What are the 3 possible solutions when solving a system of equations?

Answer:

[tex]1)2 ~real ~ solutions[/tex]

[tex]2) 0 ~ real ~solutions[/tex]

[tex]3) 1~real ~solutions[/tex]

Step-by-step explanation:.

[tex]1) x^2+y^2=17[/tex]

[tex]y=-1/2x[/tex]

[tex]x^2+1/4x^2=17[/tex]

[tex]4x^2+x^2=68[/tex]

[tex]5x^2=68[/tex]

[tex]x^2=68[/tex]

[tex]x=[/tex] ± [tex]\sqrt{68/5}[/tex]

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

[tex]2) y=x^2-7x+10[/tex]

[tex]y=-6x+5[/tex]

[tex]-6x+5=x2-7x+10[/tex]

[tex]x^2-x+5=0[/tex]

[tex]a=1[/tex]

[tex]b=-1[/tex]

[tex]c=5[/tex]

[tex]D=b^2-4ac[/tex]

[tex]=1-20[/tex]

[tex]=-19[/tex]

[tex]\sqrt{0} =\sqrt{-19}[/tex]

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

[tex]3) y=-2x^2+19[/tex]

[tex]8x-y=-17[/tex]

[tex]8x+2x^2-9=-17[/tex]

[tex]8x+2x^2+8=0[/tex]

[tex]4x+x^2+4=0[/tex]

[tex]x^2+4x+4=0[/tex]

[tex]x^2+2x+2x+4=0[/tex]

[tex]x(x+2)+2(x+2)=0[/tex]

[tex](x+2)(x+2)^2=0[/tex]

[tex](x+2)^2=0[/tex]

[tex]x=-2[/tex]

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

hope it helps...

have a great day!!!

Answer:

65

Step-by-step explanation:

20% is 1/5 of 100.

multiply 13 by 5 to get the original amount of numbers. you can proof check it by doing

13/65 which is 0.2. multiply the decimal by 100 and you get 20. which is 20%

Answer:

The area is the square unit.

Let the scale factor is k.

The unit circle has area of π.

Similar circle is k times the unit circle.

The ratio of areas is the square of the scale factor:

If the scale factor is r, then the area of the circle with radius of r is:

Since A₁ = π, the area of A₂ is:

Answer:

c. infinitely many solutions

Step-by-step explanation:

hope this helps :)

The range of possible perimeters of the square=10.583

Area of a rectangle (A) is the product of its length (l) and width (w).

A= l. w

here, we have,

A rectangle has a perimeter of 16 centimeters.

The lengths of the sides of the rectangle are between 1 centimeter and 7 centimeters.

let, x represents the length of a side of the rectangle,

then the rectangle's area is represented by x(8-x) square centimeters.

i.e. area of square = 8x-x^2

the side = √x(8-x)

perimeter= 4×√x(8-x)

Hence, the range of possible perimeters of the square=10.583

To learn more on Area click:

brainly.com/question/20693059

#SPJ2

Answer:

Answer c 1,800

Step-by-step explanation:

The total interest at the rate of 4.5% interest of the amount of $8000 will be $1800 hence option (C) will be correct.

Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time.

Simple interest has a constant principal amount, as opposed to compound interest, which multiplies the interest from the principal of previous years to calculate the interest of the subsequent year.

Given that

Principle amount (P) = $8000

Rate of interest (R) = 4.5%

Time period (T) = 5 years.

The interest in the T time period has been given by

Total interest = PRT/100

So,

Total interest  = 8000×4.5×5/100  = 1800

So total interest of the given amount will be $1800.

For more about simple interests,

https://brainly.com/question/25845758

#SPJ2

Answer:

I got 126.12 in my notes

Step-by-step explanation:

Answer:

Step-by-step explanation:

1436 is the answer

Answer: 1271

Step-by-step explanation:

620 + (105% × 620) =

620 + 105% × 620 =

(1 + 105%) × 620 =

(100% + 105%) × 620 =

205% × 620 =

205 ÷ 100 × 620 =

205 × 620 ÷ 100 =

127,100 ÷ 100 =

1,271

Answer:

14π

Step-by-step explanation:

Area πr^2= 49π sq cm

so r= 7 cm

perimeter= 2πr= 14π

The cheapest way of buying exactly 7 litres with no extra is buying 500 ml bottle for £1.40

The amount of buying 7 litres of orange juice at the cheapest buy is £2.52

500 ml bottle for £1.40

Convert ml to liters:

500 ml = 0.5 liters

Unit rate = 0.5/1.40

= £0.36 per liter

2 litre carton for £2.50

Unit rate = 2/2.50

= £0.8 per liter

2 cartons for £4.50

Unit rate = 2/4.50

= $0.44 per carton

3 litre carton for £3.50

Unit rate = 3 / 3.50

= £0.86 per liter

The cheapest buy per liter of the orange juice is buying 500 ml bottle for £1.40.

