2. Write an inequality statement whose solution is an empty set.
3. Write an inequality statement whose solution is some but not all real numbers. Graph the solution on a number line.
4. Write an inequality statement whose solution is all real numbers. Graph the solution on a number line.
5. Write an inequality statement whose solution is exactly one number. Graph the solution on a number line.

To find the slope of the tarp, we can use the concept of rise over run, which is the ratio of the vertical change (the rise) to the horizontal change (the run). In this case, the rise is the distance from the corner of the tarp to the top of the pole, and the run is the distance from the corner of the tarp to the bottom of the pole.

We can use the Pythagorean theorem to find the length of the hypotenuse of the right-angled triangle formed by the corner of the tarp, the bottom of the pole and the top of the pole.

The length of the hypotenuse is the distance from the corner of the tarp to the top of the pole and the length of the adjacent side is the distance from the corner of the tarp to the bottom of the pole.

We know that:

adjacent side = 10 ft

Hypotenuse = h

Applying the Pythagorean theorem:

h^2 = 10^2 + 6^2

h = √(10^2 + 6^2)

h = √(100 + 36) = √136 = 11.66 ft

Now we can calculate the slope:

slope = rise/run = (h-10) / 6

slope = (11.66-10) / 6 = 1.66/6 = 0.277

So the slope of the tarp from the corner to the top of the pole is 0.277 or approximately 0.28.

The another equivalent expression of total liquid is (x+2)/4.

Expressions that perform similarly but differ in appearance are said to be equivalent expressions. When the same value for the variable is entered, two algebraic expressions that are equivalent will have the same result.

x quarts liquid in the container 3/4 part of liquid is removed

Then remaining liquid in container = X - [tex]\frac{3}{4}X[/tex]

Then remaining liquid in container = x/4quarts

Another 1/2 quart is poured into container

Then total liquid = [tex]X-\frac{3}{4}X+\frac{1}{2}[/tex] quarts

total liquid = [tex]\frac{X+2}{4}[/tex] quarts

So, then the another equivalent expression of total liquid is (x+2)/4.

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Answer:

42

Step-by-step explanation:

(2x + 3) = 7

7x7=49

note:the other 7 is from the exponent 2

49-7=42

The rectangular solid with the maximum volume would be a cube.

The surface area of a cube = 6A,

where A = the area of any one side

hence, the area of one side = 150/6 = 25 sq in.

The length of one face,

L = 25^0.5 = 5 in.

The volume, V of a cube = L^3.

Surface area

Surface area is the amount of space covering the outside of a three-dimensional shape.

volume

Volume is a three-dimensional quantity that is used to measure the capacity of a solid shape. It means the amount of three-dimensional space a closed figure can occupy is measured by its volume.

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Answer:

y=1/2x+2

Step-by-step explanation:

given the 2 equations, you know the following:

when x=2, you get a value of 3, let's call it Y

same with the next equation: when x=6, Y = 5

so the slope will be the diff b/w ys and then divided by diff of x's

so 5-3=2 is the diff of y

6-2=4 is the diff of x

divide 2/4 = 1/2 so the slope is 1/2

then you know the equation would be something like y=1/2 x but then you need to decide the intercept

1/2 of x when x=6 is 3, but Y =5

so you know the intercept is 2..

so the linear f(x) would be y=1/2x+2

done

It will cost $12.87 for driving 100 miles.

Based on the given problem, we have identified the given information as follows:

Then, we identify the unknown quantity which is the total cost of gasoline, and represent this as C. Now, this can be solved by using the formula

         [tex]C = \frac{distance traveled by car}{25.70 miles per gallon} * Cost of gasoline per gallon[/tex]

By substituting the given to the variable given in the formula above, we have,

            [tex]C = \frac{100}{25.70} * 3.309[/tex]

           C = $ 12.87

The obtained value of C is $12.87, therefore, we can conclude that it costs 12.87 dollars for driving 100 miles.

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In statistics, we use samples to make inferences about population

That is the great advantage of the whole role of distribution. Once you know a particular situation or experiment, that you can associate to one specific distribution and compute parameters, you can obtain from a relative smaller quantity of data and  with good approximation, inferences about the whole population.

Statistical inference is the method of using data analysis to infer characteristics of a probability distribution.

Inferential statistics is the branch of statistics that uses sample statistics to estimate a population parameter or test a hypothesis about such a parameter.

statistics

Statistics is the science concerned with developing and studying methods for collecting, analyzing, interpreting and presenting empirical data.

