Which could be the area of one face of the rectangular prism?Check all that apply

[tex]g(x)=e^{ax}+f(x)\implies g'(x)=ae^{ax}+f'(x)\implies g''(x)=a^2e^{ax}+f''(x)[/tex]

Given that [tex]f'(0)=5[/tex] and [tex]f''(0)=7[/tex], it follows that

[tex]g'(0)=a+5[/tex]

[tex]g''(0)=a^2+7[/tex]

###

[tex]h(x)=\cos(kx)f(x)+\sin x\implies h'(x)=-k\sin(kx)f(x)+\cos(kx)f'(x)+\cos x[/tex]

When [tex]x=0[/tex], we have

[tex]h(0)=\cos0f(0)+\sin0=f(0)=3[/tex]

The slope of the line tangent to [tex]h(x)[/tex] at (0, 3) has slope [tex]h'(0)[/tex],

[tex]h'(0)=-k\sin0f(0)+\cos0f'(0)+\cos0=5+1=6[/tex]

Then the tangent line at this point has equation

[tex]y-3=6(x-0)\implies y=6x+3[/tex]

###

Differentiating both sides of

[tex]4x^2+y^2=48+2xy[/tex]

with respect to [tex]x[/tex] yields

[tex]8x+2y\dfrac{\mathrm dy}{\mathrm dx}=2y+2x\dfrac{\mathrm dy}{\mathrm dx}[/tex]

[tex]\implies(2y-2x)\dfrac{\mathrm dy}{\mathrm dx}=2y-8x[/tex]

[tex]\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{y-4x}{y-x}[/tex]

On this curve, when [tex]x=2[/tex] we have

[tex]4(2)^2+y^2=48+2(2)y\implies y^2-4y-32=(y-8)(y+4)=0\implies y=8[/tex]

(ignoring the negative solution because we don't care about it)

The tangent to this curve at the point [tex](x,y)[/tex] has slope [tex]\dfrac{\mathrm dy}{\mathrm dx}[/tex]. This tangent line is horizontal when its slope is 0. This happens for

[tex]\dfrac{y-4x}{y-x}=0\implies y-4x=0\implies y=4x[/tex]

and when [tex]x=2[/tex], there is a horizontal tangent line to the curve at the point (2, 8).

The equation for the line tangent to the graph of h at x = 0 is:

y - 3 = 6(x - 0)

y = 6x + 3

The function g is given by:

g(x) = a[tex]e^x[/tex]+ f(x)

where a is a constant. We are given that f(0) = 3, f'(0) = 5, and f''(0) = 7.

To find g'(0), we need to differentiate g(x):

g'(x) = a[tex]e^x[/tex]+ f'(x)

Substituting x = 0, we get:

g'(0) = a[tex]e^0[/tex] + f'(0) = a + 5

To find g''(0), we need to differentiate g'(x):

g''(x) = a[tex]e^x[/tex] + f''(x)

Substituting x = 0, we get:

g''(0) = a[tex]e^0[/tex]+ f''(0) = a + 7

Therefore, g'(0) = a + 5 and g''(0) = a + 7.

To Find h'(x) and write an equation for the line tangent to the graph of h at x = 0

The function h is given by:

h(x) = cos(kx)[f(x)] + sin(x)

where k is a constant. We need to find h'(x):

h'(x) = -ksin(kx)[f(x)] + cos(kx)f'(x) + cos(x)

Substituting x = 0, we get:

h'(0) = -ksin(0)[f(0)] + cos(0)f'(0) + cos(0)

h'(0) = f'(0) + 1

We are given that f'(0) = 5, so h'(0) = 6.

To find the equation for the line tangent to the graph of h at x = 0, we need to use the point-slope form of the equation of a line:

y - y1 = m(x - x1)

where:

y is the y-coordinate of any point on the line

y1 is the y-coordinate of the point where the line intersects the graph

m is the slope of the line

x is the x-coordinate of any point on the line

x1 is the x-coordinate of the point where the line intersects the graph

We know that x1 = 0 and h'(0) = m = 6. We also know that h(0) = cos(0)[f(0)] + sin(0) = 3 + 0 = 3.

