What is the approximate length of arc s on the circle below? Use 3.14 for Pi. Round your answer to the nearest tenth. A circle is shown. 2 rays form an angle of 45 degrees. The length of the rays is 8 inches. Arc s contains the angle measuring 45 degrees.

Answer:

[tex]\displaystyle \sin \theta = \frac{4}{5}[/tex] if [tex]\displaystyle \cos\theta = -\frac{3}{5}[/tex] and [tex]\theta[/tex] is in the second quadrant.

Step-by-step explanation:

By the Pythagorean Trigonometric Identity:

[tex]\left(\sin \theta\right)^2 + \left(\cos\theta)^2 = 1[/tex] for all real [tex]\theta[/tex] values.

In this question:

[tex]\displaystyle \left(\cos\theta\right)^2 = \left(-\frac{3}{5}\right)^2 = \frac{9}{25}[/tex].

Therefore:

[tex]\begin{aligned} \left(\sin\theta\right)^2 &= 1 -\left(\cos\theta\right)^2 \\ &= 1 - \left(\frac{3}{5}\right)^2 = \frac{16}{25}\end{aligned}[/tex].

Note, that depending on [tex]\theta[/tex], the sign [tex]\sin \theta[/tex] can either be positive or negative. The sine of any angles above the [tex]x[/tex] axis should be positive. That region includes the first quadrant, the positive [tex]y[/tex]-axis, and the second quadrant.

According to this question, the [tex]\theta[/tex] here is in the second quadrant of the cartesian plane, which is indeed above the [tex]x[/tex]-axis. As a result, the sine of this

It was already found (using the Pythagorean Trigonometric Identity) that:

[tex]\displaystyle \left(\sin\theta\right)^2 = \frac{16}{25}[/tex].

Take the positive square root of both sides to find the value of [tex]\sin \theta[/tex]:

[tex]\displaystyle \sin\theta =\sqrt{\frac{16}{25}} = \frac{4}{5}[/tex].

Answer:

0.726 galones

Step-by-step explanation:

De la pregunta anterior, se nos dice que

1 botella = 2.75 litros de agua

Se nos pide encontrar cuántos galones puede contener.

En la pregunta, nos dicen

1 litro = 0.264 galones

2.75 litros =

Multiplicación cruzada

2.75 litros × 0.264 galones

= 0.726 galones.

Por lo tanto, 0.726 galones pueden caber en la botella

Answer:

Got u 8382 for

Step-by-step explanation:

The one is the one for owing me owning this world haha 8282

Answer:

14°

Step-by-step explanation:

Calculate the common side ZX to both right triangles.

Using the tangent ratio in the upper right triangle.

tan70° = [tex]\frac{opposite}{asjacent}[/tex] = [tex]\frac{ZX}{3}[/tex] ( multiply both sides by 3 )

3 × tan70° = ZX , thus

ZX ≈ 8.24

Using the cosine ratio in the lower right triangle.

cos ZXY = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{XY}{ZX}[/tex] = [tex]\frac{8}{8.24}[/tex] , thus

∠ ZXY = [tex]cos^{-1}[/tex] ([tex]\frac{8}{8.24}[/tex] ) ≈ 14° ( to the nearest degree )

Answer:

a) $1520

b) [tex]S_7 =[/tex] $209195

Step-by-step explanation:

The range of salaries forms an arithmetic sequence with the first term as 25325 and its 7th term as 34445:

a) The raise the person can get each year is the common difference of the progression, d.

The nth term of an arithmetic progression is given generally as:

[tex]a_n = a + (n - 1)d[/tex]

where a = first term = 25325

d = common difference

Therefore, the 7th term (34445) will be:

34445 = 25325 + (7 - 1)d

34445 = 25325 + 6d

=> 6d = 34445 - 25325 = 9120

d = 9120 / 6 = $1520

Therefore, the raise the person gets each year (common difference) is $1520.

b) The total amount the person will earn after 7 years is the sum of the salaries of all 7 yeas.

