = 25a+5b+cUse substitution, elimination, or a matrix to solve that system. I'll skip steps, but you should get (a,b,c) = (1/4, 1/2, -19/4) as the solution to that system.
In other words
a = 1/4, b = 1/2, c = -19/4
We go from y = ax^2+bx+c to y = (1/4)x^2+(1/2)x-19/4
----------
Next we complete the square
y = (1/4)x^2+(1/2)x-19/4
y = (1/4)( x^2+2x )-19/4
y = (1/4)( x^2+2x+0 )-19/4
y = (1/4)( x^2+2x+1-1 )-19/4
y = (1/4)( (x^2+2x+1)-1 )-19/4
y = (1/4)( (x+1)^2-1 )-19/4
y = (1/4)(x+1)^2- 1/4 - 19/4
y = (1/4)(x+1)^2 + (-1-19)/4
y = (1/4)(x+1)^2 - 20/4
y = (1/4)(x+1)^2 - 5
The equation is in vertex form with (-1,-5) as the vertex. It's the lowest point on this parabola. Placing it into vertex form allows us to find the inverse fairly quickly.
----------
The last batch of steps is to find the inverse.
Swap x and y. Then solve for y.
y = (1/4)(x+1)^2 - 5
x = (1/4)(y+1)^2 - 5
x+5 = (1/4)(y+1)^2
(1/4)(y+1)^2 = x+5
(y+1)^2 = 4(x+5)
y+1 = sqrt(4(x+5))
y = sqrt(4(x+5)) - 1
I'll let the student check each point to confirm they are on the curve y = sqrt(4(x+5)) - 1.
You can also use a tool like GeoGebra to verify the answer.
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a) The triangles in this problem are congruent.
b) The reason is the SAS congruence theorem.
What is the Side-Angle-Side congruence theorem?The Side-Angle-Side (SAS) congruence theorem states that if two sides of two similar triangles form a proportional relationship, and the angle measure between these two triangles is the same, then the two triangles are congruent.
The equal sides for this problem are given as follows:
Hypotenuses and PS.
As angle P is bisected, we have <1 = <2, which are the angles between the equal sides, hence the SAS theorem holds true for this problem.
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A package of 25 fishing hooks costs $9.95 , while a package with 40 hooks costs $13.99 . Which is the better buy? Round your answer to the nearest cent if necessary.
Therefore, the package with 40 hooks is the better buy in terms of cost efficiency.
To determine which package is the better buy, we need to compare the cost per hook for each package.
For the package of 25 hooks costing $9.95, we divide the total cost by the number of hooks:
Cost per hook = $9.95 / 25 = $0.398
Rounding to the nearest cent, the cost per hook is $0.40.
For the package of 40 hooks costing $13.99, we divide the total cost by the number of hooks:
Cost per hook = $13.99 / 40 = $0.3498
Rounding to the nearest cent, the cost per hook is $0.35.
Comparing the two costs per hook, we can see that the package with 40 hooks for $13.99 offers a better deal, as the cost per hook is lower at $0.35.
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(36)^x+2= 6
Solve and round to the nearest 100th
Please help I am confused and need an explanation
As the given equation is (36)ˣ⁺² = 6 , then the solution for the given equation is x ≈ -1.54.
The given equation in the question is (36)ˣ⁺² = 6
according to the given equation , the goal is to solve the equation for x.
For solving this equation ,
we'll have to use logarithmic operations which is as follows:
log36(6) = x+2.
We will be further using a calculator to determine the logarithmic value: log36(6) ≈ 0.4607.
Now, By subtracting 2 from both sides, we will get the value of x as:
x ≈ -1.54.
When we round off this value to the nearest 100th, we will get -1.54.
Thus , the solution for the given equation is x ≈ -1.54.
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log3(x+25) -log(x - 1) = 3
Please help my teacher didn’t teach me this and I need help
Solve the problem and explain and if needed round to the nearest 100th
The value of x is 1.08
What is logarithm ?A logarithm is the power to which a number must be raised in order to get some other number.
For example log 100 = 2 . This means that the base 10 logarithm of 100 is 2 and we can also say that 10² = 100
Similarly, solving the equation;
log3(x+25) -log(x - 1) = 3
using law of logarithm
log( 3(x+25)/x-1) = log 1000
therefore;
3x + 75= 1000x -1000
1075 = 1000x -3x
1075= 997x
x = 1075/997
x = 1.08
Therefore the value of x is 1.08
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Answer:
The given triangles APSR and APQR are congruent by S.A.S. criteria.
Step-by-step explanation:
The S.A.S. (Side-Angle-Side) congruence criteria states that two triangles are congruent if their corresponding two sides and included angles are congruent to one another's corresponding two sides and included angle.
Here, we can observe that both triangles share the same side AP.
PR and PQ on the side are congruent.
- Both triangles share Angle P.
The supplied triangles APSR and APQR are therefore congruent according to S.A.S. requirements.
so we can conclude: S.A.S. for the triangles being congruent.
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The length of CF, considering the Pythagorean Theorem in this problem, is given as follows:
CF = 26.08 m.
What is the Pythagorean Theorem?The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side, is equals to the sum of the squares of the lengths of the other two sides.
Hence the equation for the theorem is given as follows:
c² = a² + b².
In which:
c > a and c > b is the length of the hypotenuse.a and b are the lengths of the other two sides (the legs) of the right-angled triangle.The length of EC is given as follows:
(EC)² = 10² + 24²
[tex]EC = \sqrt{10^2 + 24^2}[/tex]
EC = 26.
Then the length of CF is given as follows:
CF² = 26² + 2²
[tex]CF = \sqrt{26^2 + 2^2}[/tex]
CF = 26.08 m.
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60, 69, 79, 80, 86, 86, 86, 89, 90, 100
Which test score is an outlier?
60
69
90
100
The test score that is an outlier is 60. Option A
What is an outlierA data point that dramatically deviates from the dataset's main pattern or trend is referred to as an outlier.
From the information given, we have that;
The score are;
60, 69, 79, 80, 86, 86, 86, 89, 90, and 100.
We can see that the outlier is 60.
This is due to the fact that all of the other scores, which range from 69 to 100, are considerably higher and closer in value.
The score of 60, however, is considerably lower than the others pupils.
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(6x+9)/2=?
please help
The value of x in the expression given is -7/6
Solving the given equation(6x + 9)/2 =
First step is to cross multiply
6x + 9 = 2
Collect like terms
6x = 2 - 9
6x = -7
divide both sides by 6 to isolate x
x = -7/6
Therefore the value of x in the expression given is -7/6
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Find value of x in trapezoid
Answer:
x = 1
Step-by-step explanation:
You want to know the value of x in the trapezoid with adjacent angles (43x+2)° and 135°.
Supplementary anglesThe two marked angles can be considered "consecutive interior angles" where a transversal crosses parallel lines. As such, they are supplementary.
(43x +2)° +135° = 180°
43x = 43 . . . . . . . . . . . . . . divide by °, subtract 137
x = 1 . . . . . . . . . . . . . . . divide by 43
The value of x is 1.
__
Additional comment
Given that the figure is a trapezoid, we have to assume that the top and bottom horizontal lines are the parallel bases.
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Which equations represent the line that is parallel to 3x - 4y = 7 and passes through the point (-4,-2)? Select two
options.
Oy=-3x+1
03x-4y=-4
4x-3y=-3
Oy-2=-(x-4)
Oy+2=2(x+4)
The equations that represent a line parallel to 3x - 4y = 7 and passes through the point (-4, -2) are:
0 = 3x - 4y - 4
3x - 4y = 4
To determine which equations represent a line that is parallel to the given line and passes through the point (-4, -2), we need to find the equations that have the same slope as the given line.
