What is this expression in simplest form? (x+2)/(4x^2+5x+1) * (4x+1)/(x^2-4)

Sum of interior angles of a triangle = 180°

x+40+30= 180°

x+ 70=180

x= 180-70

x= 110°

Answer:

x = 110

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180° , then

x + 40° + 30° = 180°

x + 70° = 180° ( subtract 70° from both sides )

x = 110°

Answer:

x = cost of each t-shirt

y = cost of each sweatshirt

Step-by-step explanation:

Given equation:

2x + 2y = 26 (1)

x + 3y = 33 (2)

From (2)

x = 33 - 3y

Substitute x = 33 - 3y into (1)

2x + 2y = 26 (1)

2(33 - 3y) + 2y = 26

66 - 6y + 2y = 26

- 6y + 2y = 26 - 66

-4y = -40

y = -40/-4

y = 10

Substitute y = 10 into (2)

x + 3y = 33 (2)

x + 3(10) = 33

x + 30 = 33

x = 33 - 30

x = 3

Where,

x = cost of each t-shirt = $3

y = cost of each sweatshirt = $10

Answer:

173

Step-by-step explanation:

Area of dirt in the flower bed = area of flowerbed - area of 3 trapezoids

Area of flowerbed:

The flowerbed is in the shape of a parallelogram

The area of a parallelogram can be calculated by multiplying the base length times the height

Base length = 20ft

Height = 10ft

Area of flowerbed = 10 * 20 = 200ft^2

Area of rockbeds

The rockbeds are in the shape of trapezoids

The area of a trapezoid can be calculated using this formula

A = (a + b)/2 * h

Where a and b = bases and h = height

The rockbeds of base lengths of 2 and 4 and have heights of 3

So area of rockbeds = (4 + 2)/2 * 3

4 + 2 = 6

6 / 2 = 3

3 * 3 = 9

We then multiply that by 3 ( because there are three rockbeds )

9 * 3 = 27

Finally we subtract the areas

200 - 27 = 173

Answer:

C

Step-by-step explanation:

We are given that:

[tex]\sin \theta +\csc \theta = 2[/tex]

And we want to find the value of:

[tex]\sin^2\theta + \csc^2\theta[/tex]

From the first equation, we can square both sides:

[tex](\sin \theta + \csc \theta)^2=(2)^2[/tex]

Square:

[tex]\sin ^2\theta +2\sin\theta\csc\theta +\csc^2\theta =4[/tex]

Let csc(θ) = 1 / sin(θ):

[tex]\displaystyle \sin ^2\theta +2\sin\theta\left(\frac{1}{\sin \theta}\right) +\csc^2\theta =4[/tex]

Simplify:

[tex]\displaystyle \sin ^2\theta +2(1) +\csc^2\theta =4[/tex]

Therefore:

[tex]\sin ^2\theta + \csc^2\theta =2[/tex]

Our answer is C.

Answer:

5

Step-by-step explanation:

Answer:

We can't see the graph

Step-by-step explanation:

Answer:

18 T-shirts

Step-by-step explanation:

$4×18= $72 $72+$34=$106

Answer:

Find the volume of this prism.

Answer:

5050 = 225f + 125p

If p = 17 this month, then, f = 13

Step-by-step explanation:

Kiri owns a coworking space that has two primary types of memberships, full time and part-time. In order to pay her bills each month (rent on the building, electricity, internet, and so on) she needs to make $5050. Full-time memberships (f) cost $225 per month, and part-time memberships (p) cost $125 per month.

If Kiri has 17 part-time members this month, how many full-time members does she need according to your equation?

Total cost = $5050

cost of full-time memberships = $225

number of full time members = f

cost of part-time memberships = $125

number of part-time members = p

Total cost = cost of full-time memberships * number of full time members + cost of part-time memberships * number of part-time members

5050 = 225f + 125p

If p = 17 this month,

5050 = 225f + 125p

5050 = 225f + 125(17)

5050 = 225f + 2,125

5050 - 2,125 = 225f

2,925 = 225f

f = 2,925/225

f = 13

number of full time members = f = 13

If p = 17 this month, then, f = 13

Answer:

true

Step-by-step explanation:

AUB=A+B-(A∩B)

Answer:

A and C are functions.

