Using Pythagoras' theorem, work out the
length of the hypotenuse of this right-angled
triangle.
Give your answer to the nearest centimetre.
7 cm
19 cm
Not drawn accurately

The product of the quotient of a and b and the quotient of c and d is ac/bd.

In mathematics, a quotient simply means a quantity produced through the division of two numbers.

From the information, the product of the quotient of a and b and the quotient of c and d.

The product will be:

= a/b × c/d

= ac / bd

The product is ac/bd.

Learn more quotient on:

brainly.com/question/11418015

#SPJ1

Jacob run 7/12 of the total distance around the school track.

What is distance?

Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in ordinary language.

Given: Sarah ran 7/8 of the distance around the school track.

Jacob ran 2/3 of Sarah‘s distance.

To find what fraction of the total distance around the track Jacob ran, we will find when solving 2/3 of 7/8 or symbolically

[tex](\frac{2}{3})(\frac{7}{8}) = \frac{14}{24} = \frac{7}{12}[/tex]

Hence, Jacob run 7 / 12 of the total distance around the school track.

To know more about the distance, click on the link

https://brainly.com/question/26046491

#SPJ1

Answer:

Below

Step-by-step explanation:

Need the drawing but take the two cm measurements and multiply them together then multiply by 4   and then multiply by 4 again to get ft^2

The positive difference the  numbers is given as 6.

We are told here that there is a pair of natural numbers whose sum is 52 and whose product is 667. We have to make use of the idea of simultaneous equations to obtain the numbers.

Let the numbers be x and y thus we have;

x + y = 52 ---- (1)

xy = 667 ------ (2)

x = 52 - y ------ (3)

Substituting (3) into (2)

(52 - y)y = 667

52y - y^2 = 667

y^2 - 52y + 667 = 0

Solving the quadratic equation we have;

y=23 or y=29

The difference between the numbers then becomes 29 - 23

= 6

Learn more about simultaneous equations:https://brainly.com/question/16763389

#SPJ1

The graph of the  absolute value function is attached below.

The absolute value function is defined by the following piecewise rule, depending on the input of the function:

|x| = x, x ≥ 0.

|x| = -x, x < 0.

The absolute value measures the distance of a point x to the origin, hence, for example, |-4| = |4| = 0, and has vertex(turning point) at (0,0).

We have to grpah the absolute value function of y = 5x.

Thus, the function is linear function.

The graph of the function is attached below.

More can be learned about functions a;

brainly.com/question/24808124

#SPJ1

The width or short side is 12 feet

The length or long side is 18 feet

What is Area?

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.

On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.

Consider your square as being composed of smaller unit squares. The number of unit squares necessary to completely cover the surface area of a specific 2-D shape is used to calculate the area of a figure. Some common units for measuring area include square cms, square feet, square inches, square meters, etc.

Let Width= x feet

so, as per question Length = x+6 feet

Area = Length x Width = x(x+6) = [tex]x^{2} +6x[/tex]

According to the question each side is increased 6 feet

New Length = x+12 feet

New Width = x+6 feet

New Area = Length x Width[tex]= 2x(x+6)[/tex] <the area is multiplied by 2>

Length x Width=[tex](x+6)(x+12) = 2x(x+6)[/tex]

x+12=2x

x=12 feet

so, original width = 12 feet

original length = 18 feet

Learn more about Area from the ink below

https://brainly.com/question/27683633

#SPJ1

Answer:

9.37

Step-by-step explanation:

twelve surgeons

112.44 / 12 = 9.37

Answer:

$9.37

Step-by-step explanation:

112.44 ÷ 12

Answer:

m< 2= 48°

Step-by-step explanation:

Complementary angles sum up to 90 degrees

We know that m< 1 = 42°

All we have to do is subtract 90 from 42 to find m< 2:

m< 2= 90 - 42

m< 2= 48°

Hope this answers your question :)

How to find the vertex?

The general form of an absolute value function:

Given function is:

Its vertex is (- 3, - 2), this is our first point to plot, point A.

How to find x-intercepts?

Set y = 0 and solve for x:

So the x-intercepts are ( - 5, 0) and (- 2, 0), points B and C.

Connect the vertex (- 3, - 2) with points ( - 5, 0) and (- 2, 0) and here is your graph.