The equation 3x - 4y = 7 can be rewritten in slope-intercept form as y = (3/4)x - 7/4. From this form, we can see that the slope of the given line is 3/4.
Now let's analyze the options:
Oy = -3x + 1: This equation has a slope of -3, which is not equal to the slope of the given line (3/4). Therefore, this option does not represent a line parallel to the given line.
0 = 3x - 4y - 4: This equation can be rewritten as 3x - 4y = 4. Comparing this to the given line, we can see that it has the same coefficients of x and y, which means it has the same slope of 3/4. Therefore, this option represents a line parallel to the given line.
4x - 3y = -3: This equation has a slope of 4/3, which is not equal to the slope of the given line (3/4). Therefore, this option does not represent a line parallel to the given line.
Oy - 2 = -(x - 4): This equation can be rewritten as y = -x + 2. The slope of this line is -1, which is not equal to the slope of the given line (3/4). Therefore, this option does not represent a line parallel to the given line.
Oy + 2 = 2(x + 4): This equation can be rewritten as y = 2x + 6. The slope of this line is 2, which is not equal to the slope of the given line (3/4). Therefore, this option does not represent a line parallel to the given line.
In conclusion, the equations that represent a line parallel to 3x - 4y = 7 and passes through the point (-4, -2) are:
0 = 3x - 4y - 4
3x - 4y = 4
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1. Which one of the following is NOT true about polynomial functions f(x) and g(x) if deg (f) = man * d deg * (g) =n?
A. deg (f + g) = max(m, n)
B. deg (f_{g}) <= m + n
C. If g is a factor of f then deg( f )<= m
D. The deg (f ^ 3) = 3m
The option that is not true about polynomial functions is:
Option D. The deg (f ^ 3) = 3m
How to Interpret the degree of Polynomial functions?For polynomial functions f(x) and g(x), if deg(f) = m * deg(g) = n, then we have the following:
Option A: deg(f + g) = max(m, n)
This is true because we know that the degree of the sum of two polynomials is the maximum of their individual degrees.
Option B: deg(f * g) <= m + n
This is true because we know that the degree of the product of two polynomials is at most the sum of their individual degrees.
Option C: If g is a factor of f, then deg(f) <= m
This is true because If g is a factor of f, it means that f can be divided by g without leaving a remainder. In this case, the degree of f is less than or equal to the degree of g.
D. The deg(f ^ 3) = 3m
This is not true because the degree of the polynomial f raised to the power of 3 is not necessarily equal to 3 times the degree of f. The degree of f^3 will depend on the individual terms and their exponents.
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What is the equation of the line that passes through the point (-3, 7) and has a slope of -5/3?
The equation of the line that passes through the point (-3, 7) and has a slope of -5/3 is y - 7 = (-5/3)(x + 3).
We are given the point (-3, 7) and the slope of the line as -5/3.The slope-intercept form of a line is y = mx + b where m is the slope and b is the y-intercept.
To obtain the equation of the line, we need to substitute the values of slope and point in the slope-intercept form and solve for b.(7) = (-5/3)(-3) + b 21/3 = b.
Now we have the value of b, and we can substitute the values of m and b in the slope-intercept form.y = (-5/3)x + 21/3 is the equation of the line in slope-intercept form.
To obtain the equation in the standard form Ax + By = C, we multiply each term by 3.3y = -5x + 7Add 5x to both sides5x + 3y = 7.
This is the equation of the line in standard form.
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
The scaled triangle will be larger than the initial size by a factor 2.
The scaled square will be smaller than the initial side by a factor 4
What is dilation?Dilation refers to a transformation that changes the size of a geometric figure without altering its shape.
Dilation involves scaling an object by a certain factor, that might result in enlarging or reducing its dimensions uniformly in all directions.
Based on the given diagram, the new length and size of the object is calculated as follows;
For the triangle, (measure the length with ruler)
new lengths = 2 times the original lengthoriginal length = 2 cm, new length = 4 cmthe new size of the triangle will increase by a factor 2For the square; (measure the length with ruler)
new lengths = 0.25 times the original lengthoriginal length = 4 cm, new length = 2 cmthe new size of the square will decrease by a factor 4Learn more about dilation here: https://brainly.com/question/20482938
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Identify the y-coordinate
(9,[?])