The domain is x and the range is y

Step-by-step explanation:

Each x - value can have only one y -value

Function= unique x-values

Y can be the same answer but the X has to be different

Answer:

16.6 inches

Step-by-step explanation:

using the pythagorean theorem which is a^2 + b^2 = c^2 you can add 9^2 + 14^ together to get 277 and when you find the square root of 277 you get 16.6

Step-by-step explanation:

v = u + at

u+at=v

at = v-u

a = v-u

t

Hope this helps you :)

Answer:

£ 84

Step-by-step explanation:

Let :-

Given ratio :-

→ Sum of ratios = 4 + 3 + 5 = 12 .

According to Question :-

→ 3/12 × x = £21

→ x = £21 × 12/3

→ x = £ 84 .

Answer:

£84.

Step-by-step explanation:

There are 4 + 3 + 5 = 12 parts.

The second person got 3 parts so we can write:

3/12 x = 21      where x is the required amount of money

x = 21 * 12/3

= 21 * 4

= £84.

Answer:

186

Step-by-step explanation:

Your entire surface area is

216

the area of the rectangle on the bottom is 30

substract 30 from 216

Answer:

V≈421.88

Step-by-step explanation:

Answer:

Angles 1 and 5 are corresponding

Answer:

the longest side of the first triangle is 32 cm

Step-by-step explanation:

Given;

dimension of the smaller triangle =  4.5cm 6cm and 8 cm.

the longest side of this smaller triangle = 8 cm

Perimeter of the first triangle = 74 cm

let the increase in dimension of the similar first triangle = x

the longest side of the first triangle = 8x

4.5x + 6x + 8x = 74

18.5x = 74

x = 74/18.5

x = 4

the longest side of the first triangle = 8 x 4 = 32 cm

Answer:

the answer is 36

Step-by-step explanation:

Answer:

55% or 0.55 or 11/20

Step-by-step explanation:

probability the person chosen is an adult or child out of all

so 19+36/19+36+45

55/100

The probability that the selected person is not a teenager is [tex]\frac{11}{20}[/tex].

Probability is a measure of happening or non happening of the outcomes of the random experiment.

P(E) = Total number favorable of outcomes/ Total number of outcomes

Where,

P(E) is the probability of an event.

According to the given question.

Total number of adults in the audience = 19

Total number of teenagers in the audience = 45

Total number of children in the audience = 36

Total audience = 19 + 45 + 36 = 100

Now, the probability that the selected person is teenager = [tex]\frac{45}{100} = \frac{9}{20}[/tex]

Therefore,

The probability that a selected person is not a teenager

= [tex]1 -\frac{9}{20}[/tex]

= [tex]\frac{11}{20}[/tex]

Hence, the probability that the selected person is not a teenager is [tex]\frac{11}{20}[/tex].

Find out more information about probability here:

https://brainly.com/question/11234923

#SPJ2

Answer:

mean: 38

range: 27

median: 40

Step-by-step explanation:

mean: 40+13+49+52+35 / 5

range: 40 - 13

median : 40

Answer:

Mean = 38

Range = 40

Median = 40

Step-by-step explanation:

Arrange the terms in ascending order :

13, 35 , 40 , 49 , 53

[tex]Mean = \frac{40 + 13 + 49 + 53 + 35}{5} = 38[/tex]

[tex]Range = {53 - 13} = 40[/tex]

[tex]Median = \ the \ middle \ term = 40[/tex]

Answer:

-2

Step-by-step explanation:

I hope it helps

Answer:

Step-by-step explanation:

Answer:

t = 3 hours

Step-by-step explanation:

The distance between A and B is 198 km

Kenan traveled by car from A to B at an average speed of 66km/h

We need to find the time taken to complete the journey. It can be solved as follows :

[tex]v=\dfrac{d}{t}\\\\t=\dfrac{d}{v}\\\\t=\dfrac{198}{66}\\\\t=3\ h[/tex]

So, the required time is equal to 3 hours.

Answer:

X^2/3

Step-by-step explanation:

Answer:

Step-by-step explanation:

She made the -2(6) as a positive 12. it should've been a negative 12 because a negative multiplied by a positive is a negative.