Translate the sentence into an equation. Five more than the quotient of a number and 7 is equal to 8 . Use the variable c for the unknown number .

Answer:

Case I

$115

Case II

$125

Step-by-step explanation:

Bugles rent for $10 per month

Drums rent for $5 per month

Case I

7 bugles and 9 drums

7 *  bugle cost per month + 9 *  drum cost per month

7 * 10 + 9* 5

70 + 45

$115

Case II

9 bugles and 7 drums

9 *  bugle cost per month + 7 *  drum cost per month

9 * 10 + 7* 5

90 + 35

$125

Answer:

Part a) The number of visits mus be greater than or equal to [tex]4[/tex]

Part b)

with season pass

The total cost is [tex]\$64[/tex]

without season pass

The total cost is [tex]\$58.5[/tex]

Step-by-step explanation:

Let

x---> the number of visit to the water park

y---> the total cost to visit the water park per person

we know that

[tex]y=(14.50+5)x=19.5x[/tex]  

so

Part a) How many visits to the water park would you have to use for the season pass to be a better deal?

For [tex]y=\$64[/tex]

Substitute the value of y in the equation and solve for x

[tex]64=19.5x[/tex]

[tex]x=64/19.5=3.28\ visits[/tex]

therefore

The number of visits mus be greater than or equal to [tex]4[/tex]

Part b) What would the total cost be for 3 visits with and without a season pass?

with season pass

The total cost is [tex]\$64[/tex]

without season pass

The total cost for [tex]x=3\ visits[/tex] is

[tex]y==19.5(3)=\$58.5[/tex]  

Answer:

x=3/2,  x=-4

Step-by-step explanation:

2x^2 + 5x - 12

First lets see if we can factor this

(2x    ) ( x      )

-12 = -1*12     1*-12

    -  2*6        2 * -12

    -  3*4       3 * -4

2 * one of these pairs - the other pair = +5  

2*4 -3 = 5

Put the -3 in the first spot and the 4 in the second spot

(2x-3)  ( x+4)

Using the zero product property

2x-3 =0     x+4=0

2x=3             x=-4

x = 3/2

The answer is x > -4

To get this answer, you divide both sides by 5. This is to undo the multiplication that happens to the 'x' in '5x'. Note that 5x means 5*x or 5 times x, where x is just a placeholder for some unknown number.

Saying x > -4 means you can pick any number larger than -4.

Answer: $36.69

Step-by-step explanation:

Okay, so let's first write the equation:

2.59*10 + 3d = 135.97

Now, let's work on isolating d by first simplifying the equation:

25.9 + 3d = 135.97

25.9 + 3d - 25.9 = 135.97 - 25.9

3d = 110.07

3d/3 = 110.07/3

d = 36.69

Okay, now let's check:

2.59*10 + 3*36.69  = 135.97

25.9 + 110.07 = 135.97

135.97 = 135.97

Okay, so so it costs $36.69 per pair of shoe.

Answer:

Step-by-step explanation:O would say the first answer choice

Answer:

The first one.

Step-by-step explanation: Well it is simple, the total has to be 36, none of the other ones show 36 as the total.

Answer:0.16 and 6%

Step-by-step explanation:

Answer:

a. y= -1/5x+1

Step-by-step explanation:

If we have 2 points , we can find the slope using the formula

m = (y2-y1)/(x2-x1)

  = (-1-2)/(10--5)

   =(-1-2)/(10+5)

  = -3/15

  = -1/5

The slope if -1/5

We can use the point slope form of a line to write an equation

y-y1= m(x-x1)

y-2 = -1/5(x--5)

y-2 =-1/5(x+5)

Distribute the -1/5

y-2=-1/5x -1

Add 2 to each side

y-2+2 = -1/5x -1+2

y = -1/5x+1

Step-by-step explanation:

Use this formula: Y2 - Y1

                              X2 -X1

Then, use point slope form: y - Y1 = m (x - X1)

Finally, it'll reveal your answer!!! :)

Answer:

$9

Step-by-step explanation:

The artist buys 8 brushes that cost $5 each, then all brushes cost

[tex]\$5\cdot 8=\$40.[/tex]

He pays $94 for all brushes and cans of paint, then all cans of paint cost

[tex]\$94-\$40=\$54.[/tex]

If he buys 6 cans of paint, then one can of paint costs

[tex]\$54:6=\$9.[/tex]

[tex]\left\{\begin{array}{ccc}2x+7y=1\\2x-4y=12&\text{change the signs}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}2x+7y=1\\-2x+4y=-12\end{array}\right}\qquad\text{add both sides of equations}\\.\qquad\qquad11y=-11\qquad\text{divide both sides by 11}\\.\qquad\qquad \boxed{y=-1}\\\\\text{Put the value of y to the first equation:}\\\\2x+7(-1)=1\\2x-7=1\qquad\text{add 7 to both sides}\\2x=8\qquad\text{divide both sides by 2}\\\boxed{x=4}\\\\Answer:\ \boxed{x=4\ and\ y=-1\to(4,\ -1)}[/tex]

Answer:

$29.50

Step-by-step explanation:

Answer:

x=-2

Step-by-step explanation:

Remove parenthesis 3(-x+(2x+1))=x-1

Collect the like terms 3(-x+2x+1)=x-1

Multiply parenthesis by 3 3(x+1)=x-1

Move terms 3x+3=x-1

Collect the like terms and calculate 3x-x=-1-3

Divide both sides by 2 2x=-4

Answer: x=-2

Step-by-step explanation:

Answerthe answer is b

Step-by-step explanation:

Answer:

1/4 (n-64)

Step-by-step explanation:

1/4  n-16

We need to factor out 1/4 from each term which means divide each term by 1/4

1/4 ( 1/4 n / (1/4) - 16 / (1/4))

Remember copy dot flip when dividing fractions)

1/4 ( n - 16 * 4/1)

1/4 (n-64)

Answer:

(f+g)(x) = -4^x + 5x - 2

Step-by-step explanation:

if f(x) = -4^x - 8 and g(x) = 5x + 6,

(f+g)(x) = f(x) + g(x)

= -4^x - 8 + 5x + 6

= -4^x + 5x - 2

Answer:

-4^x + 5x - 2

Step-by-step explanation:

By the additive property of function, (f+g)(x) = f(x) + g(x)

Given f(x) = -4^x - 8 and g(x) = 5x + 6

(f+g)(x) = f(x) + g(x)

= -4^x - 8 + 5x + 6

= -4^x + 5x - 2

Answer:

16 logs

Step-by-step explanation:

4 logs in 2 hours

8 logs in 4 hours

12 logs in 6 hours

16 logs in 8 hours

Answer:

16

Step-by-step explanation:

16 Because 2 divided by 8 equals 4 then 4x4=16

Substitute the values of x, y and z to the expression:

[tex]x=5,\ y=3,\ z=14\\\\\dfrac{5x-6y+20z}{4yz}=\dfrac{(5)(5)-(6)(3)+(20)(14)}{(4)(3)(14)}=\dfrac{25-18+280}{(12)(14)}\\\\=\dfrac{7+280}{168}=\dfrac{287}{168}=1\dfrac{119}{168}=1\dfrac{119:7}{168:7}=1\dfrac{17}{24}[/tex]

Answer:

y ≈ 0.7

Step-by-step explanation:

locate [tex]\frac{\pi }{4}[/tex] on the x-axis, move up the vertical line until meeting the graph then the horizontal reading gives y ≈ 0.7

Answer:

There would be 144 red cars.

Step-by-step explanation:

3:5 is equal to 3/5

240 * (3/5) = 144

Answer:

90 red cars

Step-by-step explanation:

sum the parts of the ratio 3 + 5 = 8 parts

divide 240 by 8 to find one part of the ratio

240 ÷ 8 = 30 ← 1 part of the ratio

3 parts = 3 × 30 = 90 ← number of red cars

5 parts = 5 × 30 = 150 ← number of blue cars

Answer:

[tex]x^2+6x+6y=0[/tex]

Step-by-step explanation:

The distance between the parabola focus and the directrix is 3, then

[tex]p=3.[/tex]

Parabola vertex is placed on the perpendicular line to the directrix and this perpendicular line passes trough the focus. Its equation is x=-3 and parabola vertex coordinates are (-3,1.5).

Branches of the parabola go in negative y-direction, then the equation of the parabola is

[tex](x-(-3))^2=-2\cdot 3(y-1.5),\\ \\(x+3)^2=-6(y-1.5),\\ \\x^2+6x+9=-6y+9,\\ \\x^2+6x+6y=0.[/tex]

Answer:

y2=-12x

Step-by-step explanation:

Answer: 4

Step-by-step explanation:

Melinda: y = 10x + 22

George: y = 13x + 10

13x + 10 = 10x + 22

-10x          -10x          

 3x   + 10 =         22

         -10         -10

3x            =         12

÷3                      ÷3

  x            =          4

Lets say Y is the amount they will save.

So Melinda's savings could be described by the equation Y=22+10X, where X is the number of weeks. The same goes to George, but his equation would be Y=10+13X.

To save the same amount, their equations must match:

22+10X = 10+13X

Solving this, one gets

12 = 3x

=> 4=x

So the answer is 4 weeks.

The system results in a false statement

Answer:21

Step-by-step explanation:

Divide 630 by 30. 30 goes into 630 21 times

Answer:

21 stacks

Step-by-step explanation:

Divide 630/30

21 stacks

Enjoy!

B. (0, 9)

Reflection across x=a is represented by the transformation ...

... (x, y) ⇒(2a-x, y)

Reflection across y=b is represented by the transformation ...

... (x, y) ⇒ (x, 2b-y)

The double reflection, across x=2, y=1 will result in the transformation ...

... (x, y) ⇒ (2·2-x, y) ⇒ (4-x, 2·1-y) ⇒ (4-x, 2-y)

For (x, y) = X(4, -7), the transformed point is ...

... X''(4-4, 2-(-7)) = X''(0, 9)

The double reflection across x=2 and y=1 transforms the point X(4, -7) to X''(0, 9), illustrating the sequential application of reflection transformations (4-x, 2-y).

The correct answer is option B.

A reflection across the vertical line x=a is represented by the transformation (x, y) ⇒ (2a-x, y). Similarly, a reflection across the horizontal line y=b is represented by the transformation (x, y) ⇒ (x, 2b-y). The double reflection, across x=2 and y=1, can be expressed by applying these transformations sequentially.

Starting with the point (x, y), the first reflection across x=2 yields (2·2-x, y), and then, the reflection across y=1 gives (4-x, 2·1-y). Combining these transformations, the double reflection is represented by the transformation (x, y) ⇒ (4-x, 2-y).

Now, applying this double reflection to the given point X(4, -7), we get X''(4-4, 2-(-7)) = X''(0, 9). Therefore, the transformed point after the double reflection is X''(0, 9) making option B the correct option.

Learn more about Transformations here:

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Answer:

A. -4

Step-by-step explanation:

J= Jake's Number

A= Amy's Number

2j = 3j+2

-j = 2

j = -2

check: 2(-2) = 3(-2)+2

-4 = -6+2

-4 = -4 (correct)

Jake's number is -2. Amy's is -4

To graph the equation 2x + 3y + z = 6, which represents a three-dimensional plane, isolate one variable (e.g. z = 6 - 2x - 3y) and choose arbitrary values for the other two variables, then calculate z. The obtained ordered triplets (x, y, z) represent points on the plane and can be plotted to give a visual of the plane.

In order to graph the equation 2x + 3y + z = 6, we first need to understand that this is a linear equation in three variables representing a plane in three-dimensional space. Unfortunately, it's challenging to graph a three-dimensional plane manually without specific technology or software.

However, I can explain how you'd approach plotting this. The general process involves initially isolating one variable then choosing arbitrary values for the other two variables. Let's isolate z, for example:

z = 6 - 2x - 3y.

Now, you can choose values for x and y, and subsequently calculate z. You can form ordered triplets (x, y, z) and these would be points of the plane that satisfies the equation. A sufficient number of these points, plotted and confined, will depict a visual of the plane.

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To graph the equation 2x + 3y + z = 6, find the intercepts by setting two variables to zero and solving for the third. Plot these intercepts (0,2,0), (3,0,0), and (0,0,6) on a 3D coordinate system and draw a plane through these points.

To graph the equation 2x + 3y + z = 6, you need to understand that this is an equation of a plane in three-dimensional space. Unlike graphing a line, where you only need two points, graphing a plane requires you to find at least three non-collinear points (points not on the same line) to form a flat surface.

Here is a step-by-step method to graph this plane:

Set z = 0 and solve for y when x = 0 to find the y-intercept. (2(0) + 3y + 0 = 6 gives y = 2).

Set z = 0 and solve for x when y = 0 to find the x-intercept. (2x + 3(0) + 0 = 6 gives x = 3).

Set x = 0 and solve for z when y = 0 to find the z-intercept. (2(0) + 3(0) + z = 6 gives z = 6).

Plot these intercepts on a three-dimensional coordinate system.

Draw a plane that passes through these three points.

These three intercepts, (0,2,0), (3,0,0), and (0,0,6), are enough to define the plane uniquely. Connect these points to form a triangular shape which implies the plane extending infinitely in all directions within the given slope constraints.

Answer:

7. n = 5r + 10

9.  [tex] 28.50j + 18s \le 100 [/tex]

Step-by-step explanation:

7.

