What are formulas in maths?

PQ=11

PS^2+SR^2=QR^2

PS^2+PS^2=PQ^2

9514 1404 393

Answer:

  11 cm

Step-by-step explanation:

The law of cosines can be helpful here. In order to find PQ, we must know the cosine of the angle R. Fortunately, SOH CAH TOA reminds us it is ...

  Cos = Adjacent/Hypotenuse

  cos(R) = 10/14 = 5/7

__

The law of cosines gives us the relation ...

  PQ^2 = PR^2 +QR^2 -2·PR·QR·cos(R)

  PQ^2 = 15^2 +14^2 -2(15)(14)(5/7) = 121

  PQ = √121 = 11

The length of PQ is 11 cm.

_____

Alternate solution

This can be solved using the Pythagorean theorem twice.

  QS^2 = QR^2 -SR^2 = 14^2 -10^2 = 96

  PQ^2 = PS^2 +QS^2 = 5^2 +96 = 121

  PQ = √121 = 11

Answer:

y=5/2x+5

Step-by-step explanation:

Slope intercept form is y=mx+b

m is the slope, and b is the y intercept

FIrst we have to find the slope which is rise/run

Since our points are (-2,0) and (0,5) the equation will be:

5-0/0-(-2)

5/2

The slope is 5/2

Next we have to plug in 5/2 for m:

y=5/2x+b

We know that the y intercept is 5 from the coordinate (0,5)

y=5/2x+5

Answer:

y is  5/2 and x is 5

Step-by-step explanation:

i just know it already x3

Answer:

To find the x-intercept, simply plug in the value y = 0 into your equation and then solve for x. To find the y-intercept, plug in x = 0 and solve for y.

The 25 points determine a total of 2300 triangles when no three points are collinear.

To determine the number of triangles that can be formed using 25 points in the plane, we can use the concept of combinations.

In general, for any given set of n points, the number of triangles that can be formed using these points is given by the formula:

Number of triangles = nC3 = n! / (3! * (n-3)!)

In this case, we have 25 points. Substituting n = 25 into the formula, we get:

Number of triangles = 25C3 = 25! / (3! * (25-3)!)

Simplifying the equation, we have:

Number of triangles = 25! / (3! * 22!)

Since 3! = 3 * 2 * 1 = 6, we can further simplify the equation:

Number of triangles = 25 * 24 * 23 / 6 = 2300

Therefore, the 25 points determine a total of 2300 triangles.

It's important to note that this calculation assumes that no three points are collinear, meaning that no three points lie on the same straight line.

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To find the height of the shuttle, we can use trigonometry and the concept of similar triangles. The height of the shuttle is approximately 468.675 meters.

Let's assume that the height of the shuttle is represented by 'h' meters. From the information given, we know that the distance between the camera and the launch pad is 750 meters, and the angle of elevation from the camera to the shuttle is 32 degrees.

Using trigonometry, we can set up the following equation:

tan(32°) = h / 750

To find the value of h, we can rearrange the equation:

h = tan(32°) * 750

Using a calculator, we can find the value of tan(32°) ≈ 0.6249.

Now we can calculate the height of the shuttle:

h ≈ 0.6249 * 750

h ≈ 468.675 meters

Therefore, the height of the shuttle is approximately 468.675 meters.

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The total gross salary for FICA taxes is $4896 with the tax rates 6.2% and 1.45%.

The amount you earn each month before taxes and other deductions is referred to as your monthly gross income. In other words, it's your annual salary divided by 12. It's only a simple metric to aid in budgeting and other routine financial computations.

Annual Salary Amount / Number of Pay Periods = Gross Pay.

Gross pay equals the number of hours worked in a pay period multiplied by the hourly rate (+ overtime hours multiplied by the hourly overtime rate).

Given,

Tax rate=6.2%

=64000(6.2/100)

=3968

And also given another tax rate is 1.45%

=64000(1.45/100)

=92.8

Total=3968+928

=$4896

Therefore, the total gross salary for FICA taxes is $4896.

The total gross salary for FICA taxes is $4896 with the tax rates 6.2% and 1.45%.

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Answer:

Step-by-step explanation:

(5x)² + ∛(x²+6)

Answer:

Log 5x^2 ( x^2 + 6) ^(1/3)

Step-by-step explanation:

Explanation shown in the attachment; this could have been further simplified using binomial expansion

Answer:

AC = 13.3

Make proportional relationship:

\(\dfrac{\text{AB}}{\text{AC}} =\dfrac{\text{AM}}{\text{AN}}\)

Insert values

\(\rightarrow\dfrac{10}{\text{AC}} =\dfrac{6}{8}\)

Cross multiply

\(\rightarrow \text{AC}=\dfrac{10(8)}{6}\)

Simplify

\(\rightarrow \text{AC}=13.3\)

Answer:

C

Step-by-step explanation:

Answer:

Given equations are,

5x+2y=−2        (1)

3x−5y=17.4      (2)

Multiply equation (1) by 5 and equation (2) by 2, we get,

5(5x+2y)=5×−2

∴25x+10y=−10          (3)

