What kind of transformation is illustrated in this figure?

a. rotation
b. dilation
c. reflection
d. translation

Answer:

The  height of the cone is 5.09 inches

Step-by-step explanation:

Given:

The volume of the cone  =  12 cubic inches

The diameter of the cone  = 3 inches

To Find :

The height of the cone  =  ?

Solution:

We know that the volume of the cone is

Volume  = [tex]\pi r^2\frac{h}{3}[/tex]

where

r is the radius of the cone

h is the  height of the cone

Now substituting the given values

[tex]12 = \pi (1.5)^2 \frac{ h }{3}[/tex]

[tex]\frac{12}{\pi 2.25} = \frac{h}{3}[/tex]

[tex]h = \frac{12}{ 2.25 \pi} \times 3[/tex]

[tex]h = \frac{ 12}{7.065} \times 3[/tex]

[tex]h = 1.698 \times 3[/tex]

h =  5.09  inches

Answer: Sam used systematic random sampling .

Step-by-step explanation:

Here , Sam tested every 50th candy bar from the assembly line to make sure there were enough peanuts in each bar.

i.e. the period of selecting candy bars is fixed as 50.

By definition of systematic random sampling  , we can cay that Sam used systematic random sampling .

Sam is using systematic sampling in his testing, which is where elements from an ordered dataset are selected at regular intervals. This method is popular in quality checking in manufacturing due to its simplicity and efficiency.

In the situation described, Sam is using a type of sampling known as systematic sampling. Systematic sampling is a method in which elements from an ordered dataset are selected at regular intervals. In this case, Sam checks on every 50th candy bar, which is consistent with this type of sampling approach.

It's important to note that while he is taking samples at regular intervals, there's an element of randomness because we don't know the order in which the candy bars with fewer or more peanuts come onto the assembly line. Systematic sampling is often useful when there's no reason to expect a pattern that might affect the sample, like in this case with the peanuts in the candy bars.

Manufacturers, like in this case Sam, often use this type of sampling when testing product quality due to its simplicity and efficiency. However, the key is to ensure that the interval at which you're sampling doesn't align with any potential pattern in the population to avoid bias.

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The quantity b squared minus 4 ac is called the​ Discriminate of a quadratic equation.

If it is​ negative the equation has no real solution.

The quantity b squared minus 4 ac is called the​ ______ of a quadratic equation.

If it is​ ______, the equation has no real solution.

Quadratic equations are equations that are often called a second degree.

It means that it consists of at least one term which is squared. Because of this reason, it is called “quad” meaning square.

The general form of a quadratic equation is [tex]\rm ax^2+bc+c=0[/tex] where a, b, and c are numerical coefficients or constants, and the value of x is unknown.

One fundamental rule is that the value of the first constant never can be zero.

Here, [tex]\rm ax^2+bc+c=0[/tex] is the equation.

Then,

Therefore, The quantity b squared minus 4 ac is called the​ Discriminate of a quadratic equation.

If it is​ negative the equation has no real solution.

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Answer:

Step-by-step explanation:

Set your compass to length say AB and draw a circle centre A, without adjusting the compass, draw another circle with centre B. Name their intersectin C and D, erase the other part of the circle and leave just the intersect C and D. Draw a circle with centre A that passes through the intersection C and D, also draw a straight line that passes through centre C and D. Make an intersection say E on the circle by puting your comass on C and D. Join C and D to this intersection E.

Answer:

Its degree can be at least 1970

Step-by-step explanation:

for each root of the form √q, where q is not a square, we have a root -√q. Therefore, we need to find, among the numbers below to 1000, how many sqaures there are.

Since √1000 = 31.6, we have a total of 30 squares:

2², 3², 4², ...., 30², 31²

Each square gives one root and the non squares (there are 1000-30 = 970 of them) gives 2 roots (one for them and one for the opposite). Hence the smallest degree a rational polynomial can have is

970*2 + 30 = 1970

Answer:

The answer to your question is Antony bought 5 pens

Step-by-step explanation:

Data

pens = p = $0.35

pencils = n = $0.15

total amount = 12

total money spent = $2.80

Process

1.- Write equations

               p  +  n  = 12                -------------- (l)

        0.35p  +  0.15n = 2.80      --------------(ll)

