The ratio of triangle BOY to triangle GRL is 1:2. If BO=x+3 and GRL=3x-1, then the length of GR is

explain the math behind it please and thank you

A.5
B.7
C.10
D.20

Answers

Answer 1

Answer: B. 7

The ratio of the two triangles indicates that BOY is 1/2 the size of GRL. Therefore, the ratio of the sides of the triangles is also 1:2. Since the length of BO is given as x + 3, this means that the length of GR must be 2(x + 3) - 1 = 2x + 5. Therefore, the length of GR is 7.


Related Questions

Select a counter-example that makes the conclusion false. 7 - 3 = 4, 8 - 5 = 3, 9 - 8 = 1 Conclusion: the difference of two positive numbers is always positive. Counterexample:

Answers

Counter example:

3 - 7 = -4

5 - 8 = -3

8 -9 = -1

Conclusion: the difference between two positive numbers can also be a negative number.

What is meant by negative numbers?

Given are given a set of difference of positive numbers.

7 - 3 = 4

8 - 5 = 3

9 - 8 = 1

The conclusion for this difference is given as the difference between two positive numbers is always positive.

We are asked to give a counter example.

Now a counterexample means an example that makes the given conclusion invalid.

So the counterexample of given example would be to prove the difference between positive numbers can also be a negative number.

For example,

3 - 7 = -4

5 - 8 = -3

8 -9 = -1

Therefore using the same numbers but subtracting the larger numbers from smaller number, we proved that the difference between positive numbers can also be a negative number.

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a pilot is plying over a straight highway. He determines the angles of depression to two mileposts to be 32 degrees and 56 degrees. The pilot is flying at an altitude of 25,00ft. Find the distance between the two points

Answers

The distance between the two points, we can use the trigonometric equation distance = altitude/tan(angle of depression). Using this equation, we can calculate the distance to be approximately  6,665.93 ft.

Pilot is at point A. The angles of depression to mileposts B and C are 32 degrees and 56 degrees, respectively. We are asked to find the distance between B and C.

Let AB = x, BC = y, and AD = CD = h = 25,000 ft.

tan(32°) = h/AB

tan(56°) = h/AC = h/(AB + BC)

We can use the first equation to solve for AB:

AB = h/tan(32°) = 25,000/tan(32°) ≈ 44,908.55 ft

We can use the second equation to solve for AC:

tan(56°) = h/(AB + BC)

tan(56°) = 25,000/(AB + BC)

AB + BC = 25,000/tan(56°)

BC = 25,000/tan(56°) - AB ≈ 38,242.62 ft

Therefore, the distance between the two mileposts is:

BC ≈ 38,242.62 - 44,908.55 ≈ 6,665.93 ft

So the distance between the two mileposts is approximately 6,665.93 ft.

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Solve the system of equations below using a method of your choosing.

help please

Answers

The solution to the system of equations is x = 5 and y = -2, or (5,-2) in coordinate form.

Describe Equation?

An equation is a mathematical statement that shows that two expressions are equal. It is usually written as an expression on the left-hand side (LHS) and an expression on the right-hand side (RHS) separated by an equal sign (=).

The expressions on both sides of the equation can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The variables in an equation represent unknown values that can vary, while the constants are fixed values that do not change.

Equations are used to represent mathematical relationships or describe real-world situations. They can be used to solve problems, make predictions, and test hypotheses.

To solve an equation, one must find the value of the variable that makes the LHS equal to the RHS. This is done by performing mathematical operations on both sides of the equation to isolate the variable. The goal is to get the variable by itself on one side of the equation, with a specific value on the other side.

Equations can be simple or complex, linear or nonlinear, and can involve one or more variables. Examples of equations include:

2x + 5 = 13

y = 3x^2 - 2x + 7

4a + 2b - 3c = 10

Equations are used in many areas of mathematics and science, including physics, chemistry, and engineering, among others.

Substitute the value of y in the second equation with the expression for y from the first equation:

2x + 3(4x-22) = 4

Simplify and solve for x:

2x + 12x - 66 = 4

14x = 70

x = 5

Substitute the value of x in the first equation to solve for y:

y = 4(5) - 22

y = -2

Therefore, the solution to the system of equations is x = 5 and y = -2, or (5,-2) in coordinate form.

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help me plsssssssssssss

Answers

Answer: i think its 40

Step-by-step explanation: because triangles in general are supposed to have the angle 180 and 40 add 400 add 100 equals 180

why is 41 a prime number ?

Answers

The number 41 is a prime number because it can be divided only by the number one and itself to yield remainder zero.

A prime number is defined as the number which is an integer, greater than one and has the ability to divide only by one and the number itself. The division here indicates that remainder should be zero.

Now, we see that 41 is an integer and it is greater than one. Additionally, it can not be divided by other numbers expect one and itself. These reasons make 41 a prime number.

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how to find point of inflection

Answers

To find a point of inflection, take the second derivative of the function, set it equal to zero and solve for x, and verify the point by checking the sign of the second derivative on either side of the point.

Follow these steps to locate a point of inflection:

Take the function's second derivative. The derivative of the first derivative is the second derivative. This will give you the concavity of the function.Put the second derivative to zero and find x. This will show you where the concavity changes.At this stage, check to see if the sign of the second derivative changes. The point is a point of inflection if the second derivative is positive to the left of the point and negative to the right of the point. The point is not an inflection point if the sign of the second derivative does not change.Check the concavity of the curve on each side of the point to verify it.

It is a point of inflection if the curve shifts from concave up to concave down at the point. It is also a point of inflection if it transitions from concave down to concave up.

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A biased four-sided die with faces labelled 1, 2,3 and 4 is rolled and recorded. Let be the
result obtained when the die is rolled. The probability distribution for is given in the
following table where p and are constants(Found value of p and q they are 0/4 and 0.6 respectively)

Answers

The required values are;

q = 09.2 and p = 0.4.

And P(X > 2) = 0.3

What is the probability?

The possibility of an event in time is known as probability in mathematics. How frequently does the incidence occur over the course of a specific time period, in plain English?

Given:

A die labeled 1, 2. 3, and 4 is rolled.

The total probability is 1.

∑P (X = x) = 1>

Which is,

p + 0.3 + q + 0.1 = 1  

p + q = 0.6  {equation 1}

And E(X) = 2  {equation 2}

(1 x p) + (2 x 0.3) + (3 x q) + (4 x 0.1) = 2   {equation 3}

p + 0.6 + 3q + 0.4 = 2   {equation 4}

p + 3q = 1    {equation 5}.

Solving 3 and 5,

we get,

q = 09.2 and p = 0.4.

And P(X > 2) = 0.2 + 0.1 = 0.3.

Therefore, P(X > 2) = 0.3.

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how far is san antonio from dallas

Answers

Dallas and San Antonio, Texas are separated by approximately 240 miles (386 kilometres) by road. The predicted journey time is around 4 hours, although this may vary based on traffic and other conditions.

Dallas is located in Texas, in the country's southern central area. It is the ninth-largest city in the United States and the third-largest in Texas in terms of population. Dallas is part of the Dallas-Fort Worth metropolitan area, which is one of the largest in the United States. Dallas, in North Texas, is surrounded by a variety of suburban towns. Dallas and San Antonio are approximately 240 miles apart.

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4. What is the magnitude and direction of MN with tail and head points M(-3,-2) and N(4,0)?
7.3 units, 15.9° south of west
O 7.3 units, 15.9° north of east
6.4 units, 74.1° north of east
O 6.4 units, 74.1° south of west

Answers

The magnitude and direction of the vector is 7.3 units and 15.9° north of east respectively.

option B.

What is the magnitude and direction of the vector?

To find the magnitude and direction of MN, we can use the distance formula and trigonometry.

The distance formula is:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Using the coordinates of M(-3,-2) and N(4,0), we get:

d = √((4 - (-3))² + (0 - (-2))²)

d = √(49 + 4)

d = √(53)

d ≈ 7.3 units

To find the direction, we can use trigonometry. We can first find the angle between the line and the positive x-axis using:

tan θ = (y₂ - y₁)/(x₂ - x₁)

tan θ = (0 - (-2))/(4 - (-3))

tan θ = 2/7

θ = arc tan (2/7) =  15.9°

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A store is having a sale on almonds and jelly beans today. The table below shows the amount of each type of food (in pounds) and the total cost (in dollars) of
two purchases today.
First
purchase
Second
purchase
Amount of
almonds
(In pounds)
3
12
Amount of
jelly beans
(In pounds)
5
2
Total cost
(in dollars)
17
23
O

Answers

Cost for each pound of almonds is $1.5 and cost for each pound of jelly beans is $2.5.

What is a System of Linear Equations?

Linear equations involve one or more expressions including variables and constants and the highest exponent of the variable is 1.

System of linear equations involve two or more linear equations.

Let x be the cost of each pound of almond and y be the cost of each pound of jelly beans.

Then from the first purchase, we have the equation,

3x + 5y = 17

Similarly, from the second purchase, we have,

12x + 2y = 23

So the system of equations are

3x + 5y = 17 and 12x + 2y = 23

Solving these, we will get the values of x and y which is the cost of each pound of almond and jelly beans.

3x + 5y = 17

12x + 2y = 23

Multiplying the first equation with 4, we get,

12x + 20y = 68

Subtracting 12x + 2y = 23 from 12x + 20y = 68,

18y = 45

y = $2.5

Substituting y = 2.5 in any of the equation above, we get,

x = $1.5

Hence the cost for each pound of almond and jelly beans are $1.5 and $2.5 respectively.

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Graph the following features: Slope = −2 Y-intercept = 6

Answers

Answer and Step-by-step explanation:

To graph the equation with a slope of -2 and a y-intercept of 6, we can use the slope-intercept form of the equation of a line, which is:

y = mx + b

where m is the slope and b is the y-intercept.

Substituting in the given values, we get:

y = -2x + 6

To graph this line, we can start by plotting the y-intercept, which is the point (0, 6). Then, we can use the slope to find additional points on the line. The slope of -2 means that for every increase of 1 in the x-direction, the y-value decreases by 2. So, we can plot another point by starting at the y-intercept and moving down 2 units and to the right 1 unit. This gives us the point (1, 4). We can continue this pattern to plot more points and draw the line.

Here's what the graph looks like:

Step-by-step explanation:

We are given the slope -2 and the y intercept -6. So we can create a linear equation using this data:

[tex]y=-2x+6[/tex]

Now all we have to do is graph it.

(graph below)

the average height for 14 year old boy is

Answers

According to the Centers for Disease Control and Prevention (CDC) growth charts, the average height for a 14-year-old guy in the United States is about 5 feet, 5 inches (165 cm). Some 14-year-old guys may be taller or shorter than the average.

Height is a measure of the distance between the base of an object and its highest point. Human height is commonly described as the vertical distance between the bottom of the feet and the top of the head. Height is generally measured in centimetres or feet and inches. Height is an important physical feature that can be influenced by both inherited and environmental factors such as nutrition and physical activity.

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what is the rectangular form of 6(cos(225o) i sin(225o))? negative 3 startroot 2 endroot minus 3 startroot 2 endroot i negative 3 startroot 2 endroot 3 startroot 2 endroot i 3 startroot 2 endroot minus 3 startroot 2 endroot i

Answers

The rectangular form of 6{(cos225°) +i(sin225°) }is -3√2-3i√2.The shape that complex numbers typically take is referred to as rectangle form: z = a + bi.

What are polar form and rectangular form?

Polar notation depicts a complex number in terms of the lengths of the vector and the angular direction from the starting point. In rectangle notation, a complex number is represented by its vertical and horizontal dimensions. The system is referred to be rectangular because the angles made by the axes at the origin and the measurements at point p are both 90 degrees. As a result, the measurement results in a rectangle with sides Xp and Yp.

