7. A shopkeeper can buy 36 toys for $20.52. What will he pay for 120 toys

Step by step explansion ​

Answer:

Step-by-step explanation:

We are to show that [tex]\sqrt{3} cosec140^{0} - sec140^{0} = 4\\[/tex]

Proof:

From trigonometry identity;

[tex]cosec \theta = \frac{1}{sin\theta} \\sec\theta = \frac{1}{cos\theta}[/tex]

[tex]\sqrt{3} cosec140^{0} - sec140^{0} \\= \frac{\sqrt{3} }{sin140} - \frac{1}{cos140} \\= \frac{\sqrt{3}cos140-sin140 }{sin140cos140} \\[/tex]

From trigonometry, 2sinAcosA = Sin2A

[tex]= \frac{\sqrt{3}cos140-sin140 }{sin140cos140} \\\\= \frac{\sqrt{3}cos140-sin140 }{sin280/2}\\= \frac{4(\sqrt{3}/2cos140-1/2sin140) }{2sin280}\\\\= \frac{4(\sqrt{3}/2cos140-1/2sin140) }{sin280}\\since sin420 = \sqrt{3}/2 \ and \ cos420 = 1/2 \\ then\\\frac{4(sin420cos140-cos420sin140) }{sin280}[/tex]

Also note that sin(B-C) = sinBcosC - cosBsinC

sin420cos140 - cos420sin140 = sin(420-140)

The resulting equation becomes;

[tex]\frac{4(sin(420-140)) }{sin280}[/tex]

= [tex]\frac{4sin280}{sin280}\\ = 4 \ Proved![/tex]

Answer:

B

Step-by-step explanation:

M is a factor of N and [tex](1+r)^t[/tex], which is not influenced by N. This is because N is just the initial amount of people, and does not change no matter the rate of new members. Hope this helps!

Answer:

postulates, common notions, and axioms

Answer:

$50

Step-by-step explanation:

If he pays $10 every month, and he pays for 5 months, it would be 10 x 5, which means he would be $50 in debt.

Answer:

b = a² + 2a

Step-by-step explanation:

a + 1 = √(b + 1)

(a + 1)² = b + 1 (Square both sides)

a² + 2a + 1 = b + 1 (Expand left side)

a² + 2a = b (Subtract 1)

Answer:

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-4-2)/(-1-2)

m=-6/-3

m=2

Answer:

Step-by-step explanation:

The multiplicity of a root of a polynomial equation is the number of times it appears in the solution.

Multiplicity is important because it can tell us two things about the polynomial that we work on and how it is graphed. first: it tells us the number repeating factor a polynomial has to determine the number of the real (positive or negative) roots and complex roots of the polynomial.

About graph behaves at the roots : Behavior of a polynomial function near a multiple root

The root −4 is a 'simple' root (of multiplicity 1), and therefore the graph crosses the x-axis at this root. The root 1 is of even multiplicity and therefore the graph bounces off the x-axis at this root.

Answer:

To find this out, you simply multiply 6x5 which is 30

Answer:

x=35.44

Step-by-step explanation:

x=ky^3 and√z

x=k(y^3)(√z)

Find k when

x=7

y=2

z=4

7=k(2^3)(√4)

7=k(8)(2)

7=k(16)

7=16k

k=7/16

Find x when y=3, z=9

x=k(y^3)(√z)

x=(7/16)(3^3)(√9)

x=(7/16)(27)(3)

=7/16(81)

=567/16

x=35.4375

Approximate to 2 decimal places

x=35.44

Answer:

301.44 cm ^ 2

Step-by-step explanation:

We have that the total surface area of a cone would be the sum of the base area and the lateral surface area.

the area of the base, being a circle is pi * r ^ 2

the lateral area would come being the multiplication between the inclined height, the radius and the number pi, that is to say pi * r * l

the inclined height is calculated using the Pythagorean theorem, the legs being the radius and the altitude, thus:

l ^ 2 = 6 ^ 2 + 8 ^ 2

l ^ 2 = 100

l = 10

Therefore, we can replace:

A = 3.14 * 6 ^ 2 + 3.14 * 10 * 6

A = 301.44

It means that the total surface area is 301.44 cm ^ 2

Answer:

43.6%

Step-by-step explanation:

curved surface area (green) is found by circumference multiply by height

[tex]\pi[/tex] x d x h = [tex]\pi[/tex] x (15 x 2) x 12 = 360[tex]\pi[/tex]

total surface area is

blue circle + total curved surface area (blue + green)

