What is the solution to this system of equations using the linear combination method?
5x+y=2
4x+y=5

(im really bad at math so an explanation would be helpful so i can understand better)

Answer: 1. -90

Step-by-step explanation:

5xy², if x=-2 and y=-3

You substitute the value into the original expression

 5xy²

=5(-2)(-3)² ⇔ substitution

=(-10)(9) ⇔ multiply 5 and -2, and simplify (-3)²

=-90

Hope this helps!! :)

Steps to solve:

5xy²; x = -2, y = -3

~Substitute

5(-2)(-3)²

~Solve the exponent to y

5(-2)(9)

~Multiply inside

5(-18)

~Multiply

-90 (Option 1)

Best of Luck!

Answer:

Vacuous proof is used.

Step-by-step explanation:

Given:

Proposition p(n) :

"if n is a positive integer greater than 1, then n² > n"

To prove:

Prove the proposition p (0)

Solution:

Using the proposition p(n) the proposition p(0) becomes:

p(0) = "if 0 is a positive integer greater than 1, then 0² > 0"

The proposition that "0 is a positive integer greater than 1" is false

Since the premises "if 0 is a positive integer greater than 1" is false this means the overall proposition/ statement is true.

Thus this is the vacuous proof which states that:

if a premise p ("0 is a positive integer greater than 1") is false then the implication or conditional statement p->q ("if n is a positive integer greater than 1, then n² > n") is trivially true.

So in vacuous proof, the implication i.e."if n is a positive integer greater than 1, then n2 > n." is only true when the antecedent i.e. "0 is a positive integer greater than 1" cannot be satisfied.

Answer:

-32 - 36i.

Step-by-step explanation:

(4 - 8i)(2 – 5i)

= 4*2 + 4*-5i + 2*-8i  + (-8i*-5i)

= 8 - 20i - 16i + 40i^2      Now i^2 = -1 so:

= 8 - 36i - 40

= -32 - 36i.

Hi there! :)

Answer:

[tex]\huge\boxed{-32 - 36i}[/tex]

(4 - 8i) (2 - 5i)

FOIL:

(4 · 2) + (4 · (-5i) + ((-8i) · 2) + ((-8i) · (-5i))  =

Simplify: (Remember, i² = -1:

8 + ( - 20i) + (-16i) + (40i²) =

8 - 20i - 16i - 40

Combine like terms:

-32 - 36i

Answer:

False

Step-by-step explanation:

Equilateral triangles can only be acute.

Because a triangle can only have 180 degrees in angles, in an equilateral triangle all angles must be less than 90 degrees since they all measure the same (60 degrees)

I hope this helps!

-TheBusinessMan

Answer: False.

Step-by-step explanation:

All the angles of an equilateral triangle are 60° all less than 90° so only acute is correct.

Answer:

(x + [tex]\frac{1}{2}[/tex] + [tex]\frac{\sqrt{41} }{2}[/tex] )(x + [tex]\frac{1}{2}[/tex] - [tex]\frac{\sqrt{41} }{2}[/tex] )

Step-by-step explanation:

solve the polynomial for x then express in product of factor form

Solve

x² + x - 10 = 0 ( add 10 to both sides )

x² + x = 10

Using the method of completing the square

add ( half the coefficient of the x- term )² to both sides

x² + 2([tex]\frac{1}{2}[/tex] )x + [tex]\frac{1}{4}[/tex] = 10 + [tex]\frac{1}{4}[/tex]

(x + [tex]\frac{1}{2}[/tex] )² = [tex]\frac{41}{4}[/tex] ( take the square root of both sides )

x + [tex]\frac{1}{2}[/tex] = ± [tex]\sqrt{\frac{41}{4} }[/tex] = ± [tex]\frac{\sqrt{41} }{2}[/tex] ( subtract [tex]\frac{1}{2}[/tex] from both sides )

x = - [tex]\frac{1}{2}[/tex] ± [tex]\frac{\sqrt{41} }{2}[/tex]

