solve each system using substitution
y=1/2x+4
x-y=8

Answers

Answer 1

We are given the following system of equations:

y = (1/2)x + 4 ---(1)

x - y = 8 ---(2)

We can solve this system of equations by substitution method.

From equation (2), we have:

x - y = 8

Solving for x, we get:

x = y + 8

Substitute this value of x in equation (1):

y = (1/2)(y+8) + 4

Simplifying and solving for y, we get:

y = 2

Now, substitute this value of y back in equation (2) to find the value of x:

x - 2 = 8

x = 10

Therefore, the solution of the given system of equations is (x, y) = (10, 2).


Related Questions

Lori is 8 years old. In 5 ​years, her cousin Philip will be twice as old as Lori will be. Write the ratio of​ Philip's age now to​ Lori's age now.

Answers

Answer: 13:26

Step-by-step explanation:

8 + 5 = 13. Philip will be twice as old as Lori will be.

13 x 2 = 26

So, the ratio will be 13:26

Hope this helps!


13:26 is the ratio of Phillips age now to Loris age now

A skateboard ramp is 4.1 feet high and 6 feet long along the horizontal. To the nearest
tenth of a degree, what is the measure of the angle that the ramp makes with a
horizontal line?
34.3°
55.7°
90°
46.9⁰

Answers

Answer: :)

Step-by-step explanation:

To find the angle that the ramp makes with a horizontal line, we need to use trigonometry. The angle we are looking for is the angle between the ramp and the ground, which is the same as the angle between the hypotenuse of a right triangle (the ramp) and its adjacent side (the ground).

We can use the tangent function to find this angle:

tan(theta) = opposite/adjacent

In this case, the opposite side is the height of the ramp (4.1 feet) and the adjacent side is the length of the ramp along the ground (6 feet). So we have:

tan(theta) = 4.1/6

Using a calculator, we can solve for theta:

theta = tan^-1(4.1/6)

theta ≈ 34.3°

Therefore, to the nearest tenth of a degree, the measure of the angle that the ramp makes with a horizontal line is 34.3°.

Review the graph of function f(x). On a coordinate plane, a graph approaches x = negative 3 in quadrant 2, has inflection point (negative 1, 0) and approaches x = 1 in quadrant 4. A graph approaches x = 1 in quadrant 1, and curves down and approaches the x-axis in quadrant 1. Which statement describes Limit of f (x) as x approaches 1?

Answers

The correct statement regarding the limit of f(x) as x -> 1 is given as follows:

lim x -> 1 f(x) = -∞.

How to calculate the lateral limits?

To obtain lateral limits, we need to take the limit of a function as it approaches a point from the left-hand side and the right-hand side separately.

If the two limits are equal, then this is the limit of the function, while if the lateral limits are different, then the limit of the function does not exist for the value of x.

From quadrant 2, the function approaches x = 1 on quadrant 4, hence the limit to the left is given as follows:

lim x -> 1^- f(x) = -∞.

A graph approaches x = 1 in quadrant 1, and curves down and approaches the x-axis in quadrant 1, hence the limit to the right is given as follows:

lim x -> 1^+ f(x) = -∞.

As the lateral limits are equal, the limit of the function is given as follows:

lim x -> 1 f(x) = -∞.

Missing Information

The problem describes the graph of the function.

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PLS HELP- A satellite can move at 17,000 miles per hour. How many hours will it take to reach a star that is three light years away? Recall that 1 light year = 9.5 ∙ 1012 kilometers and 1 kilometer = 0.62 miles. Show your work.

Answers

Answer:

3.465 x 10⁸ hours

or

346,500,000 hours

Step-by-step explanation:

Distance to travel to star = 9.5 x 10¹² kilometers

1 kilometer = 0.62mile

Therefore

9.5 x 10¹² km = 9.5 x x 10¹ x 0.6 miles
= 5.89 x 10¹² miles

Speed of satellite = 17,000 mph

In scientific notation
17,000 = 17 x 10³ = 1.7 x 10⁴ mph

Time taken to reach star at distance of 5.89 x 10¹² miles

= 5.89 x 10¹² miles/1.7 x 10⁴ mph = 5.89/1.7  x 10¹²/10⁴

= 3.465 x 10¹²⁻⁴

= 3.465 x 10⁸ hours

= 346,500,000 hours

Write the equation of the conic section shown below.

