Answers
Answer:
Your answer should be -2x
Step-by-step explanation:
I am not sure if your teacher taught you the short cut way of doing derivatives yet.
That equation is just a long way to do derivatives. The picture below shows the shortcut way to do dervatives.
So basically you plug in x+h into the equation given to you.
[tex]\frac{g(x+h)-g(x)}{h} \\\\\frac{(6-(x+h)^2)-g(x)}{h} \\\\\frac{(6-(x^2+2xh+h^2))-(6-x^2)}{h}\\\\ \frac{(6-x^2-2xh-h^2)-(6-x^2)}{h}\\\\ \frac{6-x^2-2xh-h^2-(6-x^2)}{h}\\\\ \frac{6-x^2-xh-h^2-6+x^2}{h}\\\\[/tex]
[tex]\frac{(x^2-x^2)+(6-6)-2xh-h^2}{h}\\\\ \frac{(0)+(0)-2xh-h^2}{h}\\\\ \frac{-2xh-h^2}{h}\\\\ \frac{h(-2x-h)}{h}\\\\ -2x-h[/tex]
Plug in h = 0
then your answer is -2x
Related Questions
I will mark you brainiest!
The conditional probability of an event B in relationship to an event A is the probability that event B occurs given that event A has already occurred. The notation for conditional probability is P(B|A), read as the probability of B given A.
A) True
B) False
Answers
Answer:
A) True
Step-by-step explanation:
The statement is true. Conditional probability is a fundamental concept in probability theory that allows us to calculate the probability of an event given that another event has already occurred. The notation for conditional probability is P(B|A), which represents the probability of event B occurring given that event A has already occurred. In other words, we restrict our attention to the sample space where event A has occurred and calculate the probability of event B in that space.
Please solve for slope and y intercept with steps
Answers
The values are given as;
1. The intercept, c = -1.5, Slope, m = -1/4
2. Intercept = 0. 5, Slope, m = -3/5
How to determine the slopeThe general formula for the equation of a line is represented thus;
y = mx + c
Given that the parameter are;
y is a point on the y -axism is the slope or gradient of the linex is a point on the x - axisc is the intercept of the line on the y - axisFor the first graph
The intercept, c = -1.5
The slope, m = y₂ - y₁/x₂ - x₁
Substitute the values as shown in the graph
Slope, m = -2-(-3)/- 3- 1
Slope, m = -2 + 3/-4
Slope, m = -1/4
For the second graph, we have
Intercept = 0. 5
The slope, m = y₂ - y₁/x₂ - x₁
Substitute the values
Slope, m = 2 - (-1)/3 - (-2)
Slope, m = -3/5
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Challenge) Solve for a. Answer as a mixed number. A=______
Answers
Answer:
Step-by-step explanation:
o.ooo27 in scientific notation ?
Answers
Answer:
2.700 × 10-7
Step-by-step explanation:
Answer: 2.7*10^-4
step by step explanation:
1. Make the number a new number between 1 and 10
More Icon
Move the decimal point to make 0.00027 a new number between 1 and 10. Because our original number is less than one, we move the decimal point to the right. Drop any zeroes in front of the number. Keep track of how many times we move the decimal point.
0.00027 -> 2.7
Our new number is 2.7. We moved the decimal point 4 times.
2. Define the power of 10
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Because our original number was less than one, the exponent defining the power of 10 is negative. Remember, we moved the decimal point 4 times, so the exponent is negative 4
10^(-4)
3. Final result
2.7*10^(-4)
According to the drag equation the velocity of an object moving through a fluid can be modeled by the equation 2 dvkvdt=− where k is a constant. a) Find the general solution to this equation. b) An object moving through the water has an initial velocity of 40 m/s. Two seconds later, the velocity has decreased to 30 m/s. What will the velocity be after ten seconds?
Answers
Answer:
The given differential equation is:
2dv/dt = -kv
where k is a constant.
a) To find the general solution to this differential equation, we can use separation of variables.
2dv/v = -k dt
Integrating both sides, we get:
2ln|v| = -kt + C1
where C1 is the constant of integration.
Taking exponential of both sides, we get:
|v|^2 = e^(C1) e^(-kt)
Since v can be either positive or negative, we can simplify the above equation as:
v = ±√(Ae^(-kt))
where A = e^(C1).