Therefore, the equation for the line tangent to the graph of h at x = 0 is:

y - 3 = 6(x - 0)

y = 6x + 3

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2)  

x^2 - 14x - 32  = x^2 - 16x + 2x - 32  = x(x-16) + 2(x-16) = (x - 16)(x + 2)

---------

3)  

2n^2 - 7n - 15  =

= 2n^2 - 10n + 3n - 15 =

=  2n(n - 5) + 3(n - 5) =

= (n - 5)(2n + 3)

---------

4)  

For this case we have the following expression:

[tex]4p + 3 = -5[/tex]

We must indicate an equivalent verbal expression.

If "p" is a variable that represents any number, we can write:

Four times a number plus 3 equals -5.

Answer:

Four times a number plus 3 equals -5.

Option D

Answer:

2x10^8 / 2x10^3

The answer is n=2*10^8/2*10^3.

It is given that the buckets have a height of 25 inches and a diameter of 10 inches. The volume of a cylinder is

V=[tex]\pi[/tex]r²h

V1= [tex]\pi[/tex](10/2)²(25)

=[tex]\pi[/tex](5)²(25)

=625[tex]\pi[/tex]

=1963.495

The scientific notation is

V1= 1.963* 10³

≅2*10³

The warehouse is 100 feet long, 50 feet wide, and 20 feet long.

1 feet = 12 inches

The volume of a cube is

V=Length*breadth*height

Using the above conversion the volume of cube in cubic inches is  

V2=(100*12)*(50*12)*(20*12)

V2= 172800000

The scientific notation is

V2= 1.728*10^8

V2≅2*10^8

The number of buckets of rocks she could store in a warehouse is

n=2*10^8/2*10^3.

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The answer is: [tex]T(\°C)=204.44\°C[/tex]

To convert from Fahrenheit degrees to Celsius degrees, we must use the following formula:

[tex]T(\°C)=(T(\°C)-32)*\frac{5}{9}[/tex]

We are given the temperature: 400°F

So, converting we have:

[tex]T(\°C)=(400\°F-32)*\frac{5}{9}=368*\frac{5}{9}=204.44\°C[/tex]

Hence, the 400°F is equal to 204.44°C.

Have a nice day!

Answer:

Step-by-step explanation:

23A:   Simplify

V^2  + 11V + 10

There are no like terms

Answer when simplify: V^2 + 11V + 10

23B.  Factor:

Steps: V^2  +  11V  + 10

Break the expression into groups:

(V^2  + V)  +  (10V   +  10)

Factor out: V From V^2  + V:   V(V  + 1)

Factor out:  10 From  10V  +  10:   10(V  +  1)

V(V  +  1)  +  10(V  +  1)

Factor out common term:  V  +  1

Factor: Therefore your Answer: (V  + 1) (V  +  10)

24:  Factor

Steps: k^2   +  11k  + 30

Break the expression into groups:

(K^2 + 5K)(6K + 30)

Factor out: k from K^2 + 5K ====>  K(K + 5)

Factor out 6  from 6K + 30 ===> 6(K + 5)

=  k(k + 5)  +  6(k  + 5)

Factor out common term: k  + 5

Factor:  Therefore your Answer is: (K + 5) (K + 6)

25:  Factor

Steps:     R^2   -   1

Rewrite:  1  as  1^2

R^2   -  1^2

Apply difference of two square formulas:

x^2   -   y^2   =   (x   +   y)(x   -  y)

r^2   -  1^2  =  (r  +  1)(r   -  1)

Therefore your answer:  (r  + 1)(r  -  1)

26:  Factor

Steps:  V^2  -  V  - 2

Break the expressions into groups:

(V^2  + V)  +   ( -2V   -  2)

Factor out V from V^2  + V:    V(V  +  1)

Factor out  -2  from  -2v   - 2:    -2(V  +  1)

V(V   +   1)   - 2(V  +  1)

Factor out common term:  V   +  1

Therefore your answer: (V  +  1)(V  -  2)

27:  Factor

Steps:  4N^2  -  15N   -  25

Break expression into groups:

(4N^2  +  5N)   +   ( -20N  -  25)

Factor out N from 4N^2  +  5N:   4(4N  +  5)

Factor out   -5   from  -20N  -  25:    -5(4N   +  5)

N(4N  +  5)  -  5(4N   +   5)

Factor out common term:  4N   +   5

Therefore your answer:   (4n  +  5)(N   -  5)

28: Factor:

Steps:   N^2   +  3N   -  54

Break the expression into group:

(N^2  -  6N)   +   (9N   -  54)

Factor out N from N^2  -  6N:    N(N   - 6)

Factor out   9  From 9N  -  54:    9(N  -  6)

N(N  -  6)    +   9(N   -   6)

Factor out common term:    N    -    6

Therefore your answer:   (N   -  6)(N   +   9)

Hope that helps, Have an awesome day!     :)

The correct answer is: C. The demand for drug X shifts to the left, and the supply curve for drug X shifts to the left. The result is an unknown change in the equilibrium price for drug X and a fall in the equilibrium quantity of drug X.

Explanation:

1. The study showing that drug X is less effective than drug Y implies a decrease in the perceived effectiveness of drug X. This could lead to a decrease in the demand for drug X as consumers may prefer the more effective drug Y.

2. The increase in the price of ingredients used to produce drug X would lead to an increase in the production cost of drug X. This could cause a leftward shift in the supply curve for drug X, as producers may be less willing or able to supply the same quantity at the previous prices.

Both a decrease in demand and a leftward shift in the supply curve would result in a fall in the equilibrium quantity of drug X. The impact on the equilibrium price is uncertain and would depend on the magnitude of the shifts in demand and supply. Therefore, option C reflects these potential changes in demand and supply without making specific predictions about the equilibrium price.

The correct answer is C: The demand for drug X shifts to the left, and the supply curve for drug X shifts to the left, resulting in an unknown change in equilibrium price for drug X and a decrease in the equilibrium quantity.

The student asked about the consequences on equilibrium price and equilibrium quantity for drug X following two events: a study showing drug X is less effective than drug Y, and an increase in the price of ingredients used to produce drug X.

Analyze each event's impact on demand and supply separately: The less effective study would cause the demand for drug X to shift to the left, implying a decrease in the quantity demanded at each price because consumers now prefer drug Y. Additionally, the increase in production costs would create a supply curve shift for drug X to the left, representing a decrease in supply at each price point. When both supply and demand shift to the left, the equilibrium quantity will clearly decrease; however, the impact on the equilibrium price is uncertain without knowing the relative magnitude of the shifts.

Choosing from the provided options, answer C is correct: The demand for drug X shifts to the left, and the supply curve for drug X shifts to the left. The result is an unknown change in the equilibrium price for drug X and a fall in the equilibrium quantity of drug X.

Answer:

136

Step-by-step explanation:

since AB and BC are congruent, then angles BAC and BCA are congruent, so if angle BAC is 22 degrees, BCA is also 22 degrees. 22 + 22 = 44 and since the angles inside of a triangle always add up to 180, you can subtract 44 from 180 to get the measure of the angle ABC = 136. Hope this help 0.0

Answer:

Step-by-step explanation:

The "fundamental theorem of algebra" says a polynomial of degree n will have n zeros. If the polynomial has real coefficients, the complex zeros will appear in conjugate pairs.

The graph of this quadratic (degree = 2) does not cross the x-axis, so there are no real values of x that make y=0. That means the two zeros are both complex.

