evaluate 1/3 m - 1 - 1/2 n when m = 21 and n = 12

Answer:

3/4x-6=42

x=64

Step-by-step explanation:

Let the number of students be x hence 3/4 of this number will be 3/4x

Since the number was 42 if they were 3/4x less six, it means minus six hence

3/4x-6=42

Therefore, the equation will be

3/4x-6=42

Solving the equation

3/4 x=42+6=48

3/4x=48

X=62

Answer:

The answer is x= 7 good luck though. also what you want to do it get the x's together and also get rid of the 42

Answer:

[tex] Standard \: form :\:y= {x}^{2} - 4x - 5\\

Factored\: from:\:y = (x + 1) (x - 5)[/tex]

Step-by-step explanation:

[tex]y = (x - 2)^{2} - 9 \\ y= {x}^{2} - 4x + 4 - 9 \\ \red{ \boxed{ \bold{y= {x}^{2} - 4x - 5}}} \\ is \: in \: standard \: form \\ \\ y = (x - 2)^{2} - 9 \\ y = (x - 2)^{2} - {3}^{2} \\ y = \{(x - 2) + 3\} \{(x - 2) - 3 \} \\ y = \{x - 2 + 3\} \{x - 2- 3 \} \\ \purple{ \boxed{ \bold{y = (x + 1) (x - 5)}}} \\ is \: in \: factored \: form[/tex]

Answer:

FIRST FOUR (4) TERM = 6, 18, 54,162.

COMMON RATIO = 3

Step-by-step explanation:

In geometric expression.

Tn = the nth term

a = first term

r = common ratio.

Let's take the First term of the G.P as 6 and the third term as 54. Let's find the common ratio.

3rd term will be written as:

T3 = ar² = 54

Given the first term as 6.

T3 = 6r² = 54

6r² = 54

r² = 54 / 6

r² = 9

r= √9

r = 3

Therefore common ratio = 3.

Let's use this information to get the fourth term.

T4 = ar³

when a = 6

and r = 3.

T4 = 6 * 3³

T4 = 6 * 27

T4 = 162

The first four terms of the geometric sequence are [tex]\(a_1 = 5\), \(a_2 = 15\), \(a_3 = 45\), and \(a_4 = 135\).[/tex]  The common ratio is r= 3 and the rule for the nth term is [tex]\(a_n = 5 \cdot 3^{(n-1)}\).[/tex]

To find the common ratio r of a geometric sequence, one divides a term in the sequence by the previous term.

Given the first four terms as [tex]\(a_1 = 5\), \(a_2 = 15\), \(a_3 = 45\), and \(a_4 = 135\),[/tex] we can calculate the common ratio using the first two terms:

[tex]\[ r = \frac{a_2}{a_1} = \frac{15}{5} = 3 \][/tex]

We can verify this by calculating the ratio of the third term to the second term:

[tex]\[ r = \frac{a_3}{a_2} = \frac{45}{15} = 3 \][/tex]

And again with the fourth term and the third term:

[tex]\[ r = \frac{a_4}{a_3} = \frac{135}{45} = 3 \][/tex]

Since the ratio is consistent across these terms, we can confirm that the common ratio r is indeed 3.

The rule for the nth term of a geometric sequence is given by:

[tex]\[ a_n = a_1 \cdot r^{(n-1)} \][/tex]

[tex]\[ a_n = 5 \cdot 3^{(n-1)} \][/tex]

This is the rule for the nth term of the given geometric sequence.

Answer:

Daily: $5,389.41

Monthly: $5,389.00

Semi-annually: $5,386.92

Annually:$5,384.45

Step-by-step explanation:

Answer:

Lily babysit for less than 4 hours.

Step-by-step explanation:

Given:

Lucy spends in a week babysitting for 4 hours.

Lily spends seven-eighths of 4 hours.

Now, to find whether Lily babysit for more than 4 hours or less than that.

Number of hours Lucy babysit = 4 hours.

So, to get the hours Lily babysit:

[tex]\frac{7}{8}\ of\ 4\ hours.[/tex]

[tex]=\frac{7}{8}\times 4\\\\=\frac{28}{8} \\\\[/tex]

On simplifying we get:

[tex]=\frac{7}{2} \\\\=3\frac{1}{2}\ hours.[/tex]

Thus, Lily spends [tex]3\frac{1}{2}\ hours[/tex]  for babysitting which is less than 4 hours.

Therefore, Lily babysit for less than 4 hours.

Lily babysits for 3.5 hours weekly, which is less than Lucy's 4 hours of babysitting.

Lucy spends 4 hours a week babysitting, and Lily spends seven eighths as much time babysitting. To calculate how much time Lily spends, we multiply Lucy's hours by seven eighths:

4 hours × (7/8) = 28/8 hours = 3.5 hours.

