Lisa represented the phrase '9 less than a number' with the expression 9-n.
Is her expression correct? Explain why or why not.

Answer:

(a) h = 160 - 5·x

(b) V = 4·x² × h = 4·x² × (160 - 5·x) = 640·x² - 20·x³ = 20·x²·(32 - x)

∴ V = 20·x²·(32 - x)

Step-by-step explanation:

(a) The given dimensions of the cuboid (rectangular prism) are;

'4·x' meters by 'x' meters by 'h' meters

Let the 4·x meters represent the length, 'l', of the cuboid, let the x meters represent the width, 'w', of the cuboid, and let the h meters represent the height 'h' of the cuboid

Therefore, we are given that the cuboid is a wire cage, with the total length of the sides (edges) of the cuboid equal to 640 meters

Therefore, the sum of the edges are;

Top(4·x + x + 4·x + x) + Side(h + h + h + h) + Bottom(4·x + x + 4·x + x) = 640

20·x + 4·h = 640

∴ h = (640 - 20·x)/4 = 160 - 5·x

h = 160 - 5·x

(b) The volume of a cuboid, V, is given as follows;

V = The area of the base of the cuboid × The height of the cuboid

The area of the base of the cuboid = l × w = 4·x × x = 4·x²

The height of the cuboid = h = 160 - 5·x

∴ V = 4·x² × (160 - 5·x) = 640·x² - 20·x³

V = 640·x² - 20·x³ = 20·x²·(32 - x)

∴ V = 20·x²·(32 - x) QED.

The fraction would be the part of the number over the actual number.

The fraction would be 60/90

Dividing both numbers by 30, the fraction reduces to 2/3

The answer is 2/3

Answer:

Solution given:

let fraction be x.

equation becomes:

60/x=90

doing crisscrossed multiplication

60=90x

dividing both side by 90

60/90=90x/90

x=60/90

reduced the term

x=⅔

⅔ is fraction of 60 to get 90

Answer:

I believe it is 5 I'm not sure if it is right

Answer:

A. 5

Step-by-step explanation:

use pythagorean theorem: a^2 + b^2 = c^2

but since we are finding the value of A; we'll use a= (square root) c^2 - b^2

A= 13^2- 12^2

A= 169 - 144

A= 25

A= 5 ( because we square root 25)

Answer:

[tex]b = 6 \sqrt{3} [/tex]

Step-by-step explanation:

Please see the attached picture for the full solution.

Answer:

no solution

Step-by-step explanation:

2x - 6 = -2 + 2x

0 = 4

no solution

Step-by-step explanation:

5x-17 and 3x-11 are supplementary angles

They add up to 180 degrees

5x-17 + 3x - 11 = 180

8x - 28 = 180

8x= 208

x= 26

3x-11, 90, and 2y + 5 added together equal 180

3x-11 + 90 + 2y + 5 = 180

3(26) - 11 + 2y + 5 = 90

78 - 6 + 2y = 90

72 + 2y = 90

2y = 18

y = 9

I hope this helps!!!

Answer:

x = -2

Step-by-step explanation:

If it’s parallel to the y-axis, it must be an x value that is straight up and down. The x coordinate here is -2 so the line must be vertical from -2 on the x-axis.

Answer:

plus 4 each month

Step-by-step explanation:

Answer:

Graph (1)

Step-by-step explanation:

Given equation of the graph is,

y = 20(1.25)ˣ

Table for the input - output values of the function,

x          -2          -1          0          

y         12.8        16        20  

These points lie on curve (1).

Therefore, curve (1) will be the graph represented by the equation.

Answer:

12 INCHES

Step-by-step explanation:

lol

also might have to do with the ratio tho......but i forgot

Answer:

I think the answer is "D" 12 inches

Step-by-step explanation:

I think this because on the right it says 12 inches and the left and the right look like the same length. Hope this helped and if it's wrong I'm so sorry.

Answer:

14.2 units

Step-by-step explanation:

use the distance formula -  take the square root of the following:

([tex]y_{2}[/tex]-[tex]y_{1}[/tex])^2 +([tex]x_{2}[/tex]-[tex]x_{1}[/tex])^2

should be sq rt of 202, or approx 14.2 units

Answer:

Samuel's hourly rate after n seasons with the company is f(n)= 12.50 + 0.35*n.  After 18 seasons with the company, Samuel's hourly rate will be 18.8 $ /hr.

Step-by-step explanation:

You know that Samuel's starting pay is $12.50/hr and for each season Samuel remains with the company, he receives a $0.35/hr raise.

Samuel's hourly rate after n seasons at the company will then be:

f(n)= 12.50 + 0.35*n

To determine the hourly rate after 18 seasons, you must replace the value n with 18:

f(18)= 12.50 + 0.35*18

Solving you get:

f(18)= 12.50 + 6.3

f(18)= 18.8

Samuel's hourly rate after n seasons with the company is f(n)= 12.50 + 0.35*n.  After 18 seasons with the company, Samuel's hourly rate will be 18.8 $ /hr.

Step-by-step explanation:

The number of people to paint the bridge is inversely proportional to the number of hours it takes.

(If there are more people, it will take less time etc.)

9 people can paint the bridge in 5 hours.

=> 2 people can paint the bridge in 5 * (9/2) = 22.5 hours.

Answer:

2$

Step-by-step explanation:

16$ times 5 = 80

80 divided by 40 =2

Answer:

$2

Step-by-step explanation:

Answer:

[tex]f(-1)=-5[/tex]

Step-by-step explanation:

Numeric Value of a Function

Given:

[tex]f(x)=4x^2-9[/tex]

It's required to find f(-1).

It can be calculated by substituting the value x=-1 in the function:

[tex]f(-1)=4(-1)^2-9[/tex]

Calculating:

[tex]f(-1)=4*1-9[/tex]

[tex]f(-1)=4-9[/tex]

[tex]\boxed{f(-1)=-5}[/tex]

9514 1404 393

Answer:

  (x, y) = (0, -3)

Step-by-step explanation:

Using the second equation, we can substitute for x in the first equation:

  6(y+3) -5y = 15

  y +18 = 15 . . . . . collect terms

  y = -3 . . . . . . . . . subtract 18

Using the second equation:

  x = y +3 = (-3) +3 = 0

The solution is ...

  x = 0

  y = -3

Answer:

0.118

Step-by-step explanation:

11.8 = 118/10

= 118/10 × 1/100

= 118× 1/10×100

= 118/1,000

= 0.118

Answer:

350N, 800 N

Step-by-step explanation:

for question no 6

mass (m) = 70 kg

acceleration (a) = 5 m/s²

Force (F) = m * a = 70 * 5 = 350 N

for question no 7

mass (m) = 80 kg

acceleration (a) = 10 m/s²

Force (F) = m * a = 80 * 10 = 800 N

Hope it will help :)❤

Answer: 350N, 800 N

Step-by-step explanation:

for question no 6

mass (m) = 70 kg

acceleration (a) = 5 m/s²

Force (F) = m * a = 70 * 5 = 350 N

for question no 7

mass (m) = 80 kg

acceleration (a) = 10 m/s²

Force (F) = m * a = 80 * 10 = 800 N

Answer:

Area=63.96

Step-by-step explanation:

Given data

A flower bed is 2 meters wide and 3 meters long

convert to feets

1m to feet 3.28084

2m to feet x

x= 3.28084*2

x=6.5ft

3m to feet

=3.28084*3

=9.84ft

Area= 6.5*9.84

Area=63.96

Step-by-step explanation:

2y + z = 13

2x + z = 11

x + y + z=12

x= -1

y= 0

z= 13

Answer:

1/3=2/6

Step-by-step explanation:

1*2=2

3*2=6

Answer: 1/3=2/6

Step-by-step explanation: the numerator (1) in the first fraction is half it is in the second (2). This means the denominator in the first question (unknown) will be half the second (6). Half of (6) is (3). Your answer is 3.

Answer:

its b lol

Step-by-step explanation:

Answer is 203.

Average:

The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.

Given,

For double queen beds increment is $120 x 3% => $120 x (3/100) => 3.6.

The total rate for double queen beds = $120 + $3.6 = $123.6

For king beds increment is $140 x 3% => $140 x (3/100) => 4.2

The total rate for double queen beds = $140 + $4.2 = $144.2

For junior suite increment is $210 x 3% => $210 x (3/100) => 6.3

The total rate for junior suite = $210 + 6.3 = $216.3

For luxury suite increment is $320 x (3/100) => 9.6

The total rate for luxury suite = $320 + 9.6 = $329.6

The average rate =  ($123.6 + $144.2 + $216.3 + $329.6) / 4

=> $203.425 i.e., $203

Learn more about  average (or) mean here:

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Answer:

x=-3

Step-by-step explanation:

5x=12+3

5x=15

divide both sides by 5

x=3

Answer:

We know that no. of days is inversely propotional to the provision for men.

So for 120 men the provision would last for 30days. (given)

Therefore, the provision for 1 men would sustain for. 120 *30 = 3600 days.

Let after the joining of 5 men (after 5 days) the no of more days the provision would last is x days

A.t.q 120*30 = 120*5+125*x

(120*30) - (120*5)= 125x

120(30-5)=125x

120 * 25 = 125x

120 = 5x

x=120/5

x= 24

so the provision would remain for more 24 days.

Answer:

$739.50

Step-by-step explanation:

Linda brought =63 pairs of gloves

when she brought 4 she actually got 5 by "buy 4 get 1 free." offer.

This means she got 60/5 = 12 pairs for free out of 63 pairs.

So, she had to pay for only = 63-12 =51 pairs

Therefore, money did Linda spend on all the gloves =51*14.50 = $739.50

Answer:

Option C (48x)

Step-by-step explanation:

Measure of sides of square = 12x in.

Formula for perimeter of a square = 4s (where s = sides of a square)

So, the expression will be = 4(12x) = 48x

Answer:

$1,956.95

Step-by-step explanation:

The school bought 47 sandwiches for $40.60

= 47 × 40.60

= 1,908.2

They also bought 39 bags of chips for $1.25

= 1.25×39

= 48.75

Therefore the total amount spent can be calculated as follows

= 48.75 + 1,908.2

= 1,956.95

Hence the total amount spent by the school is $1,956.95

The LCM is 6,46,800

The smallest positive integer that is divisible by both a and b is the least common multiple, lowest common multiple, or smallest common multiple of two integers a and b, which is typically denoted by lcm (a, b) in arithmetic and number theory.

Given A = 2³ x 5 x 7² x 11

B = 2⁴ x 7 x 11

C = 3 x 5²

LCM(A,B,C) = 2³ x 5 x 7² x 11 x 2 x 3 x 5

LCM(A,B,C) = 6,46,800

Hence LCM(A,B,C) is 6,46,800

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Answer: (-7,-4) is right

Step-by-step explanation:

Just cause