Thus corresponding factors are

(x - (- [tex]\frac{1}{2}[/tex] - [tex]\frac{\sqrt{41} }{2}[/tex] ) ) and (x - (- [tex]\frac{1}{2}[/tex] + [tex]\frac{\sqrt{41} }{2}[/tex] ), that is

(x + [tex]\frac{1}{2}[/tex] + [tex]\frac{\sqrt{41} }{2}[/tex] ) and ( x + [tex]\frac{1}{2}[/tex] - [tex]\frac{\sqrt{41} }{2}[/tex] )

Thus

x² + x - 10 = ( x + [tex]\frac{1}{2}[/tex] + [tex]\frac{\sqrt{41} }{2}[/tex] )(x + [tex]\frac{1}{2}[/tex] - [tex]\frac{\sqrt{41} }{2}[/tex] ) ← in factored form

Answer:

[tex] \frac{3(n)}{9} \: or \: 3n \div 9 [/tex]

Step-by-step explanation:

[tex] \frac{3(n)}{9} = \frac{3n}{9} [/tex]

The number is 'n'.

Hope this helps ;) ❤❤❤

Answer:

8

Step-by-step explanation:

The formula for the area of a square is s^2, where s is the length of one side.  64 is a perfect square, so square root it and you find that one side is 8.

Answer:

Meteorite A= 46  Meteorite B = 23

Step-by-step explanation:

We can solve this problem by making an equation in which we add the weights, A + B = 69

We are told that A is equal to 2 times the weight of meteorite B, in other words, A is equal to 2B

We can make this into an equation and solve for B'

In order to solve for A, we simply input B=23 into 2B

Check:

A + B = 69

46+23 = 69

69 = 69

Answer:

Step-by-step explanation:

Hello!!!

from the problem statement we can infer that Jamal had a container of water where he fetches from to fill the graduated cylinder.

More so, after some couple of trails he recorded as follows

25.85, 24.1, and 24.56.

Hence the total amount of water he measured out of the container after three trials is

25.85+24.1+24.56=  74.51 ml

(assuming the cylinder is calibrated in ml)

The total volume of water he measures is  74.51 ml

Answer:

Hey there!

Thus, the vehicle can cover 20 m per second and would have a speed of 20 meters per second.

Let me know if this helps :)

Explanation:

Everywhere you see an x, replace it with 5. Then simplify using PEMDAS

f(x) = x^2 - 3x

f(5) = 5^2 - 3(5) ... plug in x = 5

f(5) = 25 - 15

f(5) = 10

Answer:i

Step-by-step explanatio

The number i¹³ is given by the equation A = i

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

The complex number is n = i¹³

Now , the value of A is A = i¹³

On simplifying the equation , we get

i = √ ( -1 )

i² = -1

i³ = -i

i⁴ = 1

So ,

i¹³ = i¹² ( i )

The value of i¹² = ( i⁴ )³

The value of i¹² = ( 1 )³

The value of i¹² = 1

Now , the value of i¹³ = i¹² x i

On simplifying the equation , we get

The value of i¹³ = 1 x i

The value of i¹³ = i

Hence , the value of i¹³ = i

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Answer:

x=5/2

Step-by-step explanation:

(2/7)^2x *(2/7)=(2/7)^6

(2/7)^(2x+1)=(2/7)^6

Equate indices

2x+1=6

2x=6-1

2x=5

x=5/2

Answer:

When multiplying the same number, raised to different powers, you carry the number forward so (2/7)^6  is part of the answer.

Now, we have to calculate the exponent.

2x + 1 = 6

So, the answer is x = 2.5 which means

[2/7]^(2*2.5) x [2/7]^1 = [2/7]^6 which equals

[2/7]^5 x [2/7]^1  = [2/7]^6

Step-by-step explanation:

Answer:

x+4 = 8

(❁´◡`❁)(❁´◡`❁)(❁´◡`❁)

Step-by-step explanation:

An example would be x+4 = 8

(❁´◡`❁)(❁´◡`❁)(❁´◡`❁)

Answer:

Velocity in still air is = 960 miles per hour  

Velocity of wind  = 230 miles per hour.

Step-by-step explanation:

The velocity when flying against the wind = 2920 / 4 = 730 miles per hour.

The velocity when flying with the wind = 7140 / 6 = 1190

Let the rate of jet in still Air = x

Let the rate of jet in wind = y

Therefore, velocity against wind = x-y and wind = x + y

x - y = 730

x + y = 1190

Add both equation, 2x = 1920

x = 960

Now find the value of “y” = 1190 – 960 = 230

Thus, velocity in still air is = 960 miles per hour  

Velocity of wind  = 230 miles per hour.

Answer:

Rate of jet in still air = 960 miles/ hr

Rate of the wind = 230 miles/ hr

Step-by-step explanation:

Let the speed of jet in still air = [tex]u[/tex] miles/hr

Let the speed of air = [tex]v[/tex] miles/hr

So, against the wind, the resultant speed = [tex](u-v)[/tex] miles/hr

And, with the wind, the resultant speed = [tex](u+v)[/tex] miles/hr

Distance traveled against the wind = 2920 miles

Time taken against the wind = 4 hrs

Formula for distance is:

[tex]\bold{Distance =Speed \times Time}[/tex]

[tex]2920 = (u-v)\times 4\\\Rightarrow u-v=\dfrac{2920}{4}\\\Rightarrow u-v=730\ miles/hr...... (1)[/tex]

Distance traveled with the wind = 7140 miles

Time taken against the wind = 6 hrs

[tex]\bold{Distance =Speed \times Time}[/tex]

[tex]7140 = (u+v)\times 6\\\Rightarrow u+v=\dfrac{7140}{6}\\\Rightarrow u+v= 1190 \ miles/hr...... (2)[/tex]

Adding (1) and (2):

[tex]2u = 1920\\\Rightarrow \bold{u = 960 miles/hr}[/tex]

Putting [tex]u[/tex] in (1):

[tex]960 -v = 730 \\\Rightarrow \bold{v=230\ miles/hr}[/tex]

Therefore, the answer is:

Rate of jet in still air = 960 miles/ hr

Rate of the wind = 230 miles/ hr

Answer: X=11

Step-by-step explanation:

                                     7x+ 13 = 90

                                                          (bring like terms together)

                                      7x=90-13

                                      7x=77

                                           therefore x= 11

HOPE THIS HELPS YOU....

AND MARK THE BRAINLIEST

Answer:

7.4

Step-by-step explanation:

NOT 8.1 !!

The length of arc RQ is 7.35 inch.

The distance between two places along a segment of a curve is known as the arc length.

Arc Length Formula (if θ is in degrees) s = 2 π r (θ/360°)

Given:

Angle = 65

radius = 6.48 inch

So, length of Arc

= 2πr( [tex]\theta[/tex]/ 360)

= 2 x 3.14 x 6.48 (65/360)

= 40.6944 x 0.1805

= 7.3453392

Hence, the length of arc is 7.35 inch.

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Answer:

88.

Step-by-step explanation:

428-360 = 88

Answer:

8x + 24

Step-by-step explanation:

Length = 8

Width = x + 3

Area of the rectangle = 8(x + 3)

= 8x + 24

Answer:

Option 2

Step-by-step explanation:

When completing the square, you have to find the number that will allow you to find the perfect square trinomials and when you factor that it should get the form a^2 + 2ab + b^2 and if a is equal to 1, then to find b, you have to take the half of the coefficient and square it because of the equation, and to maintain a balanced equation, you have to add it to both sides (same to both sides)

Hope this helped.

Answer:

[tex]\huge \boxed{\mathrm{Option \ 2 }}[/tex]

[tex]\rule[225]{225}{2}[/tex]

Step-by-step explanation:

When completing the square, we add the square of half the coefficient of x to both sides of the equation.