Answer:

Step-by-step explanation:

f(x) is an easy one.  Because it's a parabola, it's standard form is

[tex]y=ax^2+bx+c[/tex]

But even simpler than that, look at a point on the graph, in particular, (2, 4).  If x = 2 and y = 4, we can square 2 to get 4, so the equation for that is the parent graph, [tex]y=x^2[/tex], plain and simple.

The next one requires a bit of doing.  Pick 3 points on the graph because we have 3 unknowns to find: a, b, and c.  The points that are easy to pick are (0, -2), (2, -4), (-2, -4).  Use the x and y coordinates from each one of those points to fill in the standard form of the parabola.  Because this parabola is "upside down" the leading coefficient is negative.  Start with the first coordinate first:

[tex](0, -2)-->-2=-a(0)^2+b(0)+c[/tex] which gives us that c = -2.  That's good...one down, 2 to go.

Next we will use the remaining 2 points to create a system of equations that we can solve simultaneously for a and b.  Using the second coordinate pair (2, -4):

[tex]-4=-a(2)^2+b(2)-2[/tex] gives us the simplified equation:

***-2 = -4a + 2b***

I put the stars in front and behind because we will need to come back to that one in a minute.

Using the last coordinate pair (-2, -4):

[tex]-4=-a(-2)^2-b(2)-2[/tex] simplifies down to:

***-2 = -4a - 2b***

Now put these together and solve the system by elimination, and you see that 2b and the -2b cancel each other out, leaving you with -4 = -8a, so a = 1/2.  Now we know a:  1/2 and c:  -2 and we can find b:

If -2 = -4a + 2b, then -2 = -4(1/2) + 2b, and b = 0.  That means that the equation for the upside down parabola is

[tex]y=-\frac{1}{2}x^2-2[/tex]

Answer:

You can view a kite as 4 triangles

Step-by-step explanation:

A geometric kite can easily be viewed as 4 triangles.  The formula to calculate the area of a kite (width x height)/2 is very similar to the one of a triangle (base x height)/2.

According to the formula to calculate the area of a kite, we would get:

(36 x 30)/2 = 540.

If we take the approach of using 4 triangles, we could imagine a shape formed by 4 triangles measuring 18 inches wide with a height of 15.

The area of each triangle would then be: (18 x 15)/2 = 135

If we multiply this 135 by 4... we get 540.

Answer:

Draw a vertical line to break the kite into two equal triangles with a base of 36 and a height of 15. Use the formula A = 1/2bh to find the area of each. The sum of the areas is the area of the kite.

Step-by-step explanation:

Answer:

Option A is the correct answer.

Step-by-step explanation:

The slope intercept form is: y=mx+b

We need to find m slope and b is the y intercept.

So, first we find the slope m of the given points.

[tex]m = \frac{y_{2} -y_{1}}{x_{2} -x_{1}} \\m= \frac{8-(-4)}{-1-(5)}\\ m= \frac{12}{-6}\\ m=-2[/tex]

After finding the slope, we can find the y intercept.

So, Option A is the correct answer.

Answer:

A

Step-by-step explanation:

Answer:

x= 1.8

Step-by-step explanation:

We have been given the equation;

-(6)^(x-1)+5=(2/3)^(2-x)

We are required to determine the value of via graphing. To do this we can split up the right and the left hand sides of the equation to form the following two separate equations;

y = -(6)^(x-1)+5

y = (2/3)^(2-x)

We then proceed to graph the two equations on the same graph. The solution will be the point where the equations will intersect. Find the attachment below for the graph;

The value of x is 1.785. To the nearest tenth we have x = 1.8

Answer:

1.8

Step-by-step explanation:

Answer:

x = ±(√y)/3

x = ±(√2)/3

Step-by-step explanation:

Put the given information in the given equation and solve for x:

f(x) = 2

2 = 9x^2 . . . . . use 2 in place of f(x)

2/9 = x^2 . . . . divide by 9

±√(2/9) = x . . . take the square root

x = ±(√2)/3 . . . simplify

_____

Using this as an example, we can solve f(x) = y in the same way:

y = 9x^2 . . . . use y for f(x)

y/9 = x^2 . . . divide by the coefficient of x^2

±√(y/9) = x . . . take the square root; next, simplify

x = ±(√y)/3 . . . . the equation solved for x. Note this matches the above when y=2.