Answer:

x = y/3 + 4/3

Step-by-step explanation:

Solve for x:

y = 3 x - 4

y = 3 x - 4 is equivalent to 3 x - 4 = y:

3 x - 4 = y

Add 4 to both sides:

3 x = y + 4

Divide both sides by 3:

Answer: x = y/3 + 4/3

Answer:

2nd one is the best division

The expressions equivalent to 4^10​ are 2^20, 4^4 . 4^6, and  4^4 / 4^-6. Option B, option C, and option E are correct.

Some laws of exponents are:

We need to find all the expressions equivalent to 4^10​.

We will use laws of exponents for all the options one by one.

Option A:

2^5 . 2^2 = 2^(5 + 2) = 2^7

This is not equivalent to 4^10​.

Option B:

2^10 = 2^(2 * 10) = (2^2)^10 = 4^10

This is equivalent to 4^10​.

Option C:

4^4 . 4^6 = 4^(4 + 6) = 4^10

This is equivalent to 4^10​.

Option D:

4^7 . 4^-3 = 4^(7 + (-3)) = 4^4

This is not equivalent to 4^10​.

Option E:

4^4 / 4^-6 = 4^(4 - (-6)) = 4^10

This is equivalent to 4^10​.

So, 2^20, 4^4 . 4^6, and  4^4 / 4^-6 are equivalent to 4^10​.

So, option B, option C, and option E are correct.

Thus, the expressions equivalent to 4^10​ are 2^20, 4^4 . 4^6, and  4^4 / 4^-6. Option B, option C, and option E are correct.

To learn more about laws of exponent visit:

brainly.com/question/28966438

#SPJ1

The two expressions equivalent to v are:

Here we have the equation:

5*(3a - 1) - 2*(3a + 2) = 3*(a + 2) + v

And we want to find expressions equivalent to v, so to do that, we just need to isolate the variable v in one side of the equation, if we subtract:

3*(a + 2) in both sides we will get:

5*(3a - 1) - 2*(3a + 2) = 3*(a + 2) + v

5*(3a - 1) - 2*(3a + 2) - 3*(a + 2) = v

That is one of the equivalent expressions, to get the other, we can just simplify the left side.

5*(3a - 1) - 2*(3a + 2) - 3*(a + 2) = v

15a - 5 - 6a - 4 - 3a - 6 = v

Now we can group like terms:

15a - 6a - 3a - 5 - 4 - 6

6a - 15 = v

That is the other equivalent expression to v.

Learn more about equivalent expressions:

https://brainly.com/question/2972832

#SPJ1

For the gross pay of $238.61 and given deduction Anita's net pay is equal to $181.59 at the rate of $9.45 per hour and she works for 25.25 hours.

When Anita works for 31 hours with the given conditions her gross pay and net pay is equal to $292.95 and $235.93 respectively.

As given in the question,

a. Anita get pay per hour = $9.45

Gross pay received by Anita = $238.61

Deductions :

Federal tax = $28.63

Society tax : $14.79

Medicare : $3.46

State tax : $10.14

Total deduction = $ ( 28.63 + 14.79 + 3.46 + 10.14 )

                          = $57.02

Net pay = Gross pay - total deduction

             = $ ( 238.61 - 57.02 )

             = $ 181.59

Let us consider Anita works for 'h' hours at the rate of $9.45,

9.45h = 238.61

⇒ h = 238.61/ 9.45

⇒ h = 25.25 hours

b. When Anita works for 31 hours

Her gross pay = 31 × 9.45

                       = $ 292.95

Deductions are same

Net pay = $ ( 292.95 - 57.02 )

            = $ 235.93

Therefore, for the gross pay of $238.61 and given deduction Anita's net pay is equal to $181.59 at the rate of $9.45 per hour and she works for 25.25 hours.

When Anita works for 31 hours with the given conditions her gross pay and net pay is equal to $292.95 and $235.93 respectively.

Learn more about gross pay here

brainly.com/question/13143081

#SPJ1

x=-3.645 and x=1.645 is the solution for the given inequality.

A quadratic equation is a second-order polynomial equation in a single variable x , ax2+bx+c=0. with a ≠ 0 .

