A student began a proof of the law of sines using triangle xyz. His work is shown. The student has ____ started the proof. The next step in the proof is to ____. Then the student should _____.

We should multiply the expression by (9+√14) fraction.

Multiplication is the mathematical operation that is used to determine the product of two or more numbers.

To rationalize the terms, we multiply both the denominator and denominator by the conjugate of the denominator.

The denominator is 9-√14 and its conjugate is; (9+√14).

(5-√7)/(9-√14) = (5-√7)(9+√14)/(9-√14)(9+√14)

                       =  (5-√7)(9+√14)/(9²-14)

                      = (45 + 5√14 - 9√7 - √98)/(81-14)

                       =  (45 + 5√14 - 9√7 - √98)/67

                       = (45 + 5√14 - 9√7 - 7√2)67

This is the rationalized expression.  

The denominator is (9-√14) and its conjugate is (9+√14).

Learn more about multiplications;

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Answer:

x = 17

Step-by-step explanation:

We can infer that the angles are equivalent based on the opposite angle theorem and we can set the equations equal to one another:

(8x-22)=(5x+29)

from here, we can subtract 5x from each side leaving us with:

3x-22=29

Now add 22 to both sides:

3x=51

Now divide both sides by 3, leaving us with the value of x:

x=17

Answer:

x = 48 degrees

Step-by-step explanation:

(2x + 2) + (x + 34) = 180

3x + 36 = 180

3x = 180 - 36

3x = 144

x = 144 / 3

x = 48 degrees

I hope this helps :)

Answer:

B. x = 48

Step-by-step explanation:

(x + 34)+(2x + 2) = 180°. Angles on a straight line

x+2x = 180 - (34+2)

3x = 180 - 36

3x ÷3 = 144 ÷3

x = 48°

Answer:

The formula for circumfernce is C=pixd D is diameter

Step-by-step explanation:

Answer:

33

Step-by-step explanation:

(3×3 )+(1/2 ×3×4) ×4 = 33

9514 1404 393

Answer:

  3x -5y = -38

Step-by-step explanation:

The equation of the perpendicular line can be formed by swapping the coefficients of x and y in the given equation, negating one of them. The new constant will be the one that lets the given point satisfy the equation.

  given: 5x +3y = 5

  perpendicular: 3x -5y = constant

At the given point, the constant is ...

  3(-6) -5(4) = -18 -20 = -38

So, the desired equation is ...

  3x -5y = -38

Answer:

Radius of the circle is 5 units.

Step-by-step explanation:

JKLMN is a regular polygon inscribed in a circle.

Since, its a regular polygon,

JN = NM = 5.88 units

"Perpendicular drawn from the center of the circle to any chord is the bisector of the chord"

Therefore, PQ will be the perpendicular bisector of chord NM.

QM = [tex]\frac{1}{2}(NM)[/tex]

QM = [tex]\frac{1}{2}(5.88)[/tex]

QM = 2.94 units

By applying Pythagoras theorem in ΔPQM,

PM² = PQ² + QM²

PM² = (4.05)² + (2.94)²

PM = [tex]\sqrt{16.4025+8.6436}[/tex]

PM = [tex]\sqrt{25.0461}[/tex]

PM = 5 units

Therefore, radius of the circle is 5 units.

Answer:

x=3 and y=1 so the answer is b

Step-by-step explanation:

hope it helped have a good day<3

Answer:

B

Step-by-step explanation:

image attached is the step by step "explanation

Step-by-step explanation:

Sam, Raj and Jade have 12 sweets each

(one person has 12 sweets)

Sam has 12 sweets

one quarter of Sam sweet is blue

1/4 = one quarter

1/4 * 12 = 3

Sam has 3 blue sweets.

Answer:

sam has 3 blue sweets

Step-by-step explanation:

[tex]\frac{1}{4} of 12 = 3[/tex]

if sam has 12 sweets and one quarter are blue then we need to work out one quarter of the twelve sweets. you need to do [tex]\frac{1}{4} of 12[/tex] which is 3 and [tex]\frac{1}{4} of 12[/tex]  is the same as [tex]\frac{1}{4} times 12[/tex]

Answer:

10 children, 20 adults

Step-by-step explanation:

Children=1/2Adults

adults+children=30

adults + 1/2 adults=30

1 1/2 adults =30

adults = 20

children =1/2 adults

children = 1/2(20)

children=10

Answer:

can u copy the text and send it to help u

Answer:

I think yes because u will have 760 leftover

Answer:

3.1 A) 49; 64; and 81

B) 343; 512; and 729

C) 28; 36; and 45

3.2 A) 1²; 2²; 3²...

B) 1³; 2³; 3³...

C) 1; 1+2; 1+2+3; ...

3.3 A) aₙ = n²

B) aₙ = n³

C) aₙ = n·(n + 1)/2

3.4 A) 10,000

B) 1,000,000

C) 5,050

Step-by-step explanation:

The given sequences are;

A 1; 4; 9; 16; 25; 36...

B 1; 8; 27; 64; 125; 216...

C 1; 3; 6; 10; 15; 21;...

3.1 A) The terms, aₙ, of sequence 'A' are given as follows;

aₙ = n², where, n = 1, 2, 3,...

The next three terms of sequence 'A' are therefore;

a₇ = 7³ = 49, a₈ = 8² = 64, and a₉ = 9² = 81

The next three terms of sequence 'A' are ; 49; 64; and 81

B) The terms, aₙ, of sequence 'B' are given as follows;

aₙ = n³, where, n = 1, 2, 3,...

The next three terms of sequence 'B' are therefore;

a₇ = 7³ = 343, a₈ = 8³ = 512, and a₉ = 9³ = 729

The next three terms of sequence 'B' are; 343; 512; and 729

C) The terms, aₙ, of sequence 'C' are given as follows;

aₙ = n·(n + 1)/2, where, n = 1, 2, 3,...

