Find the following measure for this figure.

Lateral area =
55 square units
5√(47) square units
5√(146) square units

Answer:

The distance  from the plane to SCCA is 34,203.0 feet approximately,  and the horizontal distance is 32,708.5 feet approximately.

Step-by-step explanation:

You can draw a right triangle like the one shown in the figure attached, where:

x: horizontal distance.

y: distance from the plane to SCCA.

You can calculate x as following:

[tex]tan\alpha=\frac{opposit}{adjacent}[/tex]

Where:

[tex]\alpha=17\°\\opposite=10,000\\adjacent=x[/tex]

Substitute and solve for x:

[tex]tan(17\°)=\frac{10,000}{x}\\\\x=\frac{10,000}{tan(17\°)}\\\\x=32,708.5ft[/tex]

You can calculate y as following:

[tex]sin\alpha=\frac{opposit}{hypotenuse}[/tex]

Where:

[tex]\alpha=17\°\\opposite=10,000\\hypotenuse=y[/tex]

Substitute and solve for y:

[tex]sin(17\°)=\frac{10,000}{y}\\\\y=\frac{10,000}{sin(17\°)}\\\\y=34,203.0ft[/tex]

Answer:

Step-by-step explanation:

(x - 4)

What you are being asked to do is find the exact same binomial in the top as is in the bottom.

But there's a small catch. You must stipulate that x cannot equal 4. If it does, then you will get 0/0 which is undefined. You can't have that happening -- not at this level.

Any other value for x is fine.

Answer:

Step-by-step explanation:

[tex]a_1=5,\ a_2=6,\ a_n=a_{n-1}+a_{n-2}\\\\a_3=a_2+a_1\\a_4=a_3+a_2\\a_5=a_4+a_3\\\\\text{first term:}\ 5\\\text{second term:}\ 6\\\text{third term:}\ 6+5=11\\\text{fourth term:}\ 11+6=17\\\text{fifth term:}\ 17+11=28[/tex]

Area = 1/2(diagonal) * √4*side^2 - diagonal^2

Area = 1/2(16)*√(4*17^2 - 16^2)

Area = 8 * √(4*289-256)

Area = 8 *√900

Area = 8 * 30

Area = 240 m^2

Answer:

∠BAM=30°

Step-by-step explanation:

Points A and B split the circle into two arcs. If the measure of minor arc AB is 150°, then the measure of the major arc AB is 360°-150°=210°.

If point M splits major arc with the ratio 2:5, then

Angles BOM and AOM together form angle with the measure 210°, thus

2x+5x=210,

7x=210,

x=30°

and ∠BOM=60°, ∠AOM=150°.

Consider isosceles triangle BOM. In this triangle,

∠OBM=1/2(180°-60°)=60°.

Consider isosceles triangle AOB. In this triangle,

∠OAB=1/2(180°-150°)=15°.

Consider isosceles triangle AOM. In this triangle,

∠OAM=1/2(180°-150°)=15°.

Thus, ∠BAM=15°+15°=30°

Answer:

arc BAM =  300°

Step-by-step explanation:

Refer to the figure attached.

arc AB = 150°

then:

arc AMB = 360° - 150° = 210°

arc AMB can be decomposed as:  

arc AM + arc MB = arc AMB (eq. 1)

From data:

arc MB/arc AM = 2/5

arc MB*(5/2) = arc AM (eq. 2)

Replacing equation 2 into equation 1:

arc MB*(5/2) + arc MB = 210°

arc MB*(7/2) =  210°

arc MB = (2/7)*210° = 60°

On the other hand:

arc MB + arc BAM = 360°

arc BAM = 360° - 60° =  300°

Answer:

4√34

Step-by-step explanation:

the question asks for the value of the hypotenuse

Applying the Pythagorean equation

a²+b²=c² where a=12cm, b=20cm and c?

substituting values to equation

12²+20²=c²

144+400=c²

544=c²

√544=c

√16 × √34 =c

4×√34

4√34

ANSWER

[tex] 4 \sqrt{34} cm[/tex]

EXPLANATION

The missing side is the hypotenuse of the right triangle.

According to the Pythagoras Theorem, the length of the square of the hypotenuse is equal to the sum of the length of the squares of the two shorter legs.

