The reflector of a flashlight is in the shape of a paraboloid of revolution. Its diameter is 8 centimeters and its depth is 4 centimeters. How far from the vertex should the light bulb be placed so that the rays will be reflected parallel to the axis?
Answers
Answe: The distance of light bulb can be calculated using equation of parabola. The parabola is a plane curve which is U-shaped.
Step-by-step explanation:
Related Questions
The height distributions of two different classes at Dover elementary school are shown below both groups, have the same interquartile range how many times the third quartile range is the difference between the median height of the third grade class in the fourth grade class 1/4 1/2 two or four
Answers
The third quartile range is the difference between the median height of the third grade class and the fourth grade class, so the answer is two times.
The sum of 2 vector forces is <5, -3>. What is the magnitude of the resulting force?
Answers
According to the question the magnitude of the resulting force is 5.83.
What is magnitude?Magnitude is a measure of the size or intensity of a physical quantity. It is an expression of how large or small a quantity is in comparison to a reference value. Magnitude is typically used in physics and astronomy, but it can also be used in other areas such as engineering and seismology. Magnitude is not an absolute measurement; rather, it is a relative measure of how much larger or smaller one quantity is compared to another. For example, the magnitude of a star's brightness is a measure of how much brighter it is compared to other stars.
The magnitude of the resulting force can be calculated using the Pythagorean theorem. The formula for calculating the magnitude of a vector is:
[tex]\sqrt[]{(x2 + y2)}[/tex]
In this case, x = 5 and y = -3, which gives us:
[tex]\sqrt{(52 + (-3)2)}[/tex] = [tex]\sqrt{(25 + 9)}[/tex] = √[tex]\sqrt{(34)}[/tex] = 5.83.
Therefore, the magnitude of the resulting force is 5.83.
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if you dilate triangle ABC by a scale factor of 3 and (0,0) is the center, what will be the length of AB?
Answers
the new length of AB after a dilation by a scale factor of 3 with (0,0) as the center would be 3 times the original length of AB.
How to solve the question?
To find the new length of AB after a dilation by a scale factor of 3 with (0,0) as the center, we can use the following formula:
AB' = AB x 3
where AB' is the length of AB after the dilation, and AB is the original length of AB.
However, we need to first determine the length of AB in the original right triangle ABC. To do this, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
Let's assume that AB is the hypotenuse of the right triangle ABC, and that AC and BC are the other two sides. Then we have:
AB²= AC²+ BC²
Without more information about the lengths of AC and BC, we cannot determine the value of AB. However, once we have determined the length of AB, we can use the formula above to find the new length of AB after dilation.
Assuming we know the length of AB in the original right triangle ABC, we can now use the formula for dilation to find the new length of AB:
AB' = AB x 3
For example, if AB is 5 units long in the original triangle, then after dilation, AB' would be:
AB' = 5 x 3 = 15 units
Therefore, the new length of AB after a dilation by a scale factor of 3 with (0,0) as the center would be 3 times the original length of AB.
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Jeremy and Aksa were finding the volume of this prism. They agreed that 4 layers can be added together to find the volume. Jeremy says that he can see on the end of the prism that each layer will have 16 cubes in it. Aksa says that each layer has 24 cubes in it. Who is right? Explain your answer.
Answers
Both Jeremy and Aksa could be right, depending on how they are counting the cubes for finding the volume of a prism.
What is a prism?A prism is a three-dimensional solid shape with a constant cross-section, usually a polygon. It is characterized by two identical end faces, parallel and congruent bases, and straight lateral faces connecting the bases.
According to the given information:Both Jeremy and Aksa could be right, depending on how they are counting the cubes.
If the prism has a square base with 4 cubes along each side, then there would be 16 cubes in each layer. If there are 4 layers, then the total volume would be 16 x 4 = 64 cubic units.
However, if the prism has a rectangular base with 6 cubes along one side and 4 cubes along the other side, then there would be 24 cubes in each layer. If there are 4 layers, then the total volume would be 24 x 4 = 96 cubic units.
Therefore, the answer depends on the shape of the prism and how the layers are counted.
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I BEG U FOR HELP WILL GIVE BRAINLIEST PLLSSSS
Answers
Answer:
3,4,5 is the answer
Step-by-step explanation:
for the explanation using pythagoras theoem
[tex] {3}^{2} + {4}^{2} = {5 \\ }^{2} \\ 3 \times 3 + 4 \times 4 = 5 \times 5 \\ 9 + 16 = 25 \\ 25 = 25[/tex]
may you give me branliest as you promised
Polygon KLMN is drawn with vertices at K(0, 0), L(5, 2), M(5, −5), N(0, −3). Determine the image vertices of K′L′M′N′ if the preimage is rotated 270° clockwise.
K′(0, 0), L′(−2, 5), M′(5, 5), N′(3, 0)
K′(0, 0), L′(−2, −5), M′(−5, 5), N′(−3, 0)
K′(0, 0), L′(−5, −2), M′(5, −5), N′(3, 0)
K′(0, 0), L′(−5, −2), M′(−5, −5), N′(0, 3)
Answers
The image vertices of K′L′M′N′ under a rotation of 270° clockwise are:
K′(0, 0), L′(−2, 5), M′(5, 5), N′(3, 0).
What is coordinates?
Coordinates are numerical values used to represent the position of a point in a particular space or system. coordinates are used to identify the position of a point in a given plane or space. Typically, two or three numbers are used to describe the location of a point in a two-dimensional or three-dimensional space, respectively.
To rotate a point by 270° clockwise about the origin, we can swap the coordinates and negate the new x-coordinate. Let's apply this transformation to each vertex of the polygon:
For point K(0, 0), we have K′(0, 0) (since the origin is its own image under any rotation).
For point L(5, 2), we have L′(−2, 5) (swapping the coordinates gives (2, 5), and negating the x-coordinate gives (−2, 5)).
For point M(5, −5), we have M′(5, 5) (swapping the coordinates gives (−5, 5), and negating the x-coordinate gives (5, 5)).
For point N(0, −3), we have N′(3, 0) (swapping the coordinates gives (−3, 0), and negating the x-coordinate gives (3, 0)).
Therefore, the image vertices of K′L′M′N′ under a rotation of 270° clockwise are:
=> K′(0, 0), L′(−2, 5), M′(5, 5), N′(3, 0)
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Can someone help me to answer these questions pleases
Listen to Kerry Washington perform Sojourner Truth's speech Ain't I a Woman. Then go to ST's version at the Sojourner Truth Project's website. Compare the differences between Frances Gage's (the one Washington read) and Marius Robinson's earlier version (the one ST read). You can read them here.
Answer the following questions:
1. List 3 differences between the Robinson version and the Gage version of the speech.
2. Why do you think it is important to hear both versions of the speech?
3. How do you think the differences changed the way people (in the north and the south) understood the context of her speech? How about now?
4. How does hearing the differences in dialect change the way you think about the speech?
answer them in at least 10 sentences.
When women’s rights activists spoke out, who were they advocating for, white women or African-American women?
What are the distinct arguments that Truth makes in her speech?
What is Truth saying about women’s rights?
Who is going to give them these rights?
How does Truth’s speech reflect intersectionality?
What passages in the speech reflect this?
Answers
1. In the Robinson version, Truth asks "And ain't I a woman?" four times, while in the Gage version she only asks it three times. 2. It is important to hear both versions of the speech because they highlight the ways in which historical documents can be altered and manipulated over time. 3. The differences between the two versions of the speech likely changed the way people in the north and south understood the context of her speech in significant ways. 4. Hearing the differences in dialect changes the way we think about the speech by highlighting the unique voice and perspective of the speaker.
What is speech?Speech is the act of expressing thoughts, ideas, or emotions through spoken words. It is a form of communication that allows individuals to convey information, share opinions, ask questions, and express feelings to others.
According to question:1. Three differences between the Robinson version and the Gage version of the speech are:
In the Robinson version, Truth says "I have as much muscle as any man" while in the Gage version she says "I have ploughed and planted, and gathered into barns, and no man could head me!".
In the Robinson version, Truth asks "And ain't I a woman?" four times, while in the Gage version she only asks it three times.
In the Robinson version, Truth refers to herself as a "colored woman" while in the Gage version she uses the term "African American".
2. It is important to hear both versions of the speech because they highlight the ways in which historical documents can be altered and manipulated over time. The differences between the two versions show how editors and publishers can change the meaning and impact of a text by making small modifications to it. Additionally, hearing both versions allows us to appreciate the nuances of language and dialect, and how different speakers can bring their own interpretations and emphasis to a text.
3. The differences between the two versions of the speech likely changed the way people in the north and south understood the context of her speech in significant ways. For example, the reference to "colored women" in the Robinson version would have been seen as more confrontational and controversial in certain regions. Today, the differences may help us appreciate the diversity and complexity of language, and how it reflects the cultural and historical contexts in which it is spoken.
4. Hearing the differences in dialect changes the way we think about the speech by highlighting the unique voice and perspective of the speaker. The dialect used in each version reflects the cultural and historical context of the time, and the different audiences that the speeches were intended for. By hearing the dialect of each version, we can better appreciate the ways in which language shapes our understanding of history and identity.
As for the next set of questions:
When women's rights activists spoke out, they were advocating for both white women and African-American women, although the experiences and struggles of African-American women were often ignored or marginalized within the movement.
Truth makes several distinct arguments in her speech, including that women deserve the same rights and respect as men, that the stereotype of women as weak and dependent is unjust, and that the experiences of African-American women are often overlooked in discussions of women's rights.
Truth is saying that women deserve equal rights and respect as men, and that the societal norms that limit women's opportunities and autonomy are unjust and unfounded.
Truth is arguing that women need to fight for their own rights, rather than waiting for men to give them these rights. She also emphasizes the importance of solidarity and mutual support among women.
Truth's speech reflects intersectionality by recognizing the ways in which race and gender intersect to create unique experiences of oppression and marginalization. She argues that the struggles of African-American women cannot be separated from the struggles of all women, and that a truly equitable society must address the needs and concerns of all marginalized groups. One passage that reflects this is when she says, "I have borne thirteen children, and seen most all sold off to slavery, and when I cried out with my mother's grief, none but Jesus heard me! And ain't I a woman?" This passage highlights the intersection of race, gender, and motherhood in Truth's experience.
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Suppose that the functions fand g are defined as follows.
f(x)=2x-1
g(x)=√3x-5
Answers
The composite functions (f/g)(x) and (f-g)(x) are (2x-1)/√(3x-5) and (2x-1) -√(3x-5)
Calculating the composite functions (f/g)(x) and (f-g)(x)To calculate (f/g)(x), we need to divide f(x) by g(x):
(f/g)(x) = f(x)/g(x) = (2x-1)/√(3x-5)
The domain of (f/g)(x) is the set of all x-values for which the denominator √(3x-5) is not equal to zero and non-negative
3x-5 ≥ 0, or x ≥ 5/3
Therefore, the domain of (f/g)(x) is x ≥ 5/3.
To calculate (f-g)(x), we need to subtract g(x) from f(x):
(f-g)(x) = f(x) - g(x) = (2x-1) - √(3x-5)
The domain of (f-g)(x) is the set of all x-values for which the expression inside the square root is non-negative:
3x-5 ≥ 0, or x ≥ 5/3
Therefore, the domain of (f-g)(x) is x ≥ 5/3.
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An economy is operating with output $400 billion above its natural level, and fiscal policymakers want to close this expansionary gap. The central bank agrees to adjust the money supply to hold the interest rate constant, so there is no crowding out. The marginal propensity to consume is 3/4, and the price level is completely fixed in the short run.
to close the expansionary gap, the government would need to increase or decrease spending by $ billion.
Answers
Hence, to close the expansionary gap, the government would need to decrease spending by $100 billion.
To close the expansionary gap, the government would need to decrease spending by $100 billion.
The formula to calculate the change in equilibrium output due to a change in government spending is:
∆Y = (∆G / (1 - MPC))
Where:
∆Y = change in equilibrium output
∆G = change in government spending
MPC = marginal propensity to consume
Here, the output is $400 billion above its natural level, and the central bank agrees to adjust the money supply to hold the interest rate constant, so there is no crowding out. Therefore, we can assume that the change in government spending (∆G) would have a one-to-one effect on the equilibrium output (∆Y).
Given that MPC = 3/4, we can plug in the values into the formula:
400 = (∆G / (1 - 3/4))
∆G = (1 - 3/4) * 400
∆G = (1/4) * 400
∆G = 100
Hence, to close the expansionary gap, the government would need to decrease spending by $100 billion.
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In triangle BC, point D is on AC such that AD = 12 and CD = 12. If angle ABC = angle BDC = 90 degrees, then what is BD?
Answers
Answer:
Step-by-step explanation:
BD is craxking treys and cracking treys is gd dissing bd you can look it up i ffrom o block and bd is the opps im telling so you wont lose yo life so please play right if you gdk be gdk if u gd be gd we aint bd ofn
In art class students are mixing blue and red paint to make purple paint. Deondra
mixes 6 cups of blue paint and 7 cups of red paint. Arun mixes 2 cups of blue paint
and 3 cups of red paint. Use Deondra and Arun's percent of red paint to determine
whose purple paint will be redder.
Deondra percent of red paint (to nearest whole number) =
Arun percent of red paint (to nearest whole number) =
O Deondra's purple paint will be redder.
O Arun's purple paint will be redder.
o The two purple paints will be equally red.
Submit Answer
%
%
attempt 1 out of 2
Answers
Arun's purple paint will be redder.
Define percentagePercentage is a way of expressing a proportion or a fraction as a number out of 100. It is represented by the symbol "%". For example, if you say that 20% of students in a class scored an A grade in a test, it means that 20 out of every 100 students received an A grade.
Deondra mixed 6 cups of blue paint and 7 cups of red paint, so the percent of red paint in her mixture is:
7 / (6 + 7) × 100% = 53.8%, which rounds to 54%.
Arun mixed 2 cups of blue paint and 3 cups of red paint, so the percent of red paint in his mixture is:
3 / (2 + 3) × 100% = 60%.
Since Arun's mixture has a higher percentage of red paint, his purple paint will be redder than Deondra's.
Therefore, the answer is Arun's purple paint will be redder.
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I need help solving this thank you
Answers
The negation is the fourth option.
6 + 3 ≠ 9 or 6 - 3 ≠ 9
How to write the negation?The negation of an equation is an inequality such that we just change the equal sign, by the "≠" sign.
Here we start with the two equations.
6 + 3 = 9 or 6 - 3 = 9
Just change the equal signs for different signs:
6 + 3 ≠ 9 or 6 - 3 ≠ 9
That is the negation, fourth option.
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What is the range of the relation whose graph is shown?
Answers
The range of the relation whose graph is shown include the following: C. -1 ≤ y ≤ 1.
What is a domain?In Mathematics and Geometry, a domain is the set of all real numbers for which a particular function is defined.
Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = {-4, 4} or -4 ≤ x ≤ 4.
Range = {-1, 1} or -1 ≤ y ≤ 1.
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You want to be able to withdraw $40,000 each year for 15 years. Your account earns 5% interest.
a) How much do you need in your account at the beginning?
b) How much total money will you pull out of the account?
c) How much of that money is interest?
Answers
a) you would need $450,332.81 in your account at the beginning. b) the total money that will be pulled out of the account is $600,000.
How to determine How much do you need in your account at the beginninga) To calculate the amount needed in the account at the beginning, we can use the present value formula:
PV = PMT * ((1 - (1 + r)^-n) / r)
Where PV is the present value, PMT is the annual payment, r is the annual interest rate, and n is the number of periods.
Plugging in the values, we get:
PV = 40000 * ((1 - (1 + 0.05)^-15) / 0.05)
PV = $450,332.81
Therefore, you would need $450,332.81 in your account at the beginning.
b) To calculate the total money that will be pulled out of the account, we can simply multiply the annual payment by the number of years:
Total money = PMT * n
Total money = 40000 * 15
Total money = $600,000
Therefore, the total money that will be pulled out of the account is $600,000.
c) To calculate the amount of money that is interest, we can subtract the initial investment from the total money pulled out:
Interest = Total money - Initial investment
Interest = $600,000 - $450,332.81
Interest = $149,667.19
Therefore, $149,667.19 of the money pulled out is interest.
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Help Please...
You have 67 coins consisting of half-dollars and quarters. The number of quarters is 7 more than three times the number of half-dollars.
How many quarters do you have?
How many half -dollars do you have?
Answers
There are 52 quarters and 15 half-dollars
To solve this problem
Let's represent the number of half-dollars as "x" and the number of quarters as "y".
From the problem statement, we know that:
x + y = 67 (because there are a total of 67 coins)
y = 3x + 7 (because the number of quarters is 7 more than three times the number of half-dollars)
We can use substitution to solve for x:
x + (3x + 7) = 67
4x + 7 = 67
4x = 60
x = 15
So there are 15 half-dollars. We can use this to find the number of quarters:
y = 3x + 7
y = 3(15) + 7
y = 52
So there are 52 quarters.
Therefore, there are 52 quarters and 15 half-dollars.
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The sum of a number and three is no more than eight
Answers
Answer:5
Step-by-step explanation: hope this helps
Choose scales for the coordinate plane shown so that you can graph the points J (5, 50), K(3, 50), L (4, -40), M (-2, 40), and N (-5, -10). on the x-axis use a scale of ____ units for each grid square. on the y-axis use a scale of ____ units of each grid square. complete the explanation for using these scales for each axis. the x-coordinates range from ____ to ____, and the y-coordinates range from ____ to ____.
Answers
On the x-axis use a scale of 2 units for each grid square. on the y-axis use a scale of 10 units of each grid square. The x-coordinates range from -5 to 5. y-coordinates range from -40 to 50.
What is coordinate plane?In mathematics, points and functions are represented and graphed on the coordinate plane, commonly known as the Cartesian plane. The x-axis and y-axis are two perpendicular number lines that meet at the origin to form the plane (0,0).
On the coordinate plane, points are denoted by ordered pairs (x, y), where x denotes the point's separation from the y-axis and y denotes its separation from the x-axis.
For the given coordinates the range of x and y coordinates are:
x-coordinates range from -5 to 5
y-coordinates range from -40 to 50.
Thus, we use a scale of 2 on the x-axis and 10 units on the y axis.
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1:20 - salesman allows a 5% discount for cash payment. What will be the discount allowed for a ash payment of GH¢5,600.00? A. GH 250.00
Answers
The discount allowed for a cash payment of GH 5,600.00 is given as follows:
GHC 280.00.
How to obtain the discount?The discount allowed for a cash payment of GH 5,600.00 is obtained applying the proportions in the context of the problem.
There is a 5% discount, hence the value of the discount is obtained as follows:
0.05 x 5600 = GHC 280.00.
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Will mark brainliest if answer is correct
Answers
Answer:
[tex]3( {2}^{2} ) - {2}^{2} + 4 = 12[/tex]
[tex] {2}^{3} + b( {2}^{2} ) + 43(2) - 126 = 4b - 204[/tex]
[tex]4b - 32 = 12[/tex]
[tex]4b = 44[/tex]
[tex]b = 11[/tex]
For this value of b, these graphs will intersect at (2, 12). Please use your graphing calculator to confirm that this is the only point of intersection.
Find the area of a rectangle with length 4.3 cm and breadth 3.9 cm
Answers
Answer:
16.77 cm²
Step-by-step explanation:
Area of rectangle = L x W
L = 4.3 cm
Width = 3.9 cm
Let' solve
4.3 x 3.9 = 16.77 cm²
So, the area of the rectangle is 16.77 cm²
7. Can the following be the lengths of the sides of a triangle?
a. 20 cm, 40 cm, 50 cm
b. 20 cm, 40 cm, 60 cm
c. 41 cm, 250 mm, 12 cm
Answers
Answer:
B
Step-by-step explanation:
THE TWO SMALLER SIDES = THE LARGER SIDE HENCE ITS A TRIANGLE
Find an equation of the osculating plane and an equation of the normal
plane of the curve x = sin 2t, y = t, z = cos 2t at the point (0, π, 1).
Answers
The equation of the normal plane is 4y = 4π, or equivalently, y = π.
What is osculating plane?The word osculate comes from the Latin osculatus, which is a past participle of the verb osculari, which means "to kiss." Thus, an osculating plane is one that "kisses" a submanifold.
To find the osculating plane and normal plane of the curve x = sin 2t, y = t, z = cos 2t at the point (0, π, 1), we need to follow these steps:
Find the first and second derivatives of the curve with respect to t.Evaluate the derivatives at t = π to get the velocity, acceleration, and curvature vectors at the point (0, π, 1).Use the velocity and acceleration vectors to find the normal vector of the osculating plane.Use the normal vector and the point (0, π, 1) to find the equation of the osculating plane.Use the curvature vector to find the normal vector of the normal plane.Use the normal vector and the point (0, π, 1) to find the equation of the normal plane.Step 1: Find the first and second derivatives of the curve with respect to t.
x' = 2cos2t
y' = 1
z' = -2sin2t
x'' = -4sin2t
y'' = 0
z'' = -4cos2t
Step 2: Evaluate the derivatives at t = π.
x'(π) = 2cos2π = 2
y'(π) = 1
z'(π) = -2sin2π = 0
x''(π) = -4sin2π = 0
y''(π) = 0
z''(π) = -4cos2π = -4
So the velocity vector at the point (0, π, 1) is v = ⟨2, 1, 0⟩, the acceleration vector is a = ⟨0, 0, -4⟩, and the curvature vector is κv = ⟨0, 4, 0⟩.
Step 3: Use the velocity and acceleration vectors to find the normal vector of the osculating plane.
The normal vector of the osculating plane is given by the cross product of the velocity and acceleration vectors:
n = v × a = ⟨2, 1, 0⟩ × ⟨0, 0, -4⟩ = ⟨4, 0, 0⟩
Step 4: Use the normal vector and the point (0, π, 1) to find the equation of the osculating plane.
The equation of the osculating plane is given by:
4(x - 0) + 0(y - π) + 0(z - 1) = 0
Simplifying, we get:
4x - 4 = 0
So the equation of the osculating plane is 4x = 4, or equivalently, x = 1.
Step 5: Use the curvature vector to find the normal vector of the normal plane.
The normal vector of the normal plane is given by the curvature vector:
n' = κv = ⟨0, 4, 0⟩
Step 6: Use the normal vector and the point (0, π, 1) to find the equation of the normal plane.
The equation of the normal plane is given by:
0(x - 0) + 4(y - π) + 0(z - 1) = 0
Simplifying, we get:
4y - 4π = 0
So, the equation of the normal plane is 4y = 4π, or equivalently, y = π.
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Which of the numbers 0, 1, 2, 3 or 4 make the equation 8/y2 + 2 true?
Answers
None of the given numbers make the equation 8/y² + 2 true.
What is algebra?
Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.
To solve this problem, we can substitute each of the given numbers (0, 1, 2, 3, 4) for y in the equation 8/y² + 2 and see if the equation is true.
Substituting y=0 would make the denominator of the fraction zero, which is undefined, so y=0 is not a valid choice.
Substituting y=1 would give us:
8/1² + 2 = 8 + 2 = 10
So, 1 is not the answer.
Substituting y=2 would give us:
8/2² + 2 = 8/4 + 2 = 2 + 2 = 4
So, 2 is not the answer.
Substituting y=3 would give us:
8/3² + 2 = 8/9 + 2 = 0.888 + 2 = 2.888
So, 3 is not the answer.
Substituting y=4 would give us:
8/4² + 2 = 8/16 + 2 = 0.5 + 2 = 2.5
So, 4 is not the answer.
Therefore, none of the given numbers make the equation 8/y² + 2 true.
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(a) What is the value of x? Show your work.
(b) What is the measure of angle C? Show your work.
Answers
In triangle ABC
a) The value of x = 29⁰
b) The angle c equal to 93⁰
What is a triangle?A triangle is a closed plane figure that is formed by connecting three line segments, also known as sides, at their endpoints. The three endpoints, or vertices, where the sides of the triangle meet are not collinear. Triangles are important in mathematics and geometry because they are the simplest polygon that can exist in two-dimensional space.
According to the given informationIn a triangle, the sum of all interior angles is always 180 degrees. Therefore, we can use this fact to find the value of x and angle c.
We know that:
angle a = 35⁰
angle b = 52⁰
angle c = 3(x+2)⁰
Using the fact that the sum of all interior angles in a triangle is 180 degrees, we can write:
angle a + angle b + angle c = 180
Substituting the values we know, we get:
35 + 52 + 3(x+2) = 180
Simplifying the equation, we get:
87 + 3x + 6 = 180
3x + 93 = 180
3x = 87
x = 29
Therefore, x = 29⁰
To find angle c, we can substitute the value of x into the equation we were given for angle c:
angle c = 3(x+2)
angle c = 3(29+2)
angle c = 3(31)
angle c = 93
Therefore, angle c is equal to 93⁰.
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Please help and hurry
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The equation of the parabola with vertex at point (2, -11) and passes through the point (0, 5) is y = 4(x - 2)² - 11.
What is linear and quadratic equation?A straight line can be used to symbolise a function that is linear, meaning that for each unit change in the input, the output (y) changes by a fixed amount (x). While a parabola can be used to depict a function, a quadratic function has an output (y) that changes by a non-constant amount for each unit change in the input (x). In other words, a quadratic function curves because of the squared term in its equation.
Given, the parabola has vertex at point (2, -11) and passes through the point (0, 5).
Thus, the equation of parabola in vertex form is:
y = a(x - 2)² - 11
Now, the parabola passes through the point (0, 5) we have:
5 = a(0 - 2)² - 11
5 = 4a - 11
16 = 4a
a = 4
Hence, the equation of the parabola with vertex at point (2, -11) and passes through the point (0, 5) is y = 4(x - 2)² - 11.
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Marlo uses 252
lb of gravel to cover a garden plot of 36 ft2
How many pounds of gravel does it take to cover one square foot?
Answers
Marlo will need 7 pounds of gravel to cover one square foot if he uses 252 lb of gravel to cover a garden plot of 36 ft²
What does a pound mean?In general, a pound (lb) is a unit of measurement for weight, which is commonly used in the United States and other countries that follow the imperial system of units. 1 pound is equal to 16 ounces or approximately 0.45 kilograms. The pound is derived from the Latin word "libra," which means balance or scales, and has been used as a unit of weight since ancient Roman times.
To find out how many pounds of gravel it takes to cover one square foot, we need to divide the total amount of gravel used by the area of the garden plot:
pounds per square foot = total pounds / area
In this case, Marlo used 252 lb of gravel to cover a garden plot of 36 ft², so:
pounds per square foot = 252 lb / 36 ft²
Simplifying this expression, we get:
pounds per square foot = 7 lb/ft²
Therefore, it takes 7 pounds of gravel to cover one square foot.
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find the area and perimeter of each figure below.
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Answer:
finding the perimeter, you sumthe distance all round that is 7+7.5+17.8+6=38.3
38.3 is the perimeter
Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options. 2(x2 + 6x + 9) = 3 + 18 2(x2 + 6x) = –3 2(x2 + 6x) = 3 x + 3 = Plus or minus StartRoot StartFraction 21 Over 2 EndFraction EndRoot 2(x2 + 6x + 9) = –3 + 9
Answers
The answer is , (a) For equation 1 Use the quadratic formula , (b) For equation 2 use of Factor out the common factor , (c) For equation 3 use of Complete the square.
What is Quadratic equation?A quadratic equation is a type of equation in algebra that contains a variable of degree 2, meaning that the highest power of the variable is 2.
Quadratic equations can have two real roots, one real root, or two complex roots, depending on the value of the discriminant (b² - 4ac). If discriminant is positive, equation has two real roots, if it is zero, equation has one real root (a "double root"), and if it is negative, equation has two complex roots.
Inga can use the following steps to solve the quadratic equation 2x² + 12x - 3 = 0:
Use the quadratic formula: Inga can use the quadratic formula, which is x = (-b ± √(b² - 4ac)) / 2a, where a, b, and c are the coefficients of the quadratic equation. In this case, a = 2, b = 12, and c = -3.Factor out the common factor: Inga can factor out the common factor of 2 from the equation to get 2(x² + 6x - 3/2) = 0.Complete the square: Inga can complete the square by adding (6/2)² = 9 to both sides of the equation to get 2(x² +6x +9 -9/2) = 9.Therefore, steps that Inga could use to solve quadratic equation are given:
Use the quadratic formula
Factor out the common factor
Complete the square
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A drawer contains 10 blue pens, 12 black pens, and 3 red pens. Without looking, Mr. Lopez is going to take one pen from the drawer, use it, and then put it back into the drawer. Then he is going to take another pen from the drawer to use. What is the probability of Mr. Lopez taking a red pen first and then taking a blue pen?
Answers
Answer: 4.8%
Step-by-step explanation: the total amount of pens in the drawer is (10+12+3) = 25
the amount of red pens in the drawer is 3
the probability of picking out a red pen from the drawer = 3/25
the amount of blue pens in the drawer is 10
the probability of picking out a red pen from the drawer = 10/25
the probability of picking out a red pen then a blue pen afterwards = (10/25 x 3/25) = 4.8%
HELP ASAP!!!!
The diameter of a circular cookie cake is 14 inches. How many square inches make up half of the cookie cake? Approximate using π = 3.14. 615.44 square inches 307.72 square inches 153.86 square inches 76.93 square inches
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The number of square inches to make up half the cookie cake is 76.93 in² area.
How to calculate for the half square inches areaThe diameter of the circular cookie cake is 14 inches, so its radius will be r = 7 inches. Using the formula for area of circle we have:
area of cookies cake = 3.14 × 7 in × 7 in
area of cookies cake = 153.84 in²
half the area of the cookie cake = 153.84 in²/2
half the area of the cookie cake = 76.93 in²
Therefore, the number of square inches to make up half the cookie cake is 76.93 in² area.
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