Answers

The equation of the conic section shown below is x² + y² + 10x + 2y - 20 = 0

Describe Circle?

A circle is a two-dimensional geometric shape that consists of a set of points in a plane that are equidistant from a fixed point called the center. The distance from the center to any point on the circle is called the radius.

A circle can be defined by its center point and radius or by its circumference, which is the distance around the perimeter of the circle. The circumference of a circle can be calculated using the formula:

C = 2πr

where C is the circumference, r is the radius, and π (pi) is a mathematical constant approximately equal to 3.14.

The center of the circle is (-5,-1) and its radius is the distance from the center to any point on the circle. Using the distance formula, we can find the radius:

r = √((0 - (-1))² + (-10 - (-5))²) = √(1 + 25) = √(26)

So, the equation of the circle in standard form is:

(x + 5)² + (y + 1)² = 26

Alternatively, in general form, it can be written as:

x² + y² + 10x + 2y - 20 = 0

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Domain
V
m
d
1 of 5 (1 point) | Question Attempt: 1 of 1
Relation 1
t
Function
O Not a function
O Function
Relation 3
Domain Range
d
pencil
sky
sky
sky
Not function.
b
V
N
Range
Domain
Z
X
y
k
O Function
O Not a function
Relation 2
Relation 4
Domain Range
3
-1
-6
-1
-5
4
7
-9
-1
2
Range help please ASAP

Answers

Answer:

A part of basic arithmetic, long division is a method of solving and finding the answer and remainder for division problems that involve numbers with at least two digits. Learning the basic steps of long division will allow you to divide numbers of any length, including both integers (positive,negative and zero) and decimals. This process is an easy one to learn, and the ability to do long division will help you sharpen and have more understanding of mathematics in ways that will be beneficial both in school and in other parts of your life.[1]

Step-by-step explanation:

A part of basic arithmetic, long division is a method of solving and finding the answer and remainder for division problems that involve numbers with at least two digits. Learning the basic steps of long division will allow you to divide numbers of any length, including both integers (positive,negative and zero) and decimals. This process is an easy one to learn, and the ability to do long division will help you sharpen and have more understanding of mathematics in ways that will be beneficial both in school and in other parts of your life.[1]

The graph shows the cube root parent function

Answers

The true statement is A, for x < 0 the function is negative.

Which statements describe the graph of the function?

On the image we can see the graph of the parent cube root function.

y = ∛x

And we want to see which statements are true. Remember that the function is negative if the graph is below the x-axis and positive if it is above, using that we can analyze the graph.

First, notice that for x < 0 the graph is below the x-axis, then the first statement is true.

When x < 0, the function is negative.

So the only correct option is A.

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Simplify the radical: √32x

(I understand how to simplify radicals I just don’t know how to do it with an unknown variable in it)

Answers

The expression when evaluated is 4√2x

How to evaluate the expression

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

√32x

Express 32 as the product of 16 and 2

So, we have

√32x = √(16 * 2x)

Take the LCM of 16

So, we have the following representation

√32x = 4√2x

Hence, the solution is 4√2x

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Solve for x 2x+3-4=10

Answers

Answer:

x = 5.5

Step-by-step explanation:

2x + 3 - 4 = 10

2x - 1 = 10

2x = 11

x = 5.5

Let's check

2(5.5) + 3 - 4 = 10

11 + 3 - 4  = 10

14 - 4 = 10

10 = 10

So, x = 5.5 is the correct answer.

Answer: x = 5.5

Step-by-step explanation:

To solve, we will isolate the variable x.

      Given:

             2x + 3 - 4 = 10

      Combine like terms on the left side:

             2x - 1 = 10

      Add 1 to both sides of the equation:

             2x = 11

      Divide both sides of the equation by 2:

             x = 5.5

Find the future value (in dollars) of a 2-year investment of $6,525 into a simple interest rate account that has an annual simple interest rate of 3.7%.

Answers

$7,008 is the future value of a 2-year investment of $6,525 into a simple interest rate account with an annual interest rate of 3.7%.

