Solve the following non-linear system of equations algebraically.
y = - 2x² - 4x + 5 and
y = 2x^2 + 4x + 5

Answer:

42 = 8x + 13x

42 = 21x

x = 2

8 = 8c -4(c + 8)

8 = 8c - 4c - 32

8 = 4c - 32

40 = 4c

c = 10

Answer:

42 = 21x

42/21 = x

x = 2

check:

42 = 8*2 + 13*2

42 = 16 + 26

8 = 8c -4*c -4*8

8 = 8c - 4c - 32

8 + 32 = 4c

40 = 4c

40/4 = c

c = 10

Check:

8 = 8*10 - 4(10+8)

8 = 80 - 4*18

8 = 80 - 72

Answer:

62

Step-by-step explanation:

4x + 6

4(14) + 6 (substituting x = 14)

56 + 6

62

Answer:

x=2

y=3

Step-by-step explanation:

x/2+y/3=2   so      

3x/6+2y/6=12/6

then multiply by 6

3x+2y=12    

equation number 2

x/3+y/2=13/6

2x/6+3y/6=13/6

multiply by 6

2x+3y=13

so the system is now

3x+2y=12  

2x+3y=13

from the first equation 2y=12-3x,  y=6 -  3x/2

then put  y in  the second equation

2x+3*(6-3x/2)=13

2x+18-9x/2=13

2x-9x/2=13-18

4x/2-9x/2=-5

-5x/2=-5

*(-1/5)    *(-1/5)

x/2=1

*2    *2

x=2

so y=6-3*2/2=6-3

y=3

Step-by-step explanation:

Given that:

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

(1/3x)+(1/2y) = 13/6-----(2)

Put 1/x = a and 1/y = b then

(1) becomes

(a/2 )+( b/3) = 2

⇛ (3a+2b)/6 = 2

⇛ 3a+2b = 2×6

⇛ 3a+2b = 12 --------(3)

(2) becomes

(a/3)+(b/2)=13/6

⇛ (2a+3b)/6 = 13/6

⇛ 2a+3b=13----------(4)

On adding (3)&(4) then

3a+2b=12

2a+3b=13

(+)

_________

5a+5b = 25

_________

⇛ 5a+5b = 25

⇛ 5(a+b)=25

⇛ a+b=25/5

⇛ a+b=5 -------------(5)

On subtracting (3) from (4)

2a+3b=13

3a+2b=12

(-)

_________

-a+b = 1

_________

⇛ -a+b = 1

⇛ b = 1+a --------(6)

On Substituting the value of b in (5) then

a+1+a = 5

⇛2a+1 = 5

⇛ 2a = 5-1

⇛ 2a = 4

⇛ a = 4/2

⇛ a = 2

On Substituting the value of a in (6) then

b = 1+2

b = 3

Now,

a = 2

⇛ 1/x=2

⇛ “x” = 1/2

and

b= 3

⇛ 1/y = 3

⇛“y” = 1/3

Answer:- Hence, the value of x and y with be 1/2 and 1/3 respectively.

The solution for the given problem is (1/2,1/3)

Check:-

If x = 1/2 and y = 1/3 then

LHS = (1/2x)+(1/3y)

= 1/2(1/2)+1/3(1/3)

= 1/(2/2)+1/(3/3)

= (1/1)+(1/1)

= 1+1

=2

= RHS

LHS=RHS is true

and

LHS=(1/3x)+(1/2y)

⇛ 1/3(1/2)+ 1/2(1/3)

⇛ 1/(3/2)+1/(2/3)

⇛ (2/3)+(3/2)

⇛ (4+9)/6

⇛ 13/6

⇛ RHS

LHS = RHS is true

also read similar questions: Simultaneous equations: 1. 2x+2y=10 X+2y=6 2. 3x+y=18 2x+y=13 3. X+y=1 X-y=5 4. 3x+4y=29 X-4y=-17 5. 4c+3y=11 2x+y=7

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Answer:

The answer is $12,000. 12 months × $1,000 per month = $12,000 minimum annual base rent; $435,000 gross sales × 2% = $8,700. The tenant paid $12,000 because the minimum base rent was more than the percentage of gross sales.

Step-by-step explanation:

Step-by-step explanation:

let f(x)=y

y=7x-13

y+13=7x

y+13/7=x

f-1(x)=x+13/7

Answer:

5/6 pounds

Step-by-step explanation:

A group of people buys 5 pounds of corn meal to divide equally among 6 families write a fraction or mixed number that shows how many pounds of corn meal each family gets'.