2(3x−5y)=2×17.4

∴6x−10y=34.8          (4)

Adding equations (3) and (4), we get,

31x=24.8

∴x=

31

24.8

​

Put this value in equation (1), we get,

5(

31

24.8

​

)+2y=−2

∴

31

124

​

+2y=−2

∴2y=−2−

31

124

​

∴2y=

31

−186

​

∴y=

31

−93

​

Step-by-step explanation:

\((x_1, y_1) = (6,-10),~~ (x_2, y_2) = (3,-13)\\\\\\\text{Slope,}~ m = \dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{-13 +10}{3 -6} =\dfrac{-3}{-3} =1\)

Answer:

B. 35

Step-by-step explanation:

The range of a set of numbers is the difference between the highest and lowest numbers in the set.

1. Find the highest and lowest numbers from the set. Arranging them from least to greatest can make this easier.

-15, -12, 6, 18, 20

The lowest number is -15 and the highest is 20.

2. Subtract these two numbers to find the range.

20 -- 15

Two minus signs like that make a positive, so it becomes an addition problem.

20 + 15 = 35

Answer is b.

I also think the right option is B)- 35

Answer:

2 > x or x < 2

Step-by-step explanation:

-1 + 6(-1 - 3x) > -39 - 2x

-1 - 6 - 18x > -39 - 2x

-7 - 18x > -39 - 2x

32 > 16x

2 > x or x < 2

the reason that x < 2 is because of the negative sign. I solved it so that x stays positive but if you solve the equation with x on the other side like -16x > -32 then when you divide by -16 it changes to x < 2

PLEASE RATE!!! I hope this helps!!

(I have verified my answer on an online calculator)

answer: the range is 41.

to find the range of this data set, we first need to find the minimum and maximum values - which are 59 and 100.

then we subtract the minimum from the maximum.

59 - 100 = 41.

Answer:

  x = 22

Step-by-step explanation:

Two chords are shown at the same distance from the center of the circle, each with its perpendicular bisector. Half the length of one chord is shown; the length of the other chord is wanted.

The length of a chord of a circle will depend on its distance from the center. Chords at the same distance have the same length.

The perpendicular bisector of a chord intersects the center of the circle. A segment drawn from the midpoint of a chord to the circle center will be perpendicular to the chord.

These facts allow us to conclude that the geometry of each of the chords shown is the same. Both segments from the center bisect the chord at right angles. Because those segments are the same length, the chords are the same length.

If the full length of the bottom chord is what is being indicated by x, then ...

  x = 2×11

  x = 22

There are 10730 students total as shown in the bottom right hand corner. So, the probability that the student receives aid and is a graduate is given by:

Round to the nearest percent is 17.5%

Answer: 17.5%

Answer:

There are a total of 10730 students and 1879 students who are graduates as well as receiving financial aid. So the probability would be

(1879/10730)*100 = 17.51%

Answer:

X = ( 40/11 )

Y = ( -58/11 )

Step-by-step explanation:

6x + 3y = 6

7x + 9y = -22

-------------------------

-3(6x + 3y = 6)

= -18x - 9y = -18

-------------------------

-18x - 9y = -18

7x + 9y = -22

-11x = -40

÷-11   ÷-11

x = ( 40/11 )

------------------------

6( 40/11 ) + 3y = 6

( 240/11 ) + 3y = 6

-( 240/11 )      -( 240/11 )

3y = ( -174/11 )

÷3          ÷3

y =  ( -58/11 )

---------------------------

I hope this helps!

Answer:

\(x=\frac{40}{11}\)
\(y=-\frac{58}{11}\)

Step-by-step explanation:          \(\left \{ {{6x+3y=6} \atop {7x+9y=-22}} \right.\)

Multiply both sides of the equation by a coefficient

\(\left \{ {{3\left(6x+3y\right)=6\times3} \atop {7x+9y=-22}} \right.\)

Apply the Distributive Property
\(\left \{ {{18x+9y=6\times3} \atop {7x+9y=-22}} \right.\)

Calculate the product or quotient

\(\left \{ {{18x+9y=18} \atop {7x+9y=-22}} \right.\)

Subtract the two equations
\(18x+9y-(7x+9y)=18-(-22)\)

Remove parentheses
\(18x+9y-7x-9y=18+22\)

Cancel one variable
\(18x-7x=18+22\)

Combine like terms
\(11x=18+22\)

Calculate the sum or difference
\(11x=40\)

Divide both sides of the equation by the coefficient of variable
\(x=\frac{40}{11}\)

Substitute into one of the equations
\(7\times\frac{40}{11}+9y=-22\)

Write as a single fraction
\(\frac{7\times40}{11}+9y=-22\)

Calculate the product or quotient
\(\frac{280}{11}+9y=-22\)

Multiply both sides of the equation by the common denominator
\(\frac{280\times11}{11}+9y\times11=-22\times11\)

Reduce the fractions
\(280+9y\times11=-22\times11\)

Multiply the monomials
\(280+99y=-22\times11\)

Calculate the product or quotient
\(280+99y=-242\)

Rearrange variables to the left side of the equation
\(99y=-242-280\)

Calculate the sum or difference
\(99y=-522\)

Divide both sides of the equation by the coefficient of variable
\(y=-\frac{522}{99}\)

Cross out the common factor
\(y=-\frac{58}{11}\)

The solution of the system is
\(\left \{ {{x=\frac{40}{11}} \atop {y=-\frac{58}{11}}} \right.\)

I hope this helps you

:)

Answer:

Solution given:

4x-16+2x+16=180{linear pair are supplementary]

6x=180

x=180/6

x=30

is a required answer.