Therefore, the cost of 7 liters at the cheapest buy

= £0.36 per liter × 7

= £2.52

Read more unit rate:

https://brainly.com/question/19493296

#SPJ1

eat a peppermint it will stimulate your small brain

0.7n+0.8n=2.1

1.5n=2.1

n=1.4

Therefore, the answer is B.

Answer:

B). n = 1.40

Step-by-step explanation:

0.7n + 0.8n = 2.1

(0.7n + 0.8n) = 2.1

1.5n = 2.1

/1.5 /1.5

n = 1.40

hope this helped!

Answer:

A. 83 is the correct option.

Step-by-step explanation:

all angles of a triangle are always equal to 180.

46 + 51 + y = 180

97 + y = 180

180 - 97 = 83

Have a nice day! :-)

Answer: 6 1/10

Step-by-step explanation:

After diving the polynomials, the quotient and remainder is q(x)=-x^2+1 and r(x)=-1 respectively.

What are polynomials?

The word "polynomial" is derived from the Greek words "poly" and "nominal," which combined translate to "many phrases." There is no limit to the number of terms that can exist in a polynomial.

The polynomials are -

a(x)=-x^4

b(x)=x^2+1

Divide a(x) by b(x).

-x^4/x^2+1 = -x^2+1 with remainder as -1.

The quotient is obtained as q(x)=-x^2+1 and the remainder is r(x)=-1.

The given equation is -

a(x)/b(x)=q(x)+[r(x)/b(x)]

Plugging in all the values -

-x^4/x^2+1=-x^2+1+[-1/x^2+1]

[-x^4/x^2+1]-[-1/x^2+1]=-x^2-1

-x^4+1/x^2+1=-x^2-1

-x^4+1=[-x^2+1][x^2+1]

-x^4+1=(-x)^2[x^2+1]+(1)[x^2+1]

-x^4+1=-x^4-x^2+x^2+1

-x^4+1=-x^4-1

So, LHS=RHS is proved using the equation.

Therefore, the quotient is q(x)=-x^2+1 and the remainder is r(x)=-1.

To learn more about polynomials from the given link

https://brainly.com/question/4142886

#SPJ1

Answer:

3

Step-by-step explanation:

Answer:

i belive those are the ones that are under 90 persent

Step-by-step explanation:

Answer:

the answer should be 3/4

The ratio of the length of arc BC to length of arc DE is calculated as: 1/2.

Length of an arc = ∅r, where r is radius, and ∅ is angle measure in radians.

AD = 2/3AB

Length of DE:

∅ = 1.18 + 2.36 = 3.54 radians

r = 2/3AB

Length of arc DE = (3.54)(2/3AB) = 2.36(AB)

Length of BC:

∅ = 1.18 radians

r = AB

Length of arc BC = (1.18)(AB) = 1.18(AB)

Ratio of the length of BC to DE = 1.18(AB) / 2.36(AB) = 1.18/2.36 = 1/2

Learn more about Length of arc on:

https://brainly.com/question/2005046

#SPJ2

By unitary method 24 students/(64/9) yards squared times 1600 yards squared equals 5400 students.

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

Students traverse a total area of 40 yards by 40 yards, or 1600 yards.

24 kids covered an area of 8 ft x 8 ft, or (8 ft x 1 yd/3 ft)2 = [(8/3) yard]2 = (64/9) yd.

The number of students present is calculated by multiplying the number of students per yard, or 24 students/(64/9) yd2, by the area that students cover.

Therefore: 24 students/(64/9) yards squared times 1600 yards squared equals 5400 students.

To know more about unitary method  visit:

https://brainly.com/question/28276953

#SPJ4

Answer:

There are three ways to solve systems of linear equations: substitution, elimination, and graphing.

Answer:

Step-by-step explanation:

2/8 = 1/4

2/8 = 200/800

and so on.

There are an infinite number of possibilities here.