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The true solution to the equation [tex]\(x + 5 - \sqrt{x} = 3\)[/tex] is [tex]\(x = \frac{4}{9}\)[/tex], and there are no extraneous solutions.

To find the true solution(s) to the equation, we need to solve for x and check if the obtained solutions satisfy the original equation. The extraneous solution(s), if any, will be the solutions that do not satisfy the original equation.

To solve the equation, we can start by isolating one of the square root terms. Rearranging the equation, we have:

[tex]\sqrt{x + 5} = 3 + \sqrt{x}[/tex].

The equation can be evaluated as:

[tex]\sqrt{x + 5} - \sqrt{x} &= 3 \\(\sqrt{x + 5})^2 &= (3 + \sqrt{x})^2 \\x + 5 &= 9 + 6\sqrt{x} + x \\6\sqrt{x} &= -4 \\\sqrt{x} &= \frac{-2}{3} \\x &= \frac{4}{9}\end{align*}[/tex]

Therefore, the true solution to the equation [tex]\(x + 5 - \sqrt{x} = 3\)[/tex] is [tex]\(x = \frac{4}{9}\)[/tex], and there are no extraneous solutions.

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The complete question:

Solve the following equation and identify the true solution(s) as well as the extraneous solution(s):

[tex]\sqrt{x + 5} - \sqrt{x} = 3[/tex].

The expression that only uses multiplication and that is equivalent to x reduced by 1/8 of x is: x * (1 - 1/8).

An expression in mathematics is a combination of numbers, variables, and operations that represent a value or set of values.

The expression calculates the reduction of x by 1/8 of x by subtracting 1/8 of x from x, which is x * 1/8. By subtracting this from x, the expression calculates x reduced by 1/8 of x. The expression that only uses multiplication and that is equivalent to x reduced by 1/8 of x is:

x * (1 - 1/8).

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Answer:

Step-by-step explanation:

Yes, it is worth the extra drive to going the far store for buying the chicken. The difference between the both store worth is about $1.24.

We have to buy some chicken for dinner tonight. We found an ad showing that the store across town has it on sale for $3.09 a pound, which is cheaper than our usual neighborhood store, which sells it for $3.19 a pound.

$3.09 ×3 = $19.14 (far store)

$3.19 × 3 = $20.34 (near store)

For the neighbourhood store :

Distance = 2.3 mile

Multiply by 2 because we not only have to drive there, but also back home for the round trip: so, total distance = 2.3 miles × 2 = 4.6 miles

As car average is 19 miles per gallon

= 4.6 mile/ 19 miles per gallon

= 0.24 gallon < 13 gallons

Now, costs to travel to each store from the gas used. Cost of gas is $3.62/gallon,

total cost = 0.2421 gallons×$3.62 /gallons = $0.88

Similarly for far store : distance from home to store = 8.7 miles but take double of it we get, 8.7 miles × 2 = 17.4 miles

As car average is 19 miles per gallon

= 17.4 miles /19 miles per gallons

= 0.915 gallons < 13 gallons

The cost of gas for the respective trip = 0.915 gallons × $3.62 /gallons = $3.32

Now, let's add the gas and chicken costs together to get total worth

$19.14 + $3.32 = $22.46 to the far store

$20.34+ $0.88 = $21.22 to the near store

Hence, the worth in travelling far store is greater than neighbourhoid store.

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Complete question:

You need to buy some chicken for dinner tonight. You found an ad showing that the store across town has it on sale for $3.09 a pound, which is cheaper than your usual neighborhood store, which sells it for $3.19 a pound. Is it worth the extra drive? First, determine what information you need to answer this question, then click here to display that info (along with other info).

How much chicken will you be buying? 3 pounds

How far apart are the two stores? My neighborhood store is 2.3 miles away, and takes about 8 minutes. The store across town is 8.7 miles away, and takes about 25 minutes.

How kind of mileage does your car get? It averages about 19 miles per gallon in the city.

How many gallons does your car hold? About 13 gallons

How much is gas? About $3.62/gallon right now.

Yes, it is worth the extra drive to the far store to get the chicken. The value of the two stores varied by around $1.24.

To make chicken for dinner tonight, we must purchase some. We discovered an advertisement indicating that the supermarket across town is selling it for $3.09 per pound, which is less expensive than our typical neighborhood grocery, which charges $3.19 per pound.

Compare the prices of chicken: We would pay for the 3 pounds of chicken that we require.

