The rules for two lines are y=x+2 and y=5 - 2x. At what point do they intersect?

Answer:

Below in bold.

Step-by-step explanation:

x^2 - y^2 = 11

2x^2  + y^2 = 97

From the first equation:

y^2 = x^2 - 11

Substituting in the second equation:

2x^2 + x^2 - 11 = 97

3x^2 = 108

x^2 = 36

x = 6, -6.

Substituting  for x in the first equation:

(6)^2 - y^2 = 11

y^2 = 36 - 11 = 25

y = 5, -5.

Answer:

LAW 2: The second law of indices tells us that when dividing a number with an exponent by the same number with an exponent, we have to subtract the powers. In algebraic form, this rule is as follows . ... Example: In this example, the powers were multiplied together to give the answer which is 3 to the power of 6.

Answer:

Q.D.E=(5+2i).(5-2i).i = (25-4i²)i = 25i-4i³

Step-by-step explanation:

Answer:

proportion

Step-by-step explanation:

6.6/1.1 = 0.3/0.05

Using cross products

6.6 * .05 = 1.1 * .3

.33 = .33

Since this is a true statement, the statement is a proportion

Answer:

100 mm

Step-by-step explanation:

Square root the area to find the length of each side

[tex]\sqrt[]{625} =25[/tex]

Multiply 25 by 4 to get the sum of all four sides for the perimeter

25 x 4 = 100

Answer:

4

Step-by-step explanation:

Since the base angles are the same, the side have to be the same

ML = MN

4x = x+3

Subtract x from each side

4x-x = x+3-x

3x= 3

Divide by 3

3x/3 = 3/3

x = 1

We want the length of MN

MN = x+3 = 1+3 = 4

The measurement of MN side is 4

The properties of the triangle are:

1. The sum of all the angles of a triangle (of all types) is equal to 180°.

2. The sum of the length of the two sides of a triangle is greater than the length of the third side.

3. In the same way, the difference between the two sides of a triangle is less than the length of the third side.

Since the base angles are the same, the side have to be the same

ML = MN

4x = x+3

Subtract x from each side

4x-x = x+3-x

3x= 3

Divide by 3

3x/3 = 3/3

x = 1

We want the length of MN

MN = x+3 = 1+3 = 4

Learn more about triangles here:

https://brainly.com/question/2773823

#SPJ7

Answer:

there is no diagram ......

The area of the trapezoid is 10 square units

The formula for finding the area of the trapezoid is expressed as:

A = 0.5(a+b)h

where:

a and b are the sides

h is the height

Given the following

a = 3

b = 2

h = 4

Substitute

A = 0.5(3 + 2)*4

A = 0.5(20)

A = 10 square units

Hence the area of the trapezoid is 10 square units

Learn more on area of trapezoid here: https://brainly.com/question/1463152

Answer:

B) 5 Square Units

Step-by-step explanation:

Answered from another colleague :)

B1 = 2

B2 = 3

H = 2

A = 1/2 (B1 + B2) H

1/2 (2+3) 2

1/2 (5) 2

(2.5)2

5

Answer:

4.67×10

4

=4.67×10000=46700

[tex]4.67 \times {10}^{4} [/tex]

[tex] = \: 4.67 \times 1000[/tex]

[tex] = \: 46700[/tex]

Answer:

θ = 60.34

Step-by-step explanation:

[tex]\frac{\left(12.8\cdot \:sin\left(90\right)\right)}{sin\left(52.3\right)}[/tex] = 16.177

[tex]\frac{\left(16.177\cdot \:sin\left(90\right)\right)}{18.6}[/tex] =  θ = .869

[tex]arcsin\left(.869\right)[/tex] = 60.34

Answer:

60.4°

Step-by-step explanation:

There are two right triangles.

One right triangle (on the left side) has an acute angle measuring 52.3°.

Its opposite leg measures 12.8 cm.