[tex]\Longrightarrow \ \displaystyle ( \frac{b}{2} ) ^2[/tex]

Where b is the coefficient of x in the equation.

[tex]\rule[225]{225}{2}[/tex]

Answer:

She forgot to flip the sign in the last step.

Step-by-step explanation:

In inequality, if you multiply or divide by a negative number, you would have to reverse the inequality sign.

Marice forgot to do this in the final step. She had to divide '-8' to get x completely on one side. All other steps are correct.

The correct answer is x ≥ -1.

Hope this helps.

Answer:

50 degree Celsius

Step-by-step explanation:

40+10 = 50

Answer:

11

Step-by-step explanation:

2 times 5 = 10 so 8+10 -7= 11

The required simplified value of the given expression at g = 7 is 11.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Given expression,
y = 8 + 2g - 7

Now put g = 5,
y = 8 + 2(5) - 7
y = 8 + 10 - 7
y = 11

Thus, the required simplified value of the given expression at g = 7 is 11.

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Answer:

3x-12 is the simplififed answer

Step-by-step explanation:

the equation is almost already simplified. when you combine -8 and -4, which are like terms, you get 3x-12. because there are no more lie temrs in the equation, it can not be simplififed any further.

Answer:

3x-12

Step-by-step explanation:

3x-8-4                        -8-4=-12

 3x-12

Answer:

86.74%

Step-by-step explanation:

72/83 = 0.8674

86.74%

Answer:

see below

Step-by-step explanation:

7.    1/3 ( n+2) = 5

Multiply each side by 3

n+2 = 5*3

n+2 = 15

Subtract 2 from each side

n+2-2 = 15-2

n = 13

8.x = bills

He started with 300 and paid 1/4 of the bills and ended up with -50

300 - 1/4 x = -50

Rearranging the order on the left

-1/4x + 300 = -50

Answer:

(A) [tex]-\frac{1}{4}x+300=-50[/tex]

Step-by-step explanation:

I "reversed" this problem to find the equation that works for it.

The balance was originally $300. If he's now at a balance of -50$ after paying off [tex]\frac{1}{4}[/tex] of his bills, then [tex]\frac{1}{4}[/tex] of his bills are $350, since [tex]300 - (-50) = 350[/tex].

If  [tex]\frac{1}{4}[/tex]  of his bills are $350, then his full bill is [tex]350\cdot4=1400[/tex]$.

So I tested each equation, where [tex]x=1400[/tex] to see if the equation worked out.

For a:

[tex]-\frac{1}{4}x + 300 = -50\\\\-\frac{1}{4}\cdot1400 + 300 = -50\\\\-350 + 300 = -50[/tex]

-350 + 300 is indeed -50, so I knew this equation works.

Hope this helped!

There are two possible answers

There are two answers because there are 2 points given. Both equations convert to the slope intercept form equation y = (3/8)x + 29/8

=================================================

Work Shown:

First we need the slope

m = (y2 - y1)/(x2 - x1)

m = (1-4)/(-7-1)

m = -3/(-8)

m = 3/8

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

Using this slope along with the point (x1,y1) = (1,4) gets us the following equation

y - y1 = m(x - x1)

y - 4 = (3/8)(x - 1)

which is one way to express the equation in point-slope form

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

Or we could easily use the other point as (x1,y1). The order of the points does not matter.

y - y1 = m(x - x1)

y - 1 = (3/8)(x - (-7))

y - 1 = (3/8)(x + 7)

is another valid answer.

Answer:

y = 3x+5

Step-by-step explanation:

[tex](2,11)=(x_1,y_1)\\y =3x-2\\m = 3\\\\Substitute \:values\:into \:point \:slope\:form\\y-y_1=m(x-x_1)\\y-11=3(x-2)\\y-11=3x-6\\y=3x-6+11\\y = 3x +5[/tex]