6th Grade Math Inequalitys

Answer:

Look at the attached image below

Step-by-step explanation:

[tex]\tt 3x-8\ge \:7[/tex]

Add 8 to both sides:-

[tex]\tt 3x\ge 7+8[/tex]

Add 7 and 8 to get 15:-

[tex]\tt 3x\ge 15[/tex]

Divide both sides by 3:-

[tex]\tt \cfrac{3x}{3}\ge \cfrac{15}{3}[/tex]

[tex]\tt x\ge \:5[/tex]

Converting the percentage to degree in the pie chart, angle PQ and UPT are 162° and 25.2° respectively

This is a statistical tool used to represent data in a chart. It is often represented using angles or percentage.

To find the value of the respectively angles, we have to convert the values from percentage to degree.

The formula to do this is given as

Percentage = angle * (100 / 360)

A)

Angle PQ = ?

Substituting the values;

45 = angle * (100 / 360)

45 = angle * (5/18)

angle = 45 / (5/18)

angle = 162°

B) Angle UPT = ?

7 = angle * (5/18)

angle = 7 / (5/18)

angle = 25.2

The angle PQ is 162 degrees, the angle UPT is 25.2 degrees

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Answer:

Step-by-step explanation:

If x² /y³ = 1 and x^4/2y³ = -1,  the value of the sum of x and y would be y^(3/2).

The fundamental procedures for altering and combining mathematical objects, such as integers and functions, are known as operations in mathematics. These operations, which are used to carry out mathematical computations on numbers, generally include sum, subtraction, multiplication, and division. Operations may also be applied to other types of mathematical objects, like as vectors, matrices, and sets, to execute more sophisticated operations such as vector addition, matrix multiplication, and set intersection. The outcome of an operation is referred to as an operand, and the procedures for combining operands are referred to as the operation's laws. A basic idea in mathematics, operations are applied in many different areas of science and math.

How to solve?

If x² /y³ = 1, then x² = y³

If x^4/2y³ = -1, then x^4 = -2y³

The sum of x and y is x + y = (x²)^1/2 + (y³)^1/3 = y^(3/2) + y

x + y = (x^4)^1/4 + (y³)^1/3 = (-2y³)^1/4 + y^(3/2) = -y + y^(3/2)

x + y = 0 + y^(3/2) = y^(3/2)

The sum of x and y is y^(3/2)

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The inequality which represents the situation is 22x + 42y < 400.

A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.

In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.

As per the given,

Cost of medium photos = 22x

Cost of large photo = 42y

Total cost < 400

22x + 42y < 400

Hence "The scenario is represented by the inequality 22x + 42y < 400.".

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Answer: -5-2x

Step-by-step explanation:

Answer: To find the missing angle, subtract the given angle from 180°.

Step-by-step explanation:

Answer:

-10

Step-by-step explanation:

When a problem asks you to find f("a number"), it's just telling you to replace x with "a number." So, substitute x with 72 to get the equation [tex]f(72)=-12+\frac{72}{36}[/tex]. The fraction simplifies to 2, and -12 plus 2 is just -10.

Answer: C= 40.25 - 0.05x

Step-by-step explanation:

C is the credit left

We know that the original is 40.25, so we put it as the beginning number.

Each minute costs $0.05x

where x is each minute

, so the equation is C= 40.25 - 0.05x

Answer:

x(x + 3)

Step-by-step explanation:

x² + 3x ← factor out x from each term

= x(x + 3)

if f(x)= 2x+7

f(x)= two points

-10 and +5

the solution is : A,,,,f(-10)=2(-10)+7

= -20+7

= -13

and

B,,,,, f(5)= 2(5)+7

= 10+7

= 17

Answer:

20w

Step-by-step explanation:

If you have 20 bottles, and each contains w ounces, we can use the following example to solve.

If there were 4oz per bottle,

20 * 4 = 80

80oz

We have w oz per bottle,

20 * w = ?

20w

The solution is Option C.

4cm , 6cm , 10 cm does not form a right angle triangle

What is a Triangle?

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Given data ,

Let the triangle be ABC which is a right angle triangle

Now , the sides of the triangle is given as

a)

6cm , 8cm , 10cm

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

So , substituting the values in the equation , we get

hypotenuse² = base² + height²

10² = 8² + 6²

100 = 64 + 36

100 = 100

Therefore , it is a right angle triangle

b)

12 cm , 35 cm , 37 cm

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

So , substituting the values in the equation , we get

hypotenuse² = base² + height²

37² = 35² + 12²

1369 = 1225 + 144

1369 = 1369

Therefore , it is a right angle triangle

c)

4 cm , 6 cm , 10 cm

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

So , substituting the values in the equation , we get

hypotenuse² = base² + height²

10² = 6² + 4²

100 = 36 + 16

100 ≠ 52

Therefore , it is not a right angle triangle

d)

10 cm , 24 cm , 26 cm

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

So , substituting the values in the equation , we get

hypotenuse² = base² + height²

26² = 24² + 10²

676 = 576 + 100

676 = 676

Therefore , it is a right angle triangle

Hence , the triangle with sides 4cm , 6cm , 10 cm does not form a right angle triangle

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The points on the line 2x - 6y = 12 is

x                y

0               -2

6                0

9                -1

12               2

What is equation of line in slope intercept form?