$3.09 ×3 = $19.14 (far store)

$3.19 × 3 = $20.34 (near store)

Let's look at the expense of driving in our car:

For the local retailer: = 2.3 miles away

Because we need to travel both ways, we must double the distance by two, making the total distance 2.3 miles x 2 = 4.6 miles.

Since the average automobile gets 19 mpg

19 miles per gallon/4.6 miles = 13 gallons x 0.24 gallons

Now, add the cost of gas used to drive to each store. Gas costs $3.62 per gallon.

Total cost = 0.2421 gallons at a cost of $0.88 per gallon.

The same goes for a far store:

the distance from home to the store is 8.7 miles, but if we double that by two, we get 17.4 miles.

Since the average automobile gets 19 mpg = 17.4 miles per gallon /19 miles per mile

13 gallons equals 0.915 gallons.

The gas price for the relevant journey is 0.915 gallons times $3.62 a gallon, or $3.32.

To determine the overall cost,

let's now combine the costs of the chicken and petrol.

$22.46 to the far store from $19.14 plus $3.32

$20.34 plus $0.88 equals $21.22 for the nearby retailer.

Therefore, a far store is more valuable than a nearby store. The difference is $1.24

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Answer:

C

Step-by-step explanation:

Answer:110

Step-by-step explanation: Add 7 shingles every row you go up.

Row 1=75

2=82

3=89

4=96

5=103

6=110

Answer:

33

Step-by-step explanation:

it starts with 75 and decreases by 7 for each row. on the 6th row youll be at 33!

STARTS AT 75

row one: 68

row two: 61

row three:54

row four: 47

row five: 40

row six: 33

Answer:

10 times larger.

The 3 in 903.7 is in the ones place, and the 3 in 4.31 is in the tenths place, which is to the left of the decimal one time.

If you were to move the 3 in 4.31 to the right of the decimal like where the 3 is in 903.7, then you would be increasing the 3s value by 10.

Step-by-step explanation:

Hope it helps! =D

Blood types A and AB are receivers from someone with type A blood donors.

What is blood type?

There are four major blood groups determined by the presence or absence of two antigens, A and B, on the surface of red blood cells. In addition to the A and B antigens, there is a protein called the Rh factor, which can be either present (+) or absent (–), creating the 8 most common blood types (A+, A-,  B+, B-,  O+, O-,  AB+, AB-).

Someone with blood type A can donate blood to individuals with blood types A and AB.

This is because type A blood has the A antigen on the red blood cells and type AB has both A and B antigens.

While type A blood doesn't have the B antigen which is present in type B and AB blood, so it cannot be donated to those with type B or type B.

It's important to note that there are also positive and negative blood types, which are determined by the presence or absence of the Rh (Rhesus) antigen on the red blood cells.

So, someone with type A negative blood can only donate to individuals with type A negative or type AB negative blood.

Therefore, for A type blood donors can donate to A and AB blood type.

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For the quadratic equation -2x²+12x-13, the range is option D: All real numbers less than or equal to 5.

What is a quadratic function?

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.

The values for x and h(x) are given in the table.

Real numbers can be said to be all continuous values of quantity, which can be negative or positive values.

The range of h, h(x), in the table given are all real numbers.

The quadratic equation from the points in the table can be deduced as -2x²+12x-13.

The maximum of the graph is at (3,5).

For a parabola ax²+bx+c with Vertex (xv,yv) -

If a<0, then the range is f(x) ≤ yv.

If a>0, then the range is f(x) ≥ yv.

Since, a = -2, then f(x)≤ 5.

Therefore, the range values of h is f(x)≤ 5.

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Answer:

1. a > 6

2. a = 6

3. 0 < a < 6

4. a is divisible by 6

Answer:
1. a>6 the answer could be, 7, 8, 9, 10 and it keeps going on.
2. the answer is 6

3. a<6 the answer is anything below 6 so 5, 4, 3, 2, 1, and more.

4. anything that is a multiple of 6 is true. like 6, 12, 18, 24, 30, 36, and it keeps going.

By evaluating an exponential equation, we will see that the population after 189 hours will be 888 bacteria.

We know that initially we have a total of 100 bacteria, and it doubles in size every 60 hours, then the population can be modeled with the exponential equation.

p(x) = 100*(2)^x

Where x is groups of 60 hours, we can rewrite:

x = t/60h

Where t is the amount of hours, and rewrite the equation as:

p(t) = 100*(2)^(t/60h)

The population in 189 hours from now willbe:

p(189 h) = 100*(2)^(198 h/60h) = 887.7

The population is 888 (where we rounded the value)

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Classification of all the angles in four different ways along with name are:

1. ∠ABC, ∠CBA, ∠B, ∠1 and the name is right angle.

2. ∠DEF, ∠FED, ∠E, ∠2 and the name is obtuse angle.

3. ∠LMN, ∠NML, ∠M, ∠3 and the name is straight angle.

4. ∠XYZ, ∠ZYX, ∠Y, ∠4 and the name is acute angle.

5. ∠KLM, ∠MLK, ∠L, ∠5 and the name is acute angle.

6. ∠RST, ∠TSR, ∠S, ∠6 and the name is obtuse angle.

Figure is attached.

Classification of the all the angles in the attached figure in four different ways with their names are:

1. Different name of the angles : ∠ABC, ∠CBA, ∠B, ∠1 .

Measure of the angle is 90°, it is right angle.

2. Different name of the angles : ∠DEF, ∠FED, ∠E, ∠2

Measure of the angle is more than 90°, it is obtuse angle.

3. Different name of the angles : ∠LMN, ∠NML, ∠M, ∠3

Measure of the angle is 180°, it is straight angle.

4. Different name of the angles : ∠XYZ, ∠ZYX, ∠Y, ∠4

Measure of the angle is less than 90°, it is acute angle.

5. Different name of the angles : ∠KLM, ∠MLK, ∠L, ∠5

Measure of the angle is less than 90°, it is acute angle.

6. 2. Different name of the angles :  ∠RST, ∠TSR, ∠S, ∠6

Measure of the angle is more than 90°, it is obtuse angle.

Therefore, as per the classification of the given angles different ways to represent them are:

1. ∠ABC, ∠CBA, ∠B, ∠1 , right angle.

2. ∠DEF, ∠FED, ∠E, ∠2 , obtuse angle.

3. ∠LMN, ∠NML, ∠M, ∠3 , straight angle.

4. ∠XYZ, ∠ZYX, ∠Y, ∠4, acute angle.

5. ∠KLM, ∠MLK, ∠L, ∠5 , acute angle.

6. ∠RST, ∠TSR, ∠S, ∠6  ,obtuse angle.

The above question is incomplete , the complete question is :

Name each angle in four ways. Then classify the angle as acute, right, obtuse, or straight.

Attached figure.

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Answer: no, not a function

Step-by-step explanation: 0 is in the input twice, and if it were a function, it would only be there once. every input can only have one output

7. To show that VRHK is a square, one can observe that the opposite sides of the quadrilateral, VR and HK, are equal in length and the two adjacent sides, RH and VK, are also equal in length.

8. For VRHK to be a square, z must equal √2, so that VC = 6√2 and

VR = 12.

9. The length of RK is 12√2

10. The length of VK is 12√2

Solution:

8. We can solve this problem by using the Pythagorean Theorem. We know that the sides of a square are equal, so we can set up an equation using the theorem. VC = 6z, VR = 12, and we want the hypotenuse, VRHK, to be a square. VH² = VR² + RH² = 12√2.

VC = 6z = VH/2 = 12√2/2 = 6√2

6z = 6√2

z = √2

9. The length of RK' =  s√2 =12√2

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The room with the given dimensions has a volume of 316, 516, 800 cm^3.

The volume of a room is a measure of the amount of space inside it, and it is calculated by multiplying the length, width, and height of the room.

In this case, the room has dimensions of 9.15 meters by 9.4 meters by 3.68 meters.

To find the volume of the room in cm^3, we first need to convert the dimensions of the room from meters to centimeters.

1 meter is equal to 100 centimeters, so

9.15 meters is equivalent to 915 centimeters,

9.4 meters is equivalent to 940 centimeters,

and 3.68 meters is equivalent to 368 centimeters.

Once we have the dimensions in centimeters, we can calculate the volume by multiplying the length, width, and height:

915 cm x 940 cm x 368 cm = 316, 516, 800 cm^3.

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The value of x in the given equation will be 2/5

From the data,

We have to determine the value of x.

The given equation is: 18x-16=-12x-4

For determining the value of x, we will first shift the like terms on one side of the equation.

So, for solving the value of x we will shift the terms containing x and the constant on both sides of the equation.

So, shifting -12x from the right-hand side of the equation to the left-hand side of the equation,

We will get it as:

18x+12x = -4+16

30x=12

Now for solving the value of x we will shift x from the left side of the equation to the right side of the equation.

