B X+2 3 D E х 2 С C A x = [?]

Naddika [18.5K]

The measure of EF from the given diagram is 6 units

<h3>Secant secant theorem</h3>

The theorem states that if two secants are drawn from an external point to a circle, then the product of the measures of one secant's external parts is the same as the product of the other external part.

Mathematically according to the given figure;

4(4+2x) = 5(5+x)

Expand

16 + 8x = 25 + 5x

Collect the like terms

8x - 5x = 25 - 16

3x = 9

Divide both sides by 3

3x/3=. 9/3

x = 3

Find EF

EF = 2x

EF = 2(3) = 6

Hence the measure of EF from the given diagram is 6 units

Learn more on secant theorem here: brainly.com/question/10732273

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8 0

1 year ago

What is the maximum value of the function f(x)= 12 - 3sin (3pi/2 x)

Natali [406]

The lowest value of sinα is -1.

When x=1, you get:

$f\left( x \right) =12-3\sin { \left( \frac { 3 }{ 2 } \pi \right) } \\ \\ =12-3\left( -1 \right) \\ \\ =12+3\\ \\ =15$

So the maximum value of the function is 15.

6 0

3 years ago

Read 2 more answers

Factor the trinomial. x² + 15x + 14

MariettaO [177]

(x+1)(x+14) This would be the answer

3 0

2 years ago

Read 2 more answers

Ray has found that his new car gets 31 miles per gallon on the highwayand 26 miles per gallon in the city. He recently drove 285

Mkey [24]

Answer:

$Highway = 155\ miles$

$City = 130\ miles$

Step-by-step explanation:

Given

$Highway = 31mi/gallon$

$City = 26mi/gallon$

$Total\ Miles = 285$

$Total\ Gallons = 10$

Required

Determine the number of miles driven on the highway and on the city

Represent the gallons used on highway with h and on city with c.

So, we have:

$c + h = 10$ ---- gallons used

and

$31h + 26c = 285$ --- distance travelled

In the first equation, make c the subject

$c = 10 - h$

Substitute 10 - h for c in the second equation

$31h + 26c = 285$

$31h + 26(10 - h) = 285$

Open bracket

$31h + 260 - 26h = 285$

Collect like terms

$31h - 26h = 285 - 260$

$5h = 25$

Make h the subject

$h = \frac{25}{5}$

$h = 5$

Substitute 5 for h in $c = 10 - h$

$c = 10 - 5$

$c = 5$

If on the highway, he travels 31 miles per gallon, then his distance on the highway is:

$Highway = 31 * 5$

$Highway = 155\ miles$

If in the highway, he travels 26 miles per gallon, then his distance on the highway is:

$City = 26 * 5$

$City = 130\ miles$

8 0

2 years ago

The cost to a rent paddle boat at the county park is $8 per hour if x represent the number off hours the boat is rented and for

bazaltina [42]

Answer:

10+8x=y

Step-by-step explanation:

The 10$ is added on because it's a one time exchange and the 8 is multiplied by the x because for every hour you add 8$ to the price and y is the total price at the end depending on x.

4 0

2 years ago