What is Percentage?

percentage, a relative value indicating hundredth parts of any quantity.

The formula to calculate the future value of an investment with simple interest is:

FV = P(1 + rt)

where FV is the future value, P is the principal amount, r is the annual interest rate expressed as a decimal, and t is the time period in years.

P = $6,525

r = 0.037

t = 2 years

Plugging these values into the formula, we get:

FV = $6,525(1 + 0.037×2)

FV = $6,525(1.074)

FV = $7,008.

Therefore, the future value of a 2-year investment of $6,525 into a simple interest rate account with an annual interest rate of 3.7% is $7,008.

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22. A small coffee company claims to include 11 ounces of coffee in every bag of ground coffee it produces. Out of a random sample of 250 bags, 50 of the bags contain only 10.9 ounces. Which inferences from the results of the random sample are reasonable? Choose all that are correct.

A. It can be inferred that 5% of the bags from a second random sample will contain more than 11 ounces.

B. It is likely that a second random sample of bags will show a much lower percentage of bags with only 10.9 ounces.

C. The percentage of all bags produced that contain less than 11 ounces is likely to fall between 15% and 25%.

D. It is likely that the company's claim is true because 20% of the bags in the sample contain 10.9 ounces.

E. It is unlikely that the company's claim is true because 20% of the bags in the sample contain 10.9 ounces.

Answers

From the percentage of the coffee bags with 10.9 ounces, we can see that it is unlikely that the company's claim is true because 20% of the bags in the sample contain 10.9 ounces.

What is meant by percentage?

A figure or ratio stated as a fraction of 100 is called a percentage. Frequently, it is indicated with the per cent sign, "%". If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage, therefore, refers to a component per hundred. Per 100 is what the word per cent means. As there is no unit of measurement for percentages, they are dimensionless numbers. This is because we divide numbers with the same units in percentage calculation.

Given,

Amount of coffee in A bag of ground coffee = 11 ounces

Number of bags = 250 bags

Number of bags which contain 10.9 ounces of coffee = 50

The percentage of bags which contain 10.9 ounces of coffee

= (50/250) × 100 = 20%

This percentage shows that the company's claim is not true because they claim every bag contains 11 ounces of coffee.

Therefore from the percentage of the coffee bags with 10.9 ounces, we can see that it is unlikely that the company's claim is true because 20% of the bags in the sample contain 10.9 ounces.

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solve: 5−3|x+8|=20
(multiple choice)

x= -5
No solution
x= -13
x= 8

Answers

the solutions are x = -13 and x = -5. So, the correct answer is (A) x = -5, x = -13.

What is algebraic Expression?

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Given an algebraic expression:

5 - 3|x + 8| = 20

First, we can begin by adding 3|x+8| to both sides of the equation, giving us:

5-20 = 3|x+8|

Simplifying the left-hand side, we get:

-15 = 3|x+8|

Next, we can divide both sides by 3, giving us:

-5 = |x+8|

Now we have an absolute value equation, which has two possible solutions depending on whether x+8 is positive or negative.

If x+8 is positive, then we have:

-5 = x+8

Solving for x, we get:

x = -13

If x+8 is negative, then we have:

-5 = -(x+8)

Solving for x, we get:

x = -5

Therefore, the solutions are x = -13 and x = -5. So, the correct answer is (A) x = -5, x = -13.

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A team with 8 games out of 12 games played. What is the reduced ratio of the following:
__________ 1. Win to games played?
__________ 2. Win to losses?
__________ 3. Loss to games played?

Answers

Therefore , the solution of the given problem of ratio comes out to be 1:3 is the decreased loss-to-games-played ratio.

Explain ratio.

A collection of integers "a" as well as "b" that seem to be equal can be defined using the straightforward fraction calculation "a / b," at which "b" may be larger than zero. A ratio is created by combining two ratios. The ration would be 1:1 if there were just one male and three women. There are 1/4 guys and 3/4 women in the group. Portions can be a divide between different things, a number, or a specific portion of the volume of a component.

