The denominator of a rational number is greater than its numerator by 2. If 5
is subtracted from the numerator and 5 is added to its denominator, the new
number becomes 1
4
. Find the number.

The answers will be :

a. The equation of perpendicular bisector of QR is y = [tex]\frac{-5}{3}[/tex] x + 3.

b. The slope of median of triangle passing through point R is 1/4.

c. The slope of the altitude of the triangle that passes through point R doesn't exists.

What is slope of a line segment ?

Slope is the ratio of the difference in y-coordinates over the equivalent x-coordinates between two different locations on a line.

It is given that the vertices of a triangle are P(-6,1), Q(-2,-5) and R(8,1).

a.

The midpoint (M) of QR will be equal to

( [tex]\frac{-2 + 8}{2} , \frac{-5 + 1}{2}[/tex] )

or

M = (-3 , 2)

Now , slope of line QR will be ;

[tex]m_{QR}[/tex] = [tex]\frac{1+5}{8+2}[/tex]

[tex]m_{QR}[/tex] = 6 / 10

We know that :

m × [tex]m_{QR}[/tex] = -1

m = -10 / 6

or

m = -5 / 3

Equation of line will be given as :

y + 2 = [tex]\frac{-5}{3}[/tex] ( x - 3 )

y = [tex]\frac{-5}{3}[/tex] x + 3

b.

The midpoint of PQ will be :

= ([tex]\frac{-6 - 2}{2} , \frac{1 - 5}{2}[/tex])

= ( -4 , -2)

The slope of median of triangle that passes through point R will be ;

m = [tex]\frac{-2 - 1}{-4-8}[/tex]

m = -3 / -12

m = 1/4

or

m = 0.25

c.

Slope of altitude of triangle that passes through point Q will be :

m = [tex]\frac{1 - 1}{-6-8}[/tex]

m = 0 / -14

m = 0

The slope in this case doesn't exist.

Therefore the answers will be :

a. The equation of perpendicular bisector of QR is y = [tex]\frac{-5}{3}[/tex] x + 3.

b. The slope of median of triangle passing through point R is 1/4.

c. The slope of the altitude of the triangle that passes through point R doesn't exists.

Learn more about slope of line here :

https://brainly.com/question/1910006

#SPJ1

Answer:

n = (W - Z)/a

Step-by-step explanation:

W = an + Z

Rearrange the equation so that the subject is alone, in the format Ax = B

W = an + Z

W - Z = an + Z - Z

W - Z = an

Isolate the subject by dividing or multiple so that the equation is in the format x = C

W - Z = an

(W - Z)/a = an/a

(W - Z)/a = n

If you have applied for two jobs a and b and the probability that you get an offer for the job a is 0.25 and the probability of being offered job b is 0.20, then the probability that you will be offered both jobs is 0.05.

Probability is that branch of mathematics that deals with the numerical description of the possibility of an event to occur. The probability of any event is a number between 0 and 1 where 0 represents the impossibility of the event to occur while 1 represents certainty of that event to occur.

As the probability of the job a and job b are independent of each other, the probability that both jobs will be offered can be determined by using the formula;

P(A∩B) = P(A) × P(B)

Here, P(A∩B) represents the probability of both the events happening together

As P(A) = 0.25

P(B) = 0.20

P(A∩B) = 0.25 × 0.20

P(A∩B) = 0.05

Hence, the probability that both jobs will be offered is calculated to be 0.05.

To learn more about probability, click here:

https://brainly.com/question/251701

#SPJ4

Answer: .8 or 4/5

Step-by-step explanation:

You can do this a couple ways.

1) what you started is right, you can change your fraction into a decimal and divide.

2/5 = .4

.32/.4 = .8

2) you can change .32 into 32/100 and divide by 2/5

32/100 divided by 2/5

When you divide fractions, you flip the divisor and multiply

32/100 x 5/2

Multiply across

160/200

Simplify

4/5

The correct statements among given statements are statement C and E.

What is a rational number ?

If p & q are any two numbers where q is not equal to 0, then the fraction in form p/q is called as rational number.

A number is given which is √22.

√22 = 4.69041576

Let's check which of the statements are correct.

A.

√22 is not rational number as the number has non - terminating decimal value which is 4.69041576 and it doesn't lies between 10 and 12. So , this option is not correct.

B.

This option is also not correct as the value of √22 nearly equals 4.69 is and not greater than 4.691.

C.

The value of √22 is 4.69041576.