We can find the length of its hypotenuse, x.

sin 52.3° = opp/hyp

sin 52.3° = 12.8 cm/x

x * sin 52.3° = 12.8 cm

x = 12.8 cm/sin 52.3°

x = 16.2 cm

Now we use the hypotenuse of the left side triangle which is a leg of the right side triangle.

For the right side triangle, we are looking for angle Θ. We know the opposite leg, 16.2 cm and the hypotenuse, 18.6 cm.

sin Θ = opp/hyp

sin Θ = 16.2/18.6

sin Θ = 0.8698

Θ = sin^-1 0.8698

Θ = 60.4°

Answer:

8.37 cm rounded

Step-by-step explanation:

C = 2π r

C = 2π (8)

C = 16 π

C = 50.24

1/6 ( 50.24)= 8.37

Answer:

its letter a

Step-by-step explanation:

I hope you help

Answer:

a)2x-3y

b)4(9a-4)

Step-by-step explanation:

we want to expand the following expression:

[tex] \displaystyle - \frac{1}{4} ( - 8x + 12y)[/tex]

well to do so we consider distributive property thus distribute:

[tex] \displaystyle - \frac{1}{4} (- 8x )+ - \frac{1}{4}( 12y)[/tex]

reduce fraction which yields:

[tex] \displaystyle - \frac{1}{4} (- 8x )+ - \frac{1}{4}( 12y) \\ \\ \displaystyle 2x + ( - 3y)[/tex]

simplify Parentheses:

[tex] \displaystyle \boxed{ 2x - 3y}[/tex]

in the expression there's a common factor of 4 therefore factor it out:

[tex] \displaystyle 9.4a - 4.4 \\ \\ \displaystyle \boxed{4(9a - 4)}[/tex]

Answer:

Since this number is small we know that the exponent will be negative.

In scientific notation the decimal must be between the first two NON zero numbers. So move the decimal and count how many positions it was moved.

1.2 x 10 ^-11

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

substitute the x- coordinate 5 into the equation and if the result is equal to the y- coordinate 0 then it is a solution

y = 5 + 5 = 10 ≠ 0

Then (5, 0 ) is not a solution to the equation

Answer:

Step-by-step explanation:

Answer:

d = 8t

Step-by-step explanation:

Answer:

the first one 2/-1, hope it helps...

Answer:

A linear equation in the standard form is written as:

y = a*x +b

where a is the slope and b is the y-intercept.

If we know that the line passes through the points (a, b) and (c, d), then the slope can be written as:

a = (d - b)/(c - a)

So we know that our line passes through the points (8, -1) and (2, -5)

then the slope will be:

a = (-5 - (-1) )/(2 - 8) = (-4/-6)  = 2/3

Then our line is something like:

y = (2/3)*x + b

to find the value of b, we can use the fact that we know that our line passes through the point (2, -5)

this means that when x = 2, we must have y = -5

replacing these values in the equation we get:

-5 = (2/3)*2 + b

-5 = 4/3 + b

-5 - 4/3 = b

-15/3 - 4/3 = b

-19/3 = b

then the equation is:

y = (2/3)*x - 19/3

(in the question you wrote the point-slope form, but you can see that it does not work for the second point, so there may be a mistake there, as the slope is missing)

The actual equation in the point-slope form is:

y + 1 = (2/3)*(x - 8)

Answer:

The answer is 2x + -3y = 19

Step-by-step explanation:

I Got It Right Instruction on edge

Answer:

One

Step-by-step explanation:

Set each equations equal to each other

[tex] {x}^{2} + 4 = 4x[/tex]

[tex] {x}^{2} - 4x + 4[/tex]

Find the discrimant.

[tex]{ - 4 {}^{2} - 4(1)(4) } = 0[/tex]

This means there is one real solution. Since the discramnt equal 0.