So, Lily babysits for 3.5 hours a week, which is less than 4 hours.

Answer:

B

Step-by-step explanation:

y = 6(x^2-6x+9)-2

y = 6x^2-36x+54-2

y = 6x^2-36x+52

The standard form of the given quadratic equation y=6(x-3)²-2 is y = 6x² - 36x + 52 after expanding the squared binomial and simplifying.

The student has asked for the standard form of the quadratic equation y=6(x-3)²-2. The standard form of a quadratic equation is ax² + bx + c = 0. To rewrite the given equation in standard form, expand the squared binomial and simplify:

So, the standard form of the given equation is y = 6x² - 36x + 52.

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Answer:

First Step: separate x^2 from -16

Second Step: add -16/25 to the other side.

Step-by-step explanation:

x^2 - 16/25 = 0

^^ this might be easier if you separate x^2 and -16

First Step-

so rewrite the problem as x^2/25  -16/25 = 0

then...

Second Step-

add -16/25 to the other side. This makes it: x^2/25 = 16/25

Continuation-

Now, you can multiply 25 on both sides to cancel it out.

so you have x^2 = -16

Message me if you want to solve for x.

Explanation:

If the data wasn't sorted, then the first step would be to arrange the elements from smallest to largest. However, that is already done for us.

The middle most value in the set {15, 19, 20, 25, 31, 38, 41} is 25 because there are three values below it {15,19,20} and three values above it {31,38,41}

Focus on the lower half {15,19,20} and note the middle of this subset is element 19. This is the value of Q1 or the first quartile.

The third quartile Q3 is 38 because the middle of the upper half data set {31,38,41} is 38.

We now subtract the values of Q3 = 38 and Q1 = 19 to get the interquartile range (IQR)

IQR = Q3 - Q1 = 38 - 19 = 19

Answer:

19

Step-by-step explanation:

Hope this helps and I got it right on the quiz on edge

Answer:

13.5 mi/h

Step-by-step explanation:

The average speed of the car can be written as

[tex]v=\frac{d}{t}[/tex]

where

d = 4.8 miles is the total distance covered

[tex]t=6\cdot (8 min) = 48 min \cdot \frac{1}{60}=0.8 h[/tex] is the  time elapsed

So the average speed is

[tex]d=\frac{4.8}{0.8}=6 mi/h[/tex]

We also know that the total time consists of 6 8-minutes interval, and the speed of the car decreased by 3 mi/h each interval.

Calling [tex]v_1[/tex] the average speed in the 1st interval, we have:

[tex]v_2=v_1-3\\v_3=v_1-6\\v_4=v_1-9\\v_5=v_1-12\\v_6=v_1-15[/tex]

The average speed in each interval can be written as [tex]v_i=\frac{d_i}{t}[/tex], where [tex]d_i[/tex] is the distance covered in each interval and [tex]d_i = 8 min =0.133 h[/tex] is the duration of each interval, so we can write

[tex]\frac{d_2}{t}=\frac{d_1}{t} -3 \rightarrow d_2 = d_1 -3t[/tex]

And similarly,

[tex]d_3=d_1-6t\\d_4=d_1-9t\\d_5=d_1-12t\\d_6=d_1-15t[/tex]

Since the total distance is [tex]d=d_1+d_2+d_3+d_4+d_5+d_6[/tex], we have:

[tex]d=6d_1 - 3t-6t-9t-12t-15t=6d_1-45t[/tex]

And since we know that

d = 4.8 miles

and t = 0.133h, we can find d1:

[tex]d_1=\frac{d+45t}{6}=\frac{4.8+(45)(0.133)}{6}=1.8 mi[/tex]

So the average speed in the first 8-minute interval is:

[tex]v_1=\frac{d_1}{t_1}=\frac{1.8}{0.133}=13.5 mi/h[/tex]

Answer:

∠ TWV = 106°

Step-by-step explanation:

∠ TWV and ∠ SVW are same- side interior angles and are supplementary, thus

∠ TWV + ∠ SVW = 180°, that is

3x - 5 + 2x = 180

5x - 5 = 180 ( add 5 to both sides )

5x = 185 ( divide both sides by 5 )

x = 37

Thus

∠ TWV = 3x - 5 = 3(37) - 5 = 111 - 5 = 106°

Answer:

x = 24

Step-by-step explanation:

10:8

10(3) = x(3)

x = 8

30 : 24

60% of 94 is calculated by multiplying 94 by 0.60, which results in 56.4.

To find 60% of 94, you will multiply 94 by 0.60. Performing this calculation:

60% of 94 = 0.60 * 94

0.60 * 94 = 56.4

So, 60% of 94 equals 56.4.

Answer:8

Step-by-step explanation:

Answer:

answer is c

Step-by-step explanation:

Formula: h=2A/b1+b2

95(2)/(7+12)=h

190/19=h

10m=h

answer is c

Answer:

27pi cm^2

Step-by-step explanation:

Answer:

27 Pi cm2

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

183.35

Answer:

18

Step-by-step explanation:

It is 18 because 14 x 2 equal 28 so that would mean you need one stick to make 2 pizzas. Then you divide 36 by 2 and get 18

Pat needs 18 sticks of pepperoni to make 36 pizzas

The unitary method is a method in which you find the value of a unit and then the value of a required number of units

According to the problem,

Using unitary method,

To make 28 pizzas Pat needs 14 sticks of pepperoni.

∴ To make 1 pizza, Pat need  [tex]\frac{14}{28}[/tex] sticks of pepperoni

∴ To make 36 pizzas, Pat needs [tex]\frac{(14)(36)}{28}[/tex]  sticks = 18 sticks of pepperoni

So, Pat needs 18 sticks of pepperoni to make 36 pizzas

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Answer:

The length of the hypotenuse of this triangle is 150√2 mm.

Step-by-step explanation:

Consider the square ABCD shown in the image below.

The sides are 150 mm each.

All the angles of a square are 90°.

Now The square is folded in half along the diagonal BD.

The angles A, B and D are:  45°, 45° and 90°.

The hypotenuse of the right angled triangle is BD.

Compute the length of BD using the pythagoras theorem as follows:

[tex]BD^{2}=AB^{2}+AD^{2}\\=150^{2}+150^{2}\\=2\times 150^{2}\\BD=\sqrt{2\times 150^{2}}\\=150\sqrt{2}[/tex]

Thus, the length of the hypotenuse of this triangle is 150√2 mm.

Answer:

The value of [tex]'d'[/tex] is 7.83.

Step-by-step explanation:

Given:

[tex]d+(-5.004)=2.826[/tex]

We need to solve for [tex]'d'[/tex] .

Solution:

[tex]d+(-5.004)=2.826[/tex]

Now we know that;

By the rule  of Addition and subtraction for positive and negative numbers

when a positive and negative signs are met then the result is negative.

So we can say that;

[tex]d-5.004=2.826[/tex]

Now Adding both side by 5.004 using addition property of equality we get;

[tex]d-5.004+5.004=2.826+5.004\\\\d= 7.83[/tex]

Hence The value of [tex]'d'[/tex] is 7.83.

Answer:

7.83

Step-by-step explanation:

Khan academy

plz rate 5 stars and press thanks. :)

Answer:

8,760

Step-by-step explanation:

If Kaylah is reading 142 words in one minute, there is 60 minutes in an hour.

therefore,

142 x 60 = 8,760

Answer:

8520 minutes

Step-by-step explanation:

To solve, make a proportion

142 words in 1 minute, and x words in 60 minutes (1 hour).

142/1=x/60

Cross multiply

142*60=1*x

8520=x

Another way to solve is to know that each hour has 60 minutes, and she can read 142 words in 1 minute. So, we can just multiply 60 and 142.

60*142=8520

Answer:

-3, -2.1, -2, 0

Step-by-step explanation:

Least to greatest

Hope this helped you!

Answer:

-2,2-2.1,-3,0 that's your

Answer:

(x-3)(x-8)

Step-by-step explanation:

the zero are what cancel out the factors.

Answer:

(x-8) and (x - 3)

Step-by-step explanation:

Enjoy your day:)

Answer:

1/6

Step-by-step explanation:

Answer:

5/6 or 83.33%

Step-by-step explanation:

There are 6 total crayons but only one is gold. The other five aren't. If you were to randomly pick one you'd have a 1/6 chance(16.67%)to pull out the gold crayon. That means there is a 5/6(83.33%)chance that you wouldn't pull out the gold one.

Answer:

3/9

Step-by-step explanation:

You just substract the numerator :) So, 7-4= 3

Answer:

D

Step-by-step explanation:

Using the rule of radicals

[tex]\frac{\sqrt{a} }{\sqrt{b} }[/tex] = [tex]\sqrt{\frac{a}{b} }[/tex]

Given

[tex]\frac{14\sqrt{14} }{7\sqrt{2} }[/tex] ← cancel 14 and 7

= 2 × [tex]\sqrt{\frac{14}{2} }[/tex]

= 2[tex]\sqrt{7}[/tex] → D

Answer:

B) -8

Step-by-step explanation:

2*5-18=10-18=-8

Answer:

B

Step-by-step explanation:

4+1 = 5

2*5 = 10

3*6 = 18

10-18=-8

Answer:

⅓

Step-by-step explanation:

For two perpendicular lines,

m1 × m2 = -1

-3 × m2 = -1

m2 = -1/-3

m2 = 1/3