The sum of an arithmetic progression up to the nth term is given as:

[tex]S_n = \frac{n}{2}(2a + (n - 1)d)\\ \\[/tex]

Therefore, the sum of the person's salary for the 7 years is:

[tex]S_7 = \frac{7}{2}(2 * 25325 + (7 - 1)1520)\\ \\S_7 = 3.5 (50650 + 6(1520))\\\\S_7 = 3.5 (50650 + 9120)\\\\S_7 = 3.5 * 59770\\[/tex]

[tex]S_7 =[/tex] $209195

That is the total amount of salary after 7 years

Answer: D) 7 to the 3 power.

Step-by-step explanation:

Answer:

D. 7 to the 3 power

Step-by-step explanation:

I know I'm very late but dont judge :V

This is also seven t the power of three

Answer:

25 degrees

Step-by-step explanation:

The two given angles are vertical, so we can set their measures equal to each other and then solve for x.

4x + 50 = 150

4x = 100

x = 25

Answer:

x = 25

Step-by-step explanation:

The angles are vertical angles, so their measures are equal.

4x + 50 = 150

4x = 100

x = 25

Answer:

The mode is the number that occurred the most often. The range is the difference between the highest and lowest values.

Step-by-step explanation:

Answer:

Mode:The number whose repetaed the most is the set (there can be multiple)

Range: The largest number minus the smallest = The range

Step-by-step explanation:

The inequality is [tex]\frac{x}{-3}[/tex] >2

x is less than -6  and -6 is excluded so it will be represented by an empty circle and a line going toward negative values

so it's D

Answer:

∠ GDH = 67.5°

Step-by-step explanation:

The measure of the chord- chord angle GDH is half the sum of the measures of the arcs intercepted by the angle and its vertical angle.

∠ GDH = [tex]\frac{1}{2}[/tex](GH + EF) = [tex]\frac{1}{2}[/tex] (90 + 45)° = 0.5 × 135° = 67.5°

Answer:

30+48 is equivalent to 48+30

Answer:

30+48

Step-by-step explanation:

equivelent just flip them

Answer:

  7.5 times

Step-by-step explanation:

Your calculator can tell you the ratio ...

  [tex]\dfrac{3\times10^8}{4\times10^7}=\dfrac{30\times10^7}{4\times10^7}=\dfrac{30}{4}=\boxed{7.5}[/tex]

The population of the US is 7.5 times as great as the population of California.

Answer:

Step-by-step explanation:

Factorize 175 and 50

175 = 5 * 5 * 7

50  = 5 * 5 * 2

[tex]\frac{\sqrt[3]{175}}{\sqrt[3]{}50}=\sqrt[3]{\frac{175}{50}}\\\\\\ =\sqrt[3]{\frac{5*5*7}{5*5*2}}\\\\\\=\sqrt[3]{\frac{7}{2}}[/tex]

Answer:

the trig sign to use is sine

sin(73)=x/15

multiply each side by 15 giving you:

sin(73)15=x

x=14.3

Answer:

2[tex]x^{4}[/tex] + x³ - x² + 54x - 56

Step-by-step explanation:

Area (A) is calculated as

A = length × width

   = (x² - 2x + 8)(2x² + 5x - 7)

Each term in the second factor is multiplied by each term in the first factor, that is

x²(2x² + 5x - 7) - 2x(2x² + 5x - 7) + 8(2x² + 5x - 7) ← distribute all parenthesis

= 2[tex]x^{4}[/tex] + 5x³ - 7x² - 4x³ - 10x² + 14x + 16x² + 40x - 56 ← collect like terms, thus

A = 2[tex]x^{4}[/tex] +x³ - x² + 54x - 56

The expression which represents the area of Dylan’s room will be 2x⁴ - 7x³ - 21x² + 82x - 56.

What is the area?

The area is the space occupied by any shape, find out by multiplying its length and breadth.

