The height of an acute triangle can be calculated using the Pythagorean Theorem. The formula for this theorem is a2 + b2 = c2, where a and b are the two legs of a right triangle and c is the hypotenuse.
To find the height of an acute triangle, we must first identify the two legs of the triangle. The length of the two legs can be determined by measuring the lengths of the three sides of the triangle. Once we have the lengths of the two legs, we can apply the Pythagorean Theorem to calculate the length of the hypotenuse.
Once the length of the hypotenuse is determined, we can use the formula h2 = c2 - a2 - b2 to calculate the height of the triangle. This formula states that the square of the height of the triangle is equal to the square of the hypotenuse minus the square of the two legs. So, to find the height of an acute triangle, we first measure the lengths of the three sides, then use the Pythagorean Theorem to calculate the hypotenuse, and finally use the formula h2 = c2 - a2 - b2 to calculate the height of the triangle.The height of an acute triangle can be calculated using the Pythagorean Theorem. The formula for this theorem is a2 + b2 = c2, where a and b are the two legs of a right triangle and c is the hypotenuse. To find the height of an acute triangle, we must first identify the two legs of the triangle. The length of the two legs can be determined by measuring the lengths of the three sides of the triangle. Once we have the lengths of the two legs, we can apply the Pythagorean Theorem to calculate the length of the hypotenuse.
Once the length of the hypotenuse is determined, we can use the formula h2 = c2 - a2 - b2 to calculate the height of the triangle. This formula states that the square of the height of the triangle is equal to the square of the hypotenuse minus the square of the two legs. So, to find the height of an acute triangle, we first measure the lengths of the three sides, then use the Pythagorean Theorem to calculate the hypotenuse, and finally use the formula h2 = c2 - a2 - b2 to calculate the height of the triangle.
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How do you tell if a log function is increasing or decreasing?
If the derivative of the function is positive, the function is increasing; if the derivative is negative, the function is decreasing.
What is a logarithmic function?
A logarithmic function is a type of mathematical function that expresses the power to which a given number (the base) must be raised in order to produce a certain value. It is typically written in the form: [tex]f(x) = log_b(x),[/tex] where b is the base of the logarithm.
To determine whether a logarithmic function is increasing or decreasing, you can look at the sign of the derivative of the function. If the derivative is positive, the function is increasing; if the derivative is negative, the function is decreasing.
In the case of logarithmic functions, the derivative of [tex]f(x) = log_b(x)[/tex] is f'(x) = 1/x*ln(b), which is always positive for x > 0, so the logarithmic function is increasing for any base b.
Hence, if the derivative of the function is positive, the function is increasing; if the derivative is negative, the function is decreasing.
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If the derivative of the function is positive, the function is increasing; if the derivative is negative, the function is decreasing.
What is a logarithmic function?
A logarithmic function is a type of mathematical function that expresses the power to which a given number (the base) must be raised in order to produce a certain value. It is typically written in the form: [tex]f(x)=log_b(x)[/tex]. where b is the base of the logarithm.
To determine whether a logarithmic function is increasing or decreasing, you can look at the sign of the derivative of the function. If the derivative is positive, the function is increasing; if the derivative is negative, the function is decreasing.
In the case of logarithmic functions, the derivative of [tex]f(x)=log_b(x)[/tex]. is f'(x) = 1/x*ln(b), which is always positive for x > 0, so the logarithmic function is increasing for any base b.
Hence, if the derivative of the function is positive, the function is increasing; if the derivative is negative, the function is decreasing.
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On a coordinate plane, a line is drawn from point C to point D. Point C is at (negative 1, 4) and point D is at (2, 0).
Point C has the coordinates (–1, 4) and point D has the coordinates (2, 0). What is the distance between points C and D?
d = StartRoot (x 2 minus x 1) squared + (v 2 minus v 1) squared EndRoot
units
The length of the line is 5 units.
What is distance?The distance between two points is the length of the line joining the two points.
Formula: distance= √(x_2-x_1)²+(y_2-y_1)²
Given that, endpoints are (-1,4) and (2,0) of the line segment.
The length= √(2+1)²+(0-4)²
=5units
Hence, The length of the line is 5 units.
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On a coordinate plane, the center of dilation is at (0, 0). Triangle A B C is dilated to create triangle A prime A C prime. The points of A B C are (negative 3, 3), (negative 1, 1), and (negative 3, 1). The points of A prime A C prime are (negative 9, 9), (negative 3, 3), and (negative 9, 3).
The dilation DO,3 (x, y) → (3x, 3y) is performed on the pre-image △ABC to make a similar triangle. Which statements are true? Check all that apply.
