Mathematics High School

Solve the simultaneous equations
x-6y=5
xy - 2y2 = 6
-
Show clear algebraic working.

Answers

Answer 1

Answer:

(- 7, - 2 ) , (9.5, 0.75 )

Step-by-step explanation:

Given the equations

x - 6y = 5 ( add 6y to both sides )

x = 5 + 6y → (1)

xy - 2y² = 6 → (2)

Substitute x = 5 + 6y into (2)

(5 + 6y)y - 2y² = 6 ← distribute and rearrange left side

5y + 6y² - 2y² = 6

4y² + 5y = 6 ( subtract 6 from both sides )

4y² + 5y - 6 = 0 ← in standard form

(y + 2)(4y - 3) = 0 ← in factored form

Equate each factor to zero and solve for y

y + 2 = 0 ⇒ y = - 2

4y - 3 = 0 ⇒ 4y = 3 ⇒ y = [tex]\frac{3}{4}[/tex] = 0.75

Substitute these values into (1) for corresponding values of x

y = - 2 : x = 5 + 6(- 2) = 5 - 12 = - 7 ⇒ (- 7, - 2 )

y = 0.75 : x = 5 + 6(0.75) = 5 + 4.5 = 9.5 ⇒ (9.5, 0.75 )

Answer 2

(- 7, - 2 ) and  (9.5, 0.75 ) are the solutions.

What is equation?

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.

Here, we have,

Given the equations

x - 6y = 5 ( add 6y to both sides )

x = 5 + 6y → (1)

xy - 2y² = 6 → (2)

Substitute x = 5 + 6y into (2)

(5 + 6y)y - 2y² = 6 ← distribute and rearrange left side

5y + 6y² - 2y² = 6

4y² + 5y = 6 ( subtract 6 from both sides )

4y² + 5y - 6 = 0 ← in standard form

(y + 2)(4y - 3) = 0 ← in factored form

Equate each factor to zero and solve for y

y + 2 = 0 ⇒ y = - 2

4y - 3 = 0 ⇒ 4y = 3 ⇒ y =  = 0.75

Substitute these values into (1) for corresponding values of x

y = - 2 : x = 5 + 6(- 2) = 5 - 12 = - 7 ⇒ (- 7, - 2 )

y = 0.75 : x = 5 + 6(0.75) = 5 + 4.5 = 9.5 ⇒ (9.5, 0.75 )

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Related Questions

Which graph shows y=x^2+3x-4

Answers

Answer:

Third graph in the photo

Step-by-step explanation:

x^2+3x-4 can be factored as (x+4)(x-1). When y=0, x must be -4 or 1 to satisfy the equations, and thus the roots of the graph are at x=-4 and x=1. When x=0, y=(4)(-1)=-4. The only graph that satisfies both of these requirements is the third/last one.

Find the slope, m, and y-intercept, b, for the graph of the linear equation represented by the table below.

Answers

Answer: m=1/2, b=-7

Step-by-step explanation:

(0,-7) is the y-intercept on the line...

Simplify 20+16➗2


Please answer ASAP

Answers

Answer:

28, trust me

Step-by-step explanation:

Suppose f(x) = 3x*2 - 2x

Answers

Answer:

x=0

Step-by-step explanation:

0=6x-2x

0=4x

4x=0

and the answer is x=0

find the area
(not to scale)​

Answers

Answer: no

Step-by-step explanation: no

multiply
4/7 x 4 3/8 x 5/6

Answers

Look it up on quizzes

Answer:

all of them together or eahc seperate

Step-by-step explanation:

ALL FELLOW PEOPLE I NEED HELP ASAP ! WILL MARK BRAINLIEST!!EXTRA POINTS !!!!

Answers

Answer:

3) parallel

4) y = -1/2x +5

Step-by-step explanation:

3) Two equations are parallel if they have the same slope

The equations are written in y=mx+b (standard) form, where m is the slope. Both equations have a slope of 5/4

4) The two points that are plotted are (0,5) and (4,3).

We can find the slope by using the slope equation

(3) - (5) / (4) - (0) = -2/4 = -1/2

then we can plug it in both points to find b

-1/2(4) = -2

-2 + b = 3

b = 3

Alice is inventorying two different warehouses. In the first warehouse, she determines that there are 4.6X10 to the third power of boxes. In the second warehouse, she determines that there are 5X10 to the fourth power of boxes. What is the combined number of boxes in both warehouses?


PLEASE HELP!!!!

Answers

Answer:4.6 × 30= 138

5 × 40= 200

Step-by-step explanation:

The equation x²– 8x – 5 = 0 can be transformed into the equation (x - p)² = q, where p and q are real numbers. What are the values of p and q?​

Answers

The form (x - p)^2 = q is the form that completing the square will leave us with.

---Add 5 to both sides

x^2 - 8x = 5

---Divide the b term by 2, and square it. Then, add that number to both sides.

-8/2 = -4

(-4)^2 = 16

x^2 - 8x + 16 = 5 + 16

x^2 - 8x + 16 = 21

---Factor!

(x - 4)^2 = 21

p = 4

q = 21

Hope this helps!! :)

P and q have values of 4 and 21, respectively.

What is an expression?

In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.

The form (x - p)²= q is what we get when we complete the square.

Adding the number 5 on both sides,

x² - 8x = 5

After dividing by two, square the b term. Then divide both sides by that figure.

-8/2 = -4

(-4)² = 16

x² - 8x + 16 = 5 + 16

x² - 8x + 16 = 21

Solve the factors,

(x - 4)² = 21

p = 4

q = 21

As a result, the values of p and q are 4 and 21, respectively.

To know more about an expression follow

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Richard had 180 total minutes to do
homework, mow the grass, and walk the dog.
He spent 3(x + 4) minutes mowing the
grass.
He spent (x + 3) minutes working on
homework
He walked the dog for x minutes.
How many minutes did Richard spend
mowing the grass?

Answers

3(x+4)= 3x+12
3x+12+x+3+x=5x + 15
5x+15=180
5x=180-15
5x=165
x=165/5
x= 33min

mowing the grass = 3(x+4)
= 3(33+4)
=99+12
=111 min mowing grass

Which equation represents “fifteen more than r is sixty-one?”

Answers

Answer:

r + 15 = 61

Step-by-step explanation:


Alicia wants a pair of shoes that cost $68.48. If 17% sales tax must be added to the price, approximately
how much will the shoes cost including sales tax?

Answers

Answer:

$80.12; approx. $80

Step-by-step explanation:

- multiply 68.48 x 17% or 68.48 x 0.17 = 11.64

- the tax is 11.64

- add 68.48 + 11.64

- her total is $80.12

- rounded it would be $80

Hope this helped!

factor completely p^3 -27z^6

Answers

Answer:

gb

Step-by-step explanation:

uhygt

Please please help me with this question please now and show your steps

Answers

y = x^2 - 8x + 7

a) y-intercept

The y-intercept is the point where it crosses the y axis so x would 0.
So putting in 0 for x:
y = x^2 - 8x + 7
y = 0^2 - 8(0) + 7
y = 0 - 0 + 7
y = 7
The y intercept is at the point (0,7).

b)
The zeroes are the points where it crosses the x axis so it’s when the y is set to 0.

0 = x^2 - 8x + 7
Since it’s a quadratic equation we have to factor it. We fill in 2 numbers that add to -8 and multiplied to equal 7.
(x +____)(x+ ____)

The 2 numbers are 7 and -1 because -1*-7=7 and -7+(-1)=-8. So:
0 = (x-7)(x-1)

So now we have x-7 and x-1 equaling some quantity. If either of those happens to equal zero, it makes the whole equation 0, because (x-7)0=0 and 0(x-1)=0

So we can set each of it separately to 0 to solve for x.
x-7=0
x= 7

x-1=0
x= 1

The zeroes are at the points (1, 0) and (7, 0)

C.
The Vertex Form of a Quadratic is:
y = a(x-h)^2 + k. And the vertex is (h, k)

y = x^2 - 8x + 7
y - 7 = x^2 - 8x

We want to complete the square by adding some number to both sides of the equation so that when we factor it we are going to get (x-a)(x-a).

So take half of 8 to get two equal numbers that would be our “a”. 8/2=4 so we want (x - 4)(x- 4).

(x-4)(x-4) multiplies out to x^2 - 8 + 16.

continuing,
y - 7 = x^2 - 8x

Add 16 to both sides.
y - 7 + 16 = x^2 - 8x + 16

y + 9 = (x-4)(x-4)
y + 9 = (x-4)^2
y = (x-4)^2 - 9 is the vertex form.

The vertex is at the point (4, -9). So the axis of symmetry is at the line x = 4.

D. The vertex is solved in C as the point (-4, -9).

draw a suitable line on the grid and use your graphs to solve the equation 2/x - x^2 =5x​

Answers

Answer:

I graphed the answer above in the image

[tex]\sqrt4x -\sqrt9x\\\\[/tex]

Answers

Answer:

Step-by-step explanation:

Peyton made a 40% on her Math test. If she got 12 questions correct, how many total questions were on the test?

Answers

Answer: 30

Step-by-step explanation:

 40% = 12  |  40% + 40% = 80%  |   80% = 24  |  12 / 2 = 6  |  6 = 20%  | 40% + 40% + 20% = 30 questions

Please note that i'm not a professor and i might have this wrong.

Which relationship is NOT a function?

Answers

Answer:

a

Step-by-step explanation:

Answer:

If it is possible to draw any vertical line (a line of constant x) which crosses the graph of the relation more than once, then the relation is not a function. If more than one intersection point exists, then the intersections correspond to multiple values of y for a single value of x (one-to-many).

Step-by-step explanation:

Holly's soccer team is trying to raise $2,100 to travel to a tournament in Florida, so they decided to host a pancake breakfast. Each person must pay $30 for the breakfast. How many people need to attend their breakfast in order to raise $2,100?

Answers

Answer:

70 people

Step-by-step explanation:

30 dollars for each person, so you divide 2,100 by 30 to find how many people.

2,100/30=70

Answer:

70

Step-by-step explanation:

Target=$2,100

Money Earned from a single person=$30

Number of persons=$2,100 /$30 = 70

Thus, 70 people need to attend their breakfast in order to raise $2,100

Somebody please help me !!

Answers

1. (-1, 1

2. (-2,-2)

3. (-3, 1)

hope this helps!!

10 ft 8 ft 6 ft Find the area of this figure. Round your answer to the nearest hundredth. Use 3.14 to approximate n. A = [ ? ] ft? ​

Answers

Answer:

l×b×h-this is the order

10×8

=80 --area 1:maximum

10×6= 60--area2: minimum area

8×6=48--area3:middle area

if you follow the order

the answer is= 60ft

Can someone please help me with this I really need help.

Answers

Answer:

The angle mPQO is 86°

Step-by-step explanation:

123°-37°

Find the missing side of each triangle. Round your answers to the nearest tenth if necessary.
(Please show your work)

Answers

Answer:

Below

Step-by-step explanation:

Use reverse pythagorean theorem

     c^2 = a^2 + b^2

You can either rearrange the equations, or plug the values in an solve for b :

     b^2 = c^2 - a^2

            = 15.1^2 + 9.7^2

            = 1339.2

Square root this number

            = 11.5723809

        x  = 11.6 in

Hope this helps! Best of luck <3

>> Answer

___________

[tex] \: [/tex]

[tex]\boxed{ \rm{answer \: by \: { \boxed{ \rm{☆HayabusaBrainly}}}}}[/tex]

Step by step :

x² = (15,1)² - (9,7)²

x² = 228,01 - 94,09

x² = 133,92

x = 11,6in✔

If a triangle has an area of 192 mm2, and the
height measures 12 mm, what is the measure
of the base?

Answers

Answer:32mm

Step-by-step explanation:

area of triangle = 1/2 *base * height

192mm2 = 1/2 *b* 12mm

192 =6b

base=192/6

base= 32mm

HELP IM IN THE MIDDLE OF A TEST!!
Choose the correct slope of the line that passes through the points (1, -3) and (3, -5).
A. -1
B. 1
C. 0
D. 1/2

Answers

Th correct answer would be D

Yolanda would like to attend a 12-month program that will certify her as a court reporter. The program costs $8,500 in tuition, fees, and books and will allow her to make
about $31,250 a year when she becomes certified. She will not have time to work during the year of training. Assuming she could make $18,000 a year without the
training, how many years will it take her to recoup her investment? years

Answers

Answer:

15 months and 8 days  

Step-by-step explanation:

31,250 / 12 = 2604.16667  8,500/ 2604.16667 =  3.264 months of second year   12 + 3.264 = 15.264 months  days 30 * 0.264= 7.92  add the together = 15 months and 8 days  

Given the definitions of f(x)f(x) and g(x)g(x) below, find the value of (f\circ g)(2).(f∘g)(2). f(x)= f(x)= \,\,-5x-11 −5x−11 g(x)= g(x)= \,\,2x^2+2x-5 2x 2 +2x−5

Answers

ounces is In the apothecary system of measurement, equal to one apothecary pound. a) eight O b) 16 c) 12 d) four

Please help me ASAP

Answers

Answer:

x ≤ -17

Step-by-step explanation:

please help me its due in 3 mins

Answers

They’re vertical angles so it’d be 106° I’m pretty sure. Unless you’re doing something different than me

Answer:

s = 19°

Step-by-step explanation:

The angles that are directly opposite to each other are known as opposite angles. They are also termed as vertical angles or vertically opposite angles and are equal to each other.

so

106 = 6s - 8

106 + 8 = 6s

114 = 6s

s = 114 : 6

s =  19°

-----------

check

6 * 19 - 8 =

106°

the answer is good


ndjsjdjdjdjdjjxndjxjusnsu j

Answers

Answer:

B

Step-by-step explanation:

bcoz sin and cos 45 have 1/root2

Answer:

B. 45°

Step-by-step explanation:

sin(45) = √2/2

cos(45) = √2/2

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