We have,

Lenght =  (x² – 2x + 8)

and

Breadth = (2x² + 5x – 7)

Now, simplifying the above expressions,

(x² – 2x + 8)

It can be written as , Using middle term split method,

x² – 4x + 2x + 8

= x(x – 4) - 2(x - 4)

= (x – 4) (x - 2)

In the same way,

(2x² + 5x – 7)

= 2x² +7x  - 2x – 7

= x(2x +7)  - 1(2x + 7)

= (x - 1) (2x +7)

So,

So,

Using the area formula,

i.e.

Area = Length × Breadth

Area =  (x² – 2x + 8) ×  (2x² + 5x – 7) = (x – 4) (x - 2) (x - 1) (2x +7)

Now,

Area = 2x⁴ - 7x³ - 21x² + 82x - 56

Hence we can say that the expression which represents the area of Dylan’s room will be  2x⁴ - 7x³ - 21x² + 82x - 56.

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Answer:

Distance= y - 4  

Step-by-step explanation:

The number of boxes can't be negative or in fractions.

so the domain would be "All whole numbers from 0 to 10"

Answer:

A) All whole numbers from 0 to 10.

Step-by-step explanation:

The domain of a function is given by the available values of the independent variable.

In this case you have that the independent variable is the number of boxes, and the available values of this variable are integers in between 0 and 10, by including 0 and 10.

Then, the domain of the functions composed by all positive integers number from 0 to 10 including 0 and 10.

A) All whole numbers from 0 to 10.

Answer:

a) 294

b) 180

c) 75

d) 168

e) 105

Step-by-step explanation:

Given the numbers 0, 1, 2, 3, 4, 5 and 6.

Part A)

How many 3 digit numbers can be formed ?

Solution:

Here we have 3 spaces for the digits.

Unit's place, ten's place and hundred's place.

For unit's place, any of the numbers can be used i.e. 7 options.

For ten's place, any of the numbers can be used i.e. 7 options.

For hundred's place, 0 can not be used (because if 0 is used here, the number will become 2 digit) i.e. 6 options.

Total number of ways = [tex]7 \times 7 \times 6[/tex] = 294

Part B:

How many 3 digit numbers can be formed if repetition not allowed?

Solution:

Here we have 3 spaces for the digits.

Unit's place, ten's place and hundred's place.

For hundred's place, 0 can not be used (because if 0 is used here, the number will become 2 digit) i.e. 6 options.

Now, one digit used, So For unit's place, any of the numbers can be used i.e. 6 options.

Now, 2 digits used, so For ten's place, any of the numbers can be used i.e. 5 options.

Total number of ways = [tex]6 \times 6 \times 5[/tex] = 180

Part C)

How many odd numbers if each digit used only once ?

Solution:

For a number to be odd, the last digit must be odd i.e. unit's place can have only one of the digits from 1, 3 and 5.

Number of options for unit's place = 3

Now, one digit used and 0 can not be at hundred's place So For hundred's place, any of the numbers can be used i.e. 5 options.

Now, 2 digits used, so For ten's place, any of the numbers can be used i.e. 5 options.

Total number of ways = [tex]3 \times 5 \times 5[/tex] = 75

Part d)

How many numbers greater than 330 ?

Case 1: 4, 5 or 6 at hundred's place

Number of options for hundred's place = 3

Number of options for ten's place = 7

Number of options for unit's place = 7

Total number of ways = [tex]3 \times 7 \times 7[/tex] = 147

Case 2: 3 at hundred's place

Number of options for hundred's place = 1

Number of options for ten's place = 3 (4, 5, 6)

Number of options for unit's place = 7

Total number of ways = [tex]1 \times 3 \times 7[/tex] = 21

Total number of required ways = 147 + 21 = 168

Part e)

Case 1: 4, 5 or 6 at hundred's place

Number of options for hundred's place = 3

Number of options for ten's place = 6

Number of options for unit's place = 5

Total number of ways = [tex]3 \times 6 \times 5[/tex] = 90

Case 2: 3 at hundred's place

Number of options for hundred's place = 1

Number of options for ten's place = 3 (4, 5, 6)

Number of options for unit's place = 5

Total number of ways = [tex]1 \times 3 \times 5[/tex] = 15

Total number of required ways = 90 + 15 = 105

Answer:

see file attached

Step-by-step explanation:

Answer:

x<-14

Step-by-step explanation:

Hello,

If we multiply by positive numbers it does not change the inequality, right?

