The minima of the quadratic function is at the vertex, it is at (2, -4).
Where are the relative minima/maxima of the function?
First, we can see that our function is a quadratic function of positive leading coefficient. So it opens upwards.
Then we will only have a minima, which is located in the vertex of the parabola.
Remember that for:
y = a*x^2 + b*x + c
The x-value of the vertex is h = -b/2a
Then for g(x) = x^2 - 4x we have:
h = -(-4)/2*1 = 2
And the y-value of the vertex is:
g(2) = 2^2 - 4*2 = -4
Meaning that the minima of the function g(x) is (2, -4).
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The exact location of all the relative and absolute extrema of the function is (2, -4).
Where are the relative minima/maxima of the function?First, we can see that our function is a quadratic function of the positive leading coefficient.
Then we will only have a minimum, which is located in the vertex of the parabola.
The equation of the parabola is;
[tex]\rm y = ax^2 + bx + c[/tex]
The x-value of the vertex is h = -b/2a
Then for g(x) = x^2 - 4x we have:
h = -(-4)/2*1 = 2
And the y-value of the vertex is:
g(2) = 2^2 - 4*2 = -4
Meaning that the minima of the function g(x) are (2, -4).
Hence, the exact location of all the relative and absolute extrema of the function is (2, -4).
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25x25 in exponential form
Find the surface area of the pyramid. Round to the nearest tenth if necessary.
Answer:
197.4 yd squared
Step-by-step explanation:
7*7 = 49
10.6*7*2 = 148.4
148.4 + 49 = 197.4
Question on attached image
Answer:
Red: 144. Green: 360 Brown: 552. Yellow: 144.
Step-by-step explanation:
Okay, so, to find the probabilities of red and yellow, we gotta add green and brown probabilities and then subtract that from one. Green and brown probabilities added together are 0.76. Subtract that from one and you get 0.24. Divide that by two and we get 0.12 for both red and yellow. Now we multiply 1200 by each probability.
first question please dont just answer for points NOT helpful
help pleas im doing this for a freind bc i need the money to buy food
Step-by-step explanation:
these are 2 similar triangles.
that means they have the same angles. and all sides have the same scaling factor between the 2 triangles.
so,
10/28 = 5/h
need help with all of these questions you see on the top. there the red squares. please someone smart. this is one of the problems I need to finish this tonight
Answer:
V = 13 x 9π
Step-by-step explanation:
The figure formed by filling water is also a cylinder, so the volume formula is the same: base area times height. This means that:
V = 9π x 13
It can also be rearranged to read:
V = 13 x 9π
A unit circle has a central angle with a measure of
7π/6
radians. To the nearest hundredth, what is the length of the arc on the circle determined by the angle?
Answer:
Step-by-step explanation:
The length of the arc on the unit circle is 3.67 units
How to determine the length of the arc?The angle measure is given as:
x = 7π/6
The radius of a unit circle is:
r = 1
The length of the arc is calculated using:
L =rx
So, we have:
L = 1 * 7π/6
Evaluate
L = 3.67
Hence, the length of the arc on the unit circle is 3.67 units
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Pete went to the store. He bought 3 pounds of chili peppers, 5 pounds of habanero peppers,
and 1 pound of red bell peppers. How much did he spend?
red bell peppers
Anaheim peppers
chili peppers
habanero peppers
$2 per lb
$1 per lb
$2 per lb
$2 per lb
Help please
can someone do this for me please?! Just the answer pls
Answer:
1 is H
2 is G
3 is B
Answer:
1 is G number 2 is F
Number 1 is G
Number 2 is F
The boxplots below show the test scores for 2 different classes. First period has 20 students and 2nd period has 16 students. How many more students scored 80 or higher in class 2 than in class 1?
A box plot has 5 data descriptions. The number of students who scored 80 or higher in class 2 than in class 1 is 2.
How does a boxplot show the data points?A box plot has 5 data descriptions:
The leftmost whisker shows the minimum value in the data.The rightmost whisker shows the maximum value in the data.The leftmost line in the box shows the first quartile.The middle line shows the median, also called the second quartile.The last line of the box shows the third quartile.The number of students in the first class who scored more than 80 is 10, while the number of students in the second class who scored more than 80 is 12.
Therefore, the number of students who scored 80 or higher in class 2 than in class 1 is 2(12-10).
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A rectangular prism is made up of cubes. The prism is 8
cubes wide, 4 cubes deep, and 5 cubes tall. Describe the
front, side, and top views of the prism.
Answer:
All of the views will be rectangles. The front view will be a rectangle 8 squares wide and 5 squares tall. The side view will be a rectangle 4 squares wide and 5 squares tall. The top view will be a rectangle 8 squares wide and 4 squares tall.
Step-by-step explanation:
Evaluate tan45degrees/sin30degrees . In your final answer, include all calculations.
Answer:
2
Step-by-step explanation:
First find out what tan45 means then what sin30 means so tan45=1 and sin30=0.5, 1/0.5=2
The evaluation tan45°/sin30° is 2.
What is a trigonometric function?The fundamental 6 functions of trigonometry have a range of numbers as their result and a domain input value that is the angle of a right triangle.
The trigonometric function is only valid for the right angle triangle and it is 6 functions which are given as sin cos tan cosec sec cot.
The trigonometric functions found in the four quadrants, as well as their graphs, domains, and differentiation and integration, will all be understood.
The trigonometric function is very good and useful in real-life problems related to the right-angle triangle.
given that tan45°/sin30°
Since tan45° is 1 and sin30° is 0.5 so
By that 1/0.5 which comes out as 2.
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Which statement describes the function y = axn when a = 1 and n is odd?
Answer:
The graph is symmetric about the origin.
The graph does not pass through the origin.
Step-by-step explanation:
We're given:
the function y=axna = 1n is oddBecause a = 1, then the given function can be rewritten as y = n.
The graph opens downThe function y = n will produce a horizontal line. Any function in the form of y = a single number, such as 4 or 9.3 will produce a horizontal line.
The graph is symmetric about the origin.This is true, given the graph is a horizontal line.
The graph does not pass through the origin.This is also true. We're given that n is an odd number. The graph will only pass through the origin if n = 0, and 0 is even.
The graph has more than one x-intercept.This would only be true when n = 0, and this isn't possible. So, no.
Answer:
B: The graph is symmetric about the origin
Step-by-step explanation:
you typed the question in wrong its ax^n not axn, which makes the answer above incorrect. this should be the right one on edge.
I need a full explanation for this problem. I don’t know how to do it
Answer:
3861 cm³Step-by-step explanation:
Consider this solid as combination of two prisms, one with recrangular base and another with trapezoid base.
Find the area of bases
Rectangle
A = lw = 8*17 = 136 cm²Trapezoid
A = (1/2)(17 + 6)(22 - 8) =(1/2)(23)(14) = 161 cm²Find the total base area
B = 136 + 161 = 297 cm²Find the volume
V = BhV = 297*13 = 3861 cm³Johnny just got out of high school he has $90 then he gets a job, his job pays him 20 dollars a month, how much money does he have in 2 months.
Answer:
$130
Step-by-step explanation:
90 + (20 * 2) = 130
Consider the following vector function. R(t) = 9 2 t, e9t, e−9t (a) find the unit tangent and unit normal vectors t(t) and n(t)
The unit tangent vector is T(u) and the unit normal vector is N(t) if the vector function. R(t) is equal to 9 2 t, e9t, e−9t.
What is vector?It is defined as the quantity that has magnitude as well as direction also the vector always follows the sum triangle law.
We have vectored function:
[tex]\rm R(t) = (9\sqrt{2t}, e^{9t}, e^{-9t})[/tex]
Find its derivative:
[tex]\rm R'(t) = (9\sqrt{2}, 9e^{9t}, -9e^{-9t})[/tex]
Now its magnitude:
[tex]\rm |R'(t) |= \sqrt{(9\sqrt{2})^2+ (9e^{9t})^2+ (-9e^{-9t})^2}[/tex]
After simplifying:
[tex]\rm R'(t) = 9 \dfrac{e^{18t}+1}{e^{9t}}[/tex]
Now the unit tangent is:
[tex]\rm T(u) = \dfrac{R'(t)}{|R'(t)|}[/tex]
After dividing and simplifying, we get:
[tex]\rm T(u) = \dfrac{1}{e^{18t}+1} (\sqrt{2}e^{9t}, e^{18t}, -1)[/tex]
Now, finding the derivative of T(u), we get:
[tex]\rm T'(u) = \dfrac{1}{(e^{18t}+1)^2} (9\sqrt{2}e^{9t}(1-e^{18t}), 18e^{18t}, 18e^{18t})[/tex]
Now finding its magnitude:
[tex]\rm |T'(u) |= \dfrac{1}{(e^{18t}+1)^2} (9\sqrt{2}e^{9t}(1-e^{18t})^2+ (18e^{18t})^2+( 18e^{18t})^2)[/tex]
After simplifying, we get:
[tex]\rm |T'(u)|= \dfrac{9\sqrt{2}e^{9t}}{e^{18t}+1}[/tex]
Now for the normal vector:
Divide T'(u) and |T'(u)|
We get:
[tex]\rm N(t) = \dfrac{1}{e^{18t}+1} ( 1-e^{18t}, \sqrt{2}e^{9t}, \sqrt{2}e^{9t})[/tex]
Thus, the unit tangent vector is T(u) and the unit normal vector is N(t) if the vector function. R(t) is equal to 9 2 t, e9t, e−9t.
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Which graph represents y as a function of x?
Your favorite restaurant has a promotion where you can win free food. You will roll 2 dice. The sum of the 2 dice will determine which prize you receive.
2-column table with 11 rows. Column 1, outcome, entries 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. Column 2, probability, entries StartFraction 1 Over 36 EndFraction, StartFraction 2 Over 36 EndFraction, StartFraction 3 Over 36 EndFraction, StartFraction 4 Over 36 EndFraction, StartFraction 5 Over 36 EndFraction, StartFraction 6 Over 36 EndFraction, StartFraction 5 Over 36 EndFraction, StartFraction 4 Over 36 EndFraction, StartFraction 3 Over 36 EndFraction, StartFraction 2 Over 36 EndFraction, StartFraction 1 Over 36 EndFraction.
If a customer rolls a sum of 5 or 6, the prize is 10% off of today’s purchase.
What is the probability of receiving this discount? Enter your answer as a decimal rounded to the hundredths place.
P(10% off) =
Answer:
0.25
Step-by-step explanation:
edge '22
Answer:
D - E(evens) = E(odds) because the different probabilities and values end up balancing out, creating a fair game. Therefore, Jessica may choose whichever she likes.
Step-by-step explanation:
Is is package c a function
what do you mean package c explain more
Can someone please answer this, ill give you brainliest Would be very appreciated.
Answer:
Given function:
f(t) = (-16t - 2)(t - 1)
Part 1The zeros of the function are the values of t when f(t) = 0
⇒ f(t) = 0
⇒ (-16t - 2)(t - 1) = 0
⇒ (t - 1) = 0 ⇒ t = 1
⇒ (-16t - 2) = 0 ⇒ t = -2/16 = -1/8
Part 2The zeroes tell us the time (in seconds) when the ball is at ground level (when its height is zero).
Since time is not negative, only one zero is meaningful: t = 1
Therefore, the total journey of the ball, from throwing it to it hitting the ground, is 1 second.
Part 3The height the ball is thrown can be determined by inputting t = 0 into the function:
⇒ f(0) = (-16(0) - 2)(0 - 1)
⇒ f(0) = (0 - 2)(0 - 1)
⇒ f(0) = (-2)(-1)
⇒ f(0) = 2
Therefore, the height from which the beach ball is thrown is 2 ft.
Equation: y = (-16t-2)(t -1)
1) Finding zeros of the function?
To find zero's of the function y = 0
(-16t-2)(t -1) = 0
-16t - 2 = 0, t - 1 = 0
t = 2/-16, t = 1
t = -0.125, 1
2) What do the zero's tell us? Are they meaningful?
Answer: It tells us that the time is 1 seconds when the height of the ball is 0 or at rest.
3) From what height is the ball thrown?
Insert t = 0
y = (-16(0)-2)((0) -1)
y = 2
Ball thrown from 2 feet.
Help me pls!
Raj, Devi and Miko have managed their savings well. The sum of Raj and Devi's savings is $1181. Raj and Miko's savings sum up to $1797. The ratio of Devi to Miko's savings is 3 : 11. How much has Raj saved?
Answer:
it is easy it is 3833
Step-by-step explanation:
The money saved by Raj from the given conditions is $950.
Given that, Raj, Devi and Miko have managed their savings well.
What is the ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
The ratio of Devi to Miko's savings is 3:11.
So, Devi's saving is 3x and Devi to Miko's savings is 11x.
The sum of Raj and Devi's savings is $1181. Raj and Miko's savings sum up to $1797.
Let y be the Raj's saving.
Now, y+3x=1181 --------(I) and y+11x=1797 --------(II)
From equation (I), y=1181-3x
Substitute y=1181-3x, in equation (II), we get
1181-3x+11x=1797
⇒ 8x=1797-1181
⇒ 8x=616
⇒ x=616/8
⇒ x=77
So, y=1181-3x=1181-231
=$950
Hence, the money saved by Raj from the given conditions is $950.
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find the value of p(7, 4)
Answer:
P(7,4)= 840
Step-by-step explanation:
98. Explain in your own words, how you can tell from its equation whether a parabola opens up, down, left or right.
Answer:
The same way you tell if a parabola opens up or down, by the leading coefficient of the variable.
Step-by-step explanation:
Since the x-axis is positive to the right, a positive leading coefficient (3) means it opens to the right. eg. And a negative leading coefficient (-2) means it opens to the left.
Please help me find the area of compound shapes?!!?
Answer:
85 cm²
Step-by-step explanation:
Area = 5 x 5 + 15 x 4
Area = 25 + 60
Area = 85 cm²
The graph shows a line and two similar triangles.
On a coordinate plane, a line goes through (0, 0) and (6, 4). A small triangle has a rise of 2 and run of 3. A larger triangle has a rise of 4 and run of 6.
Which expression finds the equation of the line?
StartFraction y Over x EndFraction = three-halves
StartFraction y Over x EndFraction = two-thirds
StartFraction y Over 2 EndFraction = StartFraction 3 Over x EndFraction
StartFraction y Over 3 EndFraction = StartFraction x Over 2 EndFraction
Mark this and return
Answer:B mark me brainliest
Step-by-step explanation:Recall that slope is rise over run
slope = rise/run
The rise being the change in y, while the run is the change in x.
So we could informally think of it as slope = y/x
-----------
Since we're told that it "has a rise of 2 and run of 3", this means slope = 2/3.
The slope is both y/x and also 2/3.
Equating the two expressions leads us to y/x = 2/3. This is why choice B is the final answer.
Answer:
B) y/x=2/3
Step-by-step explanation:
Edg2022
The y-Intercept of the line whose equation is 7x - 4y= 8 is
8
7/4
-2
Answer:
-2
Step-by-step explanation:
To find the y-intercept, all we need to do is plug in 0 for x and solve for y, giving us [tex]-4y = 8[/tex], so y = -2.
I need the answer please.
Step-by-step explanation:
Hope this helps you. Anyone can correct if it's wrong.
Suppose a ramp 2 ft high makes an angle of 4.8° with the ground. Find the length of the ramp.
Answer:
23.9 ft (nearest tenth)
Step-by-step explanation:
Use the sine trig ratio to find the length of the ramp.
[tex]\sf \sin(\theta)=\dfrac{O}{H}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleH is the hypotenuse (the side opposite the right angle)Given:
[tex]\theta[/tex] = 4.8°O = height of ramp = 2 ftH = length of rampSubstituting the given values into the formula and solving for H:
[tex]\implies \sf \sin(4.8^{\circ})=\dfrac{2}{H}[/tex]
[tex]\implies \sf H=\dfrac{2}{\sin(4.8^{\circ})}[/tex]
[tex]\implies \sf H=23.9\:ft\:(nearest\:tenth)[/tex]
what does each equation have in common
The equations have operations, variable, an equal sign in common.
What is an Equation?An equation is a mathematical expression that contains an equals symbol.
As per the definition, the equation contain operations, variable, an equal sign. That means whatever be the equation then it must contain operations, variable, an equal sign.
So, all the equations have operations, variable, an equal sign these three things in common.
For example: 4a+b=0
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help please!!!(will mark brainliest)
Step-by-step explanation:
remember, a probability is always desired cases over total possible cases.
the class has 10+15 = 25 students.
and 5 of them will be picked as representatives to the school board.
how many total possibilities do we have ?
since picked students can be picked only once, and the sequence of the 5 picked students in the group does not matter, we have a combination without repetition :
C(25, 5) = 25! / (5! × (25-5)!) = 25! / (5! × 20!) =
= 25×24×23×22×21 / (5×4×3×2) =
= 5×1×23×22×21 = 53,130 possible outcomes.
how many desired outcomes ?
that would be how many options we have to pick 2 out of 10 and 3 out of 15 :
C(10,2) × C(15,3) = 10! / (2 × 8!) × 15! / (3! × 12!) =
= 10×9/2 × 15×14×13/(3×2) =
= 5×9 × 5×7×13 = 20,475 desired outcomes
and the probability is
20475 / 53130 = 4095 / 10626 = 1365 / 3542 = 195 / 506
= 0.385375494... ≈ 0.39