Let the hypotenuse be x.

Then,

[tex] {x}^{2} = {20}^{2} + {12}^{2} [/tex]

[tex]{x}^{2} = 400 + 144[/tex]

[tex] {x}^{2} = 544[/tex]

Take positive square root of both sides.

[tex]x = \sqrt{544} [/tex]

[tex]x = 4 \sqrt{34} [/tex]

ANSWER

The number is 18.

EXPLANATION

Let the number be x.

When this number is divided by 3, we obtain the quotient,

[tex] \frac{x}{3} [/tex]

When 5 is subtracted from this quotient, we get,

[tex] \frac{x}{3} - 5[/tex]

If the result is 1, then we have;

[tex] \frac{x}{3} - 5 = 1[/tex]

We group similar terms to get,

[tex] \frac{x}{3} = 1 + 5[/tex]

This gives us,

[tex] \frac{x}{3} = 6[/tex]

Multiply both sides by 3.

[tex]x = 6 \times 3[/tex]

[tex]x = 18[/tex]

Therefore the number is 18.

Answer: The rate is 7.5%.

Step-by-step explanation: The formula to calculate simple interest is:

Interest = Principal x Rate x Time

So, we need to plug our information into the formula:

$562.50 = $1,500 x R x 5

Now, perform the multiplication that you can:

$562.50 - $7,500R

Next, divide both sides by $7,500:

.075 = R

Therefore, the rate is 7.5%.

Answer:

Remainder is 691.

Step-by-step explanation:

Given function is [tex]10x^4-6x^3+5x^2-x+1[/tex].

Now we need to find remainder if we divide given function [tex]10x^4-6x^3+5x^2-x+1[/tex] by (x-3)

(x-3) means plug x=3 into [tex]10x^4-6x^3+5x^2-x+1[/tex] to find remainder.

[tex]10x^4-6x^3+5x^2-x+1[/tex]

[tex]=10(3)^4-6(3)^3+5(3)^2-(3)+1[/tex]

[tex]=10(81)-6(27)+5(9)-(3)+1[/tex]

[tex]=810-162+45-3+1[/tex]

[tex]=856-162-3[/tex]

[tex]=856-165[/tex]

[tex]=691[/tex]

Hence remainder is 691.

Answer:

The remainder = 691

Step-by-step explanation:

Let p(x) = 10x⁴ - 6x³ + 5x² - x + 1

We have to divide p(x) by (x - 3)

To find the remainder we  have to find p(3)

To find the remainder

p(x) = 10x⁴ - 6x³ + 5x² - x + 1

p(3) = 10 * (3)⁴ - 6*(3)³ + 5* (3)² - 3 + 1

 = (10 * 81 ) - ( 6 * 27 ) + (5 * 9) - 3 + 1

 = 810 - 162 + 45 - 3 + 1 = 691

Therefore the remainder is 691

I think 145 but I’m not quite sure

Answer:

116. add all and subtract respective to the date.

Step-by-step explanation:

Answer:

651 and 3/25 is 651.12 as a mixed number.

651.12 can be written as the mixed number 651 3/25.

To convert hundredths to a fraction, we write the decimal as the numerator and the place value as the denominator. T

Therefore, .12 can be written as 12/100.

651 + 12/100

= 651 12/100

Simplifying the fraction by dividing the numerator and denominator by their greatest common divisor, which is 4:

651 12/100 = 651 3/25

Therefore, 651.12 can be written as the mixed number 651 3/25.

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Answer:

lol

Step-by-step explanation:

Answer:

  8

Step-by-step explanation:

If each portion is 1/8 of the cake, there are 8 equal-size portions. That is what the denominator of the fraction means.

Sadie can cut the rectangular cake into 8 portions if each portion is 1/8 of the whole cake.

To determine how many portions Sadie can cut the rectangular cake into if each portion is 1/8, we need to understand that she is essentially dividing the cake into 8 equal parts.

Here's a step-by-step explanation:

Whole Cake: The entire rectangular cake represents one whole (1).

→ Portion Size: Each portion is 1/8 of the whole cake.

→ Calculation: We divide 1 by 1/8. Mathematically, this is the same as multiplying by the reciprocal,

so 1 ÷ (1/8) = 1 × 8

                 = 8.

Therefore, Sadie can cut the rectangular cake into 8 portions of size 1/8 each.

Answer:

C

Step-by-step explanation:

The formula we use here is:

Length of arc = [tex]\frac{\theta}{360}*2\pi r[/tex]

Where

[tex]\theta[/tex]  is the central angle

r is the radius

Putting the given information into the formula we can solve for the central angle:

[tex]LengthOfArc=\frac{\theta}{360}*2\pi r\\4=\frac{\theta}{360}*2\pi(5)\\4=\frac{\theta}{360}*10\pi\\\frac{4}{10\pi}=\frac{\theta}{360}\\\theta=\frac{4*360}{10\pi}\\\theta=45.84[/tex]

rounded to nearest degree, we have 46 degree

C is the right answer.

Answer: OPTION C

Step-by-step explanation:

To solve this problem you must apply the proccedure shown below:

- Use the following formula for calculate the measure fo the central angle:

[tex]\theta=\frac{s}{r}[/tex]

Where s is the arc length and r is the radius.

- Know the lenght of the arc and the radius, you can substitute values.

Therefore, you obtain;

[tex]\theta=\frac{4}{5}=0.8\ radians[/tex]

Convert to degrees:

[tex]\frac{(0.8)(180\°)}{\pi}=45.83\°[/tex]≈46°

Answer: The answers are 2.54x and 30.48 cm.

Step-by-step explanation: The formula to determine the number of centimeters in x inches is 2.54x. To solve for the number of centimeters in 12 inches the formula is 2.54 x 12 = 30.48 cm.

Final answer:

The factory takes 18 hours to produce 180 cars.

Explanation:

To find out how many hours the factory takes to produce 180 cars, we need to set up a proportion. Since the factory takes 6 hours to produce 60 cars, we can set up the proportion:

6 hours / 60 cars = x hours / 180 cars

Cross-multiplying, we get:

6(180) = 60(x)

Simplifying, we have:

1080 = 60x

Dividing both sides by 60, we find:

x = 18

So, the factory takes 18 hours to produce 180 cars.

Answer:

The ratio for sin(X) is [tex]\frac{\sqrt{119} }{12}[/tex]

The ratio for cos(X) is [tex]\frac{5}{12}[/tex]

Step-by-step explanation:

- The ratio of the sine of a right triangle is:

[tex]sin(\alpha)=\frac{opposite-side}{hypotenuse}[/tex]

Since we need the ratio for angle X, [tex]\alpha =X[/tex]. From the picture we can infer that the opposite side of X is [tex]\sqrt{119}[/tex]. The hypotenuse (the side opposite to the right angle) is 12, so replacing the values:

[tex]sin(X)=\frac{\sqrt{119} }{12}[/tex]

- The ratio of the cosine is:

[tex]cos(\alpha)=\frac{adjacent-side}{hypotenuse}[/tex]

Similarly, [tex]\alpha =X[/tex], adjacent side = 5, and hypotenuse = 12, so

[tex]cos(X)=\frac{5}{12}[/tex]

Answer:

Sin X =√119/12

Cs X = 5/12

Step-by-step explanation:

It is given a right angled triangle.

Points to remember

Sin θ = Opposite side/Hypotenuse

Cos θ = Adjacent side/Hypotenuse

To find the value of Sin X  

Here X is an angle

Opposite side = √119

Hypotenuse = 12

Sin X = Opposite side/Hypotenuse = ZY/XY = √119/12

To find the value of Cos X

Adjacent side of X = 5

Cos X = Adjacent side/Hypotenuse = XZ/XY = 5/12

343 is the answer because 14 tens is 1 hundred and 4 tens

The number that represents 2 hundreds, 14 tens, and 3 ones is 343, by adding each place value: 200 + 140 + 3.

The student asks how to represent the quantity consisting of 2 hundreds, 14 tens, and 3 ones in a single number.

To solve this, we can convert each quantity to its respective place value in the decimal system and sum them.

Two hundreds is equal to 200 (2 x 100), 14 tens equals 140 (14 x 10), and 3 ones equals 3 (3 x 1).

Adding them together gives us 200 + 140 + 3 = 343.

Well you didn't include a direct question but she traveled 7.5 miles on the bus and she walked .5 miles home.

Answer:

multiply the radius by 2π

Step-by-step explanation:

The formulas for circumference of a circle is

C = πD     where D is the diameter,

or

C = 2πr    where r is the radius.

Either formula is correct, but we will work with the second one since the question is asking about radius.

We see that 2π(r) = the circumference, so multiply r by 2π to get the circumference

Hello there! How are you doing? I am doing fine! I'll answer the question now.  

So basically when wanting to find the circumference of a circle you simply use the formula, C = 2 times PI times R. PI is the infamous number known for 3.1415912654... and the R represents the radius. You would multiply 2 times PI  and then after getting that you would basically multiply it by the radius. And then that would be the circumference and be the answer to any problem you face like this. Know that diameter is 2 times the radius and that all.

Hope this helped! Your welcome! I can help with other history stuff too! And byee! :)

Answer:

Each base is 40

Step-by-step explanation:

An isosceles triangle has a total of 180. An isosceles has two sides that are the same and one different. Think of “sos” in the word isosceles to help. If one is 100, then you have 80 left. 80 divided by 2 is 40.

The approximate probability that there will not be enough vegan meals is 94.88%.

To calculate the approximate probability that there will not be enough vegan meals, we need to find the probability that 18 or more vegans will come to the restaurant. Since the survey showed that approximately 4% of people in the city are vegans, we can use this information to estimate the probability.

First, we find the number of vegans in the city and surrounding area by multiplying the total population by the percentage of vegans: 600,000 * 0.04 = 24,000.

Next, we calculate the probability of 18 or more vegans showing up out of 24,000 by using a binomial distribution with n = 350 (the number of people expected on opening night) and p = 0.04 (the probability of a person being vegan). We then sum the probabilities for 18, 19, 20, ..., 350 vegans.

Using a calculator or statistical software, we find that the approximate probability is 0.9488, or 94.88%.

Answer:

V=64

Step-by-step explanation:

What you do is go based off the volume formula of a cube which is V=a^3.

You have a side length of 4.

V=4^3.

V=64.

Answer:

Step-by-step explanation:

f(x) + n - shift the graph of f(x) n units up

f(x) - n - shift the graph of f(x) n units down

f(x - n) - shift the graph of f(x) n units to the right

f(x + n) - shift the graph of f(x) n units to the left

===================================

f(x) = x² - 4x + 4 shifted 3 units to the right. Therefore g(x) = f(x - 3):

g(x) = (x - 3)² - (x - 3) + 4           use (a - b)² = a² - 2ab + b²

g(x) = x² - 2(x)(3) + 3² - x - (-3) + 4

g(x) = x² - 6x + 9 - x + 3 + 4           combine like terms

g(x) = x² + (-6x - x) + (9 + 3 + 4)

g(x) = x² - 7x + 16

Answer:

C 294

Step-by-step explanation:

We can use proportions to solve.  Put number of miles over gallons

202 miles          x miles

--------------- = ----------------

11 gallons           16 gallons

Using cross products

202*16 = 11 x

Divide by 11 on each side

202*16/11 = 11x/11

293.81818181818 =x

To the nearest whole number

294 miles =x

Answer:

Well it would come out to 2x-3y=-9

Step-by-step explanation:

Here's how you solve this problem:

1) Multiply the first equation by 2 (result:2x+2y=8).

2) Add both equations together (result:2x+x+2y-2y=8-5)

3) Simplify (result:3x=3)

The answer is 3x=3.

This could be simplified more, however, to equal x=1, since both sides are divisible by 3.

p.s. Have a good day!

Answer:

6/7

Step-by-step explanation:

8/14 simplified is 4/7.

So 2/7+4/7=6/7.

Answer:

Option a. 1C, 2A, 3B, 4D.

Step-by-step explanation:

1) We know that tan(x)=sin(x)/cos(x). If x=0, sin(x)=0 and cos(x)=1 then tan(x)=0. For that reason, we know that the graph passes through the point (0,0).