Answer:

128 cm^2

Step-by-step explanation:

The area of a trapezoid is given by

A = 1/2 (b1+b2) h

where b1 and b2 are the lengths of the bases and h is the height

A =1/2( 10+22) * 8

A = 1/2 (32)8

  = 128

Answer:

A=128 cm²

Step-by-step explanation:

Hi there!

We are given a trapezoid and we want to find the area of it

The area of a trapezoid is given as [tex]\frac{a+b}{2}h[/tex], where a and b are the bases and h is the height

The bases are the parallel sides

They are the sides marked as 10 cm and 22 cm in this case

The height is the distance between the bases

In this case, it is the side marked as 8 cm

We know everything needed for the area, let's just label everything to avoid any confusion

a=10

b=22

h=8

Now substitute into the formula

A=[tex]\frac{a+b}{2}h[/tex]

A=[tex]\frac{10+22}{2}*8[/tex]

add the numbers on the numerator together

A=[tex]\frac{32}{2}*8[/tex]

Divide 32 by 2

A=16*8

multiply

A=128 cm²

Hope this helps!

Answer:

-30z^8

Step-by-step explanation:

[tex]2 {z}^{8} - 32 {z }^{8} \\ = - 30 {z}^{8} [/tex]

Answer:

-30z^8

Step-by-step explanation:

2z^8- 32z^8

-30z^8

9514 1404 393

Answer:

  180 km

Step-by-step explanation:

The Nissan had traveled (120 km/h)(1/3 h) = 40 km when it had the puncture. It started from that location when the puncture was repaired at t = (1/3+1/2) = 5/6, where t is in hours. Then the two vehicles met (again) when ...

  Matatu distance = Nissan distance

  90t = 40+120(t -5/6)

  0 = 40 +30t -100 . . . . . . subtract 90t, eliminate parentheses

  60 = 30t . . . . . . . . . . . add 60

  2 = t . . . . . . . . . . . . . 2 hours after leaving, the cars meet again

That distance from town A is ...

  y = 90t = 90(2) = 180 . . . . km

Answer:

5/12

Step-by-step explanation:

it says in the question that 1/4 +1/3 is used so in order to make it simple we have to find the common denominator that is 12. so converting 1/4 is 3/12 and 1/3 is 4/12.so u add the numerator and u get 7 over 12 .so now the whole container of peanuts is 12/12 but 7/12 is used so 12-7= 5. so ur ans is 5/12

Answer:

1 : 2 : 1

Step-by-step explanation:

2:4:2

Divide each  term by 2

2/2:4/2:2/2

1 : 2 : 1

Answer:

6(k+2) -8

Step-by-step explanation:

Start with k

k

Add 2

(k+2)

Multiply by 6

6(k+2)

Then subtract 8

6(k+2) -8

6(k+2)-8 is a required answer.

Answer:

Solution given:

Start with k.

add 2

multiply by six

subtract by 8

Answer:

129

Step-by-step explanation:

Since,

AD = BC

AD = 3x + 24

BC = 4x - 11

3x + 24 = 4x - 11

4x - 11 = 3x + 24

4x - 3x = 24 + 11

x = 35

BC = 4x - 11

= 4 ( 35 ) - 11

= 140 - 11

BC = 129

Answer:

[tex]AB=BC[/tex]

[tex]3x+24=4x-11[/tex]

[tex]3x-4x=-11-24[/tex]

[tex]x=35[/tex]

[tex]BC=4\times 35-1[/tex]

[tex]=140-11[/tex]

[tex]=129[/tex]

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

Hope it helps..

Have a great day!!

Answer:

Surface Area = 3,543.7 cm²

Step-by-step explanation:

Surface area of the cylinder = 2πr(h + r)

Where,

radius (r) = 12 cm

height (h) = 35 cm

Plug in the values into the surface area formula

S.A = 2*π*12(35 + 12)

S.A = 24π(47)

S.A = 3,543.71651 cm²

≈ 3,543.7 cm² (approximated to the nearest tenth)