∠A corresponds to ∠A'.
∠A'AC' corresponds to ∠B.
CB corresponds to C'A.
Segment A'A is parallel to segment C'C.
△ABC ~ △A'AC'.
The true statements after a dilation of scale factor 3 are,
∠A corresponds to ∠A' and Triangle ABC is similar to triangle A'B'C'.
What are transformations?Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.
Dilation: The preimage is scaled up or down to create the image.
Reflection: The picture is a preimage that has been reversed.
Rotation: Around a given point, the preimage is rotated to create the final image.
Translation: The image is translated and moved a fixed amount from the preimage.
Given, The points of ABC are (negative 3, 3), (- 1, 1), and (- 3, 1).
The points of A'BC' are (- 9, 9), (- 3, 3), and (- 9, 3) after a dilation of 3, (x, y) ⇒ (3x, 3y).
We know dilation maintains the similarity of the dilated figures.
Therefore, The statements that are true,
∠A corresponds to ∠A' as dilation maintains similarity.
Triangle ABC is similar to triangle A'B'C'.
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Answer:
Options A,B,C,E
Step-by-step explanation:
Deshaun deposits $4,000 into an account that pays simple interest at an annual rate of 6% . He does not make any more deposits. He makes no withdrawals until the end of 2 years when he withdraws all the money.
After 2 years, Deshaun will have earned $4,000 * 6% = $240 in interest.
The total amount of money in the account at the end of 2 years will be $4,000 + $240 = $4,240. This is the amount Deshaun will withdraw.
A certain movie is 105 minutes long. It started at 6:15 pm. During the movie, there were two commercial breaks, one lasting 9
minutes and one lasting 6 minutes. At what time did the movie finish?
Answer: 8:15pm
Step-by-step explanation:
9+6=15 +105 = 120, 120/60=2 hours (total duration), 6:15 + 1 hour = 7:15 + 1 hour = 8:15pm
please help me !!
literally struggling right now !!
Solve the equation 2^x=1/32•x=
Answer:
2^x=1
x=0
32•x=0
32.0=0
maybe
I don't understand help
Volume of the triangle is 1420m³ given in the question.
What is Volume?There are various volumes for various geometric shapes. Cubes, cuboids, spheres, cylinders, cones, etc. are examples of common 3D shapes that we encounter on a daily basis.
Finding the volume is simple when dealing with shapes with a flat surface, like a cube or a cuboid. Cones, cylinders, and spheres are examples of curved shapes, and it is necessary to take into account both their curved surfaces' dimensions and their overall curvature. Possibly their diameters or radii
The term "irregular solids" refers to solids that lack precise measurements or shapes. A fixed formula that can be used to calculate the volumes of such solids is typically absent. It is possible to obtain these volumes in a variety of ways, one of which is the liquid displacement method, which is based on the Archimedes Principle.
Now volume triangle = area × height
⇒ 1/2 × 20 × 14.2 × 10
= 1420m³
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8.5x + 0.5 + 3.5x - 2x
Answer:
-0.05
Step-by-step explanation:
10x+0.5
10x=-0.5
x=-0.5/10
x=-0.05
john is 7 years younger than jane. the sum of their age is 10 years ago was 55 years. how old are they now
Answer: John is 29 years old and Jane is 36 years old.
Step-by-step explanation:
There are many parts to this problem, so let's start by defining John as x and Jane as y.
We know that the sum of their age 10 years ago was 55, which gives us x+y-10=55. The reason we put -10 is because of 10 years ago. If you think about it in terms of now, 10 years back is 55, so now they would be 65 years old. So we can have either x+y-10=55 or x+y=65. For simplicity, I will use x+y=65.
We also know that John is 7 years younger than Jane, which gives x=y-7.
Luckily, we have x defined for us, so we can directly substitute that into our equation.
[tex](y-7)+y=65[/tex] [combine like terms]
[tex]2y-7=65[/tex] [add both sides by 7]
[tex]2y=72[/tex] [divide both sides by 2]
[tex]y=36[/tex]
Now we know that y=36, we can plug that into either equations to find x.
[tex]x+36=65[/tex] [subtract both sides by 36]
[tex]x=29[/tex]
This concludes that John is 29 years old and Jane is 36 years old.
Examine this set of ordered pairs. (7,9), (4,18), (−3,11), (16,18), (4,−11) Is the set of ordered pairs a function? Choose the answer that is entirely correct.
The set of ordered pairs represents the function.
What is a function?A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain.
