Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options.
A. The value of f(–10) = 82
B The graph of the function is a parabola.
C. The graph of the function opens down.
D. The graph contains the point (20, –8).
E. The graph contains the point (0, 0).
Answer:
B
Step-by-step explanation:
the graph of the function is a parabola
Work out the following sheet
Answer:
please mark as brainliest
Please solve for slope and y intercept with steps
The values are given as;
1. The intercept, c = -1.5, Slope, m = -1/4
2. Intercept = 0. 5, Slope, m = -3/5
How to determine the slopeThe general formula for the equation of a line is represented thus;
y = mx + c
Given that the parameter are;
y is a point on the y -axism is the slope or gradient of the linex is a point on the x - axisc is the intercept of the line on the y - axisFor the first graph
The intercept, c = -1.5
The slope, m = y₂ - y₁/x₂ - x₁
Substitute the values as shown in the graph
Slope, m = -2-(-3)/- 3- 1
Slope, m = -2 + 3/-4
Slope, m = -1/4
For the second graph, we have
Intercept = 0. 5
The slope, m = y₂ - y₁/x₂ - x₁
Substitute the values
Slope, m = 2 - (-1)/3 - (-2)
Slope, m = -3/5
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A donut shop that specializes in unique donuts made from potatoes wants to learn more about their business costs. Past data reveals that the cost for fifty pounds of potatoes has a mean of $75 with standard deviation $13. The normal distribution for the population is shown by the dotted black line.
The donut shop plans to take a random sample of 31 such fifty pound bags of potatoes and will calculate the mean cost of the sample to compare to the known cost. Compute the mean and standard deviation of the sampling distribution of sample means for a sample of size 31. Round your answers to the nearest tenth.
Divide. round your answer to the nearest hundredeth: 1 divided by 3 = the steps are decimals?
Answer: 1/3 or 1 divided by 3 is equivalent to 0.333333
Answer:
0,33
Step-by-step explanation:
this for sure.......
please help i’m struggling
Accοrding tο the transfοrmatiοn prοperty, the cοrrect answer is οptiοn (c): (x, y) → (- y + 2, x + 2)
What is transfοrmatiοn?Transfοrmatiοn is a functiοn that maps οne set οf pοints tο anοther set οf pοints in a way that preserves sοme structure οr prοperties οf the οriginal set. The mοst cοmmοn types οf transfοrmatiοns are geοmetric transfοrmatiοns, which preserve distance, angle, and shape, and algebraic transfοrmatiοns, which preserve algebraic prοperties such as the sum, prοduct, οr symmetry οf functiοns.
Twο triangles are similar if their cοrrespοnding angles are cοngruent and their cοrrespοnding sides are prοpοrtiοnal. Therefοre, tο determine whether a transfοrmatiοn maps triangle ABC tο a similar, but nοt a cοngruent triangle, we need tο examine hοw the transfοrmatiοn affects the angles and sides οf triangle ABC.
Let's assume that triangle ABC has vertices A(a₁, a₂), B(b₁, b₂), and C(c₁, c₂).
a) (x, y) → (x + 2, - y - 2)This transfοrmatiοn is a translatiοn that mοves each pοint οf the plane twο units tο the right and twο units dοwn. Therefοre, this transfοrmatiοn dοes nοt change the size οr shape οf triangle ABC. It οnly changes its pοsitiοn in the plane. Hence, this transfοrmatiοn dοes nοt map triangle ABC tο a similar, but nοt cοngruent triangle.
b) (x, y) → (- 4x, - 4y)
This transfοrmatiοn scales each cοοrdinate by a factοr οf -4, which reflects the triangle acrοss the οrigin and changes its size. Hοwever, this transfοrmatiοn alsο changes the οrientatiοn οf the triangle. Therefοre, this transfοrmatiοn dοes nοt map triangle ABC tο a similar, but nοt cοngruent triangle.