If x=45, then sin(45)= [tex]\frac{\sqrt{2}}{2}[/tex] and cos(45)=[tex]\frac{\sqrt{2}}{2}[/tex]. Thus tan(45)=1. The only graph that passes through the point (0,0) and is possitive when x=45 is the graph C.

2) We know that cot(x)=cos(x)/sin(x). If x=0, sin(x)=0 and cos(x)=1 then tan(x)=+∞. For that reason, we know that the graph has an asymptote in y=0, in other words, it never crosses the y-axis.

If x=45, then sin(45)= [tex]\frac{\sqrt{2}}{2}[/tex] and cos(45)=[tex]\frac{\sqrt{2}}{2}[/tex]. Thus cot(45)=1. The only graph that has an asymptote in y=0 and is possitive when x=45 is the graph A.

3) We know that -tan(x)=-sin(x)/cos(x). If x=0, sin(x)=0 and cos(x)=1 then -tan(x)=0. For that reason, we know that the graph passes through the point (0,0).

If x=45, then sin(45)= [tex]\frac{\sqrt{2}}{2}[/tex] and cos(45)=[tex]\frac{\sqrt{2}}{2}[/tex]. Thus -tan(45)=-1. The only graph that passes through the point (0,0) and is negative when x=45 is the graph B.

) We know that -cot(x)=-cos(x)/sin(x). If x=0, sin(x)=0 and cos(x)=1 then tan(x)=-∞. For that reason, we know that the graph has an asymptote in y=0, in other words, it never crosses the y-axis.

If x=45, then sin(45)= [tex]\frac{\sqrt{2}}{2}[/tex] and cos(45)=[tex]\frac{\sqrt{2}}{2}[/tex]. Thus -cot(45)=-1. The only graph that has an asymptote in y=0 and is negative when x=45 is the graph D.

The correct matches of the functions with their graphs are as follows: 1) y = tan(x) matches with graph C, 2) y = cot(x) matches with graph A, 3) y = -tan(x) matches with graph B, and 4) y = -cot(x) matches with graph D.

1) y = tan(x) matches with graph C:

  - The tangent function has a period of π (180 degrees) and is undefined at odd multiples of π/2 (90 degrees). This is why it has vertical asymptotes at x = π/2, 3π/2, etc.

  - The graph of y = tan(x) passes through (0, 0) because tan(0) = 0.

  - It has a repeating pattern where it increases to positive infinity as it approaches the vertical asymptotes and decreases to negative infinity as it approaches the odd multiples of π/2.

2) y = cot(x) matches with graph A:

  - The cotangent function is the reciprocal of the tangent function: cot(x) = 1/tan(x). It is undefined at even multiples of π/2 (0, π, 2π, etc.), which is why it has vertical asymptotes at x = 0, π, 2π, etc.

  - The graph of y = cot(x) never crosses the y-axis, and it has an asymptote at y = 0.

  - It has a repeating pattern where it approaches 0 as it approaches the vertical asymptotes.

3) y = -tan(x) matches with graph B:

  - The negative tangent function, -tan(x), is the reflection of the positive tangent function y = tan(x) about the x-axis.

  - The graph of y = -tan(x) passes through (0, 0) because -tan(0) = 0.

  - It has a repeating pattern similar to the positive tangent but is reflected about the x-axis.

4) y = -cot(x) matches with graph D:

  - The negative cotangent function, -cot(x), is the reflection of the positive cotangent function y = cot(x) about the x-axis.

  - The graph of y = -cot(x) never crosses the y-axis, similar to the positive cotangent, and it has an asymptote at y = 0.

  - It has a repeating pattern similar to the positive cotangent but is reflected about the x-axis.

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Answer:

Markup rate = 0.512 or 51.2%

Step-by-step explanation:

Mark up rate is the increase amount added to the original price.

Sales Price = $95.98

Original Price= $63.45

Gross profit margin = Sales Price - Original cost

                                = $95.98 - $63.45

                                = $ 32.53

Mark up Rate = Gross profit margin/ original price

                                  = 32.53 / 63. 45

                                  = 0.51

converting into percentage by multiplying with 100

Mark up Percentage = 0.512 * 100

                                  = 51.2 %