3. The sum of two numbers is 105 and the difference of the two numbers is 21. What are the two numbers? a) (65, 15) b) (70,49) c) (63,42) d) (65, 41) b

The value of sin 75 without using a calculator is 1/4(√2 +√6)

From the question, we have the following parameters that can be used in our computation:

sin(75)

This can be expanded as

sin(75) = sin(45 + 30)

Using the sine rule, we have

sin(75) = sin(45)sin(30) + cos(45)cos(30)

Evaluate the trigonometry ratios

So, we have

sin(75) = √2/2 * 1/2 + √2/2 * √3/2

So, we have

sin(75) = √2/4 + √6/4

Evaluate the sum

sin(75) = 1/4(√2 +√6)

Hence, the value is sin(75) = 1/4(√2 +√6)

Read mroe about trigonometry function at

https://brainly.com/question/24349828

#SPJ1

Answer:

Triangle 2

Step-by-step explanation:

a^2+b^2=c^2

6^2+8^2=10^2

36+64=100

100=100

Answer: 70 miles

Step-by-step explanation: scince the trip is 30% finished and that 30% was 21 miles you just have to multiply 21 by 3 which is 63and than you have to figure out what 1 third of 21 is which is 7 and than you just have to add 7 to 63. Hope this helps

Answer:

\(r \geqslant - 16\)

Step-by-step explanation:

\( \frac{ - 10 + r}{2} \geqslant - 13\)

multiply both sides by 2:

\( - 10 + r \geqslant - 26\)

add 10 on both sides:

\(r \geqslant - 16\)

Answer:

\(r \ge -16\)

Step-by-step explanation:

To solve any equation/inequality:

1. get the variable to show up exactly once

2. isolate it

\(\frac{-10+r}{2} \ge -13\)

Multiply both sides by 2 and simplify (note that we're multiplying by a positive, not a negative, so the direction of the inequality stays the same, whereas multiplying or dividing by a negative would have changed the direction of the inequality)

\(\frac{-10+r}{2} *2 \ge -13 *2\)

\(-10+r \ge -26\)

Add 10 to both sides, and simplify

\((-10+r)+10 \ge (-26)+10\)

\(r \ge -16\)

Answer:

7 is the answer hope this helps

The total path length covered in 5 second will be 69.45 meter.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is a train going at 70 km/h must reduce its speed to 30 km/h when passing over a bridge. It performs the operation in five seconds.

Using the first equation of motion -

v = u + at

(30 x 5/18) = (70 x 5/18) + 5a

(30 x 5/18) - (70 x 5/18)  = 5a

- (5/18) x 40 = 5a

- (200/18) = 5a

a = - (40/18)

a = - 2.22 m/s²

S = 19.44 x 5 + 0.5 x (- 2.22) x 25

S = 97.2 - 27.75

S = 69.45 meter

Therefore, the total path length covered in 5 second will be 69.45 meter.

To solve more questions on equation modelling, visit the link below-

brainly.com/question/6593383

#SPJ1

[Question translation in english -

A train going at 70 km/h must reduce its speed to 30 km/h when passing over a bridge if it performs the operation in five seconds what total path has been traveled in that time.]

The gym's regular monthly rate, r, is $18.50.

Amount is the term used to describe a quantity or size of something. It will stop to used to refer to a numbers of object items or people as well as the measure of money, time and distance.

To solve this problem, we first need to calculate the total amount of money Malik paid for the 3 months. This equals $49.50. We then divide this amount by the number of months that Malik received a discount, which is 3. This yields the discounted monthly rate of $16.50.

Now, we need to find the regular monthly rate, which is equal to the discounted monthly rate plus the amount of the discount. Therefore, the regular monthly rate, r, is equal to $16.50 + $2, or $18.50.

Therefore, the gym's regular monthly rate, r, is $18.50.

To know more about amount click-
https://brainly.com/question/19104371
#SPJ1

Answer :

\(\boxed{\textsf {The red area is the required answer . }}\)

Step-by-step explanation:

A linear inequality in two variables is given to us and we need to plot it's graph .So the the given inequality is ,

\(\sf\implies y \geq- \dfrac{1}{5}x +5 \)

So firstly let's simplify out the inequality for easy plotting of the graph .

\(\sf\implies y \geq- \dfrac{1}{5}x +5 \\\\\sf\implies y \geq \dfrac{-x+5(-5)}{5}\\\\\sf\implies y \geq \dfrac{-x-25}{5}\\\\\sf\implies y \geq -(1)\dfrac{x+25}{5}\)

Now let's put some values of x to get values of y .

• Firstly put x = 0 then we get , y is greater than or equal to 0+5/5 (-1) = 5/5(-1) = -1 . Hence we get y ≥ (-1) .

