Initial value of 100 increasing at a rate of 5%

Given:

On a unit circle, the terminal point of θ is [tex]\left(\dfrac{\sqrt{2}}{2},\dfrac{\sqrt{2}}{2}\right)[/tex].

To find:

The value of [tex]\theta[/tex].

Solution:

If the terminal point of θ is (x,y), then

[tex]\tan \theta=\dfrac{y}{x}[/tex]

On a unit circle, the terminal point of θ is [tex]\left(\dfrac{\sqrt{2}}{2},\dfrac{\sqrt{2}}{2}\right)[/tex]. So,

[tex]\tan \theta=\dfrac{\dfrac{\sqrt{2}}{2}}{\dfrac{\sqrt{2}}{2}}[/tex]

[tex]\tan \theta=1[/tex]

[tex]\tan \theta=\tan \dfrac{\pi}{4}[/tex]

[tex]\theta=\dfrac{\pi}{4}[/tex]

Therefore, the correct option is D.

Answer:

[tex]Ratio = 7:6[/tex]

Step-by-step explanation:

Given

Initially

[tex]Joe = 12oz[/tex] -- coffee

[tex]JoAnn = 12oz[/tex] -- coffee

Joe drank 2oz coffee; So, we have:

[tex]Joe = 12oz - 2oz[/tex]

[tex]Joe = 10oz[/tex] --- coffee

Joe added 2oz cream; So, we have:

[tex]Joe = 10oz[/tex] --- coffee     [tex]Joe = 2oz[/tex] --- cream

JoAnn added 2oz cream and stirred. So, we have:

[tex]Joe = 12oz[/tex] --- coffee     [tex]JoAnn = 2oz[/tex] --- cream

[tex]Total = 14oz[/tex]

JoAnn drank 2oz from the drink; the amount of drink JoAnn drank is:

[tex]JoAnn = \frac{Cream}{Total}[/tex]

[tex]JoAnn = \frac{2}{14}[/tex]

[tex]JoAnn = \frac{1}{7}[/tex]

Amount of cream left is:

[tex]Amount = [1- \frac{1}{7}] *2[/tex]

Take LCM

[tex]Amount = [\frac{7-1}{7}] * 2oz[/tex]

[tex]Amount = \frac{6}{7} * 2oz[/tex]

[tex]Amount = \frac{12}{7}oz[/tex]

So, we have:

[tex]Joe = 2oz[/tex] --- cream

[tex]JoAnn = \frac{12}{7}[/tex] cream

The ratio is:

[tex]Ratio = 2:\frac{12}{7}[/tex]

Multiply by 7

[tex]Ratio = 14:12[/tex]

Divide by 2

[tex]Ratio = 7:6[/tex]

Step-by-step explanation:

second: (2.2,-1.4)

third: (2.2,-1.35)

Step-by-step explanation:

hope it helps✨

The measure of QS is 11 units.

A line segment is defined as a measured path between two places. Line segments can make up any polygon's sides because they have a set length.

The figure given below shows a line segment QT, where the length of line segment QT refers to the distance between its endpoints, Q and T.

Q_________R___________S_________T

Given that RT= 12

And RS=7

⇒ RT= RS + ST

⇒ ST= RT - RS

⇒ ST= 12-7

Substitute the values of RT and RS,

⇒ ST= 5

⇒ QT= 16

⇒ QR = 16 - RT= 16 - 12 = 4

⇒ QS = QR + RS

Substitute the values of QR and RS,

⇒ QS = 4 + 7=11

⇒ QS = 11

Hence, the measure of QS is 11 units.

Learn more about the line segment here:

brainly.com/question/25727583

#SPJ2

Answer:

y(5y +2) -3a²

Step-by-step explanation:

that is the solution above

Answer:

[tex]{7a^{5}b^{5} c\\[/tex]

Step-by-step explanation:

 [tex]\frac{28a^{8}b^{6} c^{3} }{4a^{3}bc^{2} }[/tex]

→ First look at the first term of each expression and see if they can be simplified, and they can

[tex]\frac{7a^{8}b^{6} c^{3} }{a^{3}bc^{2} }[/tex]

→ Now look at the a terms, since a larger one is at the top, you subtract

[tex]\frac{7a^{5}b^{6} c^{3} }{bc^{2} }[/tex]

→ Now simplify the b and c terms

[tex]{7a^{5}b^{5} c[/tex]

Answer:

We want to rewrite:

q^2 = a*(p^2 - b^2)/p

as a linear equation, in the form:

y = m*x + c

So we start with:

q^2 = a*(p^2 - b^2)/p

we can expand the left side to get:

q^2 = (a/p)*p^2 - (a/p)*b^2

q^2 = a*p - (a/p)*b^2

Now we can ust define:

a*p = c

Then we can replace that to get:

q^2 = -(a/p)*b^2 + c

now we can replace:

q^2 = y

b^2 = x

Replacing these, we get:

y = -(a/p)*x + c

finally, we can replace:

-(a/p) = m

then we got the equation:

y = m*x + c

where:

y = q^2

x = b^2

c = a*p

m = -(a/p)

Step-by-step explanation:

Using Pythagoras theorem:

[tex] = \sqrt{{20}^{2} - {12}^{2} } [/tex]

[tex] = \sqrt{400 - 144}[/tex]

[tex] = \sqrt{256} [/tex]

[tex] = 16[/tex]

Step-by-step explanation:

-5x + 4y > -24

Plot and draw a graph that's it

Answer:

F

Step-by-step explanation:

add all the numbers and divide them by how many numbers there is(in this case 15) to find the average of the prices

if 60 = c,

36 = m and

x is the missing length

c² = x . m

3600 = x . 36

x = 3600/36

x = 100

Answer:

its 16

Step-by-step explanation:

rotation doesnt effect length

[tex]\huge\bold\color{blue}{⁂Answer:}[/tex]

[tex]\bold{ - \frac{6 \sqrt{x} - x - 9 }{2(x - 9)} }[/tex]

#CarryOnLearning

[tex]\bold\color{red}{༄Fairy \: Elfꨄ︎}[/tex]

Answer:

Ming has described a proportional relationship because the ordered pairs are linear and the line passes through the origin

Step-by-step explanation:

Given

x - y

5 - 10

10 - 20

15 - 30

Required

Determine if the data are proportional

The dataset is small; so, we can derive the relationship by observation.

By observing the x and y values, the relationship is:

y = 2x --- i.e. multiply x values by 2.

This is further proven by:

y = 2 * 5 = 10

y = 2 * 10 = 20

y = 2 * 15 = 30

y = 2 * 0 = 0 --- the origin

Hence, the dataset is proportional and it passes through the origin.

As we know, The volume of the square prism is twice the volume of the cylinder

To determine the relationship between the volume of the square prism and that of the cylinder, we need to find both volumes.

The volume of the square prism is V = Ah where A is the cross-sectional area and h its height. Since A = 314 square units,

V = 314 × h = 314h

Also, the volume of the cylinder is V = A'h where A' is the cross-sectional area of the cylinder and h' its height. Since the A' = 50π square units,

V' = 50π × h' = 50πh'

The ratio of the volume of the square prism to that of the cylindrical prism is V/V' = 314h/50πh'

Since the height of the square prism equals that of the cylinder, h = h'.

So, V/V' = 314h/50πh .

V/V' = 314/50π

if we take π = 3.14,

V/V' = 314/(50 × 3.14)

V/V' = 100/50

V/V' = 2

So, V = 2V'

Thus, the volume of the square prism is twice the volume of the cylinder.

So, the answer is D.

Learn more about square prisms and cylinders here:

https://brainly.com/question/23245822

Answer:

D. The volume of the square prism is twice the volume of the cylinder.

Step-by-step explanation:

took the test, got it right, comment below if you would like a step by step explanation

Answer:

G. 14:5 is the correct answer.

Step-by-step explanation:

a:b = 4:5

a:c = 2:7

so,

here in first ratio a = 4

in second ratio a = 2

making them equal:

Taking LCM of 2 and 4 = 4

so

a:c = 2/7 = (2×2)/(7×2) = 4/14

so,

a = 4

c = 14

b = 5

so ratio c : b = 14:5

Answer:

Angle of slice (θ) = 172° (Approx.)

Step-by-step explanation:

Given:

Area of pizza slice = 16 inch²

Total area of pizza = 33.49 inch²

Find:

Angle of slice (θ)

Computation:

Area of circle = [π][r²]

Area of pizza slice = [π][r²]

[π][r²] = 33.49

[3.14][r²] = 33.49

Radius = 3.26 inch (Approx.)

Area of sector = [θ/360][π][r²]

16 = [θ/360][3.14][3.26²]

16 = [θ/360][3.14][10.6276]

16 = [θ/360][33.37]

Angle of slice (θ) = 172° (Approx.)