The table gives you these values

2   20

4    30

6    40

8    50

The left side goes up by 2 each time while the right side goes up by 10 each line.

Using that pattern, fill in a few extra lines. I did it below in bold.

0    10

1     15

2   20

4    30

6    40

8    50

The line 0, 10 shows you that b in y = mx + b is 10. Also from the fist line to the second line, as x goes from 0 to 1, a difference of 1, y goes from 10 to 15, a difference of 5. The slope is difference in y over difference in x, so

slope = m = 5/1 = 5.

The equation is

y = mx + b

y = 5x + 10

The problem uses n instead of y and r instead of x, so you get

n = 5r + 10

9.

One pair of jeans costs $28.50. j is the number of jeans. j number of jeans cost 28.50j.

One shirt costs $18. s is the number of shirts. s number of shirts cost 18s.

The total cost is the cost of the jeans plus the cost of the shirts.

The total cost is 28.50j + 18s.

She can spend up to $100. The total cost of the jeans and shirts can be less than $100 or exactly $100, but it cannot be more than $100.

cost of jeans and shirts must be less than or equal to $100

[tex] 28.50j + 18s \le 100 [/tex]

The correct graph representing the total cost for a group to visit the zoo with an admission fee of $15 per person is a linear graph starting at the origin and increasing by $15 on the y-axis for each additional visitor on the x-axis.

The question asks which graph correctly represents the total cost for a group to visit the zoo, with an admission fee of $15 per person. To depict this scenario correctly, we would look for a linear graph that starts at the origin (0, 0), indicating that no cost is incurred without visitors, and then increases positively and linearly as the number of visitors increases. This is because the total cost is directly proportional to the number of visitors, with each additional visitor adding $15 to the total cost.

For example, if 1 person visits, the cost is $15; for 2 people, it's $30, and so on. This relationship would be represented graphically by a straight line, where the slope of the line represents the cost per person ($15). Therefore, the correct graph is one that shows a linear relationship with a slope of $15, where the y-axis represents the total cost and the x-axis represents the number of visitors.

Answer:

A

Step-by-step explanation:

the days are at the bottom 1-7. each day does up by 15 (cost of the tickets)

PQ because it corresponds by order.

Answer: [tex]2\sqrt{30}[/tex]

Step-by-step explanation:

               120

                 ∧

             12   10

             ∧     ∧

           3  4  2  5

               ∧

             2  2

  [tex]\sqrt{120}[/tex]

= [tex]\sqrt{2*2*2*3*5}[/tex]

= [tex]2\sqrt{2*3*5}[/tex]

= [tex]2\sqrt{30}[/tex]

Answer:

E

Step-by-step explanation:

The expression given is:  sec β - cos β ( i will write "beta" instead of the symbol β)

We know that [tex]sec(x)=\frac{1}{cos(x)}[/tex]

Substituting this into the the expression and doing some algebra manipulation, we have:

[tex]sec(beta)-cos(beta)\\=\frac{1}{cos(beta)}-cos(beta)\\=\frac{1-cos^{2}(beta)}{cos(beta)}[/tex]

Using the identity  [tex]cos^{2}(x)+sin^{2}(x)=1\\[/tex] (also [tex]sin^{2}(x)=1-cos^{2}(x)[/tex]), we can now write:

[tex]\frac{1-cos^{2}(beta)}{cos(beta)}\\=\frac{sin^2(beta)}{cos(beta)}\\=\frac{sin(beta)*sin(beta)}{cos(beta)}\\=\frac{sin(beta)}{cos(beta)}*sin(beta)[/tex]

We know [tex]tan(x)=\frac{sin(x)}{cos(x)}[/tex], substituting this, we have:

[tex]\frac{sin(beta)}{cos(beta)}*sin(beta)\\=tan(beta)*sin(beta)[/tex]

Answer choice E is the right answer.

The expression sec β - cos β in terms of sine and cosine simplifies to sin2 β. This is achieved by knowing that secant is the reciprocal of cosine and using the Pythagorean identity in trigonometry.

To write the expression in terms of sine and cosine, we start by remembering that secant is the reciprocal of cosine, so sec β = 1/cos β. So, the expression sec β - cos β is equivalent to 1/cos β - cos β.

However, to remove the quotient from the expression, we multiply through by cos β to get 1 - cos2 β. So the expression sec β - cos β simplifies to 1 - cos2 β.

But remember, based on the Pythagorean identity in trigonometry, 1 - cos2 β is also equivalent to sin2 β. So that's our final simplified expression in terms of sine and cosine.

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