Given:
The set of ordered pairs:
(7,9), (4,18), (−3,11), (16,18), (4,−11)
Pairs written as input and output of the relation.
In the attached table,
To prove function:
A relation has an input value which corresponds to an output value. When each input value has one and only one output value, that relation is a function.
And here each input is connected to precisely one output.
Therefore, this is a function.
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5 whole 1/7- 2 whole 5/21
The value of 5 1/7 minus 2 5/21 will be 2 19 / 21.
How to solve the fraction?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
Based on the information, the value of 5 1/7 minus 2 5/21 will be:
= 5 1/7 - 2 5 / 21
= 5 3/21 - 2 5 / 21
= 2 19 / 21
The value is 2 19/21.
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please help!!!!
Solving Systems of Linear Equations by Elimination
C.
0.6x = 1.2 +0.3y
2.2x-1.8y-1.6=0
By using systems of linear equations by elimination, it can be determined that x = 0.5 y +2 and 2.2x-1.8y-1.6=0 are equivalent to x=0.818182 and y+0.727273.
What do you meant by Systems of Linear Equations by Elimination ?Using elimination, let's fix your system. 0.6 x=1.2+0.3 y, 2.2 x-1.8 y-1.6=0 in the graph, and y=2 x-4, y=1.222222 x-0.88888
Step 1: Divide both sides by 0.6 to find the solution for x = 0.6 x=1.2 + 0.3 y.
[tex]$$\begin{aligned}& \frac{0.6 x}{0.6}=\frac{0.3 y+1.2}{0.6} \\& x=0.5 y+2\end{aligned}$$[/tex]
Let's figure out what x is, 2.2 x-1.8 y-1.6=0.
First, multiply both sides by 1.8 y.
[tex]$$\begin{aligned}& 2.2 x-1.8 y-1.6+1.8 y=0+1.8 y \\& 2.2 x-1.6=1.8 y\end{aligned}$$[/tex]
Add 1.6 to both sides in step two.
[tex]$$\begin{aligned}& 2.2 x-1.6+1.6=1.8 y+1.6 \\& 2.2 x=1.8 y+1.6\end{aligned}$$[/tex]
3. Multiply both sides by 2.2.
[tex]$\frac{2.2 x}{2.2}=\frac{1.8 y+1.6}{2.2}$[/tex]
x=0.818182 y+0.727273
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.25x + 0.05y = 9, x + y = 25
Answer:
x = -4
y = 29
Step-by-step explanation:
Let's take our two equations and turn the decimals into fractions for simplicity's sake. We get:
x/4 + 5y/100 = 9 x + y = 25
Simplifying a bit gives us:
x/4 + y/20 = 9 x + y = 25
Now, we will take the first equation and multiply it by 20 to get rid of the fractions. We get:
5x + y = 9
We will rearrange numbers to give us an answer to y that we can substitute in. we get:
y = 9 - 5x
Then, we will plug this into our second equation giving us:
x + 9 - 5x = 25
Combining like terms and subtracting 9 from both sides gives us:
-4x = 16
Dividing by -4 gives us:
x = -4
Then, we can substitute this into our second equation giving us:
-4 + y = 25
We will add 4 to both sides giving us:
y = 29
Hope this helped!
What is the name of the point where the two axes cross?
As per the concept of graph, the name of the point where the two axes cross is origin.
Graph in math is defined as a diagram showing the relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles.
Here we have to identify the name of the point where the two axes cross.
As we all know that the horizontal axis in the coordinate plane is called the x-axis and the vertical axis is called the y-axis.
Here we have also know that the point at which the two axes intersect is called the origin.
Where the origin is at 0 on the x-axis and 0 on the y-axis.
And these intersecting x- and y-axes divide the coordinate plane into four sections
Finally all these four sections are called quadrants.
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Adam and Kim are paid an hourly rate at their jobs. Adam earns $186 for 8 hours of work, before taxes. The table below shows the amount
Kim earns, before taxes.
Who earns the most money per hour and by how much?
A.Adam earns $5.25 more per hour than Kim.
B.Kim earns $5.25 more per hour than Adam.
C.Adam earns $42.00 more per hour than Kim.
D.Kim earns $42.00 more per hour than Adam.
H 3,7,12
$ 54,125,216
Therefore the correct answer is A. Adam earns $5.25 more per hour than Kim.
Define percentage.A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Define Fraction.Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
Adam earns $186 for 8 hours of work, so his hourly rate is $186/8 = $23.25 per hour
Kim earns $54 for 3 hours of work, so her hourly rate is $54/3 = $18.00 per hour
Kim earns $125 for 7 hours of work, so her hourly rate is $125/7 = $17.86 per hour
Kim earns $216 for 12 hours of work, so her hourly rate is $216/12 = $18.00 per hour
Adam earns $23.25 per hour and Kim earns $18.00 per hour on average.
