Rates Lin, Diego, and Elena are competing to see who can finish their book the fastest. Lin read the first 54 pages from a 270-page book in the first 3 days. Diego read the first 100 pages from a 320-page book in the first 4 days. Elena read the first 160 pages from a 480-page book in the first 5 days. If they continue to read every day at these rates, who will finish first, second, and third? Explain or show your reasoning:

Answer/Step-by-step explanation:

a. 3x + 13 = 12x - 2x

Add like terms

3x + 13 = 10x

3x = 10x - 13 (subtraction property of equality)

3x - 10x = - 13 (substraction property of equality)

-7x = -13

-7x = -13/-7 (division property of equality)

x = 13/7

b. 6j - 12 + 4j - 8 = 10

Add like terms

6j + 4j - 12 - 8 = 10

10j - 20 = 10

10j = 10 + 20 (addition property of equality)

10j = 30

10j/10 = 30/10 (division property of equality)

j = 3

c. 10y - 4y = 14 + 2y - 3y

Add like terms

6y = 14 - y

6y + y = 14 (addition property of equality)

7y = 14

7y/7 = 14/7

y = 2

d. 4p + 8 - 3p = 33

Add like terms

4p - 3p + 8 = 33

p + 8 = 33

p = 33 - 8 (subtraction property of equality)

p = 25

Answer:

26

Step-by-step explanation:

These problems always really confuse me but I took a quiz with this question and this is my answer 26

Answer:26

Step-by-step explanation:

i just took the test

Answer:

the answer is 632

Step-by-step explanation:

just do some normal multiplication. :)  

Answer:

A. would be a.

Step-by-step explanation:

Answer:

a) D

b) 4.09 cm

Step-by-step explanation:

a) P of a circle is 22/7 D

Half a circle 1/2 22/7 D

D= 2r

1/2 22/7 2x (D)

b) Find Radius

P = (3.142 * (2r) )

25.71 = 3.142 *2r

r= 4.09 cm

Answer:

8x  ft^3

Step-by-step explanation:

Step one:

given

dimension of the box

Length= 2ft

width = x ft

Height= 4 ft

Required;

the expression for the volume of the box

Step two:

We know that the volume is expressed generally as

V=L*W*H

V= 2*x*4

V= 8x  ft^3

The expression for the volume is V= 8x  ft^3

Answer: x=68, y=37

Step-by-step explanation:

The equation for the sum of two numbers is 105 would be x+y=105. You can say the larger number would be x and the smaller would be y. So, x=2y-6. then you plug that into the x in the first equation.

2y-6+y=105

3y-6=105

3y=111

y=37

Then you would plug in the y to one of the equations. I will do the second one but you can do either one.

x=2y-6

x=2*37-6

x=74-6

x=68

Answer:

( D ) x = 6

Hope this helps !! :)

Answer/Step-by-step explanation:

✔️Using trigonometric ratio, find width of the rectangle, BD:

Thus:

[tex] tan(\theta) = \frac{opposite}{adjacent} [/tex]

Where,

[tex] tan(\theta) = tan(60) = \sqrt{3} [/tex]

Opposite = BD

Adjacent = 7 cm

Plug in the values

[tex] \sqrt{3} = \frac{BD}{7} [/tex]

Multiply both sides by 7

[tex] 7\sqrt{3} = BD [/tex]

[tex] BD = 7\sqrt{3} [/tex]

✔️Using trigonometric ratio, find height of the rectangle, BF:

Thus:

[tex] tan(\theta) = \frac{opposite}{adjacent} [/tex]

Where,

[tex] tan(\theta) = tan(60) = \sqrt{3} [/tex]

Opposite = 6 cm

Adjacent = BF

Plug in the values

[tex] \sqrt{3} = \frac{6}{BF} [/tex]

[tex] BF = \frac{6}{\sqrt{3}} [/tex]

Rationalize

[tex] BF = \frac{6 \times \sqrt{3}}{\sqrt{3} \times \sqrt{3}} [/tex]

[tex] BF = \frac{6\sqrt{3}}{3} [/tex]

[tex] BF = 2\sqrt{3} [/tex]

✔️Perimeter of rectangle BDEF:

Perimeter = 2(BD + BF)

Plug in the values

[tex] Perimeter = 2(7\sqrt{3} + 2\sqrt{3}) [/tex]

[tex] Perimeter = 2(9\sqrt{3}) [/tex]

[tex] Perimeter = 18\sqrt{3} [/tex]

✔️Area of the rectangle BDEF:

Area = BD × BF

Plug in the values

[tex] Area = 7\sqrt{3} \times 2\sqrt{3} [/tex]

[tex] Area = 7 \times 2\sqrt{3 \times 3} [/tex]

[tex] Area = 14 \times 3 [/tex]

[tex] Area = 42 [/tex]

Answer:

100feet

Step-by-step explanation:

Given the height of the object modelled by the equation

y = -16x^2 + 48x + 64

We can find the maximum height reached by the object since we are not told what to find.