Answer:

1/4

Step-by-step explanation:

2/8 can be simplified to 1/4

2/8 divided by 2/2 = 1/4

but there are also many other ways

10/40,6/24, etc

Answer:

34 pounds

Step-by-step explanation:

51 pounds of plum = 27 quarts

x pounds of plum   = 18 quarts

(cross multiply)

27x = 918

divide both sides by 27

x=34 pounds

An acute triangle is a triangle with all angles measuring less than 90°.

To solve an acute triangle using trigonometry, we need to know the length of at least one side and at least one angle of the triangle.

For example, let's assume the triangle has side lengths a = 6, b = 8, and we know the angle A = 30°.

First, we can use the Law of Cosines to calculate the length of the third side, c:

c² = a² + b² - 2abcos(A)

c² = 6² + 8² - 2(6)(8)cos(30°)

c² = 64 - 96cos(30°)

c² = 64 - 48

c² = 16

c = 4

Now we can calculate the other two angles, B and C, using the Law of Sines:

sin(B) = sin(A) * c/a

sin(B) = sin(30°) * 4/6

sin(B) = 0.5 * 2/3

sin(B) = 0.3333

B ≈ 19.47°

sin(C) = sin(A) * c/b

sin(C) = sin(30°) * 4/8

sin(C) = 0.5 * 0.5

sin(C) = 0.25

C ≈ 14.04°

Therefore, the three angles of the triangle are A = 30°, B = 19.47°, and C = 14.04°, and the three sides are a = 6, b = 8, and c = 4.

Learn more about acute trianglehere:

https://brainly.com/question/16663764

#SPJ4

Answer:

it might be 2.6

Step-by-step explanation:

im assuming the 16.3 is the circumfrence, so if you follow the formula for circumfrence (2πr) the radius would be 2.6. hope this is correct

The radius r of the circle is 4.4 yd .

A circular sector, also known as circle sector or disk sector, is the portion of a disk enclosed by two radii and an arc, where the smaller area is known as the minor sector and the larger being the major sector.

For a circle, the arc length formula is θ times the radius of a circle.

 Arc Length = 2 π r (θ/360°)  

where,

r = radius of circle

θ = angle of Sector

According to the question

Arc Length of circle = 16.3 yd

Angle of sector= 240°

By using arc length formula

Arc Length = 2 π r (θ/360°)  

substituting the value

16.3 = 2π r (240°/360°)

16.3 = 2π r * [tex]\frac{2}{3}[/tex]

16.3 * 3 = 4π r

54.9 = 4π r

As π = [tex]\frac{22}{7}[/tex]

54.9 = 4 *  [tex]\frac{22}{7}[/tex] r

54.9 * 7 = 88 r

384.3 = 88 r

r = 4.4 yd

Hence, The radius r of the circle is 4.4 yd .

To know more about  sector of circle and  length of arc here:

https://brainly.com/question/2571307

#SPJ2

Answer: 4

Step-by-step explanation:

35.2/ 8.8= 4

4

Answer:

40 min per period

Step-by-step explanation:

When it has 8 periods :

Total time = 45 min per period for 8 period

Total time = 45 × 8 min

When it has 9 periods : let each period be of x min

Total time = x min per period for 9 period

Total time = x × 9 min

As total time remains same,

45 × 8 = x × 9

5 x 8 = x

40 = x

On solving the provided question, we can say that - the value of x in triangle ABD is = 60

Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is the name given to a triangle with vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.

here, in triangle ABD

x = 60

as its acute angle

To know more about triangle visit:

https://brainly.com/question/2773823

#SPJ1

Answer:

A. The car spends 2.05 hours going 55 miles per hour

B. The car spends 1 hour going 35 miles per hour

C. The trip takes 3.6 hour

Step-by-step explanation:

The equation is

55x+35y=200

Let's solve A

We know the car spends 2.5 hours going 35 miles per hour on the trip, so we put 2.5 in for y and solve for x

55x+35(2.5) = 200

55x + 87.5 = 200

55x = 112.8

x = 2.05 hours going 55 miles per hour

So, the car spends 2.05 hours going 55 miles per hour

Let's solve B

55(3)+35y=200

165 + 35y = 200

35y = 35

y = 1 hour

So, the car spends 1 hour going 35 miles per hour

Let's solve C

We know the car spends no time going 35 miles per hour, so we put 0 in for y and solve for x

55x+35(0)=200

55x = 200

x = 3.6  hours

So, the trip takes 3.6 hour

Answer:

357.5cm^2

Step-by-step explanation: