what is the value of the expression
3 1/8 divided by 1 5/8
A 4 3/4
B 3 1/5
C 1 12/13
D 1 1/2

Answer:

1. ∠YZX = 37°

2. ∠YXZ = 53°

3. XZ = 30 meters

Step-by-step explanation:

1. To solve for an unknown angle, we need to utilize the inverse of a trigonometric function.

⭐What are the inverses of the trigonometric functions?

To know which inverse of the trigonometric functions we use, we have to see the type of side lengths we are given (opposite, adjacent, or hypotenuse)

We are given side length XY, which is opposite of ∠YZX, and we are given side length YZ, which is adjacent to ∠YZX. Therefore, we will use [tex]tan^-1 (opposite/adjacent) =[/tex]

Substitute the values we are given into the function:

[tex]tan^-1 (18/24) =[/tex]

Compute this equation using a scientific calculator. I recommend using the Desmos Scientific Calculator:

[tex]= 37[/tex]

∴ ∠YZX = 37°

2. We already know 2 angles (∠YZX = 37°, and ∠ZYX = 90°) Therefore, to find ∠YXZ, we have to utilize the triangle sum theorem.

⭐ What is the triangle sum theorem?

Substitute the angles we know already (∠YZX and ∠ZYX), and solve for ∠YXZ.

[tex]< YZX + < ZYX + < YXZ = 180[/tex]

[tex]37 + 90 + YXZ = 180[/tex]

[tex]127 + YXZ = 180[/tex]

[tex]< YXZ = 53[/tex]

∴ ∠YXZ = 53°

3. We already know 2 side lengths (ZY = 24 meters, and XY = 18). Therefore, to find XZ, we have to utilize the Pythagoras' theorem.

⭐ What is the Pythagoras' theorem?

Substitute the values of the side lengths into the formula:

[tex](XZ)^2 = (XY)^2 + (ZY)^2[/tex]

[tex](XZ)^2 = 18^2 + 24^2[/tex]

Solve for XZ:

[tex](XZ)^2 = 324 + 576[/tex]

[tex](XZ)^2 = 900[/tex]

[tex]\sqrt{(XZ)^2} = \sqrt{900}[/tex]

[tex]XZ = 30[/tex]

∴ XZ = 30 meters

The equation x² + 3x - 3 = 0 has the sum of its roots as 3. This can be found by using the quadratic formula, which gives us two roots x1 and x2. Their sum is x1 + x2 = 3, which is the sum of the roots of the equation.

The correct answer is B: x² + 3x - 3 = 0

The equation has the form of ax² + bx + c = 0.

a = 1, b = 3, c = -3

The sum of the roots can be found using the quadratic formula:

x = (-b ± √(b² - 4ac))/2a

x = (-3 ± √(9 - 4*1*(-3))/(2*1)

x = (-3 ± √15)/2

x = (-3 ± 3√5)/2

x1 = (3 - 3√5)/2

x2 = (3 + 3√5)/2

The sum of the roots is x1 + x2 = 3.

Learn more about roots here

https://brainly.com/question/12716216

#SPJ4

Due to the closing of a growth plates in bones, the majority of people's height would not increase after the ages of 18 to 20. The average human height is about 6 feet, but some individuals can reach heights of more than 9 feet.

Your height varies slightly throughout the day as a result of the decompression and compression of a discs in your spine.

Thus, the formula for finding the height is -

Full height = Present height/% of full height at present x 100

To know more about the full height of a person, here

https://brainly.com/question/73194

#SPJ4

The value of the given mixed fraction 997 1 / 3 is equal to 2992 / 3.

As given in the question,

Given expression is equal to,

997 1 / 3

Simplify the mixed fraction using following method in standard form :

Q R / D = [ (  D × Q ) + R ] / D

In the  numerator multiply divisor (D) to the quotient (Q) and add it to the remainder (R).

Denominator of the expression remain same.

Here  Q = 997 , R = 1 and D = 3

Substitute the value in the formula we get,

997  1 / 3

= [ ( 3 × 997 ) + 1 ] / 3

= ( 2991 + 1 ) / 3

= 2992 / 3

Therefore, the value of the given mixed fraction is equal to 2992 / 3.