Given the following :

Amount of corn meal purchased = 5 pounds

Number of people to share = 6 families

Assume, it is divided equally among them;

Then; each family gets ;

(Pounds of corn meal purchased/number of families) ;

5 / 6 pounds of corn meal will be distributed to each family.

Answer:

373.66 cm².

Step-by-step explanation:

The following data were obtained from the question:

Pi (π) = 3.14

Radius (r) = 7 cm

Slant height (l) = 10 cm

Surface Area (SA) =?

The surface area of the cone can be obtained by using the following formula:

SA = πr² + πrl

SA = (3.14 × 7²) + (3.14 × 7 × 10)

SA = (3.14 × 49) + 219.8

SA = 153.86 + 219.8

SA = 373.66 cm²

Therefore, the surface area of the cone is 373.66 cm².

Answer:

Shade

Step-by-step explanation:

she's called Mummy shade, so I think her other child's name is shade

Answer:

Shade

Step-by-step explanation:Her name is Mummy shade

Answer:

7/8

Step-by-step explanation:

63 ÷ 9/72 ÷ 9

= 7/8

Answer:

7/8

Step-by-step explanation:

63/9 = 7

72/9 = 8

then:

63/72 = 7/8

Answer: x=0.125 or 1/8

Step-by-step explanation:

[tex]7x-\frac{3}{4}=6x-\frac{5}{8}[/tex]

add 3/4 on both sides

[tex]7x-\frac{3}{4}+\frac{3}{4}=6x-\frac{5}{8}+\frac{3}{4}[/tex]

[tex]7x=6x+\frac{1}{8}[/tex]

subtract 6x on both sides

[tex]x=\frac{1}{8}[/tex]

Answer:

x = 1/8

Step-by-step explanation:

7x - 3/4 = 6x - 5/8

7x - 3/4 + 3/4 = 6x - 5/8 + 3/4

7x = 6x + 1/8

7x - 6x = 6x + 1/8 - 6x

x = (6x - 6x) + 1/8

x = 1/8

Answer:

Step-by-step explanation:

Given functions are

y = 5 cos ( 2π / 3 ) t

y = 5 cos ( 4π / 3 ) t

y= 10 cos ( 2π / 3 ) t

y = 10 cos ( 4π / 3 ) t

The pendulum half oscillation from left extreme to right extreme takes 1.5 s

So its time period of oscillation T = 1.5 x 2 = 3 s .

standard equation of oscillation is

y = A cos ω t where A is amplitude and ω is angular frequency .

Amplitude of oscillation A = 10 / 2 = 5 inch .

Among the given equation of motion only first two has amplitude equal to 5 . So both the last two are ruled out .

The angular frequency of first motion as per given equation

ω = 2π / 3

If time period is T

2π / T = 2π / 3

T = 3 s

So it matches with the time period of oscillation of pendulum .

Hence the first equation truly represents the oscillation of pendulum.

The function models the horizontal displacement as a function of time in seconds is  [tex]\rm y = 10 sin(\dfrac{2\pi}{3})t[/tex]  and this can be determined by using the given data.

Given :

It takes 1.5 seconds for a grandfather clock's pendulum to swing from left (initial position) to right, covering a horizontal distance of 10 inches.

For the oscillation the standard equation is given below:

[tex]\rm y = A\;cos \;\omega t[/tex]

where A is the amplitude, [tex]\omega[/tex] is the angular velocity, and t is the time.

Now, determine the time period that is:

T = 1.5 [tex]\times[/tex] 2

T = 3sec

Now, the angular frequency is given by:

[tex]\omega = \dfrac{2\pi}{3}[/tex]

So, the function models the horizontal displacement as a function of time in seconds is given below:

[tex]\rm y = 10 sin(\dfrac{2\pi}{3})t[/tex]

Therefore, the correct option is C).

For more information, refer to the link given below:

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Answer:

12.5 percent; 2/16; 1/8

Step-by-step explanation:

Peter and Mary make up 2 of the clubs members, so the probability that they are chosen is 2/16. This simplifies to 1/8, and in decimal form is .125. Therefore, the percentage form of the probability they are chosen is 12.5 percent.

Answer: [tex]6+\dfrac{14}{p}[/tex] .

Step-by-step explanation:

To find : The expression is equivalent to the product of [tex]p+\dfrac73\text{ and }\dfrac6p[/tex], where p ≠0.

