What is the justification for step 1 in the solution process?

8x + 15 = 11x + 2
Step 1: 8x = 11x − 13
A.
the division property of equality
B.
the addition property of equality
C.
the subtraction property of equality
D.
the multiplication property of equality
HURRY PLEASE U GET 15 POINT PLEASE HURRY THO

Answer:

7

Step-by-step explanation:

Q1 = 14

Q3 = 21

Take 21 - 14 and it gives you the interquartile range of 7.

Final answer:

The interquartile range (IQR) for the data set with a five-number summary of 10, 14, 15.5, 21, 25 is 7, calculated as the difference between the third quartile (Q3) and the first quartile (Q1), which are 21 and 14 respectively.

Explanation:

The interquartile range (IQR) of a data set is calculated by subtracting the first quartile (Q1) from the third quartile (Q3). Given the five-number summary of 10, 14, 15.5, 21, 25, where 14 is Q1 and 21 is Q3, the IQR can be found using the formula:

IQR = Q3 - Q1

In this case:

IQR = 21 - 14

IQR = 7

Therefore, the interquartile range for this data set is 7.

Answer:

y = 3/2 x + 3

Step-by-step explanation:

-9x + 6y = 18 is in standard form (ax + by = c).

Slope-intercept form isolates the "y" variable. It looks like this:

y = mx + b

Move anything that's not "y" to the right side. Move things in reverse BEDMAS order, using reverse operations of what you want to move.

[tex]-9x + 6y = 18[/tex]                   Move -9x by doing +9x to both sides

[tex]-9x + 9x + 6y = 18 + 9x[/tex]             Simplify. -9x + 9x will cancel out.

[tex]6y = 18 + 9x[/tex]                     Move the "6" that multiplies with "y".

[tex]\frac{6y}{6} = \frac{18}{6} + \frac{9x}{6}[/tex]                     Divide each term by 6.

[tex]y = 3 + \frac{3x}{2}[/tex]                        "y" is isolated. Simplify the rest.

[tex]y = \frac{3}{2}x + 3[/tex]                        Rearrange to match slope-intercept form.

Answer:

x = 21 degrees

Step-by-step explanation:

The angles in a triangle add up to 180 degrees.

x - 4 + 3x + 100 = 180

x - 4 + 3x = 80

4x - 4 = 80

4x = 84

x = 21

Answer:

Mr. Z ?

Step-by-step explanation:

Yes because you have to convert the answers to 8/12 to 6/12

1/2 is not greater than 4/6 and the answer to the question "Is 1/2 greater than 4/6?" is no.

Solution:

Let "h" be the number of home games

Let "a" be the number of away games

The total number of games is 49

Therefore,

h + a = 49 ---------- eqn 1

They won 2/3 of the home games and 2/5 of the away games

There were 26 games won

Thus we get,

[tex]\frac{2}{3}h + \frac{2}{5}a = 26\\\\10h + 6a = 26 \times 15\\\\10h + 6a = 390\\\\[/tex]

10h + 6a = 390 --------- eqn 2

Multiply eqn 1 by 6

6h + 6a = 294 ----------- eqn 3

Subtract eqn 3 from eqn 2

10h + 6a = 390

6h + 6a = 294

( - ) ------------------

4h = 96

h = 24

Thus 24 home games were played

Answer: In 5 years time the population will reach to 56,000.

Step-by-step explanation:

This can be calculated using yearly compound interest formula

Formula for yearly compound interest

CI = P(1+R/100)ⁿ

CI = 56,000

P = 28,000

R = 15%

n= number of years

Now,

56,000 = 28,000 (1+15/100)ⁿ

56,000 = 28,000 (1+.15)ⁿ = 28,000 (1.15)ⁿ

log (56,000/28,000) = n log(1.15)

log 2 = n log (1.15)

n = log 2/log 1.15

n≅ 5

Answer:

10.166666666667

Step-by-step explanation:

Answer:

(add up all the number and divide it by 6, cause there are about 6 numbers in the list)

58 + 38 + 54 + 48 + 26 + 36 = 260 ÷ 6 = 43.3

(subtract the mean {43.3} with the same listed numbers)

43.3 - 58 = 14.7

43.3 - 38 = 5.3

43.3 - 54 = 10.7

43.3 - 48 = 4.7

43.3 - 26 = 17.3

43.3 - 36 = 7.3

(add up all the difference and divide it with 6 again)

14.7 + 5.3 + 10.7 + 4.7 + 17.3 + 7.3 = 60 ÷ 6 = 10

so our MAD (mean absolute deviation) would be 10!