If we round off to the nearest hundredth , 9 is at the hundredth place , so the value will be 4.69. This is a correct option.

D.

√22 is not a rational number as the number has non - terminating decimal value which is 4.69041576 but it lies between 4 and 5. So , this option is not correct.

E.

The value of √22 is 4.69041576. We can observe that the decimal number doesn't repeat. So , this is a correct option.

F.

As we know √22 is not a rational number we can't represent it as fraction. This option is not correct.

Therefore , the correct statements among given statements are statement C and E.

Learn more about rational number here :

brainly.com/question/1387049

#SPJ1

Answer:

i THINK im not sure but i think its C please let me know if im wrong

Step-by-step explanation:

Expand using which formula? If it is using Sum/Difference Formulas, the expanded solution would be:

Solution:

[tex]z^3-17z^2+78z-54[/tex]

Hope this helps!

12 yards

Step-by-step explanation:

18 ÷ 6=3

3 × 3=12

12 yards lost after 18 minutes

The commutative property for addition just means the sum is the same no matter what order you add the terms. This property is also true for multiplication of real numbers.

If altering the operands' order has no effect on the outcome, the binary operation is commutative in mathematics. Numerous binary operations depend on it as a fundamental property, and numerous mathematical arguments.

A commutative property in mathematics states that if integer positions are switched around or combined while performing addition or multiplication operations, the result will remain the same.

According to the commutative property, the numbers we use can be moved around or swapped around without changing the solution. For addition and multiplication, the property is true, but not for division or subtraction.

Learn more about commutative property here

https://brainly.com/question/2475734

#SPJ9

According to the question, the given rational expression can be simplified and as shown below:

Rational expression = [tex]\frac{-5x^{3} y}{15xy^{3} }[/tex]

To simplify the given rational expression, calculate the factors of the numerator as well as denominator. And later divide it from each other. These expressions are also called as polynomial expressions.

Rational expression = [tex]\frac{-x^{2} }{3y^{2} }[/tex]

The final expression of the given equation is [tex]\frac{-x^{2} }{3y^{2} }[/tex] .

What is polynomial expression?

Polynomial expression are those equation whose highest degree is two. It is also called as quadratic equation. And it is simplified by performing the factors on the given expressions.

To learn more about the polynomial expression from the given link:

brainly.com/question/1280754

#SPJ4

If the expression is log₅ 25/x. then the expansion of this looks like

(log 25-log x)/ log 5.

Given that the expression is log₅ 25/x.

We are told to find the expanded value of the expression.

The change of base formula is used in writing a logarithm operation as a fraction of logarithms with a new base.

The expression is log₅ 25/x.

log₅ 25/x=log (25/x)/log 5

(We know that [tex]log_{a} b[/tex]=log b/ log a)

=(log 25-log x)/ log 5         (We know that log (u/v)=log u-log v)

Hence if the expression is log₅ 25/x. then the expansion of this looks like (log 25-log x)/ log 5.

Learn more about base change theorem at https://brainly.com/question/14998693

#SPJ4

Answer:

Step-by-step explanation:

The simplified expression of 6 -√25 + √4 is 3

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

6 -√25 + √4

Evaluate the exponents

So, we have

6 -√25 + √4 = 6 - 5 + 2

Evaluate the difference

So, we have

6 -√25 + √4 = 1 + 2

Evaluate the sum

So, we have

6 -√25 + √4 = 3

Hence, the simplified expression of 6 -√25 + √4 is 3

Read more about expression at

https://brainly.com/question/723406

#SPJ1

Answer:

Step-by-step explanation:

6-√√25= 0.25

-2-√15/2= A, -2.94

x=5+√-49/6= C, 5/6+7/6i

Answer:

Hey!  the breadth is 12 m and the length is 12+6=18 m

Mark me as brain?

Step-by-step explanation:

let the breadth be X metre

so the length will be 6+ x metre

perimeter is equal to 60 m

2(6+x+x)=60

2 (6+2x)=60

12+4x=60

4x=60-12=48

x=48/4=12

so

Answer:

-1,093

Step-by-step explanation:

-10,844 + 9751 = -1,093

It will take the painter more than 40 hours to paint all 20 rooms in stately wayne manor .

Time taken for the first 3 rooms =9hrs

Learning curve rate = 85%

Time taken for the next 20 rooms =?

Time taken for 1 room = 9hrs / 3 rooms = 3 hrs

If it takes 3 hrs to paint 1 room

Therefore, it will take x hrs to paint 20 rooms would take;

Hence, 20 rooms multiplied 3 hrs = 60 hours

It may take 60 hours to complete painting the 20 rooms.