Adam earns $23.25 - $18.00 = $5.25 more per hour than Kim.
Therefore the correct answer is A. Adam earns $5.25 more per hour than Kim.
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if AG=5x-24 and GB=3x-12, find GB
The value of line GB is 6
How to determine the value of the lineFrom the diagram shown, we can see that AG, GB and AB form a triangle with two of its sides being equal.
Also, line AG = line GB
Where;
Line AG = 5x - 24Line GB = 3x - 12Then, we have;
Line AG = LIne GB
Substitute the expressions, we have;
5x - 24 = 3x - 12
Collect like terms
5x - 3x = - 12 + 24
Add or subtract like terms
2x = 12
Divide both sides by the coefficient of x
x = 12/ 2
x = 6
The, GB = 3(6) - 12 = 6
Hence, the value is 6
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The start of an arithmetic sequence is shown below.
Work out the nth term
Work out the 30th term in this sequence.
4 - 13 - 22 - 31
Therefore , the solution of the given problem of arithmetic mean comes out to be a(30) = 265.
Define arithmetic mean.When all of the values in a set of data have the same unit of measurement, such as when all of the numbers are heights, miles, hours, etc., this technique is utilized. Take the numbers 4, 7, 9, and 10 as an illustration. The count of numerals is 4, and the sum of the numbers is 30. 30 divided by 4 equals 7.5, which is the numbers' arithmetic mean.
Here,
Given that there is a common difference between each word, this is an arithmetic sequence. In this instance, the following term is obtained by adding 9 to the phrase before it in the sequence.
Alternatively put,
=> an=a1+d(n−1)
.Arithmetic Sequence:
d=9
This is the formula of an arithmetic sequence.
=>an=a1+d(n−1)
Substitute in the values of
=> a1 =4 and
d=9
.=>an=4+9(n−1)
Simplify each term.
Tap for more steps...
an=4+9n−9
Subtract 9 from 4
an=9n−5
Thus 30th term :
=> a(30)=9(30)−5
=> a(30) = 265
Therefore , the solution of the given problem of arithmetic mean comes out to be a(30) = 265.
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A submarine descends 175 ft underwater in 5 minutes. The rate of descent is constant. What is the rate of descent per minute?
In linear equation, 35 feet per minute is the rate of descent per minute.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
It’s 35 feet per minute. 175 divided by 5 equals 35.
A submarine descends = 175 ft
Time = 5 minutes
The rate of descent is constant = 175/5
= 35 feet per minute
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M(2,4) is the midpoint
between the points A(-2,9)
and B.
Find the coordinates of B.
The coordinates of B are (6,0).
The midpoint of a line segment is the point that is exactly halfway between the two endpoints of the segment. For a line segment with endpoints (x1, y1) and (x2, y2), the midpoint is given by the coordinates:
((x1 + x2) / 2, (y1 + y2) / 2)In this problem, we're given that the midpoint is (2, 4) and we need to find the coordinates of point B. Since we know the coordinates of the midpoint, we can set up the equation:
((x1 + x2) / 2, (y1 + y2) / 2) = (2, 4)We know that point A = (-2,9) is one endpoint, so we can substitute it into the equation
((-2 + x2) / 2, (9 + y2) / 2) = (2, 4)Solving for x2 and y2, we get x2 = 6 and y2 = 0 which is the coordinates of point B.
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What is 62% of $10.50?
Answer:
$6.51
Step-by-step explanation:
To make a percent a decimal, divide by 100
62% = .62
.62 x 10.50 = 6.51
We know that half of 10.50 is 5.25 and 625 would be a little higher and 6.51 is a little higher.
Each square inch of your body has about 6. 5 × 10^2 pores. Suppose the top of your foot has an area of about 2. 0 × 10^1 in. ^2. About how many pores are on the top of your foot?
The number of pores that are on the top of your foot is approximately 13,000 pores on the top of your foot.
To find the number of pores on the top of your foot, we can multiply the area of the top of your foot in square inches by the number of pores per square inch.
The area of the top of your foot is 2.0 x 10^1 in^2 and each square inch of your body has about 6.5 x 10^2 pores. So, the number of pores on the top of your foot can be calculated as:
2.0 x 10^1 in^2 * 6.5 x 10^2 pores/in^2 = 130 x 10^2 pores = 13000 pores
So, there are approximately 13,000 pores on the top of your foot.
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given that y=15-2x,copy and complete the table below giving the values of y for x=-4,0,4,8,12
Can you help me with this
Select the correct answer.A wooden board that is 108 inches long is cut into two equal parts. What is the length of each part in feet
4.5 is the length of each part in feet. This can be solved by using the concept of feet.
What is feet?foot, plural feet, any of a wide range of ancient, medieval, and modern linear measurements (often 25 to 34 cm) based on the length of the human foot and used only in English-speaking nations, where it typically consists of 12 inches or one-third yard.
The foot measured [tex]11^{\frac{1}{42}[/tex] inches in antiquity. The typical man's foot measures 12 inches in length nowadays.
Given that:
The length of the wooden board is given as = 108 inches.
As it is cut in 2 equal parts, it becomes: 108/2 = 54 inches in each
We have to calculate the length of each part in feet, so divide 54 by 12.
As we know,
12 inches = 1 feet
Thus, 54 inches = 54/12 feet = 4.5 feet
So, the length of each part is 4.5 feet.
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This box plot represents the marks gained by students in an exam. Nobody gained exactly 30, 48 or 70 marks. 120 students gained less than 70 marks. How many students gained more than 48 marks?
Therefore , the solution of the given problem of scatter plot comes out
to be 2 regions contain 2 x 40 (or 80) students.
Definition of a scatter plotSeveral dots are placed on a vertical and horizontal axis to form a scatter plot. In statistics, scatter plots are crucial because they can demonstrate the amount of correlation, if any, between both the quantities of observed quantities or occurrences (called variables).
Here,
A box plot separates a data set into four areas, each identified by five lines. The lowest line displays the result, while the highest line displays the result. 25% of the data points are distributed across each region, and the median score is indicated by the middle line.
In this box plot, for instance, there are lines at 10, 30, 48, 70, and 100. The fact that no student received a score exactly equal to 30, 48, or 70 allows us to deduce the following:
Because the middle two sections represent the interquartile range (IQR), which comprises the middle 50% of the data, they are frequently "boxed" together.
We are informed that 120 students received test scores below 70. Additionally, since there are three regions with scores below 70 and each region has a 25% weighting, 3 x 25% (or 75% of the students) had scores below 70.
In other words, 75% of 120 students.
If there are 120 students total throughout the three regions, then each
region has 40 pupils, or one-third of the total.
The box plot indicates that there are two areas, and since each region has 40 students, there are 80 students total in the two regions.
As a result, two zones with two sets of 40 students each make up the solution to the scatter plot problem.
Therefore , the solution of the given problem of scatter plot comes out
to be 2 regions contain 2 x 40 (or 80) students.
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Question 1
Solve for x.
x(x + 6) = 0
Write your answers as integers or as proper or improper fractions in simplest form.
X =
|
X =
Answer:
[tex]x=-6, 0[/tex]
Step-by-step explanation:
Using the zero-product property, we know that [tex]x=0[/tex] or [tex]x+6=0[/tex].
This means [tex]x=-6, 0[/tex].
two electric irons were sold at Rs.1050 each. If one was sold at a loss of Rs.300 and the other at a profit of Rs.450, what was the total cost price? Find the profit or loss
Answer:
Step-by-step explanation:
Selling price of two irons is Rs.1050 each.
Loss on one iron = Rs.300
Profit on second iron = Rs.450
We know that ,
Cost price = Selling price + loss ,when loss is given
and cost price = Selling price - profit ,when profit is given.
therefore, cost price of first iron = 1050 + 300 =1350 rupees
cost price of second iron = 1050 - 450 = 600 rupees
total cost price = 1350 + 600 = 1950 rupees
total selling price = 1050 + 1050 = 2100 rupees
since total cost price < selling price
so, there is a profit of 2100 - 1950 = 150 rupees.
Identify similarities and differences in finding the volume of cylinders, cones, and spheres.
The volume of the cone is one third the volume of the cylinder.
The volume of a sphere is 2/3 of the volume of a cylinder with same radius, and height equal to the diameter
How to illustrate the information?Similar to a prism, a cylinder has two bases, but they are circles rather than polygons. A cylinder's sides are also curved rather than flat. A cone has a vertex that is not on the base and a single circular base. The sphere is a figure in space with equal distances between each of its points and the center.
The cone's volume is one-third that of the cylinder. A sphere's volume is 2/3 that of a cylinder with the same radius, and its height is equal to its diameter.
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9. Expand :
(i) (3x - 4y + 5z)² (ii) (2a-5b-4c)²
(iii)
(5x + 3y)³
(iv) (6a - 7b)³