Mr. Gosain?(1 Aana = 31.8 m²) b) A real estate agent bought two triangular Kittas' having a common side as shown in the figure from two people for Rs 20,00,000 altogether. If he immediately sold the land in the shape of a quadrilateral at Rs 15,00,000 per Kattha, find his profit or loss.(1 Kattha= 338.63 sq. m) danta Excel in Mathematics - Book 9 86 36 m Approved by Curriculum Development Cen 20 m 29 m 25 m 21 m aktapur​

Let [tex]n[/tex] be the total number of stickers. If she puts 21 stickers on a page, she will fill up [tex]p[/tex] pages such that

[tex]n = 21p + 14[/tex]

Suzanna has between 90 and 100 stickers, so

[tex]90 \le n \le 100 \implies 76 \le n - 14 \le 86[/tex]

[tex]n-14[/tex] is a multiple of 21, and 4•21 = 84 is the only multiple of 21 in this range. So she uses up [tex]p=4[/tex] pages and

[tex]n-14 = 4\cdot21 \implies n = 4\cdot21 + 14 = \boxed{98}[/tex]

stickers.

Answer:

$2.00 each day so $2.00 x 5 = $10

The image of X after the dilation is (a) (4, 0)

From the figure, the coordinates of X are given as:

X = (4, 0)

The dilation is given as:

Do,1

This means that we dilate X across the origin by a scale factor of 1.

So, we have:

X' = 1 * (4 - 0, 0 - 0)

Evaluate

X' = (4, 0)

Hence, the image of X after the dilation is (a) (4, 0)

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Quadrilateral is a family of plane shapes that have four straight sides. Thus the sum of their internal angles is [tex]360^{o}[/tex]. Examples include rectangle, square, rhombus, trapezium, and kite.

A kite is a plane shape that has its adjacent sides to have equal measures.

The given diagram in the question is a kite that has its specific properties compared to other quadrilaterals.

Thus, the required proof is stated below:

Given: ΔCAV and ΔCEV

Prove that: ΔCAV ≅ ΔCEV

Then,

CE ≅ CA (length of side property of a kite)

EV ≅ AV (length of side property of a kite)

<ACV ≅ <ECV (bisected property of a given angle)

<AVC ≅ <EVC (bisected property of a given angle)

CV is a common side to ΔCAV and ΔCEV

Therefore it can be deduced that;

ΔCAV ≅ ΔCEV (Angle-Angle-Side congruent theorem)

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Answer:

Step-by-step explanation:

2x + 5y = 8

      -5    -5

2x = 8 - 5y

divide both sides by 2

[tex]\frac{2x}{2} = \frac{8-5y}{2}[/tex]

divide by 2 undoes the multiplication by 2

x = [tex]\frac{8- 5y}{2}[/tex]

divide 8 - 5y by 2

x = - [tex]\frac{5}{2}[/tex] y + 4

The graph of an exponential function shows a geometric increase or decrease using a curve

Exponential functions are inverse of logarithmic functions. The standard exponential function is expressed as:

y = ab^x

where

a is the base

x is the exponent

The graph of an exponential function shows a geometric increase or decrease using a curve. According to the function given there will a decrease rate due to the value of the rate value given which is less than 1. The graph of the function given is attached below;

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a. Given the 2nd order ODE

[tex]y''(x) = 4y(x) + 4[/tex]

if we substitute [tex]z(x)=y'(x)+2y(x)[/tex] and its derivative, [tex]z'(x)=y''(x)+2y'(x)[/tex], we can eliminate [tex]y(x)[/tex] and [tex]y''(x)[/tex] to end up with the ODE

[tex]z'(x) - 2y'(x) = 4\left(\dfrac{z(x)-y'(x)}2\right) + 4[/tex]

[tex]z'(x) - 2y'(x) = 2z(x) - 2y'(x) + 4[/tex]

[tex]\boxed{z'(x) = 2z(x) + 4}[/tex]

and since [tex]y(0)=y'(0)=1[/tex], it follows that [tex]z(0)=y'(0)+2y(0)=3[/tex].

b. I'll solve with an integrating factor.

