Find the value of x.
Round to the nearest tenth.
B
63
142°
61
A
C
X
x = [?
X
Law of Cosines: c² = a² + b² - 2ab cos C

f(3) = 16

Function notation is used to express a rule in terms of x and f(x), where x is independent and f(x) is dependent.

Pronunciation of Function Notation

To use function notation it is important to know how to express the function in words.

The function "f(x) = 3x + 7" would be pronounced "F of X equals three X plus 7."

So, the function is "F of" whatever variable or value is within the parentheses.

Use of Function Notation

The function y=x is similar to the function f(x)=x. As a matter of fact, when graphed they both work the same way, but the function notation seen in the question allows us to see the value of x.

This is because the value in the parentheses is the value of x. So, in this situation, the question asks what is the value of the function when x equals 3.

Solving for f(3)

To solve this function, all we have to do is plug 3 in for x and evaluate.

First, multiple 3*3

Next, add 7

Line segment AB is the same length as line segment CD.

A line segment is defined as the part of a line that is divided in parts using two or more end points for easy observation.

From the given diagram, the line segment AB is the same as the line segment CD because the line segment CD was shifted a bit from the point of origin of line segment AB.

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Let [tex]r_A[/tex] and [tex]r_B[/tex] be the respective radii of balloons A and B. If the fixed total volume is V, then

[tex]V = \dfrac{4\pi}3\left({r_A}^3 + {r_B}^3\right)[/tex]

and knowing [tex]r_A=10\,\rm cm[/tex] and [tex]r_B=9\,\rm cm[/tex] at the start, we have V = 6916π/3 cm³. Then when [tex]r_A=12\,\rm cm[/tex], the radius of the other sphere is [tex]r_B=1\,\rm cm[/tex].

Differentiating both sides with respect to time t gives a relation between the rates of change of the radii:

[tex]0 = 4\pi \left({r_A}^2 \dfrac{dr_A}{dt} + {r_B}^2 \dfrac{dr_B}{dt}\right) \implies \dfrac{dr_B}{dt} = -\left(\dfrac{r_A}{r_B}\right)^2 \dfrac{dr_A}{dt}[/tex]

We're given [tex]\frac{dr_A}{dt} = 0.1\frac{\rm cm}{\rm s}[/tex] the whole time. At the moment [tex]r_A=12\,\rm cm[/tex], the radius of balloon B is changing at a rate of

[tex]\dfrac{dr_B}{dt} = -\left(\dfrac{12\,\rm cm}{1\,\rm cm}\right)^2 \left(0.1\dfrac{\rm cm}{\rm s}\right) = \boxed{-14.4 \dfrac{\rm cm}{\rm s}}[/tex]

Completing the squares, the correct statements regarding the equation of the circle are given by:

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

In this problem, the equation is given by:

x² + y² - 2x - 8 = 0.

Completing the squares:

(x - 1)² + y² = 8 + 1²

(x - 1)² + y² = 9.

Hence the center is (1,0), the radius is 3, and the correct statements are:

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The total amount Sam will pay in all will be $2,400,000

From the question, we are to determine the interest Sam pays in all

Using the simple interest formula,

I = PRT

From the given information,

P = $2,000,000

R = 5% = 0.05

T = 4

Putting the parameters into the formula,

I = $2000000 × 0.05 × 4

I = $400000

The interest Sam will pay is $400,000

The total amount Sam will pay in all will be $2,000,000 + $400,000

= $2,400,000

Hence, the total amount Sam will pay in all will be $2,400,000

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Answer:

Step-by-step explanation:400000

Answer:

yes

Step-by-step explanation:

2/3=6/9

2/3=2/3

it is because 6 and 9 is divided by 3

Answer:

2,4,8,11,22, or 44

Step-by-step explanation:

To figure out how many rings would be in each full row with no leftovers, we need to find all the factors of 88 (outside of 1 and 8) which are 2,4,8,11,22, and 44. Since the question does not give any more information on how big the rows need to be, I can't narrow this down any further, however if I had to choose I would say rows of 8 by 11 would be the best.

Hope this helps! :)

This  is an equilateral triangle, therefore, all the angles  are 60 degrees.

3 times  60 is  180.

180 is the answer

Answer:

5. m<STP = 134

6. m<PTS = 158

Step-by-step explanation:

5. Since ray TR bisects <PTS, angles PTR and STR are congruent.

m<PTR = m<STR

3x - 8 = 2x + 17

Subtract 2x from both sides.

x - 8 = 17

Add 8 to both sides.

x = 25

m<STP = 2m<PTR

m<STP = 2(3x - 8)

m<STP = 2(3 × 25 - 8)

m<STP = 2(67)

m<STP = 134

6.

