RST and XYZ are equilateral triangles. The ratio of the perimeter of RST to the perimeter of XYZ is 1 to 2. the area of RST is 10.825 square inches. what is the area of XYZ

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:

165 ways  to choose the paintings

Step-by-step explanation:

This is clearly a Combination problem since we are selecting a few items from a group of items and the order in which we chosen the items does not matter.

The number of possible ways to choose the paintings is;

11C3 = C(11,3) = 165

C denotes the combination function. The above can be read as 11 choose 3 . The above can simply be evaluated using any modern calculator.

Answer:

165 ways

Step-by-step explanation:

Total number of painting, n = 11

Now, three of them are chosen randomly to display in the gallery window.

Hence, r = 3

Since, order doesn't matter, hence we apply the combination.

Therefore, number of ways in which 3 paintings are chosen from 11 paintings is given by

[tex]^{11}C_3[/tex]

Formula for combination is [tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]

Using this formula, we have

[tex]^{11}C_3\\\\=\frac{11!}{3!8!}\\\\=\frac{8!\times9\times10\times11}{3!8!}\\\\=\frac{9\times10\times11}{6}\\\\=165[/tex]

Therefore, total number of ways = 165

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 +.

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]  

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!

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

Answer:

To the nearest tenth, the height of the balloon is 2.9 miles

Step-by-step explanation:

The nearer point takes the greater angle of elevation.

The diagram is shown in the attachment.

The height of the balloon above the ground is c unit.

From triangle ABD,

[tex]\tan 42\degree=\frac{c}{x}[/tex]

[tex]\implies x=\frac{c}{\tan 42\degree}[/tex]...eqn1

From triangle ABC,

[tex]\tan 20\degree=\frac{c}{x+4.8}[/tex]

[tex]\implies x+4.8=\frac{c}{\tan 20\degree}[/tex]

[tex]\implies x=\frac{c}{\tan 20\degree}-4.8[/tex]..eqn2

We equate both equations and solve for c.

[tex]\frac{c}{\tan 42\degree}=\frac{c}{\tan 20\degree}-4.8[/tex]

[tex]\frac{c}{\tan 42\degree}-\frac{c}{\tan 20\degree}=-4.8[/tex]

[tex]\implies (\frac{1}{\tan 42\degree}-\frac{1}{\tan 20\degree})c=-4.8[/tex]

[tex]\implies -1.636864905c=-4.8[/tex]

[tex]\implies c=\frac{-4.8}{-1.636864905}[/tex]

[tex]c=2.932435039[/tex]

To the nearest tenth, the height of the balloon is 2.9 miles

Answer:

on usatestprep its 1.2

Step-by-step explanation:

Answer:

C: 48 straws

Step-by-step explanation:

First, find the perimeter of one picture frame: (2 x length) + (2 x width).  Convert 20 centimeters to millimeters so that you are working in the same units; there are 10 millimeters in 1 centimeter, so 20 centimeters = 200 millimeters.  

(2 x 200) + (2 x 120) = 400 + 240 = 640

Each picture frame has a perimeter of 640 millimeters.

Next, figure out how many straws are needed for one picture frame:

640/80 = 8

Jana uses 8 straws for each picture frame.  Since she is decorating 6 picture frames, solve 6 x 8 = 48.  

Jana needs 48 straws to complete her project.

Answer: First Option

−2 • f(x)

Step-by-step explanation:

The function [tex]y=log_2(x)[/tex] passes through point (2,1) since the exponential function [tex]2 ^ x = 2[/tex] when [tex]x = 1[/tex].