Answer:
(9,16)
Step-by-step explanation:
We Know
The equation y = 3x - 2
Find the y coordinate (9, ?)
We just simply put 9 in for x and solve for y
y = 3(9) - 2
y = 18 - 2
y = 16
So, the coordinate are (9,16)
Which are the solutions of x2= -13x -4
Answer: D
Step-by-step explanation:
To solve this question, we need to change the equation to standard form.
[tex]x^2=-13x-4[/tex] [add both sides by 13x and 4]
[tex]x^2+13x+4=0[/tex] [use quadratic equation]
[tex]\frac{-13+\sqrt{13^2-4(4)}}{2} , \frac{-13-\sqrt{13^2-4(4)}}{2}[/tex] [simplify]
[tex]\frac{-13+\sqrt{13^2-16}}{2} , \frac{-13-\sqrt{13^2-16}}{2}[/tex]
[tex]\frac{-13+\sqrt{169-16}}{2} , \frac{-13-\sqrt{169-16}}{2}[/tex]
[tex]\frac{-13+\sqrt{153}}{2} , \frac{-13-\sqrt{153}}{2}[/tex]
Therefore, the answer is D.
The graph of F(x), shown below, has the same shape as the graph of
G(x)=x2, but it is shifted to the left 1 unit. What is its equation?
-F(x)=
-
OA. F(x)=x²2 +1
B. F(x)=x²-1
C. F(x) = (x + 1)²
D. F(x)=(x-1)²
To shift the graph left, we need to subtract 1 from x. This gives us F(x) = (x - 1)², which matches option D. Therefore, the correct answer is D.
The graph of F(x) is a parabolic graph, just like the graph of G(x)=x². F(x) is shifted to the left by 1 unit.
The equation for the graph of F(x) is F(x) = (x - 1)². This is because when a parabolic graph is shifted left or right, it affects the x-value of the vertex of the parabola.
The standard form of the equation for a parabolic graph is y = a(x - h)² + k, where (h, k) is the vertex of the graph and a determines whether the graph is facing up or down. In this case, the vertex of the graph of G(x)=x² is (0, 0).
When we shift this graph left by 1 unit, the vertex becomes (-1, 0). Therefore, the equation for F(x) is F(x) = a(x + 1)².
To determine the value of a, we can look at the y-intercept of the graph, which is (0, 1). Plugging these values into the equation, we get 1 = a(0 + 1)², which simplifies to 1 = a.
Therefore, the equation for F(x) is F(x) = (x + 1)². However, if we expand this equation, we get F(x) = x² + 2x + 1, which is not in the form given in the options.
To shift the graph left, we need to subtract 1 from x. This gives us F(x) = (x - 1)², which matches option D. Therefore, the correct answer is D.
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NO LINKS!! URGENT HELP PLEASE!!!
NOT MULTIPLE CHOICE!!
8. a. Finish the table
b. Name the type of sequence
c. Find the equation for the following sequence
Answer:
7: 63
8: 73
arithmetic sequence
y = 10x - 7
or f(n) = 10x -7
or
[tex]a_{n}[/tex] = 3 + (n-1)10
Step-by-step explanation:
the output increases by 10 every time that the input increases by 1. That gives us our common difference or slope. The y intercept is -7. That is the value is you worked backwards until you get to n = 0. The initial value is 3. That is when n is 1.
When n is 3, f(n) is 23
When n is 2, f(n) is 13
When n is 1, f(n) is 3
When n is 0, f(n) is -7
I am not sure if this is clear. I am assuming that you have a lot of knowledge of linear equations and how to write arithmetic sequence. If my explanation is confusing it is me and not you.