The velocity of the object at its max height is zero.

dy/x = 0

dy/dx = -32x + 48

0 = -32x + 48

32x = 48

x = 48/32

x = 1.5secs

get the max height by substituting x = 1.5 into the given equation:

y = -16x^2 + 48x + 64

y = -16(1.5)^2 + 48(1.5)+ 64

y =  -36+72+64

y = 100 feet

Hence the maximum height reached by the object is 100feet

Answer:

The number of green pens sold is 96.

Step-by-step explanation:

Note: This question is not complete. The complete question is therefore provided before answering the question as follows:

A shop sells packs of black pens, packs of red pens and packs of green pens. There are:

2 pens in each pack of black pens

5 pens in each pack of red pens

6 pens in each pack of green pens

On Monday, number of packs of black pens sold : number of packs of red pens sold : number of packs of green pens sold = 7:3:4

A total of 212 pens were sold.

Work out the number of green pens sold.

The explanation of the answer is now given as follows:

Since the ratio is given in packs of pens, we have to first convert it to number of pens based on the number of pens in each pack. Therefore, we have:

7:3:4 is converted to (7 * 2) : (3 * 5) : (4 * 6) = 14 : 15 : 24

Based the new ratio, we have:

Weight of contribution of the green pens to the total number of pens sold = 24 / (14 + 15 + 24) = 24 / 53 = 0.452830188679245

The number of green pens sold can now be calculated as follows:

Number of green pens sold = Total pens sold * Weight of contribution of the green pens to the total number of pens sold = 212 * 0.452830188679245 = 96

Therefore, the number of green pens sold is 96.

Answer:

GCF: 4

LCM: 60

Answer:

x>3/11

3x - 21 + 8x + 18 >0

11x - 3 >0

11x >3

x>3/11

​

​

​​

Answer:

Step-by-step explanation:

3(x - 7) + 2(4x + 9) > 0

3x-21+8x+18>0

11x-3>0

11x>3

x>3/11

Answer:

.53 pounds of dog food each day.

Step-by-step explanation:

Use PEMDAS to solve

Answer:

C

Step-by-step explanation:

it says thousandths and a number group with a th at the end is on the right of the decimal.

Answer:

C: 0.342

Step-by-step explanation:

Here's how it works:

.(tenth)(hundredth)(thousandth)

Therefore,

"Three hundred forty-two thousandths" is 0.342.

Answer:

it's A

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Just got it correct

Answer:

x=5, y=2

Step-by-step explanation:

To solve this system, we need to find x and y. First, let's find x. In the first equation (6x+4y=42), subtract 4y on both sides to isolate 6x. This will result in 6x=42-4y. Divide by 6 on both sides to isolate x and get x=7-[tex]\frac{2}{3}[/tex]y. Now we know what x equals. Go to the second equation ad plug this into it. So instead of -3x+3y=-6, you'll have -3(7-[tex]\frac{2}{3}[/tex]y)+3y=-6. Use the distributive property to get -21+2y+3y=-6. Add 2y and 3y to get -21+5y=-6. Add 21 to both sides to isolate 5y and get 5y=15. Divide by 5 on both sides to isolate y and get y=3. Now that we know that y=3, we can plug this back into the equation that was bolded above so that we can find x, so we'll have x=7-[tex]\frac{2}{3}[/tex](3) since y=3, and we'll get x=7-[tex]\frac{6}{3}[/tex], or x=7-2, or x=5.

x=5

y=2

Answer: (5, 3)

Step-by-step explanation:

Solve by Addition/Elimination

6x + 4y = 42 −3x + 3y = −6

Multiply each equation by the value that makes the coefficients of x opposite.

      6x + 4y = 42

      (2) ⋅ (−3x + 3y) = (2) (−6)

Simplify (2) ⋅ (−3x + 3y).

      6x + 4y = 42

      −6x + 6y = (2) (−6)

Multiply 2 by −6. 6x + 4y = 42

      −6x + 6y = −12

Add the two equations together to e liminate x from the system.

      6x + 4y = 42

    ±6x + 6y = −12

             1 0y= 30

Divide each term in 10y = 30 by 10.

      10y  =     30

      10          10

Cancel the common factor of 10.

     y = 30/10

  Divide 30 by 10.

      y = 3

Substitute the value found for y into one of the original equations, then solve for x.

Substitute the value found for y into one of the original equations to solve for x. 6x + 4 (3) = 42

 Multiply 4 by 3.

      6x + 12 = 42

Move all terms not containing x to the right side of the equation.

      6x = 30

Divide each term by 6 and simplify.

      x = 5

The solution to the independent system of equations can be represented as a point.

(5, 3)

The result can be shown in multiple forms.

Point Form:

(5, 3)

Equation Form:

x = 5, y = 3

Answer:22

Step-by-step explanation:

Answer: the square root of 30 is simplified to 5...

Hope this helps! :D

Step-by-step explanation:

Answer:

Square root of 30 simplified is 5

Step-by-step explanation:

Hope this helps! c:

Answer:

Maggie

Step-by-step explanation:

Answer:

17 feet

Step-by-step explanation:

A right angle has 3 sides: the adjacent, the opposite and the hypotenuse.

The hypotenuse is the largest side of the right angle

The shorter sides are 15 feet and 8 feet which should represent opposite and adjacent sides respectively

Opposite = 15 feet

Adjacent = 8 feet

Hypotenuse = x feet

Using Pythagoras theorem to solve

Hypotenuse ² = opposite ² + adjacent ²

x² = 15² + 8²

x² = 225 + 64

x² = 289

Find the square root of both sides

√x² = √289

x = 17 feet

The 3rd side is 17 feet

Answer:

-2<x≤5

Step-by-step :

-1<x+1≤6 So fisrt what every we do to one side we must do to the other. In this case it's a bit different since we are dealing with inequalities.

-1<x+1≤6 I would start off by isolating x in the middle.

-1<x+1≤6 I subtracted 1 from all three sides.

-1     -1   -1

Now your equation should look like this:

-2<x≤5  Now there is really nothing much we can do here since we were just trying to get x by its self.

Answer : -2<x≤5

Answer:

7

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

x - y

x = 5

y = -2

Step 2: Evaluate

Answer:

64

Step-by-step explanation:

2 to the sixth power would be 2 multiplied by itself 6 times

Answer:true

Step-by-step explanation:

Answer:

225° = 5π/4 radians.

Step-by-step explanation:

hope this helps :D

The radian measure of an angle of 225 degrees is 1.25π radian or 3.925 radians.

Given,

225 degrees.

We need to find the radian measure of 225 degrees.

We have,

π radian = 180 degree

So,

2π = 360 degrees.

This is the formula for the radian of an angle.

Find the radian measure for 225 degrees.

We have,

π radian = 180 degrees

Multiply 225/180 on both sides by 180.

225/180 x π radian = 225/180 x 180 degrees

1.25 π radian = 225 degrees

or

We can take π = 22/7 = 3.14

225/180 x 3.14 radian = 225 degrees.

3.925 radian = 225 degrees

Thus the radian measure of an angle of 225 degrees is 1.25π radian or 3.925 radians.

Learn more about the measure of an angle from a radian here:

https://brainly.com/question/8916147

#SPJ2

Answer:

Therefore, we conclude that the equation x-2y=4 represents the equation of the line 'n' if lines m and n are parallel to each other.

Step-by-step explanation:

We know that the slope-intercept of line equation is  

[tex]y=mx+b[/tex]

Where m is the slope and b is the y-intercept

Given the equation of the line m

y = 1/2x - 4

comparing with the slope-intercept form of the line equation

y  = mx + b

Therefore,

The slope of line 'm' will be = 1/2

We know that parallel lines have the 'same slopes, thus the slope of the line 'n' must be also the same i.e. 1/2

Checking the equation of the line 'n'

[tex]x-2y=4[/tex]

solving for y to writing the equation in the slope-intercept form and determining the slope

[tex]x-2y=4[/tex]

Add -x to both sides.

[tex]x - 2y + (-x) = 4+(-x)[/tex]

[tex]-2y = 4 - x[/tex]

Divide both sides by -2

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

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

comparing ith the slope-intercept form of the line equation

Thus, the slope of the line 'n' will be: 1/2

Therefore, we conclude that the equation x-2y=4 represents the equation of the line 'n' if lines m and n are parallel to each other.

Answer:

so 1st, subtract 33 and 117 from 180

180-117-33= 30

then you subtract 30 from 180

180-30= 150

and your measurement of angle ACD is 150

Answer:

Let first number be x , so other numbers will be x+2,x+4 and x+6. Now sum of all these number is 4x+12=80 or x=(80–12)/4=68/4=17 . So numbers are 17,19,21 and 23.

Answer:

90% of people marry there 7th grade love. since u have read this, u will be told good news tonight. if u don't pass this on nine comments your worst week starts now this isn't fake. apparently if u copy and paste this on ten comments in the next ten minutes you will have the best day of your life tomorrow. you will either get kissed or asked out in the next 53 minutes someone will say i love you

Step-by-step explanation:

Answer:

The answer is -0.5

Step-by-step explanation:

Divide both side by the numeric factor on the left side then solve