Differentiate the function. Then find an equation of the tangent line at the indicated point on the graph of the function.
Answers
Answer:
The derivative of the function:
[tex]f'(x)=-\dfrac{1}{2\sqrt{5-x} }[/tex]
The tangent line of the function at the given point:
[tex]y=-\dfrac{1}{6}x-\dfrac{25}{3}[/tex]
Step-by-step explanation:
Find the equation of the tangent line of the given function using the given point.
[tex]f(x)=6+\sqrt{5-x}; \ (x,y)=(-4,9)[/tex]
[tex]\hrulefill[/tex]
To find the equation of the tangent line to a function at a given point, follow these step-by-step instructions:
Step 1: Identify the point of tangency
Determine the x-coordinate of the point of tangency. Let's call it x₀.Find the corresponding y-coordinate of the point of tangency. Let's call it y₀.Step 2: Find the derivative of the function
Calculate the derivative of the given function. Let's denote it as f'(x).Step 3: Substitute the x-coordinate into the derivative
Replace the variable x in the derivative function f'(x) with the x-coordinate of the point of tangency (x₀).Evaluate the derivative at x₀ to find the slope of the tangent line. Let's denote it as m.Step 4: Write the equation of the tangent line
Use the point-slope form of a line: y - y₀ = m(x - x₀).Substitute the values of m, x₀, and y₀ into the equation.Simplify and rearrange the equation to obtain the final form.Step 5: Optional - Simplify the equation
If necessary, simplify the equation by performing any algebraic manipulations.Step 6: Optional - Verify the equation
Check the obtained equation by plugging in other points along the tangent line and ensuring they satisfy the equation.[tex]\hrulefill[/tex]
Step 1:
[tex](x_0,y_0) \rightarrow (-4,9)[/tex]
Step 2:
[tex]f(x)=6+\sqrt{5-x}\\\\\\\Longrightarrow f(x)=6+(5-x)^{1/2}\\\\\\\Longrightarrow f'(x)=\dfrac{1}{2} (5-x)^{1/2-1} \cdot -1\\\\\\\therefore \boxed{f'(x)=-\dfrac{1}{2\sqrt{5-x} } }[/tex]
Step 3:
[tex]f'(x)=-\dfrac{1}{2\sqrt{5-x} } ; \ (-4,9)\\\\\\\Longrightarrow f'(-4)=-\dfrac{1}{2\sqrt{5-(-4)} } \\\\\\\Longrightarrow f'(-4)=-\dfrac{1}{2\sqrt{9}} \\\\\\\Longrightarrow f'(-4)=-\dfrac{1}{2(3)} \\\\\\\therefore \boxed{ f'(-4)=m=-\dfrac{1}{6} }[/tex]
Step 4 and 5:
[tex]y-y_0=m(x-x_0)\\\\\\\Longrightarrow y-9=-\dfrac{1}{6}(x-(-4)) \\\\\\\Longrightarrow y-9=-\dfrac{1}{6}(x+4) \\\\\\\Longrightarrow y-9=-\dfrac{1}{6}x-\dfrac{2}{3}\\\\ \\\therefore \boxed{\boxed{ y=-\dfrac{1}{6}x-\dfrac{25}{3}}}[/tex]
Thus, the problem is solved.
Related Questions
On a number line, point C is at 8, and the midpoint E of CD is at -3.
Point D is at
on the number line.
Answers
Answer: C
Step-by-step explanation:
Point D is at -14 on the number line.
How to determine the midpoint of a line segment?In Mathematics, the midpoint of a line segment with two end points can be calculated by adding each end point on a line segment together and then divide by two (2).
Since E is the midpoint of line segment CD, we can logically deduce the following relationship:
Line segment CD = Line segment C + Line segment D
Midpoint E = (point C + point D)/2
By substituting the given points into the equation above, we have the following:
-3 = (8 + D)/2
-6 = 8 + D
D = -6 - 8
D = -14
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How do we do
700/3.14 without a calculator please show a method that would work with any whole number divided by a decimal?
If answer and explanation are correct and they are understandable and useable I will rate five stars , 13PTS, a thanks and BRAINLIEST
Answers
700 divided by 3.14 is approximately 2.23.
To divide a whole number by a decimal without using a calculator, you can follow these steps:
Convert the decimal divisor into a whole number by multiplying both the numerator and denominator by a power of 10 that eliminates the decimal. In this case, we have 3.14, so we can multiply it by 100 to get 314 as the new divisor.
700 ÷ (3.14 × 100)
Perform the division using the converted divisor. Divide 700 by 314:
700 ÷ 314 = 2.229...
Round the result to the desired number of decimal places, if necessary. Since the question does not specify the level of precision required, we will round the result to two decimal places:
2.229... ≈ 2.23
Therefore, 700 divided by 3.14 is approximately 2.23.
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Which fraction is represented by point A on the number line?
Answers
The fraction represented by point A, it is crucial to have information about the scale, intervals, and the relative position of point A on the number line.
With these details, you can calculate the fraction accurately.
Point A on the number line represents a fraction that requires additional information to determine its precise value.
I can provide you with a general approach to finding the fraction corresponding to a given point on the number line.
A number line represents a range of values, typically with a specific scale or interval.
The scale can be divided into equal parts, such as units or fractions.
To determine the fraction represented by point A, we need to know the scale and the position of point A relative to that scale.
Let's consider a number line that ranges from 0 to 1, with evenly spaced tick marks representing tenths.
If point A is located halfway between the tick marks representing 0.4 and 0.5, then it represents the fraction 0.45 (or 9/20 in simplified form).
If the number line has a different scale or is divided into different intervals, the fraction represented by point A will be different.
Without specific details about the number line and the position of point A, it is impossible to determine the fraction precisely.
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Houston, TX and New Orleans, LA are 348 miles apart. On a map, these two cities are 2.3 centimeters apart. Use this scale to determine the distance between Houston, TX and Dallas, TX if they are 1.6 centimeters apart on the map.
Answers
Based on the given scale, if Houston and Dallas are 1.6 centimeters apart on the map, the estimated distance between the two cities is approximately 242.1 miles.
To determine the distance between Houston, TX and Dallas, TX using the given scale, we can set up a proportion using the distances on the map and the actual distances.
Let's denote the distance between Houston and Dallas as "x" (in miles).
According to the scale provided, 2.3 centimeters on the map represents a distance of 348 miles. This can be expressed as:
2.3 cm / 348 miles = 1.6 cm / x miles
To find the value of "x," we can cross-multiply and solve the equation:
(2.3 cm) * (x miles) = (1.6 cm) * (348 miles)
2.3x = 556.8
Divide both sides by 2.3 to isolate "x":
x = 556.8 / 2.3
x ≈ 242.0869565
Therefore, based on the given scale, if Houston and Dallas are 1.6 centimeters apart on the map, the estimated distance between the two cities is approximately 242.1 miles.
Please note that this is an approximation based on the given scale and the assumption that the scale is linear and consistent throughout the map. Actual distances may vary and should be verified using more accurate measurements or reliable sources.
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What are the solutions to the equation 0=|3x+3|+3
Answers
Therefore, the solutions to the equation 0 = |3x + 3| + 3 are x = -2 and x = 0.
To solve the equation 0 = |3x + 3| + 3, we need to eliminate the absolute value. Remember that the absolute value of a number is always non-negative.
First, let's isolate the absolute value term on one side of the equation:
|3x + 3| = -3
Since the absolute value cannot be negative, there are no solutions to the equation as it stands. However, if we modify the equation to make the right side positive, we can find a solution.
To eliminate the absolute value, we can rewrite the equation as two separate equations, considering both the positive and negative cases:
3x + 3 = -3
-(3x + 3) = -3
Solving equation 1:
3x + 3 = -3
3x = -6
x = -2
Solving equation 2:
-(3x + 3) = -3
-3x - 3 = -3
-3x = 0
x = 0
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What is the power of a lamp rated at 12 V 2 A?
Answers
Answer:
24 W
Step-by-step explanation:
7 3/8 as an inpropuar fracition
Answers
Explanation: 7*8=56
56+3=59
59/8
Solve the math word problem. A toaster has 4 slots for bread. Once the toaster is warmed up, it takes 35 seconds to make 4 slices of toast, 70 seconds to make 8 slices, and 105 seconds to make 10 slices. How long do you think it will take to make 20 slices?
Answers
To determine how long it will take to make 20 slices of toast with the given information, we can analyze the patterns and ratios observed in the data.
From the provided data, we can see that the time it takes to make toast is directly proportional to the number of slices. Specifically, as the number of slices doubles, the time doubles as well.
Using this pattern, we can calculate the estimated time it would take to make 20 slices.
Starting with the given information:
35 seconds for 4 slices
70 seconds for 8 slices
105 seconds for 10 slices
Since the time doubles as the number of slices doubles, we can estimate that it would take approximately 140 seconds for 16 slices (double of 8 slices).
Now, doubling again, we can estimate that it would take approximately 280 seconds for 20 slices (double of 10 slices).
Therefore, it is estimated that it will take around 280 seconds to make 20 slices of toast.
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Find the inverse of the function. y=x2+4x+4
Answers
The inverse of the function [tex]y = x^2 + 4x + 4 is f^(-1)(x) = -2 ± √(x - 2).[/tex]C
is correct answer
To find the inverse of the function y = x^2 + 4x + 4, we can follow the steps for finding the inverse of a function:
Step 1: Replace y with x and x with y:
[tex]x = y^2 + 4y + 4[/tex]
Step 2: Solve the equation for y:
[tex]x = y^2 + 4y + 4[/tex]
Step 3: Rearrange the equation:
[tex]y^2 + 4y + 4 - x = 0[/tex]
Step 4: Solve the quadratic equation for y using factoring or the quadratic formula. In this case, the equation can be factored:
[tex](y + 2)(y + 2) - x = 0(y + 2)^2 - x = 0[/tex]
Step 5: Expand and rearrange the equation:
[tex]y^2 + 4y + 4 - x = 0y^2 + 4y = x - 4y^2 + 4y = x - 2^2y^2 + 4y = (x - 2^2)[/tex]
Step 6: Complete the square on the left side of the equation:
[tex](y^2 + 4y + 4) = (x - 2^2) + 4(y + 2)^2 = (x - 2)[/tex]
Step 7: Take the square root of both sides:
[tex]y + 2 = ±√(x - 2)[/tex]
Step 8: Solve for y:
[tex]y = -2 ± √(x - 2)[/tex]
The inverse function of y = x^2 + 4x + 4 is given by:
[tex]f^(-1)(x) = -2 ± √(x - 2)[/tex]
Therefore, the inverse of the function y = [tex]x^2 + 4x + 4 is f^(-1)(x) = -2 ± √(x - 2).[/tex]
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Each statement describes a transformation of the graph of f(x) = x. Which statement correctly describes the graph of g(x) if g(x) = f(9x)? O It is the graph of f(x) stretched vertically by a factor of . O It is the graph of f(x) shrunk vertically by a factor of 9. O It is the graph of f(x) shrunk horizontally by a factor of 9. It is the graph of f(x) stretched horizontally by a factor of 9.
Answers
The correct statement that describes the transformation of the graph of f(x) = x when considering g(x) = f(9x) is: "It is the graph of f(x) shrunk horizontally by a factor of 9."
To understand this transformation, let's analyze the function g(x) = f(9x). When we substitute x with 9x inside f(x), we effectively compress the graph horizontally.
Since the input x is multiplied by 9, the graph is squeezed horizontally by a factor of 9. This means that the x-values on the graph of g(x) are condensed compared to those on the graph of f(x).
It is important to note that the vertical scaling remains unchanged since the coefficient multiplying x remains 1 in both functions. Therefore, there is no vertical stretching or shrinking.
In summary, the graph of g(x) = f(9x) is the graph of f(x) shrunk horizontally by a factor of 9, while the vertical scaling remains unaffected.
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The triangles shown below must be congruent.
True or false
Answers
True because corresponding sides and angles of the triangles are congrent.
For the following event, state whether you think the difference between what occurred and what you would expect by chance is statistically significant. Explain.
An airline with a 95% on-time departure rate has 16 out of 300 flights with late departures.
Answers
The difference between the observed and expected number of late departures is statistically significant, we need to perform a binomial test by calculating the probability of observing 16 or more late departures out of 300 flights assuming the null hypothesis is true. If the resulting p-value is less than 0.05, we can conclude that the difference is statistically significant.
Based on the given information, an airline with a 95% on-time departure rate has 16 out of 300 flights with late departures. The question asks whether the difference between what occurred (16 late departures) and what you would expect by chance is statistically significant.
To determine if the difference is statistically significant, we need to conduct a hypothesis test. In this case, we can use a binomial test since we are dealing with two possible outcomes: on-time departure or late departure.
The null hypothesis (H0) assumes that the observed number of late departures is equal to what would be expected by chance. The alternative hypothesis (Ha) assumes that there is a significant difference between the observed and expected values.
In this case, the expected number of late departures can be calculated by multiplying the total number of flights (300) by the expected on-time departure rate (95%). This gives us an expected value of 300 * 0.05 = 15.
To perform the binomial test, we can calculate the probability of observing 16 or more late departures out of 300 flights, assuming the null hypothesis is true. This probability can be calculated using the binomial probability formula or by using statistical software.
If the resulting probability (also known as the p-value) is less than the significance level (usually 0.05), we can reject the null hypothesis and conclude that the difference between what occurred and what would be expected by chance is statistically significant. Otherwise, if the p-value is greater than 0.05, we fail to reject the null hypothesis and conclude that the difference is not statistically significant.
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A restaurant Serves 80 Costumers 20% do not Order drinks How many. People do Order drinks?
Answers
Among the 80 customers, 64 individuals choose to order drinks at the restaurant.
To find the number of people who order drinks at the restaurant, we can start by calculating the percentage of customers who do not order drinks.
Given that 20% of the customers do not order drinks, we can calculate the number of customers who do not order drinks by multiplying 80 (total customers) by 0.20 (20% expressed as a decimal):
Number of customers who do not order drinks = 80 * 0.20 = 16.
Since the total number of customers is 80, and 16 customers do not order drinks, we can subtract the number of customers who do not order drinks from the total number of customers to find the number of customers who do order drinks:
Number of customers who order drinks = 80 - 16 = 64.
Therefore, 64 people order drinks at the restaurant.
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A triangle has two sides of length 15 cm and 17 cm. Select all the values of its third side that would make it a right triangle. A triangle has two sides of length 15 cm and 17 cm. Select all the values of its third side that would make it a right triangle.
Answers
Based on the Pythagorean theorem, in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side. So, we can use this to find the possible values of the third side of the triangle.
The two given sides are 15 cm and 17 cm. We can label the unknown side as "x". Then, we can set up an equation:
15^2 + 17^2 = x^2
Simplifying this equation, we get:
225 + 289 = x^2
514 = x^2
x = sqrt(514)
Therefore, the possible value of the third side that would make it a right triangle is approximately 22.72 cm.
2+2=? ???¿??????¿????????
Answers
Answer:4
Step-by-step explanation:1+1 is 2, so if you take 2+2 it is 4, same as 2×2 is 4.
Suppose that 6 J of work is needed to stretch a spring from its natural length of 36 cm to a length of 56 cm.
(a)
How much work (in J) is needed to stretch the spring from 44 cm to 52 cm? (Round your answer to two decimal places.)
(b)
How far beyond its natural length (in cm) will a force of 25 N keep the spring stretched? (Round your answer one decimal place.)
Answers
Answer:
To stretch the spring from 36 cm to 56 cm, we need 6 J of work. Let's call the work needed to stretch the spring from 44 cm to 56 cm W1, and the work needed to stretch it from 36 cm to 44 cm W2.
Since the work needed is proportional to the distance the spring is stretched, we can write:
W1/W2 = (56-44)/(56-36)
Solving for W1, we get:
W1 = W2 * (56-44)/(56-36)
Substituting the values, we get:
W1 = 6 * (56-44)/(56-36) = 1.5 J
So, the work needed to stretch the spring from 44 cm to 52 cm is 1.5 J.
Now, let's move on to part (b).
The force required to stretch a spring is given by:
F = kx
where F is the force applied, x is the distance the spring is stretched beyond its natural length, and k is the spring constant.
We can rearrange this equation to solve for x:
x = F/k
We are given that a force of 25 N is applied to the spring. We need to find the distance the spring is stretched beyond its natural length. To do this, we need to know the spring constant.
Unfortunately, the problem does not give us the spring constant.
Without this information, we cannot solve for x.
State if the pair of triangles are similar. If so, state how you know they are similar and complete the similarity statement.
Answers
The triangles EFG and WVU are similar by SSS
Identifying the similar triangles in the figure.from the question, we have the following parameters that can be used in our computation:
Triangle EFG and WVU
The triangles in this figure are
EFG and WVU
These triangles are similar because:
The triangles do have similar corresponding sides
i.e. Ratio = 525/252 = 875/420 = 825/396
Evaluate
Ratio = 2.083 = 2.083 = 2.083
Hence, the triangles EFG and WVU are similar
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If
to DEF?
A 23
B. 16°
C. 32°
D. 58°
Answers
The calculated measure of the angle D is (c) 32 degrees
How to determine the measure of the angleFrom the question, we have the following parameters that can be used in our computation:
The triangles ABC and DEF
The triangles are similar triangles
This means that the corresponding angles are equal
Given that
A = 32 degrees
And the corresponding angle is D
We have
D = 32 degrees
Hence, the measure of the angle is (c) 32 degrees
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I completed 2/3 of my project last month and 1/4 of it this week, what fraction of my project is not completed
Answers
Hello!
Answer:
11/12
Step-by-step explanation:
To solve this problem, we would need to find the denominator of the 2 numbers. In this case, it is 12. We will now convert the fractions to twelfths.
2/3 = 8/12
1/4 = 3/12
After we add 8/12 and 3/12, we get our answer 11/12.
onsider the following ordered pairs that represent a relation.
{(–4, –7), (0, 6), (5, –3), (5, 2)}
What can be concluded of the domain and range for this relation? Check all that apply.
The domain is the y values of the ordered pairs.
The range is the set of output values.
The given relation is a function.
Zero is included in the range of the relation.
5 is included in the domain of this relation.
Answers
the statement “Zero is included in the range of the relation” is correct and the statement “5 is included in the domain of this relation” is also correct.
if we observe the given ordered pairs we can easily determine that,The domain is the set of all x-values from the ordered pairs in the relation.
So, the domain of the given relation is {−4,0,5} because we have only three unique x-values from the given ordered pairs.
The range is the set of all y-values from the ordered pairs in the relation.
So, the range of the given relation is {−7,−3,2,6} because we have four unique y-values from the given ordered pairs.
Also, we can conclude that the given relation is not a function since we have the same x-value (5) corresponding to two different y-values (−3,2).
And it is true that the zero is included in the range of the relation since we have the ordered pair (0,6) which gives the y-value of 6.
So, the statement “The given relation is a function” is incorrect. But the statement “Zero is included in the range of the relation” is correct and the statement “5 is included in the domain of this relation” is also correct.
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Pls help I need help on this question
Answers
Answer: B
Step-by-step explanation: Hope this helps:)
Two containers designed to hold water are side by side, both in the shape of a
cylinder. Container A has a diameter of 10 feet and a height of 5 feet. Container B has
a diameter of 6 feet and a height of 9 feet. Container A is full of water and the water is
pumped into Container B until Container B is completely full.
After the pumping is complete, what is the volume of water remaining in Container A,
to the nearest tenth of a cubic foot?
Answers
The nearest tenth of a cubic foot, the volume of water remaining in Container A is approximately 138.2 cubic feet.
To find the volume of water remaining in Container A after it is completely filled and transferred to Container B, we need to calculate the difference in their volumes.
The volume of a cylinder can be calculated using the formula:
V = πr^2h
where V is the volume, r is the radius, and h is the height.
Container A:
Diameter = 10 feet
Radius (r) = 10/2 = 5 feet
Height (h) = 5 feet
Container B:
Diameter = 6 feet
Radius (r) = 6/2 = 3 feet
Height (h) = 9 feet
Now, let's calculate the volumes of both containers:
Volume of Container A = π(5^2)(5) = 125π cubic feet
Volume of Container B = π(3^2)(9) = 81π cubic feet
To find the volume of water remaining in Container A, we subtract the volume of Container B from the volume of Container A:
Volume remaining in Container A = Volume of Container A - Volume of Container B
= 125π - 81π
= 44π cubic feet
To get the volume to the nearest tenth of a cubic foot, we can use an approximation for the value of π, which is approximately 3.14:
Volume remaining in Container A ≈ 44(3.14) ≈ 138.16 cubic feet
Therefore, to the nearest tenth of a cubic foot, the volume of water remaining in Container A is approximately 138.2 cubic feet.
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Find the missing side.
+
18
12
x = [?]
Round to the nearest tenth.
Answers
[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies a=\sqrt{c^2 - o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{18}\\ a=\stackrel{adjacent}{x}\\ o=\stackrel{opposite}{12} \end{cases} \\\\\\ x=\sqrt{ 18^2 - 12^2}\implies x=\sqrt{ 324 - 144 } \implies x=\sqrt{ 180 }\implies x\approx 13.4[/tex]
The missing side of a right-angled triangle, assuming it to be the hypotenuse with other sides as 12 and 18, can be calculated using the Pythagorean theorem. The square root of the sum of 12^2 and 18^2 gives the length of the hypotenuse, which is approximately 21.6 when rounded to the nearest tenth.
Explanation:This question relates to the Pythagorean theorem which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as: a² + b² = c².
Assuming that the missing side in your question (x) is the hypotenuse and the other two sides are 12 and 18, you can calculate it using the aforementioned theorem. Therefore, you find x by calculating the square root of (12² + 18²), or √(144 + 324) which equals to √468. This value, rounded to the nearest tenth, is 21.6.
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Describe how the graph of h(x) = -2x - 4 can be obtained from one of the basic graphs. Then graph the function.
Answers
To obtain the graph of h(x) = -2x - 4, start with the graph of y = x. Stretch vertically by multiplying each x-coordinate by 2. Then reflect it across the x-axis and shift it down by 4 units
Describing how the graph of h(x) = -2x - 4 can be obtainedFrom the question, we have the following parameters that can be used in our computation:
h(x) = -2x - 4
The parent function is
f(x) = x
First, stretch vertically by a factor of 2
So, we have
f'(x) = 2x
Next, we reflect across the x-axis
So, we have
f''(x) = -2x
Lastly, we shift down by 4 units
So, we have
h(x) = -2x - 4
The graph is attached
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Please awnser asap I will brainlist
Answers
The number of vans, small truck and large truck they can buy is 130, 65 and 65 respectively.
How many of each vehicles can be bought?Total cost of vehicles = $10 million
Total number of vehicles = 260
Cost of each commercial van = $25,000
Cost of each small truck = $50,000
Cost of each large truck = $50,000
Let
c = commercial van
s = small truck
l = large truck
v = 2s
s = l
So,
v + s + l = 260
2s + s + s = 260
4s = 260
divide both sides by 4
s = 260/4
s = 65
Therefore,
v = 2s
= 2(65)
= 130
s = l
l = 65
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In the diagram, the measures of 22, 23 and 26 are 40°. The measure of 21
is 140°. Are lines cand d parallel?
محے
A. No, because 26 and 21 are not congruent.
B. Yes, because 22 and 23 are congruent.
C. No, because 21 and 22 are not congruent.
D. Yes, because 22 and 26 are congruent.
Answers
The lines c and d are not parallel.
The correct answer is A. No, because 26 and 21 are not congruent.
In order for two lines to be parallel, the corresponding angles formed by a transversal should be congruent. However, in this case, angles 26 and 21 are not congruent, as indicated by their different measures of 40° and 140°, respectively.
Therefore, we can conclude that lines c and d are not parallel. The congruence of angles 22 and 23, mentioned in option B, or the congruence of angles 22 and 26, mentioned in option D, does not provide sufficient information to determine the parallelism of lines c and d.
The key factor in determining parallel lines is the congruence of corresponding angles, which is not met in this scenario.
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Sample Answer: The vertical line test determines if one input has exactly one output on the graph. If any vertical line passes through more than one point on the graph, then the relation is not a function.
Which did you include in your response?
Draw vertical lines to intersect on a graph.
The relation is a function if there’s only one point of intersection on a graph.
The relation is not a function if there’s more than one point of intersection on a graph.
The vertical line test is used to determine if each input has exactly one output.
Answers
Answer: All of the choices in the response would be correct.
Step-by-step explanation:
Assignment
Practice using function notation.
The values in the table represent a function.
f(x)
8
X
-6
7
4
3
-5
3
-5
-2
12
Use the drop-down menus to complete the
statements.
The ordered pair given in the first row of the table can
be written using function notation as
O
f(3) is
O
f(x) = -5 when x is
Answers
In the first row, the ordered pair can be expressed as f(8) = -6 in function notation.
Of(3) is 18.
Of(x) = -5 when x is -2.
The given table represents a function, and we need to express the values in function notation and determine specific inputs that correspond to certain outputs.
In the table's first row, the ordered pair are shown which can be expressed as function notation:
f(8) = -6
This means that when the input (x) is 8, the corresponding output (f(x)) is -6.
f(x) = -5 when x is -2.
This means that when the input (x) is -2, the value of the function (f(x)) is -5.
In the table, the function is defined by the equation f(x) = 8x - 6. Each input value (x) is multiplied by 8 and then subtracted by 6 to determine the corresponding output (f(x)).
By substituting different values for x into the function, we can find the corresponding values for f(x) in the table.
when x = 3, we have:
f(3) = 8(3) - 6
f(3) = 24 - 6
f(3) = 18
So, f(3) is 18.
Similarly, when x = -2, we have:
f(-2) = 8(-2) - 6
f(-2) = -16 - 6
f(-2) = -22
Thus, when x is -2, f(x) is -22.
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A quadrilateral with 90 degree angles is shown. The lengths of the left and right sides are 10 and 2 y + 4. The lengths of the top and bottom sides are 18 and 10 + 2 x.
A quadrilateral with 90 degree angles is shown. The lengths of the left and right sides are 10 and 2 y + 4. The lengths of the top and bottom sides are 18 and 10 + 2 x.
What is the value of y?
3
4
5
6
Answers
To find the value of y, we can use the fact that opposite sides of a parallelogram are equal in length. Therefore, we can set up the following equations:
10 = 10 + 2x
2y + 4 = 18
Simplifying the first equation, we get:
2x = 0
Solving for x, we get:
x = 0
Substituting x = 0 into the second equation, we get:
2y + 4 = 18
Simplifying this equation, we get:
2y = 14
Dividing both sides by 2, we get:
y = 7
Therefore, the value of y is 7.
In the diagram, the measures of 23 and 27 are 45°. The measure of 25 is
135°. Are lines cand dparallel?
F
5
8
OA. Yes, because 23 and 27 are congruent.
OB. No, because 27 and 25 are not congruent.
C. Yes, because 25 and 27 are supplementary.
D. No, because 23 and 25 are not supplementary.
Answers
The correct answer is D. No because 23 and 25 are not supplementary.
In the given diagram, it is stated that the measures of angles 23 and 27 are 45°, and the measure of angle 25 is 135°. To determine if lines C and D are parallel, we need to analyze the angles formed by these lines.
If the alternate interior angles or corresponding angles are congruent, then the lines are parallel. However, in this case, we don't have enough information about the angles formed by lines C and D to make that determination.
The fact that angle 23 and angle 27 are congruent (both measuring 45°) doesn't provide any information about the relationship between lines C and D. Similarly, the measure of angle 25 being 135° doesn't give us any insight into the parallelism of lines C and D. Therefore, we cannot conclude that lines C and D are parallel based on the given information, and the correct answer is D.
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