So, the value of x will be = 12/30 = 2/5

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The correct question may be:

What is the value of x

18x-16=-12x-4

Enter your answer in the box.

So, the height of the tower is approximately 363.6 feet.

You can use trigonometry to solve this problem.

If we call the height of the tower "h" and the distance between the man and the base of the tower "d", then the angle of elevation is defined as the angle between the line of sight from the observer to the top of the tower and the horizontal line.

We can use the tangent function to relate the angle of elevation to the height and distance.

tan(67) = h/d

We know that the distance between the man and the tower is 200 feet. We can use this information to find the height of the tower.

h = d * tan(67)

h = 200 * tan(67)

The height of the tower is approximately 363.6 feet.

Please note that due to the approximation of the trigonometric functions, the answer may not be exactly as calculated.

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The solution to the inequality is (b) x > -2

From the question, we have the following parameters that can be used in our computation:

4.5x + 6 > -3

Collect the like terms

So, we have the following representation

4.5x > - 3 - 6

Evaluate the like terms

This gives

4.5x > -9

Divide both sides by 4.5

x > -2

Hence, the solution is (b) x > -2

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The person who is correct is Matty: (12x 0.75) + (2x 1.2 =11.4  (second option)

The total pound of cheese is the total amount of of cheese used for cheeseburgers and the total amount of cheese wasted.

Total pounds of cheese = total pounds used for cheeseburgers + total cheese wasted

= (pounds of cheese needed for one cheeseburger x number of cheeseburger) + (number of waiters x pounds of cheese dropped)

= (12 x 3/4) + (1.2 x 2)

= 9 + 2.4

= 11.4 pounds

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Answer 0.000032 km

Step-by-step explanation: divide

1. In parallelogram ABCD, the sum of ∠a and ∠b is 180 degree. So the option d "a° + b° = 180°" is correct.

2. In rectangle FGHK, FC = CH = 8. 5 cm, then the area of rectangle FGHK is 120 square cm. So the option b is correct.

3. The length of GK is 17 cm because the length of all diagonal is same in rectangle. So the option d is correct.

4. In parallelogram EFGH, the sum of ∠e and ∠f is 180 degree. So the option d "a° + b° = 180°" is correct.

1. In parallelogram ABCD, ∠a and ∠b are adjacent to each other.

So, AB║DC.

Then we get ∠a and ∠b as subsequent interior angles, both of which need to be added.

So the sum of ∠a and ∠b is 180 degree.

a° + b° = 180°

2. In rectangle FGHK, FC = CH = 8. 5 cm.

From the diagram, FG = 8 cm

FH = FC + CH

FH = 8.5 + 8.5

FH = 17 cm

Using Pythagorean Theorem to find the value of GH.

FH^2 = FG^2 + GH^2

(17)^2 = (8)^2 + GH^2

289 = 64 + GH^2

Subtract 64 on both side, we get

GH^2 = 225

Taking square root on both side, we get

GH = 15 cm

The area of rectangle = FG × GH

The area of rectangle = 8 × 15

The area of rectangle = 120 square cm

3.  In rectangle FGHK, FC = CH = 8. 5 cm.

So FH = FC + CH

FH = 8.5 + 8.5

FH = 17 cm

As, a rectangle is split into two congruent right triangles by a diagonal. The length of the rectangle's diagonals are all the same.

So GK = FH = 17 cm

4. In parallelogram EFGH, ∠e and ∠f are adjacent to each other.

So, EF║HG.

Then we get ∠e and ∠f as subsequent interior angles, both of which need to be added.

So the sum of ∠e and ∠f is 180 degree.

e° + f° = 180°

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The m∠EXD and m∠AXE are the supplementary angles.

The two angles will be linear pairs if the sum is 180° therefore, linear pair of 62° is 118°. The value of x in the figure is 113°

An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.

The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.

01)

Two angles will be linear pairs if their sum is 180°.

If the first angle is 62° then the second will be 180° - 62° = 118°

Hence "The two angles will be linear pairs if the sum is 180° therefore, linear pair of 62° is 118°".

02)

The angle x is in the same line with supplementary angle 67° so

x = 180 - 67 = 113°.

Hence "The value of x in the figure is 113°".

03)

In the figure, AXD is a straight line, therefore,

m∠EXD +  m∠AXE  = 180°

Since the sum of two angles is 180° then they are called supplementary angles.

Hence "The m∠EXD and m∠AXE are the supplementary angles".

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