How many equations are needed to solve for 1 unknown variable?

Answers

Answer 1

The number of equation/s that are needed in order to solve the problem is equal to the number of the varying variables involved. In this regard, we would say that to solve for 1 unknown variable, only 1 equation is needed.

For number of variables greater than 1, as stated above, the number of equations should be equal to that number. However, it has to be noted that the equations should be independent and not the multiplicative of another.

For the concept of multiplicity,

x + y = 0 and 2x + 2y = 0 are just the same equations.

Hence, the answer to this item is one (1).

Related Questions

how many different ways can an after school club of 13 students line up

Answers

13 x 13 = 169 different ways.

Answer: 6227020800

Step-by-step explanation:

A sequence has its first term equal to 8, and each term of the sequence is obtained by adding 6 to the previous term. If f(n) represents the nth term of the sequence, which of the following recursive functions best defines this sequence?

Answers

A recursive formula for an arithmetic sequence is:

a(n)=a(n-1)+d, where n=term number and d=common difference.

Since we are told that d=6:

a(n)=a(n-1)+6, a1=8

They may want:

f(n)=f(n-1)+6, a1=8

I never understood why they teach this instead of explicit formulas because the above is pretty useless if you simply want say the 1031st term, you would need to do a lot of calculations to find it. :P. The explicit function is:

a(n)=a+d(n-1), here a=8 and d=6 so

a(n)=8+6(n-1)

a(1031)=8+6(1031-1)=6188

Try finding the 1031st term with the recursive formula :D

Answer:

f(1) = 8 and f(n) = f(n − 1) + 6; n > 1

Jorani flips two standard american quarters. how many ways can she get at least one head?

Answers

at least means 1 or more head

she can get

1 head 1 tail
1 tail 1 head
2 tails
2 heads

3 of the ways has at least 1 head

3 ways

5. Given the following triangle side lengths, identify the triangle as acute, right or obtuse. Show your work. a. 3in, 4in, 5 in b. 5in, 6in, 7in c. 8in, 9in, 12in

Answers

although you can draw them out to see, a and c are Pythagorean triples so they are right angled. for B you might have to draw it

The triangle with measures 3 in., 4 in. and 5 in. made up right angle triangle.

What is a triangle?

A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle. The sum of all three angles of the triangle is equal to 180 degrees.

a) Given that, 3 in., 4 in. and 5 in.

By using Pythagoras theorem, we get

5²=3²+4²

25=9+16

25=25

So, the triangle is right triangle.

b) The given sides of triangle measures 5 in., 6 in. and 7 in.

To determine whether the triangle is acute, right, or obtuse, add the squares of the two smaller sides, and compare the sum to the square of the largest side.

7²<5²+6²

49<25+36

49<61

So, the triangle is acute angle triangle.

c) The given sides of triangle measures 8 in., 9 in. and 12 in.

12²>8²+9²

144>64+81

144>125

So, the triangle is obtuse angle triangle.

Therefore, the triangle with measures 3 in., 4 in. and 5 in. made up right angle triangle.

Learn more about the triangle here:

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The following is a geometric sequence.
1, 2, 6, 24

TRUE

FALSE

Answers

The answer is false

Of course answer is false

Analyze the diagram below and complete the instructions that follow.

2004-04-02-05-00_files/i0370000.jpg

Find the area of triangle QRS. Round the answer to the nearest tenth.

A.
19.4 square units
B.
91.2 square units
C.
1,040.5 square units
D.
1,052.4 square unts

Answers

The extended version of the link given shows a triangle with sides of measurements equal to 13, 16, and 15 units.

Since we are given with the measurements of all sides, we use the Heron's formula.

A = sqrt ((s)(s - a)(s - b)(s - c))

where s is the semiperimeter and a, b, and c are the measures of the sides.

s = (a + b + c) /2
s = (13 + 15 + 16) / 2 = 22

Substituting this to the equation for the area,
A = sqrt ((22)(22 - 13)(22 - 15)(22 - 16))
A = 91.19 square units

Thus, the area is approximately equal to 91.2 square units. The answer is letter B.