So let's multiply by 10 both sides, it comes

[tex]2(4x+1)+10<5(x-6) \\ \\\text{*** develop ***} \\ \\8x+2+10=8x+12 < 5x-30 \\ \\\text{*** subtract 5x ***} \\\\8x+12-5x=3x + 12 < -30 \\ \\\text{*** subtract 12 ***}\\ \\3x+12-12=3x<-30-12 \\ \\3x < -42 \\ \\\text{*** divide by 3, it does not change the inequality ***}\\ \\ x < -42/3=-14[/tex]

I did not find a good way to show you here the number line. You need to basically take all numbers which are at the left of -14 on that line.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

[tex]x < - 14[/tex]

[tex] \frac{1}{5} (4x + 1) + 1 < \frac{1}{2} (x - 6)[/tex]

[tex] \frac{4}{5} x + \frac{1}{5} < \frac{1}{2} x - 3 [/tex]

[tex]8x + 2 + 10 < 5x - 30[/tex]

[tex]8x + 12 < + 5x - 30[/tex]

[tex]8x - 5x < - 30 - 12[/tex]

[tex]3x < - 42[/tex]

[tex] \frac{3}{3} x < \frac{ - 42}{3} [/tex]

[tex]x < - 14[/tex]

Answer:

d. (x + 5)

Step-by-step explanation:

The factorization of 2x^2 - 4x - 70 is (x + 5)(2x - 14)

Answer:

2( x + 5 ) × ( x - 7 )

Step-by-step explanation:

2x² - 4x - 70

2( x² - 2x - 35)

2( x² + 5x - 7x - 35)

2(x × (x + 5) -7 (x + 5))

2(x + 5 ) × (x - 7)

Answer:

Step-by-step explanation:

Solution,

Use the BODMAS Rule:

B = Bracket

O = Of

D = Division

M= Multiplication

A = Addition

S = Subtraction

Now,

Let's solve,

[tex]2 + 8 \div 2 \times 3[/tex]

First we have to divide 8 by 2

[tex] = 2 + 4 \times 3[/tex]

Calculate the product

[tex] = 2 + 12[/tex]

Calculate the sum

[tex] = 14[/tex]

Hope this helps...

Good luck on your assignment..

Answer:

14

Step-by-step explanation:

2 + 8 ÷ 2 x 3 =

There is an addition, a division, and a multiplication. According to the correct order of operations, we do first the multiplications and divisions in the order they appear from left to right.

= 2 + 4 x 3

= 2 + 12

Now we do the addition.

= 14

Answer:

5 cm

Step-by-step explanation:

As we can see in the attached figure that G is the point at which the three medians of the triangle meet  i.e we called the centroid

And, according to the property of the centroid, it divides the medians in ratio i.e 2:1

DG: CG = 2 : 1

Since the DG is 10 cm

So, the CG would be half of DG i.e 5 cm

Hence, the CG is 5 cm

Therefore the first option is correct

Answer:

the answer is 5 cm

Step-by-step explanation:

Answer:

1) From the measure of 40°, you can write:

tan(40°) = 100/x, where x is the base from the building to the tower

⇒x=100/tan(40°) = 119,18 m

2) From the measure of 30°, you can write

tan(30°) = y / 119,18, where y is the height from the roof of Jill's building to the top of the tower.

