Write a system of equations modeling the given conditions. Then solve the system by the substitution method and find the two numbers. The sum of two numbers is 71. One number is 27 more than the other. Find the numbers. D Let x be the smaller number and y be the larger number. Write an equation that represents the fact that the sum of the numbers is 71. =71 (Simplify your answer.)​

The missing side of a right triangle without using a calculator can be found by using the Pythagoras theorem .

What is Pythagoras Theorem ?

The Pythagoras Theorem states that the square of the hypotnuse (longest side) is equal to the sum of the square of the perpendicular and base .

that means : [tex]Hypotnuse^{2} = Perpendicular^{2} + Base^{2}[/tex]  ;

let the missing side of the right triangle  be the hypotnuse ;

So , missing side can written as :  [tex]Hypotnuse = \sqrt{Perpendicular^{2} + Base^{2}}[/tex] .

For Example : Let the right triangle has sides lengths as perpendicular = 6 and hypotnuse = 10

The length of side "base" is unknown.

So ,  to find length of side b, we put the known values into theorem:

[tex]10^{2} = 6^{2} + Base^{2}[/tex] ;

[tex]base^{2} = 100 - 36[/tex] ;

So , the missing side "base" = 8 ;

Therefore , the missing side without using calculator can be found by the Pythagoras Theorem .

The given question is incomplete , the complete question is

How do you find the missing side of a right triangle without a calculator when the other two sides are given ?

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Answer:

the modulus of a complex number z = a + bi is:

Izl= √(a²+b²)

The fact that n is complex does not mean that n doesn't has a real part, so we must write our numbers as:

m = 2 + 6i

n = a + bi

Im + nl = 3√10

√(a² + b²+ 2²+ 6²)= 3√10

√(a^2 + b^2 + 40) = 3√10

squaring both side

a²+b²+40 = 3^2*10 = 9*10 =90

a²+b²= 90 - 40

a²+b²=50

So,

|n|=√(a^2 + b^2) = √50

The modulus of n must be equal to the square root of 50.

now

values a and b such

a^2 + b^2 = 50.

for example, a = 5 and b = 5

5²+5²=25+25= 50

Then a possible value for n is:

n = 5+5i

Answer:

For the first line its distributive property
The 2nd is combining like terms

4th is simplifying it

Im not sure about the last one since its just the answer of the problem

Step-by-step explanation:

Answer:

477

Step-by-step explanation:

Answer:

half of 8 is 4

4^4 = 16

16 x 3.14 = 50.24 (area of a circle)

Now we multiply it by the height:

50.24 x 19 = 954.56 rounded to the nearest hundredths place is:

954.56 yd3 is your answer.

Answer:

A. 10 points

Step-by-step explanation:

The average test score for studying 3 hours is 75, while the average test score for studying 4 hours is 85. Therefore the average rate of increase of test scores between 3 and 4 hours studied is 10 points, since 85-75=10.

Oscar Wilde creates a hilarious tone by using puns, situational irony, dramatic irony, satire, and epigrams.

Oscar Fingal O'Flahertie Wills, an Irish poet, and playwright, lived from 16 October 1854 to 30 November 1900.

He wrote in a variety of genres throughout the 1880s before becoming one of London's most well-known playwrights in the early 1890s.

The Picture of Dorian Gray, his plays and epigrams, as well as the circumstances surrounding his meningitis-related early death at age 46 and criminal conviction for gross indecency for consensual homosexual activities in "one of the earliest celebrity trials," is what people will remember him for most.

Using puns, situational irony, dramatic irony, satire, and epigrams, Oscar Wilde establishes a humorous tone.

Therefore, Oscar Wilde creates a hilarious tone by using puns, situational irony, dramatic irony, satire, and epigrams.

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Answer:

B. 1

Because of the shape you can have only one line of symmetry

Answer:

Vertex (2, 3)

Axis of Symmetry: x = 2

Step-by-step explanation:

You can look at the labeling from my last answer, the parabola is just upside down but it is still the same label.