What is the area of triangle PQR?

Answers

area = 1/2 bh = 1/2(86)(52) = 2236
answer
2236 square inches

Answer:

B. 2236square inches

Step-by-step explanation:

Formula for calculating the area of a triangle = 1/2 × base × height.

According to the triangle,

Base = QR = 86inches

Height = 52inches

Area of ∆PQR = 1/2 × 86 × 52

Area of ∆PQR = 43 × 52

Area of ∆PQR = 2236square inches

given that (-2,7) is on the graph of f(x), find the corresponding point for the function f(x+4)

Answers

it would be considered-5,7 6,8

Answer:

CORRECT ANSWER ON PLATO: -6,7

Step-by-step explanation:

someone answer and explain how to do this plz

Answers

area = 1/2 * height * base
Here height = 4 and base = 13

area = the height times the base divided by 2

13*4=52

52/2 = 26

area = 26 sq. units

Suppose your walking rate is 4 feet per second. write that in miles per hour

Answers

4 ft/sec X 3600 sec/hour = 14400 ft/hour

14400 ft/hour / 5280 ft/mile = 2.727 miles/hour

How do you write 12 hundreds

Answers

12 hundreds is 12 • 100
which equals to
1200
hope this helped!! xx

100 *12
Because it is 12 100s

The value of a $225,000 house increases at a rate of 3.5% each year. Use a graph to predict the value of the house in 8 years.
A) ≈ $276,582
B) ≈ $286,263
C) ≈ $306,652
D) ≈ $296,282

Answers

In order to determine the value of the rent after x years, we need to generate a function which would relate the value of the rent and the time in years. The rate by which the rent increases is said to be 3.5% per year. So, if we do it manually, we would have:

value of the rent = 225000 + 225000 (.035) + 225000 (.035)(.035) + ........

However, this is a tedious and long process since we need to continue until year 8. We need to simplify it to an expression. We do as follows:

value of the rent = 225000 + 225000 (.035) + 225000 (.035)(.035) + ........

We factor out the initial rent,

value of the rent = 225000 (1 + (.035) + (.035)(.035) + ........)

Then, we simplify the terms inside the first parentheses,

value of the rent = 225000 (1 + (.035))^x

where x is the number of years. We then substitute 8 to x to determine the value of the rent.

value of the rent = 225000 (1 + (.035))^8 = 296282.03

Solve for h: a = 1/2bh

h = A over 2b
h = A/b (1 /2)
h = 2Ab
h = 2A/b

Answers

The answer is: [tex]A=(1/2)bh 2A=2(1/2)bh 2A=bh (2A)/b=(bh)/b h=2A/b [/tex]

Two exterior angles of a triangle equal 100° and 150°. Find all the interior angles

Answers

180°-100°= 80° (angle 1)
180°-150°= 30° (angle 2)

180°-80°-30°= angle 3
angle 3 = 70°

∴ the interior angles are 80°, 30° and 70°

The angles of the triangle will be 70°, 30°, and 80°.

What is the triangle?

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

We know that the sum of the interior and the exterior angles is 180 degrees.

Two exterior angles of a triangle equal 100° and 150°.

The interior angle corresponding to the exterior angle of 100° will be

⇒ 180° - 100°

⇒ 80°

The interior angle corresponding to the exterior angle of 100° will be 80°.

The interior angle corresponding to the exterior angle of 150° will be

⇒ 180° - 150°

⇒ 30°

The interior angle corresponding to the exterior angle of 150° will be 30°.

Then the third angle of the triangle will be

⇒ 180° - 80° - 30°

⇒ 70°

The angles of the triangle will be 70°, 30°, and 80°.

More about the triangle link is given below.

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Two friends left school at the same time and drove in opposite directions. One friend averages 40 miles per hour and the other friend averages 35 miles per hour. when will they be 150 miles apart?

Answers

Therefore, the two friends will be 150 miles apart in 2 hours.

Answer:

The two friends will be 150 miles apart in 2 hours

Step-by-step explanation:

The two friends left the school at the same time and drove in opposite directions. One of them have a speed of 40 miles per hour while the other have a speed of 35 miles per hour .