2.- Solve the system of equations by elimination

Multiply equation l by - 0.35

         - 0.35p - 0.35n = -4.2

           0.35p + 0.15 n = 2.8

              0      - 0.2n = -1.4

Solve for n

                         n = -1.4 / -0.2

                         n = 7      He bought 7 pencils

3.- Find the value of p

              p + 7 = 12

              p = 12 - 7

              p = 5                He bought 5 pens

Answer:

a). [tex]1.128\times 10^{25}[/tex] grains

b). [tex]\frac{1}{8000}[/tex]

c). [tex]6.54305\times 10^{7}[/tex] years

Step-by-step explanation:

a). Given Sahara desert has an area of approximately = 9400000 km²

= 9400000×(10000000000) cm²

= [tex]9.4\times 10^{16}[/tex] cm²

Depth of the desert = 150 m

= 15000 cm

Volume of desert = Area × Depth

= [tex]9.4\times 10^{16}\times 15000[/tex]

= [tex]1.41\times 10^{21}[/tex] cm³

Since 1 cm³ holds sand grains = 8000

Therefore, Grains in Sahara Desert = [tex]1.41\times 10^{21}\times 8000[/tex]

= [tex]1.128\times 10^{25}[/tex]

b). Since 1 cm³ = 8000 grains

1 grain = [tex]\frac{1}{8000}[/tex] cm³

c). A truck can carry sand = 20.5 m³ Or [tex]20.5\times (10^{2})^{3} cm^{3}[/tex]

= [tex]2.05\times 10^{7}[/tex] cm³

Now time taken to recreate Sahara Desert = [tex]\frac{\text{Total amount of sand}}{\text{Sand in one truck}}\times 30[/tex] seconds

=  [tex]\frac{1.41\times 10^{21}}{2.05\times 10^{7}}\times 30[/tex]

= [tex]20.6341463\times 10^{14}[/tex] seconds

= [tex]\frac{20.6341463\times 10^{14} }{365\times \times 24\times 3600}[/tex] years

= [tex]6.54305\times 10^{7}[/tex] years

The Sahara Desert contains approximately 1.13 x 10^25 grains of sand. One grain of sand makes up a fraction of 8.85 x 10^-26 of the Sahara's total. It would take approximately 5.83 x 10^8 years for a line of small dump trucks, unloading every 30 seconds, to recreate the Sahara Desert.

First, let's convert everything to the same units. The area of the Sahara Desert is 9,400,000 km^2 which is equal to 9.4 x 10^12 m^2. The average depth is approximately 150m, so the total volume of the Sahara is 9.4 x 10^12 m^2 * 150 m = 1.41 x 10^15 m^3. Since 1 m^3 = 1 x 10^6 cm^3, we have a total of 1.41 x 10^21 cm^3.

a. Each cm^3 contains 8,000 grains of sand, so the total number of grains in the Sahara is 8,000 * 1.41 x 10^21 = 1.13 x 10^25.

b. The fraction made by one grain is simply 1 divided by the total number of grains in the Sahara, which is 1/(1.13 x 10^25) = 8.85 x 10^-26. This fraction is incredibly small because the number of grains of sand in Sahara is incredibly large.

c. A small dump truck carries approximately 20.5 m^3 of sand. If a truck dumps its load every 30 seconds, this amounts to 2,419,200 m^3 of sand per year. To transport the equivalent of the Sahara would take 1.41 x 10^15 m^3 /2,419,200 m^3 per year = approximately 5.83 x 10^8 years.

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Answer:Sally read 68 pages last week.

Step-by-step explanation:

Let x represent the number of pages that Sally read last week. The book has a total of 590 pages. She already read some of it last week.

She plans to read 50 pages tomorrow and by then, she will be 1/5 of the way through the book. This means that the total number of pages that she would have read by tomorrow would be

1/5 × 590 = 118

It means that the sum of the number of pages that she read last week and the 50 pages that she planned to read tomorrow is 118. Therefore

50 + x = 118

x = 118 - 50 = 68

Answer: Sally read 68 pages last week.

Step-by-step explanation:

x =Sally read last week. The book has a total of 590 pages. She already read some of it last week.

She plans to read 50 pages tomorrow and by then, she will be 1/5 of the way through the book. This means that the total number of pages that she would have read by tomorrow would be

1/5 × 590 = 118

It means that the sum of the number of pages that she read last week and the 50 pages that she planned to read tomorrow is 118. Therefore

50 + x = 118

x = 118 - 50 = 68

Answer:

Yes, it is.

