x = -6.
Step-by-step explanation:1. Write the equation.\(\sf \dfrac{3x+4}{3} -\dfrac{2x}{x-3} =x\)
2. Multiply by "3" on both sides ob the equation.Applying the distributive property of multiplication on the left hand side:
\(\sf (3)(\dfrac{3x+4}{3} -\dfrac{2x}{x-3}) =x(3)\\ \\ \\{3x+4} -\dfrac{(3)2x}{x-3}=3x\\ \\ \\{3x+4} -\dfrac{6x}{x-3}=3x\)
3. Multiply by "x-3" on both sides ob the equation.Applying the distributive property of multiplication:
\(\sf (x-3)({3x+4} -\dfrac{6x}{x-3})=3x(x-3)\\ \\ \\(x-3)({3x+4}) -6x=3x(x-3)\\ \\ \\(x)(3x)+(x)(4)+(-3)(3x)+(-3)(4) -[6x]=3x(x-3)\\ \\ \\\)
Check the image below to see an illustration of this process.
\(\sf 3x^{2} +4x-9x-12 -[6x]=3x(x-3)\\ \\ \\3x^{2} +4x-9x-12 -6x=3x(x-3)\\ \\ \\3x^{2} -11x-12 =3x(x-3)\)
Now simplifying on the right hand side (applying the same logic as last step).
\(\sf 3x^{2} -11x-12 =3x(x-3)\\ \\ \\3x^{2} -11x-12 =(3x)(x)+(3x)(-3)\\ \\ \\3x^{2} -11x-12 =3x^{2}-9x\)
4. Add "9x" on both sides of the equation.\(\sf 3x^{2} -11x-12+9x =3x^{2}-9x+9x\\ \\ \\3x^{2} -2x-12 =3x^{2}\)
5. Subtract "3x²" from both sides.\(\sf 3x^{2} -2x-12-3x^{2} =3x^{2}-3x^{2}\\ \\ \\-2x-12 =0\)
6. Add "12" on both sides.\(\sf -2x-12+12=0+12\\ \\ \\-2x=12\)
7. Divide by "-2" ob both sides.\(\sf \dfrac{-2x}{-2} =\dfrac{12}{-2} \\ \\ \\x =-6\)
8. Verify the answer.If "x= -6" is the correct answer, substituting "x" by "-6" on the original equation should return the same value on both sides of the equal (=) symbol. Let's test!
\(\sf \dfrac{3(-6)+4}{3} -\dfrac{2(-6)}{(-6)-3} =(-6)\\ \\-6=-6\)
That's correct!
x = -6 is the corect answer.
3. A new restaurant has been open for 6 days. The owner is tracking the number of customers served for these 6 days (day 1, 2, 3, 5, and 6). She determines the least regression equation estimating the number of customers on a given day is y = 1.03x + 229.4. If thus far the restaurant has been making a net profit of $5.82, on average per customer, which of the following statements is correct? OA. On day 7, the owner can expect 15 more customers than she has served on day 6. B. If the number of customers continues to follow the current trend, the restaurant will make a net profit of $1,377 on day 7. C. On day 12, the owner can expect a net profit of $1,300. D. Net profit for days 6 and 7 combined is expected to be less than the earned net profit on day 1.
In conclusion, none of the given statements are correct based on the information provided.
To determine the correct statement, let's analyze the given information and the regression equation:
The regression equation for estimating the number of customers on a given day is y = 1.03x + 229.4, where x represents the day number and y represents the number of customers served.
We are also given that the restaurant has been making a net profit of $5.82, on average per customer:
Now let's evaluate each statement:
A. On day 7, the owner can expect 15 more customers than she has served on day 6.
To determine the number of customers on day 7, we substitute x = 7 into the regression equation:
y = 1.03(7) + 229.4 = 7.21 + 229.4 = 236.61
So, the number of customers on day 7 is approximately 237, which is not 15 more than the number of customers served on day 6.
Therefore, statement A is incorrect.
B. If the number of customers continues to follow the current trend, the restaurant will make a net profit of $1,377 on day 7.
To calculate the net profit on day 7, we need to multiply the average net profit per customer ($5.82) by the number of customers on day 7:
Net profit on day 7 = $5.82 \(\times\) 237 ≈ $1,379.34
So, statement B is incorrect as the net profit on day 7 is not expected to be $1,377.
C. On day 12, the owner can expect a net profit of $1,300.
Since the question only provides information about the number of customers served for the first 6 days, we cannot determine the net profit on day 12.
Therefore, statement C is incorrect.