[tex]z'(x) = 2z(x) + 4[/tex]

[tex]z'(x) - 2z(x) = 4[/tex]

[tex]e^{-2x} z'(x) - 2 e^{-2x} z(x) = 4e^{-2x}[/tex]

[tex]\left(e^{-2x} z(x)\right)' = 4e^{-2x}[/tex]

[tex]e^{-2x} z(x) = -2e^{-2x} + C[/tex]

[tex]z(x) = -2 + Ce^{2x}[/tex]

Since [tex]z(0)=3[/tex], we find

[tex]3 = -2 + Ce^0 \implies C=5[/tex]

so the particular solution for [tex]z(x)[/tex] is

[tex]\boxed{z(x) = 5e^{-2x} - 2}[/tex]

c. Knowing [tex]z(x)[/tex], we recover a 1st order ODE for [tex]y(x)[/tex],

[tex]z(x) = y'(x) + 2y(x) \implies y'(x) + 2y(x) = 5e^{-2x} - 2[/tex]

Using an integrating factor again, we have

[tex]e^{2x} y'(x) + 2e^{2x} y(x) = 5 - 2e^{2x}[/tex]

[tex]\left(e^{2x} y(x)\right)' = 5 - 2e^{2x}[/tex]

[tex]e^{2x} y(x) = 5x - e^{2x} + C[/tex]

[tex]y(x) = 5xe^{-2x} - 1 + Ce^{-2x}[/tex]

Since [tex]y(0)=1[/tex], we find

[tex]1 = 0 - 1 + Ce^0 \implies C=2[/tex]

so that

[tex]\boxed{y(x) = (5x+2)e^{-2x} - 1}[/tex]

6.a) The differential equation for z(x) is z'(x) = 2z(x) + 4, z(0) = 3.

6.b) The value of z(x) is [tex]z(x) = 5e^{2x} - 2[/tex].

6.c) The value of y(x) is [tex]y(x) = \frac{5e^{2x}}{4} - \frac{1}{4e^{2x}} -1[/tex].

The given ordinary differential equation is y''(x) = 4y(x) + 4, y(0) = y'(0) = 1 ... (d).

We are also given a substitution function, z(x) = y'(x) + 2y(x) ... (z).

Putting x = 0, we get:

z(0) = y'(0) + 2y(0),

or, z(0) = 1 + 2*1 = 3.

Rearranging (z), we can write it as:

z(x) = y'(x) + 2y(x),

or, y'(x) = z(x) - 2y(x) ... (i).

Differentiating (z) with respect to x, we get:

z'(x) = y''(x) + 2y'(x),

or, y''(x) = z'(x) - 2y'(x) ... (ii).

Substituting the value of y''(x) from (ii) in (d) we get:

y''(x) = 4y(x) + 4,

or, z'(x) - 2y'(x) = 4y(x) + 4.

Substituting the value of y'(x) from (i) we get:

z'(x) - 2y'(x) = 4y(x) + 4,

or, z'(x) - 2(z(x) - 2y(x)) = 4y(x) + 4,

or, z'(x) - 2z(x) + 4y(x) = 4y(x) + 4,

or, z'(x) = 2z(x) + 4y(x) - 4y(x) + 4,

or, z'(x) = 2z(x) + 4.

The initial value of z(0) was calculated to be 3.

6.a) The differential equation for z(x) is z'(x) = 2z(x) + 4, z(0) = 3.

Transforming z(x) = dz/dx, and z = z(x), we get:

dz/dx = 2z + 4,

or, dz/(2z + 4) = dx.

Integrating both sides, we get:

∫dz/(2z + 4) = ∫dx,

or, {ln (z + 2)}/2 = x + C,

or, [tex]\sqrt{z+2} = e^{x + C}[/tex],

or, [tex]z =Ce^{2x}-2[/tex] ... (iii).