The next three terms of sequence 'A' are therefore;

a₇ = 7×(7 + 1)/2 = 28, a₈ = 8×(8 + 1)/2 = 36, and a₉ = 36 + 9×(9 + 1)/2 = 45

The next three terms of sequence 'A' are ; 28; 36; and 45

3.2 A) The pattern of the numbers in sequence 'A', consists of squaring (raising to the power of 2) each number in the sequence of natural numbers

B) The pattern of the numbers in sequence 'B', consists of raising to the power of 3 each number in the sequence of natural numbers

C) The pattern is the triangular number sequence and consists of finding half the number dots that are present in a n by (n + 1) rectangle, which is given by finding the sum of the natural numbers up to the given term in the sequence

3.3 A) The formula for the general term of sequence, A, is aₙ = n²

B) The formula for the general term of sequence, B, is aₙ = n³

C) The formula for the general term of sequence, C, is aₙ = n·(n + 1)/2

3.4 A) The 100th term of sequence 'A', a₁₀₀ = 100² = 10,000

B) The 100th term of sequence 'B', a₁₀₀ = 100³ = 1,000,000

C) The 100th term of sequence 'C', a₁₀₀ = 100 × (100 + 1)/2 = 5,050.

Answer:

c 4i think soc 4 yu need to be add

Answer:

40197 these many 5s make up 200985 so 4 are left to make 200989

Step-by-step explanation:

Answer:

40197.8

Step-by-step explanation:

200989 ÷ 5

40197.8

Answer: 2 circle to the right

Step-by-step explanation:

You would need to add 2 circles to keep it balanced.

Answer:

To factor means to express as a product. To expand means to multiply something out.

Step-by-step explanation:

please answer my question for me pleaseeee

Answer:

m < 15

Step-by-step explanation:

2m+10 < 40

Subtract 10 from each side

2m+10-10 < 40-10

2m < 30

Divide by 2

2m/2 = < 30/2

m < 15

Answer:

C, -7+12

Step-by-step explanation:

-7--12= 5

-7--12 can also be -7+12

Answer:

The answer is c

Step-by-step explanation:

-7-(-12) = 5

Answer:

New width = 12 in.

Step-by-step explanation:

Original height = 2 in.

Original width = 3 in.

New height = 8 in.

New width = x = ?

The shape of the original painting and the shape of the new painting are similar, therefore, the ratio of their corresponding linear measurement will be equal.

Thus:

New height/original height = new width/original width

8/2 = x/3

Cross multiply

2x = 3*8

2x = 24

2x/2 = 24/2

x = 12

New width = 12 in.

Answer:

The answered 5 math questions, and 5 science questions.

5 * 3 = 15

5 * 10 = 50

15 + 50 = 65

Step-by-step explanation:

Given:

An isosceles triangle has an angle that measures 40°.

To find:

The other possible angles of the triangle.

Solution:

Case 1: 40° is the measure of base angle of isosceles triangle.

Then, the other base angle is 40°.

Let x be the measure of third angle.

The sum of all interior angles of a triangle is 180 degrees. So,

[tex]x+40^\circ+40^\circ=180^\circ[/tex]

[tex]x=180^\circ-40^\circ-40^\circ[/tex]

[tex]x=100^\circ[/tex]

So, the possible angles are 40° and 100°.

Case 2: 40° is the measure of vertical angle of isosceles triangle.

Let y be the measure of base angles, then

[tex]y+y+40^\circ=180^\circ[/tex]

[tex]2y=180^\circ -40^\circ[/tex]

[tex]y=\dfrac{140^\circ}{2}[/tex]

[tex]y=70^\circ [/tex]

So, the possible angles are 40° and 70°.

Therefore, the correct options are A, B and D.

Answer:

m<F = 44°

length of FH = 15

length of GF = 21

Perimeter of ∆FGH = 50

Step-by-step explanation:

✔️Find m<F using the sum of triangle theorem:

The small box indicates angle 90°. Sum of a triangle is 180°. Therefore,

m<F = 180° - (90° + 46°)

m<F = 180° - 136°

m<F = 44°

✔️Find FH using trigonometric function:

Reference angle = 46°

Length of Opposite side = FH = ?

Length of Adjacent side = GH = 14

Apply TOA because we are concerned with the OPP and ADJ sides:

Tan 46° = Opp/Adj

Tan 46° = FH/14

14*Tan 46° = FH

14.4974243 = FH

FH = 15 (approximated to nearest whole number)

✔️Find GH by applying either a trigonometric function or just simply apply pythagorean theorem:

Pythagorean theorem is given as,

c² = a² + b²

c is the longest side (hypotenuse) = GF = ?

a = GH = 14

b = FH = 15

Thus:

GF² = 14² + 15²

GF² = 421

GF = √421

GF ≈ 21 (nearest while number)

✔️Perimeter of ∆FGH = GH + GF + FH

= 14 + 21 + 15

= 50

Answer:

m<A = 84

AC = 9

Step-by-step explanation:

We can find the measure of Angle A by using the sum of interior angles of a triangle theorem.

48+48+A=180

96+A=180

A=84

We can then use the isosceles triangle similarity theorem and reason that since this is an isosceles triangle and one of the side lengths (AB) is 9, the other (AC) would also be 9.

Answer:

A

Step-by-step explanation:

To sovle this we must combine the numbers togther and the variables togther.

We have:

8c+6-3c-2

Lets take out the c's and combine them:

8c -3c

=

5c

Now lets take out the numbers:

6-2

=

4

Now lets put these back together and we get the expression:

5c+4

This looks like A.

Hope this helps! :D