D. Net profit for days 6 and 7 combined is expected to be less than the earned net profit on day 1.
To calculate the net profit for days 6 and 7 combined, we need to calculate the number of customers on both days using the regression equation and then multiply it by the average net profit per customer.
Let's substitute x = 6 into the regression equation:
y = 1.03(6) + 229.4 = 6.18 + 229.4 ≈ 235.58
Now, let's calculate the net profit for days 6 and 7 combined:
Net profit on days 6 and 7 = ($5.82 \(\times\) 235) + ($5.82 \(\times\) 237) ≈ $2,735.2
Comparing this to the earned net profit on day 1, we cannot determine if it is less or greater without the information provided.
Therefore, statement D is incorrect.
In conclusion, none of the given statements are correct based on the information provided.
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solve the following 2x=9
Answer:
2x =9
2x/2=9/2
x=4.5
this is the answer
hope this helps
Zack is on his school's color guard and is practicing throwing and catching his flag. He throws the flag into the air from a height of 5 feet at a velocity of 30 feet per second. After the flag starts to come back down, he catches it 7 feet above the ground.
To the nearest tenth of a second, how long is the flag in the air before Zack catches it?
Hint: Use the formula h=16t2+vt+s.
The Nearest tenth of a second, the flag is in the air for approximately 0.1 seconds before Zack catches it.
To determine the time the flag is in the air before Zack catches it, we can use the kinematic equation for vertical motion:
h = 16t^2 + vt + s
Where:
h is the height of the flag,
t is the time in seconds,
v is the initial vertical velocity of the flag,
s is the initial height of the flag.
In this case, the flag is thrown into the air from a height of 5 feet (s = 5) with an initial vertical velocity of 30 feet per second (v = 30). Zack catches it at a height of 7 feet (h = 7).
We can rewrite the equation as:
7 = 16t^2 + 30t + 5
To find the time (t) when the flag is at a height of 7 feet, we can rearrange the equation and solve for t. However, since this is a quadratic equation, we can also use the quadratic formula.
The quadratic equation in this case is:
16t^2 + 30t + 5 - 7 = 0
16t^2 + 30t - 2 = 0
Now, we can use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
Applying the values from the quadratic equation, we have:
t = (-30 ± √(30^2 - 4 * 16 * (-2))) / (2 * 16)
Simplifying further:
t = (-30 ± √(900 + 128)) / 32
t = (-30 ± √1028) / 32
Using a calculator, we find two solutions:
t ≈ -1.08 seconds or t ≈ 0.06 seconds
Since time cannot be negative in this context, we discard the negative solution.
Therefore, to the nearest tenth of a second, the flag is in the air for approximately 0.1 seconds before Zack catches it.
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For each of the 4 walls of the house, John will need 9 large
planks of wood. If each plank of wood needs 8 pieces of nails
to be secured, how many nails does John need for each wall
of the house?
Bandhan Bank employee salary after 10 years
Answer:
- Banking Operations salary in India with less than 1 year of experience to 10 years ranges from ₹ 1.4 Lakhs to ₹ 7 Lakhs with an average annual salary of ₹ 3.1 Lakhs based on 261 latest salaries
If X = 6 units, Y = 4 units, and Z = 13 units, then what is the volume of the triangular pyramid shown above?
A.
44 cubic units
B.
39 cubic units
C.
104 cubic units
D.
52 cubic units
Answer:
D. 52 cubic units
Step-by-step explanation:
10x-3Y=-150
how do you solve and graph?
me no work math\(-3X+5y=-3\\y=-7+7\)
The value of 'x' is 1 and value of y is '0'.
What is an equation?An equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”.
We have the equations are:
-3x + 5y = -3 ___eq.1
and, y = -7 + 7 ___eq.2
We have to find the value of 'x' and 'y'
Now, Firstly find the value of y
We know that :
Opposite sign with same digit is cancel to each other it is always zero.
y = -7 + 7
So, y = 0
Now, We have to put the value of y in eq. 1
-3x + 5(0) = -3
-3x + 0 = -3
x = -3/-3
x = 1
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Solve each equation by completing the square.
d² - 24d + c
Answer:
d² - 24d + c = (d - 12)² - 144 + c
PLEASE HELP IF YOU KNOW THIS!!!!!
Answer:
7cm
Step-by-step explanation:
3cmx3cm=9cm
9cmx3.14=28.26
28.26/197.9=7 (plus a bunch of decimals!)