Substituting z = 3, and x = 0,  we get:

[tex]3 = Ce^{2*0} - 2\\\Rightarrow C - 2 = 3\\\Rightarrow C = 5.[/tex]

Substituting C = 5, in (iii), we get:

[tex]z = 5e^{2x} - 2[/tex].

6.b) The value of z(x) is [tex]z(x) = 5e^{2x} - 2[/tex].

Substituting the value of z(x) in (z), we get:

z(x) = y'(x) + 2y(x),

or, 5e²ˣ - 2 = y'(x) + 2y(x),

which gives us:

[tex]y(x) = \frac{5e^{2x}}{4} - \frac{1}{4e^{2x}} -1[/tex] for the initial condition y(x) = 0.

6.c) The value of y(x) is [tex]y(x) = \frac{5e^{2x}}{4} - \frac{1}{4e^{2x}} -1[/tex].

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The third side of the triangle falls between (50, 60).

Inequality triangle theorem states that the sum of any two sides of a triangle is greater than or equal to the third side.

Therefore, the other two sides are 5 cm and 55 cm. The range of the third side x can be computed using inequality triangle theorem.

Hence,

x < 5 + 55

x < 60

And,

x > 55 - 5

x > 50

Therefore, 50 < x < 60.

Hence, the third side of the triangle falls between (50, 60).

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The answer is -7.

The coefficient is the part of the variable that does not change with respect to the variable.

Hence, in the monomial -7x²y⁴, the coefficient is -7.

Answer:

x = 5

Step-by-step explanation:

There's a Secant Theorem that someone else figured out (waaaay back in history) we just need to memorize it. So a secant is a line that touches the circle in two places. Your picture has two secants that both go thru the same point that's outside the circle. The secants each have a bit that's inside the circle and a bit that's outside the circle. And we could add together the inside and outside bits and get a total for the whole thing.

The secant theorem says that the outside piece × the whole thing on one secant = the outside piece × the whole thing on the other secant.

For the secant on top the "outside" bit is 9 and the whole thing is (2x+1+9). We'll times these together.

For the bottom secant the outside piece is 10 and the whole thing is (x+3+10). We'll multiply these together.

9(2x+1+9)=10(x+3+10)

simplify.

9(2x+10) = 10(x+13)

distribute.

18x + 90 = 101x + 130

combine like terms.

8x + 90 = 130

subtract 90

8x = 40

divide by 8

x = 5

see image.

[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & 80\\ P=\textit{initial amount}\dotfill &40\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years \end{cases} \\\\\\ 80=40(1 + 0.05)^{t}\implies \cfrac{80}{40}=1.05^t\implies 2=1.05^t\implies \log(2)=\log(1.05^t) \\\\\\ \log(2)=t\log(1.05)\implies \cfrac{\log(2)}{\log(1.05)}=t\implies 14.2\approx t[/tex]

Answer:

a)

Step-by-step explanation:

Answer:

<-3,3>

Step-by-step explanation:

Answer:

0.00018

Step-by-step explanation:

formula:Divide the volume by 1e+6

Answer:

I believe it should be d

Step-by-step explanation:

Answer

square root of 128 Lies between two square numbe

121 = 11 ^ 2

(11.1) ^ 2 = 133.1

So, √128 lies between 11.0 and 11.1.

Answer:

x=90

y=148

Step-by-step explanation:

Since we know a line is 180 degrees, and we know that angle Q is 90, x must be a 90-degree angle as well.

With our given information we can add up the two given angles in the triangle which are 90 and 58

90+58=148

To find what R is, we must subtract 148 from 180 because all the angles in a triangle sum up to 180.

180-148=32

Now that we know that R is 32, because we know that a line is 180 degrees, we can subtract 32 from 180 to get our final answer for y as 148.