= [tex]\pi[/tex][tex]r^{2}[/tex] + 15(2)(8)[tex]\pi[/tex] + 360[tex]\pi[/tex]

= [tex]15^{2}[/tex][tex]\pi[/tex] + 240[tex]\pi[/tex] + 360[tex]\pi[/tex]

= 825[tex]\pi[/tex]

percentage = 360[tex]\pi[/tex]/825[tex]\pi[/tex] x 100%= 22/55 x 100% = 43.63

Answer: Area for trapezoid= 1/2(4+5×1)=4.5 m

Area of triangle= Iam not exactly sure

hope this helped you a bit

Step-by-step explanation:

Answer:

32 degrees

Step-by-step explanation:

If AB and BC are perpendicular, that means the angle is 90 degrees. They already give you 24 and 24 which add up to 48 and then you subtract 90 by 48 to find the missing value

Answer:

81:324

Step-by-step explanation:

3+12=15

405 div 15 =27

3 times 27 = 81

12 times 27 = 324

81:324

Answer: to make AB perpendicular to CD move point B until the angle between the lines, BEC measures 90 degree

Step-by-step explanation:

Answer: True

When two lines are crossed by another line (which is called the Transversal), the angles in matching corners are called corresponding angles. When the two lines are parallel Corresponding Angles are equal.

Answer:

3811.2 cubic cm

Step-by-step explanation:

Formula for sphere volume: 4/3πr^3 and since r=10, then plugging it in will be 1000*4/3π≈4188.79. The cube has side length 10*2=20 and has a volume of 20^3=8000. 8000-4188.79=3811.21≈3811.2

Answer:

its 456

Step-by-step explanation:

Answer:

yes the graph reflects over the y-axis because if you see in the y axis the line show that it is the pont to the axis

hope it helps

Answer:

x ≤ -7

Step-by-step explanation:

There is a filled in circle which means that it is either ≤ or ≥.

The graph is going to the left, which means it is ≤

The starting number is -7.

x ≤ -7

Answer:

[tex]\large \boxed{x = 10}[/tex]

Step-by-step explanation:

[tex]\begin{array}{rcll}75\left (\dfrac{1}{5}\right )^{\dfrac{x}{5}} & = & 3& \\\\\left (\dfrac{1}{5}\right )^{\dfrac{x}{5}} & = & \dfrac{3}{75}&\text{Divided each side by 75} \\\\\left (\dfrac{1}{5}\right )^{\dfrac{x}{5}} & = & \dfrac{1}{25}&\text{Simplified} \\\\\left (\dfrac{1}{5}\right )^{\dfrac{x}{5}} & = &25^{-1}&\text{Applied exponent rule} \\\\\left (\dfrac{1}{5}\right )^{\dfrac{x}{5}} & = &\left (5^{2} \right )^{-1}&\text{Converted 25 to base 5} \\\\\end{array}[/tex]

[tex]\begin{array}{rcll}\left (5^{-1}\right )^{\dfrac{x}{5}} & = &\left (5^{2} \right )^{-1}&\text{Applied exponent rule} \\\\5^{-\dfrac{x}{5}} & = &5^{-2}&\text{Multiplied exponents} \\\\-\dfrac{x}{5} & = &-2 & \text{Equated exponents}\\\\x & = & \mathbf{10} & \text{Multiplied each side by -2}\\\end{array}\\\text{The exact solution is $\large \boxed{\mathbf{x = 10}}$}[/tex]

Step-by-step explanation:

bacteria also have small, closed-circle of DNA called plasma and present in their cytoplasm .

Answer:

p(p+q-qr)

Step-by-step explanation:

p^2+pq-pqr​

Factor out a p

p(p+q-qr)

Answer:

p(p+q-qr)

Step-by-step explanation:

p^2 +pq-pqr

= p(p+q-qr)

Answer:

[tex]y = 36[/tex]

Step-by-step explanation:

Given; the triangle above

Required

Find y

This question falls under the topic/subtopic similar triangles where we need to make comparison between similar sides'

But first, it should be noted that triangle MOP is similar to triangle MLN

This implies that

Side MP is similar to MN

Side MO is similar to  ML

Mathematically; This can be represented as follows;

[tex]\frac{MP}{MN} = \frac{MO}{ML}[/tex]

Where MP =y; MN = y + 18; MO = 28; ML = 28 + 14

Substitute these values in the above expression

[tex]\frac{y}{y+18} = \frac{28}{28+14}[/tex]

[tex]\frac{y}{y+18} = \frac{28}{42}[/tex]

Multiply both sides by 42

[tex]42 * \frac{y}{y+18} = \frac{28}{42} * 42[/tex]