Step-by-step explanation:

The hypothesis made on the Hoxd13 gene expression justified the results obtained. This is because if one of the three segments is removed, the value of the expression level will be reduced to approximately below 100% of the control. Therefore, it can be inferred that the theoretical analysis justified the results obtained.

Answer:

6.6%

Step-by-step explanation:

We find the cost of the bond. Yield to maturity is the yield for bond holder but cost for the  issuer like Easy Slider.

Formula is

P=CP(1-(1+x)^-n)/x + FV/(1+x)^n

where P is the price of bond in the market. So, the selling price of Easy Slider Inc bond is 928

CP= coupon payment. Here, CP is 10% of 1000. So, $100

FV= Face value. Here, FV is $1000

n= maturity of the bond. Here, n=15

x= cost of the bond before tax

putting the value in the equation

928=100(1-(1+x)^-15)/x + 1000/(1+x)^15

solving for x, we get 0.1100

Now, if we find out after tax then

0.1100(1-T)= After tax cost

0.1100(1-0.4)

0.066 or 6.66%

Answer:20mph

Step-by-step explanation:

speed of plane = x mph

Speed of plane with wind = 485 mph

So therefore, speed of wind =

485 - x

Speed of plane against wind = 445 mph

So therefore, speed of wind =

x - 445

So therefore, equating the 2 equations of speed of wind

485 - x = x - 445

Collect like terms

485 + 445 = x + x

930 = 2x

2x = 930

x = 930/2 = 465 mph

Speed of wind = x = 465mph

So we put this value on any of the equations for speed of wind

Speed of wind = x - 445 = 465 - 445

= 20 mph

So therefore, speed of wind = 20mph

Ari and his 3 brothers do not have enough money to take a school trip to Washington, D.C. they are in short of $39.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, Ari and his 3 brothers want to take a school trip to Washington, D.C. They have $320 saved.

Ari and his 3 brothers

In total 4 of them saving $18 per week and they saved for 4 weeks

So, total money they saved

= 4×4×18

= $288

Total money they have =288+320

= $608

Difference in money

= 647-608

= $39

Hence, Ari and his 3 brothers do not have enough money to take a school trip to Washington, D.C. they are in short of $39.

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Answer the winner finished the race in 1.75 minutes

Step-by-step explanation:

Rocky finished a 200-meter race in 5/12 of a minute.

The winner finished 21/25 of Rocks time to finish the race. This means that the time that the winner took in finishing the race would be

5/12 × 21/5 = 21/12 of a minute.

Converting to decimal, it becomes

1.75 minutes

Step-by-step explanation:

5/12 x 21/25=105/300

105/300 divided by 5=21/60

21/60 divided by 3 =7/20

the winner use 7/20 of a minute or time to finish the race

hope it help you

Answer:

For this particular case they are interested on the amount of weight gained by randomly selecting some students, we need to remember that the weight can't be a discrete random variable since this random variable can take values on a specified interval and with decimals, so for this case the best conclusion is that we have  a continuous data set.

Step-by-step explanation:

Previous concepts

We need to remember that continuous random variable mans that the values are specified over an interval in the domain, so is possible to have decimal values for the possible outcomes of the random variable.

By the other hand a discrete random variable only can take integers for the possible outcomes of the random variable over the specified domain.

Solution to the problem

For this particular case they are interested on the amount of weight gained by randomly selecting some students, we need to remember that the weight can't be a discrete random variable since this random variable can take values on a specified interval and with decimals, so for this case the best conclusion is that we have  a continuous data set.

The data from a study on weight gains by college students in their first year is a continuous data set. This is because the data (weight gain) can take on any value including decimal values within a certain range.

The data collected from a study on weight gains by college students in their freshman year is considered to be a "continuous data set." This is because the weight gain, which is typically measured in pounds or kilograms, can take on any value within a certain range, including decimal values, reflecting the continuous nature of the data. For example, one student might gain 1.5 pounds, another might gain 2.3 pounds, and so on. It doesn't have to be in whole numbers, unlike in a discrete data set.