The both of them are moving apart at the rate = 40 + 35 = 75 miles per hour

let

t = time at which they are 150 miles apart

speed = distance/time

time = distance/speed

time = 150/75

time = 2 hours

The two friends will be 150 miles apart in 2 hours

Find the degree of the polynomial and indicate whether the polynomial is a monomial binomial trinomial or none of these 10x4-3w3+7w+5y5-4

Answers

Degree: Highest exponent in your polynomial expression.
Therefore; degree =5
The polynomial has five "terms", therefore, is none of the above

Final answer:

The given polynomial 10x^4-3w^3+7w+5y^5-4 has a degree of 5 as the highest power of variable is 5. Also, it has five terms, hence it is neither a monomial, binomial nor trinomial.

Explanation:

The polynomial in question is 10x4-3w3+7w+5y5-4. The degree of a polynomial is determined by the highest power of the variable in the polynomial. Here, the highest powers are 4 (from 10x4) and 5 (from 5y5). Since 5 is larger than 4, the degree of the polynomial is 5.

Furthermore, the given polynomial has five terms, so it is not a monomial, binomial or trinomial. These terms refer to polynomials with one, two, or three terms respectively. Therefore, the given polynomial does not fall under any of these categories.

Learn more about Degree of Polynomial here:

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Which number produces irrational number when added to 0.5

Answers

square root of 3 and Pi

Answer with explanation:

The number in which we have to add a number to give irrational = 0.5

[tex]0.5=\frac{5}{10}\\\\=\frac{1}{2}[/tex]

is a Rational Number as the decimal expansion terminates or denominator contains the number in the form of [tex]2^n \text{or} 5^m \text{or} 2^n \times 5^m[/tex].

→Sum of two Rationals Can't be a Irrational Number.

→Sum of Rational And Irrational is Irrational.

So, if you add any Irrational number like √2,π,∛2 to , 0.5 , it will give an Irrational Number.

⇒0.5 +Irrational Number=Irrational Number

Find all the real zeros of the function.

Answers

For the expression as a whole to equal zero, any of the three terms could equal zero ie:

[tex]-2x=0[/tex] or [tex]x-2=0[/tex] or [tex]x^{2}-25=0[/tex]

We can find one zero by solving each in turn:

[tex]-2x=0[/tex]
[tex]x=0[/tex]

[tex]x-2=0[/tex]
[tex]x=2[/tex]

[tex]x^{2}-25=0[/tex]
[tex]x^{2}=25[/tex]
[tex]x=\sqrt{25}=5[/tex]

The zeros are 0,2 and 5.

To check, plug back into the original equation and verify that f(x)=0.

Algebraic expression for 5 times a number

Answers

it could be 5x, 5 being the digit, x being "a number"

Final answer:

The algebraic expression for 5 times a number is 5x.

Explanation:

The algebraic expression for 5 times a number is 5x.

The variable x represents the unknown number.

When you multiply 5 by any number, you can represent it as 5 times that number.

So, if the number is 10, the expression would be 5 times 10, which is equal to 50.

A barge that is used to transport bulk items is the shape of a rectangular prism and is 90 feet long, 35 feet wide, and 12 feet deep. If the barge can only be filled to a height of 75% of its depth, what volume of bulk items can the barge hold? ft3

Answers

Barge volume = 90 * 35 * 12 = 37 800 ft³

75% = 75/100 = 0.75

37 800 * 0.75 = 28 350 ft³ (barge can hold).

Final answer:

The barge can hold 28,350 cubic feet of bulk items when filled to 75% of its depth, calculated by using the volume formula for a rectangular prism.

Explanation:

To calculate the volume of bulk items the barge can hold, we first determine the maximum height to which it can be filled. This is 75% of the barge's depth. Therefore, the fill height is 75% of 12 feet, which equals:

0.75 × 12 ft = 9 ft.

The volume V that the barge can hold is given by the formula for the volume of a rectangular prism:

V = length × width × height

Substituting the given dimensions and the fill height into the formula, we get:

V = 90 ft × 35 ft × 9 ft = 28,350 ft³.

