If two triangles have three corresponding angles and three corresponding sides that are equal in measure, are two triangles necessarily congruent ? Why?

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]

The probability of selecting either a pink or green marble from the 10 marbles is; 2/10

We are told that you try to select a marble ten times.

Now, we want to try to find out the best probability of selecting either a pink or a green marble.

Now, it's possible that there are other marbles but if we want to know just for this two amrbles, then we can write the probability as;

P(either pink or green marble) = 2/10

Read more about Probability of Selection at; https://brainly.com/question/251701

Answer:

3

Step-by-step explanation:

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:

D = (13, - 23 )

Step-by-step explanation:

Given the translation rule

(x, y ) → (x - 4, y + 15 )

To go in the reverse direction, that is image to original, then, reverse the operations in the translation rule.

(x , y ) → (x + 4, y - 15 ) , thus

D'(9, - 8 ) → D(9 + 4, - 8 - 15 ) → D(13, - 23 )

Answer:

(13,-23)

Step-by-step explanation:

DID IT ON EDGE 2020

Answer:

John has 18 pieces of paper.

Larry has 32 pieces of paper.

Step-by-step explanation:

Let [tex]l[/tex] be how many pieces of paper Larry has and [tex]j[/tex] be how many pieces of paper John has.

We get:

[tex]j+14=l[/tex]

[tex]j+l=50[/tex]

[tex]j+j+14=50\\\\2j+14=50[/tex]

Subtract 14 from both sides

[tex]2j=36[/tex]

Divide both sides by 2

[tex]j=18[/tex]

John has 18 pieces of paper.

[tex]j+14=l\\\\18+14=l\\\\l=32[/tex]

Larry has 32 pieces of paper.

Answer:

x ≤ 2

Step-by-step explanation:

2 red rose cost  $ 18

x flowers cost $ 11x

"At most "  means ≤.

11x + 18 ≤ 40

11x ≤ 40 - 18

11x ≤ 22

x ≤ 2

Using inequality we know that Amanda can purchase 2 lily flowers.

So, the inequality can be:

Now, the inequality will be:

Let, the number of lilies is x and Amanda purchases 2 lilies:

Therefore, using inequality we know that Amanda can purchase 2 lily flowers.

Know more about inequality here:

https://brainly.com/question/28964520

#SPJ2

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:

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:

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:

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)

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:

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)

Step-by-step explanation:

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

Answer:

20 feet

Step-by-step explanation:

Since the term -(x-7)^2 is negative, the largest height that the ball can reach is when this term is 0. 0+20=20, meaning that the highest the ball can go is 20 feet. Hope this helps!

Answer:  20 feet

Step-by-step explanation:

The vertex form of a quadratic equation is: y = a(x - h)² + k

where (h, k) is the vertex

h is the axis of symmetry (time at which maximum height is reached)

k is the maximum height

Given: y = -(x - 7)² + 20

--> h = 7, k = 20

therefore, the maximum height of the ball is 20

Answer:

The vertex form of the equation is [tex]y = -\frac{1}{3}( x-1)^{2} +1[/tex].

Step-by-step explanation:

You will use the equation [tex]y=a(x-h)^{2} +k[/tex] to solve this parabola. (h, k) is the vertex. So, we plug this into the equation to get [tex]y= a(x - 1)^{2} +1[/tex].

Then, we substitute the point as our x and y to get [tex]-2 = 9a+1[/tex] (a lot of simplifying was done here). Then, add 2 to the right side of the equation and isolate the [tex]9a[/tex] to get [tex]9a = 3[/tex]. Finally, divide by 9 on both sides to get [tex]a=\frac{1}{3}[/tex].

Now, substitute your [tex]a[/tex] back into the equation to get y = [tex]-\frac{1}{3}(x-1)^{2}+1[/tex].

This is in vertex form. If the answer is needed in standard form, simply distribute and simplify to get [tex]y = -\frac{1}{3} x^{2} +\frac{2}{3} x+\frac{2}{3}[/tex].

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:

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:

30

Step-by-step explanation:

6(5)=30

// have a great day //

Answer:

30

Step-by-step explanation:

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:

[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]

Answer:

postulates, common notions, and axioms

Answer:

Many solutions

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:

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:

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

Answer:

Step-by-step explanation:

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

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

m=-6/-3

m=2

Answer:

x=10

Step-by-step explanation:

x-4=6

To isolate x, you can add 4 to both sides of the equation:

x-4+4=6+4

x=10

Hope this helps!

Step-by-step explanation:

x=10