Exercise 4
3
2.5% = 50
2 * = 0,125
Solve the following equations:
1 3* = 81
2
5Y - 15 = 0
5
5x + 1 = 1
16* = 8
9.
1
9
4
8.
101 - x = 0,01
2(5)* = 54
(3)
5Y - 0,2 = 0
12
7 (-3)* = 1
11
5-2 = 25
10
107
Unit 3: Calculations with exponents​

Answer:

8

Step-by-step explanation:

8+22 = 30

In order to solve 8 • (8+22), we'll need to use the order of operations. First, complete what is in parenthesis.

8 • (8+22)

30

Then, multiply 30 by 8.

30 • 8 = 240.

So, you can then divide to find your answer. If you divide 240 by 30, you will find that 8 • (8+22) is 8 times larger than 8+22.

Answer:

8 times larger

Step-by-step explanation:

Answer:

775.64

Step-by-step explanation:

multiplying each number by 8

Answer: n=m divided by 8

Step-by-step explanation:

Answer:

No that would be a 90 degree

Step-by-step explanation:

Answer:

part b is 32

Step-by-step explanation:

Either the US has the highest density and Denmark has the lowest or the other way around.

Id say its that the u.s. has the highest denmark has the lowest

Answer:

Either the US has the highest density and Denmark has the lowest or the other way around.

Id say its that the u.s. has the highest denmark has the lowest

Step-by-step explanation:

Given,

Nepali speaker : 80% (Y)

Maithili speaker : 60% (X)

We know that,

Both language speaker = Y -X

Now,

Y- X

= 80- 60

= 20

Therefore, 20% people speak both languages

To solve the problem we must know about the slope of a line.

A slope is also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.

[tex]m = \dfrac{(y_2-y_1)}{(x_2-x_1)}[/tex]

The slope of the line passing through the points (-8,5) and (7,0) is [tex]\dfrac{-1}{3}[/tex].

Given to us

Points can be written as,

[tex]y_2 = 0\\y_1 = 5\\x_2=7\\x_1 = -8[/tex]

We know that the slope of a line whose two points are given is written as,

[tex]m = \dfrac{(y_2-y_1)}{(x_2-x_1)}[/tex]

Substituting the value, we get,

[tex]m = \dfrac{(0-5)}{[7-(-8)]}\\\\m = \dfrac{(0-5)}{[7+8]}\\\\m = \dfrac{(-5)}{[15]}\\\\m= \dfrac{-1}{3}[/tex]

Hence, the slope of the line passing through the points (-8,5) and (7,0) is [tex]\dfrac{-1}{3}[/tex].

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Answer:

3+20-4x=19-4x+4 3+20=19+4 23=23 xeR

Answer:

f < 7

Step-by-step explanation:

f can be any number that is less than 7

Answer:

6 and less will give you a number less then 9

Step-by-step explanation:

We know its not 7

because 7 + 2 < 9 = 9 = 9

we want something that is less then 9

1 up to 7 would give you an answer less then 9

6 + 2< 9 = 8 < 9

5 + 2 < 9 = 7 < 9

4 + 2 < 9 = 6 < 9

and more

Answer:

3x+x^2-6

Step-by-step explanation:

Have a great rest of your day.

Bye

Answer:

12

Step-by-step explanation:

Distance from (-4,1)to (-1,1) =|-4|-|-1|=3

Side of square =3

Since each side of square is equal.

3x4=12

If vertices A (-1,1) and vertices B (-4,1) of Square ABCD then  perimeter of the square ABCD is 12 units.

The length along a line or line segment between two points on the line or line segment.

The distance between A and B is 3 units, so the distance between B and C must also be 3 units since the square has equal sides.

The coordinates of C are (-4, -2) since it is directly below B.

The distance between C and D is 5 units since it is a horizontal line between the x-coordinates of C and D.

The coordinates of D are (-1, -2) since it is directly to the right of C.

Now we have the coordinates of all four vertices

A (-1,1), B (-4,1), C (-4,-2), and D (-1,-2).

To find the perimeter, we add up the lengths of all four sides:

AB = BC = CD = AD

= √[(xB - xA)² + (yB - yA)²]

= √[(-4 - (-1))² + (1 - 1)²]

= 3

So the perimeter is P = AB + BC + CD + AD

= 3 + 3 + 5 + 3

= 14

Therefore, the perimeter of the square ABCD is 12 units.

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Answer:

(3,3)

Step-by-step explanation:

Answer:

Shortest Path : A-C, C-Z

Shortest possible time = 143

Step-by-step explanation:

P.S - The exact question is -

Given -

T1 = 38

T2 = 52

T3 = 63

T4 = 67

T5 = 91

T6 = 62

T7 = 64

To find - What is the shortest path and what is the shortest possible time to travel from A to Z ?