Here,

In events played, win:

Out of the 12 games contested, 8 were victories. We can split the numerator and denominator by 4 to decrease the ratio:

=> 8/12 = 2/3

The decreased win-to-games-played ratio is 2:3.

win to loss ratio

If a squad has 8 victories, they have 4 defeats (since they have played 12 games in total). As a result, the winning/losing split is as follows:

8:4, which is further diminished by multiplying the number and denominator by 4:

=> 2:1

The decreased win-to-loss ratio is 2:1.

Played events lost:

If a squad has 4 losses and has played a total of 12 games, the ratio of losses to games played is as follows:

=> 4/12 = 1/3

=> 1:3 is the decreased loss-to-games-played ratio.

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please help i really need ittt!!!!!!!!!!!!!!!!!!!!!!!!!
A 2.5 m ramp is used to load a truck 1.0 m off of the ground. A man uses 600 N of force to load a box weighing 1200 N. What is the efficiency of the ramp? What is the mechanical advantage of the ramp?

Answers

Answer:

To find the efficiency of the ramp, we need to compare the work output to the work input. Work input is the force applied to the ramp multiplied by the distance over which the force is applied, and work output is the weight of the box multiplied by the distance it is lifted.

The force applied to the ramp is 600 N, and the distance over which it is applied is the length of the ramp, which is 2.5 m. So the work input is:

work input = force x distance = 600 N x 2.5 m = 1500 J

The weight of the box is 1200 N, and the distance it is lifted is 1.0 m (the height of the truck). So the work output is:

work output = weight x distance = 1200 N x 1.0 m = 1200 J

The efficiency of the ramp is the ratio of work output to work input:

efficiency = work output / work input = 1200 J / 1500 J = 0.8 = 80%

So the efficiency of the ramp is 80%.

To find the mechanical advantage of the ramp, we need to compare the output force to the input force. The output force is the weight of the box, which is 1200 N. The input force is the force applied to the ramp, which is 600 N.

So the mechanical advantage of the ramp is:

mechanical advantage = output force / input force = 1200 N / 600 N = 2

So the mechanical advantage of the ramp is 2.

Question 7
Type in the correct coordinates for the image after each reflection. WHEN YOU TYPE IT
IN... USE THE APPROPRIATE FORM. NO SPACES BETWEEN SYMBOLS AND NUMBERS.
USE PARENTHESIS.
Example: (2,-3)
Preimage
(1,5)
(-4,7)
(6,-2)
(-3,-8)
Reflect x-axis
(1,-5)
(4,-7)
(6,2)
(-3,8)
Reflect y-axis
(-1,5)
(4,7)
(-6,-2)
(3,-8)
Reflect yax
(5,1)
(7,-4)
(-2,6)
Iz pis
(-8,-3)

Answers

The coordinates of the image of the points following the reflection transformation can be presented as follows;

Preimage   [tex]{}[/tex] Reflect x-axis    Reflect y-axis    Reflect y = x

(1, 5)  [tex]{}[/tex]           (1, -5)                   (-1, 5)                 (5, 1)

(-4, 7) [tex]{}[/tex]          (-4, -7)                 (4, -7)                  (7, -4)

(6, -2)[tex]{}[/tex]           (6, 2)                   (-6, 2)                 (-2, 6)

(-3, -8) [tex]{}[/tex]         (-3, 8)                  (3, -8)                 (-8, -3)

What is a reflection transformation?

A reflection transformation is a transformation in which a preimage point is flipped across a line of reflection.

The coordinates of the image of the point (x, y), following a reflection across the x-axis is the point (x, -y)

The coordinates of the image of the point (x, y) following a reflection across the y-axis is the point (-x, y)

The coordinates of the image of the point (x, y) following a reflection across the line, y = x is the point (y, x)

The coordinates of the images of the specified points after the specified reflections are therefore;

The values in the table of the coordinates of the Preimages and images can therefore, be obtained as follows;

Preimage point (1, 5);

The image after a reflection across the x-axis is therefore;

(1, 5) [tex]\underrightarrow{R_{x-axis}}[/tex] (1, -5)

The image after a reflection across the y-axis, therefore;

(1, 5) [tex]\underrightarrow{R_{y-axis}}[/tex] (-1, 5)

The image after a reflection across the line y = x is therefore;

