A teacher is making multiple copies of a 1−page homework assignment. The time it takes her in seconds based on the number of copies she makes is 5 times the number of copies plus 6. How many total seconds does it take the teacher to make 1 copy? How about 2 copies or 3 copies? By how many seconds does the total time increase for each copy?

Answer:

it makes about 41 copies per minute

First note that log(x) is defined only for x > 0; log(x + 3) for x > -3; and log(x - 1) for x > 1. So if we find any solutions x ≤ 1, these will be extraneous.

Condense the right side:

log(x) = log((x + 3) / (x - 1))

Let b be the base of the logarithm. Then writing both sides as powers of this b simplifies the equation to

b^log(x) = b^log((x + 3) / (x - 1))

x = (x + 3) / (x - 1)

Solve for x :

x (x - 1) = x + 3

x ² - x = x + 3

x ² - 2x - 3 = 0

(x - 3) (x + 1) = 0

x - 3 = 0   or   x + 1 = 0

x = 3   or   x = -1

We throw out x = -1 because it's less than 1, so the only (real) solution is x = 3.

Please find attached photograph for your answer.

Answer:

Step-by-step explanation:

x can be anything so let’s use 0, 1, 2, and 3 for x values

to find the y values, we just plug in the x values into the equation

when x = 0

y = 5/4(0) -2

y = 0 -2

y = -2

(0, -2) (x = 0, y = -2)

when x = 1

y = 5/4(1) -2

y = 5/4 -2

y = 5/4 -8/4

y = -3/4

(1, -3/4) (x = 1, y = -3/4)

when x = 2

y = 5/4(2) -2

y = 10/4 -2

y = 5/2 -4/2

y = 1/2

(2, 1/2) (x = 2, y = 1/2)

when x = 3

y = 5/4(3) -2

y = 15/4 -2

y = 15/4 -8/4

y = 7/4

(3, 7/4) (x = 3, y = 7/4)

Answer:

Table shown below

Step-by-step explanation:

Table of Values

We are given the function:

[tex]\displaystyle y=\frac{5}{4}x-2[/tex]

And it's required to fill the table of values for x and y with the condition that there are only integers.

Given the expression has a denominator of 4, to ensure there are no decimals in the results, we select values of x that are multiple of 4.

Select the values: {-4,0,4,8}

Now calculate the corresponding values of y.

x=-4

[tex]\displaystyle y=\frac{5}{4}(-4)-2=-5-2=-7[/tex]

y=-7

x=0

[tex]\displaystyle y=\frac{5}{4}(0)-2=0-2=-2[/tex]

y=-2

x=4

[tex]\displaystyle y=\frac{5}{4}(4)-2=5-2=3[/tex]

y=3

x=8

[tex]\displaystyle y=\frac{5}{4}(8)-2=10-2=6[/tex]

y=8

The filled table is shown in the attached image

Answer:

DARK Blue! 0.4!

Step-by-step explanation:

Answer:

Large cup cost $4.25

Step-by-step explanation:

Medium:  x

   Large:  y

Constraints:

  7x + 10y = 68.75

  10x + 15y = 101.25

Isolate y variable:

     (7x + 10y = 68.75) * -10    ===>    -70x - 100y =  -687.50

   (10x + 15y = 101.25) * 7       ===>     70x + 105y = 708.75

                                                        ____________________

   add the two equations                                 5y = 21.25

   divide by 5                                                      y = 4.25

Answer:

4/3 because 2/3x2/1=4/3×2=8/6÷2=4/3

Answer:

The answer is 80°.

Step-by-step explanation:

360° - 100° = 260°

260° - 100° = 160°

160° / 2 = 80°

* the theorem is m < UTS = 1/2 (m < UTS - m < US)

* m = measure

The measure of m<UTS is 80 degree.

The correct option is D.

An "arc" is a smooth curve that connects two points in mathematics. In general, an arc is a section of a circle. It is essentially a portion of a circle's circumference.

A circle's arc is defined as a portion or segment of its circumference. A chord of a circle is a straight line that can be created by connecting the two ends of an arc. A semicircular arc is one whose length is exactly half that of a circle.

We have,

From the figure we can write

m < UTS = 1/2 (m < UTS - m < US)

As, m <UTS = 360 and arc US = 100

= 1/2(360° - 100° - 100)

= 160° / 2

= 80°

Thus, m< UTS is 80 degree.

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Answer:

637

Step-by-step explanation:

13 * 49 = 637

Answer:

it's 637 trust me ........

Answer:

70

Step-by-step explanation:

Answer and explanation:

We add both equations to get a simultaneous equation

y+4z=16

2y+5z=32

We solve the equations using elimination method:

Multiply equation 1 by 5 and equation 2 by 4 to cancel out z

5y+20z=80

8y+20z=160

-3y=-80

Y=26.7

Substitute y=26.7 in equation 1

26.7+4z=16

4z=16-26.7

z= -2.67

y+z=26.7+(-2.67)= 24.03

Answer:

x = 3

Each side is 19

Step-by-step explanation:

HF = FG = HG cuz this is an equilateral triangle, meaning all sides are equal.

Answer:

Gitana's work is correct

Step-by-step explanation:

Divide 40 with 100 then multiply it by 160

40 ÷ 100 × 160 = 64

Answer:

Gitana is correct.

Step-by-step explanation:

The answer would be

155

Have a good day bye!

Answer:

ur answer would be 115!

Step-by-step explanation:

I got it right on the test!!

:--)

Answer:

The independent is the 90 gallons and the dependent is the 8 minutes.

Hope this helps!

Step-by-step explanation:

Answer:

Step-by-step explanation:

Instead of dividing both sides by 5, it is multiplied

5x + 3 = 6            {Subtract 3 from both sides}

5x + 3 - 3 = 6-3

            5x = 3       {Divide both sides by 5}

           5x/5 = 3/5

                 x = 3/5

Answer:

95

Step-by-step explanation:

dct equals 140, dct also equal det plus edc, so 140 - 45 = 95

The gratuity of the hotel server has to be $8.

The tax of the restaurant server is 8.5 percent

We have tro find this based on salary

40 dollars x 0.85 = 34

The income 34 - 18

= 16

Half of 16 = 8

Hence the amount that is the percentage of gratuity is 8 percent.

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Answer:

x=10

Step-by-step explanation:

Answer:

38x / 38

Step-by-step explanation:

2 3/8 = 19/8

19/8 x16

multiply --> a x b/c = a x b over c

= 19X x 16 over 8

= 304x over 8

divide

= 38x / 38

Answer:

4.5

Step-by-step explanation:

Its the middle of all of the numbers

Answer:

Its 5

Step-by-step explanation:

3 and 4 has 4 X's

6 has also 4 X's

so it leaves with 5.

165

Is your answer

ggg do gets go t ra di

Answer:

why are we stilll here

Step-by-step explanation:

Answer:

It should be 15 pounds

Step-by-step explanation:

If you divide 5 weeks (the amount you need) by 2 weeks (the current ratio 6:2) then you get 2.5. Lastly just multiply 6 pounds to it (the other part of the ratio/ pounds per 2 weeks)

Answer:

C. 1/8

Step-by-step explanation:

on edge

Answer:

1/8

Step-by-step explanation:

Answer:

The length of o is 24 centimeters

Step-by-step explanation:

In Δ OPQ

∵ Side p is opposite to ∠P

∵ Side q is opposite to ∠Q

∵ Side o is opposite to ∠O

→ To find side o we must use the cosine rule

∴ o = [tex]\sqrt{p^{2}+q^{2}-2(p)(q).cos(O) }[/tex]

∵ p = 38 cm

∵ q = 29 cm

∵ m∠O = 39°

→ Substitute them in the rule to find o

∴ o = [tex]\sqrt{(38)^{2}+(29)^{2}-2(38)(29).cos(39)}[/tex]

∴ o = 23.92008154

→ Round it to the nearest centimeter (whole number)

∴ o = 24 centimeters

∴ The length of o is 24 centimeters

The required sum of -3x, 5x + y, and 7x - 8 - 3y in descending order is 9x - 2y - 8.

Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression. The goal is to obtain an expression that is easier to work with, manipulate, or solve.

Here,
To add -3x, 5x + y, and 7x - 8 - 3y, we can first combine like terms.

Group the x-terms together:

-3x + 5x + 7x = 9x

Group the y-terms together:

y - 3y = -2y

Group the constants together:

-8

Putting it all together, we get:

9x - 2y - 8

Therefore, the sum of -3x, 5x + y, and 7x - 8 - 3y in descending order is 9x - 2y - 8.

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Answer:

= 2      

1. Rearrange terms

2.Distribute

3. add 2  to both sides of the equation

4.Simplify

5.Subtract 3  from both sides of the equation

6. Simplify again

7. Divide both sides of the equation by the same term

8. Simplify one more time

=======================================================

Explanation:

Any point on the x axis always has its y coordinate equal to 0.

Plug in y = 0 and solve for x

y = 4x-28

0 = 4x-28

4x-28 = 0

4x = 28

x = 28/4

x = 7

Therefore, the point (7, 0) is on the line y = 4x-28 and also on the x axis. This is known as an x intercept.

Comparing (7, 0) this to (a, b) shows that a = 7 and b = 0.

Answer:

12 will come in the blank

Step-by-step explanation:

Distributive property is used

a(b + c)  = a*b + a*c

36 + 48 = 12*3 + 12*4

           = 12(3 + 4)