All categories

3 years ago

How do you solve for X and A?

Mathematics

1 answer:

Ainat [17]3 years ago

4 0

9514 1404 393

Answer:

3. x = 10

4. a = 8

Step-by-step explanation:

A reasonably simple rule to remember for secants outside the circle or chords inside the circle: the product of the lengths from the point of intersection of the lines to the points of intersection of the circle is the same for each line.

When the external line is tangent to the circle, the two points of intersection of the line with the circle are the same: the point of tangency. Effectively, this means the length is squared.

3. For line QP, the product is 3(3+5) = 24.

For line QR, the product is 2(2+x). The rule above says these are equal:

24 = 2(2+x)

12 = 2+x . . . . . divide by 2

10 = x . . . . . . . subtract 2

4. For line BC, the product is (a)(a) = a^2.

For line GC, the product is 4(12+4) = 64. The rule above says these are equal:

a^2 = 64

a = √64 . . . . take the square root

a = 8

You might be interested in

aleksandr82 [10.1K]

Step-by-step explanation:

Let A be the set of people who speak English.

B be the set of people who speak French.

A - B be the set of people who speak English and not French.

B - A be the set of people who speak French and not English.

A ∩ B be the set of people who speak both French and English.

Given

n(A) = 72 n(B) = 43 n(A ∪ B) = 100

Now, n(A ∩ B) = n(A) + n(B) - n(A ∪ B)

= 72 + 43 - 100

= 115 - 100

= 15

Therefore, Number of persons who speak both French and English

= 15

n(A) = n(A - B) + n(A ∩ B)

⇒ n(A - B) = n(A) - n(A ∩ B)

= 72 - 15

= 57

and n(B - A) = n(B) - n(A ∩ B)

= 43 - 15 = 28

Therefore, Number of people speaking English only = 57

Number of people speaking French only = 28

8 0

3 years ago

Read 2 more answers

How many triangles can be constructed with sides measuring 15 cm, 7 cm, and 5 cm? Explain. Be sure to use complete sentences and

Hatshy [7]

Answer: No triangles can be formed.

Step-by-step explanation: Given Dimensions = 15cm , 7cm , 5cm

Inequality property = Sum of 2 shorter sides ≥ 3rd side

∴ 7 + 5 is not greater than 15

∴ No triangles can be formed.

3 0

3 years ago

NGC is a hot air balloon in the sky from her spot on the ground. The angle of elevation from Angie to the balloon is 40°. If she

Goshia [24]

Answer:

The distance from hot air balloon to the ground $AC=50.1457 ft$ .

Step-by-step explanation:

Labelled diagram of given scenario is shown below.

Given that,

An angle of elevation of Hot air balloon by Angie is $40$ °.

When she stepped back $200 ft$ then angle of elevation was $10$ °.

Height of Angie is $5.5 ft$ .

To find: How far off the ground is a hot air balloon.

So, from figure

Height of Angie $(BC) = 5.5ft$

In triangle Δ $ABD$ ,

⇒ $tan {40\si {\degree}} = \frac{AB}{BD}$

⇒ $AB = tan (40) \times BD$ ....................(1)

Now, In triangle Δ $ABE$

⇒ $tan (10)= \frac{AB}{200+BD}$

⇒ $AB = tan(10)\times (200+BD)$

Here, substituting the value $AB$ from Equation (1) we get,

$tan(10)\times (200+BD)= tan(40)\times BD$

$tan(10)\times 200+tan(10)\times BD= tan(40)\times BD$

⇒ $BD\times (tan(40)-tan(10))=tan(10)\times 20$

⇒ $BD\times 0.6628 = 35.2654$

⇒ $BD = \frac{35.2654}{0.6628} =53.2067 ft$

Now, finding the value of $AB$ from equation (1)

$AB= tan(40)\times 53.2067=0.8391\times 53.2067$

$AB=44.6457 ft$

Therefore Length of $AC= AB+BC$ = $(44.6457 + 5.5) ft$

$AC=50.1457 ft$ .

Hence,

The distance from hot air balloon to the ground $AC=50.1457 ft$ .

6 0

3 years ago

Sarah polled 40 randomly selected students at her high school and found that 20% ( = 0.2) are happy with the quality of the cafe

Anna71 [15]

Given:
n = 40, sample size
Confidence level = 99% => z* = 2.58
$\hat{p} = 20\%=0.2$ , sample proportion.

By definition, the margin of error is
$z^{*} \sqrt{ \frac{\hat{p}(1-\hat{p})}{n} } = 2.58 \sqrt{ \frac{(0.2)(0.8)}{40} }= 0.1632$

Answer:
According to Sarah's poll, she can conclude with 99% confidence level that 20% of the high school population is happy with the quality of the cafeteria food, with a margin of error of +/- 16.3%.

5 0

4 years ago

Read 2 more answers

What number is 55% of 60?

tatyana61 [14]

33. "Of" in math problems means multiply therefore 55% or 0.55 multiplied by 60 is 33

4 0

3 years ago

Read 2 more answers

How do you solve for X and A? ​

How do you solve for X and A?