c) (x, y) → (- y + 2, x + 2)
This transfοrmatiοn is a rοtatiοn οf 90 degrees cοunterclοckwise arοund the pοint (2, 2). Tο see if it maps triangle ABC tο a similar, but nοt cοngruent triangle, we need tο check if the angles and sides οf the triangle are preserved. Since this transfοrmatiοn is a rοtatiοn, it preserves the angles οf the triangle. Tο check if it preserves the sides, we need tο cοmpute the length οf each side οf the transfοrmed triangle and cοmpare it tο the cοrrespοnding side οf the οriginal triangle:
AB: distance between (- a₂ + 2, a₁ + 2) and (- b₂ + 2, b₁ + 2) is equal tο the distance between A(a₁, a₂) and B(b₁, b₂)
AC: distance between (- a₂ + 2, a₁ + 2) and (- c₂ + 2, c₁ + 2) is equal tο the distance between A(a₁, a₂) and C(c₁, c₂)
BC: distance between (- b₂ + 2, b₁ + 2) and (- c₂ + 2, c₁ + 2) is equal tο the distance between B(b₁, b₂) and C(c₁, c₂)
Since the angles and sides are preserved, this transfοrmatiοn maps triangle ABC tο a similar, but nοt cοngruent triangle.
d) (x, y) → (- y, - x)
This transfοrmatiοn is a reflectiοn acrοss the line y = x. Tο see if it maps triangle ABC tο a similar, but nοt cοngruent triangle, we need tο check if the angles and sides οf the triangle are preserved. Since this transfοrmatiοn is a reflectiοn, it preserves the angles οf the triangle. Hοwever, it alsο changes the οrientatiοn οf the triangle. Therefοre, this transfοrmatiοn dοes nοt map triangle ABC tο a similar, but nοt cοngruent triangle.
Therefοre, the answer is οptiοn (c): (x, y) → (- y + 2, x + 2)
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Write a congruence statement for the triangles
Triangle ABC is congruent to triangle PQR, where A corresponds to P, B corresponds to Q, and C corresponds to R.
What is congruency?
In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.
To write a congruence statement for two triangles, we need to identify their corresponding parts and ensure that they are congruent in both triangles.
The congruence statement can be written in the following form:
Triangle ABC is congruent to triangle PQR, where A corresponds to P, B corresponds to Q, and C corresponds to R.
For example, if we have two triangles with vertices A, B, and C and P, Q, and R respectively, and we know that the following pairs of corresponding parts are congruent:
AB ≅ PQ
BC ≅ QR
AC ≅ PR
Then, we can write the congruence statement as:
Hence, Triangle ABC is congruent to triangle PQR, where A corresponds to P, B corresponds to Q, and C corresponds to R.
The symbol ≅ means "is congruent to."
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Every hour, the amount of water in a tank decreases by 14%.
At 1 pm, the tank contains 1870 litres of water.
How many litres of water will drain from the tank between 5 pm and 6 pm?
Give your answer to 1 d.p.
The amount of water drained from the tank between 5 pm and 6 pm is given as follows:
143 liters.
How to model an exponential function?An exponential function is modeled as follows:
y = ab^x.
In which the parameters are represented as follows:
a is the initial value.b is the rate of change.The parameter values for this problem are given as follows:
a = 1870 -> At 1 pm, the tank contains 1870 litres of water.b = 0.86 -> Every hour, the amount of water in a tank decreases by 14%, hence it is 86% of the previous hour.Hence the function giving the amount of water in x hours after 1 pm is presented as follows:
y = 1870(0.86)^x.
At 5pm and 6 pm, the amounts are given as follows:
y = 1870 x (0.86)^4 = 1023 liters.y = 1870 x (0.86)^5 = 880 liters.Hence the amount drained is of:
1023 - 880 = 143 liters.
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15. Which of the following expressions are equivalent?
1. (x-4)² - 1
11. x² - 8x - 17
II.
III. x² + 15
IV.X² - 8x + 15
V. (x - 5)(x-3)
VI.X2 - 17
A.
B.
C.
D.
