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marin [14]
1 year ago
6

What is the value of x? Enter your answer, as a decimal, in the box. x= A right triangle with vertices labeled as A, B, and C. S

ide C B is the base and the top vertex is A. Side A B contains a midpoint D. A line segment drawn from C to D bisects angle A C B into two parts labeled as A C D and B C D. Angles A C D and B C D are marked with single arc. Side A C is labeled as 5. Base C B is labeled as 6. Segment A D is labeled as x. Segment B D is labeled as 4.2.
Mathematics
1 answer:
____ [38]1 year ago
6 0

x=3.95

Explanation

From the given information we find that the triangle is right angled at C. CB is the base,AC is the height and AB is the hypotenuse.

Given that D is the hypotenuse of the hypotenuse AB.

BC=6

BD=4.2

AD=x

the height and the base of the triangle is given.

Using pythagoras theorem, we can find the hypotenuse AB.

AB=\sqrt{AC^2+CB^2} \\=\sqrt{5^2+6^2} \\=\sqrt{25+36} \\=\sqrt{61} \\

D is the midpoint of AB

therefore AD=AB/2=\sqrt{61}/2

=3.905

x=3.905 cm

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serg [7]

Answer:

3 − √11

Step-by-step explanation:

For polynomials with rational coefficients, any radical roots must come in conjugate pairs.  To find the conjugate, simply reverse the sign of the radical.

4 0
2 years ago
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A while back, either James borrowed $12 from his friend Rita or she borrowed $12 from him, but he can’t quite remember which. Ei
Tamiku [17]

Answer:

First option is correct.

Step-by-step explanation:

Let amounts of money James may have after he sees Rita be x.

It is given that either James borrowed $12 from his friend Rita or she borrowed $12 from him.

So meeting Rita second time either he will $12 or he will receive $12.

The amounts of money James may have after second meeting with Rita is:

Case 1: If he pays $12.

x=42.80-12             .... (1)

Case 1: If he receives $12.

x=42.80+12           .... (2)

On combining equation (1) and (2), we get

x=42.80\pm 12

Subtract 42.80 from both sides.

x-42.80=\pm 12

It can be written as

|x-42.80|=12

Therefore first option is correct.

4 0
1 year ago
Read 2 more answers
Given: WXYZ is a parallelogram, ZX ≅ WY
Mrrafil [7]

Answer:

Step-by-step explanation:

Given: WXYZ is a parallelogram, ZX ≅ WY

Prove: WXYZ is a rectangle

Proof:

Step 1. WXYZ is a parallelogram and ZX ≅ WY (Given)

Step 2. ZY ≅ WX (Opposite sides of parallelogram are congruent)

Step 3. YX ≅ YX  (Reflexive Property)

Step 4. Consider △ZYX and △WXY, we have

ZX ≅ WY (Given)

ZY ≅ WX (Opposite sides of parallelogram are congruent)

YX ≅ YX  (Reflexive Property)

Thus, by SSS rule, △ZYX ≅ △WXY

Step 5. By CPCTC, ∠ZYX ≅ ∠WXY

Step 6.  m∠ZYX ≅ m∠WXY (Definition of congruency)

Step 7.  m∠ZYX + m∠WXY = 180° ( consecutive ∠s in a parallelogram are supplementary)

Step 8. m∠ZYX + m∠ZYX = 180° (Substitution)

Step 9. 2(m∠ZYX) = 180° (Simplification)

Step 10.  m∠ZYX = 90° (Dividing property of equality)

Step 11. WXYZ is a rectangle (Rectangle angle theorem)

Hence proved.

5 0
1 year ago
Triangle PQR with vertices P(3, −6), Q(6, −9), and R(−15, 3) is dilated by a scale factor of 3 to obtain triangle P′Q′R′. Which
vovangra [49]

Answer:

Option C.

Step-by-step explanation:

The vertices of triangle PQR are P(3, −6), Q(6, −9), and R(−15, 3).

It is given that triangle PQR dilated by a scale factor of 3 to obtain triangle P′Q′R′.

We know that a figure and its image after dilation are similar. It means triangle PQR and triangle P′Q′R′

If a figure dilated by factor k about the origin then

(x,y)\rightarrow (kx,ky)

PQR dilated by a scale factor of 3, so

(x,y)\rightarrow (3x,3y)

Using this rule we get

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R(-15,3)\rightarrow R'(3(-15),3(3))=R'(-45,9)

The vertices of image are P'(9,-18), Q'(18,-27) and R'(-45,9).

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Ronch [10]

Answer:

10(2M+3S)

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