The rocket's maximum height is 800 feet. It reached its maximum height at 5 seconds after launch.
To solve this problem, we need to find the vertex of the parabola represented by the equation Y= -16t^2+160t. The vertex of a parabola is the point where the parabola changes direction, from increasing to decreasing or vice versa.
The vertex of the parabola is given by the following formula:
(-b/2a, c - b^2/4a)
In this case, the value of b is 160 and the value of a is -16. Plugging these values into the formula, we get the following:
(-160/2(-16), 800 - 160^2/4(-16))
(5, 800)
Therefore, the rocket reached its maximum height at 5 seconds after launch. The maximum height is 800 feet.
Gross profit does not appear
no it dose not
your right whats the question
Solve for x. Round to the nearest tenth
The values of the distance are;
1. 4. 49 feet
2. 7. 73 feet
How to determine the valuesWe need to know the trigonometric identities and their ratios. We have;
sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent
Now, substitute the values, we have;
1. Adjacent = d
Hypotenuse = 12
Angle = 68 degrees
cos 68 = adjacent/hypotenuse
cos 68 = d/12
cross multiply the values, we get;
d = 4. 49 feet
2.
cos 25 = 7/x
cross multiply the values, we have;
x = 7/0. 9063
divide the values, we get;
x = 7. 73 feet
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please help, i don’t understand this at all
The smallest subset containing 7.83 among the common subsets is Q.
We are given that;
The number 7.83
Now,
Subset of a given set is a set whose all elements are in the original set of which it is subset.
So if B is subset of A, then all elements of B are in A but it is not necessary that all elements of A are in B.
If B is subset of A, then A is superset of B.
The smallest subset containing the value 7.83 is the set of rational numbers. A rational number is a number that can be written as a fraction of two integers, such as 7.83 = 783/100. The set of rational numbers is denoted by Q and it is a subset of the set of real numbers R.
Therefore, by subsets the answer will be Q.
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I don’t know how to do this problem help me!!
[tex]x-9z^5+4z+11+2z^5+14=-5z^5-3z+25\\x=2z^5-7z[/tex]
Therefore, it's [tex]2z^5-7z[/tex].
10-10=69.420!!!!!!!!!!
The diagram shows triangle ABC.
ADC and DEB are straight lines.
AD = 4.4cm
BC = 8.6cm
E is the midpoint of DB.
Angle CDB = 90°
Angle DCB = 40°
Work out the size of angle EAD. Give your answer correct to 1 decimal place.
You must show all your working.
Please help
The size of angle EAD is 40°.
To find the size of angle EAD, we can use the information given in the diagram and apply some basic trigonometry principles. Let's go step by step.
First, we notice that triangle CDB is a right triangle since angle CDB is given as 90°. We also know that angle DCB is 40°. This means that angle CBD can be found by subtracting 40° from 90°:
angle CBD = 90° - 40° = 50°.
Since E is the midpoint of DB, we can conclude that angle CBE is also 50°, as it is vertically opposite to angle CBD.
Now, let's consider triangle ADE. We know that angle EAD is the angle we're trying to find. We can use the fact that the angles in a triangle add up to 180° to write the equation:
angle EAD + angle ADE + angle DEA = 180°.
Since E is the midpoint of DB, we can conclude that angle ADE is equal to angle CDE. Angle DEA is equal to angle CEA. Therefore, we can rewrite the equation as:
angle EAD + angle CDE + angle CEA = 180°.
We can substitute the values we know: angle CDE is 90° (since it's a right angle), and angle CEA is 50° (since it's vertically opposite to angle CEB).
angle EAD + 90° + 50° = 180°.
Simplifying the equation:
angle EAD = 180° - 90° - 50° = 40°.
Therefore, the size of angle EAD is 40°.
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The Glen Oaks Village Co-op is represented by s shares. Sage owns r shares. Express the percent of shares he owns algebraically.
There are 400 employees. If there is one manager for every 9 engineers. Find the number of managers in company.
answer is 45
400/9 = 44.44...
so with the extra employees you need another manager.
Answer:
40 managers
Step-by-step explanation:
If there is one manager for every 9 engineers, we can assume that each manager is responsible for a group of 9 engineers. To determine the number of managers in the company, we need to divide the total number of engineers by 9.
First, we need to determine the total number of engineers in the company. Since there is one manager for every 9 engineers, the ratio of engineers to managers is 9:1. This means that for every 10 people (9 engineers and 1 manager), there is 1 manager. So we can find the total number of groups of 10 people by dividing the total number of employees by 10:
400 employees / 10 = 40 groups of 10 people
This means that there are 40 groups of 10 employees (1 manager and 9 engineers) in the company. Since there is 1 manager in each group, the total number of managers in the company is equal to the number of groups:
Number of managers = Number of groups = 40
You deposit $80 in an
investment account
that earns 4.8%
annual interest
compounded monthly.
Write a function that
represents the balance
y (in dollars) of the
investment account
after t years.
y =
What is the balance of
the account after 7
years?
Answer:
y = (1)(1.004)^^(84)
y ≈ 1.610
Therefore, the balance of the investment account after 7 years, assuming an initial principal of 1 dollar, is approximately 1.610 dollars.
If sing, which of the following are possible for the same value of a?
A. sec9 =
B. cose =
C. cose =
√5
3
D. sece=
√5
3
and tang =
and tang
8=-2 and 1
-7/5
3
and tang =
tang =
-7/5
25
Like
SUBMIT
The possible trigonometric ratios for the angle θ are given as follows:
A. [tex]\sec{\theta} = \frac{3}{\sqrt{5}}[/tex] and [tex]\tan{\theta} = \frac{2}{\sqrt{5}}[/tex]
B. [tex]\cos{\theta} = \pm \frac{\sqrt{5}}{3}[/tex] and [tex]\tan{\theta} = \frac{2}{\sqrt{5}}[/tex]
How to obtain the trigonometric ratios?The sine for the angle θ is given as follows:
sin(θ) = 2/3.
The identity relating the sine and the cosine is given as follows:
sin²(θ) + cos²(θ) = 1.
Hence the cosine of the angle is given as follows:
cos²(θ) = 1 - 4/9
cos²(θ) = 5/9
[tex]\cos{\theta} = \pm \frac{\sqrt{5}}{3}[/tex]
The tangent is given by the division of the sine by the cosine, hence it is calculated as follows:
[tex]\tan{\theta} = \frac{2}{\sqrt{5}}[/tex]
(if the cosine is negative, the tangent is then negative, as the sine is positive).
The secant is the division of one by the cosine, that is, it is the inverse fraction of the cosine, hence:
[tex]\sec{\theta} = \frac{3}{\sqrt{5}}[/tex]
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Help Due !!!!.. ASAP
(a) The inverse variation equation that relates to x and y is y = -20/x.
(b) The value of y when x = 25 is -0.8 or -4/5
What is inverse variation?Inverse variation is the relationships between variables that are represented in the form of y = k/x, where x and y are two variables and k is the constant value.
(a) To write the inverse variation equation that relates to x and y, we look for the constant k connecting x and y
From the questiuon,
y ∝ 1/xTo remove the proprotionality/Variation sign, we introduce a constant k
y = k/x................ Equation 1Given:
x = 2, y = -10Substitute into equation 1 and solve for k
2 = k/-10k = 2×(-10)k = -20Hence, the equation is y = -20/x.
(b) To find the value of y when x = 25, we subtitute into the equation
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Roger sprinted 89 yards. Lara sprinted 270 feet.
Who sprinted the longer distance? How much
greater? Show your work.
Answer: Lara
Step-by-step explanation:
convert yards into feet
yards*3= feet
89 yards * 3 = 267 feet
Since 270 is greater than 267 Lara. Lara's distance is greater by 3 feet since 270-267 is 3
Find the y-intercept and the slope of the line.
-8x -4y =5
Given statement solution is :- The slope (m) of the line is -2, and the y-intercept (b) is -5/4.
To find the y-intercept and slope of the line represented by the equation -8x - 4y = 5, we need to rearrange the equation into slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.
Let's begin by isolating the term with y:
-8x - 4y = 5
Subtract -8x from both sides:
-4y = 8x + 5
Next, divide both sides of the equation by -4 to solve for y:
y = (-8/4)x - (5/4)
Simplifying further:
y = -2x - 5/4
Now we can identify the slope and the y-intercept:
The slope (m) of the line is -2, and the y-intercept (b) is -5/4.
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A manager notes that there is a .125 probability that any employee will arrive late for work. What is the probability that no more than one person in a six-person department will arrive late for work on any given day?
Answer:
21
Step-by-step explanation:
100 Points! Algebra question. Photo attached. Please show as much work as possible. Thank you!
the answer is of the inequality is x>8
Planes A and B are shown.
m
Mark this and return
If a new line, p, is drawn parallel to line /, which
statement is true?
O Line p must be drawn in plane B.
Line p must be perpendicular to line m.
O Line p must be drawn so that it can lie in the same
plane as line /.
O Line p must be drawn in the same plane as line n.
Save and Exit
Next
Submit
The correct statement is that "Line p must be drawn in plane B."
If a new line, p, is drawn parallel to line /, the statement that is true is "Line p must be drawn in plane B."
To understand this, let's analyze the given information:
Planes A and B are shown.
Line m is shown in plane A.
Line n is shown in plane B.
Line / is the line that connects planes A and B.
When a new line, p, is drawn parallel to line /, it means that line p will also connect planes A and B. However, since line / itself is connecting planes A and B, line p must also lie in plane B to maintain its parallel relationship with line /. This is because parallel lines lie in the same plane.
This ensures that line p remains parallel to line / and maintains its connection between planes A and B.
It is important to note that line p being drawn in plane B does not necessarily imply that it intersects with line n. It simply means that line p lies within plane B and remains parallel to line /.
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100 Points! Algebra question. Sketch the angle. Then find its reference angle. Show your calculations. Photo attached. Thank you!
The reference angle of 13π/8 is 3π/8 and the sketch of the angle is attached
How to sketch the angle and find the reference angleFrom the question, we have the following parameters that can be used in our computation:
Angle = 13π/8
Rewrite as
θ = 13π/8
The above angle is in the fourth quadrant
So, we subtract it from 2π to calculate the reference angle
Using the above as a guide, we have the following:
Reference angle = 2π - 13π/8
Evaluate the difference
Reference angle = 3π/8
Hence, the reference angle is 3π/8 and the sketch of the angle is added as an attachment
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An equation is shown below: 5(3x − 15) + 16 = 5x + 11 Part A: Write the steps you will use to solve the equation, and explain each step. (8 points) Part B: What value of x makes the equation true? (2 points)
The result of the unknown variable x is equivalent to 7
Solving linear equationsLinear equations are equation that has a leading degree of 1. Given the expression below:
5(3x − 15) + 16 = 5x + 11
Expand the expression
5(3x) - 5(15) + 16 = 5x + 11
15x - 75 + 16 = 5x + 11
15x - 5x - 59 - 11 = 0
10x - 70 = 0
10x = 70
Divide both sides by 10
10x/10 = 70/10
x = 7
Hence the value of x makes the equation true is 7
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21. Find the perimeter of the polygon.
The perimeter of the polygon which is a triangle is
72 units
How to find the perimeter of the polygonThe perimeter of the polygon is solved using the knowledge of tangents
This is applied as follows
perimeter of the triangle = GH + HL + GJ
GH = (4 + 32 - 15) = 21
HL = 15 + 4 = 19
GJ = 32
plugging in the values we have
perimeter of the triangle = 21 + 19 + 32
perimeter of the triangle = 72 units
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what type of scale is used on the map?
The type of scale commonly used on maps is a graphic scale, which uses a line or bar to represent distances accurately.
The type of scale used on a map is known as a map scale. It is a graphical representation that shows the relationship between distances on the map and their corresponding measurements in the real world. A map scale allows us to understand the size and proportion of features depicted on the map.
There are three main types of map scales: verbal scales, graphic scales, and representative fraction scales.
Verbal Scale: A verbal scale uses words to describe the relationship between distances on the map and real-world measurements. For example, a verbal scale might state "1 inch represents 1 mile" or "1 centimeter represents 10 kilometers." Verbal scales are commonly used on small-scale maps, where the level of detail is not as important.
Graphic Scale: A graphic scale, also known as a bar scale or linear scale, uses a line or a bar marked with specific distances. This line is divided into equal segments that represent units of measurement. By comparing the length of the line on the map to the corresponding distance in the real world, you can determine distances accurately. Graphic scales are often found on the margin or the legend of a map and are commonly used on medium- to large-scale maps.
Representative Fraction (RF) Scale: A representative fraction scale expresses the relationship between map distances and real-world distances using a ratio. For example, a representative fraction of 1:100,000 means that one unit of measurement on the map represents 100,000 of the same units in the real world. This type of scale is useful because it allows for precise calculations and conversions between map distances and real-world distances. Representative fraction scales are commonly used on topographic maps and engineering plans.
It's important to note that a map may include multiple scales to accommodate different levels of detail. For instance, a large-scale map of a city may have a more detailed scale than a small-scale map of an entire country.
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Solve the proportional equation below
The solution to the proportional equation 5/8 = 8/a is a = 64/5 or a = 12.8.
To solve the proportional equation 5/8 = 8/a, we can cross-multiply.
Cross-multiplying means multiplying the numerator of the first fraction by the denominator of the second fraction and vice versa.
We have:
5 × a = 8 × 8
5a = 64
To isolate the variable a, we divide both sides of the equation by 5:
a = 64/5
We may cross-multiply the proportional equation 5/8 = 8/a to find the solution.
Cross-multiplication is the process of multiplying the denominator of the second fraction by the first fraction's numerator, and vice versa.
We possess
5 × a = 8 × 8 5a = 64
We divide both sides of the equation by 5 to identify the variable a:
a = 64/5.
We may cross-multiply to find the solution to the proportional equation 5/8 = 8/a.
Cross-multiplication is the process of multiplying one fraction's numerator by another's denominator and vice versa.
There are:
5 × a = 8 × 8 5a
= 64
By multiplying both sides of the equation by 5, we may separate the variable a:
a = 64/5.
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100 Points! Algebra question. Photo attached. Please show as much work as possible. Thank you!
Answer:
A. 440°, -280°
B. 17π/6, -7π/6
Step-by-step explanation:
You want angles coterminal with the given angle, one with a positive sign, and one with a negative sign.
Coterminal anglesAdding an integer multiple of 360° = 2π radians to any angle will give the measure of a coterminal angle.
A. 80°A positive coterminal angle is ...
80° +360° = 440°
A negative coterminal angle is ...
80° -360° = -280°
B. 5π/6A positive coterminal angle is ...
5π/6 +2π = 17π/6
A negative coterminal angle is ...
5π/6 -2π = -7π/6
__
Additional comment
We have used the smallest multiples of 1 full rotation around the origin. You could choose others. For example, adding 3600° to the first angle will give 3680° as a positive angle coterminal with 80°.
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is the long hand on a clock is on 6 and the shorthand is between 9 and 10 what is the time
Answer:
9:30
Step-by-step explanation:
A spinner has 8 equal-sized sections. Six of the sections are blue.
What is the probability that the spinner will land on blue?
Answer:
[tex]\frac{3}{4}[/tex] or 75%
Step-by-step explanation:
There are 8 equal-sized sections, 6 being blue. 6/8 = 3/4 = 0.75 which is 75%. That is the probability that the spinner lands on blue.
a decagon with a side of 20 meters
The area of the decagon is 3077.68 square meters
Calculating the area of the decagonfrom the question, we have the following parameters that can be used in our computation:
A decagon with a side of 20 meters
This means that
a = 20
The area of the decagon is then calculated as
A = 2.5a² * √(5 + 2√5)
substitute the known values in the above equation, so, we have the following representation
A = 2.5 * 20² * √(5 + 2√5)
Evaluate
A = 3077.68
Hence, the area of the decagon is 3077.68 square meters
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Complete question
A decagon with a side of 20 meters. What is the area?
What is the slope-intercept form of this equation? Show all your work.
-8x + 2y = 14 HELP FAST!!!
Answer: y=4x+7
Step-by-step explanation:
-8x+2y=14
Convert to y=kx+b
2y=8x+14
y=4x+7
The first shelf on Hannah’s bookshelf hoods an equal number of fiction and nonfiction. If Hannah’s selects 5 books randomly, what is the probability that 3 of the books will be fiction and 2 will be nonfiction
Answer:
The correct option is (D) one of the non-fiction books on the bottom shelf and a second non-fiction book from the bottom shelf.
Step-by-step explanation:
What is probability?
Probability is the branch of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely it is that a claim is true.
To find which 2 books describe a pair of dependent events:
A pair of two dependent events are simply those in which the selection of the second item is contingent on the selection of the first item, causing the probability to change.
Because the sample size is lowered when the initial item is taken without replacement, choosing the exact same item reduces the chance.
Now, in regard to the question, this means that for two of the occurrences to be independent, they must be on the same shelf and of the same type of book, so that the second book cannot be selected until the first one is.
Option D, where both books are on the same shelf and are of the same type, is the only option that fulfills this requirement.
Therefore, the correct option is (D) one of the non-fiction books on the bottom shelf and a second non-fiction book from the bottom shelf.
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50 POINTS TO BEST ANSWER
A function is shown below where b is a real number.
f(x)=x²+bx+118
The minimum of the function is 37.
Create an equivalent equation of the function in the form f(x)=(x-h)²+k.
Type your numerical answers below for h and k. Use the hyphen (-) for the negative sign if
necessary.
h=
k=
I did some research and found that for quadratic equations in the form of [tex]y = ax^2 + bx + c[/tex], you can find the minimum value using the equation [tex]$\text{minimum} = c - \frac{b^2}{4a}[/tex] .
We can substitute our given values in the formula and get the following: [tex]$37 = 118 - \frac{b^2}{4}$[/tex] .
We can go ahead and solve it, and get the following:
[tex]-81 = -\frac{b^{2}}{4}[/tex]
[tex]324 = b^2[/tex]
[tex]\pm{18} = b[/tex]
Now we know that the equation is either [tex]$f(x)=x^2+18x+118$[/tex] or [tex]$f(x)=x^2-18x+118$[/tex] .
We will solve using both equations, but we will solve the one with a positive b-value first. Substituting [tex]f(x)[/tex] for [tex]$37$[/tex], the minimum or y-value of the vertex, we can now solve for the x-value of the vertex.
We have:
[tex]37 = x^2+18x+118[/tex]
[tex]0=x^2+18x+81[/tex]
[tex]0=(x+9)^2[/tex]
[tex]x+9=0\\x=-9[/tex]
Doing the same thing with the second equation, we get:
[tex]37 = x^2-18x+118[/tex]
[tex]0=x^2-18x+81[/tex]
[tex]0=(x-9)^2[/tex]
[tex]x-9=0\\x=9[/tex]
After all of this, we know our vertex's x-values are either [tex]9[/tex] or [tex]-9[/tex], and that our y-value is [tex]37\\[/tex].
We can conclude that our k-value (y-value of the vertex in vertex form) is [tex]37[/tex], and our h-value (x-value of the vertex in vertex form) is [tex]9[/tex] or [tex]-9[/tex].
Conclusion: [tex]h = -9, 9[/tex]
[tex]k=37[/tex]
9) Solve
(x² + 3x)³-16(x² + 3x) - 36 = 0
for x by using substitution.
a) x = -3,1,2,6
b) x = -4,0,1,5
c) x = -5,-1,0,4
d) x = -6, -2,-1,3
e) x = -7,-3, -2,2
Answer: 0
Step-by-step explanation:
To solve the equation (x² + 3x)³ - 16(x² + 3x) - 36 = 0 using substitution, let's make a substitution:
Let u = x² + 3x.
Now, we can rewrite the equation in terms of u:
u³ - 16u - 36 = 0.
Let's solve this equation for u by factoring:
(u - 6)(u² + 6u + 6) = 0.
Now, we have two possible cases:
Case 1: u - 6 = 0.
This gives us u = 6.
Case 2: u² + 6u + 6 = 0.
To solve this quadratic equation, we can use the quadratic formula:
u = (-b ± √(b² - 4ac)) / (2a),
where a = 1, b = 6, and c = 6.
Plugging in these values, we get:
u = (-6 ± √(6² - 4(1)(6))) / (2(1)),
u = (-6 ± √(36 - 24)) / 2,
u = (-6 ± √12) / 2,
u = (-6 ± 2√3) / 2,
u = -3 ± √3.
Now that we have the possible values of u, let's substitute back to find the corresponding values of x:
Case 1: u = 6.
Since u = x² + 3x, we have x² + 3x = 6.
Rearranging, we get x² + 3x - 6 = 0.
Hope it helps!
Omaha’s factory has yet another type of cost structure. Its cost function is provided graphically. Its maximum capacity is 38,000 units per day.
a) At what rate is the cost per unit decreasing for production levels above 12,000?
b) State the function for the domain over [12000, 38000].
c) What is the cost per unit at the production level of 19,000?
Omaha’s city council approved a special growth incentive that decreases the company’s tax burden for production levels above last year’s average. Explain how this is reflected by the Cost Function for Omaha’s factory.
Need this ASAP
a)
The cost per unit decreasing by 0.00001 for production levels above 12,000.
Given,
From the graph it is clear that the graph passes through the points (12000,0.85) and (38000,0.59).
Now,
If a line passes through two points then the slope of the line is
m = y2 - y1 / x2 - x1
The rate of change in cost per unit for production levels above 12,000 is
m = 0.59 - 0.85 / 38000 - 12000
m = -0.00001
Here negative sign represents the decreasing rate. It means the cost per unit decreasing by 0.00001 for production levels above 12,000.
b)
The function for the domain over [12000, 38000] is :
y = -0.00001x + 0.97
The point slope form of a linear function is,
(y-y1) = m (x - x1)
m = slope.
The slope of the line over [12000, 38000] is -0.00001 and the point is (12000,0.85). So, the function for the domain over [12000, 38000] is
y-0.85 = -0.00001(x-12000)
y = -0.00001x + 0.97
c)
The cost per unit at the production level of 19,000 is 0.78.
Substitute x=19000 in the above equation, to find the cost per unit at the production level of 19,000.
y = -0.00001(19000) + 0.97
y = 0.78
Thus the cost per unit at the production level of 19,000 is 0.78.
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50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answer:
(B) sin(60°) = 4/x
Step-by-step explanation:
You want an equation for finding the hypotenuse of a 30°-60°-90° triangle with the middle-length side being 4 units.
SineThe trig relation between the side opposite and angle and the hypotenuse of the right triangle is ...
Sin = Opposite/Hypotenuse
ApplicationIn this triangle, this relation means ...
sin(60°) = 4/x . . . . . matches choice (B)
__
Additional comment
The middle-length side is opposite the middle length angle.
This is a "special" right triangle with sides in the ratios 1 : √3 : 2. The length x will be 4(2/√3) = (8/3)√3. It can be useful to remember the side length ratios for this triangle.
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