Therefore, the general solution to the given differential equation is:
v(t) = ±√(Ae^(-kt))
b) We are given that the initial velocity is 40 m/s and after 2 seconds, the velocity has decreased to 30 m/s. Let's use this information to find the value of A.
When t = 0, v = 40. Therefore,
40 = ±√(Ae^0)
40^2 = A
A = 1600
Now we can use the value of A to find the velocity after 10 seconds.
v(10) = ±√(1600e^(-10k))
We can use the information that the velocity has decreased to 30 m/s after 2 seconds to find the value of k.
30 = ±√(1600e^(-2k))
900 = 1600e^(-2k)
e^(-2k) = 0.5625
-2k = ln(0.5625)
k = -0.5 ln(0.5625)
Now we can substitute this value of k into the expression for v(10) to get:
v(10) = ±√(1600e^(5ln(0.5625)))
v(10) = ±√(1600(0.5625)^5)
v(10) = ±20.11 m/s
Therefore, the velocity of the object after ten seconds will be approximately 20.11 m/s.
define petition and state 3 ways in which petitions from the youth can help improve service delivery in their communities
Answers
A petition is just a formal request outlining the grounds for requesting a court order. It is often the first stage of a lawsuit and can be filed by an individual, a group, or an institution.
Explain about the petitions and its features?A petition is a formal letter or written request asking someone or an organization to take a certain action or make a certain change.
The petition is typically signed by a number of people who agree with the subject or problem being raised.
Awareness-building: Petitions can help people learn more about the problems that young people in their communities are facing.Feedback: Petitions can give local authorities insightful information about the wants and concerns of young people in their communities.Petitions can be used as an advocacy tool to help young people express their needs and desires to people in positions of authority.know more about the petitions
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U6d11 area using trig
Answers
Area of a triangle is 88.37cm²
What is the area of triangle?The area of a triangle is given by the formula:
[tex]Area = \frac{(base * height)}{2}[/tex]
where "base" refers to the length of the base of the triangle, and "height" refers to the height of the triangle measured perpendicularly from the base to the highest point of the triangle.
As per figure we have to find out the area of triangle, first we have to find out the height of triangle,
by using sine rule:
Sin 67° = [tex]\frac{height}{12 cm}[/tex]
height = 12 Sin 67° (Here, Sin 67° = 0.92)
height = 12 × 0.92
height = 11.046cm
[tex]Area = \frac{(base * height)}{2}[/tex]
[tex]Area = \frac{(16 X 11.046)}{2}[/tex]
[tex]Area = 88.37cm^{2}[/tex]
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i need help with question 15 i tried doing the problem 15 but i got stick on the problem 15
(Car Sales) Of the cars sold during the month of July, 87 had air conditioning, 99 had automatic transmission, and 73 had power steering. 8 cars had all three of these extras. 24 cars had none of these extras. 24 cars had only air conditioning, 64 cars had only automatic transmissions, and 35 cars had only power steering. 9 cars had both automatic transmission and power steering. How many cars had exactly two of the given options?
a) 64
b) 56
c) 96
d) 1
e) 82
Answers
Therefore , the solution of the given problem of unitary method comes out to be 25 vehicles had precisely two of the available options.
An unitary method is what?By multiplying the data obtained with such a nanosection variable whilst also two that used the unilateral strategy, the job can be finished. In essence, this mean that whenever a desired item appears, the specified entity is set or the colour space of both production runs is skipped. A varying fee of Inr ($1.01) might have been necessary for forty pens.
Here,
We can apply the inclusion-exclusion concept to resolve this issue. To begin, let's draw a Venn diagram to symbolise the supplied data:
where A is the proportion of vehicles with air conditioning, B is the proportion of vehicles with automatic gearbox, and C is the proportion of vehicles with power steering.
The information provided lets us know:
=> A = 87 + 8 + 24 = 119
=> B = 99 + 8 + 9 = 116
=> C = 73 + 8 + 9 = 90
=> A ∩ B ∩ C = 8
=> A ∩ B ∩ C' = 24 - 8 = 16
=> A ∩ B' ∩ C = 9
=> A ∩ B' ∩ C' = 64 - 9 - 8 - 16 = 31
=> A' ∩ B ∩ C = 0
=> A' ∩ B ∩ C' = 35 - 9 - 8 - 16 = 2
=> A' ∩ B' ∩ C = 0
=> A' ∩ B' ∩ C' = 24 - 8 - 16 - 2 = -2
Since there cannot be fewer than 0 cars without any extras, this number must be negative.
=> (A ∩ B' ∩ C) + (A ∩ B ∩ C') + (A' ∩ B ∩ C) = 9 + 16 + 0 = 25
As a result, 25 vehicles had precisely two of the available options. There may have been a mistake in the problem or the answer alternatives since the correct response is not one of the available choices.
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I will mark you brainiest!
Knowing that ΔQPT ≅ ΔARZ, a congruent angle pair is:
A) ∠Q ≅ ∠R
B) ∠P ≅ ∠A
C) ∠T ≅ ∠Z
D) ∠P ≅ ∠Z
Answers
Answer:
Since ΔQPT ≅ ΔARZ, we know that their corresponding angles are congruent.
Step-by-step explanation:
The congruent angle pair is:
C) ∠T ≅ ∠Z.
Note that ∠Q and ∠R are not necessarily congruent to each other, ∠P and ∠A are not necessarily congruent to each other, and ∠P and ∠Z are not necessarily congruent to each other.
If you draw a card with a value of five or less from a standard deck of cards, I will pay you $49
. If not, you pay me $25
. (Aces are considered the highest card in the deck.)
Step 1 of 2 : Find the expected value of the proposition. Round your answer to two decimal places. Losses must be expressed as negative values.
Answers
The expected value of the proposition is $18.23.
What is Probability?Probability is a branch of mathematics that deals with the study of random events or outcomes. It is the measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1. An event with a probability of 0 is impossible, while an event with a probability of 1 is certain to occur.
Given by the question.
Step 1 of 2 : Find the expected value of the proposition. Round your answer to two decimal places. Losses must be expressed as negative values.
The probability of drawing a card with a value of five or less is:
4 cards with a value of 2 + 4 cards with a value of 3 + 4 cards with a value of 4 + 4 cards with a value of 5 + 4 aces = 20/52 = 5/13
The probability of not drawing a card with a value of five or less is:
1 - 5/13 = 8/13
The expected value of the proposition can be calculated as follows:
Expected value = (probability of winning * amount won) + (probability of losing * amount lost)
Expected value = (5/13 * $49) + (8/13 * (-$25))
Expected value = $18.23 (rounded to two decimal places)
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A clock is in the shape of a square pyramid. The dimensions are shown in the net.
What is the surface area of the clock, including the base?
______________________________________
(reporting wrong/spam answers)
(giving brainliest to the correct answer)
______________________________________
Answers
The square pyramid-shaped clock has a surface area of 144 square inches, including the base.
What is surface area ?Surface area is the total area of the exposed surfaces of a 3-dimensional object, or an object with length, width and height. It is the sum of all of the areas of the faces of the object, including curved surfaces. It is measured in square units, such as square centimeters or square meters. Surface area is important in fields such as engineering and materials science, where it is used to calculate the amount of material needed for a given object.
To calculated to the total area, multiply by the length of the base, b, by the height, h. A = b × h is the equation- for to the area, A, of a square or rectangle area.
Surface area and arc length of curves differ in a number of ways, one of which is that surface area cannot simply be defined as the maximum area of polyhedral shapes that approximate a given smooth surface.
Since each of the triangle has one side as 9,
if we split it down to the middle and should rearrange it,
we get a 3×9 rectangle
that is = 27 inches
there are 4 of for those = 4x27 = 108.
the square in the middle is = 36 inches
36+108= 144
144 square inches
The surface area of the clock is 144 square inches.
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The weight of Amara to the weight of toyin is 3:5, if Amara weighs 30 kg , how many more does Toyin weight?
Answers
Answer:
Toyin weighs 50 kg, which is 20 kg more than Amara.
Step-by-step explanation:
If Amara weighs 30 kg and the ratio of the weight of Amara to the weight of Toyin is 3:5, then we can set up a proportion:
3/5 = 30/x
where x is the weight of Toyin in kg.
To solve for x, we can cross-multiply:
3x = 150
x = 50
Therefore, Toyin weighs 50 kg, which is 20 kg more than Amara.
what are the possible numbers of positive, negative, and complex zeros of f(x)=3x^4-5x^3-x^2
Answers
Answer:
Counting the number of sign changes in the function f(x)
The number of positive roots is equal to the number of sign changes in the function f(x) or less than that by an even integer.
Here, f(x)=3x^4-5x^3-x^2 has two sign changes (from + to -, and from - to +), so the number of positive roots is either 2 or 0.
Counting the number of sign changes in the function f(-x)
The number of negative roots is equal to the number of sign changes in the function f(-x) or less than that by an even integer.
Here, f(-x)=3x^4+5x^3-x^2 has one sign change (from - to +), so the number of negative roots is either 1 or 0.
Counting the number of non-real roots (complex roots)
The number of non-real roots (complex roots) is equal to the difference between the total number of roots (4 in this case) and the number of real roots (which we found above).
Therefore, the possible number of positive roots is 2 or 0, the possible number of negative roots is 1 or 0, and the possible number of complex roots is 2 or 4.
Step-by-step explanation:
Wave heights at Folly Beach are normally distributed with a mean of 4 feet and a standard deviation of 1.5 feet.
What is the probability that a wave has a height of exactly 3 feet?
Answers
Answer:
Since wave heights at Folly Beach are normally distributed with a mean of 4 feet and a standard deviation of 1.5 feet, we can use the normal distribution formula to find the probability of a wave having a height of exactly 3 feet.
The formula for the normal distribution is:
P(x) = (1 / (σ * sqrt(2π))) * e^(-(x - μ)^2 / (2 * σ^2))
where:
P(x) is the probability density function
σ is the standard deviation
μ is the mean
e is the base of the natural logarithm
x is the value of the variable
Substituting the values given in the problem, we get:
P(3) = (1 / (1.5 * sqrt(2π))) * e^(-(3 - 4)^2 / (2 * 1.5^2))
P(3) = 0.176
Therefore, the probability that a wave has a height of exactly 3 feet is 0.176 or approximately 17.6%.
A straight line is drawn on the graph.
Enter an equation in slope-intercept form. Use y = mx + b, where m is the slope and b is the y-intercept.
Answers
An equation of the line in slope-intercept form drawn on the graph is y = 3x/2 + 8.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of any straight line can be determined by using this mathematical expression:
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.Next, we would determine the slope;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (20 - 8)/(8 - 0)
Slope (m) = 12/8
Slope (m) = 3/2
At data point (0, 8) and a slope of 3/2, a linear equation for this line can be determined by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 8 = 3/2(x - 0)
y = 3x/2 + 8
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Find the perimeter of the figure
Answers
Find the value of the unknown base.
Log n 1/4=-1/2
Answers
Answer:
Therefore, the value of the unknown base is n = 16.
Step-by-step explanation:
Using the definition of logarithms, we have:
log_n(1/4) = -1/2
This equation can be rewritten as:
n^(-1/2) = 1/4
To solve for n, we can raise both sides to the -2 power:
n^(-1/2)^(-2) = (1/4)^(-2)
n = 16
Therefore, the value of the unknown base is n = 16.
area is 14 sq feet what is it after dilation with a scale factor of 2
Answers
The area after dilation with a scale factor of 2 will be 56 sq feet.
How to calculate The area after dilationWhen a figure is dilated with a scale factor of 2, the area of the figure is multiplied by the square of the scale factor.
So, if the original area is 14 sq feet, then the new area after dilation will be:
New area = Original area x (scale factor)^2
= 14 x 2^2
= 14 x 4
= 56 sq feet.
Therefore, the new area of the figure after dilation with a scale factor of 2 is 56 sq feet.
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Ms. Jan brought cookies for her class. She gave out half of them in the morning. At lunch, she gave out 12 more. She had 10 cookies left. How many cookies did she bring in?
Answers
Answer:
Step-by-step explanation:
44
Answer:
Step-by-step explanation:
Let [tex]c[/tex] be the total cookies.
[tex]\frac{1}{2}c+12+10=c[/tex]
[tex]\frac{1}{2}c+22=c[/tex]
[tex]c+44=2c[/tex] (multiplied both sides by 2)
[tex]44=c[/tex] (subtracted c from both sides)
[tex]c=44[/tex]
She began with 44 cookies.
Jose's family is renting a car for their family vacation. The car rental agency rents cars for $64 plus an additional charge of $0.20 per mile. The equation below represents the total cost of renting the car where x represents the number of miles driven.
Answers
No matter how many miles are travelled, only the standard rental fee of equation $64 is paid. The total cost of the rental is determined by multiplying the miles driven by the additional $0.20 per mile price.
What is equation?An equation is a mathematical statement that proves the equality of two expressions connected by an equal sign '='. For instance, 2x – 5 = 13. Expressions include 2x-5 and 13. '=' is the character that links the two expressions. A mathematical formula that has two algebraic expressions on either side of an equal sign (=) is known as an equation. It depicts the equivalency relationship between the left and right formulas. L.H.S. = R.H.S. (left side = right side) in any formula.
The following equation is used to calculate the overall cost of renting a car:
C(x) = 0.20x + 64
where x is the amount of miles driven and C(x) is the rental car's total cost.
No matter how many miles are travelled, only the standard rental fee of $64 is paid. The total cost of the rental is determined by multiplying the miles driven by the additional $0.20 per mile price.
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Determine whether the following study described is observational or an experiment. If the study is an experiment, identify the control and treatment groups, and discuss whether single- or double-blinding is necessary. If the study is observational, state whether it is a retrospective study, and if so, identify the cases and controls.
A study by university social scientists found that 19.1
%
of first-year women students surveyed at a regional college experienced sexual assault during that first year.
Answers
The study that we have here is an observational study. The study is not retrospective in nature.
What type of research study is thisThis study is observational because the researchers are observing and collecting data on a group without manipulating any variables.
It is not a retrospective study because the data is collected in real-time during the first year of college, rather than looking back on past experiences.
Therefore, there are no treatment or control groups, and there is no need for blinding. The study simply reports the percentage of first-year women students who experienced sexual assault during their first year at the regional college.
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A car is taken to a mechanic for repair. The mechanic charges 85 dollars for parts, plus 37 dollars per hour for labor. Write a linear equation , in slope-intercept form , that models this situation . (Note: "y=" is already given just enter the right side of the equation.) y = In the equation, the variable x represents which of the following ? (Choose one) total cost of the repair (dollars ) cost for parts ( dollars ) Ohourly cost of labor (dollars per hour ) time spent repairing the vehicle (hours) In the equation, the variable y represents which of the following? (Choose one) cost for parts (dollars ) time spent repairing the vehicle (hours) Ototal cost of the repair (dollars )
Answers
Answer: The linear equation in slope-intercept form that models this situation is:
y = 37x + 85
In this equation, the variable x represents the time spent repairing the vehicle in hours.
The variable y represents the total cost of the repair in dollars.
Step-by-step explanation:
ABC and XYZ are similar. Find the missing side length.
AA
54
2,
CX 5
А
?
B
45
Y
(The triangles are not drawn to scale.)
6
Answers
Therefore, the missing side length is 162 when triangle ABC and XYZ are similar.
What is triangle?A triangle is a closed two-dimensional plane figure with three straight sides and three angles. It is one of the basic shapes in geometry, and it is formed by connecting three non-collinear points with line segments. The sum of the three angles in a triangle is always 180 degrees. Triangles can be classified based on their side lengths and angle measures, and they have important properties and applications in various fields, including mathematics, science, engineering, and art.
Here,
Since triangles ABC and XYZ are similar, their corresponding sides are in proportion. We can set up the following proportion using the given side lengths:
AC/XY = BC/YZ
Substituting the given values, we get:
2/54 = 6/x
Cross-multiplying, we get:
2x = 54 × 6
2x = 324
Dividing both sides by 2, we get:
x = 162 units
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find the vertex
(x^2)-8x+14
Answers
Answer: (4,-2)
Explanation: (I was forced to put one)
The vertex form of a quadratic function is f(x) = a(x – h)2 + k, where a, h, and k are constants.
Suppose you have $8,295 in savings when the price level index is at 100. If inflation pushes the price level up by 9 percent, calculate the real value of your savings.
Answers
Answer: To calculate the real value of your savings after inflation, you need to adjust your savings for the increase in the price level. Here's how to do it:
Calculate the amount of inflation:
Inflation rate = (New price level index - Old price level index) / Old price level index
In this case, the old price level index is 100, and the new price level index is 109 (100 + 9%). So:
Inflation rate = (109 - 100) / 100 = 0.09
Adjust your savings for inflation:
Real value of savings = Nominal value of savings / (1 + inflation rate)
In this case:
Real value of savings = 8,295 / (1 + 0.09) = 7,614.22
Therefore, the real value of your savings after inflation is $7,614.22.
Step-by-step explanation:
-8 times f(0)+4 times g(-8)
Answers
The value of the given expression is -60. The solution has been obtained by using arithmetic operations.
What are arithmetic operations?
The four basic operations, also referred to as "arithmetic operations," are said to be able to describe all real numbers. The four mathematical operations following division, multiplication, addition, and subtraction are quotient, product, sum, and difference.
We are given two functions as f(x) = [tex]\frac{2x}{3}[/tex] + 7 and g(x) = 2x + 15
So,
⇒f (0) = [tex]\frac{0}{3}[/tex] + 7
⇒f (0) = 7
Similarly,
⇒g (-8) = 2 (-8) + 15
⇒g (-8) = -16 + 15
⇒g (-8) = -1
Now, on substituting these in the expression, we get
⇒-8 * f (0) + 4 * g (-8)
⇒-8 * 7 + 4 * (-1)
Now using the arithmetic operations, we get
⇒-56 -4
⇒-60
Hence, the value of the given expression is -60.
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Question:
If the following equations represent the functions f(x) and g(x).
f(x) = 2/3x + 7 and g(x) = 2x + 15
Calculate the value of -8 * f(0) + 4 * g(-8)
Shift the graph of y=x+1 up 5 units
Answers
The equation for the shifted graph is y = x + 6.This equation represents the same line as the original equation, y = x + 1, but shifted up by 5 units.
Define shifting of graph?Shifting a graph involves moving it horizontally or vertically while maintaining the same shape and orientation.
To shift the graph of y = x + 1 up by 5 units, you need to add 5 to the y-coordinate of every point on the graph.
The original graph of y = x + 1 is a straight line with slope 1 and y-intercept 1.
To create the shifted graph, you can start by plotting a few points on the original graph and then adding 5 to their y-coordinates to get the corresponding points on the shifted graph.
Alternatively, you can use the general equation for a straight line, y = mx + b, where m is the slope and b is the y-intercept, to find the equation for the shifted graph.
The slope of the original graph is 1, so the slope of the shifted graph is also 1.
To find the y-intercept of the shifted graph, you can plug in x = 0 and y = 6 (since you want the graph to pass through the point (0, 6)) and solve for b:
6 = 1(0) + b
b = 6
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Suppose c = 9 and A = 50 degrees.
Find:
Answers
Therefore , the solution of the given problem of triangle comes out to be a length measures about 5.64 units in length.
What is a triangle exactly?If a polygon has more than one extra sections, it is a hexagon. It has a straightforward square form. Something like this configuration can only be distinguished from a conventional triangle by the sides A and B. The borders continue to be precisely collinear, but Euclidean geometry only yields a section rather than the entire cube. A triangular has three sides and three angles.
Here,
Let's determine the length of side b using the sine function:
opposite/hypotenuse of sin(A)
=> b/9 sin(50) = 9*sin(50) b = 7.021
Side B is therefore roughly 7.021 units long.
We can use the knowledge that the sum of the angles in a triangle is 180 degrees to determine the size of angle B:
=> angle B = 180 - angle A - 90
=> angle B = 180 - 50 - 90
=> angle B = 40 degrees
B's angle therefore has a 40 degree value.
The Pythagorean formula can also be used to determine the length of side a:
The equation is:
=> a² + b² = c²
=> a² + 7.021² = 9²
=> a² + 49.24 = 81
=> a² = 31.76
=> a ≈ 5.64
Side a therefore measures about 5.64 units in length.
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Increase the number 15/16 by 3/5 of it of it. Then increase the resulting number by 3/5 of it.
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Answer:
Step-by-step explanation: 0.3375 by simple algebra.
Write a congruence statement for the triangles
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Triangle ABC is congruent to triangle PQR, where A corresponds to P, B corresponds to Q, and C corresponds to R.
What is congruency?
In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.
To write a congruence statement for two triangles, we need to identify their corresponding parts and ensure that they are congruent in both triangles.
The congruence statement can be written in the following form:
Triangle ABC is congruent to triangle PQR, where A corresponds to P, B corresponds to Q, and C corresponds to R.
For example, if we have two triangles with vertices A, B, and C and P, Q, and R respectively, and we know that the following pairs of corresponding parts are congruent:
AB ≅ PQ
BC ≅ QR
AC ≅ PR
Then, we can write the congruence statement as:
Hence, Triangle ABC is congruent to triangle PQR, where A corresponds to P, B corresponds to Q, and C corresponds to R.
The symbol ≅ means "is congruent to."
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