Answer:
a. 63,73
b. Arithmetic sequence
c.t(n)=10n-7
Explanation:
a. Here is the completed table:
n | t(n)
4 | 33
5 | 43
6 | 53
7 | 63
8 | 73
b.
The type of sequence is arithmetic.
An arithmetic sequence is a sequence of numbers where the difference between any two consecutive terms is constant.
In this case, the difference between any two consecutive terms is 10.
c.
The equation for the arithmetic sequence is:
t(n)=a+(n-1)d
where:
t(n) is the nth term in the sequencen is the term numberd is the common differencea is the first termFor Question:
d=43-33=10a=?Now
equation becomes:
t(4) = a+(4-1)10
33=a+30
a=33-30
a=3
Now, the Equation becomes
t(n) = 3+(n-1)10
t(n) = 3+10n-10
t(n)=10n-7
In 2020 there were 18,700 students at college a with a projected enrollment increase of 500 students per year in the same year there were 26,200 soon as a College been with a projected enrollment decline of 1000 students per year according to these projections when will the colleges have the same enrollment what will be the Roman each college at that time
In 5 years from 2020, the two colleges will have the same enrollment and At that time, both colleges will have an enrollment of 21,200 students.
To determine when the two colleges will have the same enrollment, we can set up an equation based on the given information.
Let's assume "x" represents the number of years from 2020.
For College A, the projected enrollment can be expressed as:
Enrollment_A = 18,700 + 500x
For College B, the projected enrollment can be expressed as:
Enrollment_B = 26,200 - 1000x
To find when the two enrollments will be equal, we set Enrollment_A equal to Enrollment_B and solve for "x":
18,700 + 500x = 26,200 - 1000x
Combining like terms:
1500x = 7,500
Dividing both sides by 1500:
x = 5
Therefore, in 5 years from 2020, the two colleges will have the same enrollment.
To find the enrollment at that time, we substitute "x = 5" into either of the enrollment equations. Let's use Enrollment_A:
Enrollment_A = 18,700 + 500(5)
Enrollment_A = 18,700 + 2500
Enrollment_A = 21,200
At that time, both colleges will have an enrollment of 21,200 students.
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the midpoint of a and b is (-3,-5) and point a is (-.5,0) what is point b
Therefore, the coordinates of point B are (-5.5, -10).
To find the coordinates of point B, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint between two points (x1, y1) and (x2, y2) are given by:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
We are given the midpoint coordinates as (-3, -5) and the coordinates of point A as (-0.5, 0). Let's assume the coordinates of point B as (x, y). Plugging the known values into the midpoint formula, we have:
(-3, -5) = ((-0.5 + x) / 2, (0 + y) / 2)
Simplifying, we get:
-3 = (-0.5 + x) / 2 ... (1)
-5 = y / 2 ... (2)
From equation (2), we can solve for y:
y = -5 * 2
y = -10
Now, substituting this value of y in equation (1), we can solve for x:
-3 = (-0.5 + x) / 2
-6 = -0.5 + x
x = -6 + 0.5
x = -5.5
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Select the correct answer.
Which expression is equivalent to 107-8y +3? Assume that the denominator does not equal zero.
O A. y2 (10y³ - 8y² + 3)
О в.
10³ - 8y² + 3
V
O c.
y (10y³
OD. 10²¹ - $y² +3
8y² + 3)
Reset
Next
The correct answer is option B: 10³ - 8y² + 3.
To obtain the equivalent expression, we can simplify the given expression by combining like terms. We have 107 as a constant term, -8y as the coefficient of the y term, and 3 as another constant term.
So, combining these terms, we get 10³ - 8y² + 3, which is equivalent to the given expression.
Option A is incorrect because it introduces an additional y term in the form of y², which is not present in the original expression.
Option C is incorrect because it only includes the y term and its coefficients, without considering the constant terms.
Option D is unrelated to the original expression as it introduces unrelated numbers and symbols.
Therefore, the correct equivalent expression is 10³ - 8y² + 3, as stated in option B.
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