2m<PTR = m<PTS

2(x - 23) = x + 56

2x - 46 = x + 56

x = 102

m<PTS = x + 56

m<PTS = 102 + 56

m<PTS = 158

Answer:

[tex]\displaystyle \large{\cos \theta = \dfrac{-3}{\sqrt{34}} = -\dfrac{3\sqrt{34}}{34}}\\\\\displaystyle \large{\csc \theta = \dfrac{\sqrt{34}}{5}}\\\\\displaystyle \large{\tan \theta = -\dfrac{5}{3}}[/tex]

Step-by-step explanation:

Accorded to trigonometric formula, we know that:

[tex]\displaystyle \large{\cos \theta = \dfrac{x}{r}}\\\\\displaystyle \large{\csc \theta = \dfrac{1}{\sin \theta} = \dfrac{1}{\frac{y}{r}} = \dfrac{r}{y}}\\\\\displaystyle \large{\tan \theta = \dfrac{\sin \theta}{\cos \theta} = \dfrac{y}{x}}[/tex]

We know what x and y are but not yet knowing what r is. We can find r (radius) using the formula:

[tex]\displaystyle \large{r=\sqrt{x^2+y^2}}[/tex]

Input x = -3 and y = 5 in.

[tex]\displaystyle \large{r=\sqrt{(-3)^2+(5)^2}}\\\\\displaystyle \large{r=\sqrt{9+25}}\\\\\displaystyle \large{r=\sqrt{34}}[/tex]

Hence, radius is √34 and we know all we need now. Substitute x = -3, y = 5 and r = √34 in respective areas.

[tex]\displaystyle \large{\cos \theta = \dfrac{-3}{\sqrt{34}} = -\dfrac{3\sqrt{34}}{34}}\\\\\displaystyle \large{\csc \theta = \dfrac{\sqrt{34}}{5}}\\\\\displaystyle \large{\tan \theta = -\dfrac{5}{3}}[/tex]

These are the answers to your question. Please let me know if you have any questions regarding my answer or explanation!

The Correct match up is:

The first proof of complex numbers was done by an Italian mathematicians known to be Girolamo Cardano and Raphael Bombelli.

The person who illustrated geometry of iterations is Gaston Maurice Julia.

Benoit Mandelbrot is known to have discover fractal geometry. Rene Descartes is known to be famous for making a connection between geometry and algebra.

Therefore, from the above, you can see that the only correct matchup is Leonhard Euler - developed geometry of curved surfaces

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Answer :

proof of complex functions --- > Maryam Mirzakhani

illustrated geometry of iterations --- > Benoit Mandelbrot

developed geometry of curved surfaces --- > Leonhard Euler

In the 15th century, Rene Descartes developed the field of analytical geometry by using functions to describe lines and curves in a coordinate plane. In the 18th century, Leonhard Euler extended geometric analysis to curved surfaces. in the late 20th century, Benoit Mandelbrot used computers to illustrate the geometry of iterations (fractals). In 2014, Maryam Mirzakhani received the Fields Medal for her work on geometric proofs involving complex functions.

The volume of the cylinder that is not occupied by the sphere is 2πr³/3

Since the object is a sphere in a cylinder, we need to know the volume of sphere and cylinder.

The volume of a cylinder is given by V '= πr²h where

Since the height of the cylinder equals the diameter of the sphere, h = 2r

So, V' = πr²h

V' = πr² × 2r

V' = 2πr³

The volume of a sphere of radius r is given by V = 4πr³/3

The volume of the cylinder not occupied by the sphere is V" = V' - V

=  2πr³ - 4πr³/3

= (6πr³ - 4πr³)/3

= 2πr³/3

So, the volume of the cylinder that is not occupied by the sphere is 2πr³/3

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Answer:

3. 16.67

4. 25

Step-by-step explanation:

3. x+2÷8=14/6 (similar triangles have corresponding proportional sides)

x+2=(7×8)/3

x=56/3-6/3 (LCM)

x= 50/3

4. 27/72= (-4+4x)/64

3/2= (-1+x)/16

-1+x=24

x=24+1

Answer:

4/8

Step-by-step explanation:

15 1/8 - 1/2(4/8) = 14 5/8

The value of sin⁻¹ (sin 17°) is 17° or 17 degree after applying the trigonometric identity sin⁻¹ (sinx) = x

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have:

= sin⁻¹ (sin 17°)

The above expression represents an angle.

Let's suppose the angle is x and sin of x is sinx

sinx is a ratio of side opposite to the angle to hypotenuse.