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Answer:

We get

$225+324+441+576+784+1125+2304+3136+4900+11025=24840$

Step-by-step explanation:

$(1\cdot 3\cdot 5)^2 = 15^2 = 225$

$(1\cdot 3\cdot 6)^2 = 18^2 = 324$

$(1\cdot 3\cdot 7)^2 = 21^2 = 441$

$(1\cdot 4\cdot 6)^2 = 24^2 = 576$

$(1\cdot 4\cdot 7)^2 = 28^2 = 784$

$(1\cdot 5\cdot 7)^2 = 35^2 = 1125$

$(2\cdot 4\cdot 6)^2 = 48^2 = 2304$

$(2\cdot 7\cdot 7)^2 = 56^2 = 3136$

$(2\cdot 5\cdot 7)^2 = 70^2 = 4900$

$(3\cdot 5\cdot 7)^2 = 105^2 = 11025$

We get

$225+324+441+576+784+1125+2304+3136+4900+11025=24840$

Answer:

  the object is at 288 feet 2 seconds and 9 seconds after launch

Step-by-step explanation:

The equation of motion is given as ...

  h(t) = -16t² +176t

and we are asked to find when the object is at height 288 ft. Putting that number into the equation, we have ...

  288 = -16t² +176t

  -18 = t² -11t . . . . . . . . divide by -16

  -18 +30.25 = t² -11t +30.25 . . . . . . add (11/2)² to complete the square

  12.25 = (t -5.5)² . . . . . . simplify a bit

  ±3.5 = t -5.5 . . . . . . . . .square root

  t = 5.5 ± 3.5 = {2, 9}

The object is 288 feet high after 2 seconds or 9 seconds.

Answer:

1080 orders is made after 4hours

When profit exceeds $1000, the time will be 7:22 PM

Step-by-step explanation:

1.  Let No of order be O and time be T

O ∝ T

O = KT

K = O ÷ T

K = 18 ÷ 4 = 4.5

Total no of orders in 4hrs (240min) will be

O = 4.5 × 240 = 1080 orders

2. Total orders made from profit of $1000 is evaluated.

10 orders give $11

x orders will give 909.09091 orders

time required to reach 909.09091 orders is then evaluated

1080 orders is placed in 4hrs

909.09091 orders will be placed in x hours

upon cross multiplication

x = 3.3670034 hours which is equivalent to 202.020202 minutes

When that's added to 4:00 PM, the answer is 7:22PM minutes to the nearest minute.

1080 pies are sold in 4 hours based on their order rate, and the phone order profit will exceed $1,000 around 7:22 PM, assuming a constant profit rate.

The student asked two questions related to pizza orders.

Firstly, they wanted to know how many pies are sold in 4 hours based on a constant rate of 18 orders in a 4-minute period.

Secondly, they asked when phone order profit would exceed $1,000 assuming a profit of $11 on 10 orders.

Calculating Pies Sold in 4 Hours

To calculate the number of pies sold in 4 hours (240 minutes) when 18 orders are received every 4 minutes, we need to determine how many 4-minute periods are in 240 minutes.

This is 240 minutes / 4 minutes = 60 periods.

Since 18 orders are received per period, the total number of pies sold is 18 orders × 60 periods = 1080 pies.

Calculating When Phone Order Profit Exceeds $1,000

To calculate when the profit exceeds $1,000, note that for every 10 orders, a profit of $11 is made.

First, calculate the total number of orders needed to exceed $1,000 profit.

Given: $1,000 / $11 = approximately 91 sets of 10 orders.

Therefore, total orders needed = 91 sets × 10

                                                    = 910 orders.

Since 18 orders are taken every 4 minutes, we find the total time by dividing 910 orders by the rate of 4.5 orders per minute (18 orders / 4 minutes).

This gives approximately 202.2 minutes from the start time (4:00 PM), which rounds to 7:22 PM when the profit exceeds $1,000.

Answer:the speed of the wind is 20 miles per hour.

Step-by-step explanation:

A Plane flies at x miles per hour in still air. This means that the normal speed of the plane is x miles per hour.

Let y represent the speed of the wind.

Flying with a tailwind, it's speed is 485 miles per hour. This means that

the total speed of the plane would be x + y. Therefore

x + y = 485 - - - - - - - - 1

Against the wind, it's air speed is only 445 miles per hour. This means that

the total speed of the plane would be x - y. Therefore

x - y = 445 - - - - - - - - - 2

Adding equation 1 and equation 2, it becomes

2x = 930

x = 930/2 = 465

Substituting x = 465 into equation 1, it becomes

465 + y = 485

y = 485 - 465

y = 20 miles per hour

Answer:

The required probability is 0.927

Step-by-step explanation:

Consider the provided information.

Surveys indicate that 5% of the students who took the SATs had enrolled in an SAT prep course.

That means 95% of students didn't enrolled in SAT prep course.

Let P(SAT) represents the enrolled in SAT prep course.

P(SAT)=0.05 and P(not SAT) = 0.95

30% of the SAT prep students were admitted to their first choice college, as were 20% of the other students.

P(F) represents the first choice college.

The probability he didn't take an SAT prep course is:

[tex]P[\text{not SAT} |P(F)]=\dfrac{P(\text{not SAT})\cap P(F) }{P(F)}[/tex]

Substitute the respective values.

[tex]P[\text{not SAT} |P(F)]=\dfrac{0.95\times0.20 }{0.05\times0.30+0.95\times0.20}[/tex]

[tex]P[\text{not SAT} |P(F)]\approx0.927[/tex]

Hence, the required probability is 0.927

To find the probability that the student didn't take an SAT prep course, we use conditional probability. The probability is approximately 0.6842 or 68.42%.

To find the probability that the student didn't take an SAT prep course, we need to use conditional probability. Let's denote the events as follows:

The probability that the student didn't take an SAT prep course can be calculated using the formula:

P(A' | B') = (P(B') - P(A ∩ B')) / P(B')

We are given that 5% of the students took an SAT prep course, so P(B') = 1 - 0.05 = 0.95. We are also given that 30% of the SAT prep students were admitted to their first choice college, so P(A ∩ B') = 0.3. Finally, we are given that 20% of the other students were admitted to their first choice college, so P(A' ∩ B') = 0.2. Plugging these values into the formula:

P(A' | B') = (0.95 - 0.3) / 0.95 = 0.6842

Therefore, the probability that the student didn't take an SAT prep course is approximately 0.6842 or 68.42%.

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Answer:

D. all of the above

Step-by-step explanation:

In a programming software, depending on the type of input or coding given, the software application has the power to executes the following statement:

when the coding/input state x = y + 5

the computer will

A. retrieves the value of y (the value of y will have been stated earlier)

B. calculates the total of 5 and the value of y (sum the value of y with 5)

C. stores the result of the calculation in the variable x  (store the result of value of x in case if it is been call for again, or store nit until a new value is gotten for x)

them, the computer can either print out the result of xor wait for the next action.

the correct option for this question is D. all of the above

Answer:

x - 24 = 12; x = 36

or

x - 12 = 24; x = 36

Step-by-step explanation:

Missing Portion of actual question:

In actual question, the scale provided on the map is 1 inch = 2.5 miles. (Picture is attached)

Answer:

3 inch

Step-by-step explanation:

Part a):

Actual distance between Saugerties and Kingston is 10 miles (4*2.5) because in map distance is 4 inch while 1 inch is equivalent to 2.5 miles.

Part b):

Actual distance between Saugerties and Catskill is 15 miles hence on this map distance will be 6 inch (15/2.5) because 1 inch is equivalent to 2.5 miles.

Part c):

On another map where distance between Saugerties and Kingston is 2 inches (half of the one shown in the given map), the distance between Saugerties and Catskill will be 3 inches. As the map is scaled double than the map given in the question i.e. 1 inch = 5 miles.

Answer:

Below.

Step-by-step explanation:

3. LF + 27 = 45

5. 18/45 = 16/40

6. 2/5 =  2/5

8.

The initial speed of the ball is approximately [tex]\( 24.38 \ m/s \)[/tex].

To find the initial speed of the ball, we can use the projectile motion equations. The horizontal displacement (range) can be expressed as:

[tex]\[ R = \frac{V_0^2 \sin 2\theta}{g} \][/tex]

where:

- [tex]\( R \)[/tex] is the horizontal displacement (60.6 m),

- [tex]\( V_0 \)[/tex] is the initial speed,

- [tex]\( \theta \)[/tex] is the launch angle (45.0º),

- [tex]\( g \)[/tex] is the acceleration due to gravity (9.8 m/s²).

First, convert the launch angle to radians: [tex]\( \theta = 45.0º \times \frac{\pi}{180} \approx 0.785 \ rad \)[/tex].

Now, substitute the values into the range equation and solve for [tex]\( V_0 \)[/tex]:

[tex]\[ 60.6 = \frac{V_0^2 \sin 2 \times 0.785}{9.8} \][/tex]

[tex]\[ V_0^2 = \frac{60.6 \times 9.8}{\sin 1.57} \][/tex]

[tex]\[ V_0^2 \approx \frac{60.6 \times 9.8}{1} \][/tex]

[tex]\[ V_0^2 \approx 594.48 \][/tex]

[tex]\[ V_0 \approx \sqrt{594.48} \][/tex]

[tex]\[ V_0 \approx 24.38 \ m/s \][/tex]

So, the initial speed of the ball is approximately [tex]\( 24.38 \ m/s \)[/tex].

Step-by-step explanation:

For solving this, it's important to know basic trigonometric functions:

sin = opposite side / hypotenuse

cos = adjacent side / hypotenuse

tan = opposite side / adjacent side

It's also important to know that it is necessary to know their values for special right triangles and angles of 30°, 45° and 60°

1. We are given angle if 45° and its adjacent side of 13. We want to know the opposite side (x) and hypotenuse (y). So:

tan = opposite side / adjacent side

tan 45 = x / 13

1 = x / 13

x = 13

Remember that tangent of 45° angle is 1.

We found the opposite side to be also 13.

To find y we can use:

sin = opposite side / hypotenuse

sin 45 = 13 / y

(√2)/2 = 13 / y

y = 13√2

Important to remember, sin 45 and cos 45 are (√2)/2

2. We are given 45° angle and hypotenuse of 30. We need to find opposite side (x) and adjacent side (y).

sin = opposite side / hypotenuse

sin 45 = x / 30

(√2)/2 = x / 30

x = 15√2

Also:

cos = adjacent side / hypotenuse

cos 45 = y / 30

(√2)/2 = y / 30

y = 15√2

We can conclude that in the right triangle, when angle is 45°, opposite and adjacent sides are equal.

3. We are given angle of 60° and adjacent side of 3. We need to find opposite side (y) and hypotenuse (x).

cos = adjacent side / hypotenuse

cos 60° = 3 / x

1/2 = 3 / x

x = 6

Note that cos 60° equals 1/2.

sin = opposite side / hypotenuse

sin 60° = y / 6

(√3)/2 = y / 6

y = 3√3

Note that sin 60° equals (√3)/2.

4. We are given angle of 30° and hypotenuse of 34. We need to find opposite side (y) and adjacent side (x).

sin = opposite side / hypotenuse

sin 30° = y / 34

1/2 = y / 34

y = 17

Note that sin 30° equals to cos 60° equals 1/2.

cos = adjacent side / hypotenuse

cos 30° = x / 34

(√3)/2 = x / 34

x = 17√3

Remember that cos 30° equals to sin 60° which is (√3)/2.

5. We are given an angle of 45° and hypotenuse of 10√2. We need to find the opposite side (y) and adjacent side (x).

sin = opposite side / hypotenuse

sin 45° = y / 10√2

(√2)/2 = y / 10√2

y = 10

To save time, we already said that opposite and adjacent sides are equal in right triangle with 45° angle, so x = y = 10.

6. We are given angle of 60° and opposite side of 25√3. We need to find adjacent side (y) and hypotenuse (x).

sin = opposite side / hypotenuse

sin 60° = 25√3 / x

(√3)/2 = 25√3 / x

x = 50.

tan = opposite side / adjacent side

tan 60° = 25√3 / y

√3 = 25√3 / y

y = 25.

Remember that tangent of 60° angle is √3.

7. We are given angle of 45° and hypotenuse of 2√14. We need to find adjacent side (x) and opposite side (y).

cos = adjacent side / hypotenuse

cos 45° = x / 2√14

(√2)/2 = x / 2√14

x = √28

Again, adjacent and opposite sides are equal in 45° right triangle, so x = y = √28.

8. We are given an angle of 30° and an adjacent side of 24. We need to find the opposite side (y) and hypotenuse (x).

tan = opposite side / adjacent side

tan 30° = y / 24

(√3)/3 = y / 24

y = 8√3

sin = opposite side / hypotenuse

sin 30° = 8√3 / x

1/2 = 8√3 / x

x = 16√3

Note that tan = sin/cos, so tan 30° = sin 30° / cos 30°

tan 30° = 1/2 / (√3)/2 = (√3)/3

I'm showing you this, so you don't have to memorize tan for special angles, you can find it from sin and cos.

9. We are given an angle of 60° and hypotenuse of 22√3. We need to find the opposite side (y) and adjacent side (x).

sin = opposite side / hypotenuse

sin 60° = y / 22√3

(√3)/2 = y / 22√3

y = 33

cos = adjacent side / hypotenuse

cos 60° = x / 22√3

1/2 = x / 22√3

x = 11√3

10. We are given an angle of 30° and the opposite side of √6. We need to find the adjacent side (x) and hypotenuse (y).

sin = opposite side / hypotenuse

sin 30° = √6 / y

1/2 = √6 / y

y = 2√6

tan = opposite side / adjacent side

tan 30° = √6 / x

(√3)/3 = √6 / x

x = √18

11. We are given an angle of 45° and an adjacent side of √10. We need to find the opposite side (x) and hypotenuse (y).

In this triangle opposite and adjacent sides are equal (45° angle), so x = √10

sin = opposite side / hypotenuse

sin 45° = √10 / y

(√2)/2 = √10 / y

y = √20 = 2√5

12. We are given an angle of 60° and the opposite side of 4√21. We need to find the adjacent side (x) and hypotenuse (y).

sin = opposite side / hypotenuse

sin 60° = 4√21 / y

(√3)/2 = 4√21 / y

y = 8√7

tan = opposite side / adjacent side

tan 60° = 4√21 / x

√3 = 4√21 / x

x = 4√7

13. Now things get a little trickier. We are given an angle of 30° and the opposite side of 17. We need to find the adjacent side (x).

Note that, at the moment, we are only dealing with this smaller triangle.

tan = opposite side / adjacent side

tan 30° = 17 / x

(√3)/3 = 17 / x

x = 17√3

Now, note that hypotenuse of the smaller triangle is the same length as the side z (adjacent and opposite side of 45° angle)

With Pythagorean theorem, we can find the hypotenuse of the smaller triangle, which equals to z.

z = √(17^2 + (17√3)^2)

z = 34

And now, finally to find y (hypotenuse of bigger triangle). We are given 45° angle and adjacent side z (34).

cos = adjacent side / hypotenuse

cos 45° = 34 / y

(√2)/2 = 34 / y

y = 34√2

14. Photo added

Correct responses;

Solutions:

1. An acute angle of the right triangle is 45°, therefore, the triangle is an isosceles triangle, and the leg lengths are equal.

Therefore;

The length of the hypotenuse side of an isosceles right triangle = A leg length × √2

Therefore;

2. An interior angle of the triangle = 45°

Therefore;

x = y

30 = x·√2

Which gives;

[tex]x = \dfrac{30}{\sqrt{2} } = \dfrac{30 \cdot \sqrt{2} }{2} = \mathbf{15 \cdot \sqrt{2}} = y[/tex]

3. The interior angle adjacent to the leg of length 3 = 60°

Therefore;

The hypotenuse side, x = 2 × adjacent leg length

Which gives;

In a right triangle having an interior angle of 60°, we have;

2 × Opposite leg length = √3 × The length of the hypotenuse

Therefore;

2 × y = √3 × x

Which gives;

2 × y = √3 × 6

4. The leg lengths are, x and y

An interior angle opposite to the leg length y is 30°

The hypotenuse side = 34

The length of the hypotenuse side = 2 × The leg length opposite the 30° angle

Therefore;

34 = 2 × y

[tex]y = \dfrac{34}{2} = \mathbf{17}[/tex]

The leg with length x is adjacent to the 30° angle, which gives;

2·x = √3 × 34

5. An acute interior angle is 45°

Therefore, the relationship are;

x = y

x·√2 = 10·√2

Which gives;

6. An acute interior angle is 60°, which in relation to the position of the sides gives;

x·√3 = 2 × 25·√3

Therefore;

x = 2 × 25 = 50

x = 50

y = x ÷ 2

Therefore;

y = 50 ÷ 2 = 25

7. An acute interior angle is 45°, which gives;

x·√2 = 2·√14

[tex]x = \dfrac{2 \cdot \sqrt{14} }{\sqrt{2} } = \sqrt{2} \times \sqrt{14} = \sqrt{28} = 2 \cdot \sqrt{7} [/tex]

8. An interior angle is 30°

With regards to the location of the variables, we have;

2 × 24 = x·√3

Therefore;

2·y = x

Therefore;

[tex]y = \dfrac{x}{2} [/tex]

Which gives;

[tex]y = \dfrac{16 \cdot \sqrt{2} }{2} = \mathbf{8 \cdot \sqrt{2} }[/tex]

9. An interior angle is 60°, which gives;

[tex]y = \dfrac{22 \cdot \sqrt{3} }{2} = 11 \cdot \sqrt{3} [/tex]

√3 × 22·√3 = 2 × x

x = 11·√3 × √3 = 33

10. An angle of the right triangle is 30°

With respect to the location of the variables, we have;

y = 2 × √6 = 2·√6

y·√3 = 2 × x

Therefore;

2·√6 × √3 = 2 × x

x = √(18) = 3·√2

11. Right triangle with a 45° interior angle

y = √(10) × √2 = √(20) = 2·√5

12. Interior angle of the right triangle is 60°

y·√3 = 2 × 4·√(21) = 8 × √7 × √3

[tex]x = \dfrac{y}{2} [/tex]

Therefore;

[tex]x = \dfrac{8 \cdot \sqrt{7} }{2} = \mathbf{ 4 \cdot \sqrt{7} }[/tex]

13. The ratio of the adjacent leg to the opposite leg to the 30° angle is √3, therefore;

The hypotenuse side = 2 × 17 = 34

The hypotenuse side of the right triangle having a 30° angle is a leg in

the right triangle that has the 45° angle, therefore;

14. In the 60° right triangle, we have;

x·√3 = 2 × 27 = 54 = 18 × 3

[tex]Length \ of \ the \ common \ side = \dfrac{x}{2} [/tex]

Which gives;

[tex]Length \ of \ the \ common \ side = \dfrac{18 \cdot \sqrt{3} }{2} = 9 \cdot \sqrt{3} [/tex]

Length of the common side = 9·√3

In the 30° right triangle, we have;

x·√3 = 9·√3

Therefore;

y = 2·x

Therefore;

Learn more about special right triangles here:

https://brainly.com/question/10635635

Answer:

Ann had $296 money at first.

Step-by-step explanation:

Let the money her sister have be 'x'.

Given:

Ann had $198 more than her sister.

So we can say that;

Money Ann had = [tex]x+198[/tex]

Now Given:

mother gave Ann $20 and her sister $60.

Now,

Money Ann had after mother gave her money = [tex]x+198+20 = x+218[/tex]

Money her sister had after mother gave her money = [tex]x+60[/tex]

Also given:

Ann had twice as much money as her sister.

So we can say that Money Ann had after mother gave her money is equal to 2 times Money her sister had after mother gave her money.

framing in equation form we get;

[tex]x+218=2(x+60)[/tex]

Applying Distributive property we get;

[tex]x+218=2x+120[/tex]

Combining like terms we get;

[tex]2x-x=218-120\\\\x = \$98[/tex]

Money sister had first = $98

Money Ann had first = [tex]x+198 = 98+198 = \$296[/tex]

Hence Ann had $296 money at first.

Answer: OPTION A.

Step-by-step explanation:

By definition, the area of a triangle can be calculated with the following formula:

[tex]A=\frac{bh}{2}[/tex]

Where "A" is the area of the triangle, "b" is the base of the triangle and "h" is the height of the triangle.

In this case, you need to observe the triangular piece shown in the picture given in the exercise.

You can identify that the base and the height of the triangle are:

[tex]b=3.6\ ft\\\\h=4.8\ ft[/tex]

Therefore, you must substitute those values into the formula. Then:

[tex]A=\frac{(3.6\ ft)(4.8\ ft)}{2}[/tex]

Finally, you must evaluate in order to find the area of the triangle.

You get the following result:

[tex]A=\frac{17.28\ ft^2}{2}\\\\A=8.64\ ft^2[/tex]

Answer:

28feet

Step-by-step explanation: To calculate how far Jose walked after 7seconds, we use the formular: Distance travelled/ Time = Speed

Mathematically, v=d/t

Where v=4ft/sec , t= 7seconds

Substituting these values in

4 =d/ 7

Cross multiplying

4×7=d

28=d

Distance Jose walked =28ft