Latoya created a factor tree and wrote the prime factorization of 90 shown below. A factor tree of 90. 90 branches to 9 and 10. 9 branches to 3 and 3. 10 branches to 2 and 5. The equation is 90 = 2 times 3 times 5. What is Latoya's error? She should not have found the factors of 9. She should have included an exponent of 2 on the 3. She should have included 9 and 10 in the prime factorization. She should have started the tree with 2 times 45.

Answer:

[tex]\theta =2n\pi, \;\frac{\pi}2+2n\pi \;\;\text{for all}\; n=0,1,2,...[/tex]

Step-by-step explanation:

[tex]\frac 1{\text{cosec} \theta}+\cot \theta-\frac 1{\sin \theta}=\frac 1{\sin \theta}-\frac 1{\text{cosec} \theta}-\cot \theta[/tex]

[tex]\Rightarrow \frac 2{\text{cosec} \theta}+2\cot \theta-\frac 2{\sin \theta}=0[/tex]

[tex]\Rightarrow \frac 1{\text{cosec} \theta}+\cot \theta-\frac 1{\sin \theta}=0[/tex]

[tex]\Rightarrow \sin \theta -\frac 1{\sin \theta}+\frac{\cos \theta}{\sin \theta}=0[/tex]

[tex]\Rightarrow \frac{\sin ^2\theta-1+\cos \theta}{\sin \theta}=0[/tex]

[tex]\Rightarrow \frac{-\cos ^2\theta+\cos \theta}{\sin \theta}=0\Rightarrow\frac{\cos \theta-\cos ^2\theta}{\sin \theta}=0[/tex]

[tex]\Rightarrow \cot \theta(1-\cos \theta)=0[/tex]

[tex]\text{If} \;\;1-\cos \theta=0\Rightarrow \cos \theta=1[/tex]

[tex]\Rightarrow \theta=2n\pi\;\; \text{for all}\; n=0,1,2,.....[/tex]

[tex]\text{If} \cot \theta=0\Rightarrow \frac{\cos \theta}{\sin \theta}=0\Rightarrow \cos \theta=0[/tex]

[tex]\Righarrow \theta =\frac{\pi}2+2n\pi\;\;\text{for all}\; n=0,1,2,...[/tex]

Hence, [tex]\theta =2n\pi, \;\frac{\pi}2+2n\pi \;\;\text{for all}\; n=0,1,2,...[/tex]

Answer:

n/(4-5)

Step-by-step explanation:

A quotient of a number and... means that the number is being divided by whatever comes after. In this case the number that comes after is '4 decreased by 5', which is 4 - 5 as the -5 takes 5 away so it 'decreases it by 5'. Therefore is the expression is 'the quotient of a number and four decreased by five' then it is expressed in the following way (using n for number):

n/(4-5)

Hope this helped!

Answer:

7:21 am

Step-by-step explanation:

9    18   27  36

12 .24 36

36 minutes later  

Answer:

Step-by-step explanation:

Given function:

Putting this into slope-intercept form: y = mx + b

Replacing y with f(x)

Answer:

4+5-52*4=-199

Step-by-step explanation:

Answer:

17

Step-by-step explanation:

Answer:

See Below

Step-by-step explanation:

Isolate f

h =  4 + f

-4   -4

h - 4 = f

Or  f = h-4

Answer:

[tex]3x-y=14[/tex]

Step-by-step explanation:

To convert an equation into standard form, we want to get into the form [tex]ax + by = c[/tex].

If we have [tex]y=3x-14[/tex], our first step is to get the x term on the left side. We can do this by subtracting 3x from both sides.

[tex]-3x + y = -14[/tex]

I find it easier now to just divide both sides by -1, so that we have a more consistent equation.

[tex]3x - y = 14[/tex]

Hope this helped!

Answer:

No solution it IS STUPID.

Step-by-step explanation:

Answer:

that question is stupid.

Answer:

Hi there!

She used rounding to estimate the sum!

1 mile * 5280 ft * 12 in = 63360 in

There are 63360 inches in one mile

Answer:

63360

Step-by-step explanation:

5280 × 12 = 63360

Answer:

C. An = 5(2)^n-1

Step-by-step explanation:

Tower 1 2 3 4 5

Number of blocks 5 10 20 40 80

Where,

n = tower number

An = number of blocks

A. an = n + 80

B. an = 2n + 5

C. An = 5(2)^n-1

D. an = 10(5)^n

Checking all options

A. An = n + 80

When n = 1

An = 1 + 80

= 81

B. An = 2n + 5

When n = 1

= 2(1) + 5

= 2 + 5

= 7

C. An = 5(2)^n-1

When n = 1

= 5(2)^1-1

= 5(2)^0

2^0 = 1

= 5(1)

= 5

D. An = 10(5)^n

When n = 1

= 10(5)^1

5^1 = 5

= 10(5)

= 50

The explicit formula which correctly represents the number of blocks, an, in terms of the tower number, n is C. An = 5(2)^n-1

Answer:

C

Step-by-step explanation:

I took the map test

Answer:

2x+2y+z

Step-by-step explanation:

The Answer: x= −12/7

Answer:

Measure the distance from one endpoint to the other.

Answer:

a line segment is a portion of a straight line which is directly connected to two given points. the given points has coordinate x and y

distance = √(x2-x1)²+(y2-y1)²

example : find distance between two points (2,6) and (3,4) ( find the length of a segment)

d = √(3-2)²+(4-6)

d=√1²+2²

d=√5

Answer:

x + 5

Step-by-step explanation:

Step 1: Write expression

x + 2 + 3

Step 2: Combine like terms (constants)

x + 5

Answer:

The measure of x = 45 degrees

Answer:

x is equal to 50.

Explanation:

The three lines intersect creating a triangle. All angle measures for triangles in Euclidean geometry must have a sum of 180 degrees. Because of the Vertical angles theorem, which states if two angles are opposite they are congruent, this means the angle across from 40 degrees is also 40 degrees. Since we know that the second angle is 90 degrees based on the right angle sign. By adding 40 and 90 you get a sum of 130. Now you subtract 130 from 180. This gives you 50 degrees. Since the Vertical angle theorem states two opposite angles are congruent we know the x is equal to 50 degrees.

Answer:

y = x - 2

Step-by-step explanation:

8 + 5y = 5x - 2

5y = 5x -2 - 8

5y = 5x - 10

5y/5 = (5x - 10)/5

y = x - 2

The equation 5x - 2 = 8 + 5y can be written as in terms of x as y = x - 2; the answer is y = x - 2.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

The equation is:

5x - 2 = 8 + 5y

The above equation represents the linear equation in one variable.

To solve for y make the subject as y

5y = 5x - 2 - 8

5y = 5x - 10

y = (5x - 10)/5

y = x - 2

Thus, the equation 5x - 2 = 8 + 5y can be written as in terms of x as y = x - 2; the answer is y = x - 2.

Learn more about the linear equation here:

brainly.com/question/11897796

#SPJ2

Answer:

x = 2

Step-by-step explanation:

Answer: 2

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

Because R is the vertex and you always name a angle with its vertex in the middle, R would have to be in the middle. So the only possible answer is C.

Answer:

thats easy you don't need help

Step-by-step explanation:

Answer:

1=163 degrees

2=×=10 degrees

3=×=3

Step-by-step explanation:

54x+1+9x-10=180 we are using this expression because alternate angles add up to 180 degrees

54x+9x+1-10=180

63x-9=180

63×=180+9

63×=189

63×÷63×=189÷63×

X=3

Angle in bold print is (54x+1)

54×3=162

162+1=163 degrees

No.2 Find x

7x+35+x+65 =180

7x+x+35×65=180

8x+100=180

8x=180-100

8x=80

8x÷8x=80÷8

X=10 degrees

No.3 Find x

54x+1+9x-10=180

54x+9x+1-10=180

63x-9=180

63x=180+9

63x=189

63x÷63x=189÷63

X=3

I hope I was of help

Answer:

The values of x and y are;

x = 7 and y = 4.5

Step-by-step explanation:

The question is a word problem, given that the shape of the kite Karl makes is a parallelogram

The coordinates of the vertices are;

D(3, 6), G(1, 3), H(4, y), and E(x, 6)

From the properties of a parallelogram we have;

The diagonals bisect each other

Therefore;

GH = EH = 1/2·GE

Therefore, we have;

The coordinates of the point H = The coordinate of the midpoint of the line EG

The coordinates of the midpoint of a line with end points, (x₁, y₁) and (x₂, y₂) is given as follows;

The coordinates of the midpoint of a line = ((x₁ + x₂)/2, (y₁ + y₂)/2)

Therefore;

The coordinates of the midpoint of the line EG  are ((1 + x)/2, (3 + 6)/2)

Given that the midpoint of EG is the point H and the coordinate of the point H is (4, y), we have;

(1 + x)/2 = 4, therefore;

2 × 4 = 1 + x

8 = 1 + x

x = 8 - 1 = 7

Similarly, we have from the coordinate of point H which is given as follows;

((1 + x)/2, (3 + 6)/2) = (4, y)

y = (3 + 6)/2 = 9/2 = 4.5

Therefore, x = 7, y = 4.5.

Parallel sides of a parallelogram have the same slope

The values of x and y are 6 and 3, respectively.

The coordinate points are given as:

[tex]\mathbf{D =(3,6)}[/tex]

[tex]\mathbf{G =(1,3)}[/tex]

[tex]\mathbf{H =(4,y)}[/tex]

[tex]\mathbf{E =(x,6)}[/tex]

Lines DG and HE are parallel.

This means that they have the same slope (m)

The slope is calculated as:

[tex]\mathbf{m = \frac{y_2 - y_1}{x_2 - x_1}}[/tex]

So, we have:

[tex]\mathbf{m_{DG} = \frac{3 - 6}{1 - 3}}[/tex]

[tex]\mathbf{m_{DG} = \frac{- 3}{- 2}}[/tex]

[tex]\mathbf{m_{DG} = \frac{3}{2}}[/tex]

Similarly

[tex]\mathbf{m_{HE} = \frac{6 - y}{x - 4}}[/tex]

The slopes are equal.

So, we have:

[tex]\mathbf{\frac{6 - y}{x - 4} = \frac 32}[/tex]

By comparison:

[tex]\mathbf{6 - y = 3}[/tex] and [tex]\mathbf{x - 4 = 2}[/tex]

Solve for y in [tex]\mathbf{6 - y = 3}[/tex]

[tex]\mathbf{y = 3}[/tex]

Solve for x in [tex]\mathbf{x - 4 = 2}[/tex]

[tex]\mathbf{x = 6}[/tex]

Hence, the values of x and y are 6 and 3, respectively.

Read more about parallelogram and slopes at:

https://brainly.com/question/19654204

Answer:

(2,2)

Step-by-step explanation:

Answer:

x = 5

Step-by-step explanation:

instructions in pic :)

4x - 6 = x + 9

4x - 6 - x - 9 = x + 9 - x - 9        [Subtract x + 9 from both sides]

3x - 15 = 0

3x - 15 + 15 = 0 + 15                  [Add 15 to both sides]

3x = 15

3x/3 = 15/3                                [Divide both sides by 3]

x = 5

Answer:

Step-by-step explanation:

Perimeter of a rectangle = 2l + 2w

where

l is the length

w is the width

From the question

l = 9 cm

w = 6 cm

Substitute the values into the above formula and solve

We have

P = 2(9) + 2(6)

= 18 + 12

We have the final answer as

Hope this helps you

Answer: d.30cm

Step-by-step explanation:

the formula for perimeter is P=2L+2W

Substitute the length and width

P= 2(9)+2(6)

Multiply

P= 18+16

Add

P=30

Add the unit

P= 30cm