A garment store sells a particular brand of a shirt at ₹x and a particular brand of a trouser at ₹y. John buys 5 shirts and 3 trousers from the store at ₹9000. Frame an equation to model the above situation.

Answer:

Step-by-step explanation:

combine like terms

-7x + 3x - 15y - 2y

-4x - 17y

Answer:

[tex]\bold{x = \dfrac{8}{9}}[/tex]

Step-by-step explanation:

We have to rewrite the below as simplified fraction.

[tex]\large{0.\overline{8} = {?}}[/tex]

Solution:

Let [tex]x =0.\overline 8[/tex] which means [tex]x =0.888888.......[/tex]

Here a bar over 8 means that there the given decimal value is non terminating and there are a large numbers of 8 present after the decimal.

To solve the given non terminating decimal as fractions, we will have to eliminate the bar term from the given value.

So, we can rewrite [tex]x[/tex] as:

[tex]x =0.8\overline8[/tex] ......(1)

Now, let us multiply the above with 10.

[tex]10x = 0.8\overline 8 \times 10\\\Rightarrow 10 x= 8.\overline8[/tex] ....... (2)

Now, let us subtract (1) from (2):

[tex]10x-x=8.\overline8 - 0.\overline8\\\Rightarrow 9x = 8\\\Rightarrow \bold{x = \dfrac{8}{9}}[/tex]

So, in simplified fractions:

[tex]\large{0.\overline{8} = \bold{\dfrac{8}{9}}}[/tex]

Answer:

There is no statements/info.

Step-by-step explanation:

Answer:

Infinite Number of Solutions

Step-by-step explanation:

Since 4*x= 4x

and 4*4= 16

its 4x+16

which is 4x+16=4x+16

Since there are the same, and both equal each other, there are an infinite number of solutions.

Answer:

infinite number of solutions

Step-by-step explanation:

4(x + 4) = 4x + 16

Distribute on the left side.

4x + 16 = 4x + 16

Subtract 16 from both sides.

4x = 4x

Divide both sides by 4.

x = x

x = x is a true equation for every value of x.

Answer: infinite number of solutions

Answer:

In step 1

Step-by-step explanation:

She has [tex]27(36)=27(3+12)[/tex]

this mean that 36=3+12

that's her mistake

Answer:

step 1

Step-by-step explanation:

Answer:

A) 4 Hours (of running)

B) 5 Hours (of biking)

Step-by-step explanation:

So Suzette ran and biked for a total of 80 miles,

and she did all of that in 9 hours.

Let x equal the total hours of Suzette ran and let y equal the total hours of Suzette biked.

Therefore:

[tex]x+y=9[/tex]

This represents the total hours. We know that the hours she had ran and biked totals 9. Thus, x plus y must equal 9.

And also:

[tex]5x+12y=80[/tex]

The 5x represents the miles she had ran in x hours, while the 12x represents the miles she had biked in y hours. All together, they must equal 80 miles total.

Therefore, our system is:

[tex]x+y=9\\5x+12y=9[/tex]

We can solve this using substitution. First, subtract x from the top equation:

[tex]x+y=9\\y=9-x[/tex]

Now, substitute the y into the second equation:

[tex]5x+12y=80\\5x+12(9-x)=80[/tex]

Distribute:

[tex]5x+108-12x=80[/tex]

Combine like terms:

[tex]-7x+108=80[/tex]

Subtract 108 from both sides:

[tex](-7x+108)-108=(80)-108\\-7x=-28[/tex]

Divide both sides by -4:

[tex]x=4[/tex]

Therefore, Suzette ran for a total of 4 hours.

Since she biked and ran for a total of 9 hours, she must have biked for 9-4 or 5 hours.

Checking:

4 hours of running plus 5 hours of biking does indeed equal 9 hours total:

[tex]4(5)+5(12)=20+60=80[/tex]

So by running 5mph for 4 hours and by biking 12mph for 5 hours, she did indeed reach a total of 80 miles.

