(trigonometry) solve for x

Answer:

x = 15

Step-by-step explanation:

cross multiply -->

8x = 120 *divide by 8 on both sides*

x = 15

CHECK:

5/8 + 15/24

multiply by 3 to get the second fraction

Answer:

x=15

Step-by-step explanation:

Answer:

-1/2y

Step-by-step explanation:

2/4  =  1/2

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:

Joe: 3 hrs

Janet: 6hrs

Step-by-step explanation:

joe takes x hours

so in 1 hr he does 1/x of the garden

janet takes 2x hours

so in 1 hr she does 1/(2x) of the garden

In one hour together they do 1/2 of the garden

1/x + 1/(2x) = 1/2

2/(2x) + 1/(2x) = 1/2

3/(2x) = 1/2

Cross multiply

6 = 2x

x = 3

Joe: 3 hrs

Janet: 6hrs

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

Answer:

C

Step-by-step explanation:

Answer:

E

Step-by-step explanation:

E represents the number of moths initially with the darkest wing colour, and the number of these will increase if the moth's predator (hawks) finds it more difficult to locate them, as the moths with the darkest colour wings will be more likely to survive to reproduce so will increase in number (natural selection).

Hope this helps!

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:

z = 3.2 units

Step-by-step explanation:

sin 76°/z = sin 51°/2.6

cross-multiply to get:

z·(sin 51°) = 2.6·(sin 76°)

z = 2.6·(sin 76°) ÷ (sin 51°)

z = 3.2

Answer:

The formula for circumfernce is C=pixd D is diameter

Step-by-step explanation:

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:

how do you plot?

Step-by-step explanation:

To the top right quadrant, the second bottom square, moving 4 units up.

Answer:

I think yes because u will have 760 leftover

Answer:

c 4i think soc 4 yu need to be add

Answer:

12x+8-30x+5=2x-16-42x+24

-18x+13=-40x+8

22x=-5

x=-5/22

hopefully i did it with out mistakes

Answer:

33

Step-by-step explanation:

(3×3 )+(1/2 ×3×4) ×4 = 33

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:

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:

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

Answer:

Option B

Step-by-step explanation:

By applying Pythagoras theorem in the given right triangle,

(Hypotenuse)² = (leg 1)² + (leg 2)²

By substituting the values in the given expression,

7² = x² + 2²

49 = x² + 4

x² = 49 - 4

x² = 45

x = √45

x = 3√5

x = 6.7 ft

Option B will be the correct option.

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:

$ 656.1

Step-by-step explanation:

a = 1000(1 - .1)^4

a = 1000(.9)^4

a = 656.1

Answer: 2 circle to the right

Step-by-step explanation:

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

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:

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:

-0.708073 this is the exact answer im not sure if they want you to round or not

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]