(1, 5) [tex]\underrightarrow{R_{y = x}}[/tex] (5, 1)

Preimage point (-4, 7);

The image after a reflection across the x-axis is therefore;

(-4, 7) [tex]\underrightarrow{R_{x-axis}}[/tex] (-4, -7)

The image after a reflection across the y-axis, therefore;

(-4, 7) [tex]\underrightarrow{R_{y-axis}}[/tex] (4, 7)

The image after a reflection across the line y = x is therefore;

(-4, 7) [tex]\underrightarrow{R_{y = x}}[/tex] (7, -4)

Preimage point (6, -2);

The image after a reflection across the x-axis is therefore;

(6, -2 [tex]\underrightarrow{R_{x-axis}}[/tex] (6, 2)

The image after a reflection across the y-axis, therefore;

(6, -2) [tex]\underrightarrow{R_{y-axis}}[/tex] (-6, -2)

The image after a reflection across the line y = x is therefore;

(6, -2) [tex]\underrightarrow{R_{y = x}}[/tex] (-2, 6)

Preimage point (-3, -8);

The image after a reflection across the x-axis is therefore;

(-3, -8) [tex]\underrightarrow{R_{x-axis}}[/tex] (-3, 8)

The image after a reflection across the y-axis, therefore;

(-3, -8) [tex]\underrightarrow{R_{y-axis}}[/tex] (3, -8)

The image after a reflection across the line y = x is therefore;

(-3, -8) [tex]\underrightarrow{R_{y = x}}[/tex] (-8, -3)

Please find above the completed table including the coordinates of the images following the reflection across the x, y-axis and the line y = x

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Find the value of x.

Answers

Answer: x = 60 degrees

Step-by-step explanation:

As we see, there is a 90 degree angle formed the top left corner. You divided it by 2 and it is formed by both triangles and u get 45 degrees.

Now, according to angle sum property:

angle A + Angle B + Angle C = 180 degrees

therefore, 75 + 45 + angle c = 180

and by linear equation , angle c = 180 - [75 + 45]

                                                       =  180 -120

                                                       = 60

therefore, x = 60

Answer:

60 degrees

Step-by-step explanation:

A right triangle is 180 degrees. 60+75+a= 180degrees. It shows a right angle, with a line right at the middle. half of 90 is 45, so put that in the equation and you get 60+75+45=180 degrees. to solve for ? you want to take 45 + 75 + ? = 180 degrees 45 plus 74 is 135 so take 180-135 is 60. the ? will be 60 degrees.

I hope this helps : )

At a restaurant any slice of pizza cost $250 the restaurant is serving pepperoni and sausage pizza which expression represents the cost of x number of pepperoni slices and wine number of sausage slices of pizza

Answers

Assuming that a slice of pizza costs the same regardless of its topping, the expression that represents the cost of x number of pepperoni slices and y number of sausage slices of pizza would be:

$250 * (x + y)

Here, (x + y) represents the total number of slices of pizza ordered, and multiplying by $250 gives the total cost of the order in dollars.

help pls with my homework​

Answers

Answer:

300.20

Step-by-step explanation:

because it was a nice guesss

The faunal exam scores in a statistics class were normally distributed with a mean of 63 And a standard deviation of 5 . Find the probability that a randomly selected students scored of then 65 on the exam

Answers

Probability that a randomly selected students scored of then 65 on the  faunal exam is 65.54%.

Explain about the normal distribution?An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range while the remaining ones taper off symmetrically towards either the extreme. The distribution's mean is another name for the center of the range.

mean μ = 63

standard deviation  σ = 5

x = 65

Find z-score:

z = (x - μ)/σ

z = (65 - 63)/5

z = 2/5

z = 0.4

Using z score table:

Probability that a randomly selected students scored of then 65 on the  faunal exam is :

P(x = 65) = P(z = 0.4)

P(x = 65) = 0.6554

Thus, Probability that a randomly selected students scored of then 65 on the  faunal exam is 65.54%.

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Please help I only have part A incorrect I can’t figure it out

Answers

By similarity ratio of triangles, we have;

ΔPQR ∼ ΔPSR ∼ ΔRSQ

PS/PR = PR/PQ

PQ/RQ = RQ/SQ

How to solve similar triangles?