Proof -

Choices for shortest path is -

Choice 1 : A-B, B-E, E-Z ;

Choice 2 : A-C, C-Z ;

Choice 3 : A-B, B-D, D-Z

Now,

For Choice 1 : A-B, B-E, E-Z

Distance between A-B = T1 = 38

Distance between B-E = T4 = 67

Distance between E-Z = T7 = 64

So,

The distance = 38 + 67 + 64 = 169

Now,

For Choice 2 : A-C, C-Z

Distance between A-C = T2 = 52

Distance between C-Z = T5 = 91

So,

The distance = 52 + 91 = 143

Now,

For Choice 3 : A-B, B-D, D-Z

Distance between A-B = T1 = 38

Distance between B-D = T3 = 63

Distance between D-Z = T6 = 62

So,

The distance = 38 + 63 + 62 = 163

∴ By comparing we get

Shortest Path = A-C, C-Z

Shortest possible time = 143

The shortest path is A→C→Z and the shortest possible time is 143 units option second is correct.

It is given that the traveler is trying to determine the fastest way to travel from city A to city Z.

It is required to find the shortest path and the shortest possible time to travel from A to Z.

It is defined as the path in which all the sum of the path will be shortest in a weighted diagram known as the shortest path.

We have the time required to travel from A to B is T1 = 38 units

Similarly, for the path A to C is T2= 52 units

For the path B to D is T3= 63 units

For the path B to E is T4 = 67 units

For the path C to Z is T5 = 91 units

For the path D to Z is T6 = 62 units

For the path E to Z is T7 = 64 units

For the path A→B→E→Z

The total time required = T1+T4+T7

                                       = 38+67+64 ⇒169 units.

For the path A→C→Z

The total time required = T2+T5

                                       = 52+91 ⇒143 units.

For the path A→B→D→Z

The total time required = T1+T3+T6

                                       = 38+63+62 ⇒ 163 units.

Thus, the shortest path is A→C→Z and the shortest possible time is 143 units option seconds is correct.

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Answer:  

Scale distance on map representation = 2.4 cm

Step-by-step explanation:

Given:

Scale factor [6 cm - 15 Km]

Actual distance = 6 km

Find:

Scale distance on map representation

Computation:

Scale distance on map representation = Actual distance[6cm / 15km]

Scale distance on map representation = 6km [6cm / 15km]

Scale distance on map representation = 36 / 15

Scale distance on map representation = 2.4 cm

Answer:

A. 8π / 3

Step-by-step explanation:

Answer:

25 miles per hour

Step-by-step explanation:

Given

[tex]W = Wind\ resistance[/tex]

[tex]A = Surface\ Area[/tex]

[tex]V = Velocity[/tex]

The joint variation can be represented as:

[tex]W\ \alpha\ A*V[/tex]

Where:

[tex]V = 55; A = 20; W = 220[/tex]

Required

Find V,  when: [tex]A = 55; W = 275[/tex]

We have:

[tex]W\ \alpha\ A*V[/tex]

Express as an equation

[tex]W= k *A*V[/tex]

Where k is the constant of variation

Make k the subject

[tex]k = \frac{W}{A*V}[/tex]

When: [tex]V = 55; A = 20; W = 220[/tex]

We have:

[tex]k = \frac{220}{20 *55 }[/tex]

[tex]k = \frac{220}{1100}[/tex]

[tex]k = 0.2[/tex]

When: [tex]A = 55; W = 275[/tex]

We have:

[tex]k = \frac{W}{A*V}[/tex]

Substitute: [tex]A = 55; W = 275[/tex] and [tex]k = 0.2[/tex]

[tex]0.2 = \frac{275}{55 * V}[/tex]

Make V the subject

[tex]V= \frac{275}{55 * 0.2}[/tex]

[tex]V= \frac{275}{11}[/tex]

[tex]V= 25[/tex]

Answer:

Cos Y = 12/13

Step-by-step explanation:

Recall, SOHCAHTOA.

Cos Y = Adjacent/Hypotenuse

Reference angle = Y

Adjacent = 12

Hypotenuse = 13

Therefore:

Cos Y = 12/13

The probability it will be a ride = total number of rides / total attractions.