Product of [tex]p+\dfrac73\text{ and }\dfrac6p[/tex] = [tex](p+\dfrac73)\times\dfrac6p[/tex]

Using distributive property:  [tex](b+c)a= ba+ca[/tex]

[tex](p+\dfrac73)\times\dfrac6p=p\times\dfrac6p+\dfrac73\times\dfrac6p\\\\= 6+\dfrac{7}{1}\times\dfrac2p\\\\=6+\dfrac{14}{p}[/tex]

Hence, the required expression is [tex]6+\dfrac{14}{p}[/tex] .

Answer:

B!!!

Step-by-step explanation:

Multiply then divide every number by 2 to simplify.

Answer:

C. 33.

Step-by-step explanation:

The sides of a 45-45-90 triangle are in the ratio 1:1:√2 so the side opposite to 45 degrees = 11√6 / √2.

Consider the larger triangle containing the 60 degree angle:

tan 60 = x / (11√6 / √2).

x = tan 60 * 11√6 / √2

x = 33.

The value of the variable x will be 33 units. Then the correct option is C.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

The diagram is shown below.

Let h be the height of the triangle.

The value of h is given by the sine of angle 45°. Then the value of the height h will be

sin 45° = h / 11√6

h = 11√6 × 1/√2

h = 11√3 units

The value of h is given by the tangent of angle 60°. Then the value of the height h will be

tan 60° = x / h

x = 11√3 × √3

x = 11 × 3

x = 33 units

Thus, the value of the variable x will be 33 units.

Then the correct option is C.

More about the right-angle triangle link is given below.

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Answer as a fraction = 1/720

Answer in decimal form (approximate) = 0.001388

Answer in percent form (approximate) = 0.1388%

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

Explanation:

Let A = 1 to indicate the number of ways to get the names to line up in alphabetical order.

There are B = 6*5*4*3*2*1 = 720 different ways to arrange the six people. Notice how I started at 6 and counted my way down to 1, multiplying all along the way. This can be shortened to factorial notation to say 6! = 720. Or you could use the nPr permutation formula to get the same result (use n = 6 and r = 6).

Once you have the values of A and B, we form the fraction A/B = 1/720 which is the probability of getting the names in alphabetical order.

If you need the answer in decimal form, then use your calculator to find

1/720 = 0.001388

which converts over to 0.1388%

Answer:

Step-by-step explanation:

Rectangle:

length = l = 12 cm

Width = w = 0.8 cm

Use Pythagorean theorem to find the diagonal

Diagonal² =  l² + w²

                = 12² + 0.8²

                = 144 + 0.64

                = 144.64

Diagonal = √144.64 = 12.03 cm

Diagonal of square  = diagonal of rectangle

                               = 12.03 cm

To find the side of square again use Pythagorean theorem,

side² + side² = 12.03²

2 sides² = 144.64

  side² = 144.64/2

  side² = 72.32

 side = √72.32

Side = 8.50 cm

Answer:

slope = - [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (3, 1)

m = [tex]\frac{1-2}{3-0}[/tex] = - [tex]\frac{1}{3}[/tex]

Answer:

a) b⁹

Step-by-step explanation:

b³ • b⁻⁵ • b¹¹

add the exponents

b³ ⁺ ⁽⁻⁵⁾ ⁺ ¹¹

b⁹

Answer:

b^9

Step-by-step explanation:

b^3·b^−5·b^11

Since the bases are the same, and we are multiplying, we can add the exponents

b^(3+-5+11)

b^9

Answer:

d=4

Step-by-step explanation:

Agency 1:

Total cost of renting a car=24.50d + 15.99

Agency 2:

Total cost of renting a car=27.50d + 3.99

Where, d=No. of days of renting the car

Which equation could be used to find the number of days, d, at which the rental fee is the same for both agencies?

The equation is by equating agency 1 and agency 2 equation

24.50d + 15.99 = 27.50d + 3.99

Collect like terms

24.50d - 27.50d = 3.99 - 15.99

-3d = -12

Divide both sides by -3

d= -12 / -3

=4

d=4

Check

Agency 1:

24.50d + 15.99

= 24.50(4) + 15.99

= 98 + 15.99

= 113.99

Agency 2:

27.50d + 3.99

= 27.50(4) + 3.99

= 110 + 3.99

= 133.99

Answer:

24.5d + 15.99 = 27.5d + 3.99

Step-by-step explanation:

The other person who answered this question was correct, they just explained it all the way through and since you guys skim through everything instead of reading, I'll put the answer. :)

Answer:

The area would be 128ft^2

2^4 i= 2x2x2x2

2^3 = 2x2x2

multiply them and you get 128ft6^2

Answer:

128ft^2

Step-by-step explanation:

took the quiz just now :D

Question

In circle L, arc MNOP is 120° and the radius is 5 units. Which statement best describes the length of arc MNOP?