[tex]\frac{42y}{y+18} = \frac{28*42}{42}[/tex]

[tex]\frac{42y}{y+18} = 28[/tex]

Multiply both sides by y + 18

[tex](y+18)*\frac{42y}{y+18} = 28 * (y+18)[/tex]

[tex]42y = 28 * (y+18)[/tex]

Open Bracket

[tex]42y = 28 * y+28 * 18[/tex]

[tex]42y = 28y+504[/tex]

Subtract 28y from both sides

[tex]42y - 28y = 28y - 28y +504[/tex]

[tex]14y = 504[/tex]

Divide both sides by 14

[tex]\frac{14y}{14} = \frac{504}{14}[/tex]

[tex]y = \frac{504}{14}[/tex]

[tex]y = 36[/tex]

Answer:

y= 36

Step-by-step explanation:

also ily, no homo

Answer:

1 litro de leche cuesta 2.5

1 kg de jamón serrano cuesta 35

1 litro de aceite de oliva cuesta 7,5

Step-by-step explanation:

Pregunta correcta completa

Un cliente de un supermercado ha pagado un total de 240 por 16 litros de leche,4kg de hamon serrano y 8 litros de aceite de oliva. Sabiendo que 1 litro de aceite cuesta el tripe de 1 litro de leche; que 1kg de jamon cuesta igual que el cliente tendria que pagar si hubiera comprado 5 litros de leche y 3 litros de aceite de oliva. Calcule el precio de cada artículo.

Solución

Deje que el precio de un litro de leche, un kilogramo de jamón serrano y un litro de aceite de oliva sea x, y y z respectivamente.

16 litros de leche, 4 kg de hamon serrano y 8 litros de aceite de oliva cuestan 240

16x + 4y + 8z = 240 (ecuación 1)

1 litro de aceite cuesta el triple de 1 litro de leche

z = 3x (ecuación 2)

Y ese 1 kg de jamón cuesta lo mismo que el cliente tendría que pagar si hubiera comprado 5 litros de leche y 3 litros de aceite de oliva.

y = 5x + 3z (ecuación 3)

Sustituyendo las ecuaciones 2 y 3 en la ecuación 1

16x + 4(5x + 3z) + 8(3x) = 240

16x + 20x + 12z + 24x = 240

Recordemos que z = 3x

36x + 12(3x) + 24x = 240

36x + 36x + 24x = 240

96x = 240

x = (240/96) = 2.5

z = 3x = 3 × 2.5 = 7.5

y = 5x + 3z = (5×2.5) + (3×7.5) = 35

English Translation

A supermarket customer has paid a total of 240 for 16 liters of milk, 4kg of hamon serrano and 8 liters of olive oil. Knowing that 1 liter of oil costs the tripe of 1 liter of milk; t that 1kg of ham costs the same as the customer would have to pay if he had bought 5 liters of milk and 3 liters of olive oil. Calculate the price of each item.

Solution

Let the price of a liter of milk, a kilogram of Serrano ham and a liter of olive oil be x, y and z respectively.

16 liters of milk, 4kg of hamon serrano and 8 liters of olive oil cost 240

16x + 4y + 8z = 240 (eqn 1)

1 liter of oil costs the triple of 1 liter of milk

z = 3x (eqn 2)

And that 1kg of ham costs the same as the customer would have to pay if he had bought 5 liters of milk and 3 liters of olive oil

y = 5x + 3z (eqn 3)

Substituting eqn 2 and 3 into eqn 1

16x + 4(5x + 3z) + 8(3x) = 240

16x + 20x + 12z + 24x = 240

Recall that z = 3x

36x + 12(3x) + 24x = 240

36x + 36x + 24x = 240

96x = 240

x = (240/96) = 2.5

z = 3x = 3 × 2.5 = 7.5

y = 5x + 3z = (5×2.5) + (3×7.5) = 35

1 liter of milk costs 2.5

1 kg of Serrano ham costs 35

1 liter of olive oil costs 7.5

Hope this Helps!!!

Answer:

27.73 cm^2

Step-by-step explanation:

Answer:

Guys its 27.73- Please trust me i have done this one on khan multiple times

Step-by-step explanation:

Please please please like my answer or vote one of my answers brainliest.

Answer:

C

Vertex at (-4 , 18)

Step-by-step explanation:

The vertex's x-coordinate is -4

To find the y-coordinate plug -4 into any of the equations but I recommend using the third one because it'll be the fastest route.

-2 (-4 + 4)^2 + 18

-2(0)^2 + 18

= 18

Vertex at (-4, 18)