Answer:

7.5

Step-by-step explanation:

How long does it take a car to travel 1 mile if its average speed is 40 mph? The answer is 1/40 of an hour or 1.5 minutes. multiply this by 5

Answer:

0.1 hours to the nearest tenth (0.125 hours exact)

Step-by-step explanation:

For this problem, we simply need to do a conversion to find the length of time.

We are given the rate 40 miles per hour, and the distance of 5 miles.  We simply need to know the amount of time.

5 miles * (1 hour per 40 miles) =  1 hour / 8

Note, the distance unit cancels out.

So, to travel 5 miles it will take 1/8 of an hour.

1/8 as a decimal is equal to 0.125.  The answer rounded to the nearest tenth would be 0.1 hours, since the 2 rounds down.

Cheers.

Answer:

[tex]\bold{x = 34^\circ}[/tex]

Step-by-step explanation:

Given:

[tex]cos x = sin (x + 22^\circ)[/tex]

To solve:

The given equation.

Solution:

First of all, let us consider an important property of sine and cosine.

[tex]sin(90^\circ-\theta )=cos\theta[/tex]

OR

[tex]cos(90^\circ-\theta )=sin\theta[/tex]

We can apply above property to solve for [tex]x[/tex] as per given equation.

[tex]cos x = sin (x + 22^\circ)[/tex]

Changing [tex]cosx[/tex] to sine form:

[tex]cosx=sin(90^\circ-x)[/tex]

[tex]cosx=sin(90^\circ-x) = sin(x+22^\circ)[/tex]

[tex]\therefore 90^\circ-x=x+22^\circ\\\Rightarrow 90^\circ-22^\circ=x+x\\\Rightarrow 2x=68^\circ\\\Rightarrow \bold{x = 34^\circ}[/tex]

So, solution to the equation [tex]cos x = sin (x + 22^\circ)[/tex] is:

[tex]\bold{x = 34^\circ}[/tex]

Answer:

  35

Step-by-step explanation:

The law of sines tells us ...

  sin(C)/c = sin(A)/a

  a·sin(3A) = c·sin(A)

Using the identity sin(3x) = 3cos(x)·sin(x) -sin(x)^3 and sin(x)^2 +cos(x)^2 = 1, we can simplify this to ...

  sin(A)(4cos(A)^2 -1) = (c/a)sin(A)

  4cos(A)^2 = c/a +1 = (48+27)/27 = 75/27 = 25/9

  cos(A)^2 = 25/36

  cos(A) = 5/6

__

Now, the angle B will be the difference between 180° and the sum of the other two angles:

  B = 180° -A -3A = 180° -4A

Using appropriate trig identities, we can write ...

  sin(B) = 4cos(A)^3sin(A) -4sin(A)^3cos(A)

  = 4sin(A)cos(A)(cos(A)^2 -sin(A)^2)

  = 4sin(A)cos(A)(2cos(A)^2 -1)

Filling in our value for cos(A), this becomes ...

  sin(B) = 4sin(A)(5/6)(2(5/6)^2-1) = sin(A)(35/27)

__

The law of sines tells us ...

  b/sin(B) = a/sin(A)

  b = a·sin(B)/sin(A) = 27(35/27)sin(A)/sin(A) = 35

The length of side b is 35 units.

Answer:

Step-by-step explanation:

Hello, please consider the following.

[tex]3x^2+ 7x - 11 =0\\\\\Delta=b^2-4ac=7^2-4*3*(-11)=49+132=181\\\\x_1=\dfrac{-b-\sqrt{\Delta}}{2a}=\dfrac{-7-\sqrt{181}}{6}=-3.40894...\\\\x_2=\dfrac{-b+\sqrt{\Delta}}{2a}=\dfrac{-7+\sqrt{181}}{6}=1.075604...[/tex]

So, it gives -3.41 and 1.08

Thank you.