The given inequality is

y<x²+2x-6

a=1, b=2, c=-6

x=-b±√b²-4ac/2a

=-2±√2²-4(1)(-6)/2(1)

=-2±√4+24/2=

=-2±√28/2=

=-2+√28/2

=-2+5.29/2

=1.645

and -2-5.29/2

x=-3.645

Hence x=-3.645 and x=1.645 is the solution for the given inequality.

To learn more on Quadratic equation click:

https://brainly.com/question/17177510

#SPJ1

According to the trignonmentry of half angles, the value of sin(x/2) is  √(1-5/6)/2, cos(x/2) is √(1+5/6)/2 and the value of tan(x/2) is √11/6/(√(1 + 5/6)

Trigonometry of half angles

Trigonometry of half-angle formula is used to determine the exact values of the trigonometric ratios of angles such as 15° that is half of the standard angle 30° and 22.5° that is the half of the standard angle 45 and so on. So if θ is an angle, then the half angle is represented by θ/2.

Given,

Here we need to find if cos(x)=5/6 , and x is in quadrant I, determine the exact value of each of the following.

sin(x/2), cos(x/2), tan(x/2).

According to the concepts in trigonometry,

We know that the following formulas.

=> sin(x/2) = √(1-cosx)/2

=> cos(x/2) = √(1+cosx)/2

=> tan( x/2)=sin x/1+cosx

Here we know that cos (x) = 5/6

Thus implies that 5 is the opposite and 6 is the hypotenuse, then the adjacent is

Therefore, we can calculate the value of the adjacent a as,

=> a = √(6²-5²)

=> a = √36-25

=> a= √11

Therefore the value of sin x= √11/6

So, the value of sin(x/2)= √(1 - 5/6)/2

And the value of cos(x/2)= √(1 + 5/6)/2

Finally, the value of tan(x/2)=√11/6/(√(1 + 5/6)

To know more about Trignonmentry of half angles here.

https://brainly.com/question/16946858

#SPJ1

The arrangement of the fraction from least to greatest is A. 5/8, 8/12, 3/4.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator, as well as the denominator, are both integers

The fraction can be changed to percentage to make it easier.

5/8 = 5/8 × 100 = 62.5%

8/12 = 8/12 × 100 = 66.7%

3/4 = 3/4 × 100 = 75%

The arrangement is 5/8, 8/12, 3/4.

Learn more about fractions on:

brainly.com/question/17220365

#SPJ1

Answer:

100

Step-by-step explanation:

.001*100=.1

Answer:

100 thousandths

Step-by-step explanation:

Answer:

  21/3100000 ≈ 1/147619

Step-by-step explanation:

You want the scale of a map on which 4.2 cm corresponds to an actual distance of 6.2 km.

The scale of a drawing is the ratio of drawing distance to actual distance. It can be expressed a couple of ways. We can write the given scale as ...

  4.2 cm : 6.2 km

or, we can reduce it to ...

  2.1 cm : 3.1 km

Often, we like to have a single unit of map distance in this ratio, which would make it be approximately ...

  1 cm : 1.47619 km

Another way to write the scale of a map is as a fraction.

  (4.2 cm)/(6.2 km) = (0.042 m)/(6200 m) = 21/3100000

When this is expressed as a unit fraction, the denominator is a repeating decimal with a 6-digit repeat. We can round it to ...

  ≈ 1/147619 . . . . map scale

The scale of the map is ...

  21/3100000 ≈ 1/147619   or   2.1 cm : 3.1 km   or   ≈ 1 cm : 1.47619 km

__

Additional comment

You may need to round the answer to match one of your answer choices.

<95141404393>

Answer:2 years

Step-by-step explanation:

Answer:

Step-by-step explanation:

the answer is 2 years

Rate Pratap can row in still water is 6.75 and Rate of current is 2.25

Step: 1

Let's y = speed of water and x = his speed of rowing in still water

Speed = Distance/Time (or)

Rate = Distance/Time

Step: 2

he row downstream in 2 hours

Rate in downstream = 18/2

Rate in downstream = 9

i.e.

x + y = 9

x = 9 - y ---(i)

Now, time taken by min to row in upstream = 4 hours

Rate in upstream = Distance/Time = 18/4

Rate in upstream = 4.5

i.e., x-y = 4.5 ---(ii)

Putting the value of x from equation (i) in equation(ii)

9 - y - y = 4.5

9 - 2y = 4.5

9 - 4.5 = 2y

y = 4.5/2

y = 2.25

Putting the value of y in equation (ii)

x - 2.25 = 4.5

x = 4.5 + 2.25

x = 6.75

x = Rate Pratap can row in still water = 6.75

y = Rate of current = 2.25

To know more about Speed check below link:

https://brainly.com/question/13943409

#SPJ1

t = d/220 is the equation that shows how many hours (t) a trip takes in terms of the trip's distance (d).