• Secondly put x = 1 , then we get , y is greater than or equal to 1+5/5(-1)=6/5(-1) = -6/5 . Hence we get y ≥ -6/5 .

• Thirdly put x = -1 , then we get y is greater than or equal to -1+5/5(-1) = -4/5 . Hence we get y ≥ -4/5

• Fourthly put x = (-5) , then we get y is greater than or equal to -5+5/5(-1) = 0 .Hence we get y ≥ 0 .

With reference to these let's plot a graph . For the graph kindly refer to the attachment :) .

Here in the graph the red area shows the possible values of x and y .

The surface area of the rectangular prism is 1476 square units

From the question, we have the following parameters that can be used in our computation:

30 mm by 12 mm by 9 mm

The surface area of the rectangular prism is calculated as

Surface area = 2 * (Length * Width + Length * Height + Width * Height)

Substitute the known values in the above equation, so, we have the following representation

Area = 2 * (30 * 12 + 30 * 9 + 12 * 9)

Evaluate

Area = 1476

Hence, the area is 1476 square units

Read more about surface area at

brainly.com/question/26403859

#SPJ9

Answer:

\(\huge\boxed{\sf 10}\)

Step-by-step explanation:

\(\sf =q + f \div \ e - r\\\\Given \ that \ q = 6 , f = 10, e=2 , r = 1\\\\= 6 + 10 \div 2 -1\\\\According \ to \ DMAS \ rule\\\\We'll \ divide \ first\\\\= 6 + 5 - 1\\\\Now \ go \ from \ left \ to \ right\\\\= 11 - 1 \\\\= 10\\\\This \ is \ the \ required\ answer.\\\\\rule[225]{225}{2}\)

Hope this helped!

Answer:

C. -1 over 2

Step-by-step explanation:

Points: (-2,2) and (0.1)

slope is m=(y2-y1)/(x2-x1)= (1-2)/(0+2)= -1/2

Option C

Answer:

1 a)8 miles per hour 1 b) 1 hour and 90 minutes  2 a) 24 hours and 6minutes  2 b) 3hours 3 a) 260 hours and 45 minutes 3 b) 40 minutes

Step-by-step explanation:

I don't know for sure if this is all correct but at least you'll have something to write down

Answer:

1a. 8 miles per hour

1b. 32 km per hour

2a. 28 miles

2b. 3 hours

3a. 2925

3b. 1/4 hour or 15 minutes

Step-by-step explanation:

For number 1a, think of 2 1/2 hours equals 20 miles as 2 1/2x=20. The x being hours, and the 20 being 20 miles. You want the equation to become x=?. So you divide 2 1/2x=20 by 2 1/2 to make the equation start with x=. You end up with x=8. Or you could just think of it as divide 20 miles by 2 1/2 hours. Either way, you end up with 8 miles per hour. For number 1b, you do the same thing as before, but you have to make 4 hours and 45 minutes a fraction. So, the are 60 minutes in an hour, so the fraction would be 45/60. Then you simplify that down to 3/4. So, 152 km divided by 4 3/4 is 32 km per hour.

For number 2a, set aside 30 minutes for now. She can go 24 miles in 3 hours. Because 8 miles times 3 hours equals 24 miles. It’s like instrad of 8 miles per hour, it’s 24 miles per 3 hours. Then, because 30 minutes is half of an hour, 8 divided by 2 would make it 4 miles per half an hour. So 24 plus 4 is 28 miles. For number 2b, you want to know how many hours it took to travel 1980 miles. Since you already knowmthat is takes one hour to go 660 miles, pretend that each 660 miles is one hour. So you divide 1980 by 660 so see how many one hours fit. You get 3. So, an airplane can fly 1980 miles in 3 hours.

For number 3a, like 2a, you basically multiply the constant speed by the full hours then the fraction, and add them together. You could also just multiply the constant speed by the number 3 3/4. That way you get the miles per 3 3/4 hours. 3 3/4 times 780 is 2925. So the plane can fly 2925. For number 3b, to get the 2 miles per ? hours, you have to divde 8 by 4 to get to 2. So you divide 1 hour by 4 to get the answer. So it’s 1/4, (one fourth of an hour) or 15 minutes 1/4 of 60 (the amount of minutes in an hour) for Mary to go 2 miles.

