Which of the following expressions are equivalent to (9 7/8 + 2 4/5) - 1/2

Answer:

1-  S < L

2-  Spending is less than the limit.

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

Step-by-step explanation:

Answer:

Step-by-step explanation:

The answer is 16

Answer:

8/27  is the solution and the alternative form is 0.296 or 2/3 to the power of 3

Answer:

Step-by-step explanation:

[tex]-15=(3x-10)-5x\\\\-15=3x-10-5x\qquad\text{combine like terms}\\\\-15=(3x-5x)-10\\\\-15=-2x-10\qquad\text{add 10 to both sides}\\\\-15+10=-2x-10+10\\\\-5=-2x\qquad\text{divide both sides by (-2)}\\\\\dfrac{-5}{-5}=\dfrac{-2x}{-2}\\\\2.5=x\to x=2.5[/tex]

Answer:

exact form x=5/2 decimal form2.5 mixed number form 2 1/2

Step-by-step explanation:

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

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:

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! :)

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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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:

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:

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:

400

Step-by-step explanation:

0.30 * x = 240

x = 240/0.30 = 800

0.50 * 800 = 400

Answer:

The value of 50 % of number is 400  .

Step-by-step explanation:

Given as :

Let The number be x

According to statement

30 percent of a number is 240

I.e 30 % of x = 240

Or, [tex]\frac{30}{100}[/tex] × x = 240

Or, 0.3 × x = 240

So.  x = [tex]\frac{240}{0.3}[/tex]

∴     x = 800

SO, The number is 800 .

Now again 50 percent of that number = y

I.e y = 50 % of x

or, y =  50 % of 800

Or, y =  [tex]\frac{50}{100}[/tex] × 800

Or, y = 0.5 × 800

∴    y = 400

Hence The value of 50 % of number is 400  . Answer

Answer:

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

Step-by-step explanation:

60/12 = 12n/12

5 = n

Answer:

343

Step-by-step explanation:

-(-7^3)=-(-7*-7*-7)=-(-343)=343

Answer:

Step-by-step explanation:

-(-7 to the power 3)

=-(-7×-7×-7)= -(-343)

=343

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

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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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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Final answer:

The probability of rolling an even number on a 9-sided die is 4/9.

Explanation:

To find the probability of rolling an even number on a 9-sided die, we need to determine the number of favorable outcomes (even numbers) and divide it by the total number of possible outcomes.

In this case, there are 4 even numbers on the die: 2, 4, 6, and 8. The total number of possible outcomes is 9 (since there are 9 sides on the die).

Therefore, the probability of rolling an even number is 4/9.

Answer:

23,490

Step-by-step explanation:

10% = 0.1

234900 x 0.1 = 23490

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 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:

This over here

Step-by-step explanation:

This over that

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:

-(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:

parallel lines

Answer:

lines

Step-by-step explanation:

The coordinates of the image after dilation are

A (-12 , -12) , B (6 , -3) , C (3 , 3) ⇒ answer B

Step-by-step explanation:

A dilation is a transformation that produces an image that is the

same shape as the original, but in a different size

When you dilate a figure, with

Then the coordinates of each point of the figure is multiplied by k

to find the image of the figure after dilation

∵ ABC has coordinates of A (-8 , -8), B (4 , -2), and C (2 , 2)

∵ ABC is dilated by scale factor 1.5

∵ The center of dilation is the origin

- Multiply the coordinates of points A, B, and C by 1.5

∴ The image of point A = (-8 × 1.5 , -8 × 1.5) = (-12 , -12)

∴ The image of point B = (4 × 1.5 , -2 × 1.5) = (-6 , -3)

∴ The image of point C = (2 × 1.5 , 2 × 1.5) = (3 , 3)

The coordinates of the image after dilation are

A (-12 , -12) , B (6 , -3) , C (3 , 3)

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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.

Answer:

Step-by-step explanation:

2 • (xy - 4cs)

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.

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.