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3 years ago

Find the measure of m∠K

Mathematics

1 answer:

Jobisdone [24]3 years ago

5 0

Answer:

<k = 20

Step-by-step explanation:

Inscribed Angle = 1/2Intercepted Arc

<K = 1/2 (40)

<k = 20

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Find the value of x. If necessary, round your answer to the nearest tenth. The figures are not drawn to scale.

REY [17]

Answer:

9.93

Step-by-step explanation:

Secant-Tangent theorem tells us that the product of the secant segment with its external segment is equal to the square of the tangent segment.

From the diagram, we can say (let the unknown part of secant line, the part left of the segment length 5, be y):

(15+y)(10) = 17^2

Solving for y we get:

$(15+y)(10) = 17^2\\150+10y=289\\10y=289-150\\10y=139\\y=13.9$

Now we can use the chord theorem to solve for x. Chord theorem tells us that when 2 intersecting chords create 4 segments, the product of the individual chord segments are equal. Thus we can say:

5 * 13.9 = 7 * x

Now solving, we get:

$5 * 13.9 = 7 * x\\69.5=7x\\x=\frac{69.5}{7}\\x=9.93$

Thus x = 9.93

last answer choice is right.

4 0

3 years ago

The ages of three siblings Jason John and Jackson totals 21 years. Jason is one year older than John. Jackson is three times as

Ymorist [56]

Answer:Jason is 5 years old.

John is 4 years old.

Jackson is 12 years old.

Step-by-step explanation:

Let x represent the age of Jason.

Let y represent the age of John.

Let z represent the age of Jackson.

The ages of three siblings Jason John and Jackson totals 21 years. It means that

x + y + z = 21 - - - - - - - - - - -1

Jason is one year older than John. It means that

x = y + 1

Jackson is three times as old as John. It means that

z = 3y

Substituting x = y + 1 and z = 3y into equation 1, it becomes

y + 1 + y + 3y = 21

5y = 21 - 1 = 20

y = 20/5 = 4

x = y + 1 = 4 + 1

x = 5

z = 3y = 3 × 4

z = 12

6 0

3 years ago

I need help?????????

amid [387]

Answer: I got D i'm not sure if that right though..

Step-by-step explanation:

3 0

3 years ago

Triangle ABC and DEF are right triangles, as shown. Triangle ABC is similar to triangle DEF. which ratios are equal to sin C?

Dafna11 [192]

Answer:

First option and Fourth option.

Step-by-step explanation:

To solve this exercise you need to use the following Trigonometric Identity:

$sin\alpha=\frac{opposite}{hypotenuse}$

In this case you know that:

$\alpha =C$

Since triangle ABC is similar to triangle DEF:

$\angle C=\angle F$

Let's begin with the triangle ABC.

You can identify that:

$opposite=AB\\hypotenuse=AC$

Then, substituing values, you get:

$sinC=\frac{AB}{AC}$

In triangle DEF, you know that:

$opposite=DE\\hypotenuse=DF$

So, substituing values, you get:

$sinF=sinC=\frac{DE}{DF}$

4 0

3 years ago

Use the value of the first integral I to evaluate the two given integrals. I = integral^3_0 (x^3 - 4x)dx = 9/4 A. integral^3_0 (

Troyanec [42]

Answer:

A) -9/2

B) 9/4

C) -9/2, same as A)

Step-by-step explanation:

We are given that $I=\int_0^3 x^3-4x dx=9/4$ . We use the properties of integrals to write the new integrals in terms of I.

A) $\int_0^3 8x-2x^3 dx=\int_0^3 -2(x^3-4x) dx=-2\int_0^3 x^3-4x dx=-2I=-9/2$ . We have used that ∫cf dx=c∫f dx.

B) $\int_3^0 4x - x^3 dx=-\int_0^3 (4x-x^3) dx=\int_0^3-(4x-x^3) dx=\int_0^3 x^3-4x dx=I=9/4$ . Here we used that reversing the limits of integration changes the sign of the integral.

C) It's the same integral in A)

4 0

3 years ago