So, the barge can hold 28,350 cubic feet of bulk items when filled to 75% of its depth.

What is the perimeter of the nonagon below?

Answers

The correct answer is D. 94 units. You can find this answer by simply adding all of the values around the nonagon because the perimeter is the total distance around something.

Answer:

Step-by-step explanation:

Alright, lets get started.

The sides of nonagon are given as below :

So, the perimeter will be addition of these sides.

Hence he perimeter is = [tex]13+8+5+11+10+9+10+7+21 = 94[/tex]

Hence the perimeter is 94 units (D) : Answer

Hope it will help :)

Read the following statement: x + 6 = 6 + x. This statement demonstrates:

the substitution property.
the reflexive property.
the symmetric property.
the transitive property.

Answers

The reflexive property because the reflexive property states that anything is equal to itself, and x+6 is the same as 6+x

the reflexive property

one teaspoon equals 0.5 centimeters. how many liters equals 50 teaspoons? Round the answer to the nearest hundredth.

Answers

50 teaspoons would equal 50*0.5 = 25 centimeters

1 cm = 0.001 liter

25*0.001 = 0.025 liters

12.252525... is an example of a ___ decimal?

Answers

Repeating decimal, these should be expressed as rational numbers...

If x=12.25...

100x-x=1225.25...-12.25...

99x=1213

x=1213/99

x=12 25/99

HELP ME!!!! PLEASE!!!! Ughhh

Answers

A 12/5. Opposite/Adjacent

tan(α)= Opposite / Adjacent
Opposite =12
Adjacent = 5

tan(67°) = 12/5

Can someone help me please ? Thanks!

Answers

Use pythagorean theorem for all of them
a. 3, 4, 5
3^2+4^2?5^2
9+16?25
25=25
right

b. 5, 6, 7
5^2+6^2=7^2
25+36=49
61>49
acute

c. 64+81=144
145>144
acute

hope this helps!

I will give you the general approach and you can do the calculations by yourself.

Assume 3 vertices are a,b,c

if a^2 + b^2 < c^2 ->it's obtuse

a^2 + b^2 = c^2 ->it's right

a^2 + b^2 > c^2 ->it's acute

First one is right apparently, similar combination of right triangle include 6,8,10

NEED HELP!!!!
Which of the following types of statement cannot be used to explain the steps of a proof? Check all that apply.
1.Postulate
2.Theorem
3.Conjecture
4.Guess
Choose more then 1

Answers

Answer:

Please don't use the answer that was given ,,, the correct answer is GUESS and Conjecture

Step-by-step explanation:

Find the surface area of a hemisphere with a diameter of 26 cm. Round your answer to the nearest tenth.

Answers

The surface area of a sphere is [tex]4 \pi r^{2} [/tex].

Hence, the surface area of a hemisphere is half that, [tex]2 \pi r^{2} [/tex].

If the base is also included then the surface area will be [tex]3 \pi r^{2} [/tex].

Given,

Diameter = 26 cm

Therefore, Radius = [tex] \frac{26}{2} [/tex] = 13 cm

Thus,

Area = [tex]3 * \pi * 13^{2} = 3 * \pi * 169 = 507 \pi = [/tex] = 1592.8 [tex] cm^{2} [/tex] [approx.]

Choose the linear inequality that describes the graph. The gray area represents the shaded region

Answers

(0,3)(1,-2)
slope = (-2-3) / (1 - 0) = -5

y int is (0,3)

line is dashed, means no equal sign....shading above the line, means greater then

ur inequality is : y > -5x + 3

Answer:

y > -5x + 3

Step-by-step explanation:

?? Please help answer and solve, showing the steps you took

Answers

We apply the concept of calculus here. You can determine the minimum or maximum in here if you take the derivative of a function and equate it to zero. The solution is as follows:

n = 20t² - 20t +120
dn/dt = 0 = 40t - 20 + 0
40t - 20 = 0
40t = 20
t = 20/40
t = 1/2 or 0.5

Therefore, the number of bacteria would be minimal at 0.5°C.

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