Then, if the transformed function passes through the point (2, -2) then this means that f(x) was multiplied by a factor of -2. So if an ordered pair [tex](x_0, y_0)[/tex] belonged to f(x), then [tex](x_0, -2y_0)[/tex] belongs to the transformed function. Therefore, if [tex]f(x) = log_2 (x)[/tex] passed through point (2, 1) then the transformed function passes through point (2, -2)

The transformation that multiplies to f(x) by a factor of -2 is:

[tex]y = -2 * f (x)[/tex]

and the transformed function is:

[tex]y = -2log_2 (x)[/tex]

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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Answer:

The determinant of A (the main matrix) is -3; the determinant of y is 30; the determinant of x is 18; the solution to the system is (-6, -10)

Step-by-step explanation:

Set up the matrix to find the determinant of the main matrix.  Find the determinant by multiplying the numbers on the major axis and subtract from that the multiplication of the numbers on the minor axis:

[tex]\left[\begin{array}{ccc}2&-1&\\1&-2\\\end{array}\right][/tex]

Find the determinant by multiplication:

(2×-2)-(1×-1)= -3

To find the determinant of y, replace the second column with the solutions to have a matrix that looks like this:

[tex]\left[\begin{array}{ccc}2&-2\\1&14\\\end{array}\right][/tex]

To find the determinant of that matrix by multiplication:

(2×14)- (1× -2) = 30

Lastly, find the determinant of x by replacing the first column with the solutions.  That matrix will look like this:

[tex]\left[\begin{array}{ccc}-2&-1\\14&-2\\\end{array}\right][/tex]

Find the determinant of x by multiplication:

(-2 × -2) - (14 × -1) = 18

Now we want Cramer's Rule that tells us if we divide the determinant of [tex]A_{x}[/tex]

by the determinant of A, we will find the value of x:

[tex]\frac{A_{x} }{A}=\frac{18}{-3}  =-6[/tex]

and the same for y:

[tex]\frac{A_{y} }{A}=\frac{30}{-3}=-10[/tex]

So the solution to the system is (-6, -10)

2x - y = -2

x = 14 + 2y

2x - y = -2

x - 2y = 14

The system determinant = -3

2 (-2) - 1 (-1)

-4 + 1

-3

The y-determinant = 30

(14) - 1 (-2)

28 + 2

30

The x-determinant = 18

-2 (-2) - 14 (-1)

4 + 14

18

The solution is x = -6 and y = -10 or (-6,-10)

x = 18/-3

x = -6

y = 30/-3

y = -10

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

191 is closest to nearest whole number.

EXPLANATION

Let the distance from the top of the tree to the tip of the shadow be l feet as shown in the diagram.

This is the same as the hypotenuse of the right triangle.

The given side length, 130 ft is adjacent to the angle of elevation which is 47°

We use the cosine ratio to obtain,

[tex] \cos(47 \degree)= \frac{adjacent}{hypotenuse} [/tex]

[tex]\cos(47 \degree)= \frac{130ft}{l} [/tex]

[tex]l= \frac{130ft}{\cos(47 \degree)} [/tex]

[tex]l =190.6162941[/tex]

The distance from the top of the tree to the tip of the shadow, given the length of the shadow is 130 feet and the angle of elevation is 47 degrees, is approximately 180 feet.

The question is asking us to find the distance from the top of the tree to the tip of the shadow using given information: the shadow cast by the tree is 130 feet long, and the angle of elevation is 47 degrees. For this, we can use the tangent function in trigonometry, which is defined as the opposite side over the adjacent side in a right triangle. Here, the length of the shadow (130 feet) serves as the adjacent side, and the height of the tree serves as the opposite side.

To find the hypotenuse (the distance from the top of the tree to the tip of the shadow), you can use the formula: Hypotenuse = Adjacent / cos(angle). So, the Hypotenuse = 130 feet / cos(47) = approximately 180 feet.

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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

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:

[tex]\large\boxed{(4x^2 + 8x - 2) - (2x^2 - 4x + 3)=2x^2+12x-5}[/tex]

Step-by-step explanation:

[tex](4x^2 + 8x - 2) - (2x^2 - 4x + 3)\\\\=4x^2 + 8x - 2 -2x^2 -(- 4x)- 3\\\\=4x^2+8x-2-2x^2+4x-3\qquad\text{combine like terms}\\\\=(4x^2-2x^2)+(8x+4x)+(-2-3)\\\\=2x^2+12x-5[/tex]

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.