The most general form of equation of line in slope intercept form is given by y = mx + c

Where m is the slope of the line and c is the y intercept of the line.

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If  [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m =  [tex]tan \theta[/tex]

The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.

The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.

a)The equation is 2x - 6y = 12

For x = 0,

[tex]2 \times 0- 6y = 12\\6y = -12\\y = -\frac{12}{6}\\y = -2[/tex]

For x = 6,

[tex]2 \times 6 - 6y = 12\\6y = 0\\y = 0[/tex]

For x = 9

[tex]2 \times 9 -6y = 12\\18 - 6y = 12\\6y = 12 - 18\\6y = -6\\y = -\frac{6}{6}\\y = -1[/tex]

For x = 12

[tex]2 \times 12 - 6y = 12\\-6y = 12 - 24\\-6y = -12\\y = \frac{12}{6}\\y = 2[/tex]

x                y

0               -2

6                0

9                -1

12               2

b) The graph has been attached

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The standard deviation gives information about how values are distributed around the mean. The range between the lowest and highest number is more constrained when the standard deviation is low. Values will so tend to group together around the mean.

What is explained by the standard deviation?

The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.

                                     When comparing data sets that may have the same mean but a different range, it is helpful. The mean of the following two numbers, for instance, is the same: 15, 15, 15, 14, 16 and 2, 7, 14, 22, 30.

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The length and width of the rectangular pen that optimizes the area are 400 feet and 200 feet, respectively, according to the perimeter of a rectangle.

The perimeter of a shape is the sum of the lengths of all its edges. For example, a triangle has three edges, hence its perimeter is equal to the sum of those three lengths.The perimeter of a form can be calculated by adding the lengths of all its sides. A perimeter example is what? A field with a length of 24 yards and a width of 15 yards, for instance, will have a perimeter of 78 yards.

calculation

In order to construct a hog pen, I have 800 feet of fencing.

Assume that "l" represents the rectangle's length and "w" its width.

One of your properties borders a river that I own.

I can secure my property with fencing on its three sides.

because of this, the fencing's necessary perimeter p = l + 2w

The fencing's perimeter is now equal to

⇒ l + 2w = 800

= l = 800 - 2w

now the  rectangle's area  = A = lw

Therefore,  A = l * w = w ( 800 - 2w ) = 800w - [tex]2w^{2}[/tex]

By diffusing the area equation, we can figure out the rectangle's greatest area.

Therefore, A' = 800 - 4w

Again, A" = -4

The rectangle has the largest area since the second order differentiation is constant negative.

Put simply, we obtain: A' = 0 , A' = 800- 4w

⇒800- 4w = 0

⇒ 4 w = 800

⇒ w = 200

So the rectangle has a 200-foot width.

The rectangle's length is currently:

l = 800 - 2w = 800 - 2 ( 200 ) = l = 400 feet

The length and width of the rectangular pen that optimizes the area are 400 feet and 200 feet, respectively, according to the perimeter of a rectangle.

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Answer:

y = 6.08871x + 63.9274

Step-by-step explanation:

You can use Desmos a free graphing calculator to do this.  

Bar graph can best compare the number of school days in California, Kansas, Alabama, and Rhode island.

What is Bar graph?

A bar chart or bar chart is a chart or graph that represents categorical data in rectangular bars whose height or length is proportional to the value they represent. Bars can be drawn vertically or horizontally. Column charts are sometimes called vertical bar charts.

Bar charts show comparisons between discrete categories. One axis of the chart shows the specific category to be compared and the other axis represents the measured values. Some bar charts represent bars grouped into multiple groups to show values ​​for multiple measurement variables.

Therefore, Bar graph can best compare the number of school days in California, Kansas, Alabama, and Rhode island.

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Answer:

n = 0.3

Step-by-step explanation:

0.09(100n + 1) = 0.3(n + 9) ← distribute parenthesis on both sides

9n + 0.09 = 0.3n + 2.7 ( subtract 0.3n from both sides )

8.7n + 0.09 = 2.7 ( subtract 0.09 from both sides )

8.7n = 2.61 ( divide both sides by 8.7 )

n = 0.3

A relative minimum is a point in which neighborhood values will be bigger thus, in the given graph the only "b" point is relative minima.

The graph is a geometrical representation of a function and can be plotted by taking x's and y's corresponding values within the interval.

For example plot of y = x³,y = sinx.

As per the given graph,

The point where the slope is zero and the smallest among its neighborhood points then it will be relative minima.

In the given graph the point b is the smallest among its neighborhood thus b will be the relative minimum.

Hence "A relative minimum is a point in which neighborhood values will be bigger thus, in the given graph the only "b" point is relative minima".

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Answer:

the length of RB is 18 cm.

Step-by-step explanation:

In △QRS, since point A is between points Q and R, and point B is between points R and S, we have that QR > QA > 0 and RS > RB > 0. Additionally, since AB∥QS, we know that the segment AB is parallel to the segment QS.