IV and V
I and II
I, IV, V
I, III, V
Answer:
I, IV, V
Step-by-step explanation:
To determine which of the given expressions are equivalent, we can expand and simplify them.
I. (x - 4)² - 1
Expanding the square, we get:
(x - 4)² = x² - 8x + 16
So, (x - 4)² - 1 = x² - 8x + 15
II. x² - 8x - 17
III. x² + 15
IV. x² - 8x + 15
V. (x - 5)(x - 3)
Expanding the product, we get:
(x - 5)(x - 3) = x² - 8x + 15
VI. x² - 17
From the above expressions, we can see that the following expressions are equivalent:
I. (x - 4)² - 1 and IV. x² - 8x + 15
Also, V. (x - 5)(x - 3) is equivalent to both I. and IV.
Therefore, the answer is (C) I, IV, V.
I don’t understand this someone please help
Answer:
I tried my best by helping
Step-by-step explanation:
So it is asking what are the probability of you getting the power ball lottery a player must get 5 white balls and a red one. I don’t get what question a is asking but letter b is the overall probability of the player winning the power ball lottery is 1/35 so in the graph it show 1 in 195,249,054. So that will be the answer of explaining the probability.
Jeff has 10 CDs and Ben has 15 CDs. In the inequalities below, k represents the number
of CDs Kevin has.
k> 10
k<15
How many CDs does Kevin have?
Group of answer choices
13
10
9
16
Answer:
Kevin has 11 CDs.
Solve the following using elimination, substitution, or graphing. Tickets for The Phantom of the Opera cost $6 for children and $12 for adults. A local school group paid $252 for 36 tickets. How many of each did they purchase?
Answer: 30 Child tickets 6 Adult tickets.
Step-by-step explanation:
Set up your system of equations to solve.
36 tickets are purchased, meaning a number of child tickets, and a different number of adult tickets add up to 36. We can write this as x+y=36.
The price of the tickets add up to 252 dollars. We can write this as 6 (the child price) times x + 12 (the adult price) times y = 252
So, x+y=36 and 6x+12y=252.
I will solve this using the substitution method.
So, first, we need to isolate a variable, I will choose the first equation to do so.
x+y=36 ---> x=36-y
Now, plug the value of x into the second equation.
6(36-y)+12y=252.
Distribute.
216-6y+12y=252
Combine like terms.
216+6y=252.
Subtract 216 from both sides.
6y=36
Divide by 6 on both sides.
y=6
Now plug this value of y into the previous equation to get x.
x+6=36
Subtract 6 from both sides.
x=30
Remember x was children's tickets and y was adult tickets. (It is better to use variables like C and A in this case).
what is the difference between the longest and shortest distances the glider flew
Answer: 6
Step-by-step explanation:
If mDA =(23x -14), mDB =(9x-4), and m
x=?
Arc DA= ?
A
i had this question it's right
If mDA =(23x -14), mDB =(9x-4), and mx=?Arc DA= ?
Determine whether the following study described is observational or an experiment. If the study is an experiment, identify the control and treatment groups, and discuss whether single- or double-blinding is necessary. If the study is observational, state whether it is a retrospective study, and if so, identify the cases and controls.
A study by university social scientists found that 19.1
%
of first-year women students surveyed at a regional college experienced sexual assault during that first year.
The study that we have here is an observational study. The study is not retrospective in nature.
What type of research study is thisThis study is observational because the researchers are observing and collecting data on a group without manipulating any variables.
It is not a retrospective study because the data is collected in real-time during the first year of college, rather than looking back on past experiences.
Therefore, there are no treatment or control groups, and there is no need for blinding. The study simply reports the percentage of first-year women students who experienced sexual assault during their first year at the regional college.
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what is the quotient of 14 divided by 5?
A. 4/5
B. 2 2/3
C.3 3/4
D. 4 4/15
Answer:
5divided by 14 is 2 with a remainder of 3
Find the following a-e please ! College algebra
Given functions f(x) = 2x² + 1 and g(x) = 7x - 8, then [tex]f[g(2) = 73\end{array}$[/tex].
What is function?A technical definitiοn οf a functiοn is: a relatiοn frοm a set οf inputs tο a set οf pοssible οutputs where each input is related tο exactly οne οutput.
This means that if the οbject x is in the set οf inputs (called the dοmain) then a functiοn f will map the οbject x tο exactly οne οbject f(x) in the set οf pοssible οutputs (called the cοdοmain).
The nοtiοn οf a functiοn is easily understοοd using the metaphοr οf a functiοn machine that takes in an οbject fοr its input and, based οn that input, spits οut anοther οbject as its οutput.
Given f(x) = 2x² + 1 and g(x) = 7x - 8
Then
a)
[tex]$\begin{array}{l c l}{f[g(2)]=f[(7*2-8)]=f(6)}\\ {f[g(2)]=2(6)^{2}+1=72+1}\\f[g(2) = 73\end{array}$[/tex]
b)
[tex]$\begin{array}{l}{{f[g(x)]=f(7x-1)=2[7x-8]^{2}+1}}\\ {{f[g(x)]=2(49x^{2}+64-112x)+1}}\\ {{f[g(x)]=98x^{2}-224x+129}}\end{array}$[/tex]
c)
[tex]$\begin{array}}{g[f(x)]=g[2x^{2}+1]=7[2x^{2}+1]-8}\\ {g[f(x)]=14x^{2}-1}\end{array}$[/tex]
d) (g · g)(x) = g{g(x)} = g(7x - 8)
= 7(7x - 8) - 8
= 49x−64
e) (f · f)(-2) = f{f(-2)} = f(2(-2)²)
= 2(2(-2)²)²
= 128
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Find two 2×2 matrices A and B:
The two 2×2 matrices A and B with real entries sucah that (AB)^2 is not equal to A^2 B^2 is given below:
How to solveLet A = [[1, 0], [0, -1]] and B = [[0, 1], [1, 0]] be two 2x2 matrices with real entries. Then,
AB = [[0, 1], [-1, 0]] and AB^2 = [[-1, 0], [0, -1]]
A^2 = [[1, 0], [0, 1]] and B^2 = [[0, 1], [1, 0]]
So, A^2B^2 = [[0, 1], [1, 0]] and (AB)^2 = ABAB = [[0, 1], [-1, 0]][[0, 1], [-1, 0]] = [[-1, 0], [0, -1]]
Therefore, (AB)^2 is not equal to A^2B^2 for the matrices A and B defined above.
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Find the linear function with the following properties.
f(0)=8
Slope of f=−6
Answer
Therefore , the solution of the given problem of function comes out to be f(x) = -6x + 8 .
Describe function.Numerous subjects, including numbers, numbers, as well as their subsets, as well as building, construction, and both real and fictitious geographic locations, are covered in the mathematics programme. The relationships between variable elements that all cooperate to create the same outcome are covered in a work. A utility is composed of several unique parts that, when combined, give particular outcomes for each input.
Here,
The linear function with a slope of -6 can be written in slope-intercept form as:
=> f(x) = -6x + b
where "b" is the y-intercept. We are also given that f(0) = 8, so we can substitute those values in to solve for "b":
=> f(0) = -6(0) + b = 8
=> b = 8
Therefore, the linear function we are looking for is:
=> f(x) = -6x + 8
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o.ooo27 in scientific notation ?
Answer:
2.700 × 10-7
Step-by-step explanation:
Answer: 2.7*10^-4
step by step explanation:
1. Make the number a new number between 1 and 10
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Move the decimal point to make 0.00027 a new number between 1 and 10. Because our original number is less than one, we move the decimal point to the right. Drop any zeroes in front of the number. Keep track of how many times we move the decimal point.
0.00027 -> 2.7
Our new number is 2.7. We moved the decimal point 4 times.
2. Define the power of 10
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Because our original number was less than one, the exponent defining the power of 10 is negative. Remember, we moved the decimal point 4 times, so the exponent is negative 4
10^(-4)
3. Final result
2.7*10^(-4)
These values have an average of 10. What is the average distance of those values from that average of 10? 2 6 12 14 16
Answer:10-2= 8
Step-by-step explanation:
What is the area of the figure below?
A. 48 square meters
B. 66 square meters
C. 72 square meters
D. 84 square meters
The area of the figure is 72 square meters
How to determine the area of the figureFrom the question, we have the following parameters that can be used in our computation:
A composite figure
The area of the figure is calculated as
Area = Sum of areas of the individual figures
From the figure, we have
Number of rectangles that make up the composite =3
Using the above as a guide, we have the following:
Area = 8 * 5 + 4 * 7 + 2 * 2
Evaluate
Area = 72
Hence, the area is 72 square meters
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Find the value of x that makes triangle DEF and triangle XYZ.
When it happens, the ratio of their corresponding side will not change. The value of x is 8.
What are properties of triangle?
The sum of the interior angles of a triangle is always 180°.
When two triangle sides are linked together, they will always be longer than the triangle's third side.
Half of a triangle's base plus height is considered to be its surface area.
Already mentioned the ΔDEF and ΔXYZ are similar.
When it happens, the ratio of their corresponding side will not change.
So,
7/14=6/12=2x-5/22
We take last two,
6/12=2x-5/22
Or, 24x-60=132
Or, x= 192/24
Or, x=8
Hence, the value of x is 8.
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From Rs. 62,500 if we can by 500 US dollar. How much US dollar can be bought if Nepali currency is devaluated by 5%.
Devaluation of 5%:
125+(125x5%)=187,5
Many US dollars can be bought if Nepali currency is devaluated by 5%=
62.500:187,5=333 dollar
Prove that 7^7-7^6 is divisible by 6
Answer:
To prove that 7^7 - 7^6 is divisible by 6, we can factor out 7^6 from the expression:
7^7 - 7^6 = 7^6 (7 - 1)
Simplifying the expression, we get:
7^7 - 7^6 = 7^6 (6)
We can see that 7^6 is a common factor in the expression, and 6 is also a factor. Therefore, we can conclude that 7^7 - 7^6 is divisible by 6.
Step-by-step explanation:
which of the following is the equation of the function below?
A. y=2csc[0.5(x+pi/2)]-1
B. y=2csc[2(x+pi/4)]-1
C. y=0.5csc[0.5(x+pi/2)]-1
D. y=0.5csc[2(x+pi/4)]-1
The equation of the graph is option (c) i.e. y = 0.5 csc [0.5(x + π/2)] - 1 which is solve below.
What is Graph?In elementary mathematics, term "graph" denotes a plot or a function graph. A graph, in the language of mathematicians, a set of points and connections between some subset of those points (which may empty).
If the equation y = A csc (B(x + C)) + D
Amplitude is A, the Amplitude is the height from the centre line to the peak . Or we can measure height from highest to lowest points and divide that by 2
Period is 2π/B, the Period goes from one peak to the next
Phase shift is C (positive is to the left), the Phase Shift is how far the function is shifted horizontally from the usual position.
Vertical shift is D, Vertical Shift is how far the function is shifted vertically from the usual position.
If y = csc(x), then A = 1 , B = 1 , C = 0 , D = 0
That means amplitude is 1, the period is 2π, So there is no phase shift or vertical shift
Now lets solve the problem from the graph
[tex]The\ amplitude = \frac{(-0.5 - (-1.5))}{2} = 0.5[/tex]
∴ [tex]A = 0.5[/tex]
The period is from 2.5π to -1.5π
∴ [tex]The \ period\ is\ 4\pi[/tex]
∵ [tex]The\ period = \frac{2\pi }{B}[/tex]
∴ [tex]4\pi = \frac{2\pi }{B}, by\ cross \ multiplication[/tex]
∴ [tex]B = \frac{2\pi }{4\pi } = \frac{1}{2} = 0.5[/tex]
There is only one answer which has value A = 0.5 and B = 0.5
∴ y = 0.5 csc[0.5(x + π/2)] - 1
So, The Correct equation of the graph is 0.5 csc[0.5(x + π/2)] - 1
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Answer:
The answer is c
Step-by-step explanation:
edge
Question
What is the volume of the prism?
Enter your answer, as a mixed number in simplest form, in the box.
cm³
The figure contains a right rectangular prism. The length of the prism is labeled 3 and one half centimeters, the width is labeled 6 centimeters, and the height is labeled 5 and one half centimeters.
The volume of the prism is 115.5 cubic centimeters.
What is a rectangular prism?A three-dimensional structure called a right rectangular prism has six rectangular faces, each of which has four right angles. The length, breadth, and height of a right rectangular prism are perpendicular to one another, and the opposing sides are congruent and parallel to one another. The prism's dimensions—also referred to as its length, breadth, and height—can be utilised to determine its volume. Multiplying the prism's length, width, and height yields the volume of a right rectangular prism.
The volume of the rectangular prism is given by the formula:
Volume = Length x Width x Height
Substituting the values we have:
Volume = 3.5 cm x 6 cm x 5.5 cm
Volume = 115.5 cubic centimeters
Hence, the volume of the prism is 115.5 cubic centimeters.
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A line passes through the points (2, 17) and (3, 24). Find the slope m of the line.
7
the first order pair is always x and the second is y
slope m =Y2_Y1 ÷ X2_X1
then 24_ 17 ÷3 _2= 7
a) Assume that the height h(t) of the mass is a sinusoidal function, where t is the time in seconds, sketch a graph of h from t = 0 to t = 0.8 seconds. t = 0 is the time at which the mass is released
The graph of the sinusoidal function shows that the mass oscillates up and down around the equilibrium position with an amplitude of 0.1 meters.
What is the graph of the functionwe can use a general form of sinusoidal function
h(t) = A sin(ωt + φ) + C
where:
A = amplitude (maximum displacement from the mean position)
ω = angular frequency (radians per second)
φ = phase angle (initial position of the oscillation)
C = vertical displacement (position of the mean or equilibrium position)
Since the mass is released from rest, we can assume that the initial displacement is zero, i.e., C = 0. Also, we know that the period of the oscillation is 1/f, where f is the frequency. Therefore, we can find the frequency from the given time period of 0.8 seconds.
Let's assume that the height of the mass oscillates with an amplitude of 0.1 meters and a frequency of 5π radians per second (corresponding to a period of 0.4 seconds), and the phase angle is 0.
h(t) = 0.1 sin(5πt)
We can plot this function for t ranging from 0 to 0.8 seconds using a graphing tool or by hand. Here is the resulting graph
|
0.1 + . * .
| .* *.
| . .
| * *
| * *
| . .
| . .
| .* *.
| .* *.
-0.1 +----------------------------------------------
0 0.2 0.4 0.6 0.8
The x-axis represents time in seconds, and the y-axis represents the height of the mass in meters. The graph shows that the mass oscillates up and down around the equilibrium position with an amplitude of 0.1 meters. The maximum height occurs at t = 0.1 seconds and t = 0.5 seconds, while the minimum height occurs at t = 0.3 seconds and t = 0.7 seconds. At t = 0.4 seconds and t = 0.8 seconds, the mass returns to the equilibrium position.
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WHATS THE NUMERATOR FOR THE FOLLOWING RATIONAL EXPRESSION 7/V+3/V=?
The numerator of the rational expression 7/V + 3/V is 10. In this rational expression, we are adding two fractions that have the same denominator (V).
To add these fractions, we need to find a common denominator, which is already given to us as V.
Then, we add the numerators of the two fractions, which are 7 and 3, to get:
7/V + 3/V = (7+3)/V
Simplifying the numerator by adding 7 and 3, we get:
10/V
The numerator for the rational expression 7/V + 3/V is:
7 + 3 = 10
Therefore, the numerator is 10.
Therefore, the numerator of the rational expression 7/V + 3/V is 10.
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