Hope it makes sense :)

Answer:

Axis of Symmetry:  x = 2

Vertex:  (2, 3)

Step-by-step explanation:

find axis of symmetry:  x = -b/2a

x = -8 ÷ 2(-2)

x = 2

find vertex by substituting 2 for 'x':

y = -2(2²) + 8(2) - 5

y = -8 + 16 - 5

y = 8 - 5

y = 3

Vertex:  (2, 3)

Answer:

12.9

Step-by-step explanation:

cos 72 = 4/x

x = 4/cos72

x = 12.9

Answer:

Name as a person

Step-by-step explanation:

Answer:

In the name of a person.

Step-by-step explanation:

The seasons are not written with capital letters unless they form part of a name. For example:

I am leaving in the winter.

I live near Winter Mountain River.

Answer:

1408 yards

Step-by-step explanation:

A horse walks 4224 feet in 12 minutes, so to find out how many yards the horse walks in twelve minutes, we need to convert 4224 feet to yards. Since there are 3 feet in a yard, we can divide 4224 by 3 to find the number of yards:

4224 feet / 3 feet/yard = 1408 yards

So a horse walks 1408 yards in 12 minutes.

Answer:

y-intercept is -9

Step-by-step explanation:

g(0) = -3(0)² - 5(0) - 9

g(0) = 0 - 9

g(0) = -9

The number of machine fed copies are 25 and the number of hand fed copies are 55. This is solved forming simultaneous equations.

What are simultaneous equations?

Two or more algebraic equations that share variables, such as x and y, are said to be simultaneous equations. Since the equations are solved simultaneously, they are known as simultaneous equations. These equations alone could have an infinite number of solutions.

Given cost per page of machine fed copies = $0.08

          cost per page of hand fed copies = $0.20

Let,

  number of machine fed copies = x

 number of hand fed copies = y

Given the total number of copies = 80

So we can write the equation as

  x + y = 80  ⇒   (1)

It is also given that the total cost of the movie script is $13

So we can the equation as

0.08x + 0.20y = 13 ⇒ (2)

Solving the simultaneous equations (1) and (2)

From (1),

x = 80 - y

Substituting the above in (2)

0.08(80 - y) + 0.20y = 13

0.12y = 6.6

y = 55

x = 80 - 55 = 25

Therefore the number of machine fed copies are 25 and the number of  hand fed copies are 55.

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Answer:

This equation involves three variables: a, b, and c. Each variable is multiplied by a coefficient and then added together to equal a constant. To solve the equation, we must first determine what the value of the three variables are. To do this, we must use the coefficients to isolate each variable. We can start by isolating c. Divide both sides of the equation by 4 to get 2a + 9b = c. Now we can isolate b by subtracting 2a from both sides to get 9b = c - 2a. Divide both sides by 9 to get b = (c - 2a)/9. Finally, we can isolate a by subtracting 9b from both sides to get 2a = 4c - 9b. Divide both sides by 2 to get a = (4c - 9b)/2. Once we have the values of the three variables, we can substitute them into the original equation to check our work.

Step-by-step explanation:

Answer:

a=\frac{4c-9b}{2}

The time taken for 21,000 spectators to vacate the stadium, if only 15 exits are functional is 28 minutes

A variation is a relation between a set of values of one variable and a set of values of other variables

Let E, N and T represent the number of exits, the number of spectators and the time taken to exit the stadium respectively

We can write the variation as:

T α N/E

T = kN/E  (where k is constant of proportionality)

when N = 25,000, E = 25, T = 20:

T = kN/E

k = TE/N

k = (20×25)/25000 = 0.02

when N = 21,000 and E = 15:

T = kN/E

T = (0.02×21,000)/15 = 28 minutes

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Apply arithmetic operations on both sides of the equation to move the variable to one side and all other values to the opposite side.

Let's begin with a basic equation: x + 2 = 7.

How may x be obtained on its own?

x + 2 - 2 = 7 - 2 x = 5 after deducting 2 from both sides.

Put the solution, x = 5, back into the equation to confirm it. We get 5 + 2= 7.

Since LHS = RHS

In the triangle, find x.

Use triangle properties or the Pythagorean theorem to find the value of x, the unknown side or angle in a triangle.

Let's use an example to better understand how to solve for x in a triangle.