Then, y = tan(30°) * 119,18 = 68,81 m

3) The height of Jill's building is 100 - 68,81 = 31,19 m

When the height of the tower is 100 meters, the height of Jill's apartment building is 31.19m

Let the base from the building to the Rowe be represented by x. Based on the information given, the value will be:

x = 100/tan 40°

x = 119.18m

The height can be represented as:

= 100 - [tan30° × 119.18]

= 100 - 68.81

= 31.19m

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Answer:

3, 5, 7

Step-by-step explanation:

As per triangle inequality theorem:

Assume the sides are equal to 3 smallest odd numbers: 1,3 and 5

The next triple is: 3, 5 and 7

So 3, 5, 7 is the combination of smallest odd numbers to make sides of a triangle

Answer:

Option C is the correct option

Step-by-step explanation:

Given

Point = ( -7 , - 9 )

Slope = - 4

Equation of line ( Point slope form )

[tex]y - y1 = m(x - x1)[/tex]

when point = ( -7 , - 9 )

Hope I helped...

Best regards!!

The equation of the line is 4x + y = -37 then option C is correct.

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

The given point is ( -7, - 9 ) and the slope is - 4.

The equation of the line is calculated by,

y - y₁ = m ( x - x₁ )

y - 9 = -4 ( x + 7 )

y = -4x -28 - 9

y = -4x -37

4x + y = -37

Therefore, the equation of the line is 4x + y = -37 then option C is correct.

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(4, 7) lies on the graph of [tex]y=3f(2x)+1[/tex], so plugging in [tex]x=4[/tex] gives [tex]y=7[/tex]:

[tex]7=3f(2\cdot4)+1\implies f(8)=2[/tex]

i.e. if [tex]x=8[/tex], then [tex]y=2[/tex], so the point (8, 2) lies on the graph of [tex]y=f(x)[/tex]. The sum of this point's coordinates is 8 + 2 = 10.

Answer:

50.27

Step-by-step explanation:

First, we have to find the volume of the cone using the formula V=πr^2h/3, where pi is 3.14. After plugging everything in, we get V = 75.4. Then, we have to find 2/3 of that. Rounding to the nearest hundredth, we get 2/3 x 75.4 = 50.27.

Answer:

The dots plotted on the scatterplot closely follow a graph of exponential decline. The large number-- around 350 texts per day-- by 18-22year-olds, seems to decline exponentially as age increases. With a little work, it may be possible to plot the curve and write an equation to model the decline.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The question is incomplete. Here is the complete question.

Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length using the Pythagorean theorem and then find the value of the indicated trigonometric function of the given angle. Rationalize the denominator if applicable. Find tan B when a = 96 and c = 100.

Pythagoras theorem states that the square of the hypotenuse side of a right angled triangle is equal to the sum of the square of its other two sides. Mathematically c² = a²+b² where c is the hypotenuse and a,b are the other two sides.

From the question, we are given a = 96 and c = 100, to get the unknown side 'b', we will substitute the given values into the formula above;

c² = a²+b²

100²  = 96² +b²

b²  = 100²  - 96²

b²  = 10,000 - 9216

b²  = 784

b = √784

b = 28

Hence, the unknown length is 28.

To get tanB, we will use the SOH, CAH, TOA trigonometry identity

According to TOA, tan B = opposite/adjacent

tan B = b/a (note that side b is the opposite in this case since the angle we are considering is B)

Given b = 28 and a = 96

tan B = 28/96

tan B = 4*7/4*24

tan B = 7/24

Answer:

[tex]\boxed{15}[/tex]

Step-by-step explanation:

Set the output equal to 0.

[tex]-2x^2 +20x+150=0[/tex]

Factor left side of the equation.

[tex]-2(x+5)(x-15)=0[/tex]

Set factors equal to 0.

First possibility:

[tex]-2(x+5)=0\\x+5=0\\x=-5[/tex]

Second possibility:

[tex]x-15=0\\x=15[/tex]

The value or prize cannot be negative.

[tex]x\neq -5\\ x=15[/tex]