Probability = 6/16

Probability = 3/8

Answer:

Probability is defined as the favourable outcomes divided by total outcomes

Probability = Favourable Outcome/Total outcomes

Probability = 6/16

Probability = 3/8

[tex] \\ [/tex]

Answer:

One Way: 79 + 62H + 15H = X

Second Way: 79 + ((62 + 15) x H) = X

Step-by-step explanation:

Given that a plumber charges a customer a one-time service fee of $ 79, $ 62 per hour for labor, and a surcharge of $ 15 per hour due to the call being an emergency, to write an expression to represent the total charges for the plumber in two different ways, with H representing the number of hours the job takes, the following equations should be formulated:

79 + 62H + 15H = X

So, for example, if the job had lasted 2 hours, the equation would apply as follows:

79 + 62x2 + 15x2 = X

79 + 124 + 30 = X

233 = X

79 + ((62 + 15) x H) = X

In the case, if the work had lasted 1 hour, the equation would apply as follows:

79 + (62 + 15) x 1) = X

79 + 77 x 1 = X

79 + 77 = X

156 = X

The total charge when there is an emergency is $79 + $77h. The total charge when there is no emergency is $79 + $62h.

There are two ways of representing the total charges of the plumber,one when there is an emergency call and two when there is no emergency call. The total charge a function of the one-time service fee, labor charge and the surcharge.

Total charge when there is an emergency = one-time service fee + labor charge per hour + surcharge per hour

$79 + $62h + $15h

= $79 + $77h

Total charge when there is no emergency = one-time service fee + labor charge per hour

$79 + $62h

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Answer:

The constant of proportionality of the equation is 1.5.

Step-by-step explanation:

Equation of proportional measures:

Suppose that y and x are proportional measures. This situation can be equatialized is:

y = ax

In which a is the constant of proportionality.

y = 1.5x. What is the constant of proportionality of the equation?

a = 1.5, so the constant of proportionality of the equation is 1.5.

Answer:

15inx3.3

=

to my dad lol

https://youtu.be/WYNfQabLpuk

Answer:

y=45x+115

Step-by-step explanation:

We can find the slope of a line tangent to a curve at a point by evaluating the derivative of the function at that point.

We are given the function

f ( x ) = 4 x 3 + 12 x 2 + 9 x + 7

= f ( x ) = 4 x 3 + 12 x 2 + 9 x 1 + 7 x 0

Using the power rule, let's now compute the derivative of  f( x )

f ' ( x ) = ( 3 ⋅ 4 x 2 ) + ( 2 ⋅ 12 x ) + ( 1 ⋅ 9 x 0 ) + 0 ⋅ 7 x − 1

f ' ( x ) = 12 x 2 + 24 x + 9

We can now find the slope of  f ( x )  at  x = − 3  by substituting this value into f ' ( x )

f ' ( − 3 ) = 12 ( − 3 ) 2 + 24 ( − 3 ) + 9

f'(-3)=12(9)+24(-3)+9

f'(-3)=108-72+9

f'(-3)=45(slope of the tangent line at  x = − 3

Now that we have a slope for the tangent line, we need to identify a point on the line.

We know the tangent line touches the function  f ( x )  at the point  x = − 3 , so let's find the value of  f ( x )  at this point:

f(-3)=4(-3)3+12(-3)2+9(-3)+7

f(-3)=4(-27)+12(9)+9(-3)+7

f(-3)=108+108-27+7

f'(-3)=-20

So we know the tangent line goes through the point

(-3,-20)

Finally, we can use the point-slope formula for a line to find the equation of the tangent line.

y=mx+b

To find the value of  b , substitute the values we have calculated for the point and slope of the tangent line:

(-20)=(45)(-3)+b

-20=-135+b

b=115

So our final answer for the equation of the tangent line is:

y=45x+115

Answer:

7) 24 8) 75 9) .9

Step-by-step explanation:

You multiply the denominatior with the whole number.

Answer:

x = 24   b = 75   s = 0.9

Step-by-step explanation:

7. Multiply both sides by 2 and you get x = 24

8. Multiply both sides by 5 and you get b = 75

9. Multiply both sides by 0.3 and you get s = 0.9

Answer:

Step-by-step explanation:

Answer:

24.5x = 30

      x = 30/ 24.5

         = 1.22448979592

hope this answer helps you.....

Answer:

x= 30/24.5=1.22448

Step-by-step explanation:

we have :

2.24x=30 ---------------->> 224x/2.24=30/2.224 ------------->> x= 30/24.5=1.22448

Answer:

A. [tex] \frac{5}{6}\pi x^2 [/tex]

Step-by-step explanation:

Central angle of shaded part

[tex] \theta = 360\degree-60\degree= 300\degree[/tex]

Radius (r) = x unit

Area of the shaded part of [tex] \odot K[/tex]

[tex] = \frac{\theta}{360\degree} \times \pi r^2 [/tex]

[tex] = \frac{300\degree}{360\degree} \times \pi x^2 [/tex]

[tex] = \frac{5}{6}\pi x^2 [/tex]