Using the Pythagorean theorem, we obtain AC2 = AB2 + BC2 where x2 = 72 + 242 x = 49 + 576 x = 625 x = 25 units.

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Answer:

Answer:

1. A=bh/2

2. I don’t know, I‘m sorry :(((( but if I had to guess I’d pick A = s x s

3. A = πr² (might be wrong, i’m so sorry)

Step-by-step explanation:

1.  The formula for area of a triangle is A = bh/2

2. The formula for area of a square is s x s.

3. The formula for area of a circe is A = πr².

The formula used in getting the area of the shaded region is (1/2)bh, s * s and  πr²

An area is the amount of space occupied by a two dimensional shape or object.

1) The area of a triangle = (1/2) * base (b) * height (h) = (1/2)bh

2) Area of square = side (s) * side(s) = s * s

3) Area of circle = π * radius (r)²= πr²

The formula used in getting the area of the shaded region is (1/2)bh, s * s and  πr²

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Answer:

75 hope it helps you

thank you

Answer: To solve a division problem of the form a ÷ b = c, you need to find the value of c that makes the equation true. This means that if you multiply b by c, the result should be equal to a.

a) In the problem 3.2 ÷ 0.8 = ?, we are looking for the value of c that makes the equation true.

To solve this problem, we can multiply 0.8 by c to find the value of c that makes the equation true:

0.8 * c = 3.2

Dividing both sides of the equation by 0.8, we get:

c = 4

Therefore, the value of c that makes the equation 3.2 ÷ 0.8 = ? true is 4.

b) In the problem 7.5 ÷ 0.5 = ?, we are looking for the value of c that makes the equation true.

To solve this problem, we can multiply 0.5 by c to find the value of c that makes the equation true:

0.5 * c = 7.5

Dividing both sides of the equation by 0.5, we get:

c = 15

Therefore, the value of c that makes the equation 7.5 ÷ 0.5 = ? true is 15.

P.S. I don't need a brainliest, i am just happy that I am helping someone

Step-by-step explanation:

log 30+ log 6 is not equivalent to log 36

Equivalent expressions are expressions that perform the same function not with standing their appearance. If two algebraic expressions are equivalent, they have the same value when the same value(s) for the variable are used (s).

The original phrase is as follows

Log 36

Following that, we write the alternatives (a) log 2+ log 18

Apply the logarithmic rule log 2+ log 18 log (218)

Log 2 plus log 18 log (36)

Remove the bracket

Log 2 plus log 18 log36

(a) Log 2+ Log 18 is the same as log 36.

(b) Log 30 plus log 6

Use the logarithms’ law. 30 logs or more 6 logs (30 x 6)

Log 30 plus log 6 Equals log (180)

Remove the bracket

Log 30-plus log 6-log180

Hence,

(c) Log 30+log 6 does not equal log 36.

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Answer:

(-5, -1)

Step-by-step explanation:

Equation Form:

x = -5

y = -1

Answer:

Solve the System of Equations

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Point Form:

(−5,−1)

Equation Form:

x= −5, y= −1

Answer:

[tex]11 \: minutes = 99 \: gallons \\ 1 \: minute = (\frac{1 \times 99}{11} ) \: gallons \\ = 9 \: gallos \: per \: minute[/tex]

Answer:

graph 1= 3. graph 2= -3

Step-by-step explanation:

the y-intercept is where it cuts the line

therefore,

graph 1=3

graph 2=-3

Answer:

5 (x + 4)

Step-by-step explanation:

5x = 5 * x

20 = 5 * 4

5 is the only thing thye have in common, so we put 5 in front and add x + 4

5 (x + 4)

5(x+4) is the correct answer

Answer:

Step-by-step explanation:

a. we konw triangle have 180°

b. A straight line have 180°， so

∠abc=180-5x-12=168-5x,

∠bca=180-10x+37=217-10x

∠cab=180-9x-1=179-9x

then  add them all 564 - 24x = 180

c.384=24x, x=16

d.so ∠bca=217-10·16=57.

Answer:

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

Sum of exterior angles is 360°:

The exterior angle at vertex C is:

The ∠BCA is the linear pair with 123°:

Answer:

2

Step-by-step explanation: