Alvin’s first step in solving the given system of equations is to multiply the first equation by 2 and the second equation by –3. Which linear combination of Alvin’s system of equations reveals the number of solutions to the system?

9x + 4y = 36

6x + 2.5y = 24

Infinite solutions: 0x – 0y = 0
No solutions: 0x + 15.5y = 144
One solution: 0x + 0.5y = 0
Two solutions: 0x – 0.5y = 60

Answer:

1. about 11.18

2. about 8.66

Step-by-step explanation:

1. 5^2 + 10^2= 125

square root of 125 equals about 11.18

2. 10^2-5^2=75

square root of 75 equals about 8.66

Answer:

92

Step-by-step explanation:

180-88

Answer:

x=17

Step-by-step explanation:

These are alternate interior angles and alternate interior angles are equal when the lines are parallel

9x+23= 10x+6

Subtract 9x from each side

9x+23 -9x= 10x-9x+6

23 = x+6

Subtract 6 from each side

23-6 = x+6-6

17 =x

Answer:

=17x²-x

Step-by-step explanation:

=x.(9x²+18x-x-2)-x.(9x²-1)

=x.(9x²+17x-2-9x²+1)

=x.(17x-1)

=17x²-x

Step-by-step explanation:

Answer 1 to find the base to apply the Pythagoras theorem..of finding length..

Hypotenuse²= Base²+ Height²

So,

(H)²= (B)²+(H)²

12²= 8²+y²

144-64=y²

80=y²

√80= y

√2×2×2×2×5= y

2×2√5= y ( take one 2 from each pair)

4√5= y

hope it helps...

Answer:

4 sqrt(5); 41.0

Step-by-step explanation:

Question 7:

Using Pythagoras theorem:

y = sqrt(12^2 - 8^2)

y = sqrt(80)

y = 4 sqrt(5)

Question 8:

A = Area rectangle + Area circle

A = 2.4 × 4.4 + pi × 4.4^2 ÷ 2

A = 10.56 + 9.68 pi

A = 41.0

Step-by-step explanation:

we first find area of the whole shape outer core which is

we use the fomulae of a circle 22/7 represent pie

=1/2 *22/7*8,5

=13,36

then we find the inner core of the shape which is

1/2*22/7*5,5

=8,64

then we substracte to get the shaded part 13,36-8,64

=4,72cm

Answer:

≈ 16.5 cm²

Step-by-step explanation:

The area of the bar (A) is

(area of outer circle - area of inner circle) ÷ 2

r₂ = 8.5 ÷ 2 = 4.25 , r₁ = 5.5 ÷ 2 = 2.75 , then

A = (πr₂² - πr₁²) ÷ 2

   = (π(r₂² - r₁²) ) ÷ 2

   = (π(4.25² - 2.75²) ) ÷ 2

   = (π(18.0625 - 7.5625) ) ÷ 2

   = (10.5π)÷ 2

   ≈ 16.5 cm² ( to the nearest tenth )

Answer:

$445.20

Step-by-step explanation:

First, find his pay after the 5% raise:

400(1.05)

= 420

Find his pay after the 6% raise:

420(1.06)

= 445.2

So, his weekly pay is now $445.20

Answer:

The radius is 3.5cm

Step-by-step explanation:

Given

[tex]V = 192.5cm^3[/tex]

[tex]h = 5cm[/tex]

Required

The volume (V)

The volume of the vase is:

[tex]V = \pi r^2h[/tex]

So, we have:

[tex]192.5 = 22/7 * r^2 * 5[/tex]

Divide by 5

[tex]38.5 = 22/7 * r^2[/tex]

Multiply by 7/22

[tex]12.25= r^2[/tex]

Take positive square roots

[tex]r = 3.5[/tex]

Step-by-step explanation:

the number which has the highest value as8 is

6586.34

Answer:

x= 12  or x = -12

Step-by-step explanation:

|x| means take the positive value of x

|x| =12

We make two equations one positive and one negative

x= 12  or x = -12

Answer:

h = 3/8

Step-by-step explanation:

1/2(6h-4) = -5h+1

Distribute

3h -2 = -5h+1

Add 5h to each side

3h-2+5h = -5h+1+5h

8h-2 = 1

Add 2 to each side

8h-2 +2 = 1+2

8h = 3

Divide by 8

8h/8 = 3/8

h = 3/8

Answer:

x=2 is incorrect

Step-by-step explanation:

Y(2)=(3/4)*x^2=(3/4)*4=3

Answer:

Step-by-step explanation:

i. 5/12

ii. 1/8

iii. 11/24

iiii. 7/8

Answer:

(a): x is 3 and ky is -1

(b): k is -2

Step-by-step explanation:

Let: 3x + ky = 8 be equation (a)

x - 2 ky = 5 be equation (b)

Then multiply equation (a) by 2:

→ 6x + 2ky = 16, let it be equation (c)

Then equation (c) + equation (b):

[tex] { \sf{(6 + 1)x + (2 - 2)ky = (16 + 5)}} \\ { \sf{7x = 21}} \\ { \sf{x = 3}}[/tex]

Then ky :

[tex]{ \sf{2ky = 3 - 5}} \\ { \sf{ky = - 1}}[/tex]

[tex]{ \bf{y = \frac{1}{2} }} \\ { \sf{ky = - 1}} \\ { \sf{k = - 2}}[/tex]

Simultaneous equations are used to represent a system of related equations.