Similar triangles are defined as triangles that have the same shape, but their sizes may vary. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

Thus, applying the concept of similar triangle ratio we can say that;

ΔPQR ∼ ΔPSR ∼ ΔRSQ

Similarly, by similarity ratio of triangles, we have;

PS/PR = PR/PQ

We also have;

PQ/RQ = RQ/SQ

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3.
A bag contains:
• 5 red marbles
.
6 blue marbles
3 green marbles

4 black marbles
2 yellow marbles
A marble will be drawn from the bag and replaced. If the experiment is repeated 100
times, what is a reasonable prediction for the number of times a green or black
marble will be drawn?

Answers

Answer:

300

Step-by-step explanation:

because you do it for 1 hundred years you multiply it by 100 and it would be 3x100=300

A family is considering selling a four-wheeler they had purchased for $8,200. They discover that a used four-wheeler depreciates at 12% per year. Write an equivalent equation using the monthly decay factor. What is the monthly decay rate of the four-wheeler?

Answers

The monthly decay factor is 0.0733 of the four-wheeler, and the equation is x = P(D)ˣ.

What does it mean by depreciation?

Depreciation is an important subject in finance and economics since it is used to determine an asset's worth over time. For accounting and financial reporting needs, it enables people and businesses to monitor the fall in the value of their assets. Depreciation may be utilised to lower taxable income, which in turn lowers tax liabilities, hence it also plays a part in tax legislation.

The yearly decay factor is given as:

yearly decay factor = 1 - depreciation rate

yearly decay factor = 1 - 0.12

yearly decay factor = 0.88

Divide the yearly decay factor by 12:

monthly decay factor = yearly decay factor / 12

monthly decay factor = 0.88 / 12

monthly decay factor = 0.0733

n equivalent equation using the monthly decay factor as follows:

value after x months = initial value x (monthly decay factor)ˣ

x = P(D)ˣ

Hence, the monthly decay factor is 0.0733 of the four-wheeler, and the equation is x = P(D)ˣ

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ALGEBRA 1 HW!! 35 POINTS!!I WILL GIVE BRAINLYEST FOR ANSWERS​​

Answers

The value of the ratio g(24)/g(21) is 729, and other solutions are shown below

The pattern of the infinite sequence

The domain and the range of h(n)

Given that

h(n) is the number of houses

The possible values of n and h(n) are whole numbers

So, we have

Domain: All set of whole numbersRange: All set of whole numbers

The values of h(5) and h(11)

Based on the patterns in the sequence, we have

h(n) = n

So, we have

h(5) = 5

h(11) = 11

The explicit function of h(n)

In (b), we have

h(n) = n

The values of s(4) and s(7)

Given that

s(n) is the number of segments

Based on the patterns in the sequence, we have

s(n) = 2n

So, we have

s(4) = 8

s(7) = 14

The growth pattern of s(n)

Above, we have

s(n) = 2n

The above equation is a proportional equation

This means that

The growth pattern of s(n) is linear, with a constant rate of change

The explicit function of s(n)

Above, we have

s(n) = 2n

The table of the infinite sequence

Complete the table for f(5) and f(7)

From the table, we can see that

As n increases, the value of f(n) is divided by 2 to get the next term

So, we have

f(5) = 2/2 = 1

f(7) = 1/2/2 = 1/4

The domain of f(n)

The possible values of n are real numbers

So, we have

Domain: All set of real numbers

The observation of the function

Above, we have

As n increases, the value of f(n) is divided by 2 to get the next term

This means that

As n gets larger and larger, the value of f(n) get halved

A doubling sequence g(n)

The value of g(4)

From the question, we have

First term, a = 9

Common ratio, r = 2

This means that

g(n) = 2(9)^n-1

So, we have

g(4) = 2(9)^3

g(4) = 1458

Completing the statements

Based on the function definitions, the statements when completed are

g(n) = g(n - 1) * 2g(n) = g(n - 2) * 4g(n) = g(n - 3) * 8

The value of the ratio

Recall that

g(n) = 2(9)^n-1

So, we have

g(24) = 2(9)^23

g(21) = 2(9)^20

Divide the equations

g(24) = 2(9)^23

-------     ----------

g(21) = 2(9)^20

Evaluate

g(24)/g(21) = 729

Hence, the value of the ratio is 729

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help on this of math

Answers

The required value of x for the given figure is 2√7 units.