So 7cm is your height
Answer:
7.50 is the answer so either 7 or 8
Step-by-step explanation:
h= (A/2piR) -r
Plug in the area and the radius and you got the answer. Use 3.14 as pi
Point D is located on the segment CE. If CD = 24 and DE = x and CE = 5x, what is the measurement of segment CE
Answer:
30
Step-by-step explanation:
If point D is located on the segment CE, then point C, D and E lies on the same line i.e they are collinear. Mathematically, CD+DE = CE
Given CD = 24 and DE = x and CE = 5x, on substituting this values in the equation we have;
Since CE = 5x, CE = 5(6) = 30
Two numbers have a sum of 1195 and a difference of 505?
Answer:
x = 850 and y = 345
Step-by-step explanation:
x + y = 1195
x - y = 505
Add the two equations
2x + 0y = 1700
2x = 1700
x = 850
Sub x = 850 into the first equation:
850 + y = 1195
y = 345
Thus, x = 850 and y = 345
A florist wants to determine if a new additive would extend the life of cut flowers longer than the original additive. The florist selects the first 20 carnations from the ones recently delivered by the greenhouse and assigns the first 10 to the new additive and the rest to the original additive. After three weeks, 6 carnations placed in the new additive still looked healthy, and 2 carnations placed in the original additive still looked healthy. The proportion of healthy carnations with the new additive was significantly greater than the proportion of healthy carnations with the original additive.
Which of the following is a valid conclusion?
It can be inferred that the new additive caused the extended life of the cut flowers, and this inference can be applied to all carnations.
It cannot be inferred that the new additive caused the extended life of the cut flowers, and this inference cannot be applied to the carnations from the greenhouse.
It can be inferred that the new additive caused the extended life of the cut flowers, and this inference can only be applied to the carnations from the greenhouse.
It cannot be inferred that the new additive caused the extended life of the cut flowers, and this inference can only be applied to the carnations from the greenhouse.
The option that is a valid conclusion of the experiment is; It cannot be inferred that the new additive caused the extended life of the cut flowers, and this inference cannot be applied to the carnations from the greenhouse.
What is a Valid Conclusion of the Experiment?We are told that the florist wants to carry out a research to determine if a new additive would extend the life of cut flowers longer than the original additive.
Now, the first 20 carnations from the recently delivered ones are selected and the first 10 are assigned to the new additive and the rest to the original additive.
Now, after a while, the proportion of healthy carnations with the new additive was significantly greater than the proportion of healthy carnations with the original additive.
Now, we can't say that the new additive caused the extended life of the cut flowers. This is because of sampling error and also it cannot be applied to the carnations from the greenhouse.
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The parent absolute value function is reflected across the x-axis and translated right 2 units. Which function is represented by the graph?
–|x – 2|
–|x + 2|
|–x| – 2
|–x| + 2
The function represented by the graph with the given transformations is |–x| + 2.
The function represented by the given transformations is |–x| + 2.
Let's analyze the transformations step by step:
Reflection across the x-axis:
Reflecting the parent absolute value function across the x-axis changes the sign of the function. The positive slopes become negative, and the negative slopes become positive. This transformation is denoted by a negative sign in front of the function.
Translation right 2 units:
Translating the function right 2 units shifts the entire graph horizontally to the right. This transformation is denoted by subtracting the value being translated from the input of the function.
Combining these transformations, the function |–x| + 2 results. The negative sign reflects the function across the x-axis, and the subtraction of 2 units translates it right. The absolute value is applied to the negated x, ensuring that the function always returns a positive value.
Thus, the function represented by the graph with the given transformations is |–x| + 2.
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Answer: -lx-2l
Step-by-step explanation:
Help pls!Pls and ty!
Answer:
a
Step-by-step explanation:
Another one the last one ASAP
Answer:
13m²
Step-by-step explanation:
Area=6.5*4÷2=13
Answer:
13m
Step-by-step explanation:
1/2 × bas × perpendicular height
Which data set could be represented by the box plot shown below
Que sucede cuando dividimos un numero entre si mismo
Answer:
no pasa nada
Step-by-step explanation:
espero que eso te ayude:)
Answer:
Cualquier número dividido entre si mismo da como resultado 1
a playground is 750 M long and 250 m broad find the cost of levelling at rupees 16 per 100 square metres
Answer:
Area of play ground = Length × Breadth = 750 × 250 = 187500. a Cost of levelling the ground = 187500 × 16 100 = Rs . 30000
dont GET THIS HELP!!!!!!!!!
Answer:
Ellen have left 56 glasses to wash.
Step-by-step explanation:
Given that:
Number of glasses to be washed = 175
Percentage of glasses Ellen washed = 68%
Number of glasses Ellen washed = \(\frac{68}{100}*175\)
Number of glasses Ellen washed = 119
Number of glasses left = Total glasses - Number of glasses washed
Number of glasses left = 175 - 119 = 56
Hence,
Ellen have left 56 glasses to wash.
A bike path is 12.5 miles. Dominic is 70% of the way to the end. How far is Dominic on the path?
The percentage of the distance Dominic is on the path is his distance
travelled as a fraction of the total distance when equivalent to 100.
The distance he has travelled on the path is 8.75 miles.
The given parameter are;
Length of Dominic's path = 12.5 miles
The length of the way Dominic is to the end = 70%
Required:
The distance Dominic has travelled on the path
The distance Dominic has travelled, D is 70% of 12.5 miles.
70% of 12.5 miles = 70% × 12.5 miles = 8.75 miles
The distance Dominic has travelled on the path, D = 8.75 miles
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The volleyball team raised $350 from its fundraiser. It wants to buy jerseys and volleyballs. The jerseys cost $12 each, and the team needs 22 jerseys. Volleyballs cost $15 each. What is the maximum number of volleyballs the team can buy and still have money left? Write your answer and explain the steps you took. WILL GIVE BRAIKNLIEST IF RIGHT!!!!!!!!
Answer:
6
Step-by-step explanation:
Answer:
The team can buy 5 volleyballs at maximum with no money left over.
Step-by-step explanation:
First, you need to find the money that the jerseys used:
12 × 22 = $264
Next, you have to subtract that from the total amount:
350 - 264 = $86
Finally, you have to see how many volleyballs you can buy:
If volleyballs cost $15 each then, 86 ÷ 15 = 5.73333333(Infinite)
But you can not buy part of a volleyball so you would have to buy 5 volleyballs. Then you would only have .7333333(Infinite) money left over, but that wouldn't be good for anything.
Is this a good answer????
it is 4.5 miles from moulton to filby via Burnham and denton how far is it between denton and filby
Answer: I think that the answer is 3/4 miles
Step-by-step explanation:
Enter the sum of the numbers as the product of their GCF and another sum.
35 + 56
The sum of the numbers as a product of their GCF is . please help im on a test!
Answer:
8
Step-by-step explanation:
Explanation: The GCF of 56 and 64 is 8 , as 8 goes into 56 exactly 7 times and into 64 exactly 8 times. 8(8)+7(8)=8(7+8).
Find the volume of the figure. For calculations involving , give both the exact value and an approximation to the nearest hundredth of a unit. Let d = 10 and h = 18.
________ ft3 ≈ _________ft3
Thus, the volume of cylinder with the given height and diameter is found as 1413 ft³.
Explain about the shape of cylinder:A cylinder is three-dimensional. It's not a flat thing. There are parallel circular bases in this shape. These bases have a curved face affixed to them. A cylinder in this instance has three faces. Along both end of a curved face, which rounds back to the face's origin, are two spherical bases.
Given that-
diameter d = 10 ftRadius r = 10/2 = 5 ftHeight h = 18 ftVolume of cylinder = πr²h
Volume of cylinder = 3.14 *5²*18
Volume of cylinder = 3.14*25*18
Volume of cylinder = 1413 ft³
Thus, the volume of cylinder with the given height and diameter is found as 1413 ft³.
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help :(((((((((((((!!!!!!!!!!!!
Answer:
6 cans.
Explanation:
area of parallelogram: base * height
Here the base is 14 inch height is 9 inch
using the formula: 14 * 9 = 126 inch²
1 can covers 24 inch²
so he needs: 126/24 = 5.25
He needs 6 cans to paint 126 inch² of the wood.
Circle Project 1. Draw a point at (1, -2) 2. Draw an 8-unit long radius 3. Using a compass, Draw a circle with your point from step one as your center and the point from step two as the side. 4. Using a protractor, draw a 70 degree arc 5. Draw a central angle which intercepts your arc 6. Draw an inscribed angle which intercepts a 40 degree arc 7. Draw a tangent line 8. Draw a secant line 9. Write the equation of your circle.
Answer:
I can explain how to complete each of the steps you have provided.
1. Draw a point at (1, -2)
This is a simple step. Just mark a dot on your paper at the coordinates (1, -2).
2.
Draw an 8-unit long radius
Using your compass, set the radius to 8 units. Place the compass on the point you drew in step 1 and draw a circle around it, making sure that the radius is 8 units long.
3. Using a compass
Draw a circle with your point from step one as your center and the point from step two as the side: This step is already completed in step 2.
4. Using a protractor draw a 70 degree arc
Place your protractor on the center of the circle (the point you drew in step 1) and draw a 70 degree arc on the circle.
5. Draw a central angle which intercepts your arc
Use a straight edge to draw a line from the center of the circle to each endpoint of the arc you drew in step 4. This creates a central angle, which is an angle whose vertex is at the center of the circle and whose sides intercept the circle.
6. Draw an inscribed angle which intercepts a 40 degree arc
Use a straight edge to draw a line from one endpoint of the 70 degree arc to the other endpoint. Then, draw a perpendicular bisector of this line, which intersects the center of the circle. This creates a 40 degree arc on the circle. Draw a line from the center of the circle to one endpoint of the 40 degree arc, and draw a line from that endpoint to the other endpoint of the 40 degree arc. This creates an inscribed angle, which is an angle whose vertex is on the circle and whose sides intercept the circle.
7. Draw a tangent line
Choose a point on the circle that is not on the 70 degree arc. Draw a line from that point tangent to the circle.
8. Draw a secant line
Choose two points on the circle that are not on the 70 degree arc. Draw a line through those points, which intersects the circle at two points.
9. Equation of your circle
The equation of a circle with center (a,b) and radius r is (x-a)^2 + (y-b)^2 = r^2. Using the coordinates of the center from step 1 and the radius from step 2, the equation of the circle is (x-1)^2 + (y+2)^2 = 64.
How do you write equations in Point-slope form?
For a line with a slope a and a known point (h, k), the point-slope form is:
y = a*(x - h) + k
How to write an equation in point slope form?A general linear equation can be written in slope-intercept form as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If we know that a line passes through a point (h, k), then the point-slope form of that line is:
y = a*(x - h) + k
Notice that particularly, the y-intercept can be written as (0, b), then the slope-intercept form is also a point-slope:
y = a*(x - 0) + b
y = a*x + b
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For the question of total area of the cuboid is 200cm^.
I understand where we divide 150 by 4.
But why do I need to multiply by 5, when there are 6 faces.
You need to multiply by 5 instead of 6 because each pair of opposite faces on a cuboid has the same area, so by considering one face from each pair, you ensure that you don't count any face twice.
When calculating the total surface area of a cuboid, you need to understand the concept of face pairs.
A cuboid has six faces, but each face has a pair that is identical in size and shape.
Let's break down the reasoning behind multiplying by 5 instead of 6 in the given scenario.
To find the surface area of a cuboid, you can add up the areas of all its faces.
However, each pair of opposite faces has the same area, so you avoid double-counting by only considering one face from each pair. In this case, you have five pairs of faces:
(1) top and bottom, (2) front and back, (3) left and right, (4) left and back, and (5) right and front.
By multiplying the average area of a pair of faces by 5, you account for all the distinct face pairs.
Essentially, you are considering one face from each pair and then summing their areas.
Since all the pairs have the same area, multiplying the average area by 5 gives you the total surface area.
When dividing 150 by 4 (to find the average area of a pair of faces), you are essentially finding the area of a single face.
Then, by multiplying this average area by 5, you ensure that you account for all five pairs of faces, providing the total surface area of the cuboid.
Thus, multiplying by 5 is necessary to correctly calculate the total surface area of the cuboid by accounting for the face pairs while avoiding double-counting.
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(SAT Prep) Find the value of x.
The angle measure of x is 115°.
What is a parallelogram?A parallelogram is a four-sided shape with two sets of parallel sides, which means that opposite sides are both parallel and have equal length. Parallelograms also have opposite angles with the same measure, and their diagonals intersect at the midpoint and bisect each other. This results in the parallelogram being divided into two triangles that are congruent. Examples of parallelograms include rectangles, squares, and rhombuses, and they are commonly used in both geometry and everyday life, particularly in the design of buildings and other structures.
We can call this figure ACDEF. Let us join CB.
Now we can see that BDEF is a parallelogram. Opposite angles of a parallelogram are equal, hence ∠DBF = ∠DEF = x°
And also consider the triangle ABC,
∠BAC = 50°
∠ABC = 180 - ∠DBF = 180° - x° (linear pair)
∠ACB = 180 - ∠ACD = 180° - x° (linear pair)
We know that all the angles of a triangle adds up to 180°.
Using this we can find x°:
∠BAC + ∠ABC + ∠ACB = 180°
50° + 180° - x° + 180° - x° = 180°
-2x° + 410 = 180°
-2x° = 180° - 410° = -230°
x° = -230/ -2
x ° = 115°
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