What is the value of x?

avanturin [10]

We know that
applying the law of sines
50/sin 40=60/sin x
50*sin x=60*sin 40
sin x=[60*sin 40]/50
sin x=0.7713
x=arc sin (0.7713)----> x=50.47°--------> x=50.5°

the answer is
x=50.5 °

3 0

3 years ago

3. Mrs.Galicia bought 3 tacos and 2 sodas and paid $9.75. The next day she went back and bought 5 tacos and 1 soda and paid $12.

andrey2020 [161]

Answer:

a) 3x + 2y = 9.75, 5x + y = 12.75 is the required system of equations.

b) The cost of 1 soda = $1. 5

c) The cost of 1 taco = $2.25

Step-by-step explanation:

Let the cost of each taco = $x

Let the cost of each soda = $y

Now, according to the question:

3x + 2y = $9.75

5x + y = $12.75 are the required system of equations.

Now, substituting the value of y = 12.75 - 5x in (1).

⇒The equation 3x + 2y = 9.75 becomes 3x + 2(12.75 -5x) = 9.75

or, 3x - 10x + 25.5 = 9.75

or, -7x = -15.75

⇒ x = 15.75/7 = 2.25

Hence, the cost of 1 taco = $x = $2.25

Now, y = 12.75 - 5x

= 12.75 - 5(2.25) = 12.75 - 11.25 = = 1.5

or, y = $1.5.

Hence, the cost of 1 soda = $y = $1.5

3 0

3 years ago

1. In the given figure. BEST is a cyclic quadrilateral. ES is produced so that BE=SN. If ET is the bisector of angle BES, prove

padilas [110]

The triangle NET is an isosceles triangle as ET ≅ TN and ET = TN < EN given the condition that BEST is a cyclic quadrilateral.

<h3>How to determine the existence of an isosceles triangle</h3>

In this question we must apply geometric properties of angles and triangles to determine that the triangle NET is an isosceles triangle. Isosceles triangles are triangles with two sides of equal length. In addition, we must apply the geometric concept of proportionality.

Now we proceed to prove the existence of the isosceles triangle:

BE ≅ SN Given
ET is the bisector of ∠BES Given
ET/ES = ET/EB Definition of proportionality
ES = EB (3)
ES ≅ EB Definition of congruence
ET ≅ TN SSS Theorem/Result

Therefore, the triangle NET is an isosceles triangle as ET ≅ TN and ET = TN < EN given the condition that BEST is a cyclic quadrilateral. $\blacksquare$

To learn more on isosceles triangles, we kindly invite to check this verified question: brainly.com/question/2456591

7 0

3 years ago

The Student Monitor surveys 1200 undergraduates from 100 colleges semiannually to understand trends among college students. Rece

nlexa [21]

Answer:

A sample size of 385 is needed.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.95}{2} = 0.025$

Now, we have to find z in the Ztable as such z has a pvalue of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.025 = 0.975$ , so Z = 1.96.

Now, find the margin of error M as such

$M = z\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

You feel that a reasonable estimate of the standard deviation is 10.0 hours.

This means that $\sigma = 10$

What sample size is needed so that the expected margin of error of your estimate is not larger than one hour for 95% confidence?

A sample size of n is needed. n is found when M = 1. So

$M = z\frac{\sigma}{\sqrt{n}}$

$1 = 1.96\frac{10}{\sqrt{n}}$

$\sqrt{n} = 1.96*10$

$(\sqrt{n})^2 = (1.96*10)^2$

$n = 384.16$

Rounding up:

A sample size of 385 is needed.

7 0

3 years ago

How does the volume of a cylinder change when it’s diameter is doubled

zavuch27 [327]

Recallin that, the diameter is twice as long as the radius, namely the radius is half the diameter, so, if the diameter is doubled, the radius is also doubled.

$\bf \textit{volume of a cylinder}\\\\
V=\pi r^2 h\quad 
\begin{cases}
r=radius\\
h=height\\
-----\\
r=\stackrel{doubled}{2r}
\end{cases}\implies V=\pi (2r)^2 h
\\\\\\
V=\pi (2^2r^2)h\implies V=\pi 4r^2 h\implies V=4~(\pi r^2 h)$

notice, the new volume is 4 times (πr² h), namely 4 times the original.

8 0

3 years ago