The value of k when [tex]y = \frac 12[/tex] is -2

Given that:

[tex]3x + ky = 8[/tex]

[tex]x - 2ky = 5[/tex]

[tex]y = \frac 12[/tex]

Substitute [tex]y = \frac 12[/tex] in both equations

[tex]3x + ky = 8[/tex]

[tex]3x + k \times \frac 12 = 8[/tex]

[tex]3x + \frac k2 = 8[/tex]

[tex]x - 2ky = 5[/tex]

[tex]x - 2k \times \frac 12 = 5[/tex]

[tex]x - k = 5[/tex]

Make x the subject in [tex]x - k = 5[/tex]

[tex]x = 5 + k[/tex]

Substitute [tex]x = 5 + k[/tex] in [tex]3x + \frac k2 = 8[/tex]

[tex]3(5 + k) + \frac k2 = 8[/tex]

Open bracket

[tex]15 + 3k + \frac k2 = 8[/tex]

Multiply through by 2

[tex]30 + 6k + k = 16[/tex]

[tex]30 + 7k = 16[/tex]

Collect like terms

[tex]7k = 16 - 30[/tex]

[tex]7k = - 14[/tex]

Divide both sides by 7

[tex]k = -2[/tex]

Hence, the value of constant k is -2.

Read more about simultaneous equations at:

https://brainly.com/question/16763389

Answer:

Hari finished the last two days of work that ram had left behind so that means that hari did 2 days of work.

Answer:

y = -1/5x - 3

Step-by-step explanation:

Answer:

120

Step-by-step explanation:

All the interior angles in a regular hexagon are 120 degrees.

Answer:

Last option= 30 minutes

Answer:

-9.705

Step-by-step explanation:

f-g+(-2)

Let  f = -3.005 and g = 4.7

-3.005 -4.7 -2

-9.705

Answer: -17, 17, -3, 3, -7, 7,

Step-by-step explanation:

Find all Factors of -18, (got -18 from multiplying 6 and -3)

Add the factors together. (+/- 6 and +/- 3), (+/-9 and +/-2), (+/-18 and +./-1)

Answer:

100,000m^2

Step-by-step explanation:

The area formula is length multiplied by width:

A=l x w

Substitute in the values for length and width

A= 1000 x 100

Solve for A

A= 100,000m^2

Answer: 100,000 m² or 1 × 10⁵ m²

Step-by-step explanation:

Concept:

Here, we need to know how to calculate the area of a rectangle.

Area = w · l

w = width

l = length

Solve:

Width = 100 m

Length = 1000 m

Area = w · l

Area = (100) (1000)

Area = 100,000 m²

Hope this helps!! :)

Please let me know if you have any questions

Answer:

0.804

Step-by-step explanation:

Subtract 3.218 by 2.414

Answer: 3

Step-by-step explanation:

The check mark with the line is a sauare root symbol. It means find the square root of the number next to it. The square root of something is a number times the same number to get the number. For example, the square root of 16 is 4 because 4x4 is 16. 3x3 is 9 so that’s the square root.

Answer:

Step-by-step explanation:

We are looking for the probability that (-1.10 < z < -.36)

The z score for -1.10 = .13567 and

the z score for -.36 = .35942

To find the probability that z will fall in between them, subtract the smaller from the larger to get .2237, or 22.37%

Answer:

Step-by-step explanation:

you have to do 5+1 and then you will get 6

Answer:

B

-10-10=20

10+10=20

20/20=0

Answer:

273.2

Step-by-step explanation:

Surface area of the pyramid=Area of square+4*area of triangle

Surface area of the pyramid=10^2+2*(8.66)*10

Surface area of the pyramid=100+173.2=273.2

In this question, the client will buy one item, which is composed by a boot, a pair of skis and a hat. Since the items are independent, the fundamental counting principle can be used.

Fundamental counting principle:

States that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are p*q ways to do both things.

In this question:

60 boots, 30 pairs of skis, 40 hats. So

60*30*40 = 72,000

The customer can purchase an item in 72,000 ways from the store.

For another example of the fundamental counting principle, you can check https://brainly.com/question/24067651

9514 1404 393

Answer:

  (x -2)^2/16 +(y +2)^2/4 = 1

Step-by-step explanation:

The equation of an ellipse is ...

  ((x -h)/a)^2 +((y -k)/b)^2 = 1

where (h, k) is the center, and 'a' and 'b' are the semi-axes in the x- and y-directions respectively.

Here, we have (h, k) = (2, -2), and a=6-2 = 4, b = 0-(-2) = 2. Then the equation is ...

  ((x -2)/4)^2 +((y +2)/2)^2 = 1

More conventionally, the denominators are multiplied out, so this is ...

  (x -2)^2/16 +(y +2)^2/4 = 1

Answer:

x = 54

y = 144

Step-by-step explanation:

y = (10-2)×180/10 = 144

x = 180-90-(180-144) = 54

Answered by GAUTHMATH