Speed is calculated as follows: speed = distance/time. Calculating the units for speed requires knowledge of the units for both time and distance. Since the distance is measured in meters (m) and the time is recorded in seconds, the units in this example will be meters per second (m/s) (s).

Let the distance be d and the time is t.

The given speed of the train = 220km/hr

Time = d/speed

t = d/220

This is the equation that shows how many hours (t) a trip takes in terms of the trip's distance (d).

To know more about the relationship between distance, speed, and time, visit:

https://brainly.com/question/28715393

#SPJ1

Answer:  t=220/b

Step-by-step explanation: Khan Academy said so

The y-intercept of the line is y = 2

What is an intercept?

A line's x-intercept and y-intercept are the points at which the x- and y-axes, respectively, are crossed.

Here,

A linear function has the following equation:

y = mx + b

Where m is the slope and b is the y-intercept, which is the value of y when x = 0.

We have given three points:

(-28, -54)

(-21, -40)

(-14, -26)

We use two of them to construct a system, to find values for m and b.

(-28, -54)

This means that when x = - 28 , y = - 54

so, y = mx + b

- 54 = - 28m + b

28m = b + 54

m = (b + 54)/28

Now, we have x = -21, y = -40

so, y = mx + b

- 40 = - 21m + b

we put the value of m here

- 40 = - 21 {(b + 54)/28} + b  we get,

7b - 1134 = - 40 × 28

b = 2

Hence, the y-intercept of the line is y = 2

To learn more about the intercept from the given link

https://brainly.com/question/24990033

#SPJ1

Answer:

(0,2)

Step-by-step explanation:

khan academy

The correct statement regarding the critical value of the t-distribution is given as follows:

a) [tex]t_{\frac{\alpha}{2}} = 1.6753[/tex]

What defines which distribution should be used is whether the population standard deviation is known, as follows:

As stated in the problem, the population standard deviation is not known, hence the t-distribution is used, as the sample standard deviation can be calculated from the histogram.

The critical value is obtained using a t-distribution calculator, considering that:

Hence it is given as follows:

More can be learned about the t-distribubion at https://brainly.com/question/17073112

#SPJ1

The balance on the loan after a month is $623389.25.

The following can be deduced from the information given:

Principal = $250000

Time = 25

Rate = 6%

Interest = (Principal × Rate × Time) / 100

Interest = (250000 × 6 × 25) / 100

Interest = $375000

The total amount will be:

= Principal + Interest

= $250000 + $375000

= $625000

The balance of the loan will be:

= Amount - One month payment

= $625000 - $1,610.75

= $623389.25

Learn more about interest on:

brainly.com/question/25793394

#SPJ1

Answer:

Step-by-step explanation:

so if it takes 42 days and 44 days just add them up

42 plus 42 = 82 plus 42=124 plus 42= 166plus 42= 208 plus 42 = 250 plus 42 = 292 plus 42= 334 plus 42= 376 plus 42=418

44 plus 44= 88 plus 44=132 plus 44=176 plus 44 = 220 plus 44= 274 plus 44= 318 plus 44= 362 plus 44=406 plus 44= 450 plus

just keep going

Answer:

r = 20/7

x = 13.5

Step-by-step explanation:

Hello!

Solve for r by cross-multiplying:

The value of r is 20/7.

Solve for x by cross-multipying:

The value of x is 13.5.

Answer:

Step-by-step explanation:

7) r/2 = 10/7, value of r?

→ r/2 = 10/7

→ r = (10/7) × 2

→ r = (10 × 2)/7

→ [ r = 20/7 ]

Hence, value of r is 20/7.

8) 9/4 = x/6, value of x?

→ 9/4 = x/6

→ x/6 = 9/4

→ x = (9/4) × 6

→ x = (9 × 6)/4

→ x = 54/4

→ [ x = 27/2 ]

Hence, value of x is 27/2.