The answer would be c.

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

Try this options:

a. total - 6 digits, '6' - 1 digit, then probability of rolling a '6' is 1/6;

b. total - 6 digits, '6' - 1 digit, then probability of rolling 1,2,3,4,5 is 5/6;

c. if probability of rolling a '6' is p and not rolling a '6' is q, then p+q=1;

d. if expected probability of one rolling a '6' is 1/6, then numbers of times of rolling a '6' during 120 times is 120/6=20 times.

Answer:

24 cm², 44 cm², and 66 cm²

Step-by-step explanation:

The rectangular prism has six faces.  The opposite faces have the same area, so we can say there are three faces with unique areas.

The face on the bottom of the rectangular prism has an area of:

A = 11 cm * 4 cm = 44 cm²

The face on the side of the rectangular prism has an area of:

A = 4 cm * 6 cm = 24 cm²

And the face on the front of the rectangular prism has an area of:

A = 11 cm * 6 cm = 66 cm²

So 24 cm², 44 cm², and 66 cm² are all answers that apply.

Answer:

b. all real numbers

Step-by-step explanation:

The graphs of positive and negative x^2 parabolas will always have a domain of all real numbers.  Even though you only have a portion of the graph and see a "restriction" on your domain values, it is incorrect to assume that the domain is limited to what you can see.  As the branches of the parabola keep going up and up and up, the values of x keep getting bigger and bigger and bigger.  Again, this is true for all + or - parabolas.

Answer:

The error is C and the solution is B

Step-by-step explanation:

C is because she didn't look left to right to see that is goes on forever

B because you look left and right to see

Answer:

The y-intercept is -2

The equation of the axis of symmetry is x = 1 ⇒ 3rd answer

Step-by-step explanation:

* Lets revise the general form of the quadratic function

- The general form of the quadratic function is f(x) = ax² + bx + c,

 where a, b , c are constant

# a is the coefficient of x²

# b is the coefficient of x

# c is the y-intercept

- The meaning of y-intercept is the graph of the function intersects

 the y-axis at point (0 , c)

- The axis of symmetry of the function is a vertical line

  (parallel to the y-axis) and passing through the vertex of the curve

- We can find the vertex (h , k) of the curve from a and b, where

 h is the x-coordinate of the vertex and k is the y-coordinate of it

# h = -b/a and k = f(h)

- The equation of any vertical line is x = constant

- The axis of symmetry of the quadratic function passing through

  the vertex then its equation is x = h

* Now lets solve the problem

∵ f(x) = -2x² + 4x - 2

∴ a = -2 , b = 4 , c = -2

∵ The y-intercept is c

∴ The y-intercept is -2

∵ h = -b/2a

∴ h = -4/2(-2) = -4/-4 = 1

∴ The equation of the axis of symmetry is x = 1

Answer:

Probability of the sticks weight being 2.44 oz or greater is 0.01017 .

Step-by-step explanation:

We are given that the manufacturer's website states that the average weight of each stick is 2.00 oz with a standard deviation of 0.19 oz.

Also, it is given that the weight of the drumsticks is normally distributed.

Let X = weight of the drumsticks, so X ~ N([tex]\mu = 2,\sigma^{2} = 0.19^{2}[/tex])

The standard normal z distribution is given by;

               Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)

Now, probability of the sticks weight being 2.44 oz or greater = P(X >= 2.44)

P(X >= 2.44) = P( [tex]\frac{X-\mu}{\sigma}[/tex] >= [tex]\frac{2.44-2}{0.19}[/tex] ) = P(Z >= 2.32) = 1 - P(Z < 2.32)

                                                     = 1 - 0.98983 = 0.01017

Therefore, the probability of the sticks weight being 2.44 oz or greater is 0.01017 .

Final answer:

The probability of the sticks weighing 2.44 oz or more is approximately 0.01017.

