Name:
Unit 1 Lesson 7 Practice
kylie
Hour:
1. A scale drawing of a school bus has a scale of Vainch to 5 feet. If the length
of the school bus is 4 va inches on the scale drawing, what is the actual
length of the school bus? Explain or show your reasoning.

[tex]\\ \sf\longmapsto a+\dfrac{1}{a}=\sqrt{3}[/tex]

[tex]\\ \sf\longmapsto \left(a+\dfrac{1}{a}\right)^3=\sqrt{3}^3[/tex]

[tex]\\ \sf\longmapsto a^3+\dfrac{1}{a^3}+\dfrac{3a^2}{a}+\dfrac{3a}{a^2}=3\sqrt{3}[/tex]

[tex]\\ \sf\longmapsto a^3+\dfrac{1}{a^3}+3a+\dfrac{3}{a}=3\sqrt{3}[/tex]

[tex]\\ \sf\longmapsto a^3+\dfrac{1}{a^3}=3\sqrt{3}-3a-\dfrac{3}{a}[/tex]

[tex]\\ \sf\longmapsto a^3+\dfrac{1}{a^3}=3\left(\sqrt{3}-a-\dfrac{1}{a}\right)[/tex]

[tex]\\ \sf\longmapsto a^3+\dfrac{1}{a^3}=3(0)[/tex]

[tex]\\ \sf\longmapsto a^3+\dfrac{1}{a^3}=0[/tex]

Answer:

Tn=a+(n−1)d, where a= First term, d= Difference between terms ... (2)

Equating (1) and (2)

6n+5=a+(n−1)d

6n+5=a+nd−d ..... (3)

Equating n terms:6n=nd

d=6 ...... (4)

Substituting (4) in (3)

6n+5=a+6n−6

5=a−6

a=11 ..... (5)

Now

Sn=2n(2a+(n−1)d)

Sn=2n(a+Tn) ....... (6)

Substituting (1) and (5) in (6)

Sn=2n(11+6n+5) 

Sn=2n(16+6n) 

Sn=n(8+3n) 

Tn=a+(n−1)d, where a= First term, d= Difference between terms ... (2)

Equating (1) and (2)

6n+5=a+(n−1)d

6n+5=a+nd−d ..... (3)

Equating n terms:6n=nd

d=6 ...... (4)

Substituting (4) in (3)

6n+5=a+6n−6

5=a−6

a=11 ..... (5)

Now

Sn=2n(2a+(n−1)d)

Sn=2n(a+Tn) ....... (6)

Substituting (1) and (5) in (6)

Sn=2n(11+6n+5) 

Sn=2n(16+6n) 

Sn=n(8+3n) 

Tn=a+(n−1)d, where a= First term, d= Difference between terms ... (2)

Equating (1) and (2)

6n+5=a+(n−1)d

6n+5=a+nd−d ..... (3)

Equating n terms:6n=nd

d=6 ...... (4)

Substituting (4) in (3)

6n+5=a+6n−6

5=a−6

a=11 ..... (5)

Now

Sn=2n(2a+(n−1)d)

Sn=2n(a+Tn) ....... (6)

Substituting (1) and (5) in (6)

Sn=2n(11+6n+5) 

Sn=2n(16+6n) 

Sn=n(8+3n) 

Answer:

Step-by-step explanation:

12$ = original price (need to add 67% mark up)

12/100 = 0.12 = 1%

0.12 x 67 = $8.04 markup

12 + 8.04 = $20.04 is the correct selling price

the error was accidently not adding the markup ($8.04) to the original price

Answer:

x = 1; not extraneous

Step-by-step explanation:

Answer:

X equals negative 11

Step-by-step explanation:

The angles in a triangle add up to be 180 degrees, and we already have 80 as one angle and 60 as the other. That equals 140 degrees. But now we have x+51. That would equal 191 degrees, so 191-180=11, so x= -11

Answer:

x=-11

What we know=

Angles A'=x+51

Angle B=60

Angle C=80

Angle B' and C'=?

Due to the vertically opposite angle rule, we know angle B' and C' are the same as angle B and C.

So, angle B' is 60 degrees. Angle C' is 80 degrees.

We can add them together to get 140 degrees.

So we have 140, x+51. We can make an equation.

[tex]180=140+51+x[/tex] We can combine like terms (140 and 51) to get 191

A triangle only adds up to 180 degrees. So now you can subtract 180-191=to get x.

Answer:

-10

Step-by-step explanation:

2x+6 = x-4

2x = x - 4 - 6

2x = x -10

2x -x = x-x - 10

x = -10

Please mark my answer as brainest

Answer:

X = 3

Mode: 11median: 9

Step-by-step explanations

3x = 3*2 = 6

(6,7,8,8,9,10,11,11,11)/9 = 81/9 = 9

The value of X = 3

Mode: 11

Median: 9

The mean is the average value which can be calculated by dividing the sum of observations by the number of observations

Mean = Sum of observations/the number of observations

Median represents the middle value of the given data when arranged in a particular order.

Mode is that number that appears most frequently in the given set of data.

We are given that  the ages in years of members of group 8, 11, 8,10 ,6, 7, 3x ,11, 11 if the mean age is 9 years

3x = 3(2 )= 6

Mean = (6,7,8,8,9,10,11,11,11)/9

= 81/9

= 9

Learn more about mean and median;

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Answer:

x<-1

Step-by-step explanation:

-5(x-1)>10, distribute the -5

-5x+5>10, subtract 5 from both sides

-5x>5, divide by -5

x<-1

(When you divide an inequality by a negative, the sign flips)

Answer:

the desired element lies in the 3rd row and 1st column, and is 25.

Step-by-step explanation:

We are given a 3 by 3 matrix:  There are 3 rows and 3 columns.

The symbol a       represents the element of this matrix that lines in row m and column 1.  Thus, the desired element lies in the 3rd row and 1st column, and is 25.

                      mn

Answer:

0.026 m / min.

Step-by-step explanation:

Volume V = π7^2h

V = 49πh

dV/dh = 49π

Rate that the volume is increasing is 4 m3/min.

So dV/dt = 4

dV/dt = dh/dt * dV/dh

4 = dh/dt * 49π

dh/dt = 4/49π

= 0.026 m / min.

The required height of the water increase is given as 0.026 m/min.

Given that,
A cylindrical tank with a radius of 7 m is being filled with water at a rate of 4 m3/min, how fast is the height of the water increasing is to be determined

Volume is defined as the ratio of the mass of an object to its density.

Here,
The volume of the cylinder =πr²h
Substitute the value in the above formula
Volume V = π7²h
V = 49πh
V/h = 49π  - - - - - - - (1)

Rate of the filling the tank is given,

V/t = 4
V = 4t
Substitute this in equation 1

4t / h = 49π
h / t = 0.026 m/s.

Thus, the required height of the water increase is given as 0.026 m/min.

Learn more about Volume here:
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Answer:

90 miles per hour

Step-by-step explanation:

Divide distance by time to get speed.

[tex]\frac{120}{80}[/tex]=1.5 miles per minute

60 minutes in an hour

1.5(60)=90 miles an hour

Answer:

130 and 211

Step-by-step explanation:

15+17= 32

17+32=49

32+49=81

49+81=130

81+130=211

Answer:

130 and 211

Step-by-step explanation:

15,17,32,49,81 _ _

15+2=17+15=32+17=49+32=81

that mean 81+ 49=130

and 81+130= 211

Hence, the answer is 130 and 211.

Answer:

X to the 4th power = 1440

Step-by-step explanation:

Answer:

Step-by-step explanation:

The first step will always be to break it down into steps.

Nathan lifted 13 boxes, each weighing 12 lb more than Steven's boxes. Steven lifted 15.

The total weight of Nathan's boxes would be the weight of 1 box times 13, because he lifts a total of 13 boxes.

S is the weight of Steven's boxes.

Steven's box + 12 lb = the weight of one of Nathan's boxes.

Then, you would multiply that number by 13 to get your answer.

Therefore, the first option is correct.

13(s + 12)

number of boxes Nathan lifted(Steven's weight + the extra pounds)

Hope this helped!

Answer:

13(s + 12)

Step-by-step explanation:

Answer:

x=20

Step-by-step explanation:

First find the common denominator

Combine fractions with common denominator

Multiply the numbers

and you should be able to do it if that point. Pretty straight forward :)

HOPE I HELPED!!

Answer:

x=20

Step-by-step explanation:

add 5 to both sides

x/20=-4+5

simplify -4+5 to

x/20=1

multiply sides by 20

x=1*20

so x=20

[tex]\:\:\:\:\:\:\:\:\:\:\therefore\bf{x=3\:and\:y=1}[/tex]

Solution

[tex]\:\:\:\bf{(2^{x+y},\:3^{x-y})=(16,9)}[/tex]

[tex]\sf{Here,}[/tex]

[tex]\:\:\:\star\tt{\:\:2^{x+y}=16\:and\:3^{x-y}=9}[/tex]

[tex]\sf{Solving,}[/tex]

[tex]\:\:\:\implies\tt{\:\:2^{x+y}=16}[/tex]

[tex]\:\:\:\implies\tt{\:\:2^{x+y}=2^4}[/tex]

[tex]\:\:\:\implies\tt{\:\:x+y=4}[/tex]

[tex]\:\:\:\bf{\:\:x=4-y-----(i)}[/tex]

[tex]\sf{Solving,}[/tex]

[tex]\:\:\:\implies\tt{\:\:3^{x-y}=9}[/tex]

[tex]\:\:\:\implies\tt{\:\:3^{x-y}=3^2}[/tex]

[tex]\:\:\:\bf{\:\:x-y=2-----(ii)}[/tex]

[tex]\sf{Putting\:the\:value\:of\:(i)\:in\:(ii),}[/tex]

[tex]\:\:\:\implies\tt{\:\:4-y-y=2}[/tex]

[tex]\:\:\:\implies\tt{\:\:4-2y=2}[/tex]

[tex]\:\:\:\implies\tt{\:\:-2y=2-4}[/tex]

[tex]\:\:\:\implies\tt{\:\:\cancel{-}2y=\cancel{-}2}[/tex]

[tex]\:\:\:\implies\tt{\:\:y=\frac{\cancel{2}}{\cancel{2}}}[/tex]

[tex]\:\:\:\bf{\:\:y = 1}[/tex]

[tex]\sf{Putting\:y = 1\:in\:(i),}[/tex]

[tex]\:\:\:\implies\tt{\:\:x=4-1}[/tex]

[tex]\:\:\:\bf{\:\:x = 3}[/tex]

[tex]\:\:[/tex]

Answer:

178g

Step-by-step explanation:

Answer:

add all the ones on the out side of that area dont do the ones on the inside show me whene done plz

Answer:

40

Step-by-step explanation:

there are 9 cow for ever 8 horses

45 is 5 sets of 9 (45/5 = 9)

so to make this ratio equal you have to multiply the amount of horses by 5 too

8*5=40

40 horses

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Answer:

About 333000 times

Step-by-step explanation:

Answer:

22.5 (B)

Step-by-step explanation:

Answer:

0.3

Step-by-step explanation:

Percent means 'per 100'. So, 30% means 30 per 100 or simply 30/100. If you divide 30 by 100, you get 0.3 (a decimal number). So, to convert from percent to decimal, simply divide by 100 and remove the '%' sign. There is a easy way to convert from percent to decimal: Just move the decimal point 2 places to the left.

Hope this helps :)

pls give brainliest :p

And let me know what you think of my pfp :0

Answer:

7 units

Step-by-step explanation:

Answer:

f(-10) = 1,100

Step-by-step explanation:

f(-10) = (-10)^2 - (-10)^3

= 100 - (-1000)

= 1,100

Answer:

48

Step-by-step explanation:

50 + 88= 132

in triangle abc,

132+L=180

L=48

Answer:

8 seeds

Step-by-step explanation:

16 = 32

4 = ?

16 ÷4 = 4

32 ÷ 4 = 8

Answer:

$20,960

Step-by-step explanation:

brainliest?

every 14 days you get payed only 10 dollars?

id say less then 1000