Julianne opens a dance studio. Her start up costs for the building, advertising, and supplies total $52,000. Each day, she spends $680 on operating costs (like utilities and wages). she earns $960 per day from her students' lesson fees.

Part A: Write an equation or inequality to represent this situation. let d be the number of days.

Part B: When will Julianne begin making profit? Show all the work you did to arrive at your answer.

Answer : The expression for the given statement is [tex]5\leq 4x-2.5[/tex]

Step-by-step explanation :

We are given a statement:

5 is no greater than 4 times a number x minus 2.5

'no greater than' in the above statement means [tex]\leq[/tex].

'minus' in the above statement means subtraction operation.

'times' in the above statement means multiplication operation.

Thus, the expression for the given statement is [tex]5\leq 4x-2.5[/tex]

The value of 'x' will be,

[tex]5\leq 4x-2.5\\\\\5+2.5\leq 4x\\\\7.5\leq 4x\\\\x\geq 1.875[/tex]

We want to write the given statement as an inequality, and then solve it.

The inequality is: 5 ≤ 4*x - 2.5

The solution is: 1.875 ≤ x

The given statement is:

"5 is not greater than 4 times a number x minus 2.5"

The "5 is not greater than..." is written as:

5 ≤

So 5 is smaller than or equal to the thing at the right.

The complete inequality will be:

5 ≤ 4*x - 2.5

Now to solve this, we start by adding 2.5 in both sides:

5 + 2.5 ≤ 4*x

7.5 ≤ 4*x

Now dividing both sides by 4 we get:

7.5/4 ≤ x

1.875 ≤ x

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I believe the answer would be 46 students

> 46 Students in Tom's school are Left-Handed

What's the equation?

Without knowing the specific equation, it's difficult to definitively judge the student's conclusion. Assuming the equation is correctly simplified, if both sides of the equation are identical, then it has infinitely many solutions.

The student's claim about the equation having infinitely many solutions is valid only if, upon reducing the equation to its simplest form, both sides are completely identical. Unfortunately, without knowing the specific equation in question, it's impossible to precisely identify whether the conclusion is correct or not.  However, if we assume the student has correctly simplified the equation and found that both sides match exactly, then we can say that statement C: 'The conclusion is correct because when simplified, both sides of the equation are equivalent' is valid.

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We are given sides of the triangle by expression

First side : n

Second side : m = 5n-5.

Third side : l = 5/4 m - n.

Perimeter is 90.

Therefore, first equation could be set :

n +m +l = 90   --------------equation(1)

Second equation would be

m = 5n-5        --------------equation(2)

Third equation would be

l = 5/4 m - n   --------------equation(3)

Let us solve the system of equations by substitution.

Substituting m = 5n-5 and l = 5/4 m - n in first equation.

We get

n +5n-5 +5/4 m - n= 90

Now, substituting m = 5n-5 in above equation we get

n +5n-5 +5/4 (5n-5) - n= 90

5n + 25n/4 -5 - 25/4 =90

5n + 6.25n -5-6.25 = 90.

11.25n-11.25 = 90

Adding 11.25 on both sides, we get

11.25n-11.25+11.25 = 90+11.25

11.25n = 101.25.

Dividing both sides by 11.25, we get

n=9.

Plugging n=9 in 2nd equation.

m = 5(9)-5 = 45 -5 = 40.

Plugging n=9 and m=40 in first equation, we get

9 +40 +l = 90

49 +l = 90.

Subtracting 49 from both sides, we get

49-49 +l = 90-49

l = 41.

Therefore, sides are of lengths l = 41, m= 40 and n=9.

The value of the measure of ∠K is,

⇒ ∠K = 46°

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In triangle JKL,

⇒ ∠J = 101°

⇒ ∠L = 33°

Now, We know that;

⇒ ∠J + ∠K + ∠L= 180°

⇒ 101° + ∠K + 33° = 180°

⇒ ∠K + 134° = 180°

⇒ ∠K = 180 - 134

⇒ ∠K = 46°

Thus, The value of the measure of ∠K is,

⇒ ∠K = 46°

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y² - 4y - 2x - 4 = 0

           +2x +4   +2x + 4

y² - 4y              = 2x + 4

            +4                 +4      

 (y - 2)²          = 2x + 8

             -8              -8

 (y - 2)²  - 8   = 2x

[tex]\frac{(y - 2)^{2}}{2} - \frac{8}{2} = \frac{2x}{2}[/tex]

[tex]\frac{1}{2}[/tex](y - 2)² - 4 = x

x = [tex]\frac{1}{2}[/tex](y - 2)² - 4

Note: this is a parabola whose axis of symmetry is y = 2 and vertex is (-4, 2)

1. d. d = 66t

The maximum speed of the wildebeest is v=66 ft/s. Speed is defined as the ratio between the distance covered (d) and the time taken (t):

[tex]v=\frac{d}{t}[/tex]

Re-arranging the formula, we get

[tex]d=vt[/tex]

And substituting v=66 ft/s, we find

[tex]d=66t[/tex]

2. c. y = 5 - n

In fact, we can check that this rule satisfies all the numbers of the sequence:

n=3 --> y = 5 - 3 = 2

n=4 --> y = 5 - 4 = 1

n=5 --> y = 5 - 5 = 0

n=6 --> y = 5 - 6 = -1

3. d. $5.50, $11.00, $16.50; E = 5.50h

In fact, if we use the rule E=5.50 h, we see that the table is completed as follows:

h=1 --> E=(5.50)(1 h)=5.50$

h=2 --> E=(5.50)(2 h)=11.00 $

h=3 --> E=(5.50)(3 h)=16.50$

h=4 --> E=(5.50)(4 h)=22.00$

h=5 --> E=(5.50)(5 h)=27.50$

4. c. if d ≥ 5 then C = 4.70d, if d < 5 then C = 4.70d - 1; $17.80, $32.90

If the number of days is more than 5, the cost is 4.70$ per day, therefore c=4.70d (where d is the number of days); if the number of days is less than 5, one dollar is returned, so the cost will be C=4.70d-1. By applying this rule, we can calculate the rental cost after d=4 days and d=7 days:

- d=4 --> c=4.70*4-1=17.80$

- d=7 --> c=4.70*7=32.90$

5. b. y = 3x + 3

In fact, we can check this is the correct rule by substituting the numbers:

x=0 --> y=3*0+3=3

x=1 --> y=3*1+3=6

x=2 --> y=3*2+3=9

x=3 --> y=3*3+3=12

x=4 --> y=3*4+3=15

7. x -2 -1 0 1 2

y (-16 ) (-6 ) (4 ) (14 ) (24 )

The rule we have to apply is:

-10x + y = 4

Re-arranging it, we can solve for y:

y = 10x + 4

So, let's substitute the different values of x:

x=-2 --> 10*(-2)+4=-20+4= -16

x=-1 --> 10*(-1)+4=-10+4= -6

x=0 --> 10*0+4= 4

x=1 --> 10*1+4=10+4= 14

x=2 --> 10*2 +4 =20+4 = 24

8. y = -5x - 1

In fact, if substitute the different values of x given by the problem, we find:

x = -2 --> y = -5*(-2) -1= 10 -1 = 9

x = -1 --> y = -5*(-1) -1 = 5 -1 = 4

x = 0 --> y = -5*0 -1 = -1

x = 1 --> y = -5*1 - 1 = -6

x = 2 --> y = -5*2 -1 = -11

Answer:

1)  D

2) C

3) D

4) C

5) B

6) B

Step-by-step explanation:

Here is the equation:

[tex]4x+y=z[/tex]

You need to find x. To do that, the variable must be alone on one side. On the right side, you have:

[tex]4x+y[/tex]

To leave 4x by itself, you need to remove y by doing the opposite sign of it. Since it's +y, you need to -y(subtract y) from both sides.

[tex]4x+y-y = z-y \\ 4x=z-y[/tex]

Now the variable is alone. You have 4x and you need to find x alone. To do that, you need to divide both sides by 4.

[tex]\frac{4x}{4} = \frac{z-y}{4}[/tex]

Your answer is:

[tex]x = \frac{z-y}{4}\ \checkmark[/tex]

If you have any questions, feel free to ask! :)

[tex]\left(\dfrac{1}{3}\right)^2\cdot\left(\dfrac{1}{3}\right)^x=\dfrac{1}{729}\\\\\left(\dfrac{1}{3}\right)^{2+x}=\left(\dfrac{1}{3}\right)^6\iff2+x=6\ \ \ \ |-2\\\\\boxed{x=4}\\\\\text{used:}\\\\a^n\cdot a^m=a^{n+m}[/tex]

(a) 32 orange marbles

the ratio of red : blue = 18 : 48 = 3 : 8 ( in simplest form )

the ratio of green : orange = 3 : 8 ( equal ratio )

divide green by 3 to obtain 1 part of ratio then multiply this value by 8 to obtain the amount of orange marbles

3 parts → 12

8 parts → 12 × [tex]\frac{8}{3}[/tex] = 32 orange marbles

ANSWER

[tex]x=-6y-\frac{21}{2} [/tex]

EXPLANATION

We have

[tex]\frac{2}{3}x +4y=-7[/tex].

Expressing  [tex]x[/tex]  in terms of  [tex]y[/tex] means we should rewrite the relation such that  [tex]x[/tex]  will remain on one side of the equation while  [tex]y[/tex]  and any other constant will be at the other side.

To make [tex]x[/tex] the subject, we add [tex]-4y[/tex] to both sides of the equation.

[tex]\frac{2}{3}x =-4y-7[/tex].

we now multiply the whole equation by the reciprocal of the coefficient of [tex]x[/tex], which is [tex]\frac{3}{2}[/tex].

This implies that;

[tex]\frac{3}{2} \times \frac{2}{3} x=\frac{3}{2} \times (-4y)-\frac{3}{2} \times 7[/tex]

This simplifies to;

[tex]x=-6y-\frac{21}{2} [/tex]

Answer: Isaiah earned $400.16

Step-by-step explanation:

1. You have that Isaiah earns a weekly salary of $320 and a comission of 3% on all of his sales and the last week this sales were $2,672.

2. Therefore, to solve this problem you must caculate the 3% of $2,672 and add this result to his weekly salary, as following:

[tex](2,672)(0.03)=80.16[/tex] dollars

[tex]320+80.16=400.16[/tex] dollars

To determine how many bottles of soda are needed for 12 bowls of punch, we use the given ratio of 7 bowls to 5 bottles and set up a proportion. We find that 9 bottles of soda are needed for 12 bowls of punch.

The question asks us to figure out how many bottles of soda we need to make a larger amount of punch based on a known ratio. Since it is given that 7 bowls of punch require 5 bottles of soda, we can set up a proportion to find out how many bottles of soda we need for 12 bowls of punch. To do this, we use the initial ratio (7 bowls/5 bottles) and set it equal to the desired ratio (12 bowls/x bottles), where x represents the unknown number of bottles needed for 12 bowls.

We can solve for x by cross-multiplying and dividing:

Set up the proportion: (7 bowls / 5 bottles) = (12 bowls / x bottles)

Cross-multiply: 7 * x = 5 * 12

Simplify: 7x = 60

Divide both sides by 7: x = 60 / 7

Since 60 divided by 7 is not a whole number, we round up, because you can't have a fraction of a bottle in this context. Therefore, x
= 9 bottles (rounded up from 8.57)

So, we would need 9 bottles of soda to make 12 bowls of punch.

4 refrigerators = 1000

2 dishwashers = 300

add em up to 1300

Answer:

Domain =R-{6}

Range =R-[-2,0)

Step-by-step explanation:

edge 2021

Answer:

the answer is y=1/2

Step-by-step explanation:

Answer:the answer is y=1/2

Step-by-step explanation:

Answer: B) 122 and 58

Supplementary angles add to 180 degrees. In other words, they form a straight angle or a straight line when you combine them together (make sure they don't overlap and that there isn't any gap between them).

Choice B is the only pair of angles where they add to 180 since 122+58 = 180. The values in choice A and choice D add to 90; the values in choice C adds to 270.

Note: complementary angles add to 90 degrees. One way to remember "supplementary" vs "complementary" is to think "S for straight, C for corner". By "corner", I mean a 90 degree corner.

To answer this, you will first need to simply the expressions.

[tex]4\sqrt{27} = 12\sqrt{3}[/tex]

[tex]6\sqrt{75} = 30\sqrt{3}[/tex]

Now with the expressions simplified, you'll add the two together getting [tex]42\sqrt{3}[/tex]

So firstly, we have to simplify the radicals. Using the product rule of radicals, simplify these radicals as such:

4√27 = 4 × √9 × √3 = 4 × 3 × √3 = 12√3

6√75 = 6 × √5 × √15 = 6 × √5 × √5 × √3 = 6 × 5 × √3 = 30√3

Now, add these two simplified radicals as such:

12√3 + 30√3 = 42√3

42√3 is your final answer.

Range represents all of the y-values possible for the function.  

What is the highest point on the graph? The coordinate is (2, 50) so the y-value of the highest point is 50.

What is the lowest point on the graph? there isn't one because it continues downward to infinity.

Range: (-∞, 50]

I hope this helped!

Answer : option A

To find the range of scores that represents the middle 50 % of the student who took the test , we find inter quartile

Inter quartile range is the middle 50% of the given range of scores.

The difference between the upper quartile and lower quartile is the inter quartile that is middle 50%

From the diagram , we can see that

Upper quartile = 89

lower quartile = 65

So range is 65%  to 89%

Answer:

[tex]x=3\sqrt{3i} \\or\\x=-3\sqrt{3i}[/tex]

Step-by-step explanation:

What is the solution of the equation when solved over the complex numbers?

x2+27=0

Enter your answers, as exact values, in the boxes.

x =  [tex]3\sqrt{3i}[/tex]  or x =[tex]-3\sqrt{3i}[/tex]

For the graph of given function ,

At x=2, the graph crosses x axis

At x=-6, the graph touches x axis

At x=-12, the graph crosses x axis

Given :

Equation of a function  [tex]f\left(x\right)\:=\:\left(x\:-\:2\right)^3\left(x\:+\:6\right)^2\left(x\:+\:12\right)\:[/tex]

Lets find out the roots and analyze

lets set each factor =0 and solve for x

Exponent in each factor tell us the multiplicity . Using multiplicity we check whether crosses or touches x axis

When multiplicity is odd then graph crosses x axis .

when multiplicity is even then graph touches x axis.

[tex]f\left(x\right)\:=\:\left(x\:-\:2\right)^3\left(x\:+\:6\right)^2\left(x\:+\:12\right)\:\\(x-2)^3= 0\\x-2=0\\x=2[/tex]

Root is x=2  with multiplicity 3. 3 is odd

At x=2, the graph crosses x axis

[tex](x+6)^2=0\\x+6=0\\x=-6[/tex]

At x=-6, multiplicity is 2 that is even .

At x=-6, the graph touches x axis

[tex]x+12=0\\x=-12[/tex]

x=-12  with multiplicity 1. 1 is odd

At x=-12, the graph crosses x axis

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