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Bezzdna [24]
3 years ago
9

What is the reason for each step in the solution of the inequality? −2(x+3)−4>4x+30

Mathematics
2 answers:
Valentin [98]3 years ago
6 0
Distribute the -2 to the (x+3) because of distributive property
-2x-6-4>4x+30
add like terms because you aren't changing anything
-2x-10>4x+30
add 2x to both sides (addition property of equality,  when b=b and a=a, a+b=a+b)
also addative inverse, a+(-a)=0, the 2x canceld the -2x
-10>6x+30
minus 30 from both sides (subtraction property of equality again) and addative inverse, the -30 cancleled the 30
-40>6x
divide both sides by 6 (division property of equality)
-20/3>x
property of 1 division (if a=a then a/a=1
x<-20/3
DochEvi [55]3 years ago
5 0
You would have to first distribute the -2 to the x+3 which gives you -2x-6.  Then you would subtract the 4 which gives you -2x-10 on the left side.  Now you have the equation -2x-10>4x+30.  Move the 4x to the other side giving you         -6x-10>30.  Now add the 10 from the other side which leaves you with -6x>40.  Now remember when you divide by a negative in an inequality, you HAVE TO flip the sign giving you the answer of x<-20/3.

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The first quartile of the dataset {1, 2, 3, 4, 5, 6} is _______. (give your answer as a whole number.
notsponge [240]

The first quartile of the dataset {1, 2, 3, 4, 5, 6} is 2.

Given data set: {1,2,3,4,5,6}

Median of the given data set =3.5

The data set can be split into 2 parts as, {1,2,3} and {4,5,6}. The first quartile is calculated by simply finding the median of the first part of the data set.

Thus, the first quartile is 2.

The quarter divides the distribution into four groups and calculates the range of values above and below the mean.

A quartile separates the dataset into four categories by dividing the data into three points: the lowest, median, and upper quartiles.

The interquartile range, a measurement of variation around the median, is calculated using quartiles.

Learn more about quartiles here:

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5 0
1 year ago
The base of a solid right pyramid is a square with an
zhuklara [117]

Answer:

Volume = ⅓n²(n-1) or ⅓(n³ - n²)

Step-by-step explanation:

Given

Solid Shape: Right pyramid

Edge= n units

Height= n - 1 units

Required

Volume of the pyramid

The volume of a right pyramid is

Volume = ⅓Ah

Where A represents the area of the base

h represent the height of the pyramid

Since it has a square base;

The area is calculated as follows

Area, A = edge * edge

A = n * n

A = n²

Recall that

Volume = ⅓Ah

Substitute n² for A and n - 1 for h

The expression becomes

Volume = ⅓ * n² * (n - 1)

Volume = ⅓n²(n-1)

The expression can be solved further by opening the bracket

Volume = ⅓(n³ - n²)

6 0
3 years ago
The radius of this ball is 15 inches. Which equation gives the ball's surface area, in square inches?
victus00 [196]

Answer:

\large\boxed{S.A.=4500\pi\ in^2\approx14130\ in^2}

Step-by-step explanation:

The formula of a surface area of a ball (sphere):

S.A.=\dfrac{4}{3}\pi R^3

R - radius

We have R = 15in. Substitute:

S.A.=\dfrac{4}{3}\pi(15^3)=\dfrac{4}{3}\pi(3375)=4500\pi\ in^2

If you want to get an approximation, then:

\pi\approx3.14\\\\S.A.\approx(4500)(3.14)=14130\ in^2

5 0
3 years ago
Which relation has a domain of (2, 4) and a rang of (2, 8)
Brums [2.3K]
Domain: x values
Range: y values
The relation would need to have (2, y) and (4, y). And also (x, 2) and (x, 8)
See which ones match

Solution: B
7 0
3 years ago
Describe the domain of this function d=4300x/x^2 +40
Mashcka [7]

Step-by-step explanation:

The domain would be all real numbers

7 0
3 years ago
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