• one half the area of circle L

• one third the area of circle L

• one half the circumference of circle L • one third the circumference of circle L

Answer:

• one third the circumference of circle L

Step-by-step explanation:

In the question, we are told that:

In circle L, arc MNOP is 120° and the radius is 5 units.

We are asked to find the statement amongst the options that describes the arc length MNOP of Circle L

Step 1

Find the Area of circle

Area of a circle = πr²

r = 5 units

Area of a circle = π × 5²

Area of a circle = π × 25

Area of a circle = 78.53981634 square units

Step 2

Find the arc length of a circle

Arc length = 2πr × θ /360

r = 5 units

θ = 120°

Arc length = 2 × π × r × 120/360

Arc length = 2 × π × r × (1/3)

Arc length = 2 × π × 5 × (1/3)

Arc length = 10.47198 units

Step 3

Circumference of a circle = 2πr

= 2 × π × 5

= 31.415926536 units

Since the Circumference of a circle = 2πr

Arc length of the circle for the above calculation, = 2πr × 1/3

Therefore, the statement that best describes the arc length MNOP of Circle L is:

" the arc length MNOP is one third the circumference of circle L"

Answer:

the arc length MNOP is one third the circumference of circle L

Step-by-step explanation:

i fishie yupo

The answer is shown below:

An expression in math is a sentence with a minimum of two numbers/variables and at least one math operation in it. Let us understand how to write expressions. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression.

1+5.2 + (1+3)²

=1+10 + 16

=27

0.25*4³-1

=0.25*64-1

=16-1

=15

4+8(1/4+2)

=4+8(9/4)

=4+2*9

=4+18

=22

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Answer:

f(x) = 2x + 10

Step-by-step explanation:

Let's call this function f(x), where f(x) is time to get the order ready and x is the number of parts:

2x is the time to manufacture all parts of the order and 10 min is the time to pack them.

Answer:

2x + 10 is the correct answer :)

Answer:

Slope:[tex]\frac{2}{3}[/tex]

y-intercept:-2

Step-by-step explanation:

Answer:

w=10

Step-by-step explanation:

-2=-(w-8)

2=w-8

w=10

Question:

-2=-(w-8)

Answer:

-2=-w+8

w=8+2

w=10

Step-by-step explanation:

A.

A - selecting a milk chocolate

[tex]P(A)=1-\dfrac{1}{5}-\dfrac{1}{3}=\dfrac{15}{15}-\dfrac{3}{15}-\dfrac{5}{15}=\dfrac{7}{15}[/tex]

B.

The number of the chocolates must be a multiple of 15, so there can be 15,30,45,... etc. chocolates in the box.

Answer:

49

Step-by-step explanation

5v + w

5(5) + 24

25 + 24

49

First you have to substitute the variables with numbers given (v=5 ; w=24)

Start with multiplying 5*5 which equals 25, then finish off with adding the two numbers.

Answer:

5v+w = 5(5)+24 = 49

Step-by-step explanation:

As you can see we have two variables

v & w

And we have no coefficient to w but we do to v which is...

5

So... we must replace the variables (v & w) replacing them with the numbers you gave us, 5 for v and 24 for w.

The sentence is

5v+w= ?

If you replace v with 5 it becomes...

5(5)+w

When seeing a number & a variable or numerous variables that placed right next to each other, it means that the number and the variable(s) are to be multiplied together.

So now we have 5(5)+w meaning 5 times 5 plus the variable w

The second value you gave us is 24 which is supposed to be subbed in for w.

So... when we replace w with 24 we get...

5(5)+24

Now we evaluate the expression.

According to PEMDAS... since we have no parenthesis or exponents we do m, multiplication first. 5*5=25

We are now left with...

25+24

25 + 24 = 49.

So...

5v+w is now 5(5)+24 which is equal to...

49

Hopefully this helped you!

Have a good day!

Answer:

62

Step-by-step explanation:

hope that helps! if it is an answer

The Phrase is: "The resulting number is 62."

We have the expression as

52 + 2x

Now, To evaluate the expression 52 + 2x when x = 5,

we substitute the value of x into the expression and simplify:

=52 + 2(5)

= 52 + 10

= 62.

Thus, The resulting number is 62.

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