Answer:

a. Smart Dot Company: C = 12 + 0.5·t

Communications Plus: C = 2.5·t

b. Please find attached the required tables created using MS Excel cell function tool

c. Please find attached the graph of both relationship created on the same grid with

Step-by-step explanation:

a. The monthly cost of the Smart Dot Company = $12

The hourly cost for internet use on Smart Dot Company = $0.50

The hourly cost of using the Communications Plus = $2.50

Therefore, the total monthly cost, C, for the duration of hours used, t, is given as follows;

Smart Dot Company: C = 12 + 0.5·t

Communication Plus: C = 2.5·t

b. The table of values are created using MS Excel as follows;

[tex]\begin{array}{ll}Smart \ Dot \ Company&\\Time \ (hours)&Cost \ (dollars)\\0&12\\2&13\\4&14\\6&15\\8&16\\10&17\end{array}[/tex]    [tex]\begin{array}{ll}Communications\ \ Plus&\\Time \ (hours)&Cost \ (dollars)\\0&0\\2&5\\4&10\\6&15\\8&20\\10&25\end{array}[/tex]

c. Please find attached the graph of both relationship created on the same grid with MS Excel

Answer:

eşnatto eşmatoroorlfld

Answer:

Now , Piyush age =3+Honey age

Step-by-step explanation:

Honey age=x

Piyush age=y

1 year ago,Honey age=x-1

Piyush age=y-1

the ratio of Honey and Piyush age=2:3

x-1:y-1=2:3

x-1/y-1=2/3

3(x-1)=2(y-1)

3x-3=2y-2

3x-2y= -2+3

3x-2y=1 eq _1

after 5 years from now,

Honey age=x+5

Piyush age=y+5

the ratio of them=4:5

x+5/y+5=4/5

5(x+5) =4(y+5)

5x+25=4y+20

5x-4y=20-25

5x-4y=-5 _eq2

eq1and 2_

5x-4y= -5

3x-2y= 1

-

2x-2y=-6

x-y =-3

-y=-3-x

y=3+x

Answer:

81

Step-by-step explanation:

9x + 100 = 829

9x =829-100

= 729

x = 729/9

x = 81

Answer: x = 81

Step-by-step explanation:

You'd want to isolate x, meaning subtracting 100 on both sides to remove that from the equation. This results in 9x = 729, divide by 9 on both sides to remove that too from the equation and you'd be left with x = 81.

Answer:

Step-by-step explanation:

Answer:

1.00 am

Step-by-step explanation:

Find the LCM of 12,18,20 and 25

=900 min ....change it to hrs =15 hrs

10.00am___1000hrs

1000hrs+15hrs

=0100hrs

=1:00 am

Answer:

Step-by-step explanation:

Answer:

[tex]-\frac{3p^8}{4q^3}[/tex]

Step-by-step explanation:

One is given the following expression,

[tex]\frac{15p^-^4q^-^6}{-20p^-^1^2q^-^3}[/tex]

Since (15) and (-20) are both divisible by (5), one can divide both terms by (5) to simplify it.

[tex]\frac{3p^-^4q^-^6}{-4p^-^1^2q^-^3}[/tex]

Now bring all of the terms with a negative exponent to the numerator. Multiply the exponents by (-1), then add them to the exponents of the like term in the numerator. Simplify the resulting exponents

[tex]\frac{3p^-^4q^-^6}{-4p^-^1^2q^-^3}[/tex]

[tex]\frac{3p^-^4^+^(^-^1^)^(^-^1^2^)q^-^6^+^(^-^1^)^(^-^3^)}{-4}[/tex]

[tex]\frac{3p^-^4^+^1^2q^-^6^+^3}{-4}[/tex]

[tex]\frac{3p^8q^-^3}{-4}[/tex]

Rewrite the fraction such that there are no negative exponents. Remember the rule, when bringing a number from the numerator to the denominator and back, multiply the exponent of the number by (-1). One can only switch numbers between the numerator and the denominator when all operations are multiplication or division.

[tex]\frac{3p^8q^-^3}{-4}[/tex]

[tex]-\frac{3p^8}{4q^3}[/tex]

Answer:

the first one gat to be x=4

Answer: 17

Step-by-step explanation: :)

Answer:

No.

Step-by-step explanation:

They are not correct because the "| |" signs mean absolute value. What ever is inside the signs must be positive. So -9 becomes 9 and 9 is greater than 4. So, the student is not correct.

Answer:

B

Step-by-step explanation:

according to pythagorean

[tex]7^{2} + 24^{2} =x^{2}[/tex] (x>0)

=> [tex]x^{2} =625[/tex]

=>[tex]x=\sqrt{625}[/tex] = 25

2

[tex]\\ \sf\longmapsto 5.5\times 10^3[/tex]

[tex]\\ \sf\longmapsto 55\times 10^4[/tex]

We know

Hence number of significant figures is 2

9514 1404 393

Answer:

  2

Step-by-step explanation:

When a number is written in scientific notation, all of the digits of the mantissa are considered significant. The mantissa is 5.5, which has 2 digits.

There are 2 significant digits in the number.