180-32=148

Answer:

The equation of the line is y = -1.x + 9

Graph is provided in the attached figure

Step-by-step explanation:

The slope intercept equation of a line in 2D(x,y) coordinates is given by the equation

[tex]y = mx + c[/tex]

where m is the slope of the line and c the y-intercept i.e. where the line crosses the y axis at x = 0

Given slope = -1, we can find c and the equation of the line

Since (3,6) is a point on the graph, these coordinates must satisfy the above equation

Substitute for y = 6 and x = 3

[tex]6 = (-1)3 + c\\\\c = 9\\\\\textrm{Equation of line is }\\y = -1.x + 9 \\y = 9-x[/tex]

In the attached figure you can see that (3,6) is on the line

Answer:

A cone has one -third times the volume of a cylinder with the same base and altitude. True

The answer is A. True.

Assuming the cylinder and cone have same base and altitude, the formulas are :

Based on this, we can understand that :

A cone has one-third times the volume of a cylinder with the same base and altitude.

Answer:

it's simple, put the values in the equation.

5 + d( 3b-2d) = 5 + 4( 3×-3 - 2× 4)

= 5 + 4( -9-8)

= 5+ 4 × -17

= 5-68 = -63 ans.

Answer:

The statement "q + 5 is odd" is FALSE.

Step-by-step explanation:

Let p = 2 and q = 3.

A. p + q is odd ... 2 + 3 = 5   TRUE

B. pq is even ... 2*3 = 6   TRUE

C. q + 1 is even ... 3 + 1 = 4   TRUE

D. q + 5 is odd ... 3 + 5 = 8   FALSE

The time requires to catch up to him will be 3 hours.

Speed is defined as the ratio of the time distance traveled by the body to the time taken by the body to cover the distance. Speed is a scalar quantity it does not require any direction only needs magnitude to represent.

Given that Hunter leaves his house to go on a bike ride. He starts at a speed of 15 km/hr. Hunter's brother decides to join Hunter and leaves the house 30 minutes after him at a speed of 18 km/hr.

The time will be calculated as below:-

30 minutes = 0.5 hour

15x = 18(x - 0.5)

15x = 18x - 9

-3x = -9

x = 3 hours

Therefore, the time requires to catch up to him will be 3 hours.

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Answer: A

Step-by-step explanation:

The total value of the prizes is [tex]1000+500+2(50)=1600[/tex].

The total cost of the tickets is [tex]1000(4.00)=4000[/tex].

So, the total loss is $2400.

Dividing this by 1000 tickets gives $-2.40.

The correct equation is [tex]x\cdot6=3x-4[/tex].

Let the number be [tex]x[/tex].

According to the question,

Number multiplied by [tex]6[/tex] [tex]=6x[/tex].

[tex]4[/tex] less than thrice the number  [tex]=3x-4[/tex].

Hence, the correct equation will be [tex]x\cdot6=3x-4[/tex].

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Answer:

36Q

Step-by-step explanation:

multiply all together we have 36Q

The decision is to fail to reject the null given that p value is not ≤ 0.05.

The hypothesis

H0 = p = 0.63

H1 = p < 0.63

α = 0.05

sample proportion = 71/125 = 0.568

x = 71

n = 125

standard error of the proportion

√0.63(1-0.63)/125

= 0.0431

The null hypothesis follows a standard normal distribution. This is a left tailed test.

We are to reject the null if the p value is less than 0.05

p < 0.05

This probability test is a z probability test.

Z test = 0.568 - 0.63 / 0.0431

test statistic = -1.436

-Z0.05 =

Critical value =  -1.645

p(z < -1.436)

p value = 0.0755

The decision would be to fail to reject the null hypothesis. The reason would be due to the fact that p value is greater than significance.

P-value is not ≤ α 0.05

0.0755 > 0.05

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Answer:

x = 48/7

Step-by-step explanation:

There's two good ways to do this problem.

Option 1:

Translate "x varies directly as y" into the equation y=kx

Then you have to find k. After you "reset" your y=kx equation, fill in k and then solve for x. See image.

Option 2:

Translate "varies directly" into a proportion, which is two fractions equal to each other:

x/y = x/y

Fill in the three numbers given and cross multiply and solve to find the fourth number. See image.