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3 years ago

13

you have $2.50. Each sugar free gumball in a gumball machine cost $0.25. Write and solve an inequality that represents the numbe

r of gumballs you can buy.

1 answer:

Crank3 years ago

8 0

2.50/0.25, so this will equal 10.

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Given: △ABC, AB=5sqrt2 <br> m∠A=45°, m∠C=30°<br> Find: BC and AC

Marysya12 [62]

BC is 10 units and AC is $5+5\sqrt{3}$ units

Step-by-step explanation:

Let us revise the sine rule

In ΔABC:

$\frac{AB}{sin(C)}=\frac{BC}{sin(A)}=\frac{AC}{sin(B)}$
AB is opposite to ∠C
BC is opposite to ∠A
AC is opposite to ∠B

Let us use this rule to solve the problem

In ΔABC:

∵ m∠A = 45°

∵ m∠C = 30°

- The sum of measures of the interior angles of a triangle is 180°

∵ m∠A + m∠B + m∠C = 180

∴ 45 + m∠B + 30 = 180

- Add the like terms

∴ m∠B + 75 = 180

- Subtract 75 from both sides

∴ m∠B = 105°

∵ $\frac{AB}{sin(C)}=\frac{BC}{sin(A)}$

∵ AB = $5\sqrt{2}$

- Substitute AB and the 3 angles in the rule above

∴ $\frac{5\sqrt{2}}{sin(30)}=\frac{BC}{sin(45)}$

- By using cross multiplication

∴ (BC) × sin(30) = $5\sqrt{2}$ × sin(45)

∵ sin(30) = 0.5 and sin(45) = $\frac{1}{\sqrt{2}}$

∴ 0.5 (BC) = 5

- Divide both sides by 0.5

∴ BC = 10 units

∵ $\frac{AB}{sin(C)}=\frac{AC}{sin(B)}$

- Substitute AB and the 3 angles in the rule above

∴ $\frac{5\sqrt{2}}{sin(30)}=\frac{AC}{sin(105)}$

- By using cross multiplication

∴ (AC) × sin(30) = $5\sqrt{2}$ × sin(105)

∵ sin(105) = $\frac{\sqrt{6}+\sqrt{2}}{4}$

∴ 0.5 (AC) = $\frac{5+5\sqrt{3}}{2}$

- Divide both sides by 0.5

∴ AC = $5+5\sqrt{3}$ units

BC is 10 units and AC is $5+5\sqrt{3}$ units

Learn more:

You can learn more about the sine rule in brainly.com/question/12985572

#LearnwithBrainly

6 0

4 years ago

WILL MARK YOU AS BRAINLIEST!!!!!!!!!! PLEASE HELP DUE TODAY AT 1 :(((((

Alika [10]

Answer: here is a app to use

Socratic by Google

Step-by-step explanation:

Socratic by Google its on iphone and sumsung

5 0

3 years ago

Complete the calculation how to find partial products<br><br> 1 2 4<br> × 2<br> ----------

a_sh-v [17]

The first step is to write each factor in expanding notation.

This is:

- 124 = 100 + 20 + 4
- 2 = 2

Now muliply 2 times each term of the terms 100, 20 and 4

=> 2 * 100 = 200

2 * 20 = 40

2 * 4 = 8

Then,

    (100 + 20 + 4 )
x                     2
-----------------------
                       8
               40
                   200
------------------------
                   248

6 0

3 years ago

Consider the surface f (x comma y comma z )f(x,y,z)equals=negative 2 x squared plus 2 y squared minus 3 z squared plus 3 equals

trapecia [35]

Answer:

a) (8,8,-6)

b) 4x+4y+3z = -3

Step-by-step explanation:

a)

The surface is given by the equation

f(x,y,z) = 0 where

$f(x,y,z)=-2x^2+2y^2-3z^2+3$

The gradient of this function is the vector

$(\frac{\partial f}{\partial x},\frac{\partial f}{\partial y},\frac{\partial f}{\partial z})=(-4x,4y,-6z)$

If we evaluate it in the point P = (-2,2,1) we obtain the point

(8,8,-6)

b)

The vectors with their tails at P are of the form

(-2,2,1)-(x,y,z) = (-2-x, 2-y, 1-z)

as they must be orthogonal to the gradient, they must be orthogonal to the vector (8,8,6) so their inner product is 0

$(-2-x,2-y,1-z)\cdot(8,8,6)=0\Rightarrow -16-8x+16-8y+6-6z=0\Rightarrow 4x+4y+3z=-3$

and the equation of the desired plane is

4x+4y+3z = -3

3 0

4 years ago

If 2 years on earth equals 5 months in another dimension, what are the equations to find the time in earth and that other dimens

Ede4ka [16]

Let x be the length of a month on the other dimension. Since a year value is 365.242 days

We have 2 × 365.242 = 5 × x

It means that 5x = 730,484

and that x = 730,484 / 5 ≈ 146,1 days rounded to the decimal

This means that a month length in the other dimension is of roughly 146 days.. and If we assume that a month in the other dimension is of 30 days approximately, then one day length would be of 146,1 / 30 ≈ 4.87 days

6 0

3 years ago