Answer:

a = √10

Step-by-step explanation:

a² + b² = c²

a² + 9² = (√91)²

a² + 81 = 91

a² = 10

a = √10

hope this helps :)

Answer:

square root of 10

Step-by-step explanation:

a^2 + b^2 = c^2

=> a^2 + 9^2 = square root of 91^2

=> a^2 + 81 = 91

=> a^2 = 91 - 81

=> a^2 = 10

=> a = square root of 10

The bottom face is a circle of area pi*r^2 = pi*5^2 = 25pi square feet

The lateral surface area is pi*r*L = pi*5*13 = 65pi square feet

Those two areas combine to 25pi+65pi = 90pi square feet

The surface area of the cone is 65π square ft or 65π ft² option (D) 65π ft² is correct if the radius of the cone base is 5 ft and the slant height is 13 ft.

It is defined as a three-dimensional shape in which the base is a circular shape and the diameter of the circle decreases as we move from the circular base to the vertex.

[tex]\rm V=\pi r^2\dfrac{h}{3}[/tex]

We have a cone shown in the picture.

The radius of the cone r = 5 ft

The slant height l = 13 ft

As we know, the lateral surface is given by:

S = πrl

Here,

S is the surface area

r is the radius of the cone base

l is the slant height.

S = π(5)(13)

S = 65π square ft

Thus, the surface area of the cone is 65π square ft or 65π ft² option (D) 65π ft² is correct if the radius of the cone base is 5 ft and the slant height is 13 ft.

Learn more about the cone here:

brainly.com/question/16394302

#SPJ5

Answer:

Lines a and b are parallel because their corresponding angles are congruent

Step-by-step explanation:

The corresponding angle postulate states that Two lines are said to be parallel if when cut by a transversal, their corresponding angles are congruent.

Therefore given line a and line b which is cut by transversal e, both corresponding angles are equal to 110 (congruent), therefore according to the corresponding angle postulate, we can say that line a and line b are parallel to each other.

Answer: A

Step-by-step explanation:

Answer:

[tex]96ft^{2}[/tex]

Step-by-step explanation:

Step 1: Find the area of the base

[tex]\frac{bh}{2} =\frac{(8)(6)}{2}=\frac{48}{2}=24ft^{2}[/tex]

Step 2: Find volume

[tex]=\frac{1}{3}(24)(12) \\=\frac{1}{3}(288)\\=96ft^{3}[/tex]

x - the first number,

y - the second number

We have:

[tex]\begin{cases}y=5x\\y+21=2(x+21)\end{cases}\\\\\\\begin{cases}y=5x\\y+21=2x+42\end{cases}\\\\\\\begin{cases}y=5x\\5x+21=2x+42\end{cases}\\\\\\\begin{cases}y=5x\\3x=21\quad|:3\end{cases}\\\\\\\begin{cases}y=5x\\\boxed{x=7}\end{cases}\\\\y=5x\\\\y=5\cdot7\\\\\boxed{y=35}[/tex]

So answer is 7 and 35.

Answer:

6 kg/m

Step-by-step explanation:

mass m = 3x^2.

rho ρ= dm/dx =6x

ρ(1) =6 Kg/m

linear density is the derivative of mass (m)  with respect to position(x)

that is how fast is the mass changing at that position.

Answer:

Christianity and Islamic religion

Step-by-step explanation:

Based on the picture you provided It would be Christianity and Islamic religion.

Based on the Events of the Common Era (year 0) was the birth of Jesus of Nazareth. From Year 0 to year 29 Jesus of Nazareth expanded his faith. During the 29th year Jesus of Nazareth was crusified in Jeruselem.

Estimated around Year 570 Muhammad  (the Prophet of Islam) was born and rose his religion to great heights. In 632 Muhammad died.

Hope this helps

Answer:

Christianity and Islam

Step-by-step explanation:

Answer:

[tex](3y+5)(9y^{2} -15y+25)[/tex]

Step-by-step explanation:

Answer:

1.47 is the answer

Answer:

1.4666667 rounded off to 1.47

Step-by-step explanation:

Answer:

[tex]-4d[/tex]

Step-by-step explanation:

We can subtract a term from another if they have the same variable. Both [tex]3d[/tex] and [tex]7d[/tex] have the variable [tex]d[/tex], so we can subtract them.

When subtracting these terms, we subtract the coefficients and keep the variable.

So:

[tex]3d - 7d = 3-7(d) = -4d[/tex]

Hope this helped!

Answer:

-4d

Step-by-step explanation:

3d - 7d

=> 3 x D - 7 x D

=> (3 - 7)(D)

=> -4 x D

=> -4d

Answer:

5 + 7

Step-by-step explanation:

3 + 2 = 5, 4 + 3 = 7

Answer:

Simplified expression: 5 + 7

Answer: 12

Step-by-step explanation:

Answer:

  f(x) = |x -1|

Step-by-step explanation:

The parent absolute value function f(x) = |x| is shifted one unit to the right. We know that replacing x with (x-h) will shift a function h units to the right. Here, we want h=1. The shifted function is ...

  f(x) = |x -1|

Answer:

64,890

Step-by-step explanation:

105×3 =315

103×2= 206

315×206= 64,890

Answer:

6.489× 10⁴

Step-by-step explanation:

(3×105)×(2×103)

315× 206

64,890

6.489×10⁴

Answer:

18.72 cubic feet

Step-by-step explanation:

Volume of the aquarium = lwh

V = 5.2*1.8*2 = 18.72 cubic feet

Answer:

0.0009

Step-by-step explanation:

9*10⁻⁴ = 0.0009

Answer:

T > (L + D)/B...multiply by B

TB > L + D ... subtract L

TB - L > D

can you plz mark me brainiest ;<

tank chu hope this helps TwT

Answer:

Right angle triangle

Step-by-step explanation:

12m

15m

9m

Assume the Longest side=15m

Using Pythagoras theorem

c^2=a^2 + b^2

Where,

c=hypotenuse

a=adjacent

b=opposite

Let a=9m

b=12m

c^2=a^2 + b^2

=9^2 + 12^2

=81 + 144

c^2=225

c=√225

=15m

Therefore, the triangle XYZ is a right angle triangle

Answer:

Fencing required = 1586 m

Step-by-step explanation:

The given statements can be thought of a triangle [tex]\triangle ABC[/tex] as shown in the diagram attached.

A be the 1st vertex, B be the 2nd vertex and C be the 3rd vertex.

Distance between 1st and 2nd vertex, AB = 435 m

Distance between 2nd and 3rd vertex, AC = 656 m

[tex]\angle A =49^\circ[/tex]

To find:

Fencing required for the triangular field.

Solution:

Here, we know two sides of a triangle and the angle between them.

To find the fencing or perimeter of the triangle, we need the third side.

Let us use Cosine Rule to find the third side.

Formula for cosine rule:

[tex]cos A = \dfrac{b^{2}+c^{2}-a^{2}}{2bc}[/tex]

Where  

a is the side opposite to [tex]\angle A[/tex]

b is the side opposite to [tex]\angle B[/tex]

c is the side opposite to [tex]\angle C[/tex]

[tex]\Rightarrow cos 49^\circ = \dfrac{656^{2}+435^{2}-BC^{2}}{2\times 435\times 656}\\\Rightarrow BC^2 = 430336+189225-2 (435)(656)cos49^\circ\\\Rightarrow BC^2 = 430336+189225-570720\times cos49^\circ\\\Rightarrow BC^2 =619561-570720\times cos49^\circ\\\Rightarrow BC \approx 495\ m[/tex]

Perimeter of the triangle = Sum of three sides = AB + BC + AC

Perimeter of the triangle = 435 + 495 + 656 = 1586 m

Fencing required = 1586 m

Answer:

-1.2 Hope this helps!

Step-by-step explanation:

Answer:

The correct answer is $4.75/month.

Step-by-step explanation:

To find the unit price per month, or the amount that of the subscription that will be paid each month, we must divide the total price ($28.50) by the number of months covered (6 months).  

$28.50/6 = $4.75

Therefore, the unit price per month is $4.75/month.

Hope this helps!