All categories

2 years ago

AD and CD are tangents to the circle below Calculate the size of angle 0

Mathematics

1 answer:

RoseWind [281]2 years ago

7 0

Answer: $59^{\circ}$

Step-by-step explanation:

In triangle ABC, we know that $\angle ABC=130^{\circ}-\theta$ . So, by the inscribed angle theorem, minor arc AC is equal to $260^{\circ}-2\theta$ .

Thus, major arc AC is equal to $100^{\circ}+2\theta$ .

Using the fact that the angle formed by the two tangents is 38 degrees,

$\frac{(100^{\circ}+2\theta)-(260^{\circ}-2\theta)}{2}=38^{\circ}\\\\100^{\circ}+2\theta-260^{\circ}+2\theta=76^{\circ}\\\\4\theta-160^{\circ}=76^{\circ}\\\\4\theta=236^{\circ}\\\\\theta=\boxed{59^{\circ}}$

You might be interested in

The accompanying data represent the daily (for example, Monday to Tuesday) movement of Johnson & Johnson (JNJ) stock for

egoroff_w [7]

Supposing that the stock increases in 37 days, the 95% confidence interval for the proportion of days JMJ stock increases is: (0.484, 0.7292)

The lower bound is of 0.484.
The upper bound is of 0.7292.

The interpretation is that we are 95% sure that the true proportion of all days in which the JMJ stock increases is between 0.484 and 0.7292.

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the z-score that has a p-value of $\frac{1+\alpha}{2}$ .

Supposing that it increases on 37 out of 61 days:

$n = 61, \pi = \frac{37}{61} = 0.6066$

95% confidence level

So $\alpha = 0.95$ , z is the value of Z that has a p-value of $\frac{1+0.95}{2} = 0.975$ , so $z = 1.96$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6066 - 1.96\sqrt{\frac{0.6066(0.3934)}{61}} = 0.484$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6066 + 1.96\sqrt{\frac{0.6066(0.3934)}{61}} = 0.7292$

The 95% confidence interval for the proportion of days JMJ stock increases is (0.484, 0.7292), in which 0.484 is the lower bound and 0.7292 is the upper bound.

The interpretation is that we are 95% sure that the true proportion of all days in which the JMJ stock increases is between 0.484 and 0.7292.

A similar problem is given at brainly.com/question/16807970

4 0

2 years ago

Write g(x)=4x^2+88 in vertex form

umka21 [38]

Answer:

(

)

−

484

Step-by-step explanation:

5 0

4 years ago

Cedric and Insha solved the same equation using the calculations below.

Mariulka [41]

The first working out is correct, z = 3

3 0

3 years ago

If m<BEG = (19x + 3)° and m<EGC = (m<GCB + 4x)°, which of the following statements is true about quadrilateral BEGC? Se

viktelen [127]

Answer:

The sum of all exterior angles of BEGC is equal to 360° ⇒ answer F only

Step-by-step explanation:

* Lets revise some facts about the quadrilateral

- Quadrilateral is a polygon of 4 sides

- The sum of measures of the interior angles of any quadrilateral is 360°

- The sum of measures of the exterior angles of any quadrilateral is 360°

* Lets solve the problem

- DEGC is a quadrilateral

∵ m∠BEG = (19x + 3)°

∵ m∠EGC = (m∠GCB + 4x)°

∵ The sum of the measures of its interior angles is 360°

∴ m∠BEG + m∠EGC + m∠GCB + m∠CBE = 360

∴ (19x + 3) + (m∠GCB + 4x) + m∠GCB + m∠CBE = 360 ⇒ add the like terms

∴ (19x + 4x) + (m∠GCB + m∠GCB) + m∠CBE + 3 = 360 ⇒ -3 from both sides

∴ 23x + 2m∠GCB + m∠CBE = 375

∵ The sum of measures of the exterior angles of any quadrilateral is 360°

∴ The statement in answer F is only true

3 0

3 years ago

What is the rate of change for 2y+3=3x

Elenna [48]

The rate of change in z at (4,9) as we change x but hold y fixed is = 3/[2sqrt(3x+2y)] put x = 4 , y = 9 = 3/[2sqrt(12+18) = 3/[2sqrt(30)] The rate of change in z at (4,9) as we change y but hold x fixed is = 1/sqrt(3x+2y) put x = 4, y =9 = 1/sqrt(30)

5 0

3 years ago