Answer:

41 meters

Step-by-step explanation:

\(\frac{31}{64}\) = \(\frac{19.8}{x}\)

31x = (19.8)(64)

31x = 1267.2  Divide both sides by 31 and round

x = 41

In differentiation , qA = 13/5  , qB = 11/5 are  values of qA and qB maximize the revenue .

What does mathematics differentiation serve?

In mathematics, differentiation is used to compute rates of change. For instance, in mechanics, velocity is the amount at which a displacement changes over time.

                   The acceleration is the speed at which velocity is changing with respect to time.

R = 40qA + 50qB − 6qA2 − 9qB2 − 4qAqB

Let aA = x , qB = y

so,

 R= 40x + 50y - 6x² - 9y² - xy

Partially differentiate above equation with respect to x and y .

Rx = 40 - 12x - 4y

Ry = 50 - 18y - 4y

Set Rx = 0 and Ry = 0 solve x and y .

40 - 12x - 4y = 0

50 - 18y - 4x = 0

Solving above questions

 x = 13/5 , y = 11/5

therefore,

      qA = 13/5  , qB = 11/5

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Answer:

2/3

Step-by-step explanation:

10/15=2/3

The 10 is 2/3 part of 15 by dividing common factor that is 5.

What is simplest form ?

In mathematics, the simplest form is the fraction that has the smallest equivalent value.

Here, the given fraction is :

10/15 which when converting to smallest equivalent value by dividing common factor that is 5 :

10/15 = 2/3

Therefore, the 10 is 2/3 part of 15.

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Answer:

Step-by-step explanation:

1. multiplication property of equality.

2.division property of equality.

Answer:

900cm^3

Step-by-step explanation:

1 cm= 10 mm

x=300mm (criss cross)

1cm*300mm/10mm= 10mm*x/10mm

30cm=x

30cm=300mm

1m=100cm

0.2m=x

1m*x/1m=0.2m*100cm/1m

x=0.2*100cm

x=20cm

0.2m=20cm

l=15cm

w=30cm

h=20cm

v=l*w*h

v=15cm*30cm*20cm

v=450cm^2*20cm

v=900cm^3

Answer:

9000cm^3

Step-by-step explanation:

Width:300mm=30cm

Height:15cm=15cm

Depth:0.2m=20cm

V=DxWxH

V= 20x30x15

V=9000cm^3

Answer:

4, or it could be 8 but mostly 4

Step-by-step explanation:

The union of X and Y is {a,e,i,o,u}, the intersection of X and Z is {i,o} and the intersection of all the three is {o}.

The ordered pair is the pair of two numbers which represented in a manner that it provides a particular order.

In an order pair, the first term indicates the x-coordinate, while the second term indicate the y coordinates. The ordered pair are written in close bracket in the following way.

\((x,y)\)

The given set is U(a,e,i,o,u), in which,

\(X=(a,i,o)\\Y=(o,e,u)\\Z=(i,o,u)\)

For the union, write all the terms of  X and Y set.

\(X\cup Y=(a,e,i,o,u)\)

For the intersection, write all the common terms of  X and Z set.

\(X\cap Z=(i,o)\)

For the intersection, write all the common terms of  X , Y and Z set.

\(X\cap Y\cap Z=(o)\)

Hence, the union of X and Y is {a,e,i,o,u}, the intersection of X and Z is {i,o} and the intersection of all the three is {o}.

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Answer:

f(3) = 3 + 1 = 4

Step-by-step explanation:

Since 3 > 0, we need to focus on the part of the function where x > 0. So:

f(3) = 3 + 1 = 4.

Answer:

i dont know

Step-by-step explanation:

i believe this because i do not know the answer

Answer: x = √-6 - 4

Step-by-step explanation:

x^2+8x+22=0

(x+4)^2 - 16 + 22 = 0

(x+4)^2 + 6 = 0

(x+4)^2 = -6

√(x+4)^2 = √-6

x = √-6 - 4            

√6 = 2.449

The scale of the map is 1/10,000.

The formula used to find the formula to find the scale is

scale = length on the map / actual length

Given,

Actual length of the golf park = 2.5 km

length on map = 250 mm

Here, we need to convert both lengths into the same units

2.5 km = 2.5 x 1000 m/km x 1000 mm/m = 2,500,000 mm

we know that,

scale = length on the map / actual length

= 250 mm / 2,500,000 mm

= 1/10,000.

Therefore, the scale of the map is 1/10,000.

i.e, one unit on the map is equal to 10,000 units of length in reality.

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