Answer:

108

Step-by-step explanation:

These are alternate exterior angles and alternate exterior angles are equal when the lines are parallel

A = B

6x+18 = x+93

Subtract x from each side

6x+18 -x = x+93-x

5x +18 = 93

Subtract 18 from each side

5x + 18-18 = 93-18

5x =75

Divide by 5

5x/5 = 75/5

x = 15

Angle B

x+93

15+93

108

Answer:

Solution given:

<A+<B=180°[ alternate exterior angle are equal]

6x+18=x+93

6x-x=93-18

5x= 75

x=15

now

<B=15+93=108°

Answer:

hello

Step-by-step explanation:

\(137 = - 151 + t \\ 137 + 151 = t \\ t = 288\)

hope this is correct.

The value of cos(45°) is √2/2. The correct answer choice is D. √2.

In the given diagram, the angle labeled as 45° is part of a right triangle. To find the value of cos(45°), we need to determine the ratio of the adjacent side to the hypotenuse.

Since the angle is 45°, we can assume that the triangle is an isosceles right triangle, meaning the two legs are congruent. Let's assume the length of one leg is x. Then, by the Pythagorean theorem, the length of the hypotenuse would be x√2.

Now, using the definition of cosine, which is adjacent/hypotenuse, we can substitute the values:

cos(45°) = x/(x√2) = 1/√2

Simplifying further, we rationalize the denominator:

cos(45°) = 1/√2 * √2/√2 = √2/2

Therefore, the value of cos(45°) is √2/2.

The correct answer choice is D. √2.

for such more question on angle

https://brainly.com/question/25716982

#SPJ8

Based on the information provided, the missing number would be number 6.

When it comes to finding missing numbers, the first step is to decipher or identify the pattern. This can be either a sequence of numbers or the application of a specific mathematical operation such as subtraction or addition.

In this case, we can see there is a sequence of numbers that seems to go from 1 to 9. However, if you check carefully, the number 6 is missing, which is the number you need to add.

Learn more about numbers in https://brainly.com/question/24908711

#SPJ1

Answer:

17.32 meters

Step-by-step explanation:

Let’s call the height of the tower H. The distance from the point to the base of the tower is 10 m. The angle of elevation from the point to the top of the tower is 60 degrees.

Using trigonometry, we can calculate that:

tan (60) = H / 10

H = 10 * tan (60)

H = 10 * √3

H = 17.32 m

Therefore, the height of the tower is 17.32 meters.

Let me know if I helped :)

Answer:

f(5)=123

Step-by-step explanation:

f(x) = 22x + 13

Let x = 5

f(5) = 22(5) +13

       =110+13

      =123

Answer:

Step-by-step explanation:

Let b and c represent the rates of the boat and current, respectively. The speed upstream is ...

  speed = distance/time

  b -c = (124 km)/(4 h) = 31 km/h

And the speed downstream is ...

  b +c = (180 km)/(4 h) = 45 km/h

Adding the two equations gives ...

  2b = 76

  b = 38

From the first equation, ...

  c = b -31 = 38 -31 = 7

The rate of the boat in still water is 38 km/h; the rate of the current is 7 km/h.

After answering the provided question, we can conclude that Therefore, the area of the triangle is approximately 49.808 square units.

A triangle is a closed, double-symmetrical object that consists of three line segments called ends of the spectrum that intersect at three points called vertices. Triangles can be distinguished by their sides and angles. Triangles can be equilateral (equal factions), isosceles, or scalene based on their sides. Triangles are classified as acute (all angles less than 90 degrees), okay (one angle equal to 90 degrees), or orbicular (all angles greater than 90 degrees) (all angles greater than 90 degrees). The region of a triangle can be calculated using the formula A = (1/2)bh, where an is the neighbourhood, b is the triangle's base, and h is its height.

1. Using Heron's Formula:

a = √[(-8-1)² + (7-(-6))²] = √170

b = √[(1-5)² + (-6-9)²] = √221

c = √[(-8-5)² + (7-9)²] = √170

where a, b, c are the lengths of the sides of the triangle.

\(s = (a+b+c)/2 = (\sqrt170 + \sqrt 221 + \sqrt 170)/2 = 10.231\\A = \sqrt s(s-a)(s-b)(s-c)= \sqrt 10.231(10.231-\sqrt 170)(10.231-\sqrt 221)(10.231-\sqrt 170)= 49.808\)

Therefore, the area of the triangle is approximately 49.808 square units.

2. Using the Base and Altitude:

\((y - 7)/(x + 8) = (9 - 7)/(5 + 8)\\(y - 7)/(x + 8) = 2/13\\y = (2/13)x + (101/13)\\\)

slope line passing through (-8,7) and (1,-6) is:

(\(-6 - 7)/(1 + 8) = -13/9\\(y + 6)/(x - 1) = 9/13\\y = (9/13)x - (63/13)\\\)

height of the triangle:

\((2/13)x + (101/13) = (9/13)x - (63/13)\\x = 32/11\\y = (9/13)(32/11) - (63/13) = -2.231\\\)

Using the formula A = (1/2)bh, we have:

\(A = (1/2)(\sqrt(1-(-8))² + (-6-7)^2)(2.231) = 49.808\)

Therefore, the area of the triangle is approximately 49.808 square units.