To determine  rectangular form, we obtain,

Let Z=6{(cos225°) +i(sin225°)}

Now, cos225°=-cos( 180°+45°)= -cos45°= -[tex]\frac{1}{√2}[/tex]

sin225°=-[tex]\frac{1}{√2}[/tex]

S0, 6{(cos225°) +i(sin225°)}= 6 ( -[tex]\frac{1}{√2}[/tex])+6i(-[tex]\frac{1}{√2}[/tex])=-3√2-3i√2.

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Answer:

A

Step-by-step explanation:

right on edge

how to convert 300m to feet?

Answers

By knowing the conversion factors, we can easily and accurately convert measurements to any unit we desire. In this case, 300m is equal to 984.252 feet.

Measurement conversions are an important aspect of mathematical calculations. They help us convert units of measurement to another, making it easier to compare and understand quantities. In this case, we will look at how to convert 300m to feet.

To convert 300m to feet, we need to know the conversion factor between the two units of measurement. One meter is equal to 3.28084 feet. Therefore, to convert 300m to feet, we need to multiply 300 by the conversion factor.

300m * 3.28084 = 984.252 feet

Therefore, 300m is equivalent to 984.252 feet.

It's important to note that when converting between units of measurement, it's important to use the correct conversion factor to ensure accurate results. Additionally, being familiar with common conversion factors can save time and make calculations easier.

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what is 187cm in feet?

Answers

187 centimeter is approximately equal to 6.1351 feet

To convert 185cm to feet, we can use the following formula:

1 cm = 0.0328 feet

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

Therefore,

The distance in feet = conversion factor × The distance in centimeter

Substitute the values in the equation

187 cm = 187 x 0.0328

Multiply the numbers

= 6.1351 feet ( rounded to four decimal places )

Therefore, 187 cm is 6.13517 feet.

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roll a six sided number cube 25 times and record the number of 4s that you observe

Answers

i think it would be 1/6 × 25 = 25/6 = 4 1/6in roll the likely chance of u observing a 4 is 1/6 so you would do 1/6 × 25 since you are rolling the dice 25 times

what are the steps i need to learn to answer this question and what is this specific problem named.

Answers

To change a mixed number to an improper fraction multiply the denominator by the whole number, and then add the numerator.
(-2 1/2) is 2x2+1 —> 5/2

(-1 3/5) is 5x1 +3 —> 8/5

(-5/2)(-8/5) = 40/10 simplify 4/1 which equals to 4
IT’s positive because negative times negative gives you positive
(-)(-)= +
(+)(+)= +
(-)(+) = -

Which could be the function?

f(x) = (x + 4)2
f(x) = x2 + 4
f(x) = (x – 4)2
f(x) = x2 – 4

Answers

All of the given expressions are functions, but the first three are quadratic functions, while the last one is a quadratic function with a negative constant term.

What is the function?

A function is a mathematical relationship between two variables, where each input value (independent variable) corresponds to exactly one output value (dependent variable). It is often represented using a formula or equation.

All of the given expressions are functions, but the first three are quadratic functions, while the last one is a quadratic function with a negative constant term.

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Homework 6: surface area of pyramids & cones

Answers

The surface area of a square base pyramid is 696.96 cm².

The surface area of the cone is 353.43 mm².

What is the surface area of the squared base pyramid?

The surface area of a square base pyramid is calculated by applying the following formula as shown below;

SA = 2bs + b²

where;

b is the base of the pyramids is the height of the triangular face

let the half of the base = x

Apply Pythagoras theorem to determine the value of x using the given heights of the right triangles

x = √ ( 17² - 15.4² )

x = 7.2 cm

The base of the pyramid = 2x = 2 (7.2 cm ) = 14.4 cm

SA = 2 x 14.4 x 17  +  ( 14.4)²

SA = 696.96 cm²

The surface area of the cone is calculated as follows;

SA = πrs + πr²

where;

r is the radius = 9mm/2 = 4.5 mms is the slant height

The slant height of the cone is calculated as follows;

s = √ (4.5²  +  20² )

s = 20.5 mm

SA = π x 4.5 x 20.5   +   π(4.5²)

SA = 353.43 mm²

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A quantity x is a least 10 and at most 20.

Answers

Answer:

10<=x <= 20

Step-by-step explanation:

Sorry but <= means less that or equal to.

What’s the answer? I gotta do it before I make bad grade

Answers

4/90 is the answer you need before u make it bad

50 sutdents went on a filed trip 23 stundets wore hats how what percent of people did not were hats

Answers

54% of the students did not wear hats on the field trip.

What is percentage ?

Percentage is a way of expressing a quantity as a fraction of 100. It is often denoted by the symbol "%". For example, if you say that something has a percentage of 50%, it means that 50 out of every 100 parts of that thing belong to the quantity being measured.

According to given condition :

To find out what percentage of people did not wear hats, we first need to find out how many of the 50 students did not wear hats.

If 23 students wore hats, then the number of students who did not wear hats is:

50 - 23 = 27

So 27 students did not wear hats. To express this as a percentage, we divide the number of students who did not wear hats by the total number of students and then multiply by 100:

(27/50) x 100 = 54%

Therefore, 54% of the students did not wear hats on the field trip.

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it is impossible to get 8 aces when selecting cards from a shuffled deck. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive. The probability is

Answers

It is not possible to get 8 aces from a standard 52 cards deck. The indicated degree of likelihood as a probability value is 0 (Zero).

The procedure for probability states that the possibility of an occurrence occurring, or P(E), equals the proportion of the number of favorable outcomes to the number of total outcomes.

Mathematically,

Possibility (E) = favorable outcomes/total outcomes.

We know that there are four aces in total in a 52-card deck.

Therefore the probability of getting 8 aces can be expressed by using the factorial of the number. This can result in a decrease of numbers by multiplying the previous number, this is called the factorial of a number.

P(8A) = 7/52 × 6/51 × 5/50 × 4/49 × 3/48 × 2/47 × 1/46 × 0/45

P(8A) = 0

The probability of getting is zero.

Therefore, it is not possible to get 8 aces from a standard 52 cards deck.

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how to convert 250 grams to pounds?

Answers

250 grams is approximately equal to 0.5511 pounds  ( rounded to four decimal places )

The conversion factor to convert grams to pounds is 0.00220462

1 gram = 0.00220462 pounds

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

The mass in pounds = The mass in grams × conversion factor

Substitute the values in the equation

1 gram = 0.00220462 pounds

250 grams =  250 × 0.00220462

Multiply the numbers

= 0.5511 pounds  ( rounded to four decimal places )

Therefore, 250 grams is 0.5511 pounds

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Kourtney accrued $1,375 after 6 months. If she deposited 50,000 at the start what was the interest rate? PLS I NEED HELP ASAP

Answers

Answer: r = 5.5%

Step-by-step explanation:

6/12 = 0.5 (years)

(I=Prt) || 1375 = 50000 * r * 0.5

1375 = 25000r

1375/25000 = 25000r/25000

0.055 = r

0.055 * 100% = r

5.5% = r

(Please correct me if I'm wrong)

Mei Mei spots an airplane on radar that is currently approaching in a straight line, and that will fly directly overhead. The plane maintains a constant altitude of 6350 feet. Mei Mei initially measures an angle of elevation of 17 to the plane at point A. At some later time, she measures an angle of elevation of 36 to the plane at point B. Find the distance the plane traveled from point A to point B. Round your answer to the nearest foot if necessary.

Answers

The distance between points A and B is 11785.2 ft.

What is algebraic expression?                      

In mathematics, an algebraic expression is an expression built up from constant algebraic numbers, variables, and the algebraic operations.

Given is that the plane maintains a constant altitude of 6350 feet. Mei Mei initially measures an angle of elevation of 17° to the plane at point A. At some later time, she measures an angle of elevation of 36° to the plane at point B.