Answer:

a. y = 1/6x + 2

Step-by-step explanation:

You divide everything by 6, then move the -1/6x to the other side, which causes the sign to flip from - to +.

The answer would be c.

[tex] \sqrt{28} [/tex]

-Original Profit-

y = 22x ; where x is the number of necklaces sold and y is the mount of profit.

y = 29x ; where x is the number of necklaces sold and y is the amount of profit.

Xavier will earn an additional $7 if he proceeded in switching to a new type of pendant. The $7 is the difference of $29 and $22 profit.

if x is the amount sold and y is the profit, then the original equation would be y = 22x since originally he was selling them for $22 dollars each. That means that in the equation y = 29x, 29 is the amount of profit per each necklace. From here it's just simple subtraction. New profit - Old profit = How much more earned $29 - $22 = $7 extra earned per necklace. he would save $7.

Answer:

.894

Step-by-step explanation:

First thing to do is to solve for the height of the triangle, BD.  That's easy.  We have the length of the hypotenuse and the base, so Pythagorean's Theorem gives us that the height is 8.003255588 which rounds nicely to 8.  Now you have to call on the fond memories you have of the geometric mean in right triangles to solve the rest.  For the sin of x you need the hypotenuse of that smaller right triangle on the left, side AB.  First let's use geometric mean to find AD.  The formula for that, now that we know the height, is

[tex]BD^2=(AD)(DC)[/tex]

Filling that in with numbers we have

[tex]8^2=(AD)16[/tex] and

64 = 16(AD).  Solve for AD to get that AD has a length of 4.  Now we know two of the three sides in that smaller triangle on the left and can solve for the hypotenuse.

[tex]8^2+4^2=c^2[/tex] and

[tex]64+16=c^2[/tex] so

c=√80 which simplifies to 4√5.  That means that the sin ratio for x is

[tex]\frac{8}{4\sqrt{5} }[/tex]

which divides out to .894

The value of Sin{x} is equivalent to 0.89.

There are six major trigonometric functions as -

We can write the relation between them as -

Given is a triangle ABC.

We can write -

cos {y} = DC/BC = 16/17.89

cos {y} = 16/17.89

cos {y} = 0.89

{y} = cos⁻¹(0.89)

{y} = 27.1°.

We can write -

∠x + ∠y + 90° = 180°

∠x + ∠y = 90°

∠x = 90 - 27.1

∠x = 62.9°

So, we can write -

Sin{x} = Sin{62.9°} = 0.89

Therefore, the value of Sin{x} is equivalent to 0.89.

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y2-y1 =M(x2-x1)

Ok Sir, you gave points : (2,1) and (3,4)

4-1/3-2 = 3

Ok we know our slope is 3, now pick any of the two points, and make an equation for this line, so lets go ahead and pick #1, (2,1)

Formula is same as before

y-1=3x-6

y=3x-5

I think its correct, pick as brainless sir, thanks.

Answer:

[tex]A(x)=\$5,000(1.04)^{x}[/tex]  

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nx}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

x is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]P=\$5,000\\ r=0.04\\n=12[/tex]  

substitute in the formula above  

[tex]A(x)=\$5,000(1+\frac{0.04}{12})^{12x}[/tex]  

[tex]A(x)=\$5,000(\frac{12.04}{12})^{12x}[/tex]  

[tex]A(x)=\$5,000(1.04)^{x}[/tex]  

What is the area of Todd's flower garden with a height of 8⃣ feet and a base of 4 feet?

Explanation:

The number before the "and" or the comma is the integer portion of the number. The decimal fraction portion follows. "Tenths", or "hundredths", or "thousandths" tells you the denominator, hence the location of the rightmost digit. Otherwise the fraction digits are represented normally. ("two hundred seventy-eight" is still 278, for example.)

a. six and two tenths: 6.2

b. seventeen and four hundredths: 17.04

c. four hundred, and thirty-five thousandths: 400.035

d. fifty-six, and two hundred seventy-eight thousandth: 56.278

_____

"thirty-five thousandths" can be written as 35/1000 or 0.035. Both are pronounced the same and mean the same thing.

Step-by-step explanation:

Consider the provided information.

Mixed decimal is a number, which consisting of an integer plus a decimal.

For example:8.128 consists an integer which is 8 plus a decimal; 0.128

The Place value chart is shown in figure 1.

Part (a)

a. Six and two tenths:

Six is an integer and tenths shows the place value just after decimal.

Which can be written as:

6.2

Part (b)

Seventeen and four hundredths:

Seventeen is an integer and place 4 at hundredths place.

Which can be written as:

17.04

Part (c)

Four hundred, and thirty-five thousandths:

Four hundred is an integer and place 35 according to the place value where 5 should be at thousandths place and 3 should be hundredths place.

Which can be written as:

400.035

Part (d)

Fifty-six, and two hundred seventy-eight thousandths:

Fifty-six is an integer and place 278 according to the place value where 8 should be at thousandths place, 7 should be hundredths place and 2 should be tenths place.

Which can be written as:

56.278

The Pythagorean theorem says that in a right triangle the sum of the areas of the two squares on the legs equals the area of the square on the hypotenuse.

So x=

[tex] \sqrt{ {12}^{2} - {5}^{2} } [/tex]

≈10.9

Answer:

x = 10.9087121146

Step-by-step explanation:

Pythagoras theorem states a² = b² + c²

In this case a = 5, b = 12 and c = x

Therefore,

→ x² = 12² - 5²

⇒ ( Simplify )

→ x² = 144 - 25

⇒ ( Simplify )

→ x² = 119

⇒ ( Square root )

→ x = 10.9087121146

Answer:

Step-by-step explanation:

If Ð1 and Ð2 are congruent, then mÐ1 = mÐ2.

We have mÐ1 = 10x - 5 and mÐ2 = 6x + 15.

The equation:

10x - 5 = 6x + 15      add 5 to both sides

10x - 5 + 5 = 6x + 15 + 5

10x = 6x + 20      subtract 6x from both sides

10x - 6x = 6x - 6x + 20

4x = 20       divide both sides by 4

4x : 4 = 20 : 4

x = 5

Put the value of x to the expression 10x - 5:

10(5) - 5 = 50 - 5 = 45

Answer:

  year 7

Step-by-step explanation:

If we assume that investment A earns interest compounded annually, its value can be modeled by the equation ...

  A = 50·(1+0.08)^(t-1) . . . . . where t is the year number

The second investment earns $3 per year, so its value can be modeled by the equation ...

  B = 60 + 3(t -1) . . . . . . . . . where t is the year number

We are interested in finding the minimum value of t such that ...

  A > B

  50·1.08^(t-1) > 60 +3(t-1)

This is a mix of exponential and polynomial terms for which no solution method is available using the tools of Algebra. A graphing calculator shows the solution to be ...

  t > 6.552

The value at the end of year 1 is found for t=1, so the values of interest are seen after 6.55 years, in year 7.

Answer:

  the zeros are x ∈ {-3, 1/2, 2}

Step-by-step explanation:

A graphing calculator shows where the zeros are. (See attached)

These suggest factors of (x +3)(x -2)(2x -1). To verify these are the factors, we can multiply this out to get ...

