Latoya, Henry, and Manuel served a total of 112 orders Monday at the school cafeteria. Latoya served 7 more orders than Henry. Manuel served 3 times as many orders as Henry. How many orders did they each serve?

Answer:

Step-by-step explanation:

So basically what you want to do is start with the distributive property.

-0.5(x+0.3) = 1.6x+0.9(x+4.8) would then equal -0.5x-0.15 = 1.6x+0.9x+4.32.

Then, add the matching terms on the right side (the x values) 1.6x+0.9x =2.5x

Your equation should the look like -0.5x-0.15 = 2.5x+4.32.

Next, add -0.5x to 2.5x giving you 3x

The equation will look like -0.15 = 3x+4.32

After that subtract 4.32 from -0.15 leaving you with -4.47=3x

Divide 3x from both sides

Your answer should be x= -1.49.

I hope this was helpful and not super confusing! Also if anything is incorrect let me know! :)

It will take the snail 9.6 minutes to travel 24cm.

Step-by-step explanation:

Distance covered in 4 minutes = 10 cm

Ratio of distance to time = 10:4

New distance = 24cm

Let,

x be the time period

Ratio of new distance to time = 24:x

Using proportions;

Ratio of distance to time :: Ratio of new distance to time

[tex]10:4::24:x[/tex]

Product of mean = Product of extreme

[tex]24*4=10*x\\96=10x\\10x=96[/tex]

Dividing both sides by 10

[tex]\frac{10x}{10}=\frac{96}{10}\\x=9.6\ minutes[/tex]

It will take the snail 9.6 minutes to travel 24cm.

Keywords: ratio, proportion

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Answer:

parallel lines

Answer:

lines

Step-by-step explanation:

You compare fractions by seeing the denominator is the same and then you add them or multiply them or diving them and that is how you compare fractions.

Answer:

2 days & 3 hours

Step-by-step explanation:

Answer: 6hrs

Step-by-step explanation:

Answer:

that is too....much? it's n = 5

Step-by-step explanation:

60/12 = 12n/12

5 = n

Answer:

Option B.) 45 units

Step-by-step explanation:

see the attached figure with letter to better understand the problem

step 1

Determine the coordinates of the corners of the rectangle

Let

A(4,5),B(1,8),C(14,21) and D(17,18)

step 2

we know that

The formula to calculate the perimeter of rectangle is equal to

[tex]P=2(AB+BC)[/tex]

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

Find the length side AB

[tex]A(4,5),B(1,8)[/tex]

substitute in the formula

[tex]d=\sqrt{(8-5)^{2}+(1-4)^{2}}[/tex]

[tex]d=\sqrt{(3)^{2}+(-3)^{2}}[/tex]

[tex]d_A_B=\sqrt{18}\ units[/tex]

Find the length side BC

[tex]B(1,8),C(14,21)[/tex]

substitute in the formula

[tex]d=\sqrt{(21-8)^{2}+(14-1)^{2}}[/tex]

[tex]d=\sqrt{(13)^{2}+(13)^{2}}[/tex]

[tex]d_B_C=\sqrt{338}\ units[/tex]

Find the perimeter

[tex]P=2(AB+BC)[/tex]

substitute the values

[tex]P=2(\sqrt{18}+\sqrt{338})[/tex]

[tex]P=45\ units[/tex]

Answer:

B) 45 units

Step-by-step explanation:

D = dx2 + dy2

W = (1-4)2 + (8-5)2

W = (-3)2 + (3)2 = 4.24264

L = (1-14)2 + (8-21)2

L = (-13)2 + (-13)2 = 18.38478

A = 2L+2W = 2(18.38478)+2(4.24264)= 45.3 units

Answer:

The three 2-gallon cans of paint  is enough  to complete the job.

Step-by-step explanation:

Given:

It takes 2 1/8 gallons of paint to coat each door and 1 3/5 to coat all of shutters. He had three 2-gallon cans of paint.

Now, to find that is he have enough paint to complete the job.

Total gallons of paint he buys = 3 × 2 = 6 gallons.

Then, let the quantity used change to improper fraction from mixed:

[tex]2\frac{1}{8} =\frac{17}{8}[/tex] and [tex]1\frac{3}{5}=\frac{8}{5}[/tex].

Now, we add the quantity of paints used to paint doors and shutters:

[tex]\frac{17}{8}+\frac{8}{5}[/tex]

[tex]=\frac{85+64}{40}[/tex]

[tex]=\frac{149}{40}[/tex]

Now, subtracting quantity used from the total quantity:

[tex]6-\frac{149}{40}[/tex]

[tex]=\frac{240-149}{40}[/tex]

[tex]=\frac{91}{40}[/tex]

[tex]=2\frac{11}{40}[/tex]

So, after painting the two doors and several shutters from 3 cans of 2-gallon paint still 2 11/40 quantity of paint is remaining.

Therefore, the three 2-gallon cans of paint is enough to complete the job.

Answer:

-(7/8) is equivalent to -7/8

B) -7/8 is correct option

-7/8 is equivalent to -(7/8).

The multiplication or division of two negative number or sign will always give a positive numbeer or sign.

By cheking all options

1. -(7/-8)=7/8     as multiplication or division of two negative number or sign will always give a positive numbeer or sign.

2. -7/8=-(7/8)

3. -(-7/8)=7/8     as multiplication of two negative sign will always give a positive sign.

4. -7/-8=7/8       as division of two negative sign will always give a positive sign.

Therefore from above it is clear that -7/8 is equivalent to -(7/8).

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Answer:

Step-by-step explanation:

The formula of a surface area of a sphere:

[tex]SA=4\pi R^2[/tex]

R - radius

We have R = 30m.

Substitute:

[tex]SA=4\pi(30^2)=4\pi(900)=3600\pi\ m^2[/tex]

Answer:

This over here

Step-by-step explanation:

This over that

Answer:

The graph that passes through (-3,-3), (-3,0) and (-3,3) does not represents linear function

Step-by-step explanation:

Mariko says that the graph that passes through (-3,-3), (-3,0) and (-3,3)

Now, the line joining (-3,-3) and (-3,0) has slope = [tex]\frac{-3 - 0}{- 3 -(- 3)} =[/tex] = ∞

Again, the line joining (-3, 0) and (-3,3) has slope = [tex]\frac{0 - 3}{- 3 -(- 3)} =[/tex] = ∞

Therefore, both the lines are parallel to y-axis and has a common point (-3,0). {Since, tan Ф = ∞, ⇒ Ф = 90°}

So, the graph that passes through (-3,-3), (-3,0) and (-3,3) does not represents linear function as the graph represents a vertical line parallel to y-axis. (Answer)

Answer:

{0 ≤ h ≤ 25}

Step-by-step explanation:

The domain of a function is the set of all values for independent variable for which the function must be defined.

Given: The amount earned by Hailey for one hour work =$9.50

She determines that her salary is modeled by the function .

Here h is the independent variable such that 's' is dependent on 'h'.

Since she never works more than 25 hours in a week.

Therefore, the maximum hours she will work = 25

Hence, the domain of this function in this situation is {0 ≤ h ≤ 25}, where h is number of hours she works.

Answer:

{0 ≤ h ≤ 25}

Step-by-step explanation:

The domain of a function is the set of all values for independent variable for which the function must be defined.

Given: The amount earned by Hailey for one hour work =$9.50

She determines that her salary is modeled by the function .

Here h is the independent variable such that 's' is dependent on 'h'.

Since she never works more than 25 hours in a week.

Therefore, the maximum hours she will work = 25

Hence, the domain of this function in this situation is {0 ≤ h ≤ 25}, where h is number of hours she works.

Answer:

m = [tex]\frac{-2}{5}[/tex]

Step-by-step explanation:

2m + 1 = -3m - 1 (Given)

2m + 1 + 1 = -3m - 1 + 1 (Addition Property of Equality)

2m + 2 = -3m (Simplify)

2m - 2m + 2 = -3m - 2m (Subtraction Property of Equality)

2 = -5m (Simplify)

[tex]\frac{2}{-5} = \frac{-5m}{-5}[/tex] (Division Property of Equality)

[tex]\frac{-2}{5}[/tex] = m (Simplify)

m = [tex]\frac{-2}{5}[/tex] (Symmetric Property of Equality)

The answer is:

Work/explanation:

Combine like terms on each side:

[tex]\sf{2m+1=-3m-1}[/tex]

Make sure all terms that contain m are on the left side and all constant terms are on the right. Don't forget to use the opposite sign when moving terms from one side to the other one.

[tex]\sf{2m+3m=-1-1}[/tex]

[tex]\sf{5m=-2}[/tex]

Divide each side by 5

[tex]\sf{m=-\dfrac{2}{5}}[/tex]

Answer:

8 17/20

Step-by-step explanation:

177/20=8 17/20

Because 8*20=160 and 177-160=17.

Final answer:

To convert 177 divided by 20 into a mixed number, divide 177 by 20. The quotient is the whole number part and the remainder is the fractional part.

Explanation:

To convert 177 divided by 20 into a mixed number, we need to find the quotient and the remainder. The quotient represents the whole number part of the mixed number, while the remainder represents the fractional part.

When we divide 177 by 20, we get a quotient of 8 and a remainder of 17. Therefore, the mixed number representation of 177 divided by 20 is 8 and 17/20.

So, 177 divided by 20 is equal to 8 and 17/20.

Final answer:

The area of the rectangle is 12.8 square inches.

Explanation:

The area of a rectangle can be found by multiplying its length by its width. In this case, the length of the rectangle is 1.6 inches and the width is 8 inches. So, the formula for the area is:

Area = length x width

Substituting the given values, we get:

Area = 1.6 inches x 8 inches = 12.8 square inches

The equation of the line that has a slope of 1/3 and passes through the point (-2, 1) is y = 1/3x + 5/3.

The subject of this question is the representation of a line in the form of an equation, specifically a line that has a slope of 1/3 and passes through a given point, (-2, 1). We can use the point-slope form of a line equation, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.

Substituting the given values, we have y - 1 = 1/3(x - (-2)). Or simplified to y - 1 = 1/3(x + 2). From here, we can rearrange this into slope-intercept form (y = mx + b) by distributing the 1/3 to x and 2, thus giving us y = 1/3x + 2/3 + 1. Finally, simplifying the equation gives y = 1/3x + 5/3, which is the equation of the line that has a slope of 1/3 and passes through the point (-2, 1).

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The factors are: x-5 and x+3

Step-by-step explanation:

Given

[tex]x^2-2x-15 = 0[/tex]

Simplifying

[tex]x^2-5x+3x-15 = 0\\x(x-5) + 3(x-5) = 0\\(x+3)(x-5) = 0[/tex]

Let us define the zero product property first

The zero product property states that

if ab=0 then either a=0 or b=0

So,

[tex]x+3 = 0\\x+3-3 = 0-3\\x = -3\\AND\\x-5 = 0\\x-5+5 = 0+5\\x = 5[/tex]

Hence,

the factors are: x-5 and x+3

Keywords: Factorization, Zero product property

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Answer:

10(n-4)

Step-by-step explanation:

10n-40=10(n-4)

If this is what you were asked to find, then that's the answer. Because 10n-40 is just an expression, it's not something you can solve for it, since it's not an equation. So I simplified this expression for you by factoring.

Answer:

A. Left by 4 units

Step-by-step explanation:

ƒ(x) = x²

It has a vertex at (0, 0), and the y-axis is the axis of symmetry

g(x) = x² + 8x + 16 = (x + 4)²

You have added 4 to the value of x, so you have shifted the graph four units to the left.

Thus, to make the graphs of ƒ(x) and g(x) coincide, you should shift ƒ(x) left by 4 units.

The diagram below shows ƒ(x) in red and g(x) in green.

Answer:

Option A) 4, 2

Step-by-step explanation:

We are given that quadrilateral ABCD is a  parallelogram with sides:

[tex]AB = 3 + x\\DC = 4x\\AD = y + 1\\BC = 2y[/tex]

Since the opposite sides of a parallelogram are equal, we can write:

[tex]AB = DC\\AD=BC[/tex]

Equating the sides we get,

[tex]\Rightarrow 3+x = 4x\\4x-x = 3\\3x = 3\\x = 1\\\Rightarrow y + 1 = 2y\\y = 1[/tex]

Putting the values of x and y, we get:

[tex]AB = 3 + x =4\\DC = 4x =4\\AD = y + 1=2\\BC = 2y=2[/tex]

Thus, the lengths of the opposite side pairs is 4,2.

Is that it on the description? No question of nothing?

Answer:

n=-19

Step-by-step explanation:

-37+n+37=-56+37

n=-19

Answer:

-37+n=-56

n= -56-(-37)

n= -19

Answer: It should be 3,500

Step-by-step explanation: If the number behind it is 5 or greater, then you round up, meaning the 3 would change to 4, but since it is lower than 2, it would stay the same (5) for it is closer to 3,500.

Answer:

The area of the square lawn is [tex]784\ m^2[/tex]

Step-by-step explanation:

Part 7)

Let

x ----> the length side of the square lawn in meters

we know that

The area of the path is equal to

[tex]A=(x+2+2)^2-x^2[/tex]

[tex]A=(x+4)^2-x^2[/tex] ----> equation A

[tex]A=240\ m^2[/tex] ----> equation B

so

[tex]240=(x+4)^2-x^2[/tex]

Solve for x

[tex]240=(x^2+8x+16)-x^2[/tex]

[tex]240=8x+16[/tex]

[tex]8x=240-16[/tex]

[tex]8x=224[/tex]

[tex]x=28\ m[/tex]

The area of the square lawn is

[tex]A=x^2[/tex]

substitute the value of x

[tex]A=28^2=784\ m^2[/tex]

Answer:

1-  S < L

2-  Spending is less than the limit.

3- 30-3x [tex]\geq[/tex] 14

Step-by-step explanation:

Answer:

39.5

Step-by-step explanation:

We put the numbers in order least to greatest and pick the middle one because that number is the median:

36, 38, 39, 39, 40, 47, 48, 51

Since 39 and 40 are tied for the median we go in between those two numbers, 39.5.  The answer is 39.5.

Answer:

C. 45%

Step-by-step explanation:

Initial credit in his account = $750.00

Credit in his account after some purchases = $412.50

⇒Decrease in credit = $750.00 - $412.50

⇒Decrease in credit = $337.5

percentage decrease of amount of available credit = [tex]\frac{decrease\ in\ credit}{initial\ credit}[/tex]×100

                                    = [tex]\frac{337.50}{750.00}[/tex]×100

                                    = [tex]\frac{9}{20}[/tex]×100

                                    = 9×5

                                    = 45%

∴Percentage decrease of the amount of available credit in Dylan's account is 45%

Answer:

Step-by-step explanation:

answer is W = 7 and A = 43.

The rate of the plane in still air is 43 miles per hour and the rate of the wind is 7 miles per hour.

Given that, Togo flew his ultralight plane to a landing field 30 miles away.

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

Let x represent the rate of the plane in still air.

Let y represent the rate of wind.

We know that, Distance = Speed × Time

Speed of flight with wind is x+y miles per hour

Speed of flight against wind is x-y miles per hour

With the wind, the flight took 3/5 hours.

Now, 30=3/5 (x+y)

50=x+y --------(I)

Returning against the wind, the flight took 5/6 hours.

30=5/6 (x-y)

36=x-y --------(II)

Add equation (I) and (II), we get

x+y+x-y=50+36

⇒ 2x=86

⇒ x=43 miles per hour

Substitute x=43 in equation (I), we get

43+y=50

⇒ y=7 miles per hour

Therefore, the rate of the plane in still air is 43 miles per hour and the rate of the wind is 7 miles per hour.

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Answer:

c

Step-by-step explanation:

It is measured in the same unit as the original unit, so x will be 1.42x

Add the service charge as it is a constant addition, and we end up with:

y = 1.42x + 13.20

the correct equation representing the monthly water bill is:

[tex]\[ y = 1.42x + 13.20 \][/tex]

The correct option is (c).

Sure, let's break down the calculation step-by-step.

1. Monthly service charge: The monthly service charge is a fixed amount, which is $13.20.

2. Usage charge: The usage charge is $1.42 for every 100 cubic feet of water used. Since x represents the amount of water used in hundreds of cubic feet, the usage charge can be calculated as \(1.42x\).

3. Total monthly cost: To determine the total monthly cost \(y\), we add the monthly service charge to the usage charge. Therefore, the equation representing the total monthly bill is:

[tex]\[ y = \text{Monthly service charge} + \text{Usage charge} \][/tex]

[tex]\[ y = 13.20 + 1.42x \][/tex]

So, the correct equation representing the monthly water bill is:

[tex]\[ y = 1.42x + 13.20 \][/tex]

Therefore, the correct answer is option C.