We can write -

tan (17°) = 6350/AC

tan (36°) = 6350/BC

Now, we can write -

AC = 6350/tan (17°)                                ... { 1 }

AC = 20483.9 ft

&

BC = 6350/tan (36°)                              ... { 2 }

BC = 8698.7 ft

We can write -

AB = AC - BC                                        ... { 3 }

AB =  20483.9 - 8698.7

AB = 11785.2 ft

Therefore, the distance between points A and B is 11785.2 ft.

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Sergio had $500.00 saved for a family trip. Six weeks later he had saved $860.00. At what rate of change did Sergio savings grow

Answers

Sergio saved at a rate of change of 34.4% when he had $500 saved for a family vacation.

what is unitary method ?

The component technique is a technique of troubles where you first calculate the worth of a single item, then multiply a certain value to get the answer. Simply defined, a single product value is extracted from either a specified multiple using the one method. For contrast, 40 pens will costs you 400 rs, or $1.01. The method used to execute this might be regulated. a solitary nation. anything seems to have a distinctive component.  (Classic Algebra, Quantitative Analysis, Math and science of Matrix or Operators).

given

1% of $500 = $5

Total Saving from $500 to $ 860

860 / 5 = 172

Now percentage of growth :-

172/500 *100

17200/500 = 34.4

Hence, the rate of change Sergio savings = 34.4%

Sergio saved at a rate of change of 34.4% when he had $500 saved for a family vacation.

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The present age of a mother is 3 times that of her daughter. If 6 years ago, the mother's age was 4 times the daughter's age, find the present age of the daughter.

Answers

Answer: 20

Step-by-step explanation:

a + b = 60.

a - 6 = 5b - 30 or a = 5b - 24

a = 60 - b

60 - b = 5 b - 24

84 = 6b

b = 14

a = 46

Mother is 46 and daughter is 14 now. After 6 years, daughter will be 20.

Hope this helped you, And if possible, could I have brainliest?

I also answered first! :D (Please don't copy what I said for the people that are going to answer this question, thank you!) :D

During a sale at the electronics store, movies sold out for 2 dollars and cd’s sold out for 1. 50 she bought a total of 5 movies and cds how many of each did she buy

Answers

She bought three movies and four CD,s and this can be found by doing sum.

we given that price for each movie= 3$.

price for each CD = 2.50$.

The total movies and CD,s bought= 7.

Total dollars spent by her = 19$.

Therefore, the number of movies bought= 3+3+3= 9. ( No. of movies= 3).

similarly, the number of CD,s bought= 2.5+2.5+2.5+2.5= 10.( No. of CD,s= 4).

Hence, out of 19$ , 10 dollars were spent to buy CD,s and the other 9 dollars were spent to buy movies.

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Complete question:- During a sale at the electronics store, movies sold for $3 and CDs sold for $2.50. Isla spent $19 and bought a total of 7 movies and CDs. How many of each did she buy?

Please help!!!

Given that angles A and B both lie between 0 and 360, and that sin A and cos B are both negative, find the values between which A + B must lie.

Answers

Answer:

A + B must lie between 90 and 450 degrees.

Explanation:

Since sin A and cos B are both negative, A and B must lie in the third quadrant or the fourth quadrant. In the third quadrant, sin A and cos B are both negative, while in the fourth quadrant, sin A is negative and cos B is positive.

Let's consider the case where A and B are both in the third quadrant. In this case, both A and B are between 180 and 270 degrees. Since A + B is the sum of two angles in this range, it follows that A + B must be between 360 and 450 degrees.

Now let's consider the case where A is in the fourth quadrant and B is in the third quadrant. In this case, A is between 270 and 360 degrees, while B is between 180 and 270 degrees. Since sin A is negative and cos B is positive, it follows that cos A and sin B are both negative. Using the identities sin(180 - x) = sin x and cos(180 - x) = -cos x, we can write:

sin A + cos B = sin(180 - (180 - A) - B) + cos(180 - (180 - A) - B)

= sin(180 - A) - cos(180 - B)

= -sin A - cos B

Therefore, A + B is the difference of two angles in the third quadrant, and it must be between 90 and 180 degrees.

Putting the two cases together, we see that A + B must lie between 90 and 450 degrees.

Other Questions
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