To know more about triangle visit:

https://brainly.com/question/2773823

#SPJ1

Answer:

30 in^2

Step-by-step explanation:

The formula for finding the area of a trapezoid is A=a+b/2 x h

In this case, a=5, b=10, and h=4

When you input those values into the formula and solve for A, you get A=30

Please mark as brainliest ;)

Answer:

  $142.32, profit on sale of the policy

Step-by-step explanation:

You want to know the expected value of a $280,000 life insurance policy sold for $270, if the probability the insured will live for the year is 0.999544.

The insurance company expects to have to pay the $280,000 death benefit for 0.000456 of the policies issued. That means their expected payout on any one policy is ...

  0.000456 × $280,000 = $127.68

The company gets a premium of $270 for the policy, so the expected value of the policy to the company is ...

  $270 -127.68 = $142.32

The expected value of the policy to the company is $142.32.

This represents its profit from sale of the policy.

__

Additional comment

Of course, the company has expenses related to the policy, perhaps including a commission to the agent selling it, and expenses related to handling claims. That is to say that not all of the difference between the premium and the average death benefit is actually profit. It is what might be called "contribution margin."

<95141404393>

Answer: I am pretty sure its C i hope this helps :D

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

\(im \: guessing \: its \: 4x {}^{2} - 3x + 1 \\ (correct \: me \: if \: im \: wrong)\)

\((a - b) {}^{2} = a {}^{2} - 2ab + {b}^{2} \)

\(4x {}^{2} = a {}^{2} \: \: \: \: \: \: \: \: \: \: \: b {}^{2} = 1 \\ a = 2x \: \: \: \: \: \: \: \: \: \: \: \: \: \: b = 1\)

\((2x - 1) {}^{2} = 4x {}^{2} -4x + 1\)

\(we \: need \: to \: add \: a \: - x \\ \: to \: the \: original \: equation\)

Answer:

75grams is the difference

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

After hour, pay increases by 10.

Answer:

3 packs

Step-by-step explanation:

1 pack = $3

To see how many she could buy divide the money she has by how much each pack costs

9/3 = 3

$3 for each pack is the same as

3+3+3 = 6+3 = 9

Answer:

The answer is 0.

Step-by-step explanation:

You need to multiply by 5 instead of 6 because each pair of opposite faces on a cuboid has the same area, so by considering one face from each pair, you ensure that you don't count any face twice.

When calculating the total surface area of a cuboid, you need to understand the concept of face pairs.

A cuboid has six faces, but each face has a pair that is identical in size and shape.

Let's break down the reasoning behind multiplying by 5 instead of 6 in the given scenario.

To find the surface area of a cuboid, you can add up the areas of all its faces.

However, each pair of opposite faces has the same area, so you avoid double-counting by only considering one face from each pair. In this case, you have five pairs of faces:

(1) top and bottom, (2) front and back, (3) left and right, (4) left and back, and (5) right and front.

By multiplying the average area of a pair of faces by 5, you account for all the distinct face pairs.

Essentially, you are considering one face from each pair and then summing their areas.

Since all the pairs have the same area, multiplying the average area by 5 gives you the total surface area.

When dividing 150 by 4 (to find the average area of a pair of faces), you are essentially finding the area of a single face.

Then, by multiplying this average area by 5, you ensure that you account for all five pairs of faces, providing the total surface area of the cuboid.

Thus, multiplying by 5 is necessary to correctly calculate the total surface area of the cuboid by accounting for the face pairs while avoiding double-counting.

For similar question on cuboid.

https://brainly.com/question/29568631  

#SPJ8

On solving the given system of equations, we found the values of the variables x and y as 4 and 3 respectively.

What is meant by the system of equations?

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system. A group of equations comprising one or more variables is known as a system of equations. The variable mappings that satisfy each component equation, or the points where all of these equations cross, are the solutions of systems of equations. A group of equations that are all satisfied by the same set of variables are referred to as a system of linear equations.

The given system of equations is:

2x + 2y = 14

4x - 2y = 10

To solve this, we have to first get rid of one variable.

Here the coefficient of variable y is the same.

So adding the equations, we get

6x = 24

x = 4

Now substituting this value of x in any one of the equations we get y.

2*4 + 2y = 14

8 + 2y = 14

2y= 6

y = 3

Therefore on solving the given system of equations, we found the values of the variables x and y as 4 and 3 respectively.

To learn more about the system of equations, follow the link.

https://brainly.com/question/13729904

#SPJ1