~hope this helps, have a good day/afternoon/nigh~

Answer:

The total students appearing in first audition = 72

Step-by-step explanation:

As given in the question:

1 out of 3 students were asked to come for second audition.

Let us assume the TOTAL STUDENT who came to first audition =  m

So, [tex](\frac{1}{3}) m[/tex] appeared for the SECOND ROUND.

Now, 75% of students appearing in second audition were offered parts.

Calculating 75% of  [tex](\frac{1}{3}) m[/tex]

[tex]\frac{75}{100} \times\frac{1}{3} m = 0.25 m[/tex]

Also, as said 18 students were offered parts.

⇒ 0. 25 m = 18

Now, solving for m, we get:

m = 18/0.25  = 72

or, m = 72

Hence, the total students appearing in first audition = 72

Final Answer:

- 24 students were asked to attend the second audition.
- 72 students auditioned initially for the first audition.

Explanation:

Let's tackle the problem step by step.
1. **Find the number of students asked to the second audition.**
We know that 18 students were eventually offered parts after the second audition. We're also given that 75% of those who were asked to the second audition were offered parts. To find out how many students were asked to the second audition, we can set up the following equation:

[tex]\[ \text{Number of students offered parts} =[/tex] [tex]\text{Percentage offered parts} \times \text{Number of students at the second audition} \][/tex]

From the given information:
[tex]\[ 18 = 0.75 \times \text{Number of students at the second audition} \][/tex]
Solving for the number of students at the second audition gives us:

[tex]\[ \text{Number of students at the second audition} = \frac{18}{0.75} = 24 \][/tex]
So 24 students were asked to the second audition.

2. **Find the total number of students who auditioned initially.**
If 1 out of 3 students who auditioned were asked to the second audition, we can infer that the ratio of students asked to the second audition to the total number of students who auditioned is 1:3.

Let's let X represent the number of students who auditioned initially. According to the ratio, we can write:

[tex]\[ \frac{1}{3} \times X = \text{Number of students at the second audition} \][/tex]
We've already solved for the number of students at the second audition, which is 24. Thus:

[tex]\[ \frac{1}{3} \times X = 24 \][/tex]
Solving for X, we get:

[tex]\[ X = 24 \times 3 = 72 \][/tex]
So 72 students auditioned initially for the first audition.

To summarize:
- 24 students were asked to attend the second audition.
- 72 students auditioned initially for the first audition.

Answer:

should be x = +2√6

Step-by-step explanation:

did test!

Answer:

We'll use the Law of Sines:

Sine (C) / c = Sine (B) / b

Sine (86) / 40 = Sine (52) / b

0.99756 / 40 = 0.78801 / b

0.024939  = .78801 / b

b = .78801 / .024939

side b = 31.5974978949  feet

Sine (42) / a = Sine (86) / 40

(0.66913 / a) = 0.024939

a = .66913 / .024939

side a = 26.8306668271  feet

******************************************************

I forgot to include the graphic.  

Step-by-step explanation:

Answer:

B. (5,2)

Step-by-step explanation:

Answer: b. 5, 2

Step-by-step explanation: got it right :p

Answer:

Convert 250 Newtons into Kilograms

25.5

Answer:

1. Solution

-3w-w=3+4

-4w=7

Therefore,w= -7/4

Step-by-step explanation:

2. Solution

3(3-3x)=2(x+3)-30

9-9x=2x+6-30

9+40-6=2x+9x

43=11x

Therefore, x=43/11

#Hope it helps u

Answer:

3/14

Step-by-step explanation:

hope this helps

Answer I DONY KNOW SO LIKE BRUH

Step-by-step explanation: GOOD LUCK

Answer:

Step-by-step explanation:

1234

Step-by-step explanation:

Numbers that cannot be written as a simple fraction are Irrational (i.e not rational) numbers.

Some examples are :

π = 3.14159...........

or

√2 = 1.41421.............

or

e = 2.718218...........

To find the number of adults and children admitted to the movie theater, we set up two equations based on the admission costs and total number of attendees. Solving these equations revealed that there were 450 adults and 225 children.

The question involves a system of equations where we are required to determine the number of adults and children who were admitted to the movie theater given the total revenue and total number of attendees.

Let's denote the number of adults by A and the number of children by C. Given the price of admission is $7 for an adult and $5 for a child, we can represent the total revenue with the equation:

7A + 5C = 4275
Also, considering the total number of people is 675, we have another equation:

A + C = 675

To solve these equations, we'll use the substitution or elimination method:

Therefore, there were 450 adults and 225 children admitted to the movie theater that day.

Answer:

M = 70

Step-by-step explanation:

Supplementary Angles = 180

180 - 110 = 70

Also linear pairs = 180.

m=70 degrees

I hope that helps you :)

Answer:

-4

Step-by-step explanation:

-4t+15=-1

Subtract 15 on both sides:

-4t=-16

Divide -4 on both sides:

t=-4

Answer:

see explanation

Step-by-step explanation:

Given

(x - 2)² + 9 = 0 ( subtract 9 from both sides )

(x - 2)² = - 9  ( take the square root of both sides )

x - 2 = ± [tex]\sqrt{-9}[/tex]

[tex]\sqrt{-9}[/tex] yields no real solutions

There is no real number when multiplied by itself gives - 9

In fact the solutions to [tex]\sqrt{-9}[/tex] are said to be imaginary, that is ± 3i

where i = [tex]\sqrt{-1}[/tex]

If interested investigate further.

Answer:

k - 9 = 3

And k = 12

Answer:

112 students

Step-by-step explanation:

Let T be the total number of students in the band.

From the question,

We were told that 37.5% of the total owns their individual instruments and this amount to 42 students

The total number of students can calculated for as follows:

37.5% x T = 42

37.5/100 x T = 42

Cross multiply to express in linear form

37.5 x T = 100 x 42

Divide both side by 37.5

T = (100 x 42) /37.5

T = 112

Therefore, there are 112 students in the band

Answer:

Step-by-step explanation:

We can recognize that the parent function for all of these graphs is going to be y=x^2. What this means is that we can graph y=x^2 and then apply transformations to it to get to all of these new graphs.

1. y = -x^2 + 5

We can see that the coefficient of the x^2 term is negative which tells us that the graph will now open downwards.

We also know that we are adding 5 on the outside of the argument which means it affect vertical shift. Therefore, we will be moving 5 units up.

2. y = x^2 - 4

We can see that the only change made to this equation is subtracting 4 on the outside of the squared part of the equation. Again, this signifies vertical movement, but since it's negative we will be moving the entire y = x^2 graph down 4 units.

3. y = -x^2 - 1

What do you notice about this graph?

- negative coefficient

- subtracting 1 outside of the argument

What do these mean?

- negative coefficient: opens downwards

- subtracting 1: move entire y = x^2 graph down 1 unit

Speed of the first car is 30 mph and that of the second car is 20 mph.

Step-by-step explanation:

Time = Distance/Speed

        = 60/x - 10 ------ (1)

Time = 90/x ------- (2)

⇒ 60/x - 10 = 90/x

⇒ 60x = 90(x-10)

⇒ 2x = 3(x - 10)

⇒ 2x = 3x - 30

⇒ -x = -30

∴ x = 30 mph

⇒ x - 10 = 30 - 10 = 20 mph