  = (x^2 +x -6)(2x -1)

  = 2x^2 +2x^2 -12x -x^2 -x +6

  = 2x^3 +x^2 -13x +6 . . . . same as the original expression

Answer:

A one-tailed t statistic

Step-by-step explanation:

Answer: Answers 2, 3, and 5

Step-by-step explanation:

In finding the volume of a prism, you can use the formula V = Bh

This happens to be one of the answers here.

Before you get to V = Bh, however, you have to find the area of the base (B).

For this you can use the are of a rectangle, or A = bh.

This is also one of the answers.

(Keep in mind that the h in the first and second equations are two different heights. The height in the volume equation refers to the height of the prism whereas the height in the area equation refers to the base's height)

Plugging in the numbers:

A = bh = 9.5 × 24 = 228

V = Bh = 228 × 6 = 1368

This is the last answer.

Answer:

1, 3, 4, 5

Step-by-step explanation:

f(x) = 7 sin (4πx) + 3. The function f(x) = 7 sin (4πx) + 3 describe a sinusoidal function whose period is 1/2, maximum value 10, minimum value -4, and it has a y-intercept of 3.

A sinudoidal function whose period is 1/2, maximum value is 10, minimum value is -4, and it has a y-intercept of 3. Let's write to the form f(x) = A sin (ωx +φ) + k, where A is the amplitude, ω is the angular velocity with ω=2πf, (ωx+φ) is the oscillation phase, φ the initial phase (horizontal shift), and k is y-intercept (vertical shift).

Calculating the amplitude:

A = |max - min/2|

A = |10 - (-4)/2| = 14/2

A = 7

calculating the ω:

The period of a sinusoidal is T = 1/f --------> f = 1 / T

ω = 2πf -------> ω = 2π ( 1/T) with T = 1/2

ω = 2π (1/(1/2) = 2π (2)

ω = 4π

The y-intercept k = 3

Writing the equation function with A = 7, ω = 4π, k = 3, φ = 0.

f(x) = A f(x) = A sin (ωx +φ) + k ----------> f(x) = 7 sin (4πx) + 3.

Answer:

40 cm

Step-by-step explanation:

If we let r represent the radius of the circle, the legs of the triangle have length 5+r and 12+r. Then the Pythagorean Theorem tells us ...

(5 +12)^2 = (5 +r)^2 +(12 +r)^2

5^2 +2·5·12 +12^2 = 5^2 +2·5·r +r^2 + 12^2 +2·12·r +r^2

120 = 34r +2r^2 . . . . subtract 5^2 +12^2

60 +8.5^2 = 8.5^2 +17r +r^2 . . . . . . divide by 2, add (17/2)^2

11.5 = 8.5 +r . . . . . . . . . . . . . . . . . . . take the square root (negative root is extraneous)

3 = r

The radius of the circle is 3 cm. The perimeter of the triangle is the sum of the side lengths:

(5 +3) cm + (12 +3) cm + (5+12) cm = 2(5 +12 +3) cm = 40 cm

To find the perimeter of the right triangle, we need to find the lengths of its three sides. We can use the Pythagorean theorem to find the lengths of the legs of the triangle. The perimeter of the triangle is the sum of the lengths of all three sides.

To find the perimeter of the right triangle, we need to find the lengths of its three sides. Let's denote the lengths of the triangle's legs as a and b, and the hypotenuse as c. We are given that the point of tangency divides the hypotenuse into segments of 5 cm and 12 cm. Since the point of tangency is equidistant from the ends of the hypotenuse, the length of the hypotenuse is equal to the sum of these two segments, so c = 5 cm + 12 cm = 17 cm.

Using the Pythagorean theorem, we can find the lengths of the legs a and b. The theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. So we have a² + b² = c². Substituting the given values, we get a² + b² = 17 cm².

Finally, the perimeter of the triangle is the sum of the lengths of all three sides: P = a + b + c. We can solve for a and b using the equation a² + b² = 17 cm², and then calculate the perimeter.

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