Learn more about value here

brainly.com/question/13799105

#SPJ4

If truth values of p be F and q be T. Then, truth value of ∼(∼p∨q) is F.

A proposition's characteristic indicating whether it is true or false is the definition of a truth value. For instance, the truth value for "7 is odd" is true and can be represented by the letter T. "1 + 1 = 3" has a false truth value, which can be represented by the letter F. Truth is crucial. People's plans can be ruined and their lives could be in danger if they believe something that is false. Legal and societal repercussions may occur from telling lies. The excellent historian, good investigator, and good scientist, on the other hand, are committed to the search of truth.

Given

If truth values of p be F and q be T. Then, truth value of ∼(∼p∨q) is

b. F

To learn more about truth value, visit:

https://brainly.com/question/10403915

#SPJ4

An asymptote is a line that a curve approaches but never touches. There are two types of asymptotes: horizontal and vertical. Few examples of asymptotes are f(x) = 1/x, f(x) = 1/x² + 1 and f(x) = 1/(x-3).

Here are some examples of functions with horizontal asymptotes:

The function f(x) = 1/x has a horizontal asymptote at y = 0.

f(x) = 1/x

As x gets larger and larger, the value of the function approaches 0, but never quite reaches it. This means that the horizontal line y = 0 is an asymptote for the function f(x) = 1/x.

The function f(x) = 1/x² + 1 has a horizontal asymptote at y = 1.

f(x) = 1/x² + 1

As x gets larger and larger, the value of the function approaches 1, but never quite reaches it. This means that the horizontal line y = 1 is an asymptote for the function f(x) = 1/x² + 1.

Here is an example of a function with a vertical asymptote:

The function f(x) = 1/(x-3) has a vertical asymptote at x = 3.

f(x) = 1/(x-3)

As x gets closer and closer to 3, the value of the function approaches infinity, but never quite reaches it. This means that the vertical line x = 3 is an asymptote for the function f(x) = 1/(x-3).

To know more on asymptotes

https://brainly.com/question/4084552

#SPJ4

The value of the Discriminant is 0 so we have equal roots  = b/2a = 6/2 = 3

The given equation is a quadratic equation.

x^2+6x+9 = 0.

To tell the nature of the roots we have to understand how to find the root of a quadratic equation.

The roots of a quadratic equation are the values of the variables that fulfil the equation. In other words, if f(α) = 0, then x = α is a root of the quadratic equation f(x).

The term Discriminant is used in quadratic equations.

The discriminant of a quadratic equation is the expression [tex](b^2 - 4ac)[/tex] in the quadratic formula. A quadratic equation's discriminant shows the nature of roots.

Discriminant important thing is that it is used to find the nature of roots.

x^2+6x+9 = 0. a =1, b = 6, c=9

discriminant d = b^2 - 4*a*c = 36-4*1*9 = 36-36 = 0

So the value of the discriminant is 0 so we have equal roots  = b/2a = 6/2 = 3

To know more about roots of quadratic equation here:

https://brainly.com/question/26926523

#SPJ4

The value of x in the given sequence is found as 225.

20/2 = 10     (0.5)

10x10 = 1      (1)

10x1.5 = 15    (1.5)

15x2 = 30     (2)

30x2.5 = 75   (2.5)

There is an increase of 0.5 in each term and then multiplies it with the previous term.

So,

{ 2.5 + 0.5 = 3 }

75x3 = 225    (3)

Thus, the value of the x in the given sequence is found as 225.

To know more about the sequence, here

https://brainly.com/question/6561461

#SPJ4

1. Your shooting percentage was 60%.

2. Your friend made 24 shots.

3. Hi Lowe's shooting percentage was 71%.

4. Julie Shootsalott made 17 shots.

5. Swish Malone's shooting percentage was 89%.

6. Slammin' Sammy made 19 shots.

7. Lightning Lizzy's shooting percentage was 94%.

8. The team's shooting percentage was 65%.

1. To calculate the shooting percentage,

divide the number of shots made (i.e..12) by the total number of shots taken(i.e.20)

                             12/20 = 0.6

Multiply this by 100 to get the percentage, which is 60%.

2. To calculate no. of shots,

multiply the shooting percentage (i.e.60%) by the total number of shots taken (i.e.40)

                                0.6 x 40 = 24

3. To calculate Hi Lowe's shooting percentage,

divide the number of shots made (i.e.25) by the total number of photos taken (i.e.35).

                                      25/35 = 0.714

Multiply this by 100 to get the percentage,

which is 71.4%

4. To calculate Julie Shootsalott's shots,

multiply the shooting percentage (34%) by the total number of shots taken (50).

                                              0.34 x 50 = 17

5. Swish Malone's shooting percentage was 89.3%. To calculate this, divide the number of shots made (i.e.25) by the total number of photos taken (i.e.28).

                                             25/28 = 0.893

Multiply this by 100 to get the percentage,

which is 89.3%

6. To calculate Slammin' Sammy shots,  

multiply the shooting percentage (i.e.95%) by the total number of shots taken (i.e.20)

                                                0.95 x 20 = 19

7. To calculate Lightning Lizzy's shooting percentage,

divide the number of shots made (i.e.34) by the total number of shots taken (i,e,36)

                                                   34/36 = 0.944

Multiply this by 100 to get the percentage,

which is 94.4%

8. To calculate The team's shooting percentage,

divide the number of shots made (i.e.44) by the total number of shots taken (i.e.68). 44/68 = 0.647

Multiply this by 100 to get the percentage,

which is 64.7%.

Learn more about Percentage:

brainly.com/question/24877689

Calculating acceleration involves dividing the change in velocity by the change in time.. The equation is a = (v-u)/t, where a is acceleration, v is the final velocity, u is the initial velocity, and t is the time.

Acceleration is the rate of change in velocity over time. To calculate acceleration, you need to know the initial velocity (u), the final velocity (v), and the time (t) of the motion. The formula for calculating acceleration is a = (v-u)/t. To use this formula, subtract the initial velocity from the final velocity and divide by the time. This will give you the acceleration. For example, if the initial velocity is 10 m/s, the final velocity is 20 m/s, and the time is 2s, then the acceleration is (20-10)/2 = 10 m/s2. This means that the velocity has increased by 10 m/s every second.If the initial velocity is 10 m/s, the final velocity is 20 m/s, and the time is 2s, then the acceleration is (20-10)/2 = 10 m/s2.

Learn more about equation here

https://brainly.com/question/29657992

#SPJ4

Answer:

1st Q: -20

2nd Q: C,B,A

Step-by-step explanation:

Its correct

Answer: a = 70%

b 6.5 times

c  green = 16%

2.  ?????  Very poorly worded question

2. a 54%

b. 46%

c. 70%

d.  27%

Step-by-step explanation:

Students in a class were asked to tell their favorite color.

a. What percent said red, blue, or yellow? __% said red, blue, or yellow.  

red is .26

blue is .40

yellow is .04

---------------------

               .70   = 70 %

b. How many times more students said red than yellow?

red  .26

yellow is .04

.26/.04 =  6.5 times

c. What percent of students said green? __% said green.

The circle must total 100 %

Red + blue + yellow + purple + green = 100

26+     40 +     4           + 14     +  green = 100

84 + green = 100

Subtract 84 from each side

84-84 + green = 100-84

green = 16

2. Which two methods could be used to find the percent of students who said green?

We can either convert the percents to decimals or the decimals to percents

The total percents must equal 100%

The total decimal must equal 1

a. Find the sum of the percents given in the circle graph.

If they only want the ones written on the graph as percents

(14+40) = 54%

b. Find the sum of the percent forms of the numbers given in the circle graph. Subtract the result from 100%.

100 - 54% = 46%

c. Find the sum of the decimal forms of the numbers given in the circle graph. Subtract that sum from 1. Change the result to a percent.

.26+.04 = .3

1-.3 = .7

70%

d. Find the sum of half of the percents given in the circle graph. Subtract that total from 50%.

1/2 (46%) = 23%

50 -23 = 27%

Converting 140 kilograms to pounds is: 308.56 pounds.

Here, we have,

given that,

Convert 140 kilograms to pounds.

now, we know that,

1 kilogram = 2.204 pounds

so, we get,

we would multiply 140 by 2.204

i.e.

140 × 2.204 = 308.56

which would give the answer which is 308.56 pounds.

Hence, Converting 140 kilograms to pounds is: 308.56 pounds.

To learn more on unit conversion click:

brainly.com/question/19420601

#SPJ6

Answer:

Therefore for this distance combined speed is to be taken. Time taken to cover 2800 miles = 2800/(60+40) = 28 hours.

Step-by-step explanation:

We can assume that B leaves Los Angeles not at noon but at 2pm Eastern Time, so 5 hours later than A leaves New York.

In 5 hours A covers 5*40=200 miles. So, A and B together should cover 3,000-200=2,800 miles.

Combined rate = 40 + 60 = 100 miles per hour.

To cover 2,800 miles they'll need 2,800/100=28 hours.

2pm Eastern Time on Monday + 28 hours = 6pm Eastern Time on Tuesday

Answer:

its provide cretion nt exit e business to advet

To see if the two triangles are similar, you first have to get them both in the same direction. You do this by rotating (turning) one shape to align with the other. Such a transformation is called a rotation.

Geometry transformations are movements of two-dimensional shapes in two dimensions, or within their plane. Like restricted game pieces on a game board, you can move two-dimensional shapes in only three ways:

Transform one of the triangles such that the orientation of the triangles is the same.

Identify the corresponding sides of the triangles and write each set of corresponding sides as a ratio. If the ratios of the side lengths are the same for all 3 sides, then the triangles are similar.

Hence, by performing two rigid motions, we can prove the congruence between these two triangles. Now once the triangles are superimposed, we can identify the corresponding parts by checking which side and angle of the initial triangle is superimposed on the transformed triangle.

For more such questions on transformations

https://brainly.com/question/14835332

#SPJ4

Answer:

Step-by-step explanation:

given the formula

[tex]h(t)=16t^{2}+230t[/tex]

Find the axis of symmetry

[tex]t=\frac{-b}{2a}[/tex]

Notice the function is of the form

[tex]h(t)=at^{2}+bt[/tex]

where

[tex]a=16, b=230[/tex]

To find the time at which the rocket reached its highest point, use the formula for the axis of symmetry. Substitute 16 for a and 230 for b. This gives you,

[tex]t=\frac{-(230)}{2(16)}[/tex]

simplify the arithmetic expression..

[tex]t=\frac{-230}{32}[/tex]

[tex]t[/tex]≈-7.2 seconds

I THINK the answer should be -7.2 seconds but I do not know how this would really play into the problem being that seconds should be positive, not negative... hope this helps!

The claim for the EC sickness benefit are filed at any SSS branch or representative office nearest the member's residence or place of work.

Here we need to find the way to notify SSS for EC sickness benefit.

In order to find the solution, we must know that what is meant by  SSS for EC sickness benefit.

The term  SSS for EC sickness benefit is defined as the  benefits under the EC program may be enjoyed simultaneously with benefits under the social security program effective June 1984.

Based on the definition, we have identified that the notification process is done through  the E-Services tab and click on "Submit SS Sickness Benefit Reimbursement Application (SBRA)."

To know more about Claim here.

https://brainly.com/question/29020855

#SPJ4

Answer:

  order of operations

Step-by-step explanation:

You want to know why -4² = -16 and (-4)² =16.

The calculator properly applied the order of operations to -4². In evaluating, this expression, the exponentiation operation is performed first. That means this is evaluated as ...

  -4² = -(4×4) = -16

When the parentheses include the minus sign, as in the second expression, the squaring operation is applied to -4, not to 4:

  (-4)² = (-4)×(-4) = 16

No, 16 is not a multiple of 3 as they leave some reminder.

Hence, No, 16 is not a multiple of 3 as they leave some reminder.

To more about multiples of 3 refer to:

https://brainly.com/question/29550012

#SPJ4

Considering the definition of an inequality, the inequality that best represents this scenario is 35x + 60y≥ 7000

An inequality is the existing inequality between two algebraic expressions, connected through the signs:

Solving an inequality consists of finding all the values ​​of the unknown for which the inequality relation holds.

In this case, you know that:

Being:

the inequality that expresses the scenario is

35x + 60y≥ 7000

Learn more about inequality:

brainly.com/question/29478602

brainly.com/question/17578702

brainly.com/question/25275758

brainly.com/question/14361489

brainly.com/question/1462764

#SPJ1

The factors of the number 36 will be 2, 2, 3, and 3. So, yes, 2 is the factor of 36.

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

It is also known as the product. If the object n is given to m times then we just simply multiply them.

The number is given below.

⇒ 36

The factor of the number 36 is given below.

36 = 2 x 2 x 3 x 3

The factors of the number 36 will be 2, 2, 3, and 3. So, yes, 2 is the factor of 36.

More about the factorization link is given below.

https://brainly.com/question/6810544

#SPJ4

I don't see the picture. Can you send it in the message.

Answer:B

Step-by-step explanation:

Which graph represents the solution set of the system of inequalities? {y>−2x−2y≤x+4 A system of 2 linear inequalities graphed on a coordinate plane. The horizontal x-axis ranges from negative 5 to 5 in increments of 1. The vertical y-axis ranges from negative 5 to 5 in increments of 1. A dashed line passes through begin ordered pair negative 0.5 comma negative 1 end ordered pair, begin ordered pair negative 1 comma 0 end ordered pair and begin ordered pair 0 comma negative 2 end ordered pair. A solid line passes through begin ordered pair negative 0.5 comma negative 1 end ordered pair, begin ordered pair 0 comma 1 end ordered pair and begin ordered pair negative 1 comma negative 3 end ordered pair. The region below the dashed line and above the solid line is shaded. A system of 2 linear inequalities graphed on a coordinate plane. The horizontal x-axis ranges from negative 5 to 5 in increments of 1. The vertical y-axis ranges from negative 5 to 5 in increments of 1. A da

The coefficient of the variable x² in the expression 3x² is 3

Given that,

The expression is 3x²

To find : The coefficient of the variable x² in the expression

Coefficient is the number that is beside the variable in the equation.

The coefficient of x in 3x²  is 3

A number multiplied by a variable is referred to as the coefficient of a number. For instance, the x2 coefficient in the formula 6x2+99 is 6

As we can see that the term that is in multiplication with x²  is 3.

Hence, the coefficient of x²  in the equation 3x²  is 3.

To learn more about the coefficient click here:

brainly.com/question/28975079

#SPJ4

The vertical asymptote of X 4 is x = 4, which means that as x approaches 4, the function approaches infinity.

The vertical asymptote of a function is an x-value at which the function tends to approach infinity. In the case of X 4, the vertical asymptote is x = 4. This means that as x approaches 4, the function X 4 approaches infinity. This can be seen by examining the function. As x approaches 4 from the left, the denominator of X 4 becomes increasingly small while the numerator remains constant. This means that the function's value becomes increasingly large as x approaches 4, eventually resulting in an infinite value. In the same way, as x approaches 4 from the right, the denominator of X 4 becomes increasingly large while the numerator remains constant. This means that the function's value becomes increasingly small, eventually resulting in an infinite value. Thus, the vertical asymptote of X 4 is x = 4.

Learn more about function here

https://brainly.com/question/29633660

#SPJ4

The probability that the mean time for the sample of 100 returns for this year is greater than 92 is 0.0764.

The term probability in math refers the possibility of occurring the event.

Here we have given that Bones brothers & associates prepare individual tax returns. Over prior years, bones brothers has maintained careful records regarding the time to prepare a return.

And we need to find the probability that the mean time for the sample of 100 returns for this year is greater than 92

As per the given question, we know the following values,

=> mean,μ=90

=> population standard deviation,σ=14

=> sample size ,n=100

Then the standard error is 1.4

Therefore, the z value is obtained by the z table is 0.9236.

Then the resulting probability is calculated.

=> 1 - 0.9236

=> 0.0764

To know more about Probability here

https://brainly.com/question/11234923

#SPJ4

Answer: 270 is the answer

Step-by-step explanation:

Answer:

(9) x = 9

(10) I cannot see the image clearly, sorry :(

(11) x = 54

(12) I cannot see the image clearly, sorry :(

(13) ∠P = 64°

(14) ∠Q = 26°

(15) ∠U = 47°

(16) ∠W = 43°

Step-by-step explanation:

(9)

To find an unknown side length in a right triangle, we need to use a trigonometric function.

⭐ What is a trigonometric function?

⭐ What are the trigonometric functions?

To determine which trigonometric function to use, we need to see which type of side lengths we are given (hypotenuse/opposite/adjacent).

We are given side length x, which is opposite of the 37 degrees, and side length 15, which is the hypotenuse of the triangle. Therefore, we will use sin(θ).

Substitute the angle measure we are given and the side lengths into sin(θ).

[tex]sin(37) = \frac{x}{15}[/tex]

[tex]15sin(37) = x[/tex]

Compute this equation into a scientific calculator. I recommend using the Desmos Scientific Calculator.

[tex]9.0 = x[/tex]

(10) I'd need to see x clearly to solve.

(11) To find an unknown side length in a right triangle, we need to use a trigonometric function.

⭐ What is a trigonometric function?

⭐ What are the trigonometric functions?

To determine which trigonometric function to use, we need to see which type of side lengths we are given (hypotenuse/opposite/adjacent).

We are given side length x, which is the hypotenuse of the triangle, and side length 14, which is adjacent to the 75 degrees. Therefore, we will use cos(θ).

Substitute the angle measure we are given and the side lengths into cos(θ).

[tex]cos(75) = \frac{14}{x}[/tex]

[tex]\frac{14}{cos(75)} = x[/tex]

Compute this equation into a scientific calculator. I recommend using the Desmos Scientific Calculator.

[tex]54 = x[/tex]

(12) I'd need to see x clearly to solve.

(13) To find the angle measure of an angle in a right angle triangle, we need to use the inverses of the trigonometric functions.

⭐ What are the inverses of the trigonometric functions?

First, we need to see the type of side lengths we are given (adjacent/hypotenuse/opposite) to determine which inverse trigonometric function we use for each angle.

∠P is adjacent to side length 8, and side length 18 is the hypotenuse of the triangle. Therefore, we will use [tex]cos^-1(adjacent/hypotenuse) =[/tex].

Substitute the side lengths and compute using a scientific calculator. I recommend using the Desmos Scientific Calculator.

[tex]cos^-1(\frac{8}{18})[/tex]

∴ ∠P = 64°

(14) To find the angle measure of an angle in a right angle triangle, we need to use the inverses of the trigonometric functions.

∠Q is opposite of side length 8, and side length 18 is the hypotenuse of the triangle. Therefore, we will use [tex]sin^-1(opposite/hypotenuse) =[/tex].

Substitute the side lengths and compute using a scientific calculator.

[tex]sin^-1(\frac{8}{18})[/tex]

∴ ∠Q = 26°

(15) To find the angle measure of an angle in a right angle triangle, we need to use the inverses of the trigonometric functions.

∠U is opposite of side length 11, and side length 15 is the hypotenuse of the triangle. Therefore, we will use [tex]sin^-1(opposite/hypotenuse) =[/tex].

Substitute the side lengths and compute using a scientific calculator.

[tex]sin^-1(\frac{11}{15})[/tex]

∴ ∠Q = 47°

(16) To find the angle measure of an angle in a right angle triangle, we need to use the inverses of the trigonometric functions.

∠W is adjacent to side length 11, and side length 15 is the hypotenuse of the triangle. Therefore, we will use [tex]cos^-1(adjacent/hypotenuse) =[/tex].

Substitute the side lengths and compute using a scientific calculator.

[tex]cos^-1(\frac{11}{15})[/tex]

∴ ∠W = 43°