We can use this information to set up an equation to solve for RB. Since AB∥QS and QA = 23 cm, we have that QR = RB + 23. We can substitute this expression into the equation QR = 41 cm to get:

RB + 23 = 41

Solving this equation for RB, we get:

RB = 41 - 23

Therefore, the length of RB is 18 cm.

Answer:

Locate the given point in the coordinate plane: for example; (−9,4)

Ans: Given that the x and y coordinate of the point are −9 and 4, respectively.

Here, the given point (−9,4) is located in the coordinate plane.  It will be located on the top left side of the coordinate plane if you drew it out.

Step-by-step explanation:

1. You have to draw two perpendicular lines, \ (x-\)axis and \ (y-\)axis.

2. From the point of origin, you have to move 5 units to the right side along the positive \ (x-\)axis.

3. Now, you have to move \ (6\) units up, parallel to the positive \ (y-\)axis

4.  Here, you mark the point of intersection and mark it as \ ((-9, 4).\)

Answer: 5

Step-by-step explanation:

Pythagorean theorem a^2 + b^2 = c^2

5^2 + x^2 = 5sqrt(2) ^ 2

25 + x^2 = 50

x^2 = 25

x = 5 square root both sides

Step-by-step explanation:

[tex]6x^2+60x+144\\\\6(x^2+10x+24)[/tex]

You are looking for two numbers that add to 10 and multiply to 24:

6 + 4 = 10

6 * 4 = 24

so [tex]x^2 + 10x + 24 = (x+6)(6+4)[/tex]

factored: [tex]6(x+6)(x+4)[/tex]

To write the equation of a line in slope-intercept form (y = mx + b), we need to find the slope of the line (m) and the y-intercept (the point where the line crosses the y-axis, which is represented by b).

We can use the point-slope formula to find the equation of the line that passes through the points (-2,-2) and (5,12):

y - y1 = m(x - x1)

Where (x1, y1) is a point on the line, and m is the slope of the line.

Plugging in the values for the given points and solving for m, we get:

m = (12 - (-2)) / (5 - (-2))

= 14 / 7

= 2

Now that we have the slope, we can use either of the given points to find the y-intercept (b). Let's use the point (-2,-2):

y = mx + b

-2 = 2(-2) + b

-2 = -4 + b

b = -2 + 4

b = 2

Therefore, the equation of the line in slope-intercept form is:

y = 2x + 2

This is the equation of the line that passes through the points (-2,-2) and (5,12).

Answer: No

Step-by-step explanation:

No, Mr.Hill can not divide 20 balls into 3 equal groups because 20/3 does not get you a whole number, and you can not have 0.66666667 of a ball.

Answer:

No.

Step-by-step explanation:

20/3 = 5 balls per team and five are left over. No he cannot, this is because Mr. Hill would need to have twenty one balls and he only has 20. So there is not enough. It’s because there are going to be leftovers.

Christina has 46 baseballs and Spencer has 74 baseballs in their collections.

Two or more expressions with an Equal sign is called as Equation.

Given,

Christina and Spencer have 120 baseballs together.

Let christina has x baseballs

Spencer has 28 more

than Christina

x+28 has Spencer

So x+x+28=120

2x+28=120

Subtract 28 from both sides

2x=120-28

2x=92

Divide both sides by 2

x=46

Hence, Christina has 46 baseballs and Spencer has 46+28=74 baseballs in their collections.

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21 miles per hour is the speed of boat still in water and 9 miles per hour is the speed of current.

Downstream - A boat is said to be moving downstream if it is moving in the same direction as the stream.

Upstream - A boat is said to be moving upstream if it is moving downstream of the stream. The term "upstream speed" in this context refers to the boat's net speed.

13) Given that, a boat traveled 280 miles downstream and back.

Time taken by boat in downstream is 7 hours and in upstream is 14 hours.

Let the speed of a boat be x miles per hour and the speed of a current be y miles per hour.

So, the total speed in downstream is x+y miles per hour and the total speed in upstream is x-y miles per hour.

We know that, Distance = Speed × Time

Now, 280=(x+y)×7

⇒ x+y=40 ------(I)

Here, 280=(x-y)×14

⇒ x-y=20 ------(II)

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

x+y+x-y=40+20

⇒ 2x=60

⇒ x=30 miles per hour

So, x+y=40

⇒ y=10 miles per hour

14) Given that, a boat traveled 252 miles downstream and back.

Time taken by boat in downstream is 12 hours and in upstream is 84 hours.

Let the speed of a boat be p miles per hour and the speed of a current be q miles per hour.

So, the total speed in downstream is p+q miles per hour and the total speed in upstream is p-q miles per hour.

We know that, Distance = Speed × Time

Now, 252=(p+q)×12

⇒ x+y=21 ------(I)

Here, 252=(p-q)×84

⇒ p-q=3 ------(II)

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

p+q+p-q=21+3

⇒ 2p=24

⇒ p=12 miles per hour

So, p+q=21

⇒ q=9 miles per hour

Therefore, the speed of boat still in water is 21 miles per hour and the speed of current is 9 miles per hour.

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