Explanation:

Given that the manufacturer's website states that the average weight of each stick is 2.00 oz with a standard deviation of 0.19 oz, we know the weight of the drumsticks is normally distributed.

Let X represent the weight of the drumsticks, with X being normally distributed with a mean (μ) of 2 and a variance  [tex](\sigma^2) \ of \ 0.19^2[/tex]

To find the probability of the sticks weighing 2.44 oz or more, we need to calculate P(X ≥ 2.44).

We can standardize X using the formula Z = (X - μ) / σ, which results in a standard normal distribution with mean 0 and standard deviation 1.

So, to find P(X ≥ 2.44), we compute P((X - μ) / σ ≥ (2.44 - 2) / 0.19), which simplifies to P(Z ≥ 2.32).

From the standard normal distribution table or a calculator, we find that P(Z < 2.32) is approximately 0.98983.

Therefore, P(Z ≥ 2.32) = 1 - P(Z < 2.32) = 1 - 0.98983 = 0.01017.

Hence, the probability of the sticks weighing 2.44 oz or more is approximately 0.01017.

That would be p times 1.97 or 1.97p (letter D) this is because each pound is worth 1.97 dollars more so if you bought 1 pound of rice you'd pay only $1.97 but if you bought 5 pounds of rice you'd pay $9.85 since 1.97 times 5 is 9.85

Hope this helped!

Let me know if this helped!

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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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.

[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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Answer:

a)  333,135,504 different plates

b) 230,315,904 different plates

c) 180,835,200 different plates

Step-by-step explanation:

Pattern: Digit(1-9)-Letter-Letter-Letter-Letter-Digit(1-9)-Digit (1-9)

We will calculate the number of possibilities for the digits part, then for the letters part, then we'll multiply them together.

For the digits, we have 3 numbers, first and last 2 positions. We can consider this is a single 3-digit number, where n = 9 (since they are non-zero digits) and r = 3.  

For the letters part, it's basically a 4-letter word, where n = 26 (A through Z) and r = 4.

(a) How many different license plate numbers are possible?

No limitation on repeats for this question:

For the digits, we have 9 * 9 * 9 = 729 (since repetition is allowed, and we can pick any digit from 0 to 9 for each position)

For the letters we have: 26 * 26 * 26 * 26 = 456,976

Because the digits and letters arrangements are independent from each other, we multiply the two numbers of possibilities to have the global number of possibilities:

P = 729 * 456976 = 333,135,504 different plates, when there's no repeat limitation.

(b) How man license plate numbers are possible if no digit appears more than once?

Repeats limitation on digits:

For the digits, we have 9 * 8 * 7 = 504 (since repetition is NOT allowed, we can pick any of 9 digits for first position, then any 8 remaining and finally any 7 remaining at the end)

For the letters we still have: 26 * 26 * 26 * 26 = 456,976

Because the digits and letters arrangements are independent from each other, we multiply the two numbers of possibilities to have the global number of possibilities:

P = 504 * 456976 = 230,315,904 different plates, when there's no repeat on the digits.

(c) How man license plate numbers are possible if no digit or letter appears more than once?

Repeats limitation on both digits and letters:

For the digits, we have 9 * 8 * 7 = 504 (

For the letters we still have: 26 * 25 * 24 * 23 = 358,800

Because the digits and letters arrangements are independent from each other, we multiply the two numbers of possibilities to have the global number of possibilities:

P = 504 * 358800 = 180,835,200 different plates, when there's no repeat on the digits AND on the letters.

Answer:

67.0 cm^3

Step-by-step explanation:

The volume of the cylinder is given by the formula ...

V = πr^2·h

The volume of the hemisphere is given by the formula ...

V = (2/3)πr^3

The volume of the two figures together will be ...

V = πr^2·h + (2/3)πr^3 = πr^2(h +2/3r)

V = π(2 cm)^2·(4 cm + 2/3·2 cm) = 64π/3 cm^3

V ≈ 67.0 cm^3

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: