Solve the following simultaneous equations :
1. x + 2y = 1, 3x - y = 17​

Formula :-

[tex]\sf \: S.I \: = \frac{P.R.T}{100} \\ [/tex]

Given that :-

The interest received on Rs 5000 = interest received on Rs 6000 , when rate of interest on Rs 6000 is 8 % .

To Find :-

The rate of interest on rupees 5000 .

Solution :-

→ S.I = P.R.T/100

→ 5000.R. 1 / 100 = 6000 × 8 × 1 / 100

→ 50 R = 60×8

→ 50 R = 480

→ R = 480/ 50

→ Rate of interest = 9.6 %

So rate on Rs 5000 is 9.6 %

Answer:

Step-by-step explanation:

length of the rectangle = 2.5 m

breadth of the rectangle = 1.6 m

Perimeter of rectangle = 2( l + b )

= 2 × 4.1

= 8.2 m

Hope this helps

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Answer: 9

Step-by-step explanation:

4+6x+5=7x

-6x -6x

=

4+5=1x

9=1x

X=9

Answer:

price of vegetables= regular price-discount

p=r-discount

Step-by-step explanation:

discount = regular price- price of vegetables

discount= r-p

OR

price of vegetables= regular price-discount

p=r-discount

percentage discount

[(original price- discounted price)/original price]*100= percent discount

Answer:

P = r - 8

Step-by-step explanation:

Got it correct.

Answer & Step-by-step explanation:

PEMDAS:

Parentheses

Exponents

Multiplication and Division left to right

Addition and Subtraction left to right

We have two forms of grouping in the expression. Do the inner-most one first, still following PEMDAS within the grouping symbol:

Simplify division:

[tex]6/4=1.5\\1.5-1=0.5\\[/tex]

Re-insert:

[tex]40/(19-1+0.5)[/tex]

Simplify subtraction and addition within parentheses:

[tex]19-1+0.5\\18+0.5\\18.5[/tex]

Re-insert:

[tex]40/18.5[/tex]

Simplify division:

[tex]40/18.5=2.162162162162162162.....[/tex]

:Done

Answer:

180° angle is supplementry angle

Step-by-step explanation:

180°

Answer:

Option a) ∠RXZ & ∠YXZ

Step-by-step explanation:

If sum of two angles are 180°, then the two angles are called supplementary.

∠RXZ & ∠YXZ forms a straight line and sum of ∠RXZ & ∠YXZ

will be 180. So, they are supplementary

Answer:

10% discounted

Step-by-step explanation:

500× X = 450

while X is the sale price

so we solve for X

(500X)÷500 = 450 ÷ 500

X = 0.9

then we turn that into percentage

0.9 × 100 = 90%

finding the discount percentage

100% - 90% = 10%

Answer:

The calculation that will give us the estimated volume is the area of the base of the pyramid of Giza in square meters multiplied by the height of the pyramid of Giza in meters divided by 3 i.e A * h/3

Step-by-step explanation:

Here in this question, we are interested in giving the calculation that will give us the estimated volume of the Great pyramid of Giza in cubic meters.

Mathematically, from the first part of the question, the formula for this is obtainable.

We are told that the formula for calculating the volume of a pyramid is A times h/3 where A represents the area of the base of the pyramid and h represents the height of the pyramid.

In equation form;

V = A * h/3

From the question, we are told that the area of the base is 53,000 m^2 while the height is 150 m

Now, plugging these values into the equation above, we have

V = 53,000 * 150/3

V = 53,000 * 50 = 2,650,000 m^3

The estimated volume of the Great Pyramid of Giza in cubic meters is 2,650,000.

Given the following data:

To calculate the estimated volume of the Great Pyramid of Giza in cubic meters:

Mathematically, the volume of a pyramid is given by the formula:

[tex]Volume = \frac{1}{3} \times base \;area \times height[/tex]

Substituting the given parameters into the formula, we have;

[tex]Volume = \frac{1}{3} \times 53000 \times 150\\\\Volume = 17,666.667 \times 150\\\\Volume = 2,650,000[/tex]

Volume of the Great Pyramid of Giza = 2,650,000 cubic meters

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Answer:

See below.

Step-by-step explanation:

Let x represent the number of days.

Since Day and Night Kennel charges a fee of $20 per day and only a one-time fee of $15:

[tex]y=20x+15[/tex]

Where y represents the total cost, 20x represents the cost for staying x days and 15 is the initial one-time fee.

For Bark Time Hotel, similarly:

[tex]y=30x+5[/tex]

Again, y represents the total cost, 30x represents the cost for staying x days, and 5 is the initial one-time fee.

Thus, the system of equations is:

[tex]y=20x+15\\y=30x+5[/tex]

The system that represents this real-world situation is:

Cost = 20d + 15

Cost = 30d + 5

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

The system that represents this real-world situation is:

Let d be the number of days the pet will be boarded.

For Day and Night Kennel:

Cost = 20d + 15

For Bark Time Hotel:

Cost = 30d + 5

In this system, d represents the number of days the pet will be boarded, the constant 20 represents the daily boarding fee charged by Day and Night Kennel, the constant 30 represents the daily boarding fee charged by Bark Time Hotel, the constant 15 represents the one-time food fee charged by Day and Night Kennel, and the constant 5 represents the one-time food fee charged by Bark Time Hotel.

Thus,

Cost = 20d + 15

Cost = 30d + 5

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Answer:

  10 minutes

Step-by-step explanation:

Answer:

Hey there!

Slope: 7-3/1-(-1), which is equal to 4/2, or 2.

Point slope: y-7=2(x-1)

So choice B is correct.

Let me know if this helps , or if you have any more questions :)

Answer:18

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

that is the answer

f(x) represents x-axis. So, for f(-1), look the point of -1. Then vertically, it reaches the point of -3 which is in the y-axis.

Answer is -3.

Answer:

E (-2, 4).

Step-by-step explanation:

(x/2 + 1)(x/2 - 2) = 0

x/2 = -1,  x/2 = 2

x = -2, 4.

The roots will be 2 times the roots of f(x).

Answer:

[tex]\Large \boxed{\mathrm{E. \ -2, \ 4}}[/tex]

Step-by-step explanation:

The zeros of f(x/2) will double the zeros of f(x).

x = -1 × 2 = -2

x = 2 × 2 = 4

Answer:

[tex]\sqrt{26}[/tex]

Answer:

Option (B)

Step-by-step explanation:

From the graph attached,

Vertical asymptotes of the function are x = -2, 5

Horizontal asymptote is y = 0

Now we take each option,

Option (A),

F(x) = [tex]\frac{x(x-5)}{(x+2)}[/tex]

No horizontal asymptote

Vertical asymptote : x = -2

Option (B),

F(x) = [tex]\frac{x}{(x+2)(x-5)}[/tex]

Horizontal asymptotes : y = 0

Vertical asymptotes : x = 5, -2  

Option (C),

F(x) = [tex]\frac{(x+2)(x-5)}{x}[/tex]

Vertical asymptote : x = 0

No horizontal asymptote.

Therefore, Function given in Option (B) matches the asymptotes given in the graph.

Option (B) represents the graph.

Function given in Option (B) matches the asymptotes given in the graph.

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Now, From the graph attached,

Vertical asymptotes of the function are x = -2, 5

And, Horizontal asymptote is y = 0

Hence, we take each option and check as,

For Option (A),

F(x) = x (x - 5) / (x + 2)

Hence, No horizontal asymptote

And, Vertical asymptote : x = -2

Option (B),

F(x) = x / (x + 2) (x - 5)

Hence, Horizontal asymptotes : y = 0

And, Vertical asymptotes : x = 5, -2  

Option (C),

F(x) = (x + 2) (x - 5) / x

Hence, Vertical asymptote : x = 0

And, No horizontal asymptote.

Therefore, Function given in Option (B) matches the asymptotes given in the graph.

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Answer:

its a formulae

we know (sinx+cosx)^3= sin^3x +cos^3x+3sinxcosx(sinx+cosx)

(a+b)^3= a^3 +b^3+3ab(a+b)

Step-by-step explanation:

(sin^2x)^3 +cos^2x)^3+3sin^2x cos^2x(sin^2x+cos^2x)

according to formulae

(sin^2x+cos^2x)^3  {as we know sin^2x+cos^2x =1}

so the (1)^3= 1

{proved}

thank u

Answer:  see proof below

Step-by-step explanation:

Use the formula for factoring a cubic:   (a³ + b³) = (a + b)(a² - ab + b²)

and the formula for a perfect square:    a² + 2ab + b² = (a + b)²

and the Pythagorean Identity:               cos²x + sin²x = 1

Proof LHS →  RHS

Given:                     sin⁶x + cos⁶x       + 3sin²x cos²x

Regroup:            (sin²x)³ + (cos²x)³     + 3sin²x cos²x

Factor Cubic:     (sin²x + cos²x)(sin⁴x - sin²x cos²x +  cos⁴x)   + 3sin²x cos²x

Pythagorean Identity:             1(sin⁴x - sin²x cos²x +  cos⁴x)   + 3sin²x cos²x

Add like terms:                         sin⁴x + 2sin²x cos²x +  cos⁴x

Regroup:                               (sin²x)² + 2sin²x cos²x +  (cos²x)²

Factor Perfect Square:                      (sin²x + cos²x)²

Pythagorean Identity:                                 (1)²

Simplify:                                                        1

LHS = RHS:   1 = 1    [tex]\checkmark\\[/tex]

Answer:

-1/3 or 1/2.

Step-by-step explanation:

Second term = ar, the third = ar^2 and the fourth = ar^3.

So we have the equation:

ar + ar^2 = 6ar^3

r + r^2 = 6r^3

6r^3 - r^2 - r = 0

r(6r^2 - r - 1) = 0

(3r + 1 )(2r -1) = 0

r = -1/3, 1/2.

Answer:

1 to 2.

We can see that the figure starts at the bottom left, and then moves to the bottom right.

So the vertical position remains constant, and the horizontal position changed, this can be a reflection around the vertical axis.

2 to 3.

Now the figure goes from the bottom right and moves to the top right, not only that, in (2) the figure is facing up, and in (3) the figure is facing down, then we have a reflection around the horizontal axis.

3 to 4.

Similar to the first case, this is a reflection over the vertical axis.

4 to 5.

Similar to the second case, this is a reflection over the horizontal axis.

(Something to notice, the movements can be called "Rotations over the ___ axis". I used reflection because it is specific for this type of motion, while rotation can be used to describe really complex types of motion)

Answer:

yes

Step-by-step explanation:

A rational number is a number that can be written as a ratio of integers

-8/5 is a ratio of integers so it is rational

Answer:

Yes.

Step-by-step explanation:

Rational numbers you can solve. They have a solution.

Answer: Option A & D are true statements.

Work:

For option A, it states 1 pound = 2.75. Now when we divide 16.50 by 6 we get 2.75, so option A is true.

Option B states 2.75 pounds = 1$. We already know this isn't true seeing as 2.75 pounds would equal 7.56, so option B is false.

Option C reads as 5 pounds equal 15.50. When we multiply 5 by 2.75, we get 13.75, so option C is also untrue.

Option D quotes 12 pounds equals 33. When we multiply 12 by 2.75, it equals 33, so this is a true statement!

Option E says the point 3,9 is on the graph, but its not. So this is not true.

Answer:

The answer is below

Step-by-step explanation:

Chicken costs $1.85 per pound, and the beef costs $3.70 per pound. Let x represent the pounds of chicken and y represent the pound of beef. If he spent a total of $12.95, therefore:

1.85x + 3.7y = 12.95           (1)

He bought twice as much beef as chicken, therefore:

y = 2x

y - 2x = 0                             (2)

Solving eqn 1 and eqn 2 simultaneously. Multiply equation (2) by 3.7 and subtract from equation (1)

9.25x = 12.95

x = 1.4 pounds

Also substitute x = 1.4 in equation 2:

y - 2(1.4) = 0

y = 2(1.4)

y = 2.8 pounds

The graph was plotted using geogra, the y coordinate of the point of intersection of the two lines, is the approximate pounds of beef.

Answer: Part A. First line= (0,0), (1,2). Second line= (0,3.5), (1,3)

Part B. 2.75 pounds

Step-by-step explanation: It's correct.

Answer:

Step-by-step explanation:

Answer:

At 7 seconds the instantaneous rate of change of the function s(t) with time which is the velocity is -11.18 m/s

Step-by-step explanation:

The given information on the height can be written as follows;

s(t) = -2.72·t² + 26.9·t + 6

Where;

s = The height (displacement) of the golf ball

t = The time taken during the motion of the golf ball

The velocity is found by finding the derivative of the displacement s as follows;

v = d(s(t))/dt = d(-2.72·t² + 26.9·t + 6)/dt = 2×(-2.72)×t + 26.9

When t = 7, v = 2×(-2.72)×7 + 26.9 = -11.18 m/s

Therefore the ball is coming down with 11.18 m/s speed at 7 seconds.

Answer:

Hey there!

p(x)=7x+25

7x+25=60

7x=35

x=5

Let me know if this helps :)

Answer:

2/3= 0.666666666667

Step-by-step explanation:

Answer:

I GOT YOU!

Step-by-step explanation:

⛅️= 10

❄️= 5

x = 8

So,

10+10+10=30

10+5+5=20

5+8= 13

10+5+8=23

I hope I helped...

Answer:

98%

Step-by-step explanation:

83%+91%+88%+?=90×4

262+?=360

?=360-262

?=98%

Answer:

98% i believe

Step-by-step explanation:

Answer:

(1) Reuse;  (2) Recycle ;  (3) Reduce

Step-by-step explanation:

The ideal sequence would be:

1) Use it again (reuse) if the object still serves its intended purpose/s

2) If not possible to the used again, send it to a recycling plant to extract from it items/parts/substance of utility for other new products

3) if it cannot be reused or recycled, the last option will be to reduce it completely.

Answer:

[tex]\bold{y=2.5x^2+7x+3.3}[/tex]

Step-by-step explanation:

Given:

Parabola with

x − intercepts (−2.2, 0) and (−0.6, 0)

and

y − intercept (0,3.3)

To find:

Equation of parabola ?

Solution:

We can use factored form to find the equation of the parabola.

[tex]y=a(x-\alpha)(x-\beta)[/tex]

Where [tex]\alpha, \beta[/tex] are the x intercepts.

Let use put

[tex]\alpha = -2.2\\\beta = -0.6[/tex]

[tex]y=a(x-(-2.2))(x-(-0.6))\\\Rightarrow y =a(x+2.2)(x+0.6)[/tex]

Now, let us put y − intercept (0,3.3) in the above equation to find the value of a.

[tex]\Rightarrow 3.3 =a(0+2.2)(0+0.6)\\\Rightarrow 33 =a(22)(0.6)\\\Rightarrow 3 = 2a\times 0.6\\\Rightarrow a = 2.5[/tex]

So, the equation becomes:

[tex]\Rightarrow y =2.5(x+2.2)(x+0.6)\\\Rightarrow \bold{y=2.5x^2+7x+3.3}[/tex]