At a learning curve rate of 85%, 15% will be the progress rate

Therefore, it will take additional 15% of 60 hours to paint the 20 room.

60+9(15% of 60) =69 hours

The painter would take more than 40 hours to paint the 20 rooms given his efficiency and learning curve rate.  The answer is derived by relating the data provided in the question to the desired answer.

To learn more about learning curve rate. Click, https://brainly.com/question/13265695

#SPJ4

The value of the expression ∛ - 7. ∛ 49 after multiplying it and simplifying it, we get the result as - 7.

We are given the expression:

∛ - 7. ∛ 49

We need to multiply and simplify it.

We will first multiply the expression:

= ∛ - 7 × 49

Solving it, we get that:

= ∛ - 343

Now this can also be written as:

= ∛ (- 7 )³

Now, simplifying the cube root to get the value of the expression:

= - 7

Therefore, we get that, the value of the expression ∛ - 7. ∛ 49 after multiplying it and simplifying it, we get the result as - 7.

Learn more about expression here:

https://brainly.com/question/723406

#SPJ4

Answer:

Step-by-step explanation:

Try the code AEAA. Let me know if its right or not.

Answer:

CHGD

Step-by-step explanation:

You should actually solve each of these puzzles to get the right code
1. To evaluate f(-2)

We have f(x) = x³ - 2x

Substitute -2 for x

==> (-2)³ - (2 x-2)
-2³ = -8
2 x -2 = -4

==> f(-2) = -8 - (-4)
==> f(-2) = -8 + 4      (two negatives make a positive
==> f(-2) = -4            Letter C

2. Evaluate g(-10)
[tex]g(x) = \dfrac{3x}{2}[/tex]

[tex]g(-10) = \dfrac{3 \times -10}{2} \\= \dfrac{-30}{2} \\\\= \boldsymbol{-15}[/tex]        Letter H

3. Evaluate h(-1)
h(x) = 2x² + x
h(1) = 2 x (-1)² - 1

= 2 x 1 - 1

= 1            Letter G

4. Evaluate f(3)
f(x) = x³ -2x
f(3) = 3³ - 2 x 3

= 27 - 6

= 21              Letter D

So the correct code is CHGD

You got everything right except the third :)

Answer:

f(-3) = -26

Step-by-step explanation:

f(n)=7n-5; f(-3)

f(-3) = 7(-3) - 5

f(-3) = -21 - 5

f(-3) = -26

I hope this helps!

Answer:Solution

Result will not divisible by 3

5

3

×2−8=250−8=242

If we divide 242 by 3 it will leave reminder 2.

Step-by-step explanation:

The equation is given by A = n³ - 8 , where n is a number

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the number be represented as n

A = 8 is subtracted from the cube of a number

Substituting the values in the equation , we get

A = n³ - 8   be equation (1)

Now , when 8 is subtracted from twice the cube of 5 , the result is not divisible by 3

So , A = 2 x 5³ - 8

A = 242 which is not divisible by 3

Hence, the equation is A = n³ - 8

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ2

Solution of exponential equation is , x =  [tex]800. 7^4[/tex]

In, mathematics a exponential equation or exponential function is inverse of logarithmic function. That means, we can easily convert the logarithmic function into exponential function and vice versa. The basic form of the logarithm function can be written as  [tex]a^x[/tex] .

where, a = the base of function

           x = main expression

Mathematically, if  [tex]log_aN = x[/tex] is an logarithmic function then, this can be converted to exponential function as  [tex]a^x = N[/tex].

There are many formulas that are given to us for solving several simple and complex problems based on exponential functions and exponential equations.

Some important formulas of exponential :

According to given statement,

[tex]7^{-4} x = 800[/tex]

=> [tex]\frac{1}{7^4} x = 800[/tex]

=> [tex]x = 800 . 7^4[/tex]

Thus solution for this equation is x =  [tex]800. 7^4[/tex]

To know more about exponential equations, visit :

brainly.com/question/28278137

#SPJ4

The complete question is :

What is the solution of each exponential equation? Check your answer.

a. 7⁻⁴x=800

b. 5.2³x=400

The function that models the inverse variation is y = -56/x.

So,

Then,

Since x · y = C then we obtain:

Therefore, the function that models the inverse variation is y = -56/x.

Know more about inverse variation here:

brainly.com/question/13998680

#SPJ4