If we take sin inverse of sinx we get an angle of x.

sin⁻¹ (sinx) = x

sin⁻¹ (sin 17°) = 17 degree

Thus, the value of sin⁻¹ (sin 17°) is 17° or 17 degree after applying the trigonometric identity sin⁻¹ (sinx) = x

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Step-by-step explanation:

the domain is the set or interval of all valid x values.

the range is the set or interval of all valid y values.

1.

domain = {-1, 2, 5}

range = {0, 2, 3, 7}

function : no, because x = -1 has 2 different y values assigned (7 and 2). that violates the definition of a function.

2.

domain = {-3, -2, -1, 1, 4}

range = {-5, -1, 0, 2}

function : yes. every x bake has exactly one y value assigned.

3.

domain = {4, 6, 7}

range = {-1, 2, 3, 5}

function : no, because x = 4 has 2 different y values assigned (2 and 5).

4.

domain = [-3, 3) "3" is not included, hence the empty dot

range = [-4, 5]

function : yes

5.

domain = (-infinity, +infinity) "infinity" is not a possible value, so the limits are not included.

range = [-1, 2]

function : yes

6.

domain = [-2, +infinity)

range = (-infinity, +infinity)

function : no. except for x = -2 all x values have 2 different y values assigned.

Answer:

69

Step-by-step explanation:

420

Answer:

The Median

Step-by-step explanation:

i did the quiz

Answer:

A. the median only

Step-by-step explanation:

Answer:

22.50

Step-by-step explanation:

25 percent 30

= (25/100)30

= (25*30)/100

= 750/100 = 7.50

$30 - $7.50 = $22.50

Answer:

a 75% chance the weather will stay dry

Step-by-step explanation:

3/4

An equation is formed of two equal expressions. The equation 7*e^0.1t=47 can be expressed as t=[ln (47/7)]/0.1.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The equation 7*e^0.1t=47 in terms of logarithm in terms of base-e can be solved as,

[tex]7e^{0.1t}=47\\\\e^{0.1t}=\dfrac{47}{7}\\\\0.1 t = {\rm ln}(\dfrac{47}{7})\\\\t = \dfrac{ {\rm ln}(\frac{47}{7})}{0.1}[/tex]

Hence, the equation 7*e^0.1t=47 can be expressed as t=[ln (47/7)]/0.1.

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Answer:

[tex]1\frac{1}{9}[/tex]

Step-by-step explanation:

Given the following question:

[tex]1\frac{2}{3} \times\frac{2}{3}[/tex]

In order to multiply the two, we have to convert the mixed number into a improper fraction and then multiply the numerator by the numerator, the denominator by the denominator.

[tex]1\frac{2}{3} =3\times1=3+2=\frac{5}{3}[/tex]
[tex]\frac{5}{3} \times\frac{2}{3}[/tex]
[tex]5\times2=10[/tex]
[tex]3\times3=9[/tex]
[tex]=\frac{10}{9}[/tex]

Convert the improper fraction into a mixed number:

[tex]\frac{10}{9}[/tex]
[tex]\frac{10}{9} =10\div9=1\frac{1}{9}[/tex]
[tex]=1\frac{1}{9}[/tex]

Your answer is "1 1/9."

Hope this helps.

Measurement is the area of the number sense that has a relationship with the quantity of ingredients used in recipes.

The measures of recipes are determined by:

So measure recipes, one can either measure them using artefacts such as cups, spoons, or other kind of containers.

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450t+550t=4,000

1000t=4000

t=4000/1000

t=4 hours they will be 4,000 apart.

------------------------------------------

20t+12(4.5-t)=70

20t+54-12t=70

8t=70-54

8t=16

t=16/8

t=2 hours at 20 mph.

proof

20*2+12(4.5-2)=70

40+12(2.5)=70

40+30=70

70=70

Answer:

2000.

Step-by-step explanation:

The hundreds digit is 9 so we round up the 1 so the answer is 2000.

Answer:

$320

Step-by-step explanation:

1. 3x + 4x = 560 (since they are ratios, x would be the same amount)

2. 7x = 560

3. x = 80

This means that 3 and 4 should be multiplied by 80 to get the $ amount. The amounts are $240 (3*80) and $320 (4*80).

So, the larger amount if $320.

Answer:

x ≤ 1/2

Step-by-step explanation:

Domain:  input values (x-values)

We cannot take a square root of a negative number, therefore

3 - 6x ≥ 0

Solving the inequality:

⇒ 3 - 6x ≥ 0

⇒ 3 ≥ 6x

⇒ 1/2 ≥ x

⇒ x ≤ 1/2

Therefore, the domain is x ≤ 1/2