What is right angled triangle?

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangled triangle, is a triangle with one right angle, or two perpendicular edges. The foundation of geometry is the relationship between the sides and other angles of the right triangle.

According to question:

In the given figure we have two triangle big and small triangle.

To find the value of x;

first we use Pythagoras theorem in big triangle.

So; let base of big triangle is b

9² = 7² + b²

b² = 81 - 49

b = √32

Now in small triangle;

(√32)² = x² + 2²

32 = x² + 4

x² = 28

x = √28

x = 2√7 units.

Thus, required value of x is 2√7 units.

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Rote tells the little monsters to do an overhead press every 12 seconds and a squat every 30 seconds. (For example, they should do their first squat 30 seconds into the drill.) How many times during the 200 second drill should the little monsters do an overhead press and a squat at the same instant?

Answers

The little monsters will do an overhead press and a squat at the same instant 3 times during the drill.

What are mathematical operations?

The term "operation" in mathematics refers to the process of computing a value utilising operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given, Rote tells the little monsters to do an overhead press every 12 seconds and a squat every 30 seconds.

The prime factorization of 12 is 2² x 3, and the prime factorization of 30 is 2 x 3 x 5.

To find the smallest common multiple, we need to take the highest power of each prime factor that appears in either factorization. Thus, the smallest common multiple of 12 and 30 are:

2² x 3 x 5 = 60

This means that the little monsters will do an overhead press and a squat at the same instant every 60 seconds.

To find out how many times this will happen during the 200-second drill, we can divide 200 by 60:

200 ÷ 60 = 3 remainder 20

This means that there will be 3 complete cycles of both exercises during the 200-second drill, with an additional 20 seconds left over.

Therefore, the little monsters will do an overhead press and a squat at the same instant 3 times during the drill.

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Find each length for a 30°−60°−90°
triangle.

Find the shorter leg and the hypotenuse if the longer leg is 9 inches

Shorter leg = ________ √ _________ in.

Hypotenuse = ________√ ________in.

Find the longer leg and the hypotenuse if the shorter leg is 4 cm.

Longer leg = _______√ _________cm.

Hypotenuse = __________cm.

(40 points)

Answers

In accordance with the provided assertion, (A) the shorter leg is 3√3 inches and the hypotenuse is 6√3 inches (B) the longer leg is 4√3 cm and the hypotenuse is 8 cm.

What do maths lengths mean?

The measurement or size of a thing end to end is referred to as its length. To put it another way, it is the bigger of the higher two or three dimensions of a geometric form or object.

For a 30°−60°−90° triangle, the ratios of the side lengths are:

Shorter leg: opposite 30° angle = xLonger leg: opposite 60° angle = x√3Hypotenuse: opposite 90° angle = 2x

Using these ratios, we can solve the problems:

If the longer leg is 9 inches, we have:

Longer leg = x√3 = 9

x = 9/√3 = 3√3

Shorter leg = x = 3√3

Hypotenuse = 2x = 2(3√3) = 6√3

Therefore, the shorter leg is 3√3 inches and the hypotenuse is 6√3 inches.

    2. If the shorter leg is 4 cm, we have:

Shorter leg = x = 4

Longer leg = x√3 = 4√3

Hypotenuse = 2x = 2(4) = 8

Therefore, the longer leg is 4√3 cm and the hypotenuse is 8 cm.

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Two docks are located on an​ east-west line 2599 ft apart. From dock​ A, the bearing of a coral reef is 58°23′. From dock​ B, the bearing of the coral reef is 328°23′. Find the distance from dock A to the coral reef.

Answers

Therefore , the solution of the given problem of trigonometry comes out to be  it is roughly 5193 feet from pier A to the coral reef.

What is a trigonometry?

Relationships between mathematics but also cubic splines When the different fields were combined, astrophysics is thought to have been born in the third century BC. With the aid of exact angle mathematical techniques, many metric issues can be resolved or the outcomes of calculating them can be ascertained. The study of the six fundamental trigonometric formulas is known as trigonometry.

Here,

The north-south distance from pier A to the coral reef, x sin(31°37′), is the other side of the triangle (relative to angle ). The east-west path from dock A to the edge of the coral reef, which is equal to x cos(31°37′), forms the opposite side of the triangle. We're looking for x's number.

The Pythagorean theory allows us to write:

=> (x cos(31°37′) + 2599) + (x sin(61°37′)) = (x sin(31°37′))

By condensing and rearrangeing, we obtain:

=> x² - 5198x + 6790401 = 0

We can use the quadratic formula to answer the following quadratic equation:

=> x = (-(-5198) ± √(-5198)^2 - 4(1)(6790401))) / (2(1))

=> x = (5198 + √(26857604)) / 2

=> x = (5198 ± 5188) / 2

=> x = 5193 or x = 5

The negative answer x = 5 does not make logic in this situation because x is a measure of distance. Consequently, it is roughly 5193 feet from pier A to the coral reef.

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Answer the following questions using the image below

a) If the slant range of the plane in the image is 14.5 km, and the ground range is 10.15 km, find the altitude of the plane to the nearest meter. Show your work and explain your thinking.

b) If this plane loses power and descends suddenly at a rate of 750 meters per minute, how much time will the pilot have before he has to land?

Answers

a) The altitude οf the plane is apprοximately 10,780 meters.

b) The pilοt will have apprοximately 14.4 minutes befοre he has tο land if the plane descends suddenly at a rate οf 750 meters per minute.

What are trigοnοmetric functiοns?  

Trigοnοmetric functiοns are mathematical fοrmulas that cοnnect a triangle's angles and side ratiοs. Sine, cοsine, and tangent are the three fundamental trigοnοmetric functiοns; they are alsο knοwn as sin, cοs, and tan, respectively. These functiοns are emplοyed in the study οf physics, engineering, and οther branches οf science as well as in the study οf geοmetry, trigοnοmetry, and οther branches οf mathematics. They can be used tο sοlve issues invοlving angles and distances, such as determining a building's height, the separatiοn between twο οbjects, οr the speed οf a mοving οbject.

a) The Pythagοrean theοrem, which relates the three sides οf a right triangle, can be used tο determine the plane's altitude. In this instance, the slant range serves as the hypοtenuse οf a right triangle, with the grοund range serving as οne οf the legs and the height serving as the οther leg. As a result, we have:

altitude² + grοund range² = slant range²

Substituting the given values, we get:

altitude² + (10.15 km)² = (14.5 km)²

Simplifying and sοlving fοr altitude, we get:

altitude² = (14.5 km)² - (10.15 km)²

altitude² = 116.205 km²

altitude = √116.205 km² ≈ 10.78 km ≈ 10,780 m

Therefοre, the altitude οf the plane is apprοximately 10,780 meters.

b) If the plane descends suddenly at a rate οf 750 meters per minute, its altitude will decrease by 750 meters every minute. Tο find hοw much time the pilοt has befοre he has tο land, we can divide the initial altitude by the rate οf descent. Therefοre, we have:

time = initial altitude/rate οf descent

Substituting the initial altitude and rate οf descent, we get:

time = 10,780 m / 750 m/min

Simplifying, we get:

time = 14.3733 min ≈ 14.4 min

Therefοre, the pilοt will have apprοximately 14.4 minutes befοre he has tο land if the plane descends suddenly at a rate οf 750 meters per minute.

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Guys i need help with these. THIS QUESTION IS EASY PLS HELP:)

Answers

(5[tex]\sqrt{3}[/tex])^2

= (25 x 3)

= 75

(2[tex]\sqrt{5}[/tex])^2

= (4 x 5)

= 20

John has three more pet birds than he has cats. If he has 11 pets in all, how many cats does he have?

Answers

Answer:

4 cats

Step-by-step explanation:

Let b represent birds and c represent cats

b = c + 3

c + b = 11

c + (c + 3) = 11

2c + 3 = 11

2c = 8

c = 4.

John has 4 cats

b = (4) + 3

b = 7

John has 7 birds

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